TSTP Solution File: SWW302+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW302+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:35 EDT 2023
% Result : Theorem 25.54s 25.39s
% Output : CNFRefutation 25.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW302+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.34 % Computer : n021.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Sun Aug 27 18:10:43 EDT 2023
% 0.11/0.34 % CPUTime :
% 0.19/0.59 start to proof:theBenchmark
% 25.12/25.26 %-------------------------------------------
% 25.12/25.26 % File :CSE---1.6
% 25.12/25.26 % Problem :theBenchmark
% 25.12/25.26 % Transform :cnf
% 25.12/25.26 % Format :tptp:raw
% 25.12/25.26 % Command :java -jar mcs_scs.jar %d %s
% 25.12/25.26
% 25.12/25.26 % Result :Theorem 19.900000s
% 25.12/25.26 % Output :CNFRefutation 19.900000s
% 25.12/25.26 %-------------------------------------------
% 25.12/25.27 %------------------------------------------------------------------------------
% 25.12/25.27 % File : SWW302+1 : TPTP v8.1.2. Released v5.2.0.
% 25.12/25.27 % Domain : Software Verification
% 25.12/25.27 % Problem : Hoare's Logic with Procedures 434833, 5000 axioms selected
% 25.12/25.27 % Version : Especial.
% 25.12/25.27 % English :
% 25.12/25.27
% 25.12/25.27 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 25.12/25.27 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 25.12/25.27 % Source : [Bla11]
% 25.12/25.27 % Names : hoare_434833.5000.p [Bla11]
% 25.12/25.27
% 25.12/25.27 % Status : Theorem
% 25.12/25.27 % Rating : 0.42 v7.5.0, 0.41 v7.4.0, 0.53 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.57 v6.4.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.70 v6.0.0, 0.57 v5.5.0, 0.70 v5.4.0, 0.71 v5.3.0, 0.78 v5.2.0
% 25.12/25.27 % Syntax : Number of formulae : 5242 (1665 unt; 0 def)
% 25.12/25.27 % Number of atoms : 12784 (4409 equ)
% 25.12/25.27 % Maximal formula atoms : 13 ( 2 avg)
% 25.12/25.27 % Number of connectives : 8527 ( 985 ~; 151 |; 705 &)
% 25.12/25.27 % ( 907 <=>;5779 =>; 0 <=; 0 <~>)
% 25.12/25.27 % Maximal formula depth : 22 ( 6 avg)
% 25.12/25.27 % Maximal term depth : 19 ( 2 avg)
% 25.12/25.27 % Number of predicates : 152 ( 151 usr; 1 prp; 0-6 aty)
% 25.12/25.27 % Number of functors : 375 ( 375 usr; 45 con; 0-7 aty)
% 25.12/25.27 % Number of variables : 16570 (16412 !; 158 ?)
% 25.12/25.27 % SPC : FOF_THM_RFO_SEQ
% 25.12/25.27
% 25.12/25.27 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 25.12/25.27 % 2011-03-01 11:32:02
% 25.12/25.27 %------------------------------------------------------------------------------
% 25.12/25.27 %----Relevant facts (4982)
% 25.12/25.27 fof(fact_ext,axiom,
% 25.12/25.27 ! [V_g_2,V_f_2] :
% 25.12/25.27 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 25.12/25.27 => V_f_2 = V_g_2 ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_equal__triple__def,axiom,
% 25.12/25.27 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.27 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(T_b)),V_x_2),V_y_2))
% 25.12/25.27 <=> V_x_2 = V_y_2 ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_Rep__triple__inject,axiom,
% 25.12/25.27 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.27 ( hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_y_2)
% 25.12/25.27 <=> V_x_2 = V_y_2 ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_equal,axiom,
% 25.12/25.27 ! [T_b] :
% 25.12/25.27 ( class_HOL_Oequal(T_b)
% 25.12/25.27 => c_HOL_Oequal__class_Oequal(T_b) = c_fequal ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_equal__refl,axiom,
% 25.12/25.27 ! [V_x,T_a] :
% 25.12/25.27 ( class_HOL_Oequal(T_a)
% 25.12/25.27 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_equal__eq,axiom,
% 25.12/25.27 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.27 ( class_HOL_Oequal(T_b)
% 25.12/25.27 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_b),V_x_2),V_y_2))
% 25.12/25.27 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_eq__equal,axiom,
% 25.12/25.27 ! [T_b] :
% 25.12/25.27 ( class_HOL_Oequal(T_b)
% 25.12/25.27 => c_fequal = c_HOL_Oequal__class_Oequal(T_b) ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_Rep__triple__inverse,axiom,
% 25.12/25.27 ! [V_x_2,T_b] : hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)) = V_x_2 ).
% 25.12/25.27
% 25.12/25.27 fof(fact_Rep__triple,axiom,
% 25.12/25.27 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),V_x_2)),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_type__definition__triple,axiom,
% 25.12/25.27 ! [T_b] : c_Typedef_Otype__definition(tc_Hoare__Mirabelle_Otriple(T_b),tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool),c_Hoare__Mirabelle_ORep__triple(T_b),c_Hoare__Mirabelle_OAbs__triple(T_b),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_Abs__triple__inverse,axiom,
% 25.12/25.27 ! [V_y_2,T_b] :
% 25.12/25.27 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.27 => hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)) = V_y_2 ) ).
% 25.12/25.27
% 25.12/25.27 fof(fact_Abs__triple__inject,axiom,
% 25.12/25.27 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.27 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_x_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.27 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.27 => ( hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_x_2) = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),V_y_2)
% 25.12/25.28 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_equalityCE,axiom,
% 25.12/25.28 ! [V_ca_2,T_b,V_B_2,V_A_2] :
% 25.12/25.28 ( V_A_2 = V_B_2
% 25.12/25.28 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.28 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) )
% 25.12/25.28 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_OAbs__inject,axiom,
% 25.12/25.28 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 25.12/25.28 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 25.12/25.28 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_OAbs__inverse,axiom,
% 25.12/25.28 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 25.12/25.28 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_ORep,axiom,
% 25.12/25.28 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_Abs__triple__induct,axiom,
% 25.12/25.28 ! [V_x_2,V_Pa_2,T_b] :
% 25.12/25.28 ( ! [B_y] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y))) )
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_Abs__triple__cases,axiom,
% 25.12/25.28 ! [T_b,V_x_2] :
% 25.12/25.28 ~ ! [B_y] :
% 25.12/25.28 ( V_x_2 = hAPP(c_Hoare__Mirabelle_OAbs__triple(T_b),B_y)
% 25.12/25.28 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),B_y),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b)))) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_Rep__triple__induct,axiom,
% 25.12/25.28 ! [V_Pa_2,V_y_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.28 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x)))
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_Rep__triple__cases,axiom,
% 25.12/25.28 ! [V_y_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),V_y_2),hAPP(c_Set_OCollect(tc_fun(tc_Datatype_Onode(tc_sum(tc_Com_Ocom,tc_fun(T_b,tc_fun(tc_Com_Ostate,tc_HOL_Obool))),tc_sum(tc_Com_Ostate,T_b)),tc_HOL_Obool)),c_Hoare__Mirabelle_Otriple_Otriple__rep__set(T_b))))
% 25.12/25.28 => ~ ! [B_x] : V_y_2 != hAPP(c_Hoare__Mirabelle_ORep__triple(T_b),B_x) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_ORep__inject,axiom,
% 25.12/25.28 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 25.12/25.28 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_ORep__inverse,axiom,
% 25.12/25.28 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_Collect__def,axiom,
% 25.12/25.28 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 25.12/25.28
% 25.12/25.28 fof(fact_eq__mem__trans,axiom,
% 25.12/25.28 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 25.12/25.28 ( V_a_2 = V_b_2
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_mem__def,axiom,
% 25.12/25.28 ! [V_A_2,V_x_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.28 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_eqset__imp__iff,axiom,
% 25.12/25.28 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 25.12/25.28 ( V_A_2 = V_B_2
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_eqelem__imp__iff,axiom,
% 25.12/25.28 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 25.12/25.28 ( V_x_2 = V_y_2
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_eq__mem,axiom,
% 25.12/25.28 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 25.12/25.28 <=> V_x_2 = V_y_2 ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_OAbs__cases,axiom,
% 25.12/25.28 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ~ ! [B_y] :
% 25.12/25.28 ( V_x_2 = hAPP(V_Abs_2,B_y)
% 25.12/25.28 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_OAbs__induct,axiom,
% 25.12/25.28 ! [V_x_2,V_Pa_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( ! [B_y] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),V_A_2))
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,hAPP(V_Abs_2,B_y))) )
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_ORep__induct,axiom,
% 25.12/25.28 ! [V_Pa_2,V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 25.12/25.28 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(V_Rep_2,B_x)))
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_type__definition_ORep__cases,axiom,
% 25.12/25.28 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.12/25.28 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 25.12/25.28 => ~ ! [B_x] : V_y_2 != hAPP(V_Rep_2,B_x) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_induct__false__def,axiom,
% 25.12/25.28 ~ c_HOL_Oinduct__false ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OatMost__iff,axiom,
% 25.12/25.28 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OatLeast__iff,axiom,
% 25.12/25.28 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OlessThan__iff,axiom,
% 25.12/25.28 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OgreaterThan__iff,axiom,
% 25.12/25.28 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 25.12/25.28 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 25.12/25.28 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 25.12/25.28 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 25.12/25.28 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 25.12/25.28 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 25.12/25.28 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 25.12/25.28 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 25.12/25.28 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 25.12/25.28 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_ballE,axiom,
% 25.12/25.28 ! [V_x_2,V_Pa_2,V_A_2,T_b] :
% 25.12/25.28 ( ! [B_x] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.28 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.28 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.12/25.28 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_bexE,axiom,
% 25.12/25.28 ! [V_Pa_2,V_A_2,T_b] :
% 25.12/25.28 ( ? [B_x] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.28 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.28 => ~ ! [B_x] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.28 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_bexI,axiom,
% 25.12/25.28 ! [V_A_2,T_b,V_x_2,V_Pa_2] :
% 25.12/25.28 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.28 => ? [B_x] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.28 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_InterE,axiom,
% 25.12/25.28 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_InterD,axiom,
% 25.12/25.28 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 25.12/25.28 ( 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)))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_UnionI,axiom,
% 25.12/25.28 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 25.12/25.28 => 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))) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_emptyE,axiom,
% 25.12/25.28 ! [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)))) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_UNIV__I,axiom,
% 25.12/25.28 ! [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)))) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_subsetD,axiom,
% 25.12/25.28 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_equalityI,axiom,
% 25.12/25.28 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.12/25.28 => V_A_2 = V_B_2 ) ) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_top1I,axiom,
% 25.12/25.28 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_empty__subsetI,axiom,
% 25.12/25.28 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 25.12/25.28
% 25.12/25.28 fof(fact_predicate1D,axiom,
% 25.12/25.28 ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 25.12/25.29 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.12/25.29 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_rev__predicate1D,axiom,
% 25.12/25.29 ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
% 25.12/25.29 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
% 25.12/25.29 => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inf__empty,axiom,
% 25.12/25.29 ! [T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => 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) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__empty,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inf__UNIV,axiom,
% 25.12/25.29 ! [T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => 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) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__UNIV,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Sup__empty,axiom,
% 25.12/25.29 ! [T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => 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) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Union__empty,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Sup__UNIV,axiom,
% 25.12/25.29 ! [T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => 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) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Union__UNIV,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_le__Inf__iff,axiom,
% 25.12/25.29 ! [V_A_2,V_b_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( 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)))
% 25.12/25.29 <=> ! [B_x] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Sup__le__iff,axiom,
% 25.12/25.29 ! [V_b_2,V_A_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( 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))
% 25.12/25.29 <=> ! [B_x] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Union__mono,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( 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))
% 25.12/25.29 => 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))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__anti__mono,axiom,
% 25.12/25.29 ! [V_A_2,V_B_2,T_b] :
% 25.12/25.29 ( 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))
% 25.12/25.29 => 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))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_equalityE,axiom,
% 25.12/25.29 ! [T_b,V_B_2,V_A_2] :
% 25.12/25.29 ( V_A_2 = V_B_2
% 25.12/25.29 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_subset__trans,axiom,
% 25.12/25.29 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_equalityD2,axiom,
% 25.12/25.29 ! [T_b,V_B_2,V_A_2] :
% 25.12/25.29 ( V_A_2 = V_B_2
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_equalityD1,axiom,
% 25.12/25.29 ! [T_b,V_B_2,V_A_2] :
% 25.12/25.29 ( V_A_2 = V_B_2
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_set__eq__subset,axiom,
% 25.12/25.29 ! [T_b,V_B_2,V_A_2] :
% 25.12/25.29 ( V_A_2 = V_B_2
% 25.12/25.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_subset__empty,axiom,
% 25.12/25.29 ! [V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.12/25.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_subset__refl,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_subset__UNIV,axiom,
% 25.12/25.29 ! [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)))) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_UNIV__not__empty,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Union__upper,axiom,
% 25.12/25.29 ! [V_A_2,V_B_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.12/25.29 => 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))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Sup__upper,axiom,
% 25.12/25.29 ! [V_A_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.29 => 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))) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__lower,axiom,
% 25.12/25.29 ! [V_A_2,V_B_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.12/25.29 => 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)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inf__lower,axiom,
% 25.12/25.29 ! [V_A_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.29 => 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)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_in__mono,axiom,
% 25.12/25.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_set__rev__mp,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_set__mp,axiom,
% 25.12/25.29 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_all__not__in__conv,axiom,
% 25.12/25.29 ! [V_A_2,T_b] :
% 25.12/25.29 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_ex__in__conv,axiom,
% 25.12/25.29 ! [V_A_2,T_b] :
% 25.12/25.29 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_empty__iff,axiom,
% 25.12/25.29 ! [V_ca_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_equals0D,axiom,
% 25.12/25.29 ! [V_a_2,T_b,V_A_2] :
% 25.12/25.29 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.12/25.29 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_empty__Collect__eq,axiom,
% 25.12/25.29 ! [V_Pa_2,T_b] :
% 25.12/25.29 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 25.12/25.29 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Collect__empty__eq,axiom,
% 25.12/25.29 ! [V_Pa_2,T_b] :
% 25.12/25.29 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.12/25.29 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__refl,axiom,
% 25.12/25.29 ! [V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Opreorder(T_a)
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_top__apply,axiom,
% 25.12/25.29 ! [V_x_2,T_c,T_b] :
% 25.12/25.29 ( class_Orderings_Otop(T_b)
% 25.12/25.29 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_bot__apply,axiom,
% 25.12/25.29 ! [V_x_2,T_c,T_b] :
% 25.12/25.29 ( class_Orderings_Obot(T_b)
% 25.12/25.29 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_iso__tuple__UNIV__I,axiom,
% 25.12/25.29 ! [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)))) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_top__greatest,axiom,
% 25.12/25.29 ! [V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Otop(T_a)
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_le__fun__def,axiom,
% 25.12/25.29 ! [V_g_2,V_f_2,T_b,T_c] :
% 25.12/25.29 ( class_Orderings_Oord(T_c)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.12/25.29 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_le__funD,axiom,
% 25.12/25.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 25.12/25.29 ( class_Orderings_Oord(T_c)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_le__funE,axiom,
% 25.12/25.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 25.12/25.29 ( class_Orderings_Oord(T_c)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_bot__least,axiom,
% 25.12/25.29 ! [V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Obot(T_a)
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_InterI,axiom,
% 25.12/25.29 ! [V_A_2,V_C_2,T_b] :
% 25.12/25.29 ( ! [B_X] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 25.12/25.29 => 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))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_UnionE,axiom,
% 25.12/25.29 ! [V_C_2,V_A_2,T_b] :
% 25.12/25.29 ( 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)))
% 25.12/25.29 => ~ ! [B_X] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 25.12/25.29 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__greatest,axiom,
% 25.12/25.29 ! [V_C_2,V_A_2,T_b] :
% 25.12/25.29 ( ! [B_X] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),B_X)) )
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_linorder__le__cases,axiom,
% 25.12/25.29 ! [V_y,V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Olinorder(T_a)
% 25.12/25.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_xt1_I6_J,axiom,
% 25.12/25.29 ! [V_z,V_x,V_y,T_a] :
% 25.12/25.29 ( class_Orderings_Oorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_xt1_I5_J,axiom,
% 25.12/25.29 ! [V_x,V_y,T_a] :
% 25.12/25.29 ( class_Orderings_Oorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.12/25.29 => V_x = V_y ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__trans,axiom,
% 25.12/25.29 ! [V_z,V_y,V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Opreorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__antisym,axiom,
% 25.12/25.29 ! [V_y,V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Oorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.12/25.29 => V_x = V_y ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_xt1_I4_J,axiom,
% 25.12/25.29 ! [V_c,V_a,V_b,T_a] :
% 25.12/25.29 ( class_Orderings_Oorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.12/25.29 => ( V_b = V_c
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_ord__le__eq__trans,axiom,
% 25.12/25.29 ! [V_c,V_b,V_a,T_a] :
% 25.12/25.29 ( class_Orderings_Oord(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.12/25.29 => ( V_b = V_c
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_xt1_I3_J,axiom,
% 25.12/25.29 ! [V_c,V_b,V_a,T_a] :
% 25.12/25.29 ( class_Orderings_Oorder(T_a)
% 25.12/25.29 => ( V_a = V_b
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_ord__eq__le__trans,axiom,
% 25.12/25.29 ! [V_c,V_b,V_a,T_a] :
% 25.12/25.29 ( class_Orderings_Oord(T_a)
% 25.12/25.29 => ( V_a = V_b
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__antisym__conv,axiom,
% 25.12/25.29 ! [V_x_2,V_y_2,T_b] :
% 25.12/25.29 ( class_Orderings_Oorder(T_b)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.12/25.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__eq__refl,axiom,
% 25.12/25.29 ! [V_y,V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Opreorder(T_a)
% 25.12/25.29 => ( V_x = V_y
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_order__eq__iff,axiom,
% 25.12/25.29 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Orderings_Oorder(T_b)
% 25.12/25.29 => ( V_x_2 = V_y_2
% 25.12/25.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.12/25.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_linorder__linear,axiom,
% 25.12/25.29 ! [V_y,V_x,T_a] :
% 25.12/25.29 ( class_Orderings_Olinorder(T_a)
% 25.12/25.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.12/25.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Powp__mono,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inter__subset,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( ! [B_X] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 25.12/25.29 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 25.12/25.29 => 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)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Union__least,axiom,
% 25.12/25.29 ! [V_C_2,V_A_2,T_b] :
% 25.12/25.29 ( ! [B_X] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) )
% 25.12/25.29 => 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)),V_C_2)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Inf__greatest,axiom,
% 25.12/25.29 ! [V_z_2,V_A_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( ! [B_x] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),B_x)) )
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Sup__least,axiom,
% 25.12/25.29 ! [V_z_2,V_A_2,T_b] :
% 25.12/25.29 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.29 => ( ! [B_x] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_z_2)) )
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_z_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_subsetI,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( ! [B_x] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_greaterThan__subset__iff,axiom,
% 25.12/25.29 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Orderings_Olinorder(T_b)
% 25.12/25.29 => ( 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)))
% 25.12/25.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_Pow__UNIV,axiom,
% 25.12/25.29 ! [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)) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_PowI,axiom,
% 25.12/25.29 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.29 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_atMost__subset__iff,axiom,
% 25.12/25.29 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Orderings_Oorder(T_b)
% 25.12/25.29 => ( 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)))
% 25.12/25.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_atLeast__subset__iff,axiom,
% 25.12/25.29 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Orderings_Oorder(T_b)
% 25.12/25.29 => ( 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)))
% 25.12/25.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 25.12/25.29
% 25.12/25.29 fof(fact_greaterThan__eq__iff,axiom,
% 25.12/25.29 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.29 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 25.12/25.30 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_atLeast__eq__iff,axiom,
% 25.12/25.30 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 25.12/25.30 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_atMost__eq__iff,axiom,
% 25.12/25.30 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 25.12/25.30 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__top,axiom,
% 25.12/25.30 ! [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))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Union__Pow__eq,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__not__empty,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__bottom,axiom,
% 25.12/25.30 ! [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))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_PowD,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__iff,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__mono,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => 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))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_atMost__iff,axiom,
% 25.12/25.30 ! [V_k_2,V_i_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oord(T_b)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_atLeast__iff,axiom,
% 25.12/25.30 ! [V_k_2,V_i_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oord(T_b)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__Pow__Union,axiom,
% 25.12/25.30 ! [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)))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__empty,axiom,
% 25.12/25.30 ! [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))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_lessThan__subset__iff,axiom,
% 25.12/25.30 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( 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)))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_INF__subset,axiom,
% 25.12/25.30 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.12/25.30 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => 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))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_SUP__subset,axiom,
% 25.12/25.30 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.12/25.30 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_greaterThanLessThan__empty,axiom,
% 25.12/25.30 ! [V_k_2,V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oorder(T_b)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 25.12/25.30 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_greaterThanAtMost__empty,axiom,
% 25.12/25.30 ! [V_k_2,V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oorder(T_b)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 25.12/25.30 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Collect__mono,axiom,
% 25.12/25.30 ! [T_b,V_Qa_2,V_Pa_2] :
% 25.12/25.30 ( ! [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.12/25.30 => hBOOL(hAPP(V_Qa_2,B_x)) )
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UNIV__eq__I,axiom,
% 25.12/25.30 ! [V_A_2,T_b] :
% 25.12/25.30 ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.30 => c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UNIV__witness,axiom,
% 25.12/25.30 ! [T_b] :
% 25.12/25.30 ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_le__funI,axiom,
% 25.12/25.30 ! [T_b,V_g_2,V_f_2,T_c] :
% 25.12/25.30 ( class_Orderings_Oord(T_c)
% 25.12/25.30 => ( ! [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)))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_equals0I,axiom,
% 25.12/25.30 ! [V_A_2,T_b] :
% 25.12/25.30 ( ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 25.12/25.30 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insertCI,axiom,
% 25.12/25.30 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 25.12/25.30 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 25.12/25.30 => V_a_2 = V_b_2 )
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insertE,axiom,
% 25.12/25.30 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 25.12/25.30 => ( V_a_2 != V_b_2
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__absorb2,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__commute,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__code,axiom,
% 25.12/25.30 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 25.12/25.30 <=> ( V_y_2 = V_x_2
% 25.12/25.30 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_lessThan__eq__iff,axiom,
% 25.12/25.30 ! [V_y_2,V_x_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 25.12/25.30 <=> V_x_2 = V_y_2 ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__absorb,axiom,
% 25.12/25.30 ! [V_A_2,V_a_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.12/25.30 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insertI2,axiom,
% 25.12/25.30 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__ident,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 25.12/25.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.12/25.30 => ( 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)
% 25.12/25.30 <=> V_A_2 = V_B_2 ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__iff,axiom,
% 25.12/25.30 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 25.12/25.30 <=> ( V_a_2 = V_b_2
% 25.12/25.30 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insertI1,axiom,
% 25.12/25.30 ! [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))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_empty__not__insert,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__not__empty,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_doubleton__eq__iff,axiom,
% 25.12/25.30 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.12/25.30 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.12/25.30 <=> ( ( V_a_2 = V_ca_2
% 25.12/25.30 & V_b_2 = V_d_2 )
% 25.12/25.30 | ( V_a_2 = V_d_2
% 25.12/25.30 & V_b_2 = V_ca_2 ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_singleton__inject,axiom,
% 25.12/25.30 ! [V_b_2,V_a_2,T_b] :
% 25.12/25.30 ( 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)))
% 25.12/25.30 => V_a_2 = V_b_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__insertI,axiom,
% 25.12/25.30 ! [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))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__insertI2,axiom,
% 25.12/25.30 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => 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))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__mono,axiom,
% 25.12/25.30 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 25.12/25.30 => 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))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_singleton__iff,axiom,
% 25.12/25.30 ! [V_a_2,V_b_2,T_b] :
% 25.12/25.30 ( 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)))))
% 25.12/25.30 <=> V_b_2 = V_a_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_singletonE,axiom,
% 25.12/25.30 ! [V_a_2,V_b_2,T_b] :
% 25.12/25.30 ( 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)))))
% 25.12/25.30 => V_b_2 = V_a_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__subset,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.12/25.30 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__insert,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 25.12/25.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.30 => ( 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)))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__singletonD,axiom,
% 25.12/25.30 ! [V_x_2,V_A_2,T_b] :
% 25.12/25.30 ( 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)))))
% 25.12/25.30 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.12/25.30 | V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Sup__singleton,axiom,
% 25.12/25.30 ! [V_a_2,T_b] :
% 25.12/25.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.30 => 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 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Inf__singleton,axiom,
% 25.12/25.30 ! [V_a_2,T_b] :
% 25.12/25.30 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.12/25.30 => 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 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_the__elem__eq,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ivl__disj__un_I1_J,axiom,
% 25.12/25.30 ! [V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => 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) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_atMost__Int__atLeast,axiom,
% 25.12/25.30 ! [V_n_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oorder(T_b)
% 25.12/25.30 => 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))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ivl__disj__un_I2_J,axiom,
% 25.12/25.30 ! [V_u_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => 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) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_diff__single__insert,axiom,
% 25.12/25.30 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.30 => 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))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_subset__insert__iff,axiom,
% 25.12/25.30 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 25.12/25.30 ( 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)))
% 25.12/25.30 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.30 => 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)) )
% 25.12/25.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__eq__Inter,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = 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))))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__eq__Union,axiom,
% 25.12/25.30 ! [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))))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ivl__disj__int_I5_J,axiom,
% 25.12/25.30 ! [V_u_2,V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oorder(T_b)
% 25.12/25.30 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_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)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ivl__disj__int_I6_J,axiom,
% 25.12/25.30 ! [V_u_2,V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Oorder(T_b)
% 25.12/25.30 => 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)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ivl__disj__un_I11_J,axiom,
% 25.12/25.30 ! [V_u_2,V_l_2,T_b] :
% 25.12/25.30 ( class_Orderings_Olinorder(T_b)
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.12/25.30 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_sup1CI,axiom,
% 25.12/25.30 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 25.12/25.30 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 25.12/25.30 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 25.12/25.30 => 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)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_sup1E,axiom,
% 25.12/25.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 25.12/25.30 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_inf1E,axiom,
% 25.12/25.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 25.12/25.30 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 25.12/25.30 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_inf1I,axiom,
% 25.12/25.30 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 25.12/25.30 ( hBOOL(hAPP(V_A_2,V_x_2))
% 25.12/25.30 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UnE,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UnCI,axiom,
% 25.12/25.30 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 25.12/25.30 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) )
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_IntI,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_IntE,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_DiffI,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_DiffE,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_inf1D2,axiom,
% 25.12/25.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 25.12/25.30 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_inf1D1,axiom,
% 25.12/25.30 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 25.12/25.30 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_sup1I2,axiom,
% 25.12/25.30 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 25.12/25.30 ( hBOOL(hAPP(V_B_2,V_x_2))
% 25.12/25.30 => 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)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_sup1I1,axiom,
% 25.12/25.30 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 25.12/25.30 ( hBOOL(hAPP(V_A_2,V_x_2))
% 25.12/25.30 => 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)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Int__crazy,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__Int2,axiom,
% 25.12/25.30 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Diff__Int,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_ball__Un,axiom,
% 25.12/25.30 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( ! [B_x] :
% 25.12/25.30 ( 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)))
% 25.12/25.30 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.30 <=> ( ! [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.30 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.30 & ! [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_bex__Un,axiom,
% 25.12/25.30 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( ? [B_x] :
% 25.12/25.30 ( 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)))
% 25.12/25.30 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.30 <=> ( ? [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.30 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.12/25.30 | ? [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 25.12/25.30 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Int__distrib2,axiom,
% 25.12/25.30 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__Un__distrib2,axiom,
% 25.12/25.30 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__Int__distrib2,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Diff,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__assoc,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__assoc,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__Diff,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Diff__cancel2,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__idemp,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Int__distrib,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__Int__distrib,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__Un__distrib,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__Un,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__Int,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__left__commute,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__left__commute,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__left__absorb,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Diff__cancel,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__left__absorb,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__commute,axiom,
% 25.12/25.30 ! [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) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__commute,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__absorb,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__absorb,axiom,
% 25.12/25.30 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__triv,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__disjoint,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__partition,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => 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 ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__subset__conv,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 <=> 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))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__Int__assoc__eq,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.12/25.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Union__Un__distrib,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Pow__Int__eq,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Inter__Un__distrib,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Union__Int__subset,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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)))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Inter__Un__subset,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__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)))) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__iff,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_DiffD1,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_DiffD2,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__iff,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 | hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UnI1,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_UnI2,axiom,
% 25.12/25.30 ! [V_A_2,V_B_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__iff,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.12/25.30 & hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_IntD1,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_IntD2,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_ca_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 25.12/25.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__cancel,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__empty,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_empty__Diff,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__empty,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.12/25.30 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__empty__right,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__empty__left,axiom,
% 25.12/25.30 ! [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 ).
% 25.12/25.30
% 25.12/25.30 fof(fact_disjoint__iff__not__equal,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( 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))
% 25.12/25.30 <=> ! [B_x] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.12/25.30 => ! [B_xa] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 25.12/25.30 => B_x != B_xa ) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__empty__right,axiom,
% 25.12/25.30 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Int__empty__left,axiom,
% 25.12/25.30 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_double__diff,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.12/25.30 => 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 ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__mono,axiom,
% 25.12/25.30 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 25.12/25.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.12/25.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 25.12/25.30 => 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))) ) ) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Diff__subset,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__insert__left,axiom,
% 25.12/25.30 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__insert__right,axiom,
% 25.12/25.30 ! [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)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_insert__inter__insert,axiom,
% 25.12/25.30 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 25.12/25.30
% 25.12/25.30 fof(fact_Un__mono,axiom,
% 25.12/25.31 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 25.12/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.12/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 25.12/25.31 => 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))) ) ) ).
% 25.12/25.31
% 25.12/25.31 fof(fact_Un__least,axiom,
% 25.12/25.31 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 25.12/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.12/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.12/25.31 => 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)) ) ) ).
% 25.12/25.31
% 25.12/25.31 fof(fact_Un__absorb2,axiom,
% 25.12/25.31 ! [V_A_2,V_B_2,T_b] :
% 25.12/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.12/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 25.12/25.31
% 25.12/25.31 fof(fact_Un__absorb1,axiom,
% 25.12/25.31 ! [V_B_2,V_A_2,T_b] :
% 25.12/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_subset__Un__eq,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.31 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Un__upper2,axiom,
% 25.26/25.31 ! [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))) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Un__upper1,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Un__UNIV__right,axiom,
% 25.26/25.31 ! [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)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Un__UNIV__left,axiom,
% 25.26/25.31 ! [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)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__mono,axiom,
% 25.26/25.31 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 25.26/25.31 => 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))) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__greatest,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 25.26/25.31 => 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))) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__absorb1,axiom,
% 25.26/25.31 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__absorb2,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__lower2,axiom,
% 25.26/25.31 ! [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__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__lower1,axiom,
% 25.26/25.31 ! [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__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__UNIV__right,axiom,
% 25.26/25.31 ! [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 ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__UNIV__left,axiom,
% 25.26/25.31 ! [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 ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Un__Pow__subset,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__Diff1,axiom,
% 25.26/25.31 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__Diff__if,axiom,
% 25.26/25.31 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 25.26/25.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.26/25.31 => 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) )
% 25.26/25.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__Diff__single,axiom,
% 25.26/25.31 ! [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) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Diff__insert2,axiom,
% 25.26/25.31 ! [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) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Diff__insert,axiom,
% 25.26/25.31 ! [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)))) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__left__if1,axiom,
% 25.26/25.31 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__right__if1,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__left__if0,axiom,
% 25.26/25.31 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 25.26/25.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__right__if0,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__left,axiom,
% 25.26/25.31 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 25.26/25.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 25.26/25.31 => 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)) )
% 25.26/25.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 25.26/25.31 => 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) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__insert__right,axiom,
% 25.26/25.31 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.31 => 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)) )
% 25.26/25.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.31 => 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) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Diff__UNIV,axiom,
% 25.26/25.31 ! [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)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Sup__insert,axiom,
% 25.26/25.31 ! [V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__is__Un,axiom,
% 25.26/25.31 ! [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) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Inf__insert,axiom,
% 25.26/25.31 ! [V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Union__disjoint,axiom,
% 25.26/25.31 ! [V_A_2,V_C_2,T_b] :
% 25.26/25.31 ( 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))
% 25.26/25.31 <=> ! [B_x] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I20_J,axiom,
% 25.26/25.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.31 => 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) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__int_I14_J,axiom,
% 25.26/25.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Union__insert,axiom,
% 25.26/25.31 ! [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)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Inter__insert,axiom,
% 25.26/25.31 ! [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)) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Diff__insert__absorb,axiom,
% 25.26/25.31 ! [V_A_2,V_x_2,T_b] :
% 25.26/25.31 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.31 => 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 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__Diff,axiom,
% 25.26/25.31 ! [V_A_2,V_a_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.31 => 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 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Sup__binary,axiom,
% 25.26/25.31 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Inf__binary,axiom,
% 25.26/25.31 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_single__Diff__lessThan,axiom,
% 25.26/25.31 ! [V_k_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I9_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__int_I3_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__int_I1_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__int_I10_J,axiom,
% 25.26/25.31 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_distrib__sup__le,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_distrib__inf__le,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_minus__apply,axiom,
% 25.26/25.31 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.31 ( class_Groups_Ominus(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__apply,axiom,
% 25.26/25.31 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.31 ( class_Lattices_Olattice(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__apply,axiom,
% 25.26/25.31 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.31 ( class_Lattices_Olattice(T_b)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__top__left,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__top__right,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__eq__top__iff,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__top(T_b)
% 25.26/25.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 25.26/25.31 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 25.26/25.31 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__top__left,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__top__right,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__top(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__absorb,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__assoc,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I6_J,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup_Oassoc,axiom,
% 25.26/25.31 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__left__commute,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I7_J,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup_Oleft__commute,axiom,
% 25.26/25.31 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__left__idem,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I8_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup_Oleft__idem,axiom,
% 25.26/25.31 ! [V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__commute,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I5_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup_Ocommute,axiom,
% 25.26/25.31 ! [V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__idem,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup_Oidem,axiom,
% 25.26/25.31 ! [V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__assoc,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I2_J,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf_Oassoc,axiom,
% 25.26/25.31 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__left__commute,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I3_J,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf_Oleft__commute,axiom,
% 25.26/25.31 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__left__idem,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I4_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf_Oleft__idem,axiom,
% 25.26/25.31 ! [V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__commute,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__aci_I1_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf_Ocommute,axiom,
% 25.26/25.31 ! [V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__idem,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf_Oidem,axiom,
% 25.26/25.31 ! [V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__supE,axiom,
% 25.26/25.31 ! [V_x,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( 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))
% 25.26/25.31 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__mono,axiom,
% 25.26/25.31 ! [V_d,V_b,V_c,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 25.26/25.31 => 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))) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__least,axiom,
% 25.26/25.31 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 25.26/25.31 => 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)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__supI,axiom,
% 25.26/25.31 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 25.26/25.31 => 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)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__absorb1,axiom,
% 25.26/25.31 ! [V_x,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__absorb2,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__supI2,axiom,
% 25.26/25.31 ! [V_a,V_b,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 25.26/25.31 => 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))) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__supI1,axiom,
% 25.26/25.31 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.31 => 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))) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__sup__iff,axiom,
% 25.26/25.31 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.31 => ( 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))
% 25.26/25.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 25.26/25.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__iff__sup,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.31 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__ge2,axiom,
% 25.26/25.31 ! [V_x,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__ord_I4_J,axiom,
% 25.26/25.31 ! [V_x,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__ge1,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.31 => 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))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__ord_I3_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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))) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__infE,axiom,
% 25.26/25.31 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( 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)))
% 25.26/25.31 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__mono,axiom,
% 25.26/25.31 ! [V_d,V_b,V_c,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 25.26/25.31 => 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))) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__greatest,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 25.26/25.31 => 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))) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__infI,axiom,
% 25.26/25.31 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 25.26/25.31 => 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))) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__absorb2,axiom,
% 25.26/25.31 ! [V_x,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__absorb1,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__infI2,axiom,
% 25.26/25.31 ! [V_a,V_x,V_b,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__infI1,axiom,
% 25.26/25.31 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__inf__iff,axiom,
% 25.26/25.31 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.31 => ( 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)))
% 25.26/25.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_le__iff__inf,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.31 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__le2,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__ord_I2_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__le1,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__ord_I1_J,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__eq__bot__iff,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__bot(T_b)
% 25.26/25.31 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 25.26/25.31 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 25.26/25.31 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__bot__right,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__bot__left,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__bot__right,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__bot__left,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Obounded__lattice__bot(T_a)
% 25.26/25.31 => 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) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__inf__distrib2,axiom,
% 25.26/25.31 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Odistrib__lattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__distrib2,axiom,
% 25.26/25.31 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.31 ( class_Lattices_Odistrib__lattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__inf__distrib1,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Odistrib__lattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_inf__sup__distrib1,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Odistrib__lattice(T_a)
% 25.26/25.31 => 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)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_sup__inf__absorb,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Lattices_Olattice(T_a)
% 25.26/25.31 => 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 ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_diff__eq__diff__less__eq,axiom,
% 25.26/25.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.31 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 25.26/25.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I5_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I4_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_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) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I13_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_psubset__insert__iff,axiom,
% 25.26/25.31 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 25.26/25.31 ( 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)))
% 25.26/25.31 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 25.26/25.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 25.26/25.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.31 => 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)) )
% 25.26/25.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I10_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_Int__Collect__mono,axiom,
% 25.26/25.31 ! [V_Qa_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.31 => ( ! [B_x] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.31 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.31 => hBOOL(hAPP(V_Qa_2,B_x)) ) )
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Qa_2)))) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 25.26/25.31 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.31 => ( 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)
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ivl__disj__un_I12_J,axiom,
% 25.26/25.31 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 25.26/25.31 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_insert__partition,axiom,
% 25.26/25.31 ! [V_F_2,V_x_2,T_b] :
% 25.26/25.31 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 25.26/25.31 => ( ! [B_x] :
% 25.26/25.31 ( 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)))
% 25.26/25.31 => ! [B_xa] :
% 25.26/25.31 ( 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)))
% 25.26/25.31 => ( B_x != B_xa
% 25.26/25.31 => 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)) ) ) )
% 25.26/25.31 => 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)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_atLeastatMost__psubset__iff,axiom,
% 25.26/25.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)))
% 25.26/25.31 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 25.26/25.31 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 25.26/25.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 25.26/25.31 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_a_2))
% 25.26/25.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 25.26/25.31 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_linorder__cases,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_a)
% 25.26/25.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => ( V_x != V_y
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__asym,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_xt1_I10_J,axiom,
% 25.26/25.31 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__trans,axiom,
% 25.26/25.31 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_xt1_I2_J,axiom,
% 25.26/25.31 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.31 => ( V_b = V_c
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ord__less__eq__trans,axiom,
% 25.26/25.31 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Orderings_Oord(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.31 => ( V_b = V_c
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_xt1_I1_J,axiom,
% 25.26/25.31 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( V_a = V_b
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_ord__eq__less__trans,axiom,
% 25.26/25.31 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.31 ( class_Orderings_Oord(T_a)
% 25.26/25.31 => ( V_a = V_b
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_xt1_I9_J,axiom,
% 25.26/25.31 ! [V_a,V_b,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__asym_H,axiom,
% 25.26/25.31 ! [V_b,V_a,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__imp__not__eq2,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => V_y != V_x ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__imp__not__eq,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => V_x != V_y ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__imp__not__less,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__not__sym,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_less__imp__neq,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Oorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => V_x != V_y ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_linorder__neqE,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_a)
% 25.26/25.31 => ( V_x != V_y
% 25.26/25.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_linorder__antisym__conv3,axiom,
% 25.26/25.31 ! [V_x_2,V_y_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 25.26/25.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_linorder__less__linear,axiom,
% 25.26/25.31 ! [V_y,V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_a)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.31 | V_x = V_y
% 25.26/25.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_not__less__iff__gr__or__eq,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 25.26/25.31 | V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_linorder__neq__iff,axiom,
% 25.26/25.31 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( V_x_2 != V_y_2
% 25.26/25.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_order__less__irrefl,axiom,
% 25.26/25.31 ! [V_x,T_a] :
% 25.26/25.31 ( class_Orderings_Opreorder(T_a)
% 25.26/25.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_psubset__trans,axiom,
% 25.26/25.31 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.26/25.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.26/25.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_atLeastatMost__empty,axiom,
% 25.26/25.31 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.31 ( class_Orderings_Oorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 25.26/25.31 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_lessThan__strict__subset__iff,axiom,
% 25.26/25.31 ! [V_n_2,V_m_2,T_b] :
% 25.26/25.31 ( class_Orderings_Olinorder(T_b)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 25.26/25.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 25.26/25.31
% 25.26/25.31 fof(fact_diff__eq__diff__less,axiom,
% 25.26/25.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.31 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 25.26/25.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 25.26/25.32 ! [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) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 25.26/25.32 ! [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) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__fun__def,axiom,
% 25.26/25.32 ! [V_g_2,V_f_2,T_b,T_c] :
% 25.26/25.32 ( class_Orderings_Oord(T_c)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.26/25.32 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__not__less,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__not__le,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__le__less__linear,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__less__le,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 & V_x_2 != V_y_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__le__not__le,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Opreorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__le__less,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 | V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_leI,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_a)
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_not__leE,axiom,
% 25.26/25.32 ! [V_x,V_y,T_a] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_a)
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__antisym__conv1,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__neq__le__trans,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( V_a != V_b
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_xt1_I12_J,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( V_a != V_b
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_leD,axiom,
% 25.26/25.32 ! [V_x,V_y,T_a] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__less__imp__le,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Opreorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__antisym__conv2,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 25.26/25.32 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__le__imp__less__or__eq,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.32 | V_x = V_y ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__le__neq__trans,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.32 => ( V_a != V_b
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_xt1_I11_J,axiom,
% 25.26/25.32 ! [V_a,V_b,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.32 => ( V_a != V_b
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__less__le__trans,axiom,
% 25.26/25.32 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Opreorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_xt1_I7_J,axiom,
% 25.26/25.32 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_order__le__less__trans,axiom,
% 25.26/25.32 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.32 ( class_Orderings_Opreorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_xt1_I8_J,axiom,
% 25.26/25.32 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.32 ( class_Orderings_Oorder(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_psubsetD,axiom,
% 25.26/25.32 ! [V_ca_2,V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_B_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_not__psubset__empty,axiom,
% 25.26/25.32 ! [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)))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__supI1,axiom,
% 25.26/25.32 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__supI2,axiom,
% 25.26/25.32 ! [V_a,V_b,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Osemilattice__sup(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__infI1,axiom,
% 25.26/25.32 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.32 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 25.26/25.32 => 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)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__infI2,axiom,
% 25.26/25.32 ! [V_a,V_x,V_b,T_a] :
% 25.26/25.32 ( class_Lattices_Osemilattice__inf(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 25.26/25.32 => 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)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_subset__psubset__trans,axiom,
% 25.26/25.32 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_psubset__subset__trans,axiom,
% 25.26/25.32 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_psubset__imp__subset,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_subset__iff__psubset__eq,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 | V_A_2 = V_B_2 ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_psubset__eq,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 & V_A_2 != V_B_2 ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__Sup__iff,axiom,
% 25.26/25.32 ! [V_S_2,V_a_2,T_b] :
% 25.26/25.32 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.32 & class_Orderings_Olinorder(T_b) )
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 25.26/25.32 <=> ? [B_x] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.26/25.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Inf__less__iff,axiom,
% 25.26/25.32 ! [V_a_2,V_S_2,T_b] :
% 25.26/25.32 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.32 & class_Orderings_Olinorder(T_b) )
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 25.26/25.32 <=> ? [B_x] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.26/25.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_lessThan__iff,axiom,
% 25.26/25.32 ! [V_k_2,V_i_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oord(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I19_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.32 => 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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 25.26/25.32 ! [V_l_2,V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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))
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 25.26/25.32 ! [V_l_2,V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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)
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_greaterThan__iff,axiom,
% 25.26/25.32 ! [V_k_2,V_i_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oord(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastatMost__empty__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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))
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastatMost__empty__iff2,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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)
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastatMost__subset__iff,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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_ca_2,V_d_2)))
% 25.26/25.32 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 25.26/25.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 25.26/25.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastAtMost__singleton_H,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( V_a_2 = V_b_2
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 25.26/25.32 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.32 <=> ( V_a_2 = V_b_2
% 25.26/25.32 & V_b_2 = V_ca_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastAtMost__singleton,axiom,
% 25.26/25.32 ! [V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_diff__eq__diff__eq,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.32 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_ca_2),V_d_2)
% 25.26/25.32 => ( V_a_2 = V_b_2
% 25.26/25.32 <=> V_ca_2 = V_d_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I22_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.32 => 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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I4_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I16_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I13_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I12_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I7_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I16_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 25.26/25.32 => 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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I7_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 25.26/25.32 => 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) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 25.26/25.32 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 25.26/25.32 ( 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))
% 25.26/25.32 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.32 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 25.26/25.32 | ? [B_x,B_y] :
% 25.26/25.32 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 25.26/25.32 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 25.26/25.32 & 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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I18_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 25.26/25.32 => 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_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I3_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 25.26/25.32 => 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_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I6_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(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) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I15_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.32 => 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)),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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Diff1__fold__graph,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_psubset__imp__ex__mem,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => ? [B_b] : hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I8_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__unique,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 25.26/25.32 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I14_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ComplI,axiom,
% 25.26/25.32 ! [V_A_2,V_ca_2,T_b] :
% 25.26/25.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__minus,axiom,
% 25.26/25.32 ! [V_a,T_a] :
% 25.26/25.32 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_equation__minus__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.32 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 25.26/25.32 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__equation__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.32 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 25.26/25.32 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_neg__equal__iff__equal,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.32 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 25.26/25.32 <=> V_a_2 = V_b_2 ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_double__compl,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_uminus__apply,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.26/25.32 ( class_Groups_Ouminus(T_b)
% 25.26/25.32 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__eq__compl__iff,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_b)
% 25.26/25.32 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 25.26/25.32 <=> V_x_2 = V_y_2 ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__mono,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__le__compl__iff,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_b)
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_le__imp__neg__le,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_a)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_neg__le__iff__le,axiom,
% 25.26/25.32 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__le__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( 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))
% 25.26/25.32 <=> 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)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_le__minus__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_neg__less__iff__less,axiom,
% 25.26/25.32 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__less__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_less__minus__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ComplE,axiom,
% 25.26/25.32 ! [V_A_2,V_ca_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 25.26/25.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ComplD,axiom,
% 25.26/25.32 ! [V_A_2,V_ca_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 25.26/25.32 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__iff,axiom,
% 25.26/25.32 ! [V_A_2,V_ca_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__diff__eq,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Groups_Oab__group__add(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__subset__Compl__iff,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 25.26/25.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__anti__mono,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__eq__iff,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 25.26/25.32 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 25.26/25.32 <=> ( V_a_2 = V_ca_2
% 25.26/25.32 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 25.26/25.32 => V_a_2 = V_ca_2 ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),V_d_2))
% 25.26/25.32 => V_b_2 = V_d_2 ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_empty__fold__graphE,axiom,
% 25.26/25.32 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 25.26/25.32 => V_x_2 = V_z_2 ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_OemptyI,axiom,
% 25.26/25.32 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 25.26/25.32 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__inf__bot,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_inf__compl__bot,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_diff__eq,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__top__eq,axiom,
% 25.26/25.32 ! [T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__bot__eq,axiom,
% 25.26/25.32 ! [T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__sup,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__inf,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_compl__sup__top,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_sup__compl__top,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oboolean__algebra(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_subset__Compl__self__eq,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( 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)))
% 25.26/25.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__empty__eq,axiom,
% 25.26/25.32 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__UNIV__eq,axiom,
% 25.26/25.32 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__disjoint,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__disjoint2,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__partition,axiom,
% 25.26/25.32 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__partition2,axiom,
% 25.26/25.32 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__Int,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__Un,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 25.26/25.32 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__Diff__eq,axiom,
% 25.26/25.32 ! [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) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Diff__eq,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Diff__Compl,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__atLeast,axiom,
% 25.26/25.32 ! [V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__lessThan,axiom,
% 25.26/25.32 ! [V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__empty,axiom,
% 25.26/25.32 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 25.26/25.32 => 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)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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)
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__empty__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => ( 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))
% 25.26/25.32 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__atMost,axiom,
% 25.26/25.32 ! [V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__greaterThan,axiom,
% 25.26/25.32 ! [V_k_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_atLeastLessThan__subset__iff,axiom,
% 25.26/25.32 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 25.26/25.32 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),V_a_2))
% 25.26/25.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I17_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph_OinsertI,axiom,
% 25.26/25.32 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__diff,axiom,
% 25.26/25.32 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 25.26/25.32 => 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) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I11_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_disjoint__eq__subset__Compl,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( 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))
% 25.26/25.32 <=> 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I21_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I15_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__un_I8_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Olinorder(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 25.26/25.32 => 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)),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) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I2_J,axiom,
% 25.26/25.32 ! [V_u_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)),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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ivl__disj__int_I9_J,axiom,
% 25.26/25.32 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 25.26/25.32 ( class_Orderings_Oorder(T_b)
% 25.26/25.32 => 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)),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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold1Set_Ointros,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph__permute__diff,axiom,
% 25.26/25.32 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 25.26/25.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Osingleton,axiom,
% 25.26/25.32 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => 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 ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold1Set__sing,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
% 25.26/25.32 <=> V_a_2 = V_b_2 ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_nonempty__iff,axiom,
% 25.26/25.32 ! [T_b,V_A_2] :
% 25.26/25.32 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.32 <=> ? [B_x,B_B] :
% 25.26/25.32 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_B)
% 25.26/25.32 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_B)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Pow__insert,axiom,
% 25.26/25.32 ! [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))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 25.26/25.32 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.32 => ? [B_y_H] :
% 25.26/25.32 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 25.26/25.32 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Inf__fin_Oidem,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Olattice(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Sup__fin_Oidem,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Olattice(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_linorder__neqE__linordered__idom,axiom,
% 25.26/25.32 ! [V_y,V_x,T_a] :
% 25.26/25.32 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.32 => ( V_x != V_y
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__eqI,axiom,
% 25.26/25.32 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 25.26/25.32 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_double__complement,axiom,
% 25.26/25.32 ! [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 ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Compl__eq__Compl__iff,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( 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)
% 25.26/25.32 <=> V_A_2 = V_B_2 ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__Pow__surj,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 25.26/25.32 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_mult__left__idem,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_mult__idem,axiom,
% 25.26/25.32 ! [V_x,T_a] :
% 25.26/25.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_times_Oidem,axiom,
% 25.26/25.32 ! [V_a,T_a] :
% 25.26/25.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 25.26/25.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 25.26/25.32 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 25.26/25.32 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.32 ( class_Groups_Oab__semigroup__mult(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fun__left__comm,axiom,
% 25.26/25.32 ! [T_b] :
% 25.26/25.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.32 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__mult__right,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Rings_Oring(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__mult__left,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Rings_Oring(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__mult__commute,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Rings_Oring(T_a)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_minus__mult__minus,axiom,
% 25.26/25.32 ! [V_b,V_a,T_a] :
% 25.26/25.32 ( class_Rings_Oring(T_a)
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_square__eq__iff,axiom,
% 25.26/25.32 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.32 ( class_Rings_Oidom(T_b)
% 25.26/25.32 => ( 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)
% 25.26/25.32 <=> ( V_a_2 = V_b_2
% 25.26/25.32 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__iff,axiom,
% 25.26/25.32 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 25.26/25.32 <=> ? [B_x] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.32 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_imageI,axiom,
% 25.26/25.32 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_rev__image__eqI,axiom,
% 25.26/25.32 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__is__empty,axiom,
% 25.26/25.32 ! [V_A_2,V_f_2,T_b,T_c] :
% 25.26/25.32 ( 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))
% 25.26/25.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__empty,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_empty__is__image,axiom,
% 25.26/25.32 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( 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)
% 25.26/25.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__insert,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__mono,axiom,
% 25.26/25.32 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_subset__image__iff,axiom,
% 25.26/25.32 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 25.26/25.32 <=> ? [B_AA] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 25.26/25.32 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__Un,axiom,
% 25.26/25.32 ! [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)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__Pow__mono,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( 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))
% 25.26/25.32 => 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_insert__image,axiom,
% 25.26/25.32 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => 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) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_range__eqI,axiom,
% 25.26/25.32 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 25.26/25.32 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_rangeI,axiom,
% 25.26/25.32 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__Int__subset,axiom,
% 25.26/25.32 ! [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)))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__diff__subset,axiom,
% 25.26/25.32 ! [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)))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__atLeastAtMost,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_type__definition_OAbs__image,axiom,
% 25.26/25.32 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.26/25.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_type__definition_ORep__range,axiom,
% 25.26/25.32 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 25.26/25.32 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 25.26/25.32 => V_y_2 = V_x_2 ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_empty__fold1SetE,axiom,
% 25.26/25.32 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold1Set__nonempty,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 25.26/25.32 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__atLeastLessThan,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 25.26/25.32 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => 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)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__lessThan,axiom,
% 25.26/25.32 ! [V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__greaterThan,axiom,
% 25.26/25.32 ! [V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__atLeast,axiom,
% 25.26/25.32 ! [V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_image__uminus__atMost,axiom,
% 25.26/25.32 ! [V_x_2,T_b] :
% 25.26/25.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.32 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph__insert__swap,axiom,
% 25.26/25.32 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 25.26/25.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_surj__Compl__image__subset,axiom,
% 25.26/25.32 ! [V_A_2,V_f_2,T_b,T_c] :
% 25.26/25.32 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_Cantors__paradox,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ~ ? [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) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Oremove,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => ( ( 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))
% 25.26/25.32 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 25.26/25.32 & ( 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))
% 25.26/25.32 => 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)))))) ) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_insert__fold1SetE,axiom,
% 25.26/25.32 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 25.26/25.32 => ~ ! [B_a,B_A] :
% 25.26/25.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 25.26/25.32 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold1Set_Oequations,axiom,
% 25.26/25.32 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 25.26/25.32 <=> ? [B_a,B_A] :
% 25.26/25.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 25.26/25.32 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 25.26/25.32 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 25.26/25.32 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.32 => ~ ! [B_y] :
% 25.26/25.32 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 25.26/25.32 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Ounion__inter,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.32 => ( 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))
% 25.26/25.32 => 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)) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Ounion__disjoint,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.32 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.32 => ( 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))
% 25.26/25.32 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Oinsert__remove,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( ( 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))
% 25.26/25.32 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 25.26/25.32 & ( 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))
% 25.26/25.32 => 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)))))) ) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite_OemptyI,axiom,
% 25.26/25.32 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite_OinsertI,axiom,
% 25.26/25.32 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__imageI,axiom,
% 25.26/25.32 ! [V_h_2,T_c,V_F_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Int,axiom,
% 25.26/25.32 ! [V_Ga_2,V_F_2,T_b] :
% 25.26/25.32 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.32 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 25.26/25.32 => 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Diff,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Inter,axiom,
% 25.26/25.32 ! [V_M_2,T_b] :
% 25.26/25.32 ( ? [B_x] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 25.26/25.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__UN,axiom,
% 25.26/25.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> ! [B_x] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( class_Finite__Set_Ofinite(T_b)
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__code,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( class_Finite__Set_Ofinite(T_b)
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Prod__UNIV,axiom,
% 25.26/25.32 ! [T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__option__UNIV,axiom,
% 25.26/25.32 ! [T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 25.26/25.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Plus__UNIV__iff,axiom,
% 25.26/25.32 ! [T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 25.26/25.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__UnionD,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Pow__iff,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 25.26/25.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite_Oequations_I1_J,axiom,
% 25.26/25.32 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__insert,axiom,
% 25.26/25.32 ! [V_A_2,V_a_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 25.26/25.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__fun__UNIVD2,axiom,
% 25.26/25.32 ! [T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__subset,axiom,
% 25.26/25.32 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_rev__finite__subset,axiom,
% 25.26/25.32 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__UNIV,axiom,
% 25.26/25.32 ! [T_b] :
% 25.26/25.32 ( class_Finite__Set_Ofinite(T_b)
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__UnI,axiom,
% 25.26/25.32 ! [V_Ga_2,V_F_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 25.26/25.32 => 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))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Un,axiom,
% 25.26/25.32 ! [V_Ga_2,V_F_2,T_b] :
% 25.26/25.32 ( 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)))
% 25.26/25.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Diff2,axiom,
% 25.26/25.32 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.32 => ( 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)))
% 25.26/25.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_fold__graph__imp__finite,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__surj,axiom,
% 25.26/25.32 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.26/25.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__Diff__insert,axiom,
% 25.26/25.32 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 25.26/25.32 ( 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))))
% 25.26/25.32 <=> 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))) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_finite__compl,axiom,
% 25.26/25.32 ! [V_A_2,T_b] :
% 25.26/25.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 25.26/25.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 25.26/25.32
% 25.26/25.32 fof(fact_folding__one_Oinsert,axiom,
% 25.26/25.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.32 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Oremove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oremove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 25.26/25.33 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => 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)))))) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oremove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 25.26/25.33 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => 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)))))) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one_Oclosed,axiom,
% 25.26/25.33 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( ! [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))))))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__image,axiom,
% 25.26/25.33 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.33 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)))))) )
% 25.26/25.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__empty__induct,axiom,
% 25.26/25.33 ! [V_Pa_2,V_A_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 25.26/25.33 => ( ! [B_a,B_A] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 25.26/25.33 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__triv,axiom,
% 25.26/25.33 ! [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 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__idem,axiom,
% 25.26/25.33 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 25.26/25.33 ( hAPP(V_f_2,V_x_2) = V_y_2
% 25.26/25.33 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__other,axiom,
% 25.26/25.33 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 25.26/25.33 ( V_z_2 != V_x_2
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__twist,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_ca_2,V_a_2] :
% 25.26/25.33 ( V_a_2 != V_ca_2
% 25.26/25.33 => 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_ca_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_ca_2,V_d_2),V_a_2,V_b_2) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__apply,axiom,
% 25.26/25.33 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 25.26/25.33 ( ( V_z_2 = V_x_2
% 25.26/25.33 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 25.26/25.33 & ( V_z_2 != V_x_2
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__same,axiom,
% 25.26/25.33 ! [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 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__upd,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__upd__idem__iff,axiom,
% 25.26/25.33 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 25.26/25.33 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Oidem,axiom,
% 25.26/25.33 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_ball__UN,axiom,
% 25.26/25.33 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.33 ( ! [B_x] :
% 25.26/25.33 ( 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)))
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.26/25.33 <=> ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.33 => ! [B_xa] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__le__Sup,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Oempty,axiom,
% 25.26/25.33 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Osingleton,axiom,
% 25.26/25.33 ! [V_x_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Osingleton,axiom,
% 25.26/25.33 ! [V_x_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oin__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_sup__Inf__absorb,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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 ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oin__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_inf__Sup__absorb,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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 ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin__Sup,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin__Inf,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Oin__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Osubset__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Osubset__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Ounion__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Ounion__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Oinsert,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oinsert,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oinsert,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => 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 )
% 25.26/25.33 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_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)))))) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => 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 )
% 25.26/25.33 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_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)))))) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Ounion__inter,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Ounion__inter,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oclosed,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( ! [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))))))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oclosed,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( ! [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))))))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__Union,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 25.26/25.33 => ( ! [B_M] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 25.26/25.33 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Ohom__commute,axiom,
% 25.26/25.33 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( ! [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))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Ohom__commute,axiom,
% 25.26/25.33 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( ! [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))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__subset__induct,axiom,
% 25.26/25.33 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.33 => ( ! [B_a,B_F] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 25.26/25.33 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 25.26/25.33 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__Un,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 25.26/25.33 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( ! [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))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold__empty,axiom,
% 25.26/25.33 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__eq__fold__idem,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__eq__fold,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__singleton__def,axiom,
% 25.26/25.33 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 25.26/25.33 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__singleton,axiom,
% 25.26/25.33 ! [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 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 25.26/25.33 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one_Oeq__fold,axiom,
% 25.26/25.33 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_union__fold__insert,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold__sup__insert,axiom,
% 25.26/25.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold__inf__insert,axiom,
% 25.26/25.33 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_sup__Sup__fold__sup,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_inf__Inf__fold__inf,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 25.26/25.33 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_OF__eq,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_OF__eq,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_sup__le__fold__sup,axiom,
% 25.26/25.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold__inf__le__inf,axiom,
% 25.26/25.33 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fold__sup,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fold__inf,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__one_Oeq__fold_H,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__belowI,axiom,
% 25.26/25.33 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_below__fold1__iff,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__insert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__Un2,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Olattice(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__insert,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_semilattice__big_OF__eq,axiom,
% 25.26/25.33 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 25.26/25.33 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold1__in,axiom,
% 25.26/25.33 ! [V_A_2,T_b] :
% 25.26/25.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( ! [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))))))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_hom__fold1__commute,axiom,
% 25.26/25.33 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.26/25.33 => ( ! [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))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.33 => ( ! [B_x] :
% 25.26/25.33 ( 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)))
% 25.26/25.33 => hAPP(V_g_2,B_x) = V_z_2 )
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 25.26/25.33 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff1__ring,axiom,
% 25.26/25.33 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Rings_Oring(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff1,axiom,
% 25.26/25.33 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)) )
% 25.26/25.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod_Oremove,axiom,
% 25.26/25.33 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff__nat__ivl,axiom,
% 25.26/25.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem__insert,axiom,
% 25.26/25.33 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem,axiom,
% 25.26/25.33 ! [T_b] :
% 25.26/25.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.26/25.33 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem__sup,axiom,
% 25.26/25.33 ! [T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.33 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fun__left__comm__idem__inf,axiom,
% 25.26/25.33 ! [T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff__nat,axiom,
% 25.26/25.33 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod_Oinsert,axiom,
% 25.26/25.33 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod__insert,axiom,
% 25.26/25.33 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod__Un__Int,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod_Ounion__inter,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff1__nat,axiom,
% 25.26/25.33 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 25.26/25.33 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)) )
% 25.26/25.33 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff,axiom,
% 25.26/25.33 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod_Oinsert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod__Un__disjoint,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setprod_Ounion__disjoint,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__strict__mono,axiom,
% 25.26/25.33 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.33 => ( ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 25.26/25.33 => 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))) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__diff1_H,axiom,
% 25.26/25.33 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum_Oremove,axiom,
% 25.26/25.33 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_inf__le__fold__inf,axiom,
% 25.26/25.33 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_fold__sup__le__sup,axiom,
% 25.26/25.33 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 25.26/25.33 ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__ivl__cong,axiom,
% 25.26/25.33 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_b,T_c] :
% 25.26/25.33 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 & class_Orderings_Oord(T_b) )
% 25.26/25.33 => ( V_a_2 = V_ca_2
% 25.26/25.33 => ( V_b_2 = V_d_2
% 25.26/25.33 => ( ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),B_x))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 25.26/25.33 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 25.26/25.33 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 25.26/25.33 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__atLeastLessThan,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__add__nat__ivl,axiom,
% 25.26/25.33 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 25.26/25.33 ! [V_N_2] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 25.26/25.33 <=> ? [B_m] :
% 25.26/25.33 ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oab__semigroup__add(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__left__cancel,axiom,
% 25.26/25.33 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Groups_Ocancel__semigroup__add(T_b)
% 25.26/25.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)
% 25.26/25.33 <=> V_b_2 = V_ca_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__right__cancel,axiom,
% 25.26/25.33 ! [V_ca_2,V_a_2,V_b_2,T_b] :
% 25.26/25.33 ( class_Groups_Ocancel__semigroup__add(T_b)
% 25.26/25.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)
% 25.26/25.33 <=> V_b_2 = V_ca_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__left__imp__eq,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ocancel__semigroup__add(T_a)
% 25.26/25.33 => ( 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)
% 25.26/25.33 => V_b = V_c ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__imp__eq,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( 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)
% 25.26/25.33 => V_b = V_c ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__right__imp__eq,axiom,
% 25.26/25.33 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.33 ( class_Groups_Ocancel__semigroup__add(T_a)
% 25.26/25.33 => ( 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)
% 25.26/25.33 => V_b = V_c ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_atLeastLessThan__add__Un,axiom,
% 25.26/25.33 ! [V_k_2,V_j_2,V_i_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 25.26/25.33 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__imp__le__left,axiom,
% 25.26/25.33 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.33 => ( 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)))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__imp__le__right,axiom,
% 25.26/25.33 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.33 => ( 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)))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__mono,axiom,
% 25.26/25.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__left__mono,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__right__mono,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__cancel__left,axiom,
% 25.26/25.33 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__cancel__right,axiom,
% 25.26/25.33 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__imp__less__left,axiom,
% 25.26/25.33 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.33 => ( 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)))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__imp__less__right,axiom,
% 25.26/25.33 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.33 => ( 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)))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__strict__mono,axiom,
% 25.26/25.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__strict__left__mono,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__strict__right__mono,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__cancel__left,axiom,
% 25.26/25.33 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_ca_2),V_b_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__cancel__right,axiom,
% 25.26/25.33 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_ca_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_combine__common__factor,axiom,
% 25.26/25.33 ! [V_c,V_b,V_e,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Osemiring(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__class_Odistrib,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__diff__cancel,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__add__cancel,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_minus__add__distrib,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_minus__add,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__minus__cancel,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_minus__add__cancel,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__less__mono,axiom,
% 25.26/25.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__le__mono,axiom,
% 25.26/25.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_eq__add__iff1,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oring(T_b)
% 25.26/25.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 25.26/25.33 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_eq__add__iff2,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oring(T_b)
% 25.26/25.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 25.26/25.33 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__def,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_ab__diff__minus,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__minus__eq__add,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add__iff1,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oordered__ring(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add__iff2,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oordered__ring(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__add__iff1,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oordered__ring(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__add__iff2,axiom,
% 25.26/25.33 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Rings_Oordered__ring(T_b)
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__Un__nat,axiom,
% 25.26/25.33 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__insert,axiom,
% 25.26/25.33 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum_Oinsert,axiom,
% 25.26/25.33 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__Un__Int,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => 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)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 25.26/25.33 => 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) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 25.26/25.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.33 => 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)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum_Oinsert__remove,axiom,
% 25.26/25.33 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => 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)))))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__Un__disjoint,axiom,
% 25.26/25.33 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => ( 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))
% 25.26/25.33 => 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)) ) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_setsum__Un,axiom,
% 25.26/25.33 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.33 ( class_Groups_Oab__group__add(T_c)
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.33 => 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))) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 25.26/25.33 ! [V_y,V_x,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__ring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__less__add__iff2,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__less__add__iff1,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> 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)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__eq__add__iff2,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 25.26/25.33 => ( 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)
% 25.26/25.33 <=> V_m_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__diff__add__eq2,axiom,
% 25.26/25.33 ! [V_n,V_m,V_u,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__le__add__iff2,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__eq__add__iff1,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 25.26/25.33 => ( 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)
% 25.26/25.33 <=> 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 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__diff__add__eq1,axiom,
% 25.26/25.33 ! [V_n,V_m,V_u,V_i,V_j] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__lessThan,axiom,
% 25.26/25.33 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__greaterThanAtMost,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__greaterThanLessThan,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__atMost,axiom,
% 25.26/25.33 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__atLeastAtMost,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_left__add__mult__distrib,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_finite__nat__set__iff__bounded,axiom,
% 25.26/25.33 ! [V_N_2] :
% 25.26/25.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 25.26/25.33 <=> ? [B_m] :
% 25.26/25.33 ! [B_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_infinite__UNIV__nat,axiom,
% 25.26/25.33 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 25.26/25.33 ! [V_c,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 25.26/25.33 ! [V_d,V_c,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 25.26/25.33 ! [V_d,V_c,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 25.26/25.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 25.26/25.33 ! [V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 25.26/25.33 ! [V_ry,V_rx,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 25.26/25.33 ! [V_ry,V_rx,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 25.26/25.33 ! [V_rx,V_ly,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 25.26/25.33 ! [V_rx,V_ly,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 25.26/25.33 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 25.26/25.33 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 25.26/25.33 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_crossproduct__eq,axiom,
% 25.26/25.33 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 25.26/25.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 25.26/25.33 => ( 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))
% 25.26/25.33 <=> ( V_w_2 = V_x_2
% 25.26/25.33 | V_y_2 = V_z_2 ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 25.26/25.33 ! [V_b,V_m,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_crossproduct__noteq,axiom,
% 25.26/25.33 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 25.26/25.33 => ( ( V_a_2 != V_b_2
% 25.26/25.33 & V_ca_2 != V_d_2 )
% 25.26/25.33 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 25.26/25.33 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__le__add__iff1,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> 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)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__diff__right,axiom,
% 25.26/25.33 ! [V_i,V_j,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__diff__conv,axiom,
% 25.26/25.33 ! [V_i_2,V_k_2,V_j_2] :
% 25.26/25.33 ( 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))
% 25.26/25.33 <=> 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add__diff,axiom,
% 25.26/25.33 ! [V_m,V_n,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add__diff__inverse,axiom,
% 25.26/25.33 ! [V_m,V_n] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__diff__assoc,axiom,
% 25.26/25.33 ! [V_i,V_j,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__diff__conv2,axiom,
% 25.26/25.33 ! [V_i_2,V_j_2,V_k_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> 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)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add__diff__inverse2,axiom,
% 25.26/25.33 ! [V_m,V_n] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__imp__diff__is__add,axiom,
% 25.26/25.33 ! [V_k_2,V_j_2,V_i_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 25.26/25.33 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 25.26/25.33 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__less__cases,axiom,
% 25.26/25.33 ! [V_Pa_2,V_n_2,V_m_2] :
% 25.26/25.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 25.26/25.33 => ( ( V_m_2 = V_n_2
% 25.26/25.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 25.26/25.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 25.26/25.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) )
% 25.26/25.33 => hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__not__refl3,axiom,
% 25.26/25.33 ! [V_t,V_s] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 25.26/25.33 => V_s != V_t ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__not__refl2,axiom,
% 25.26/25.33 ! [V_m,V_n] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 25.26/25.33 => V_m != V_n ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__irrefl__nat,axiom,
% 25.26/25.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_linorder__neqE__nat,axiom,
% 25.26/25.33 ! [V_y,V_x] :
% 25.26/25.33 ( V_x != V_y
% 25.26/25.33 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__neq__iff,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2] :
% 25.26/25.33 ( V_m_2 != V_n_2
% 25.26/25.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__not__refl,axiom,
% 25.26/25.33 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__commute,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__left__commute,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__assoc,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__left__cancel,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( 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)
% 25.26/25.33 <=> V_m_2 = V_n_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__right__cancel,axiom,
% 25.26/25.33 ! [V_n_2,V_k_2,V_m_2] :
% 25.26/25.33 ( 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)
% 25.26/25.33 <=> V_m_2 = V_n_2 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__antisym,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.33 => V_m = V_n ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__trans,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_eq__imp__le,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( V_m = V_n
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__le__linear,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__refl,axiom,
% 25.26/25.33 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__commute,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__mult__commute,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__mult__assoc,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_not__add__less1,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_not__add__less2,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__left__cancel__less,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( 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)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_trans__less__add1,axiom,
% 25.26/25.33 ! [V_m,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_trans__less__add2,axiom,
% 25.26/25.33 ! [V_m,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__mono1,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__less__mono,axiom,
% 25.26/25.33 ! [V_l,V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__add__eq__less,axiom,
% 25.26/25.33 ! [V_n,V_m,V_l,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 25.26/25.33 => ( 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)
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__lessD1,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( 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))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__or__eq__imp__le,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 | V_m = V_n )
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__neq__implies__less,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => ( V_m != V_n
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__imp__le__nat,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__eq__less__or__eq,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 | V_m_2 = V_n_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__less__le,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 & V_m_2 != V_n_2 ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__leE,axiom,
% 25.26/25.33 ! [V_n,V_k,V_m] :
% 25.26/25.33 ( 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))
% 25.26/25.33 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__leD1,axiom,
% 25.26/25.33 ! [V_n,V_k,V_m] :
% 25.26/25.33 ( 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))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__leD2,axiom,
% 25.26/25.33 ! [V_n,V_k,V_m] :
% 25.26/25.33 ( 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))
% 25.26/25.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__mono,axiom,
% 25.26/25.33 ! [V_l,V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__le__mono1,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_trans__le__add2,axiom,
% 25.26/25.33 ! [V_m,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_trans__le__add1,axiom,
% 25.26/25.33 ! [V_m,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_nat__add__left__cancel__le,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( 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)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__iff__add,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.33 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add1,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__add2,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__less__mono2,axiom,
% 25.26/25.33 ! [V_l,V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__imp__diff__less,axiom,
% 25.26/25.33 ! [V_n,V_k,V_j] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__cancel2,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__cancel,axiom,
% 25.26/25.33 ! [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) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__diff__left,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__add__inverse,axiom,
% 25.26/25.33 ! [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 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__add__inverse2,axiom,
% 25.26/25.33 ! [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 ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__mult__distrib,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__mult__distrib2,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__diff__iff,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_Nat_Odiff__diff__eq,axiom,
% 25.26/25.33 ! [V_n,V_m,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 25.26/25.33 => 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) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_eq__diff__iff,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 25.26/25.33 => ( 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)
% 25.26/25.33 <=> V_m_2 = V_n_2 ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__diff__cancel,axiom,
% 25.26/25.33 ! [V_n,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__le__mono,axiom,
% 25.26/25.33 ! [V_l,V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__le__mono2,axiom,
% 25.26/25.33 ! [V_l,V_n,V_m] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__le__self,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__square,axiom,
% 25.26/25.33 ! [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))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_le__cube,axiom,
% 25.26/25.33 ! [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)))) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_mult__le__mono1,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_mult__le__mono2,axiom,
% 25.26/25.33 ! [V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_mult__le__mono,axiom,
% 25.26/25.33 ! [V_l,V_k,V_j,V_i] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__mult__distrib2,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__mult__distrib,axiom,
% 25.26/25.33 ! [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)) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__diff__inverse,axiom,
% 25.26/25.33 ! [V_n,V_m] :
% 25.26/25.33 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.33 => 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 ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__diff__conv,axiom,
% 25.26/25.33 ! [V_k_2,V_j_2,V_i_2] :
% 25.26/25.33 ( 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)))
% 25.26/25.33 <=> 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_less__diff__iff,axiom,
% 25.26/25.33 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 25.26/25.33 => ( 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)))
% 25.26/25.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__less__mono,axiom,
% 25.26/25.33 ! [V_c,V_b,V_a] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 25.26/25.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 25.26/25.33 => 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))) ) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__add__assoc2,axiom,
% 25.26/25.33 ! [V_i,V_j,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_add__diff__assoc2,axiom,
% 25.26/25.33 ! [V_i,V_j,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.33 => 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) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_diff__add__assoc,axiom,
% 25.26/25.33 ! [V_i,V_j,V_k] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.33 => 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)) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_termination__basic__simps_I4_J,axiom,
% 25.26/25.33 ! [V_y,V_z,V_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.33 fof(fact_termination__basic__simps_I3_J,axiom,
% 25.26/25.33 ! [V_z,V_y,V_x] :
% 25.26/25.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 25.26/25.33 => 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))) ) ).
% 25.26/25.33
% 25.26/25.34 fof(fact_termination__basic__simps_I5_J,axiom,
% 25.26/25.34 ! [V_y,V_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_termination__basic__simps_I1_J,axiom,
% 25.26/25.34 ! [V_z,V_y,V_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_termination__basic__simps_I2_J,axiom,
% 25.26/25.34 ! [V_y,V_z,V_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff2__less,axiom,
% 25.26/25.34 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff1__less,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__ub__add__nat,axiom,
% 25.26/25.34 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( 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))))
% 25.26/25.34 => 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)))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__UNIV__unit,axiom,
% 25.26/25.34 hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_one__reorient,axiom,
% 25.26/25.34 ! [V_x_2,T_b] :
% 25.26/25.34 ( class_Groups_Oone(T_b)
% 25.26/25.34 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 25.26/25.34 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult_Ocomm__neutral,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__1__right,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__1,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__1__left,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__eq__1__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_F_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> ! [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__1,axiom,
% 25.26/25.34 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__1__eq__mult__iff,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 25.26/25.34 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 25.26/25.34 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__1__right,axiom,
% 25.26/25.34 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__eq__1__iff,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 25.26/25.34 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 25.26/25.34 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__lessThan,axiom,
% 25.26/25.34 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_u_2)) = V_u_2 ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Oinsert,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 25.26/25.34 ! [V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__add__one,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => 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)))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__1__mult,axiom,
% 25.26/25.34 ! [V_n,V_m,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 25.26/25.34 ! [V_m,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 25.26/25.34 ! [V_a,V_m,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 25.26/25.34 ! [V_m,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 25.26/25.34 ! [V_x,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__ring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_square__eq__1__iff,axiom,
% 25.26/25.34 ! [V_x_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.34 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.34 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_subset__card__intvl__is__intvl,axiom,
% 25.26/25.34 ! [V_k_2,V_A_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
% 25.26/25.34 => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__atLeastLessThan,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod_Oempty,axiom,
% 25.26/25.34 ! [V_g_2,T_c,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__empty,axiom,
% 25.26/25.34 ! [V_f_2,T_c,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod_Oinfinite,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__infinite,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff__insert,axiom,
% 25.26/25.34 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Oinsert__remove,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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)))))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__greaterThanAtMost,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Oremove,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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)))))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff__singleton,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff__singleton__if,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__insert__le,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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)))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__seteq,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => V_A_2 = V_B_2 ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__mono,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__image__le,axiom,
% 25.26/25.34 ! [V_f_2,T_c,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_psubset__card__mono,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Un__Int,axiom,
% 25.26/25.34 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Ounion__inter,axiom,
% 25.26/25.34 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff__subset,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff__subset__Int,axiom,
% 25.26/25.34 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__card__le__card__Diff,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => 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)))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__psubset,axiom,
% 25.26/25.34 ! [V_A_2,V_B_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Un__disjoint,axiom,
% 25.26/25.34 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Diff1__le,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 25.26/25.34 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__Un__one,axiom,
% 25.26/25.34 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_fold__Un__disjoint,axiom,
% 25.26/25.34 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__mono__one__right,axiom,
% 25.26/25.34 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.34 => 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) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__mono__one__left,axiom,
% 25.26/25.34 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.34 => 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) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Suc__Diff1,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_fold__image__Un__Int,axiom,
% 25.26/25.34 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_convex__bound__lt,axiom,
% 25.26/25.34 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 25.26/25.34 => 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)) ) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__zeroE,axiom,
% 25.26/25.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le0,axiom,
% 25.26/25.34 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__Suc,axiom,
% 25.26/25.34 ! [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))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__mono,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_lessI,axiom,
% 25.26/25.34 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_One__nat__def,axiom,
% 25.26/25.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 25.26/25.34 ! [V_k_2,V_f_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__reorient,axiom,
% 25.26/25.34 ! [V_x_2,T_b] :
% 25.26/25.34 ( class_Groups_Ozero(T_b)
% 25.26/25.34 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 25.26/25.34 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeast__Suc__greaterThan,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_greaterThan__Suc,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeast__Suc,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),V_k_2)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 25.26/25.34 ! [V_k_2,V_f_2] :
% 25.26/25.34 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 25.26/25.34 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Zero__not__Suc,axiom,
% 25.26/25.34 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat_Osimps_I2_J,axiom,
% 25.26/25.34 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_n__not__Suc__n,axiom,
% 25.26/25.34 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__not__Zero,axiom,
% 25.26/25.34 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat_Osimps_I3_J,axiom,
% 25.26/25.34 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__n__not__n,axiom,
% 25.26/25.34 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat_Oinject,axiom,
% 25.26/25.34 ! [V_nat_H_2,V_nat_2] :
% 25.26/25.34 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 25.26/25.34 <=> V_nat_2 = V_nat_H_2 ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Zero__neq__Suc,axiom,
% 25.26/25.34 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__neq__Zero,axiom,
% 25.26/25.34 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__inject,axiom,
% 25.26/25.34 ! [V_y,V_x] :
% 25.26/25.34 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 25.26/25.34 => V_x = V_y ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_greaterThan__0,axiom,
% 25.26/25.34 hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__eq__1__iff,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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))
% 25.26/25.34 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.26/25.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__Suc__eq__0__disj,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 25.26/25.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 | ? [B_j] :
% 25.26/25.34 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__Suc0,axiom,
% 25.26/25.34 ! [V_n_2] :
% 25.26/25.34 ( 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))))
% 25.26/25.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_gr0__conv__Suc,axiom,
% 25.26/25.34 ! [V_n_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 25.26/25.34 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_one__is__add,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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)
% 25.26/25.34 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.26/25.34 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.34 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__is__1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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))
% 25.26/25.34 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.26/25.34 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.34 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__pred,axiom,
% 25.26/25.34 ! [V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.34 => 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 ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__less,axiom,
% 25.26/25.34 ! [V_i,V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_n__less__m__mult__n,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( 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))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_n__less__n__mult__m,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( 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))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_one__less__mult,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( 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))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_one__le__mult__iff,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( 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))
% 25.26/25.34 & 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__eq__Suc0__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.26/25.34 <=> ? [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.34 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.26/25.34 & ! [B_xa] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 25.26/25.34 => ( B_x != B_xa
% 25.26/25.34 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__less__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__Suc__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 | V_m_2 = V_n_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__less__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__less__less__Suc__eq,axiom,
% 25.26/25.34 ! [V_m_2,V_n_2] :
% 25.26/25.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 25.26/25.34 <=> V_n_2 = V_m_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__antisym,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 25.26/25.34 => V_m = V_n ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__SucI,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__lessI,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__trans__Suc,axiom,
% 25.26/25.34 ! [V_k,V_j,V_i] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__SucE,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => V_m = V_n ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__lessD,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__less__SucD,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__Suc__shift,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__Suc,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__Suc__right,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__n__not__le__n,axiom,
% 25.26/25.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__less__eq__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__Suc__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__le__mono,axiom,
% 25.26/25.34 ! [V_m_2,V_n_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__SucI,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__SucE,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__leD,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__Suc,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__diff__diff,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__mult__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)
% 25.26/25.34 <=> V_m_2 = V_n_2 ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__0__left,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Omonoid__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__0,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_double__zero__sym,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__0__right,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Omonoid__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add_Ocomm__neutral,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__0__iff,axiom,
% 25.26/25.34 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.34 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 25.26/25.34 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_divisors__zero,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ono__zero__divisors(T_a)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_no__zero__divisors,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ono__zero__divisors(T_a)
% 25.26/25.34 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__eq__0__iff,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__no__zero__divisors(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__zero__right,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Omult__zero(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__zero__left,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Omult__zero(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_right__minus__eq,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> V_a_2 = V_b_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_eq__iff__diff__eq__0,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.34 => ( V_a_2 = V_b_2
% 25.26/25.34 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__self,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__0__right,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_one__neq__zero,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Ozero__neq__one(T_a)
% 25.26/25.34 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__neq__one,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Ozero__neq__one(T_a)
% 25.26/25.34 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_minus__zero,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__0__equal__iff__equal,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.34 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 25.26/25.34 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_equal__neg__zero,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__equal__0__iff__equal,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__equal__zero,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_fold__image__empty,axiom,
% 25.26/25.34 ! [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 ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__less0,axiom,
% 25.26/25.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neq0__conv,axiom,
% 25.26/25.34 ! [V_n_2] :
% 25.26/25.34 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__nat__zero__code,axiom,
% 25.26/25.34 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_gr__implies__not0,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_gr0I,axiom,
% 25.26/25.34 ! [V_n] :
% 25.26/25.34 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__eq__self__zero,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 25.26/25.34 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__is__0,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Nat_Oadd__0__right,axiom,
% 25.26/25.34 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 25.26/25.34
% 25.26/25.34 fof(fact_plus__nat_Oadd__0,axiom,
% 25.26/25.34 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastLessThan__singleton,axiom,
% 25.26/25.34 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_image__Suc__atLeastLessThan,axiom,
% 25.26/25.34 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 25.26/25.34 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__0__eq,axiom,
% 25.26/25.34 ! [V_n_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 25.26/25.34 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__0__eq__0,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_minus__nat_Odiff__0,axiom,
% 25.26/25.34 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__self__eq__0,axiom,
% 25.26/25.34 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diffs0__imp__equal,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => V_m = V_n ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__cancel2,axiom,
% 25.26/25.34 ! [V_n_2,V_k_2,V_m_2] :
% 25.26/25.34 ( 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)
% 25.26/25.34 <=> ( V_m_2 = V_n_2
% 25.26/25.34 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)
% 25.26/25.34 <=> ( V_m_2 = V_n_2
% 25.26/25.34 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__is__0,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__0__right,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__0,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)
% 25.26/25.34 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 | V_m_2 = V_n_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_image__Suc__atLeastAtMost,axiom,
% 25.26/25.34 ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_lessThan__Suc,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_k_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastLessThan0,axiom,
% 25.26/25.34 ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atMost__Suc,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__atMost,axiom,
% 25.26/25.34 ! [V_u_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_u_2)) = hAPP(c_Nat_OSuc,V_u_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeast__0,axiom,
% 25.26/25.34 hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_lessThan__0,axiom,
% 25.26/25.34 hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum_Oeq__fold,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum_OF__eq,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__diff__1,axiom,
% 25.26/25.34 ! [V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.34 => 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 ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atMost__0,axiom,
% 25.26/25.34 hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__op__ivl__Suc,axiom,
% 25.26/25.34 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__add__Suc1,axiom,
% 25.26/25.34 ! [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)))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__add__Suc2,axiom,
% 25.26/25.34 ! [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)))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__iff__Suc__add,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__eq__Suc__le,axiom,
% 25.26/25.34 ! [V_m_2,V_n_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__Suc__eq__le,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__le__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__imp__less__Suc,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__leI,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__less__Suc__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 25.26/25.34 <=> V_n_2 = V_m_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__le__lessD,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__cl__ivl__Suc,axiom,
% 25.26/25.34 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__less__Suc,axiom,
% 25.26/25.34 ! [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))) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__mult__less__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__Suc,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__Suc__right,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__diff__le,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__mult__le__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__nonneg__nonneg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__nonneg__eq__0__iff,axiom,
% 25.26/25.34 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__increasing,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__increasing2,axiom,
% 25.26/25.34 ! [V_a,V_b,V_c,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__nonpos__nonpos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_split__mult__neg__le,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__cancel__semiring(T_a)
% 25.26/25.34 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_split__mult__pos__le,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__ring(T_a)
% 25.26/25.34 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__mono,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__mono_H,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__left__mono__neg,axiom,
% 25.26/25.34 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__ring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__right__mono__neg,axiom,
% 25.26/25.34 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__ring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__mult__left__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__comm__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__left__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__right__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__nonpos__nonpos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__ring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__nonpos__nonneg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__cancel__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__nonneg__nonpos2,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__cancel__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__nonneg__nonpos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__cancel__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__nonneg__nonneg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Oordered__cancel__semiring(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__0__iff,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__le__mult__iff,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__le__square,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring(T_a)
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_pos__add__strict,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__neg__neg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__pos__pos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__left__mono__neg,axiom,
% 25.26/25.34 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__right__mono__neg,axiom,
% 25.26/25.34 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__mult__strict__left__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__left__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__right__mono,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__neg__neg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__neg__pos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel__left__neg,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__mult__pos2,axiom,
% 25.26/25.34 ! [V_a,V_b,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__mult__pos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__pos__neg2,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__pos__neg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__pos__pos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel__left__pos,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel__left__disj,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.26/25.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel__right__disj,axiom,
% 25.26/25.34 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
% 25.26/25.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 25.26/25.34 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__square__less__zero,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring(T_a)
% 25.26/25.34 => ~ 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__iff__diff__le__0,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 25.26/25.34 <=> 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__iff__diff__less__0,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.34 <=> 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__scale__eq__noteq,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 25.26/25.34 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 25.26/25.34 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => ( ( V_a = V_b
% 25.26/25.34 & V_c != V_d )
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__le__one,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__one__le__zero,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => ~ 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__one,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__one__less__zero,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__1,axiom,
% 25.26/25.34 ! [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 ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__0__le__iff__le,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_le__minus__self__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__le__0__iff__le,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_minus__le__self__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__0__less__iff__less,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__less__0__iff__less,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_neg__less__nonneg,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_less__minus__self__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_right__minus,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_b)
% 25.26/25.34 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 25.26/25.34 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_left__minus,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_ab__left__minus,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oab__group__add(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_minus__unique,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__0,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Groups_Ogroup__add(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastLessThanSuc,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_n_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__empty,axiom,
% 25.26/25.34 ! [V_f_2,T_c,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum_Oempty,axiom,
% 25.26/25.34 ! [V_g_2,T_c,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__infinite,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum_Oinfinite,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__pos__nat__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_S_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> ! [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastAtMostSuc__conv,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 25.26/25.34 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__zero__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 25.26/25.34 & class_Rings_Ono__zero__divisors(T_c) )
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> ? [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.34 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__zero,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Rings_Ocomm__semiring__1(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ? [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.34 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.34 => 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) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__atLeastAtMost,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__gr__0,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 25.26/25.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Oempty,axiom,
% 25.26/25.34 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__infinite,axiom,
% 25.26/25.34 ! [V_A_2,T_b] :
% 25.26/25.34 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__less,axiom,
% 25.26/25.34 ! [V_m,V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__diff,axiom,
% 25.26/25.34 ! [V_m_2,V_n_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__0__less__mult__iff,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__cancel2,axiom,
% 25.26/25.34 ! [V_n_2,V_k_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__mono1,axiom,
% 25.26/25.34 ! [V_k,V_j,V_i] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__mono2,axiom,
% 25.26/25.34 ! [V_k,V_j,V_i] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__eq__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> V_m_2 = V_n_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__less__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__add__0,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__is__0__eq_H,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__is__0__eq,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2] :
% 25.26/25.34 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__eq__self__implies__10,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 25.26/25.34 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 25.26/25.34 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__eq__0__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_F_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> ! [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_lessThan__Suc__atMost,axiom,
% 25.26/25.34 ! [V_k_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeast0LessThan,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 25.26/25.34 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.34 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__greaterThanLessThan,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),hAPP(c_Nat_OSuc,V_l_2)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeast0AtMost,axiom,
% 25.26/25.34 ! [V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_l_2,V_u_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 25.26/25.34 ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__diff__eq2,axiom,
% 25.26/25.34 ! [V_m,V_j,V_k] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__diff__eq1,axiom,
% 25.26/25.34 ! [V_m,V_j,V_k] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__nonpos__neg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__neg__nonpos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__strict__increasing2,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__strict__increasing,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__nonneg__pos,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__pos__nonneg,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__left__le__imp__le,axiom,
% 25.26/25.34 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__right__le__imp__le,axiom,
% 25.26/25.34 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__imp__less__left,axiom,
% 25.26/25.34 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__left__less__imp__less,axiom,
% 25.26/25.34 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__imp__less__right,axiom,
% 25.26/25.34 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__right__less__imp__less,axiom,
% 25.26/25.34 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring(T_a)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__less__imp__less,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__less__le__imp__less,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__mono_H,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__strict__mono,axiom,
% 25.26/25.34 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__strict(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.34 => 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))) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__cancel__left__neg,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__cancel__left__pos,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__left__le__one__le,axiom,
% 25.26/25.34 ! [V_y,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__right__le__one__le,axiom,
% 25.26/25.34 ! [V_y,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_zero__less__two,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.34 => 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)))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__eq__0__iff,axiom,
% 25.26/25.34 ! [V_A_2,T_b] :
% 25.26/25.34 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.34 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__ge__0__finite,axiom,
% 25.26/25.34 ! [V_A_2,T_b] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__diff__split,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_Pa_2] :
% 25.26/25.34 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 25.26/25.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 25.26/25.34 & ! [B_d] :
% 25.26/25.34 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__diff__split__asm,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_Pa_2] :
% 25.26/25.34 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 25.26/25.34 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.34 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 25.26/25.34 | ? [B_d] :
% 25.26/25.34 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 25.26/25.34 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__le__cancel2,axiom,
% 25.26/25.34 ! [V_n_2,V_k_2,V_m_2] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nat__mult__le__cancel1,axiom,
% 25.26/25.34 ! [V_n_2,V_m_2,V_k_2] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__eq__1__iff,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> ? [B_x] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.34 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 25.26/25.34 & ! [B_xa] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 25.26/25.34 => ( B_x != B_xa
% 25.26/25.34 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__insert__if,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__insert__disjoint,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_convex__bound__le,axiom,
% 25.26/25.34 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__semiring__1(T_a)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 25.26/25.34 => 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)) ) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__head__upt__Suc,axiom,
% 25.26/25.34 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_fold__image__insert,axiom,
% 25.26/25.34 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Oab__semigroup__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__head__Suc,axiom,
% 25.26/25.34 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__gt__0__iff,axiom,
% 25.26/25.34 ! [V_A_2,T_b] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod_OF__eq,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod_Oeq__fold,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_finite__UNIV__card__ge__0,axiom,
% 25.26/25.34 ! [T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.34 => 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))))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__insert,axiom,
% 25.26/25.34 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => 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)))))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_finite__fun__UNIVD1,axiom,
% 25.26/25.34 ! [T_c,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 25.26/25.34 => ( 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))
% 25.26/25.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_mult__eq__if,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__eq__if,axiom,
% 25.26/25.34 ! [V_n,V_m] :
% 25.26/25.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 25.26/25.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => 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)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__pred_H,axiom,
% 25.26/25.34 ! [V_n] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.34 => 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sum__squares__gt__zero__iff,axiom,
% 25.26/25.34 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( 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))))
% 25.26/25.34 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_not__sum__squares__lt__zero,axiom,
% 25.26/25.34 ! [V_y,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring(T_a)
% 25.26/25.34 => ~ 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))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sum__squares__le__zero__iff,axiom,
% 25.26/25.34 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sum__squares__ge__zero,axiom,
% 25.26/25.34 ! [V_y,V_x,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__ring(T_a)
% 25.26/25.34 => 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)))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_bot__nat__def,axiom,
% 25.26/25.34 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sum__squares__eq__zero__iff,axiom,
% 25.26/25.34 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__ring__strict(T_b)
% 25.26/25.34 => ( 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)
% 25.26/25.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__eq__plus1__left,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Suc__eq__plus1,axiom,
% 25.26/25.34 ! [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)) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 25.26/25.34 ! [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) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_ex__nat__less,axiom,
% 25.26/25.34 ! [V_Pa_2,V_n_2] :
% 25.26/25.34 ( ? [B_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 25.26/25.34 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 25.26/25.34 <=> ? [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_all__nat__less,axiom,
% 25.26/25.34 ! [V_Pa_2,V_n_2] :
% 25.26/25.34 ( ! [B_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 25.26/25.34 <=> ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_ex__nat__less__eq,axiom,
% 25.26/25.34 ! [V_Pa_2,V_n_2] :
% 25.26/25.34 ( ? [B_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 25.26/25.34 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 25.26/25.34 <=> ? [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_all__nat__less__eq,axiom,
% 25.26/25.34 ! [V_Pa_2,V_n_2] :
% 25.26/25.34 ( ! [B_m] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 25.26/25.34 <=> ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_even__less__0__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__monoid__big_OF__eq,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.34 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.26/25.34 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.34 => 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) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.34 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card_Ounion__inter__neutral,axiom,
% 25.26/25.34 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( ( ? [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)))
% 25.26/25.34 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.34 => 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)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 25.26/25.34 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.26/25.34 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.26/25.34 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.26/25.34 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_double__eq__0__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__mono2,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => ( ! [B_b] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 25.26/25.34 => 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))) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_fold__image__Un__one,axiom,
% 25.26/25.34 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 25.26/25.34 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__Un__zero,axiom,
% 25.26/25.34 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.34 => 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)) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Suc__eq,axiom,
% 25.26/25.34 ! [V_k_2,V_A_2,T_b] :
% 25.26/25.34 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 25.26/25.34 <=> ? [B_b,B_B] :
% 25.26/25.34 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 25.26/25.34 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 25.26/25.34 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 25.26/25.34 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.34 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__mono3,axiom,
% 25.26/25.34 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 25.26/25.34 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 25.26/25.34 => 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))) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__odd__less__0,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => ( 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)))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__0,axiom,
% 25.26/25.34 ! [T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__add,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__mult,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__diff,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => 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))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__1,axiom,
% 25.26/25.34 ! [T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__minus,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Oring__1(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => 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))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__double__eq__0__iff,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Int_Oring__char__0(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_Ints__odd__nonzero,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Int_Oring__char__0(T_b)
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_card__Plus__conv__if,axiom,
% 25.26/25.34 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.34 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 25.26/25.34 => 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)) )
% 25.26/25.34 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 25.26/25.34 => 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) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setprod__diff1,axiom,
% 25.26/25.34 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.34 ( class_Fields_Ofield(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.34 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 25.26/25.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.34 => 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)) )
% 25.26/25.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.34 => 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) ) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_ex__least__nat__less,axiom,
% 25.26/25.34 ! [V_n_2,V_Pa_2] :
% 25.26/25.34 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 25.26/25.34 => ( hBOOL(hAPP(V_Pa_2,V_n_2))
% 25.26/25.34 => ? [B_k] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 25.26/25.34 & ! [B_i] :
% 25.26/25.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 25.26/25.34 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 25.26/25.34 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_k),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__mono__zero__right,axiom,
% 25.26/25.34 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.34 => 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) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_setsum__mono__zero__left,axiom,
% 25.26/25.34 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 25.26/25.34 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 25.26/25.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 25.26/25.34 => ( ! [B_x] :
% 25.26/25.34 ( 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)))
% 25.26/25.34 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.34 => 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) ) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sgn__1__neg,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.34 => ( 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))
% 25.26/25.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sgn__sgn,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_divide__zero__left,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_divide__zero,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_add__divide__distrib,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_times__divide__eq__right,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_diff__divide__distrib,axiom,
% 25.26/25.34 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_divide__1,axiom,
% 25.26/25.34 ! [V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_minus__divide__left,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => 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) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sgn__0__0,axiom,
% 25.26/25.34 ! [V_a_2,T_b] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.34 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sgn0,axiom,
% 25.26/25.34 ! [T_a] :
% 25.26/25.34 ( class_Groups_Osgn__if(T_a)
% 25.26/25.34 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_sgn__times,axiom,
% 25.26/25.34 ! [V_b,V_a,T_a] :
% 25.26/25.34 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.34 => 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)) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_eq__divide__imp,axiom,
% 25.26/25.34 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 25.26/25.34 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_divide__eq__imp,axiom,
% 25.26/25.34 ! [V_a,V_b,V_c,T_a] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.34 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.34 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 25.26/25.34 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nonzero__divide__eq__eq,axiom,
% 25.26/25.34 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_b)
% 25.26/25.34 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 25.26/25.34 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_nonzero__eq__divide__eq,axiom,
% 25.26/25.34 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_b)
% 25.26/25.34 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 25.26/25.34 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 ) ) ) ).
% 25.26/25.34
% 25.26/25.34 fof(fact_right__inverse__eq,axiom,
% 25.26/25.34 ! [V_a_2,V_b_2,T_b] :
% 25.26/25.34 ( class_Rings_Odivision__ring(T_b)
% 25.26/25.34 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.34 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.35 <=> V_a_2 = V_b_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__self,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__self__if,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 25.26/25.35 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 25.26/25.35 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nonzero__minus__divide__divide,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nonzero__minus__divide__right,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Rings_Odivision__ring(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__less,axiom,
% 25.26/25.35 ! [V_a_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__greater,axiom,
% 25.26/25.35 ! [V_a_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__Plus__iff,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 25.26/25.35 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__Plus,axiom,
% 25.26/25.35 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__PlusD_I1_J,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 25.26/25.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__PlusD_I2_J,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 25.26/25.35 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__pos,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__1__pos,axiom,
% 25.26/25.35 ! [V_a_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.35 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card__Plus,axiom,
% 25.26/25.35 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.35 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__if,axiom,
% 25.26/25.35 ! [V_x,T_a] :
% 25.26/25.35 ( class_Groups_Osgn__if(T_a)
% 25.26/25.35 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 25.26/25.35 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_sgn__neg,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__left__mono__neg,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__left__mono,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__divide__le__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__le__divide__eq,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__imp__le__div__pos,axiom,
% 25.26/25.35 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => ( 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))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__imp__div__pos__le,axiom,
% 25.26/25.35 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_times__divide__times__eq,axiom,
% 25.26/25.35 ! [V_w,V_z,V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus__divide__divide,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus__divide__right,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__right__mono__neg,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__right__mono,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__le__0__iff,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__le__divide__iff,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__strict__right__mono__neg,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__strict__right__mono,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__neg__neg,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__neg__pos,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__pos__neg,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__pos__pos,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__less__0__iff,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__less__divide__iff,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__divide__eq,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 25.26/25.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) = V_b_2 )
% 25.26/25.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__eq__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = V_a_2
% 25.26/25.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2) )
% 25.26/25.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__divide__mult__cancel__right,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__divide__mult__cancel__left,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_frac__eq__eq,axiom,
% 25.26/25.35 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 25.26/25.35 ( class_Fields_Ofield(T_b)
% 25.26/25.35 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => ( 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)
% 25.26/25.35 <=> 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) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__nonneg__pos,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__nonneg__neg,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_frac__less2,axiom,
% 25.26/25.35 ! [V_z,V_w,V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 25.26/25.35 => 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))) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_frac__less,axiom,
% 25.26/25.35 ! [V_z,V_w,V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 25.26/25.35 => 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))) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_frac__le,axiom,
% 25.26/25.35 ! [V_z,V_w,V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 25.26/25.35 => 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))) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__nonpos__pos,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__nonpos__neg,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__strict__left__mono__neg,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__strict__left__mono,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__divide__less__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__less__divide__eq,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__imp__less__div__pos,axiom,
% 25.26/25.35 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => ( 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))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__imp__div__pos__less,axiom,
% 25.26/25.35 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__divide__less__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__less__divide__eq,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__less__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__divide__eq,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__num__frac,axiom,
% 25.26/25.35 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__divide__eq__iff,axiom,
% 25.26/25.35 ! [V_y,V_x,V_z,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__frac__num,axiom,
% 25.26/25.35 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__add__eq__iff,axiom,
% 25.26/25.35 ! [V_y,V_x,V_z,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__frac__eq,axiom,
% 25.26/25.35 ! [V_w,V_x,V_z,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__frac__eq,axiom,
% 25.26/25.35 ! [V_w,V_x,V_z,V_y,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__diff__eq__iff,axiom,
% 25.26/25.35 ! [V_y,V_x,V_z,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__divide__eq__iff,axiom,
% 25.26/25.35 ! [V_y,V_x,V_z,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__half__sum,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.35 => 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))))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_gt__half__sum,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__divide__eq,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__le__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__le__divide__eq,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),V_b_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__divide__le__eq,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2,V_ca_2,T_b] :
% 25.26/25.35 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),V_a_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_UNIV__Plus__UNIV,axiom,
% 25.26/25.35 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_setprod__Un,axiom,
% 25.26/25.35 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.35 ( class_Fields_Ofield(T_c)
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Plus__eq__empty__conv,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.35 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 25.26/25.35 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.35 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_field__le__mult__one__interval,axiom,
% 25.26/25.35 ! [V_y,V_x,T_a] :
% 25.26/25.35 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.35 => ( ! [B_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.35 => 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)) ) )
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_setprod__pos__nat,axiom,
% 25.26/25.35 ! [V_f_2,V_S_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_setsum__SucD,axiom,
% 25.26/25.35 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 25.26/25.35 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 25.26/25.35 => ? [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card__partition,axiom,
% 25.26/25.35 ! [V_k_2,V_C_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 25.26/25.35 => ( ! [B_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 25.26/25.35 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 25.26/25.35 => ( ! [B_c1] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 25.26/25.35 => ! [B_c2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 25.26/25.35 => ( B_c1 != B_c2
% 25.26/25.35 => 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)) ) ) )
% 25.26/25.35 => 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)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_fold__image__1,axiom,
% 25.26/25.35 ! [V_f_2,V_S_2,T_b,T_c] :
% 25.26/25.35 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.26/25.35 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card_Oneutral,axiom,
% 25.26/25.35 ! [V_A_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.35 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.35 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_fold__image__cong,axiom,
% 25.26/25.35 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.35 ( class_Groups_Oab__semigroup__mult(T_c)
% 25.26/25.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.35 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_expand__Suc,axiom,
% 25.26/25.35 ! [V_v] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card__Pow,axiom,
% 25.26/25.35 ! [V_A_2,T_b] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.35 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__number__of,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.35 & class_Int_Oring__char__0(T_b) )
% 25.26/25.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 25.26/25.35 <=> V_x_2 = V_y_2 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__reorient,axiom,
% 25.26/25.35 ! [V_x_2,V_w_2,T_b] :
% 25.26/25.35 ( class_Int_Onumber(T_b)
% 25.26/25.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 25.26/25.35 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__number__of,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.35 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__number__of,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.35 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 25.26/25.35 ! [V_q,V_y,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__add,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__number__of__eq,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__number__of__left,axiom,
% 25.26/25.35 ! [V_z,V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__mult,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_arith__simps_I32_J,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__number__of__left,axiom,
% 25.26/25.35 ! [V_z,V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__number__of__eq,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__diff,axiom,
% 25.26/25.35 ! [V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__minus,axiom,
% 25.26/25.35 ! [V_w,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_arith__simps_I30_J,axiom,
% 25.26/25.35 ! [V_w,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 25.26/25.35 ! [V_q,V_p,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 25.26/25.35 ! [V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__number__of__eq__not__less,axiom,
% 25.26/25.35 ! [V_w_2,V_v_2,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber(T_b)
% 25.26/25.35 & class_Orderings_Olinorder(T_b) )
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ~ 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_left__distrib__number__of,axiom,
% 25.26/25.35 ! [V_v,V_b,V_a,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber(T_b)
% 25.26/25.35 & class_Rings_Osemiring(T_b) )
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_right__distrib__number__of,axiom,
% 25.26/25.35 ! [V_c,V_b,V_v,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber(T_b)
% 25.26/25.35 & class_Rings_Osemiring(T_b) )
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 25.26/25.35 ! [V_q,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 25.26/25.35 ! [V_q,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 25.26/25.35 ! [V_q,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__number__of__diff1,axiom,
% 25.26/25.35 ! [V_c,V_w,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add__number__of__diff2,axiom,
% 25.26/25.35 ! [V_w,V_c,V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_right__diff__distrib__number__of,axiom,
% 25.26/25.35 ! [V_c,V_b,V_v,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber(T_b)
% 25.26/25.35 & class_Rings_Oring(T_b) )
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_left__diff__distrib__number__of,axiom,
% 25.26/25.35 ! [V_v,V_b,V_a,T_b] :
% 25.26/25.35 ( ( class_Int_Onumber(T_b)
% 25.26/25.35 & class_Rings_Oring(T_b) )
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 25.26/25.35 ! [V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 25.26/25.35 ! [V_q,V_p,V_x,T_a] :
% 25.26/25.35 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus__number__of__mult,axiom,
% 25.26/25.35 ! [V_z,V_w,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Ints__power,axiom,
% 25.26/25.35 ! [V_n_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Rings_Oring__1(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Ints__number__of,axiom,
% 25.26/25.35 ! [V_w_2,T_b] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_b)
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__divide__eq__number__of1,axiom,
% 25.26/25.35 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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))
% 25.26/25.35 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => 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 )
% 25.26/25.35 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__divide__eq__number__of,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)
% 25.26/25.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) = V_b_2 )
% 25.26/25.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__eq__eq__number__of,axiom,
% 25.26/25.35 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 25.26/25.35 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2) )
% 25.26/25.35 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__eq__eq__number__of1,axiom,
% 25.26/25.35 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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
% 25.26/25.35 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__divide__eq__number__of1,axiom,
% 25.26/25.35 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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))))
% 25.26/25.35 <=> ( ( 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)))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => ( ( 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)))
% 25.26/25.35 => 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)))) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__divide__eq__number__of,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => 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))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__less__eq__number__of,axiom,
% 25.26/25.35 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => 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))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__less__eq__number__of1,axiom,
% 25.26/25.35 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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))
% 25.26/25.35 <=> ( ( 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)))
% 25.26/25.35 => 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)))) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => ( ( 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)))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__eq__if,axiom,
% 25.26/25.35 ! [V_p,V_m] :
% 25.26/25.35 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 25.26/25.35 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => 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)))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__le__eq__number__of1,axiom,
% 25.26/25.35 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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))
% 25.26/25.35 <=> ( ( 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)))
% 25.26/25.35 => 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)))) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => ( ( 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)))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__le__eq__number__of,axiom,
% 25.26/25.35 ! [V_w_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => 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))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__divide__eq__number__of,axiom,
% 25.26/25.35 ! [V_ca_2,V_b_2,V_w_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_ca_2)))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2)),V_b_2)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_ca_2))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_ca_2))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_ca_2),c_Groups_Ozero__class_Ozero(T_b)))
% 25.26/25.35 => 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))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__divide__eq__number__of1,axiom,
% 25.26/25.35 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 25.26/25.35 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.35 & class_Int_Onumber(T_b) )
% 25.26/25.35 => ( 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))))
% 25.26/25.35 <=> ( ( 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)))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => ( ( 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)))
% 25.26/25.35 => 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)))) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__strict__mono,axiom,
% 25.26/25.35 ! [V_n,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__diff,axiom,
% 25.26/25.35 ! [V_m,V_n,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_one__less__power,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__le__imp__le__exp,axiom,
% 25.26/25.35 ! [V_n,V_m,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__increasing__iff,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__decreasing,axiom,
% 25.26/25.35 ! [V_a,V_N,V_n,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus__numeral__code_I6_J,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_plus__numeral__code_I9_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__number__of__int__code,axiom,
% 25.26/25.35 ! [V_l_2,V_k_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_times__numeral__code_I5_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus__numeral__code_I5_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__eq__number__of__int__code,axiom,
% 25.26/25.35 ! [V_l_2,V_k_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__1,axiom,
% 25.26/25.35 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__1__right,axiom,
% 25.26/25.35 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__add1__eq__le,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( 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))))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_add1__zle__eq,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( 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))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__imp__add1__zle,axiom,
% 25.26/25.35 ! [V_z,V_w] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__add1__eq,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( 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))))
% 25.26/25.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 25.26/25.35 | V_w_2 = V_z_2 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__left__mono,axiom,
% 25.26/25.35 ! [V_k,V_j,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__zless__mono,axiom,
% 25.26/25.35 ! [V_z,V_z_H,V_w,V_w_H] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__le,axiom,
% 25.26/25.35 ! [V_w_2,V_z_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 25.26/25.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 25.26/25.35 & V_z_2 != V_w_2 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__refl,axiom,
% 25.26/25.35 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__linear,axiom,
% 25.26/25.35 ! [V_w,V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 25.26/25.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__trans,axiom,
% 25.26/25.35 ! [V_k,V_j,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__antisym,axiom,
% 25.26/25.35 ! [V_w,V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 25.26/25.35 => V_z = V_w ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zminus__zminus,axiom,
% 25.26/25.35 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__zminus,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__commute,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__assoc,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__linear,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 25.26/25.35 | V_x = V_y
% 25.26/25.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__strict__right__mono,axiom,
% 25.26/25.35 ! [V_k,V_j,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__commute,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__left__commute,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__assoc,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__zmult__distrib,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__zmult__distrib2,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zminus__zadd__distrib,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__int__def__symmetric,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__int__def,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__zmult__distrib2,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__zmult__distrib,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_equal__int__def,axiom,
% 25.26/25.35 ! [V_l_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2))
% 25.26/25.35 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zminus__0,axiom,
% 25.26/25.35 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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__zless__mono2,axiom,
% 25.26/25.35 ! [V_k,V_j,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__bin__lemma,axiom,
% 25.26/25.35 ! [V_l_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 25.26/25.35 <=> 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__0,axiom,
% 25.26/25.35 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__0__right,axiom,
% 25.26/25.35 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__zminus__inverse2,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_odd__nonzero,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_odd__less__0,axiom,
% 25.26/25.35 ! [V_z_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__imp__0__less,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__one__le__iff__zero__less,axiom,
% 25.26/25.35 ! [V_z_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__diff1__eq,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( 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))))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__0__less__1,axiom,
% 25.26/25.35 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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__zmult__eq__1__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 25.26/25.35 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zsgn__def,axiom,
% 25.26/25.35 ! [V_i] :
% 25.26/25.35 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.35 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 25.26/25.35 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 25.26/25.35 => 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)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zpower__zadd__distrib,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zpower__zpower,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_field__power__not__zero,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 25.26/25.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__mult__distrib,axiom,
% 25.26/25.35 ! [V_n,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Groups_Ocomm__monoid__mult(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__commutes,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__one,axiom,
% 25.26/25.35 ! [V_n,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__mult,axiom,
% 25.26/25.35 ! [V_n,V_m,V_a,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__divide,axiom,
% 25.26/25.35 ! [V_n,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__one__right,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__le__power,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__mono,axiom,
% 25.26/25.35 ! [V_n,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__less__power,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__eq__0__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_a_2,T_b] :
% 25.26/25.35 ( ( class_Power_Opower(T_b)
% 25.26/25.35 & class_Rings_Omult__zero(T_b)
% 25.26/25.35 & class_Rings_Ono__zero__divisors(T_b)
% 25.26/25.35 & class_Rings_Ozero__neq__one(T_b) )
% 25.26/25.35 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.35 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_one__le__power,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__0__Suc,axiom,
% 25.26/25.35 ! [V_n,T_a] :
% 25.26/25.35 ( ( class_Power_Opower(T_a)
% 25.26/25.35 & class_Rings_Osemiring__0(T_a) )
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__inject__exp,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 25.26/25.35 => ( 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)
% 25.26/25.35 <=> V_m_2 = V_n_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__Suc2,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__Suc,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Power_Opower(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__0,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Power_Opower(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__add,axiom,
% 25.26/25.35 ! [V_n,V_m,V_a,T_a] :
% 25.26/25.35 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nonzero__power__divide,axiom,
% 25.26/25.35 ! [V_n,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Fields_Ofield(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__one__over,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__Suc__0,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 25.26/25.35 ! [V_m_2,V_x_2] :
% 25.26/25.35 ( 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))
% 25.26/25.35 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__power__less__imp__less,axiom,
% 25.26/25.35 ! [V_n,V_m,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__zero__less__power__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_x_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 25.26/25.35 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__less__imp__less__base,axiom,
% 25.26/25.35 ! [V_b,V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__le__imp__le__base,axiom,
% 25.26/25.35 ! [V_b,V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( 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))))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__inject__base,axiom,
% 25.26/25.35 ! [V_b,V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( 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))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.35 => V_a = V_b ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__less__power__Suc,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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)))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__gt1__lemma,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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)))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__0__left,axiom,
% 25.26/25.35 ! [V_n,T_a] :
% 25.26/25.35 ( ( class_Power_Opower(T_a)
% 25.26/25.35 & class_Rings_Osemiring__0(T_a) )
% 25.26/25.35 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__gt1,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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)))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__strict__increasing__iff,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__less__imp__less__exp,axiom,
% 25.26/25.35 ! [V_n,V_m,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__strict__increasing,axiom,
% 25.26/25.35 ! [V_a,V_N,V_n,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__increasing,axiom,
% 25.26/25.35 ! [V_a,V_N,V_n,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__minus,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Oring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__one__le__power,axiom,
% 25.26/25.35 ! [V_n,V_i] :
% 25.26/25.35 ( 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))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__Suc__less,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__eq__imp__eq__base,axiom,
% 25.26/25.35 ! [V_b,V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( 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)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => V_a = V_b ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__Suc__less__one,axiom,
% 25.26/25.35 ! [V_n,V_a,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__strict__decreasing,axiom,
% 25.26/25.35 ! [V_a,V_N,V_n,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_self__quotient__aux1,axiom,
% 25.26/25.35 ! [V_q,V_r,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( 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))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_self__quotient__aux2,axiom,
% 25.26/25.35 ! [V_q,V_r,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( 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))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_q__pos__lemma,axiom,
% 25.26/25.35 ! [V_r_H,V_q_H,V_b_H] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_q__neg__lemma,axiom,
% 25.26/25.35 ! [V_r_H,V_q_H,V_b_H] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_unique__quotient__lemma,axiom,
% 25.26/25.35 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono2__lemma,axiom,
% 25.26/25.35 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__atLeastAtMost__int,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__atLeastLessThan__int,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__greaterThanAtMost__int,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__greaterThanLessThan__int,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__is__id,axiom,
% 25.26/25.35 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__number__of__int__code,axiom,
% 25.26/25.35 ! [V_l_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__0__neq__1,axiom,
% 25.26/25.35 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__int__refl,axiom,
% 25.26/25.35 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 25.26/25.35 ! [V_u_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 25.26/25.35 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_unique__quotient__lemma__neg,axiom,
% 25.26/25.35 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_simp__from__to,axiom,
% 25.26/25.35 ! [V_i_2,V_j_2] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 25.26/25.35 ! [V_n,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 25.26/25.35 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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power__power__power,axiom,
% 25.26/25.35 ! [T_b] :
% 25.26/25.35 ( class_Power_Opower(T_b)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_infinite__UNIV__int,axiom,
% 25.26/25.35 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power_Opower_Opower__0,axiom,
% 25.26/25.35 ! [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 ).
% 25.26/25.35
% 25.26/25.35 fof(fact_power_Opower_Opower__Suc,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 25.26/25.35 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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I6_J,axiom,
% 25.26/25.35 ! [V_A_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I8_J,axiom,
% 25.26/25.35 ! [V_B_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I6_J,axiom,
% 25.26/25.35 ! [V_t_2,V_B_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I8_J,axiom,
% 25.26/25.35 ! [V_t_2,V_A_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_periodic__finite__ex,axiom,
% 25.26/25.35 ! [V_Pa_2,V_d_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 25.26/25.35 => ( ! [B_x,B_k] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.35 <=> hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),B_k),V_d_2)))) )
% 25.26/25.35 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.26/25.35 <=> ? [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2)))
% 25.26/25.35 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I4_J,axiom,
% 25.26/25.35 ! [V_A_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( B_x != V_t_2
% 25.26/25.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I3_J,axiom,
% 25.26/25.35 ! [V_B_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_B_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 25.26/25.35 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 25.26/25.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I3_J,axiom,
% 25.26/25.35 ! [V_A_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_A_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 25.26/25.35 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 25.26/25.35 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I5_J,axiom,
% 25.26/25.35 ! [V_A_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I7_J,axiom,
% 25.26/25.35 ! [V_B_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I4_J,axiom,
% 25.26/25.35 ! [V_B_2,V_t_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( B_x != V_t_2
% 25.26/25.35 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_aset_I7_J,axiom,
% 25.26/25.35 ! [V_t_2,V_A_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bset_I5_J,axiom,
% 25.26/25.35 ! [V_t_2,V_B_2,V_D_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( ! [B_xa] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
% 25.26/25.35 => ! [B_xb] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 25.26/25.35 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_tsub__def,axiom,
% 25.26/25.35 ! [V_x,V_y] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 25.26/25.35 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 25.26/25.35 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__power__div__base,axiom,
% 25.26/25.35 ! [V_k,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 25.26/25.35 => 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)))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_decr__mult__lemma,axiom,
% 25.26/25.35 ! [V_k_2,V_Pa_2,V_d_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_incr__mult__lemma,axiom,
% 25.26/25.35 ! [V_k_2,V_Pa_2,V_d_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 25.26/25.35 => ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__number__of__lemma,axiom,
% 25.26/25.35 ! [V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => ( ( 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)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ 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)))
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negative__zle,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negative__zless,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__eq__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2,T_b] :
% 25.26/25.35 ( class_Nat_Osemiring__char__0(T_b)
% 25.26/25.35 => ( 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)
% 25.26/25.35 <=> V_m_2 = V_n_2 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zero,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zminus__zminus,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zminus2,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__0,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__by__0,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__by__1,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 25.26/25.35 ! [V_A_2,V_x_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 25.26/25.35 <=> 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.35 <=> 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__neg__pos__less0,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__self,axiom,
% 25.26/25.35 ! [V_a] :
% 25.26/25.35 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__0,axiom,
% 25.26/25.35 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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__eq__0__conv,axiom,
% 25.26/25.35 ! [V_n_2] :
% 25.26/25.35 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 25.26/25.35 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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__zle__int,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 25.26/25.35 ! [V_Pa_2] :
% 25.26/25.35 ( ? [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.35 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.26/25.35 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 25.26/25.35 ! [V_Pa_2] :
% 25.26/25.35 ( ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.26/25.35 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__less__0__conv,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__int,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__int,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zadd__int__left,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zle__iff__zadd,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 25.26/25.35 <=> ? [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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__le__imp__of__nat,axiom,
% 25.26/25.35 ! [V_m,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__0__le__iff,axiom,
% 25.26/25.35 ! [V_n,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negative__eq__positive,axiom,
% 25.26/25.35 ! [V_m_2,V_n_2] :
% 25.26/25.35 ( 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)
% 25.26/25.35 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__less__0__iff,axiom,
% 25.26/25.35 ! [V_m,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ~ 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__int__zless__negative,axiom,
% 25.26/25.35 ! [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)))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__mult,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__0,axiom,
% 25.26/25.35 ! [T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__less__imp__less,axiom,
% 25.26/25.35 ! [V_n,V_m,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_less__imp__of__nat__less,axiom,
% 25.26/25.35 ! [V_n,V_m,T_a] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__less__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__1,axiom,
% 25.26/25.35 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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 25.26/25.35 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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__le__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__add,axiom,
% 25.26/25.35 ! [V_n,V_m,T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__mult,axiom,
% 25.26/25.35 ! [V_n,V_m,T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__mult1__if,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self2__is__id,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self1__is__id,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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 ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__mult2,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__mult1,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__self,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__1,axiom,
% 25.26/25.35 ! [T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Ints__of__nat,axiom,
% 25.26/25.35 ! [V_n_2,T_b] :
% 25.26/25.35 ( class_Rings_Oring__1(T_b)
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__power,axiom,
% 25.26/25.35 ! [V_n,V_m,T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__power,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zpower__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 25.26/25.35 ! [V_A_2] :
% 25.26/25.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 25.26/25.35 <=> 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 25.26/25.35 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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__eq__0__iff,axiom,
% 25.26/25.35 ! [V_k_2,V_i_2] :
% 25.26/25.35 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 25.26/25.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 25.26/25.35 ! [V_i_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 25.26/25.35 ! [V_b_2,V_a_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono2,axiom,
% 25.26/25.35 ! [V_b,V_b_H,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__nonneg__neg__le0,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__pos__pos__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 25.26/25.35 ! [V_a_2,V_b_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__nonpos__pos__le0,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono2__neg,axiom,
% 25.26/25.35 ! [V_b,V_b_H,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__neg__neg__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono1,axiom,
% 25.26/25.35 ! [V_b,V_a_H,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__mono1__neg,axiom,
% 25.26/25.35 ! [V_b,V_a_H,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__div__less__self,axiom,
% 25.26/25.35 ! [V_k,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zmult2__eq,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__le__0__conv,axiom,
% 25.26/25.35 ! [V_n_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__Suc0__eq__1,axiom,
% 25.26/25.35 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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__iff__Suc__zadd,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 25.26/25.35 <=> ? [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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__zle__neg,axiom,
% 25.26/25.35 ! [V_m_2,V_n_2] :
% 25.26/25.35 ( 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))))
% 25.26/25.35 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__Suc,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negative__zle__0,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__int,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__Suc,axiom,
% 25.26/25.35 ! [V_m,T_a] :
% 25.26/25.35 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__diff,axiom,
% 25.26/25.35 ! [V_m,V_n,T_a] :
% 25.26/25.35 ( class_Rings_Oring__1(T_a)
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self2,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self1,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__add__self1,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__add__self2,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__less__int__conv,axiom,
% 25.26/25.35 ! [V_n_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__zless__mono2__lemma,axiom,
% 25.26/25.35 ! [V_k,V_j,V_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__zle__0__negative,axiom,
% 25.26/25.35 ! [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))))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negative__zless__0,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__0__less__iff,axiom,
% 25.26/25.35 ! [V_n_2,T_b] :
% 25.26/25.35 ( class_Rings_Olinordered__semidom(T_b)
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divmod__int__rel__div__eq,axiom,
% 25.26/25.35 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 25.26/25.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__zdiv,axiom,
% 25.26/25.35 ! [V_k_2,V_n_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 25.26/25.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ! [B_i] :
% 25.26/25.35 ( ? [B_j] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ! [B_i] :
% 25.26/25.35 ( ? [B_j] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__int__split,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2))))
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_tsub__eq,axiom,
% 25.26/25.35 ! [V_x,V_y] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 25.26/25.35 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_z3div__def,axiom,
% 25.26/25.35 ! [V_k,V_l] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.35 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_setsum__bounded,axiom,
% 25.26/25.35 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.35 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 25.26/25.35 & class_Rings_Osemiring__1(T_c) )
% 25.26/25.35 => ( ! [B_i] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 25.26/25.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__pos__neg__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__neg__lemma,axiom,
% 25.26/25.35 ! [V_n_2,V_Pa_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 25.26/25.35 <=> ! [B_i,B_j] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__pos__lemma,axiom,
% 25.26/25.35 ! [V_n_2,V_Pa_2,V_k_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 25.26/25.35 <=> ! [B_i,B_j] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_of__nat__number__of__eq,axiom,
% 25.26/25.35 ! [V_v,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2] :
% 25.26/25.35 ( V_A_2 = V_B_2
% 25.26/25.35 <=> 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( 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)
% 25.26/25.35 <=> V_x_2 = V_y_2 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 25.26/25.35 ! [V_B_2,V_A_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.35 <=> 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__int__eq,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2] :
% 25.26/25.35 ( 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)
% 25.26/25.35 <=> V_m_2 = V_n_2 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__neg__int,axiom,
% 25.26/25.35 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__0,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__by__0,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__self,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__number__of__Min,axiom,
% 25.26/25.35 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__minus1__right,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mod__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__self2,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__self1,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__right__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__left__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__simps_I2_J,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__simps_I1_J,axiom,
% 25.26/25.35 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__add__cong,axiom,
% 25.26/25.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__right__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__left__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__mult1,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__mult2,axiom,
% 25.26/25.35 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__simps_I4_J,axiom,
% 25.26/25.35 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__cong,axiom,
% 25.26/25.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__diff__cong,axiom,
% 25.26/25.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 25.26/25.35 => 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) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__diff__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__diff__left__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__diff__right__eq,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__minus__cong,axiom,
% 25.26/25.35 ! [V_a_H,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__minus__eq,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Oring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__le__dividend,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__le__mono,axiom,
% 25.26/25.35 ! [V_k,V_n,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult2__eq,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__self,axiom,
% 25.26/25.35 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zero,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_rel__simps_I24_J,axiom,
% 25.26/25.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_rel__simps_I7_J,axiom,
% 25.26/25.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zmult1__eq,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__simps_I3_J,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__zmod__right,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiff__zmod__left,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus2,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus__zminus,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zminus__zmod,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zpower__zmod,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__int__code_I6_J,axiom,
% 25.26/25.35 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__neg__0,axiom,
% 25.26/25.35 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__neg__1,axiom,
% 25.26/25.35 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self1__is__0,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self2__is__0,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self2,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self1,axiom,
% 25.26/25.35 ! [V_b,V_c,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__by__1,axiom,
% 25.26/25.35 ! [V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__div__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__1,axiom,
% 25.26/25.35 ! [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 ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__less,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__mult__div__cancel__disj,axiom,
% 25.26/25.35 ! [V_n,V_m,V_k] :
% 25.26/25.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__le__nonneg__dividend,axiom,
% 25.26/25.35 ! [V_k,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__mod__bound,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__mod__bound,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__eq__0__iff,axiom,
% 25.26/25.35 ! [V_d_2,V_m_2] :
% 25.26/25.35 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_bin__less__0__simps_I2_J,axiom,
% 25.26/25.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus2__not__zero,axiom,
% 25.26/25.35 ! [V_l,V_k] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus1__not__zero,axiom,
% 25.26/25.35 ! [V_l,V_k] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_DIVISION__BY__ZERO,axiom,
% 25.26/25.35 ! [V_a] :
% 25.26/25.35 ( 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)
% 25.26/25.35 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zdiv__trivial,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zadd1__eq,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Int_OMin__def,axiom,
% 25.26/25.35 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__Min,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__minus1,axiom,
% 25.26/25.35 ! [V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__neg__eq__ge__0,axiom,
% 25.26/25.35 ! [V_x_2] :
% 25.26/25.35 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__def,axiom,
% 25.26/25.35 ! [V_Z_2] :
% 25.26/25.35 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__zminus__int,axiom,
% 25.26/25.35 ! [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))))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mod__equality,axiom,
% 25.26/25.35 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mod__equality2,axiom,
% 25.26/25.35 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__div__equality,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__div__equality2,axiom,
% 25.26/25.35 ! [V_a,V_b,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 25.26/25.35 ! [V_b,V_a,T_a] :
% 25.26/25.35 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.35 => 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 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__le__mono2,axiom,
% 25.26/25.35 ! [V_k,V_n,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__mult__div__cancel1,axiom,
% 25.26/25.35 ! [V_n,V_m,V_k] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self1__is__m,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult__self__is__m,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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 ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__less__dividend,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__minus1__right,axiom,
% 25.26/25.35 ! [V_z,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__minus1,axiom,
% 25.26/25.35 ! [V_z,T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__neg__neg__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__mod__conj,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 & 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__mod__sign,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__pos__pos__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__mod__conj,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 & 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__mod__sign,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_number__of__Min,axiom,
% 25.26/25.35 ! [T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_arith__simps_I31_J,axiom,
% 25.26/25.35 ! [T_a] :
% 25.26/25.35 ( class_Int_Onumber__ring(T_a)
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divide__minus1,axiom,
% 25.26/25.35 ! [V_x,T_a] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 & class_Int_Onumber__ring(T_a) )
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus2__eq__if,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zminus1__eq__if,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zdiv__equality,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zmult1__eq,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zmod__equality,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zmod__equality2,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__eq__1__iff,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2] :
% 25.26/25.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 25.26/25.35 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 25.26/25.35 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 25.26/25.35 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult__div__cancel,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zdiv__equality_H,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__minus1__right,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__imp__number__of__eq__0,axiom,
% 25.26/25.35 ! [V_v] :
% 25.26/25.35 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__nat__number__of,axiom,
% 25.26/25.35 ! [V_v] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__geq,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__if,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__div,axiom,
% 25.26/25.35 ! [V_k_2,V_n_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 25.26/25.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 25.26/25.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => ! [B_i,B_j] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 25.26/25.35 => ( 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)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__pos__neg__trivial,axiom,
% 25.26/25.35 ! [V_b,V_a] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_minus1__divide,axiom,
% 25.26/25.35 ! [V_x,T_a] :
% 25.26/25.35 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.35 & class_Int_Onumber__ring(T_a) )
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__eq__minus1,axiom,
% 25.26/25.35 ! [V_b] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__div__geq,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__div__lemma,axiom,
% 25.26/25.35 ! [V_m_2,V_q_2,V_n_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 25.26/25.35 => ( ( 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))
% 25.26/25.35 & 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)))) )
% 25.26/25.35 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__div_H,axiom,
% 25.26/25.35 ! [V_n_2,V_m_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 25.26/25.35 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 25.26/25.35 | ? [B_q] :
% 25.26/25.35 ( 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))
% 25.26/25.35 & 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))))
% 25.26/25.35 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__nat__number__of,axiom,
% 25.26/25.35 ! [V_v_H_2,V_v_2] :
% 25.26/25.35 ( 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)
% 25.26/25.35 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 25.26/25.35 => 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))) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 25.26/25.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 25.26/25.35 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 25.26/25.35 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__number__of__add__left,axiom,
% 25.26/25.35 ! [V_k,V_v_H,V_v] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__zmod,axiom,
% 25.26/25.35 ! [V_k_2,V_n_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 25.26/25.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 25.26/25.35 => ! [B_i,B_j] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ! [B_i,B_j] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 & 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) )
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult2__lemma__aux3,axiom,
% 25.26/25.35 ! [V_q,V_b,V_r,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult2__lemma__aux4,axiom,
% 25.26/25.35 ! [V_q,V_b,V_r,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult2__lemma__aux1,axiom,
% 25.26/25.35 ! [V_q,V_r,V_b,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmult2__lemma__aux2,axiom,
% 25.26/25.35 ! [V_q,V_r,V_b,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => 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))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_divmod__int__rel__mod__eq,axiom,
% 25.26/25.35 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 25.26/25.35 ( 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)
% 25.26/25.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 25.26/25.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__zmult2__eq,axiom,
% 25.26/25.35 ! [V_b,V_a,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zminus2__eq__if,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zdiv__zminus1__eq__if,axiom,
% 25.26/25.35 ! [V_a,V_b] :
% 25.26/25.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.35 => 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)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_z3mod__def,axiom,
% 25.26/25.35 ! [V_k,V_l] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.35 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Suc__nat__number__of__add,axiom,
% 25.26/25.35 ! [V_n,V_v] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Suc__nat__number__of,axiom,
% 25.26/25.35 ! [V_v] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 25.26/25.35 ! [V_u_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 25.26/25.35 => 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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_negD,axiom,
% 25.26/25.35 ! [V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => ? [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))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__less,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__add1__eq,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__less__eq__dividend,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__distrib,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__distrib2,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__int,axiom,
% 25.26/25.35 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__mod__distrib,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__0,axiom,
% 25.26/25.35 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 25.26/25.35 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__Suc,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.35 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__1,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__less__divisor,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_eq__nat__nat__iff,axiom,
% 25.26/25.35 ! [V_z_H_2,V_z_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 25.26/25.35 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 25.26/25.35 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_ex__nat,axiom,
% 25.26/25.35 ! [V_Pa_2] :
% 25.26/25.35 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.26/25.35 <=> ? [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.35 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_all__nat,axiom,
% 25.26/25.35 ! [V_Pa_2] :
% 25.26/25.35 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.26/25.35 <=> ! [B_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 25.26/25.35 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 25.26/25.35 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__eq__0__iff,axiom,
% 25.26/25.35 ! [V_d_2,V_m_2] :
% 25.26/25.35 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__geq,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__if,axiom,
% 25.26/25.35 ! [V_n,V_m] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self3,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult2__eq,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mult1__eq,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_le__mod__geq,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.35 => 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) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__number__of__def,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__number__of,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_div__mod__equality_H,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mult__div__cancel,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Omod__div__equality_H,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 25.26/25.35 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zmod__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_neg__nat,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 25.26/25.35 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_not__neg__nat,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 25.26/25.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 25.26/25.35 ! [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 ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__nat__number__of,axiom,
% 25.26/25.35 ! [V_v_H,V_v] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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))) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 25.26/25.35 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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__le__0,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__0__iff,axiom,
% 25.26/25.35 ! [V_i_2] :
% 25.26/25.35 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__mono__iff,axiom,
% 25.26/25.35 ! [V_w_2,V_z_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__nat__conj,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__le__divisor,axiom,
% 25.26/25.35 ! [V_m,V_n] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__1,axiom,
% 25.26/25.35 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__mult__self4,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__nat__eq,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => 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) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__eq__iff,axiom,
% 25.26/25.35 ! [V_z_2,V_m_2] :
% 25.26/25.35 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 25.26/25.35 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 25.26/25.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__0__le,axiom,
% 25.26/25.35 ! [V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zless__nat__eq__int__zless,axiom,
% 25.26/25.35 ! [V_z_2,V_m_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 25.26/25.35 <=> 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__div__distrib,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__zminus__int,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_one__mod__nat__number__of,axiom,
% 25.26/25.35 ! [V_v_H] :
% 25.26/25.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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)) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_succ__def,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_diff__bin__simps_I2_J,axiom,
% 25.26/25.35 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 25.26/25.35 ! [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) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_card__atLeastLessThan__int,axiom,
% 25.26/25.35 ! [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)) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_zero__less__nat__eq,axiom,
% 25.26/25.35 ! [V_z_2] :
% 25.26/25.35 ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__less__eq__zless,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 25.26/25.35 ! [V_y_2,V_x_2] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__eq__iff,axiom,
% 25.26/25.35 ! [V_m_2,V_w_2] :
% 25.26/25.35 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__eq__iff2,axiom,
% 25.26/25.35 ! [V_w_2,V_m_2] :
% 25.26/25.35 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 25.26/25.35 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 25.26/25.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__le__eq__zle,axiom,
% 25.26/25.35 ! [V_z_2,V_w_2] :
% 25.26/25.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 25.26/25.35 => ( 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)))
% 25.26/25.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__nat,axiom,
% 25.26/25.35 ! [V_i_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 25.26/25.35 <=> ( ! [B_n] :
% 25.26/25.35 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 25.26/25.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_split__mod,axiom,
% 25.26/25.35 ! [V_k_2,V_n_2,V_Pa_2] :
% 25.26/25.35 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 25.26/25.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,V_n_2)) )
% 25.26/25.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.35 => ! [B_i,B_j] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 25.26/25.35 => ( 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)
% 25.26/25.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_mod__lemma,axiom,
% 25.26/25.35 ! [V_q,V_b,V_r,V_c] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 25.26/25.35 => 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__add__distrib,axiom,
% 25.26/25.35 ! [V_z_H,V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_int__eq__iff__number__of,axiom,
% 25.26/25.35 ! [V_v_2,V_m_2] :
% 25.26/25.35 ( 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)
% 25.26/25.35 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 25.26/25.35 & 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))) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__mult__distrib,axiom,
% 25.26/25.35 ! [V_z_H,V_z] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.35 => 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)) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 25.26/25.35 ! [V_y,V_x] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 25.26/25.35 ! [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))) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_nat__diff__distrib,axiom,
% 25.26/25.35 ! [V_z,V_z_H] :
% 25.26/25.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 25.26/25.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 25.26/25.35 => 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)) ) ) ).
% 25.26/25.35
% 25.26/25.35 fof(fact_Suc__times__mod__eq,axiom,
% 25.26/25.35 ! [V_m,V_k] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_card__greaterThanAtMost__int,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 25.26/25.36 ! [V_n,V_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__power__eq,axiom,
% 25.26/25.36 ! [V_n,V_z] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__less__nat__eq,axiom,
% 25.26/25.36 ! [V_z_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__less__iff,axiom,
% 25.26/25.36 ! [V_m_2,V_w_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 25.26/25.36 <=> 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 25.26/25.36 ! [V_z] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__succ,axiom,
% 25.26/25.36 ! [V_k,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__mult__distrib__neg,axiom,
% 25.26/25.36 ! [V_z_H,V_z] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_div__nat__number__of,axiom,
% 25.26/25.36 ! [V_v_H,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_card__atLeastAtMost__int,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__div__nat__number__of,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_card__greaterThanLessThan__int,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__nat__number__of__number__of,axiom,
% 25.26/25.36 ! [V_w,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__nat__number__of,axiom,
% 25.26/25.36 ! [V_n,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__aux__def,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__morphism__nat__int,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 25.26/25.36 ! [V_n_2,V_m_2] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__of__nat,axiom,
% 25.26/25.36 ! [V_k,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => 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)))) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 25.26/25.36 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__eq__iff,axiom,
% 25.26/25.36 ! [V_z_2,V_w_2,T_b] :
% 25.26/25.36 ( class_Int_Oring__char__0(T_b)
% 25.26/25.36 => ( 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)
% 25.26/25.36 <=> V_w_2 = V_z_2 ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__eq,axiom,
% 25.26/25.36 ! [V_k,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_int__number__of__def,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__int__eq,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => ( V_A_2 = V_B_2
% 25.26/25.36 <=> 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 25.26/25.36 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_y)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 25.26/25.36 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 25.26/25.36 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_y)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_y)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_y)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 25.26/25.36 ! [V_n,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 25.26/25.36 ! [V_y,V_x] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x)
% 25.26/25.36 => ( c_Nat__Transfer_Ois__nat(V_y)
% 25.26/25.36 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 25.26/25.36 ! [V_A_2,V_x_2] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 25.26/25.36 <=> 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__eq__0__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Int_Oring__char__0(T_b)
% 25.26/25.36 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__0__eq__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Int_Oring__char__0(T_b)
% 25.26/25.36 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 25.26/25.36 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__0,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 25.26/25.36 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__le__iff,axiom,
% 25.26/25.36 ! [V_z_2,V_w_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__less__iff,axiom,
% 25.26/25.36 ! [V_z_2,V_w_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__add,axiom,
% 25.26/25.36 ! [V_z,V_w,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__number__of__eq,axiom,
% 25.26/25.36 ! [V_v,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__mult,axiom,
% 25.26/25.36 ! [V_z,V_w,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__1,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__diff,axiom,
% 25.26/25.36 ! [V_z,V_w,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__of__nat__eq,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__minus,axiom,
% 25.26/25.36 ! [V_z,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Ints__of__int,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Oring__1(T_b)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__power,axiom,
% 25.26/25.36 ! [V_n,V_z,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__set__def,axiom,
% 25.26/25.36 ! [V_S_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_S_2)
% 25.26/25.36 <=> ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_is__nat__def,axiom,
% 25.26/25.36 ! [V_x_2] :
% 25.26/25.36 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__m1,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 25.26/25.36 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 25.26/25.36 ! [V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__0__le__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__le__0__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__0__less__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__int__less__0__iff,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__nat__nat,axiom,
% 25.26/25.36 ! [V_z,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 25.26/25.36 ! [V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 25.26/25.36 <=> 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 25.26/25.36 ! [V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.36 <=> 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2] :
% 25.26/25.36 ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.36 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.36 <=> 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__less__imp__eq__int,axiom,
% 25.26/25.36 ! [V_k] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 25.26/25.36 => ? [B_n] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 25.26/25.36 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_decr__lemma,axiom,
% 25.26/25.36 ! [V_z,V_x,V_d] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_incr__lemma,axiom,
% 25.26/25.36 ! [V_x,V_z,V_d] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__1__add__number__of,axiom,
% 25.26/25.36 ! [V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__number__of__add__1,axiom,
% 25.26/25.36 ! [V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Pls__def,axiom,
% 25.26/25.36 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I19_J,axiom,
% 25.26/25.36 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__ge__self,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__le__D1,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__add__abs,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__mult__self,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__mult,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__minus__commute,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__one,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__minus__cancel,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__idempotent,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__zero,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__eq__0,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__int__eq,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__divide,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__abs,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__of__nat,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I2_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Pls__right,axiom,
% 25.26/25.36 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Pls,axiom,
% 25.26/25.36 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__Pls,axiom,
% 25.26/25.36 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I1_J,axiom,
% 25.26/25.36 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Pls,axiom,
% 25.26/25.36 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I37_J,axiom,
% 25.26/25.36 c_Int_OPls != c_Int_OMin ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I40_J,axiom,
% 25.26/25.36 c_Int_OMin != c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I1_J,axiom,
% 25.26/25.36 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__ge__zero,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__le__zero__iff,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__of__nonneg,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__of__pos,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__less__abs__iff,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__not__less__zero,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ~ 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__triangle__ineq,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__mult__less,axiom,
% 25.26/25.36 ! [V_d,V_b,V_c,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__triangle__ineq3,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__triangle__ineq2,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__triangle__ineq2__sym,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__le__D2,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__leI,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__le__iff,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 25.26/25.36 & 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__ge__minus__self,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__less__iff,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nonzero__abs__divide,axiom,
% 25.26/25.36 ! [V_a,V_b,T_a] :
% 25.26/25.36 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.36 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__power__minus,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__zmult__eq__1,axiom,
% 25.26/25.36 ! [V_n,V_m] :
% 25.26/25.36 ( 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)
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__Pls,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_semiring__norm_I112_J,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__numeral__0,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__numeral__0__right,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__sgn,axiom,
% 25.26/25.36 ! [V_k,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__sgn__abs,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_bin__less__0__simps_I1_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_semiring__norm_I113_J,axiom,
% 25.26/25.36 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__number__of__Pls,axiom,
% 25.26/25.36 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__is__num__zero,axiom,
% 25.26/25.36 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I23_J,axiom,
% 25.26/25.36 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I20_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I3_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I6_J,axiom,
% 25.26/25.36 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__number__of__Pls__Min,axiom,
% 25.26/25.36 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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_not__neg__number__of__Pls,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I5_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I2_J,axiom,
% 25.26/25.36 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_succ__Min,axiom,
% 25.26/25.36 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__mult__pos,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__eq__mult,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Oordered__ring__abs(T_a)
% 25.26/25.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 25.26/25.36 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__triangle__ineq4,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__diff__triangle__ineq,axiom,
% 25.26/25.36 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__of__nonpos,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__minus__le__zero,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__of__neg,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__if,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Oabs__if(T_a)
% 25.26/25.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__le__power__abs,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__div__pos,axiom,
% 25.26/25.36 ! [V_x,V_y,T_a] :
% 25.26/25.36 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__minus__one,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_a) )
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zabs__less__one__iff,axiom,
% 25.26/25.36 ! [V_z_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zabs__def,axiom,
% 25.26/25.36 ! [V_i] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__abs__mult__distrib,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__le__zpower__abs,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_divide__Numeral0,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 25.26/25.36 & class_Int_Onumber__ring(T_a) )
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__number__of__0,axiom,
% 25.26/25.36 ! [V_v_2] :
% 25.26/25.36 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__0__number__of,axiom,
% 25.26/25.36 ! [V_v_2] :
% 25.26/25.36 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of2,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__nat__number__of,axiom,
% 25.26/25.36 ! [V_v_H_2,V_v_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__nat__number__of,axiom,
% 25.26/25.36 ! [V_v_H_2,V_v_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__number__of,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_a) )
% 25.26/25.36 => ( ( 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)))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( ~ 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)))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__power__minus__one,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_a) )
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__less__zpower__abs__iff,axiom,
% 25.26/25.36 ! [V_n_2,V_x_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.36 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__special_I1_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__special_I3_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__special_I1_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__special_I3_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__0__number__of,axiom,
% 25.26/25.36 ! [V_v_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__nat__number__of,axiom,
% 25.26/25.36 ! [V_v_H,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__number__of__mult__left,axiom,
% 25.26/25.36 ! [V_k,V_v_H,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__nat__number__of,axiom,
% 25.26/25.36 ! [V_v_H,V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__special_I3_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 <=> 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)))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__special_I1_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 25.26/25.36 <=> 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)))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__number__of__diff__1,axiom,
% 25.26/25.36 ! [V_v] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nats__number__of,axiom,
% 25.26/25.36 ! [V_w_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_succ__pred,axiom,
% 25.26/25.36 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 25.26/25.36
% 25.26/25.36 fof(fact_iszero__def,axiom,
% 25.26/25.36 ! [V_z_2,T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => ( c_Int_Oiszero(T_b,V_z_2)
% 25.26/25.36 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_iszero__0,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.36 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_not__iszero__1,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.36 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__iff__pred__less,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pred__Pls,axiom,
% 25.26/25.36 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pred__def,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Min__right,axiom,
% 25.26/25.36 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Min,axiom,
% 25.26/25.36 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_iszero__Numeral0,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nats__0,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nats__add,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nats__mult,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nonzero__number__of__Min,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nats__1,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__nat__in__Nats,axiom,
% 25.26/25.36 ! [V_n_2,T_b] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__pred,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_neg__number__of__pred__iff__0,axiom,
% 25.26/25.36 ! [V_v_2] :
% 25.26/25.36 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 25.26/25.36 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__number__of__eq,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 25.26/25.36 <=> 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)))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__diff__number__of,axiom,
% 25.26/25.36 ! [V_m,V_v] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__special_I4_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.36 <=> 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))))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__special_I2_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 25.26/25.36 <=> 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)))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__special_I2_J,axiom,
% 25.26/25.36 ! [V_v,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__special_I1_J,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Bit1__Min,axiom,
% 25.26/25.36 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I43_J,axiom,
% 25.26/25.36 ! [V_l_2] :
% 25.26/25.36 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 25.26/25.36 <=> c_Int_OMin = V_l_2 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I47_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 25.26/25.36 <=> V_k_2 = c_Int_OMin ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I51_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 25.26/25.36 <=> V_k_2 = V_l_2 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__int__code_I16_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I17_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I34_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__eq__int__code_I16_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I39_J,axiom,
% 25.26/25.36 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I46_J,axiom,
% 25.26/25.36 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I16_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_bin__less__0__simps_I4_J,axiom,
% 25.26/25.36 ! [V_w_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I22_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I12_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Bit1__def,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I26_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I30_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I13_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I9_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_neg__number__of__Bit1,axiom,
% 25.26/25.36 ! [V_w_2] :
% 25.26/25.36 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 25.26/25.36 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I4_J,axiom,
% 25.26/25.36 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I10_J,axiom,
% 25.26/25.36 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Bit1,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I8_J,axiom,
% 25.26/25.36 ! [V_k2_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I12_J,axiom,
% 25.26/25.36 ! [V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_iszero__number__of__Bit1,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 & class_Int_Oring__char__0(T_a) )
% 25.26/25.36 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_succ__Pls,axiom,
% 25.26/25.36 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__Bit1,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__numeral__1,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__numeral__1__right,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_semiring__norm_I110_J,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_numeral__1__eq__1,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I29_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I5_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_divide__Numeral1,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( ( class_Fields_Ofield(T_a)
% 25.26/25.36 & class_Int_Onumber__ring(T_a) )
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_divide__numeral__1,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( ( class_Fields_Ofield(T_a)
% 25.26/25.36 & class_Int_Onumber__ring(T_a) )
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__is__num__one,axiom,
% 25.26/25.36 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Numeral1__eq1__nat,axiom,
% 25.26/25.36 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__numeral__1__eq__1,axiom,
% 25.26/25.36 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I4_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Min,axiom,
% 25.26/25.36 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 25.26/25.36 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_not__iszero__Numeral1,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_numeral__1__eq__Suc__0,axiom,
% 25.26/25.36 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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_numeral__3__eq__3,axiom,
% 25.26/25.36 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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power3__eq__cube,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 25.26/25.36 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))))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc3__eq__add__3,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 25.26/25.36 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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 25.26/25.36 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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__special_I2_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__special_I4_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__special_I2_J,axiom,
% 25.26/25.36 ! [V_y_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__special_I4_J,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Rings_Olinordered__idom(T_b) )
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__special_I3_J,axiom,
% 25.26/25.36 ! [V_v,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__special_I2_J,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 25.26/25.36 ! [V_m,V_n] :
% 25.26/25.36 ( 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))
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__gcd_Osimps,axiom,
% 25.26/25.36 ! [V_x,V_y] :
% 25.26/25.36 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.36 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 25.26/25.36 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__div__eq__add3__div,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_div__Suc__eq__div__add3,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zmod__number__of__Bit1,axiom,
% 25.26/25.36 ! [V_v,V_w] :
% 25.26/25.36 ( ( 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)))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( ~ 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)))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_neg__zmod__mult__2,axiom,
% 25.26/25.36 ! [V_b,V_a] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pos__zdiv__mult__2,axiom,
% 25.26/25.36 ! [V_b,V_a] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I50_J,axiom,
% 25.26/25.36 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I49_J,axiom,
% 25.26/25.36 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I44_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 25.26/25.36 <=> V_k_2 = c_Int_OPls ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I38_J,axiom,
% 25.26/25.36 ! [V_l_2] :
% 25.26/25.36 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 25.26/25.36 <=> c_Int_OPls = V_l_2 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Bit0__Pls,axiom,
% 25.26/25.36 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__eq__int__code_I13_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I31_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I14_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__int__code_I13_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Bit0__Bit0,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Bit0__def,axiom,
% 25.26/25.36 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I48_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 25.26/25.36 <=> V_k_2 = V_l_2 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I45_J,axiom,
% 25.26/25.36 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I42_J,axiom,
% 25.26/25.36 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Bit0,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I7_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__Bit0,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I13_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_bin__less__0__simps_I3_J,axiom,
% 25.26/25.36 ! [V_w_2] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I21_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I27_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I32_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__eq__int__code_I14_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I10_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I4_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__int__code_I15_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I16_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Bit1__Bit0,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Bit0__Bit1,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I3_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I10_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I9_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I28_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I8_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zdiv__number__of__Bit0,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_neg__number__of__Bit0,axiom,
% 25.26/25.36 ! [V_w_2] :
% 25.26/25.36 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 25.26/25.36 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pred__Bit0,axiom,
% 25.26/25.36 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pred__Bit1,axiom,
% 25.26/25.36 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I9_J,axiom,
% 25.26/25.36 ! [V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I3_J,axiom,
% 25.26/25.36 ! [V_k2_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I15_J,axiom,
% 25.26/25.36 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I14_J,axiom,
% 25.26/25.36 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OBit1(V_k2))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pred__Min,axiom,
% 25.26/25.36 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I11_J,axiom,
% 25.26/25.36 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_eq__int__code_I7_J,axiom,
% 25.26/25.36 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_iszero__number__of__Bit0,axiom,
% 25.26/25.36 ! [V_w_2,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber__ring(T_b)
% 25.26/25.36 & class_Int_Oring__char__0(T_b) )
% 25.26/25.36 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 25.26/25.36 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_succ__Bit1,axiom,
% 25.26/25.36 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_succ__Bit0,axiom,
% 25.26/25.36 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of__Bit0,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I15_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__int__code_I14_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I33_J,axiom,
% 25.26/25.36 ! [V_l_2,V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__eq__int__code_I15_J,axiom,
% 25.26/25.36 ! [V_k2_2,V_k1_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_card__UNIV__bool,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__Bit1,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I25_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_rel__simps_I11_J,axiom,
% 25.26/25.36 ! [V_k_2] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I5_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I6_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_diff__bin__simps_I8_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__Bit1__Bit1,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_double__number__of__Bit0,axiom,
% 25.26/25.36 ! [V_w,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_number__of1,axiom,
% 25.26/25.36 ! [V_n] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 => ( 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))))
% 25.26/25.36 & 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)))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 25.26/25.36 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__2__right,axiom,
% 25.26/25.36 ! [V_z,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mult__2,axiom,
% 25.26/25.36 ! [V_z,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__add__one__is__two,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__power2,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__eq__power2,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 25.26/25.36 => ( 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)
% 25.26/25.36 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_semiring__norm_I115_J,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_numeral__2__eq__2,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__eq__square,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 25.26/25.36 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))))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__2__eq__Suc_H,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__2__eq__Suc,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__power2,axiom,
% 25.26/25.36 ! [T_a] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__minus,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__mult__2__right,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__mult__2,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__even__eq,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 25.26/25.36 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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 25.26/25.36 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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__abs,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_abs__power2,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__1__add__1,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mod2__Suc__Suc,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_div2__Suc__Suc,axiom,
% 25.26/25.36 ! [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))))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zmod__number__of__Bit0,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_add__self__div__2,axiom,
% 25.26/25.36 ! [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 ).
% 25.26/25.36
% 25.26/25.36 fof(fact_half__gt__zero,axiom,
% 25.26/25.36 ! [V_r,T_a] :
% 25.26/25.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 25.26/25.36 & class_Int_Onumber__ring(T_a) )
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 25.26/25.36 => 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)))))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_half__gt__zero__iff,axiom,
% 25.26/25.36 ! [V_r_2,T_b] :
% 25.26/25.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 25.26/25.36 & class_Int_Onumber__ring(T_b) )
% 25.26/25.36 => ( 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))))))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__le__power2,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__le__imp__le,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.36 => ( 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))))))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__eq__imp__eq,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.36 => ( 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))))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.36 => V_x = V_y ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__less__0,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ~ 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__less__power2,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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))))))
% 25.26/25.36 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sum__power2__eq__zero__iff,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)
% 25.26/25.36 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__eq__square__number__of,axiom,
% 25.26/25.36 ! [V_w,T_b] :
% 25.26/25.36 ( ( class_Groups_Omonoid__mult(T_b)
% 25.26/25.36 & class_Int_Onumber(T_b) )
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__2__cases,axiom,
% 25.26/25.36 ! [V_n] :
% 25.26/25.36 ( 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)))))
% 25.26/25.36 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.36 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__2,axiom,
% 25.26/25.36 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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__eq__1__iff,axiom,
% 25.26/25.36 ! [V_a_2,T_b] :
% 25.26/25.36 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 25.26/25.36 => ( 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)
% 25.26/25.36 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 25.26/25.36 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 25.26/25.36 ! [V_n,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__minus__even,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__less__imp__less,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__semidom(T_a)
% 25.26/25.36 => ( 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))))))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sum__power2__le__zero__iff,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sum__power2__ge__zero,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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))))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sum__power2__gt__zero__iff,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_b)
% 25.26/25.36 => ( 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)))))))
% 25.26/25.36 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.26/25.36 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_not__sum__power2__lt__zero,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ~ 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__sum,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__le__even__power_H,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__odd__eq,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Groups_Omonoid__mult(T_a)
% 25.26/25.36 => 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))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 25.26/25.36 ! [V_n,V_x,T_a] :
% 25.26/25.36 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__minus1__even,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zdiv__number__of__Bit1,axiom,
% 25.26/25.36 ! [V_v,V_w] :
% 25.26/25.36 ( ( 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)))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( ~ 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)))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mod2__gr__0,axiom,
% 25.26/25.36 ! [V_m_2] :
% 25.26/25.36 ( 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))))))
% 25.26/25.36 <=> 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_div__2__gt__zero,axiom,
% 25.26/25.36 ! [V_n] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 25.26/25.36 => 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)))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power2__diff,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ( 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)))))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_odd__power__less__zero,axiom,
% 25.26/25.36 ! [V_n,V_a,T_a] :
% 25.26/25.36 ( class_Rings_Olinordered__idom(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__minus1__odd,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Rings_Oring__1(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__m1__even,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_power__m1__odd,axiom,
% 25.26/25.36 ! [V_n,T_a] :
% 25.26/25.36 ( class_Int_Onumber__ring(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 25.26/25.36 ! [V_n] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.36 => 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)))))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_of__nat__double,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( class_Rings_Osemiring__1(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pos__zmod__mult__2,axiom,
% 25.26/25.36 ! [V_b,V_a] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_neg__zdiv__mult__2,axiom,
% 25.26/25.36 ! [V_b,V_a] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_int__of__code,axiom,
% 25.26/25.36 ! [V_k] :
% 25.26/25.36 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.26/25.36 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.36 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.26/25.36 => ( ( 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)
% 25.26/25.36 => 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)))))) )
% 25.26/25.36 & ( 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)
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_one__code__numeral__code,axiom,
% 25.26/25.36 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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_int__val__lemma,axiom,
% 25.26/25.36 ! [V_k_2,V_f_2,V_n_2] :
% 25.26/25.36 ( ! [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 25.26/25.36 => 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))) )
% 25.26/25.36 => ( 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))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 25.26/25.36 => ? [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 25.26/25.36 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat0__intermed__int__val,axiom,
% 25.26/25.36 ! [V_k_2,V_f_2,V_n_2] :
% 25.26/25.36 ( ! [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 25.26/25.36 => 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))) )
% 25.26/25.36 => ( 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))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 25.26/25.36 => ? [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 25.26/25.36 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral__zero__minus__one,axiom,
% 25.26/25.36 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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_zero__code__numeral__code,axiom,
% 25.26/25.36 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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__of__aux__code,axiom,
% 25.26/25.36 ! [V_n,V_i] :
% 25.26/25.36 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.26/25.36 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 25.26/25.36 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osize_I1_J,axiom,
% 25.26/25.36 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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osize_I3_J,axiom,
% 25.26/25.36 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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 25.26/25.36 ! [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 ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osize_I4_J,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osize_I2_J,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__mod__eq__lemma,axiom,
% 25.26/25.36 ! [V_y,V_n,V_x] :
% 25.26/25.36 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 25.26/25.36 => ? [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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mod__induct__0,axiom,
% 25.26/25.36 ! [V_i_2,V_Pa_2,V_p_2] :
% 25.26/25.36 ( ! [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 25.26/25.36 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 25.26/25.36 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 25.26/25.36 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 25.26/25.36 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Oinject,axiom,
% 25.26/25.36 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 25.26/25.36 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 25.26/25.36 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 25.26/25.36 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Suc__code__numeral__minus__one,axiom,
% 25.26/25.36 ! [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 ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__intermed__int__val,axiom,
% 25.26/25.36 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 25.26/25.36 ( ! [B_i] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 25.26/25.36 => 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))) )
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 25.26/25.36 => ? [B_i] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 25.26/25.36 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_log_Osimps,axiom,
% 25.26/25.36 ! [V_i,V_b] :
% 25.26/25.36 ( ( ( 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)))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 25.26/25.36 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 25.26/25.36 & ( ~ ( 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)))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_mod__div__decomp,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Divides_Osemiring__div(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_setprod__pos,axiom,
% 25.26/25.36 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.36 ( class_Rings_Olinordered__semidom(T_c)
% 25.26/25.36 => ( ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__shift__def,axiom,
% 25.26/25.36 ! [V_r,V_l,V_k] :
% 25.26/25.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_inc__shift__def,axiom,
% 25.26/25.36 ! [V_k,V_v] :
% 25.26/25.36 ( ( V_v = V_k
% 25.26/25.36 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 25.26/25.36 & ( V_v != V_k
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_setprod__nonneg,axiom,
% 25.26/25.36 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.36 ( class_Rings_Olinordered__semidom(T_c)
% 25.26/25.36 => ( ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__induct,axiom,
% 25.26/25.36 ! [V_Pa_2,V_F_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.26/25.36 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.36 => ( ! [B_x,B_F] :
% 25.26/25.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 25.26/25.36 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 25.26/25.36 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 25.26/25.36 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_fold1__antimono,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => 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))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_field__le__epsilon,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Fields_Olinordered__field(T_a)
% 25.26/25.36 => ( ! [B_e] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 25.26/25.36 => 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))) )
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_subtract__code__numeral__def,axiom,
% 25.26/25.36 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__code__numeral__code,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__0R,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__0L,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__Suc__Suc,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oidem,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf_Oidem,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf_Ocommute,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__commute,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__left__idem,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 25.26/25.36 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__left__commute,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf_Oassoc,axiom,
% 25.26/25.36 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__assoc,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_inf__min,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( ( class_Lattices_Osemilattice__inf(T_b)
% 25.26/25.36 & class_Orderings_Olinorder(T_b) )
% 25.26/25.36 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__diff,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__diff__distrib__left,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__infE,axiom,
% 25.26/25.36 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__mono,axiom,
% 25.26/25.36 ! [V_d,V_b,V_c,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__greatest,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__infI,axiom,
% 25.26/25.36 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__absorb2,axiom,
% 25.26/25.36 ! [V_x,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__absorb1,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__infI2,axiom,
% 25.26/25.36 ! [V_a,V_x,V_b,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__infI1,axiom,
% 25.26/25.36 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__inf__iff,axiom,
% 25.26/25.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__iff__inf,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.36 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__le2,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__le1,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__le__iff__disj,axiom,
% 25.26/25.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__add__distrib__left,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oless__infI2,axiom,
% 25.26/25.36 ! [V_a,V_x,V_b,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oless__infI1,axiom,
% 25.26/25.36 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__less__iff__disj,axiom,
% 25.26/25.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__less__iff__conj,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__number__of,axiom,
% 25.26/25.36 ! [V_v,V_u,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber(T_b)
% 25.26/25.36 & class_Orderings_Oord(T_b) )
% 25.26/25.36 => ( ( 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)))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ 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)))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofold__inf__insert,axiom,
% 25.26/25.36 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastAtMostL1,axiom,
% 25.26/25.36 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastAtMostR1,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_b_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofold1__belowI,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_fold1__below__iff,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ? [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_fold1__strict__below__iff,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ? [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_strict__below__fold1__iff,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__ord__min,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Orderings_Oord(T_b)
% 25.26/25.36 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oremove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oeq__fold_H,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_inf__nat__def,axiom,
% 25.26/25.36 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Osingleton,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__le,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__in,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oin__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_OF__eq,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__antimono,axiom,
% 25.26/25.36 ! [V_N_2,V_M_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 25.26/25.36 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => 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))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__insert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Osubset__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__Un,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oinsert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oinsert__remove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Ounion__inter,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Ounion__disjoint,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( ! [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))))))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Oclosed,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( ! [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))))))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 25.26/25.36 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( ! [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))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min_Ohom__commute,axiom,
% 25.26/25.36 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( ! [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))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Max__eq__Min,axiom,
% 25.26/25.36 ! [V_S_2,T_b] :
% 25.26/25.36 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.36 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__Min__eq__Max,axiom,
% 25.26/25.36 ! [V_S_2,T_b] :
% 25.26/25.36 ( class_Groups_Olinordered__ab__group__add(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.36 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 25.26/25.36 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_ca_2),V_A_2))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Min__eqI,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ! [B_y] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Osingleton,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__ge,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__in,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__mono,axiom,
% 25.26/25.36 ! [V_N_2,V_M_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 25.26/25.36 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => 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))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oremove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__eqI,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ! [B_y] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oeq__fold_H,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Ounion__inter,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__inf__absorb,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 25.26/25.36 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 25.26/25.36 ! [V_x,V_z,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__0R,axiom,
% 25.26/25.36 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__0L,axiom,
% 25.26/25.36 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__Suc__Suc,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oidem,axiom,
% 25.26/25.36 ! [V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup_Oidem,axiom,
% 25.26/25.36 ! [V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup_Ocommute,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__commute,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 25.26/25.36 ! [V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__left__idem,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 25.26/25.36 ! [V_c,V_a,V_b,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__left__commute,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup_Oassoc,axiom,
% 25.26/25.36 ! [V_c,V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__assoc,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sup__max,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( ( class_Lattices_Osemilattice__sup(T_b)
% 25.26/25.36 & class_Orderings_Olinorder(T_b) )
% 25.26/25.36 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__diff__distrib__left,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__supE,axiom,
% 25.26/25.36 ! [V_x,V_b,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( 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))
% 25.26/25.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__mono,axiom,
% 25.26/25.36 ! [V_d,V_b,V_c,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__least,axiom,
% 25.26/25.36 ! [V_z,V_x,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__supI,axiom,
% 25.26/25.36 ! [V_b,V_x,V_a,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__absorb1,axiom,
% 25.26/25.36 ! [V_x,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__absorb2,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__supI2,axiom,
% 25.26/25.36 ! [V_a,V_b,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__supI1,axiom,
% 25.26/25.36 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__sup__iff,axiom,
% 25.26/25.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ole__iff__sup,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.26/25.36 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__maxI2,axiom,
% 25.26/25.36 ! [V_x,V_y,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__maxI1,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_le__max__iff__disj,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__add__distrib__left,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oless__supI2,axiom,
% 25.26/25.36 ! [V_a,V_b,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oless__supI1,axiom,
% 25.26/25.36 ! [V_b,V_a,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__less__iff__conj,axiom,
% 25.26/25.36 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 25.26/25.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_less__max__iff__disj,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( 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)))
% 25.26/25.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 25.26/25.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__number__of,axiom,
% 25.26/25.36 ! [V_v,V_u,T_b] :
% 25.26/25.36 ( ( class_Int_Onumber(T_b)
% 25.26/25.36 & class_Orderings_Oord(T_b) )
% 25.26/25.36 => ( ( 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)))
% 25.26/25.36 => 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) )
% 25.26/25.36 & ( ~ 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)))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Odistrib__inf__le,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Odistrib__sup__le,axiom,
% 25.26/25.36 ! [V_z,V_y,V_x,T_a] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_a)
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__min__eq__max,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_minus__max__eq__min,axiom,
% 25.26/25.36 ! [V_y,V_x,T_a] :
% 25.26/25.36 ( class_Groups_Olinordered__ab__group__add(T_a)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat__minus__add__max,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofold__sup__insert,axiom,
% 25.26/25.36 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oin__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastAtMost,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastLessThan,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__greaterThanAtMost,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__greaterThanLessThan,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastAtMostL2,axiom,
% 25.26/25.36 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_b_2) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Int__atLeastAtMostR2,axiom,
% 25.26/25.36 ! [V_d_2,V_ca_2,V_a_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_ca_2),V_d_2) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_OF__eq,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 25.26/25.36 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__insert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Osubset__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => 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 ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max__Un,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oinsert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oinsert__remove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Ounion__disjoint,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_max__ord__max,axiom,
% 25.26/25.36 ! [T_b] :
% 25.26/25.36 ( class_Orderings_Oord(T_b)
% 25.26/25.36 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Oclosed,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( ! [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))))))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OInf__le__Sup,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sup__nat__def,axiom,
% 25.26/25.36 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 25.26/25.36 ! [V_x_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => 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 ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => 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 ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 25.26/25.36 ! [V_a_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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 )
% 25.26/25.36 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)))))) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( 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))
% 25.26/25.36 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 25.26/25.36 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.36 => 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) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => ( ! [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))))))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 25.26/25.36 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( ! [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))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Max_Ohom__commute,axiom,
% 25.26/25.36 ! [V_N_2,V_h_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( ! [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))
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.36 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 25.26/25.36 ! [V_ca_2,V_b_2,V_A_2,T_b] :
% 25.26/25.36 ( class_Orderings_Olinorder(T_b)
% 25.26/25.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => ( ! [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_ca_2))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_pair__box_Osize_I1_J,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_arith__series__int,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 25.26/25.36 ! [V_w] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 => ( ( 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))))
% 25.26/25.36 => 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))) )
% 25.26/25.36 & ( ~ 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))))
% 25.26/25.36 => 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)))) ) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_nat_Osize_I2_J,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INF2__E,axiom,
% 25.26/25.36 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.36 ( 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_ca_2))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 25.26/25.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INF2__D,axiom,
% 25.26/25.36 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.36 ( 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_ca_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INF1__E,axiom,
% 25.26/25.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.36 ( 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))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 25.26/25.36 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INF1__D,axiom,
% 25.26/25.36 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.36 ( 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))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__D,axiom,
% 25.26/25.36 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__E,axiom,
% 25.26/25.36 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 25.26/25.36 ( 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)))
% 25.26/25.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 25.26/25.36 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SUP2__I,axiom,
% 25.26/25.36 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2))
% 25.26/25.36 => 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_ca_2)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__INT,axiom,
% 25.26/25.36 ! [V_A_2,T_c,V_I_2,T_b] :
% 25.26/25.36 ( ? [B_x] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 25.26/25.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_CollectI,axiom,
% 25.26/25.36 ! [T_b,V_a_2,V_Pa_2] :
% 25.26/25.36 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.26/25.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__Collect__conjI,axiom,
% 25.26/25.36 ! [V_Qa_2,V_Pa_2,T_b] :
% 25.26/25.36 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.36 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) )
% 25.26/25.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__I,axiom,
% 25.26/25.36 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 25.26/25.36 => 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))) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_SUP1__I,axiom,
% 25.26/25.36 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.36 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__Collect__less__nat,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__Collect__le__nat,axiom,
% 25.26/25.36 ! [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)))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_setsum__abs,axiom,
% 25.26/25.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_setsum__abs__ge__zero,axiom,
% 25.26/25.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.36 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.36 => 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_finite__Collect__subsets,axiom,
% 25.26/25.36 ! [V_A_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.36 => 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)))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_insert__def,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__extend__simps_I2_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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 )
% 25.26/25.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__extend__simps_I3_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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 )
% 25.26/25.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__simps_I2_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__simps_I3_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__insert,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Collect__imp__eq,axiom,
% 25.26/25.36 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sup__Un__eq,axiom,
% 25.26/25.36 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 25.26/25.36 ( 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))
% 25.26/25.36 <=> 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))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sup__Un__eq2,axiom,
% 25.26/25.36 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 25.26/25.36 ( 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))
% 25.26/25.36 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__Un__distrib,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__Un,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__simps_I7_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__simps_I6_J,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__extend__simps_I7_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Un__INT__distrib,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__extend__simps_I6_J,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Un__INT__distrib2,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Collect__disj__eq,axiom,
% 25.26/25.36 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_sup__fun__def,axiom,
% 25.26/25.36 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.36 ( class_Lattices_Olattice(T_b)
% 25.26/25.36 => 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)) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Un__Inter,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UN__absorb,axiom,
% 25.26/25.36 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 25.26/25.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 25.26/25.36 => 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) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Un__def,axiom,
% 25.26/25.36 ! [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))) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__Un,axiom,
% 25.26/25.36 ! [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)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_Union__image__eq,axiom,
% 25.26/25.36 ! [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) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_UNION__eq__Union__image,axiom,
% 25.26/25.36 ! [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_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__simps_I1_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.36 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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)) )
% 25.26/25.36 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.36 => 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) ) ) ).
% 25.26/25.36
% 25.26/25.36 fof(fact_INT__simps_I2_J,axiom,
% 25.26/25.36 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__Int__eq,axiom,
% 25.26/25.37 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__absorb,axiom,
% 25.26/25.37 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__Int__eq2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__insert,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I2_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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 )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I1_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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 )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__Union,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__Union2,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I5_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I4_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I5_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__UN__distrib,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I4_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__UN__distrib2,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__Int__distrib,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Collect__conj__eq,axiom,
% 25.26/25.37 ! [V_Qa_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__fun__def,axiom,
% 25.26/25.37 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Lattices_Olattice(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__Collect,axiom,
% 25.26/25.37 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))))
% 25.26/25.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__def,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 25.26/25.37 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__eq__setsum,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__UN__finite__eq,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 25.26/25.37 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 25.26/25.37 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat_Osize_I1_J,axiom,
% 25.26/25.37 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__eq__Suc__le__raw,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__number__of__Bit0,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__seg__image__imp__finite,axiom,
% 25.26/25.37 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 25.26/25.37 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_n_2)))
% 25.26/25.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__M__bounded__by__nat,axiom,
% 25.26/25.37 ! [V_i_2,V_Pa_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),V_Pa_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__less__iff,axiom,
% 25.26/25.37 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 & class_Orderings_Olinorder(T_b) )
% 25.26/25.37 => ( 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))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__SUP__iff,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 25.26/25.37 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 & class_Orderings_Olinorder(T_b) )
% 25.26/25.37 => ( 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)))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__addf,axiom,
% 25.26/25.37 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_le__INF__iff,axiom,
% 25.26/25.37 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => ( 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)))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP__le__iff,axiom,
% 25.26/25.37 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => ( 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))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__subset__iff,axiom,
% 25.26/25.37 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__subset__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__subset__eq2,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_c,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__lower,axiom,
% 25.26/25.37 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__subset__eq,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__upper,axiom,
% 25.26/25.37 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum_Odistrib,axiom,
% 25.26/25.37 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__leI,axiom,
% 25.26/25.37 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_le__SUPI,axiom,
% 25.26/25.37 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 25.26/25.37 ! [V_Pa_2] : c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pow__def,axiom,
% 25.26/25.37 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I3_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I3_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I4_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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 )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I7_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I6_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I7_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I6_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__diff__def,axiom,
% 25.26/25.37 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ominus(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__subtractf,axiom,
% 25.26/25.37 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_set__diff__eq,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_insert__compr,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_insert__compr__raw,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Collect__conv__if,axiom,
% 25.26/25.37 ! [T_b,V_a_2,V_Pa_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.26/25.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.26/25.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Collect__conv__if2,axiom,
% 25.26/25.37 ! [T_b,V_a_2,V_Pa_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.26/25.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.26/25.37 => hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_singleton__conv,axiom,
% 25.26/25.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_singleton__conv2,axiom,
% 25.26/25.37 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__insert__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__constant__conv,axiom,
% 25.26/25.37 ! [V_ca_2,T_c,T_b,V_A_2] :
% 25.26/25.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 25.26/25.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_abs__setprod,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Fields_Olinordered__field(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_abs__setsum__abs,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INTER__eq__Inter__image,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Inter__image__eq,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__Union,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I10_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__UN,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I10_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__image,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__ident,axiom,
% 25.26/25.37 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I10_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I10_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_int__setsum,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__insert__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_bot__empty__eq2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_bot__empty__eq,axiom,
% 25.26/25.37 ! [V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__equals__eq,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> V_R_2 = V_S_2 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__equals__eq2,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_c,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> V_R_2 = V_S_2 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_CollectE,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_CollectD,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mem__Collect__eq,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Collect__mem__eq,axiom,
% 25.26/25.37 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__Collect__disjI,axiom,
% 25.26/25.37 ! [V_Qa_2,V_Pa_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Qa_2))))
% 25.26/25.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I5_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I5_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_insert__Collect,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_Pa_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_bot__fun__def,axiom,
% 25.26/25.37 ! [V_x_2,T_c,T_b] :
% 25.26/25.37 ( class_Orderings_Obot(T_b)
% 25.26/25.37 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_empty__def,axiom,
% 25.26/25.37 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__const,axiom,
% 25.26/25.37 ! [V_M_2,T_b,V_A_2,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UNION__empty__conv_I1_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__empty2,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__constant,axiom,
% 25.26/25.37 ! [V_ca_2,T_c,T_b,V_A_2] :
% 25.26/25.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 25.26/25.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UNION__empty__conv_I2_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP__const,axiom,
% 25.26/25.37 ! [V_M_2,T_b,V_A_2,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__negf,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__timesf,axiom,
% 25.26/25.37 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__product,axiom,
% 25.26/25.37 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__0(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__left__distrib,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__0(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__right__distrib,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__0(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Collect__neg__eq,axiom,
% 25.26/25.37 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__Compl__def,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ouminus(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Compl__UN,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Compl__INT,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUPR__apply,axiom,
% 25.26/25.37 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__divide__distrib,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Fields_Ofield(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 25.26/25.37 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.26/25.37 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pow__INT__eq,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Inter__def,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__commute,axiom,
% 25.26/25.37 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INFI__apply,axiom,
% 25.26/25.37 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I8_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I8_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__box_Oinject,axiom,
% 25.26/25.37 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> ( V_a_2 = V_a_H_2
% 25.26/25.37 & V_b_2 = V_b_H_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 25.26/25.37 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Union__def,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP1__iff,axiom,
% 25.26/25.37 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__UN__flatten,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I9_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I9_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I9_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__extend__simps_I9_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP__commute,axiom,
% 25.26/25.37 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__upd__def,axiom,
% 25.26/25.37 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 25.26/25.37 ( ( V_x_2 = V_a_2
% 25.26/25.37 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 25.26/25.37 & ( V_x_2 != V_a_2
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__commute,axiom,
% 25.26/25.37 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fold__image__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I8_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I8_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_int__setprod,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__int__setsum,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Rings_Oring__1(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__int__setprod,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.37 & class_Rings_Oring__1(T_b) )
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__dividef,axiom,
% 25.26/25.37 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Fields_Ofield__inverse__zero(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Compl__eq,axiom,
% 25.26/25.37 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod_Odistrib,axiom,
% 25.26/25.37 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__extend__simps_I1_J,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__singleton,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__simps_I1_J,axiom,
% 25.26/25.37 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__atMost__UNIV,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__constant,axiom,
% 25.26/25.37 ! [V_ca_2,T_c,T_b,V_A_2] :
% 25.26/25.37 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 25.26/25.37 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_ca_2)) = V_ca_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__empty,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UNIV__def,axiom,
% 25.26/25.37 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__1,axiom,
% 25.26/25.37 ! [V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__0,axiom,
% 25.26/25.37 ! [V_A_2,T_c,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__lessThan__UNIV,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__INT__eq,axiom,
% 25.26/25.37 ! [V_x_2,V_r_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF__INT__eq2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP__UN__eq2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_range__composition,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__atLeast__UNIV,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__range__imageI,axiom,
% 25.26/25.37 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 25.26/25.37 ( 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)))))
% 25.26/25.37 => 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP__UN__eq,axiom,
% 25.26/25.37 ! [V_x_2,V_r_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__Collect__not,axiom,
% 25.26/25.37 ! [V_Pa_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))))
% 25.26/25.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 25.26/25.37 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__nat__setsum,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Int__Inter__image,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__le__add__shift,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__Pow__subset,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__nat__setprod,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.26/25.37 & class_Rings_Osemiring__1(T_b) )
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__add__atLeastLessThan,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__add__atLeastAtMost,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__delta_H,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__delta,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__constant,axiom,
% 25.26/25.37 ! [V_ca_2,T_c,V_A_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__setsum__restrict,axiom,
% 25.26/25.37 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_d)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__greaterThan__UNIV,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__delta_H,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__delta,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__eq__UN,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_if__image__distrib,axiom,
% 25.26/25.37 ! [V_S_2,V_g_2,V_f_2,V_Pa_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_Pa_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_Pa_2))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INT__simps_I4_J,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 25.26/25.37 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__constant,axiom,
% 25.26/25.37 ! [V_A_2,V_y_2,T_c,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_power__number__of__even,axiom,
% 25.26/25.37 ! [V_w_2,V_z_2,T_b] :
% 25.26/25.37 ( class_Int_Onumber__ring(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fold__image__distrib,axiom,
% 25.26/25.37 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_dual__max,axiom,
% 25.26/25.37 ! [T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_dual__min,axiom,
% 25.26/25.37 ! [T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__constant,axiom,
% 25.26/25.37 ! [V_y_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup__SUPR__fold__sup,axiom,
% 25.26/25.37 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__INFI__fold__inf,axiom,
% 25.26/25.37 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 25.26/25.37 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Nat_Onat),V_Pa_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 25.26/25.37 ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Int_Oint),V_Pa_2),c_Int_Onat)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zpower__number__of__even,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__lessThan__Suc,axiom,
% 25.26/25.37 ! [V_n_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__atMost__Suc,axiom,
% 25.26/25.37 ! [V_n_2,V_f_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Un__Union__image,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__add__int__atLeastLessThan,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Powp__Pow__eq,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__restrict__set_H,axiom,
% 25.26/25.37 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__restrict__set,axiom,
% 25.26/25.37 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__image__gen,axiom,
% 25.26/25.37 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__eq__fold__image,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_power__number__of__even__number__of,axiom,
% 25.26/25.37 ! [V_w_2,V_v_2,T_b] :
% 25.26/25.37 ( class_Int_Onumber__ring(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUPR__fold__sup,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card_Oeq__fold__g,axiom,
% 25.26/25.37 ! [V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__def,axiom,
% 25.26/25.37 ! [V_A_2,T_b] :
% 25.26/25.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fun__left__comm__idem__remove,axiom,
% 25.26/25.37 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INFI__fold__inf,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_diff__nat__eq__if,axiom,
% 25.26/25.37 ! [V_z_2,V_z_H_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg__div__mod,axiom,
% 25.26/25.37 ! [V_l,V_k] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg__minus1,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__less__Suc2,axiom,
% 25.26/25.37 ! [V_i_2,V_M_2] :
% 25.26/25.37 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__less,axiom,
% 25.26/25.37 ! [V_i_2,V_M_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__less__Suc,axiom,
% 25.26/25.37 ! [V_i_2,V_M_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 25.26/25.37 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__le__eq__Un0,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_adjust__eq,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__head,axiom,
% 25.26/25.37 ! [V_Pa_2,V_n_2,V_m_2,T_b] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__cases,axiom,
% 25.26/25.37 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_Pa_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_minus__fold__remove,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Suc__eq__number__of,axiom,
% 25.26/25.37 ! [V_v_2,V_n_2] :
% 25.26/25.37 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 25.26/25.37 <=> 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__number__of__Suc,axiom,
% 25.26/25.37 ! [V_n_2,V_v_2] :
% 25.26/25.37 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 25.26/25.37 <=> 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__number__of__Bit1,axiom,
% 25.26/25.37 ! [V_w_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 25.26/25.37 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_geometric__sum,axiom,
% 25.26/25.37 ! [V_n_2,V_x_2,T_b] :
% 25.26/25.37 ( class_Fields_Ofield(T_b)
% 25.26/25.37 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_gauss__sum,axiom,
% 25.26/25.37 ! [V_n_2,T_b] :
% 25.26/25.37 ( class_Rings_Ocomm__semiring__1(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__natinterval__difff,axiom,
% 25.26/25.37 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 25.26/25.37 ( class_Groups_Oab__group__add(T_b)
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.37 => 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)))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.26/25.37 => 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) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__Suc__number__of,axiom,
% 25.26/25.37 ! [V_v_2,V_n_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__number__of__Suc,axiom,
% 25.26/25.37 ! [V_n_2,V_v_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_le__Suc__number__of,axiom,
% 25.26/25.37 ! [V_v_2,V_n_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_le__number__of__Suc,axiom,
% 25.26/25.37 ! [V_n_2,V_v_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__Suc__number__of,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__number__of__Suc,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_power__number__of__odd,axiom,
% 25.26/25.37 ! [V_z_2,V_w_2,T_b] :
% 25.26/25.37 ( class_Int_Onumber__ring(T_b)
% 25.26/25.37 => ( ( 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)))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setprod__gen__delta,axiom,
% 25.26/25.37 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_ca_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 25.26/25.37 ! [V_x_2,V_y_2,V_ca_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 25.26/25.37 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 25.26/25.37 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 25.26/25.37 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zpower__number__of__odd,axiom,
% 25.26/25.37 ! [V_z_2,V_w_2] :
% 25.26/25.37 ( ( 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)))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_arith__series__general,axiom,
% 25.26/25.37 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 25.26/25.37 ( class_Rings_Ocomm__semiring__1(T_b)
% 25.26/25.37 => 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg_Osimps,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( ( ( 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)))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ ( 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)))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__number__of__Suc,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__Suc__number__of,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_arith__series__nat,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_power__number__of__odd__number__of,axiom,
% 25.26/25.37 ! [V_v_2,V_w_2,T_b] :
% 25.26/25.37 ( class_Int_Onumber__ring(T_b)
% 25.26/25.37 => ( ( 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)))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg__eqn__number__of,axiom,
% 25.26/25.37 ! [V_w,V_v] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( 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))))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( ~ 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))))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg__eqn,axiom,
% 25.26/25.37 ! [V_a,V_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => ( ( 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)))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_diff__nat__number__of,axiom,
% 25.26/25.37 ! [V_v_2,V_v_H_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_norm__frac_Osimps,axiom,
% 25.26/25.37 ! [V_a_2,V_b_2] :
% 25.26/25.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.37 => 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))) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__case__add__eq__if,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 25.26/25.37 ! [V_w] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( 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)))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg_Osimps,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup2CI,axiom,
% 25.26/25.37 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 25.26/25.37 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup2E,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf2I,axiom,
% 25.26/25.37 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf2E,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_bot2E,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF1__iff,axiom,
% 25.26/25.37 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_INF2__iff,axiom,
% 25.26/25.37 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_SUP2__iff,axiom,
% 25.26/25.37 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rev__predicate2D,axiom,
% 25.26/25.37 ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_predicate2D,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Qa_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__by__empty,axiom,
% 25.26/25.37 ! [V_B_2,T_b,V_A_2] :
% 25.26/25.37 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf2D1,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf2D2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup2I2,axiom,
% 25.26/25.37 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup2I1,axiom,
% 25.26/25.37 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__case__0,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__case__Suc,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__0,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__Suc1,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__Suc2,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 25.26/25.37 ! [V_n_2,V_m_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_diff__Suc,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__Suc2,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__Suc1,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__div__mod,axiom,
% 25.26/25.37 ! [V_l,V_k] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__case__number__of,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__eqn,axiom,
% 25.26/25.37 ! [V_a,V_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 25.26/25.37 => 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__eqn__number__of,axiom,
% 25.26/25.37 ! [V_w,V_v] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( 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)))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ 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)))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_in__rel__def,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__mod__code__numeral__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nitpick_Orefl_H__def,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 25.26/25.37 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_adjust__def,axiom,
% 25.26/25.37 ! [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))))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__step,axiom,
% 25.26/25.37 ! [V_m,V_n] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__rec__add__eq__if,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__rec__0,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__rec__Suc,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__zero,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__base,axiom,
% 25.26/25.37 ! [V_n,V_m] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__div__mod,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__rec__number__of,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__imageI,axiom,
% 25.26/25.37 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__int__num,axiom,
% 25.26/25.37 ! [V_k_2,T_b] :
% 25.26/25.37 ( class_Rings_Oring__1(T_b)
% 25.26/25.37 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 25.26/25.37 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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))) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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))))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 25.26/25.37 ! [V_n_2,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_splitI,axiom,
% 25.26/25.37 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod__caseI,axiom,
% 25.26/25.37 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mem__splitI,axiom,
% 25.26/25.37 ! [T_d,T_c,V_b_2,V_a_2,V_ca_2,V_z_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_splitD,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_splitD_H,axiom,
% 25.26/25.37 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_ca_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 25.26/25.37 ! [V_i_2,V_inc_2,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.37 => 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 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 25.26/25.37 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 25.26/25.37 ( class_Rings_Osemiring__1(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__paired__All,axiom,
% 25.26/25.37 ! [T_c,T_b,V_Pa_2] :
% 25.26/25.37 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.26/25.37 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pair__eq,axiom,
% 25.26/25.37 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> ( V_a_2 = V_a_H_2
% 25.26/25.37 & V_b_2 = V_b_H_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pair__inject,axiom,
% 25.26/25.37 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 25.26/25.37 ( 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)
% 25.26/25.37 => ~ ( V_a = V_a_H
% 25.26/25.37 => V_b != V_b_H ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__weak__cong,axiom,
% 25.26/25.37 ! [V_ca_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 25.26/25.37 ( V_p_2 = V_q_2
% 25.26/25.37 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_ca_2),V_q_2) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__mod__div,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod_Osimps_I2_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__conv,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__if,axiom,
% 25.26/25.37 ! [V_m_2,V_n_2] :
% 25.26/25.37 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__eta,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__twice,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nitpick_OFrac__def,axiom,
% 25.26/25.37 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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__def,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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))) ) ) ) ) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => 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))) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__pdivmod,axiom,
% 25.26/25.37 ! [V_l_2,V_k_2] :
% 25.26/25.37 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apsnd__conv,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negateSnd__def,axiom,
% 25.26/25.37 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negateSnd__eq,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pdivmod__def,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pdivmod__posDivAlg,axiom,
% 25.26/25.37 ! [V_k,V_l] :
% 25.26/25.37 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__code,axiom,
% 25.26/25.37 ! [V_l_2,V_k_2] :
% 25.26/25.37 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Nitpick_Oprod__def,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_int__ge__less__than2__def,axiom,
% 25.26/25.37 ! [V_d_2] : c_Int_Oint__ge__less__than2(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_int__ge__less__than__def,axiom,
% 25.26/25.37 ! [V_d_2] : c_Int_Oint__ge__less__than(V_d_2) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_d_2)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 25.26/25.37 ! [V_a,V_r,V_q,V_c,V_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 25.26/25.37 ! [V_c,V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__box_Osize_I2_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__unique,axiom,
% 25.26/25.37 ! [V_qr_H,V_qr,V_n,V_m] :
% 25.26/25.37 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 25.26/25.37 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 25.26/25.37 => V_qr = V_qr_H ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 25.26/25.37 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__eq,axiom,
% 25.26/25.37 ! [V_qr,V_n,V_m] :
% 25.26/25.37 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 25.26/25.37 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__eq,axiom,
% 25.26/25.37 ! [V_r,V_q,V_n,V_m] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__eq,axiom,
% 25.26/25.37 ! [V_r,V_q,V_n,V_m] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 25.26/25.37 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__box_Orecs,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__box_Osimps_I2_J,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg_Opsimps,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( ( 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)))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ ( 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)))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_accp__downward,axiom,
% 25.26/25.37 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 25.26/25.37 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_accp_Oequations,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 25.26/25.37 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_accp_Osimps,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 25.26/25.37 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_accp__subset,axiom,
% 25.26/25.37 ! [V_R2_2,V_R1_2,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg_Opsimps,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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) )
% 25.26/25.37 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_norm__frac_Opsimps,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.37 => 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)) )
% 25.26/25.37 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 25.26/25.37 => 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))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg_Opinduct,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ! [B_a,B_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( ~ ( 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)))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg_Opinduct,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ! [B_a,B_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 25.26/25.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),B_b))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__gcd_Opsimps,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 25.26/25.37 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zmult2__lemma,axiom,
% 25.26/25.37 ! [V_c,V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__0,axiom,
% 25.26/25.37 ! [V_b] :
% 25.26/25.37 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_self__remainder,axiom,
% 25.26/25.37 ! [V_r,V_q,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_unique__quotient,axiom,
% 25.26/25.37 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => V_q = V_q_H ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_unique__remainder,axiom,
% 25.26/25.37 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => V_r = V_r_H ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__neg,axiom,
% 25.26/25.37 ! [V_qr,V_b,V_a] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__correct,axiom,
% 25.26/25.37 ! [V_a,V_b] :
% 25.26/25.37 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_self__quotient,axiom,
% 25.26/25.37 ! [V_r,V_q,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__mod,axiom,
% 25.26/25.37 ! [V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__div,axiom,
% 25.26/25.37 ! [V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_negDivAlg__correct,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__div__mod,axiom,
% 25.26/25.37 ! [V_a,V_b] :
% 25.26/25.37 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_posDivAlg__correct,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zadd1__lemma,axiom,
% 25.26/25.37 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zminus1__lemma,axiom,
% 25.26/25.37 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__relI,axiom,
% 25.26/25.37 ! [V_r,V_q,V_b,V_a] :
% 25.26/25.37 ( 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)
% 25.26/25.37 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_zmult1__lemma,axiom,
% 25.26/25.37 ! [V_a,V_r,V_q,V_c,V_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__int__rel__def,axiom,
% 25.26/25.37 ! [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))))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__pos__neg__1__number__of,axiom,
% 25.26/25.37 ! [V_w] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_in__measure,axiom,
% 25.26/25.37 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_snd__apsnd,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apsnd__eq__conv,axiom,
% 25.26/25.37 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_snd__conv,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_snd__eqD,axiom,
% 25.26/25.37 ! [V_a,V_y,V_x,T_a,T_b] :
% 25.26/25.37 ( 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
% 25.26/25.37 => V_y = V_a ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_snd__def,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__int__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__neg__pos,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__pos__pos,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__pos__pos__1__number__of,axiom,
% 25.26/25.37 ! [V_w] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__pos__neg,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__neg__neg,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_norm__frac_Opinduct,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ! [B_a,B_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__pos__neg__1__number__of,axiom,
% 25.26/25.37 ! [V_w] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => 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))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pair__fst__snd__eq,axiom,
% 25.26/25.37 ! [T_c,T_b,V_t_2,V_s_2] :
% 25.26/25.37 ( V_s_2 = V_t_2
% 25.26/25.37 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 25.26/25.37 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod__eqI,axiom,
% 25.26/25.37 ! [V_q,V_p,T_b,T_a] :
% 25.26/25.37 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 25.26/25.37 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 25.26/25.37 => V_p = V_q ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fst__def,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fst__eqD,axiom,
% 25.26/25.37 ! [V_a,V_y,V_x,T_b,T_a] :
% 25.26/25.37 ( 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
% 25.26/25.37 => V_x = V_a ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fst__conv,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fst__apsnd,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__collapse,axiom,
% 25.26/25.37 ! [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 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_surjective__pairing,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod__case__beta,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__int__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mod__nat__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__comp__eq,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__beta,axiom,
% 25.26/25.37 ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_split__def,axiom,
% 25.26/25.37 ! [V_p_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__neg__pos,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__pos__pos,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__pos__pos__1__number__of,axiom,
% 25.26/25.37 ! [V_w] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__pos__neg,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__neg__neg,axiom,
% 25.26/25.37 ! [V_b,V_a] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod__size__simp,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_exI__realizer,axiom,
% 25.26/25.37 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_conjI__realizer,axiom,
% 25.26/25.37 ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
% 25.26/25.37 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 25.26/25.37 => ( hBOOL(hAPP(V_Qa_2,V_q_2))
% 25.26/25.37 => ( hBOOL(hAPP(V_Pa_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 25.26/25.37 & hBOOL(hAPP(V_Qa_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_div__nat__def,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_divmod__nat__rel__def,axiom,
% 25.26/25.37 ! [V_qr_2,V_n_2,V_m_2] :
% 25.26/25.37 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 25.26/25.37 <=> ( 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))
% 25.26/25.37 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.26/25.37 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 & 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)) ) )
% 25.26/25.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 & 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))) ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__def,axiom,
% 25.26/25.37 ! [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)))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__finite2__subset,axiom,
% 25.26/25.37 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 25.26/25.37 ( ! [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)))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__gcd_Opinduct,axiom,
% 25.26/25.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ! [B_x,B_y] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Rep__Integ__inject,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2] :
% 25.26/25.37 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 25.26/25.37 <=> V_x_2 = V_y_2 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_range,axiom,
% 25.26/25.37 ! [V_s,V_k] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__multicount,axiom,
% 25.26/25.37 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mlex__leq,axiom,
% 25.26/25.37 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mlex__less,axiom,
% 25.26/25.37 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__psubset__def,axiom,
% 25.26/25.37 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__Collect__bounded__ex,axiom,
% 25.26/25.37 ! [V_Qa_2,T_c,V_Pa_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2)))))
% 25.26/25.37 <=> ! [B_y] :
% 25.26/25.37 ( hBOOL(hAPP(V_Pa_2,B_y))
% 25.26/25.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_y)))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__image__set,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 25.26/25.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_Pa_2))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Pow__Compl,axiom,
% 25.26/25.37 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_add__Max__commute,axiom,
% 25.26/25.37 ! [V_k_2,V_N_2,T_b] :
% 25.26/25.37 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_add__Min__commute,axiom,
% 25.26/25.37 ! [V_k_2,V_N_2,T_b] :
% 25.26/25.37 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 25.26/25.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup__Inf1__distrib,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Lattices_Odistrib__lattice(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sup__Inf2__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Lattices_Odistrib__lattice(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__Sup1__distrib,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Lattices_Odistrib__lattice(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inf__Sup2__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Lattices_Odistrib__lattice(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_in__finite__psubset,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 25.26/25.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.26/25.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,T_b] :
% 25.26/25.37 ( class_Orderings_Olinorder(T_b)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat_Osize_I4_J,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_prod_Orecs,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__finite2__eq,axiom,
% 25.26/25.37 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 25.26/25.37 ( ! [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)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat__size,axiom,
% 25.26/25.37 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat_Osize_I3_J,axiom,
% 25.26/25.37 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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__finite__subset,axiom,
% 25.26/25.37 ! [V_C_2,V_A_2,T_b] :
% 25.26/25.37 ( ! [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))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__multicount__gen,axiom,
% 25.26/25.37 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 25.26/25.37 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_in__lex__prod,axiom,
% 25.26/25.37 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 25.26/25.37 | ( V_a_2 = V_a_H_2
% 25.26/25.37 & 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_same__fstI,axiom,
% 25.26/25.37 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 25.26/25.37 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__nonneg__0,axiom,
% 25.26/25.37 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Oordered__ab__group__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 25.26/25.37 => ( ! [B_i] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 25.26/25.37 => ( 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)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 25.26/25.37 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_setsum__nonneg__leq__bound,axiom,
% 25.26/25.37 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 25.26/25.37 ( class_Groups_Oordered__ab__group__add(T_c)
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 25.26/25.37 => ( ! [B_i] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 25.26/25.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_sum__diff__distrib,axiom,
% 25.26/25.37 ! [V_n_2,V_Pa_2,V_Qa_2] :
% 25.26/25.37 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_2,B_x)))
% 25.26/25.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Pa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Qa_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Qa_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apfst__apsnd,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apsnd__apfst,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_fst__apfst,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apfst__eq__conv,axiom,
% 25.26/25.37 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apfst__conv,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_snd__apfst,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_apsnd__apfst__commute,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__lessI2,axiom,
% 25.26/25.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__ext__additive,axiom,
% 25.26/25.37 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 25.26/25.37 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => ( V_A_2 = V_B_2
% 25.26/25.37 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.37 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__lessI1,axiom,
% 25.26/25.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__extp__max__ext__eq,axiom,
% 25.26/25.37 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__leqI2,axiom,
% 25.26/25.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_smax__insertI,axiom,
% 25.26/25.37 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_smax__emptyI,axiom,
% 25.26/25.37 ! [V_Y_2] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 25.26/25.37 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__strict__def,axiom,
% 25.26/25.37 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__leqI1,axiom,
% 25.26/25.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wmin__insertI,axiom,
% 25.26/25.37 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wmax__insertI,axiom,
% 25.26/25.37 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_smin__insertI,axiom,
% 25.26/25.37 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wmax__emptyI,axiom,
% 25.26/25.37 ! [V_X_2] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_smin__emptyI,axiom,
% 25.26/25.37 ! [V_X_2] :
% 25.26/25.37 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wmin__emptyI,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__weak__def,axiom,
% 25.26/25.37 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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__weak__def,axiom,
% 25.26/25.37 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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__rpair__set,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__rpair__set,axiom,
% 25.26/25.37 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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__strict__def,axiom,
% 25.26/25.37 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less__than__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_intrel__iff,axiom,
% 25.26/25.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rp__inv__image__rp,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 25.26/25.37 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 25.26/25.37 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pair__less__def,axiom,
% 25.26/25.37 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mlex__prod__def,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rp__inv__image__def,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__intrel__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2] :
% 25.26/25.37 ( 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))))
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_measure__def,axiom,
% 25.26/25.37 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__singleton,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__singleton__iff,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 25.26/25.37 ( 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))))))
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inv__image__def,axiom,
% 25.26/25.37 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__empty,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__Un,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__UN,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__Int__subset,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__mono,axiom,
% 25.26/25.37 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Un__Image,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_in__inv__image,axiom,
% 25.26/25.37 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__INT__subset,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rev__ImageI,axiom,
% 25.26/25.37 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__iff,axiom,
% 25.26/25.37 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.26/25.37 & 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__eq__UN,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_of__int,axiom,
% 25.26/25.37 ! [V_j_2,V_i_2,T_b] :
% 25.26/25.37 ( class_Rings_Oring__1(T_b)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_One__int__def,axiom,
% 25.26/25.37 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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mult,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Rep__Integ__inverse,axiom,
% 25.26/25.37 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 25.26/25.37
% 25.26/25.37 fof(fact_minus,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Zero__int__def,axiom,
% 25.26/25.37 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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_int__def,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_add,axiom,
% 25.26/25.37 ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_nat,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_minus__int__def,axiom,
% 25.26/25.37 ! [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))))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_less,axiom,
% 25.26/25.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 25.26/25.37 ( 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)))))))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_le,axiom,
% 25.26/25.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 25.26/25.37 ( 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)))))))
% 25.26/25.37 <=> 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_irrefl__def,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Relation_Oirrefl(T_b,V_r_2)
% 25.26/25.37 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__Abs__Integ,axiom,
% 25.26/25.37 ! [V_z_2] :
% 25.26/25.37 ~ ! [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))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Field__insert,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Field__Union,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Field__empty,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_mono__Field,axiom,
% 25.26/25.37 ! [V_s_2,V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Field__Un,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__Field,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 25.26/25.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__on__def,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__def,axiom,
% 25.26/25.37 ! [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)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_ImageE,axiom,
% 25.26/25.37 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 25.26/25.37 => ~ ! [B_x] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__is__empty,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__is__empty2,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__empty,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__on__def_H,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__on__empty,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Image__Id__on,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotientI,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__on__eqI,axiom,
% 25.26/25.37 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 25.26/25.37 ( V_a_2 = V_b_2
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__on__iff,axiom,
% 25.26/25.37 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 25.26/25.37 <=> ( V_x_2 = V_y_2
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_singleton__quotient,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__class__nondisjoint,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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)))))))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_subset__equiv__class,axiom,
% 25.26/25.37 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),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))))))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotientE,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ~ ! [B_x] :
% 25.26/25.37 ( 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))))
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__intrel,axiom,
% 25.26/25.37 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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Union__quotient,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => 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 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__class__self,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => 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)))))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__disj,axiom,
% 25.26/25.37 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( V_X_2 = V_Y_2
% 25.26/25.37 | 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)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__class__eq,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.26/25.37 => 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)))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__eq__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 25.26/25.37 => ( V_X_2 = V_Y_2
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__eqI,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.26/25.37 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__class__eq__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.26/25.37 <=> ( 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))))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__equiv__class__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.37 => ( 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))))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__equiv__class,axiom,
% 25.26/25.37 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( 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))))
% 25.26/25.37 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equiv__class__subset,axiom,
% 25.26/25.37 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),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)))))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__equiv__class__iff2,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.37 => ( 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)
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__equiv__class,axiom,
% 25.26/25.37 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => 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) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__equiv__class2,axiom,
% 25.26/25.37 ! [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] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 25.26/25.37 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 25.26/25.37 => 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) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equivp__equiv,axiom,
% 25.26/25.37 ! [V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 25.26/25.37 <=> 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equivp__transp,axiom,
% 25.26/25.37 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equivp__symp,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equivp__reflp,axiom,
% 25.26/25.37 ! [V_x_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.26/25.37 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_equivp__def,axiom,
% 25.26/25.37 ! [V_R_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.26/25.37 <=> ! [B_x,B_y] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 25.26/25.37 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_identity__equivp,axiom,
% 25.26/25.37 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_congruent2__implies__congruent,axiom,
% 25.26/25.37 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_congruent2D,axiom,
% 25.26/25.37 ! [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] :
% 25.26/25.37 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_congruentD,axiom,
% 25.26/25.37 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 25.26/25.37 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_congruent2__implies__congruent__UN,axiom,
% 25.26/25.37 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 25.26/25.37 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 25.26/25.37 => 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)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__equiv__class__inject,axiom,
% 25.26/25.37 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 25.26/25.37 => ( 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)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => ! [B_y] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 25.26/25.37 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 25.26/25.37 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__equiv__class__type2,axiom,
% 25.26/25.37 ! [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] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 25.26/25.37 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => ( ! [B_x1] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 25.26/25.37 => ! [B_x2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 25.26/25.37 => 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)) ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_UN__equiv__class__type,axiom,
% 25.26/25.37 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.26/25.37 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 25.26/25.37 => 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)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Integ__def,axiom,
% 25.26/25.37 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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__quotient__disjoint,axiom,
% 25.26/25.37 ! [V_r_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( 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)
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Id__onE,axiom,
% 25.26/25.37 ! [V_A_2,V_ca_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_ca_2),c_Relation_OId__on(T_b,V_A_2)))
% 25.26/25.37 => ~ ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__empty,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__uminus,axiom,
% 25.26/25.37 ! [V_A_2,T_b] :
% 25.26/25.37 ( class_Groups_Oordered__ab__group__add(T_b)
% 25.26/25.37 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 => ( 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)
% 25.26/25.37 <=> V_A_2 = V_B_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__id2,axiom,
% 25.26/25.37 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_subset__inj__on,axiom,
% 25.26/25.37 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.37 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__Int,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__diff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__def,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.26/25.37 => ! [B_xa] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 25.26/25.37 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 25.26/25.37 => B_x = B_xa ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__onD,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.37 => V_x_2 = V_y_2 ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__iff,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.37 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 25.26/25.37 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__contraD,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( V_x_2 != V_y_2
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 25.26/25.37 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__imageD,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 25.26/25.37 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 25.26/25.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__eq,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 25.26/25.37 <=> V_x_2 = V_y_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_injD,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 25.26/25.37 => V_x_2 = V_y_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__fun,axiom,
% 25.26/25.37 ! [T_d,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__image__eq__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( 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)
% 25.26/25.37 <=> V_A_2 = V_B_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__image,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => 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) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__strict__subset,axiom,
% 25.26/25.37 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.37 => 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))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_range__ex1__eq,axiom,
% 25.26/25.37 ! [V_b_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( 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)))))
% 25.26/25.37 <=> ? [B_x] :
% 25.26/25.37 ( V_b_2 = hAPP(V_f_2,B_x)
% 25.26/25.37 & ! [B_y] :
% 25.26/25.37 ( V_b_2 = hAPP(V_f_2,B_y)
% 25.26/25.37 => B_y = B_x ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__image__mem__iff,axiom,
% 25.26/25.37 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__iff__surj,axiom,
% 25.26/25.37 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 25.26/25.37 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( ? [B_f] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 25.26/25.37 & 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)) )
% 25.26/25.37 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_endo__inj__surj,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 25.26/25.37 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__surj__inj,axiom,
% 25.26/25.37 ! [V_f_2,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__UNIV__surj__inj,axiom,
% 25.26/25.37 ! [V_f_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.37 => ( 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))
% 25.26/25.37 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__UNIV__inj__surj,axiom,
% 25.26/25.37 ! [V_f_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.26/25.37 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__image__subset__iff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => ( 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)))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__image__Int,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__Int,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__iff__eq__card,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 <=> 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_eq__card__imp__inj__on,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( 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)
% 25.26/25.37 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__image__set__diff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__set__diff,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pigeonhole,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( 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)))
% 25.26/25.37 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__fun__updI,axiom,
% 25.26/25.37 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.26/25.37 => 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) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__singleton,axiom,
% 25.26/25.37 ! [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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_Rep__Integ,axiom,
% 25.26/25.37 ! [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)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__bij__eq,axiom,
% 25.26/25.37 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.37 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__image__Compl__subset,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__insert,axiom,
% 25.26/25.37 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 25.26/25.37 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 & ~ 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))))))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__Un,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.26/25.37 & 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_card__inj__on__le,axiom,
% 25.26/25.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( 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))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.37 => 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__iff__card__le,axiom,
% 25.26/25.37 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.26/25.37 => ( ? [B_f] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 25.26/25.37 & 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)) )
% 25.26/25.37 <=> 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))) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_quotient__diff1,axiom,
% 25.26/25.37 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 25.26/25.37 ( 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)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.26/25.37 => 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)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_type__definition__Integ,axiom,
% 25.26/25.37 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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_image__INT,axiom,
% 25.26/25.37 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 25.26/25.37 => 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)) )
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_the__inv__into__into,axiom,
% 25.26/25.37 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.26/25.37 => 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)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_finite__conv__nat__seg__image,axiom,
% 25.26/25.37 ! [V_A_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.26/25.37 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__add__nat,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__Suc,axiom,
% 25.26/25.37 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__of__nat,axiom,
% 25.26/25.37 ! [T_b] :
% 25.26/25.37 ( class_Nat_Osemiring__char__0(T_b)
% 25.26/25.37 => 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))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__int,axiom,
% 25.26/25.37 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))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_swap__inj__on,axiom,
% 25.26/25.37 ! [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) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_the__inv__into__f__f,axiom,
% 25.26/25.37 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => 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 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_the__inv__into__f__eq,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.26/25.37 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_the__inv__f__f,axiom,
% 25.26/25.37 ! [V_x_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.26/25.37 => 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 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_the__inv__into__onto,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => 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 ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__on__the__inv__into,axiom,
% 25.26/25.37 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => 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)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_inj__graph,axiom,
% 25.26/25.37 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_f__the__inv__into__f,axiom,
% 25.26/25.37 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 25.26/25.37 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.26/25.37 => 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 ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 25.26/25.37 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 25.26/25.37 & class_Groups_Ocomm__monoid__mult(T_b) )
% 25.26/25.37 => ( V_A_2 = V_B_2
% 25.26/25.37 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.26/25.37 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 25.26/25.37 => 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) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_accp__acc__eq,axiom,
% 25.26/25.37 ! [V_x_2,V_r_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__def,axiom,
% 25.26/25.37 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__compI,axiom,
% 25.26/25.37 ! [V_s_2,V_ca_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_ca_2)),V_s_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__UNION__distrib,axiom,
% 25.26/25.37 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__UNION__distrib2,axiom,
% 25.26/25.37 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__empty1,axiom,
% 25.26/25.37 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__empty2,axiom,
% 25.26/25.37 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__distrib,axiom,
% 25.26/25.37 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__distrib2,axiom,
% 25.26/25.37 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_O__assoc,axiom,
% 25.26/25.37 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_rel__comp__mono,axiom,
% 25.26/25.37 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_union__comp__emptyR,axiom,
% 25.26/25.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 25.26/25.37 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_union__comp__emptyL,axiom,
% 25.26/25.37 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 25.26/25.37 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_acc__subset,axiom,
% 25.26/25.37 ! [V_R2_2,V_R1_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_acc__downward,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_acc_Osimps,axiom,
% 25.26/25.37 ! [V_r_2,V_a_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 25.26/25.37 <=> ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__ext__compat,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__ext__compat,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__comp__rel__comp__eq,axiom,
% 25.26/25.37 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_reduction__pairI,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 25.26/25.37 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__extp_Oequations,axiom,
% 25.26/25.37 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 25.26/25.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 25.26/25.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 25.26/25.37 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 & ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 25.26/25.37 => ? [B_xa] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__less__than,axiom,
% 25.26/25.37 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__comp_Ointros,axiom,
% 25.26/25.37 ! [T_d,T_c,T_b,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__empty,axiom,
% 25.26/25.37 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__inv__image,axiom,
% 25.26/25.37 ! [V_f_2,T_c,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__lex__prod,axiom,
% 25.26/25.37 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 25.26/25.37 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 25.26/25.37 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__measure,axiom,
% 25.26/25.37 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__comp__self,axiom,
% 25.26/25.37 ! [V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.26/25.37 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_min__ext__wf,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__finite__psubset,axiom,
% 25.26/25.37 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_pred__comp_Oequations,axiom,
% 25.26/25.37 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 25.26/25.37 ( 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))
% 25.26/25.37 <=> ? [B_b] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 25.26/25.37 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__subset,axiom,
% 25.26/25.37 ! [V_p_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 25.26/25.37 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__Int2,axiom,
% 25.26/25.37 ! [V_r_H_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__Int1,axiom,
% 25.26/25.37 ! [V_r_H_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__mlex,axiom,
% 25.26/25.37 ! [V_f_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.26/25.37 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__pair__less,axiom,
% 25.26/25.37 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__ext__wf,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__less,axiom,
% 25.26/25.37 c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__irrefl,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__asym,axiom,
% 25.26/25.37 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__not__sym,axiom,
% 25.26/25.37 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__not__refl,axiom,
% 25.26/25.37 ! [V_a_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__int__ge__less__than,axiom,
% 25.26/25.37 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__int__ge__less__than2,axiom,
% 25.26/25.37 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_acc__wfD,axiom,
% 25.26/25.37 ! [V_x_2,V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__acc__iff,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__no__loop,axiom,
% 25.26/25.37 ! [V_R_2,T_b] :
% 25.26/25.37 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 25.26/25.37 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__union__merge,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 25.26/25.37 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 <=> ~ ? [B_f] :
% 25.26/25.37 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wfE__pf,axiom,
% 25.26/25.37 ! [V_A_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 25.26/25.37 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__union__compatible,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.26/25.37 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf,axiom,
% 25.26/25.37 ! [T_b] :
% 25.26/25.37 ( class_Orderings_Owellorder(T_b)
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_reduction__pair__def,axiom,
% 25.26/25.37 ! [V_Pa_2,T_b] :
% 25.26/25.37 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 25.26/25.37 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2))) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_reduction__pair__lemma,axiom,
% 25.26/25.37 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 25.26/25.37 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 25.26/25.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2)))
% 25.26/25.37 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__lenlex,axiom,
% 25.26/25.37 ! [V_r_2,T_b] :
% 25.26/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.26/25.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_wf__if__measure,axiom,
% 25.26/25.37 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 25.26/25.37 ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.26/25.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
% 25.26/25.37 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 25.26/25.37
% 25.26/25.37 fof(fact_max__ext_Ointros,axiom,
% 25.26/25.37 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 25.26/25.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 25.26/25.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 25.26/25.37 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.26/25.37 => ( ! [B_x] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 25.26/25.37 => ? [B_xa] :
% 25.26/25.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 25.26/25.37 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 25.54/25.37 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_pred__nat__def,axiom,
% 25.54/25.37 c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_wf__lex,axiom,
% 25.54/25.37 ! [V_r_2,T_b] :
% 25.54/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_wf__lexn,axiom,
% 25.54/25.37 ! [V_n_2,V_r_2,T_b] :
% 25.54/25.37 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.37 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_lex__def,axiom,
% 25.54/25.37 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_lexn_Osimps_I1_J,axiom,
% 25.54/25.37 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_wf__pred__nat,axiom,
% 25.54/25.37 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_wf__same__fst,axiom,
% 25.54/25.37 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 25.54/25.37 ( ! [B_x] :
% 25.54/25.37 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.37 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 25.54/25.37 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 25.54/25.37
% 25.54/25.37 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__Inter,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b,V_S_2] :
% 25.54/25.38 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 25.54/25.38 => ( ! [B_A] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 25.54/25.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 25.54/25.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oone__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Ofrac__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Collect__split,axiom,
% 25.54/25.38 ! [V_Pa_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Pa_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_the__elem__def,axiom,
% 25.54/25.38 ! [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))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__def,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__empty,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_RangeI,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__accp__iff,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 25.54/25.38 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_accp__wfPD,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 25.54/25.38 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_the__eq__trivial,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_the__sym__eq__trivial,axiom,
% 25.54/25.38 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Id__on,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__subset,axiom,
% 25.54/25.38 ! [V_p_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 25.54/25.38 => ( 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))
% 25.54/25.38 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Diff__subset,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Union,axiom,
% 25.54/25.38 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__empty,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__empty__iff,axiom,
% 25.54/25.38 ! [V_r_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Un__eq,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__Range,axiom,
% 25.54/25.38 ! [V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snd__eq__Range,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_split__paired__The,axiom,
% 25.54/25.38 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_The__split__eq,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__iff,axiom,
% 25.54/25.38 ! [V_r_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 25.54/25.38 <=> ? [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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_the__inv__into__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fold__def,axiom,
% 25.54/25.38 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__insert,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_divmod__nat__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Int__subset,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fold1__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_The__split,axiom,
% 25.54/25.38 ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__in__rel,axiom,
% 25.54/25.38 ! [V_R_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_R_2)
% 25.54/25.38 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__wf__eq,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_RangeP__Range__eq,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_flat__lub__def,axiom,
% 25.54/25.38 ! [V_b_2,V_A_2,T_b] :
% 25.54/25.38 ( ( 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)))))
% 25.54/25.38 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 25.54/25.38 & ( ~ 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)))))
% 25.54/25.38 => 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)))))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_RangeE,axiom,
% 25.54/25.38 ! [V_r_2,T_c,V_b_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 25.54/25.38 => ~ ! [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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_RangeP_Ointros,axiom,
% 25.54/25.38 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 25.54/25.38 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_RangeP_Oequations,axiom,
% 25.54/25.38 ! [V_a2_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 25.54/25.38 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__vimage__singleton,axiom,
% 25.54/25.38 ! [V_a_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => 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))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__acyclicP,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__Un,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimageI,axiom,
% 25.54/25.38 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 25.54/25.38 ( hAPP(V_f_2,V_a_2) = V_b_2
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_DomainI,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__UN,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Diff,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Un,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__mono,axiom,
% 25.54/25.38 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimageI2,axiom,
% 25.54/25.38 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimageD,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__eq,axiom,
% 25.54/25.38 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__ident,axiom,
% 25.54/25.38 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__INT,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Int,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Compl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__code,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 25.54/25.38 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Id__on,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__UNIV,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acyclic__subset,axiom,
% 25.54/25.38 ! [V_r_2,V_s_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__acyclic,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Collect__eq,axiom,
% 25.54/25.38 ! [V_Pa_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__empty,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_image__vimage__subset,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_surj__image__vimage__eq,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => 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 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__empty,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__empty__iff,axiom,
% 25.54/25.38 ! [V_r_2,T_c,T_b] :
% 25.54/25.38 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__mono,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Un__eq,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__Domain,axiom,
% 25.54/25.38 ! [V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fst__eq__Domain,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Union,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__singleton__eq,axiom,
% 25.54/25.38 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( 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))))))
% 25.54/25.38 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__insert,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__vimageD,axiom,
% 25.54/25.38 ! [V_F_2,V_h_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__subsetD,axiom,
% 25.54/25.38 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_image__vimage__eq,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__vimageI,axiom,
% 25.54/25.38 ! [V_h_2,T_c,V_F_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__vimage__image__eq,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => 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 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__const,axiom,
% 25.54/25.38 ! [T_c,V_A_2,V_ca_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__eq__UN,axiom,
% 25.54/25.38 ! [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))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__iff,axiom,
% 25.54/25.38 ! [V_r_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 25.54/25.38 <=> ? [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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__insert,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 25.54/25.38 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__acyclic__wf,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 25.54/25.38 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.38 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Int__subset,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__subsetI,axiom,
% 25.54/25.38 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Diff__subset,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Field__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__if,axiom,
% 25.54/25.38 ! [V_B_2,T_c,V_d_2,V_A_2,V_ca_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.54/25.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_ca_2),V_A_2))
% 25.54/25.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 25.54/25.38 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Union,axiom,
% 25.54/25.38 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Collect__split,axiom,
% 25.54/25.38 ! [V_Pa_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_Pa_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_DomainP__Domain__eq,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Owf_H__def,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 25.54/25.38 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.38 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 25.54/25.38 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_DomainE,axiom,
% 25.54/25.38 ! [V_r_2,T_c,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 25.54/25.38 => ~ ! [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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_DomainP_Ointros,axiom,
% 25.54/25.38 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 25.54/25.38 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_DomainP_Oequations,axiom,
% 25.54/25.38 ! [V_a1_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 25.54/25.38 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_image__split__eq__Sigma,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Rep__Integ__cases,axiom,
% 25.54/25.38 ! [V_y_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 25.54/25.38 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Rep__Integ__induct,axiom,
% 25.54/25.38 ! [V_Pa_2,V_y_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 25.54/25.38 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SigmaI,axiom,
% 25.54/25.38 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Union,axiom,
% 25.54/25.38 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__eq__cancel2,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 25.54/25.38 => ( 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))
% 25.54/25.38 <=> V_A_2 = V_B_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__empty1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_card__cartesian__product,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__cartesian__product,axiom,
% 25.54/25.38 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__empty2,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__empty,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Compl__Times__UNIV2,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Compl__Times__UNIV1,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod__cartesian__product,axiom,
% 25.54/25.38 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_b)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Un__distrib1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__Un__distrib1,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Un__distrib2,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__comp__subset__Sigma,axiom,
% 25.54/25.38 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => 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)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_swap__product,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__cartesian__product,axiom,
% 25.54/25.38 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.54/25.38 => 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)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_equiv__type,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Int__distrib2,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__Int__distrib1,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Int__distrib1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Id__on__subset__Times,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Diff__distrib2,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__Diff__distrib1,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__Diff__distrib1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_UNIV__Times__UNIV,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_mem__Sigma__iff,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SigmaD1,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SigmaD2,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SigmaE2,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_card__cartesian__product__singleton,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Times__subset__cancel2,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__subset,axiom,
% 25.54/25.38 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__cartesian__productD1,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__cartesian__productD2,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_c,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Collect__split,axiom,
% 25.54/25.38 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SetCompr__Sigma__eq,axiom,
% 25.54/25.38 ! [V_Qa_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Qa_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fst__image__times,axiom,
% 25.54/25.38 ! [V_A_2,T_c,T_b,V_B_2] :
% 25.54/25.38 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => 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)) )
% 25.54/25.38 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => 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 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snd__image__times,axiom,
% 25.54/25.38 ! [V_B_2,T_c,T_b,V_A_2] :
% 25.54/25.38 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => 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)) )
% 25.54/25.38 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => 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 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insert__times__insert,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__equiv__class,axiom,
% 25.54/25.38 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_UN__Times__distrib,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__def,axiom,
% 25.54/25.38 ! [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))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__quotient,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Rings_Osemiring__0(T_d)
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => 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))))))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 25.54/25.38 ! [V_A_2,V_I_2,T_c,T_b] :
% 25.54/25.38 ? [B_f] :
% 25.54/25.38 ( 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))
% 25.54/25.38 & 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fold__image__Sigma,axiom,
% 25.54/25.38 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_image__id,axiom,
% 25.54/25.38 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__id,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__id,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apfst__id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apsnd__id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_id__apply,axiom,
% 25.54/25.38 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 25.54/25.38
% 25.54/25.38 fof(fact_id__def,axiom,
% 25.54/25.38 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_of__int__eq__id,axiom,
% 25.54/25.38 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_surj__id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_split__Pair,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__reindex__id,axiom,
% 25.54/25.38 ! [V_B_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod__reindex__id,axiom,
% 25.54/25.38 ! [V_B_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod__Sigma,axiom,
% 25.54/25.38 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__Sigma,axiom,
% 25.54/25.38 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_d)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_card__SigmaI,axiom,
% 25.54/25.38 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__SigmaI,axiom,
% 25.54/25.38 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SigmaE,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_ca_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 25.54/25.38 => ~ ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 25.54/25.38 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__surj,axiom,
% 25.54/25.38 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__imageI,axiom,
% 25.54/25.38 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fst__map__pair,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snd__prod__fun,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__simp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__ident,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair_Oidentity,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apfst__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apsnd__def,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair_Oid,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__surj__on,axiom,
% 25.54/25.38 ! [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] :
% 25.54/25.38 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 25.54/25.38 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__map__pair__image,axiom,
% 25.54/25.38 ! [V_f_2,T_c,V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__inj__on,axiom,
% 25.54/25.38 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_prod__fun__imageE,axiom,
% 25.54/25.38 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_ca_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 25.54/25.38 => ~ ! [B_x,B_y] :
% 25.54/25.38 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 25.54/25.38 => ~ 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__def,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 <=> ( 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))))
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__INTER,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 25.54/25.38 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 => ( ! [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 25.54/25.38 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 25.54/25.38 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__Id__on,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__empty,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__Un,axiom,
% 25.54/25.38 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__Int,axiom,
% 25.54/25.38 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__onD2,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__onD1,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__onD,axiom,
% 25.54/25.38 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_reflp__def,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Predicate_Oreflp(T_b,V_r_2)
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__onI,axiom,
% 25.54/25.38 ! [V_A_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 25.54/25.38 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pigeonhole__infinite,axiom,
% 25.54/25.38 ! [V_f_2,T_c,V_A_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.54/25.38 => ? [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 & ~ 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)))))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_reflpE,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Predicate_Oreflp(T_b,V_r_2)
% 25.54/25.38 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__def_H,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 <=> ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(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)) )
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Abs__Integ__induct,axiom,
% 25.54/25.38 ! [V_x_2,V_Pa_2] :
% 25.54/25.38 ( ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Abs__Integ__cases,axiom,
% 25.54/25.38 ! [V_x_2] :
% 25.54/25.38 ~ ! [B_y] :
% 25.54/25.38 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_INFI__bool__eq,axiom,
% 25.54/25.38 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_ball__empty,axiom,
% 25.54/25.38 ! [V_Pa_2,T_b,B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Powp__def,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 25.54/25.38 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Collect__ball__eq,axiom,
% 25.54/25.38 ! [V_Pa_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_Pa_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_Pa_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_congruent__def,axiom,
% 25.54/25.38 ! [V_f_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_INTER__def,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Inf__Sup,axiom,
% 25.54/25.38 ! [V_A_2,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sup__Inf,axiom,
% 25.54/25.38 ! [V_A_2,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__UN__I,axiom,
% 25.54/25.38 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ! [B_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__diff__nat,axiom,
% 25.54/25.38 ! [V_k_2,V_N_2] :
% 25.54/25.38 ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfP__SUP,axiom,
% 25.54/25.38 ! [T_b,V_r_2,T_c] :
% 25.54/25.38 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 25.54/25.38 => ( ! [B_i,B_j] :
% 25.54/25.38 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 25.54/25.38 => 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)) )
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Inter__eq,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_mem__splitI2,axiom,
% 25.54/25.38 ! [V_ca_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 25.54/25.38 ( ! [B_a,B_b] :
% 25.54/25.38 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_mem__splitE,axiom,
% 25.54/25.38 ! [V_p_2,V_ca_2,T_d,T_c,V_z_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_ca_2),V_p_2)))
% 25.54/25.38 => ~ ! [B_x,B_y] :
% 25.54/25.38 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__Times,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair_Ocomp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair__compose,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__pair_Ocompositionality,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__surj,axiom,
% 25.54/25.38 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_image__compose,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__inj__on__iff,axiom,
% 25.54/25.38 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( 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))
% 25.54/25.38 <=> 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__inj__on,axiom,
% 25.54/25.38 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__imageI,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 25.54/25.38 ( 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)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__imageI2,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 25.54/25.38 ( 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)
% 25.54/25.38 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__comp,axiom,
% 25.54/25.38 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_K__record__comp,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,V_ca_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.54/25.38 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__eq__elim,axiom,
% 25.54/25.38 ! [V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 25.54/25.38 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 25.54/25.38 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__eq__dest,axiom,
% 25.54/25.38 ! [V_v_2,V_d_2,V_ca_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 25.54/25.38 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_ca_2),V_d_2)
% 25.54/25.38 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__apply,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__assoc,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__eq__dest__lhs,axiom,
% 25.54/25.38 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 25.54/25.38 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_ca_2
% 25.54/25.38 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__cong,axiom,
% 25.54/25.38 ! [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] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fun__upd__comp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apsnd__compose,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_apfst__compose,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_vimage__compose,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__id,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_id__o,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_o__eq__id__dest,axiom,
% 25.54/25.38 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 25.54/25.38 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_ca_2)
% 25.54/25.38 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__reindex,axiom,
% 25.54/25.38 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_d)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod__reindex,axiom,
% 25.54/25.38 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod__reindex__cong,axiom,
% 25.54/25.38 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 25.54/25.38 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 25.54/25.38 => 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) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum_Oreindex,axiom,
% 25.54/25.38 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setprod_Oreindex,axiom,
% 25.54/25.38 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_the__inv__into__comp,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fold__image__reindex,axiom,
% 25.54/25.38 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Oab__semigroup__mult(T_d)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Oremove,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__image_Oreindex,axiom,
% 25.54/25.38 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.54/25.38 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ounion,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fst__comp__map__pair,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_UN__o,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__left__comp,axiom,
% 25.54/25.38 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__comp,axiom,
% 25.54/25.38 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 25.54/25.38 ! [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] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snd__comp__map__pair,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__image_Odistrib,axiom,
% 25.54/25.38 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_split__comp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 25.54/25.38 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 25.54/25.38 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ocommute__comp_H,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Oempty,axiom,
% 25.54/25.38 ! [V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Oeq__fold,axiom,
% 25.54/25.38 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__image_Oeq__fold,axiom,
% 25.54/25.38 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Oinsert,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Ounion__inter,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding_Oinsert__remove,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__reindex__nonzero,axiom,
% 25.54/25.38 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_d)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.54/25.38 => ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 25.54/25.38 => ( B_x != B_y
% 25.54/25.38 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 25.54/25.38 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Ounion__idem,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.38 => 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)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 25.54/25.38 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Oidem__comp,axiom,
% 25.54/25.38 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_folding__idem_Oinsert__idem,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_strong__setprod__reindex__cong,axiom,
% 25.54/25.38 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => 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) )
% 25.54/25.38 => 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) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Eps__split,axiom,
% 25.54/25.38 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_Pa_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wfI__pf,axiom,
% 25.54/25.38 ! [V_R_2,T_b] :
% 25.54/25.38 ( ! [B_A] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 25.54/25.38 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tfl__some,axiom,
% 25.54/25.38 ! [T_b,B_P] :
% 25.54/25.38 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 25.54/25.38 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_someI,axiom,
% 25.54/25.38 ! [T_b,V_x_2,V_Pa_2] :
% 25.54/25.38 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_some__sym__eq__trivial,axiom,
% 25.54/25.38 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_some__eq__trivial,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_some__eq__ex,axiom,
% 25.54/25.38 ! [T_b,V_Pa_2] :
% 25.54/25.38 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 25.54/25.38 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_someI__ex,axiom,
% 25.54/25.38 ! [T_b,V_Pa_2] :
% 25.54/25.38 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_exE__some,axiom,
% 25.54/25.38 ! [T_b,V_ca_2,V_Pa_2] :
% 25.54/25.38 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.54/25.38 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,V_ca_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_split__paired__Eps,axiom,
% 25.54/25.38 ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Eps__split__eq,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sigma__mono,axiom,
% 25.54/25.38 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => 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))) )
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_not__acc__down,axiom,
% 25.54/25.38 ! [V_R_2,V_x_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 25.54/25.38 => ~ ! [B_z] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acc_OaccI,axiom,
% 25.54/25.38 ! [V_r_2,V_x_2,T_b] :
% 25.54/25.38 ( ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_max__ext_Osimps,axiom,
% 25.54/25.38 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 25.54/25.38 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 25.54/25.38 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 25.54/25.38 => ? [B_xa] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__no__infinite__down__chainE,axiom,
% 25.54/25.38 ! [V_f_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 => ~ ! [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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_iterate_Osimps,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 25.54/25.38 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__reindex__cong,axiom,
% 25.54/25.38 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_d)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.38 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 25.54/25.38 => ( ! [B_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 25.54/25.38 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 25.54/25.38 => 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) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_scomp__apply,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Pair__scomp,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_scomp__scomp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_scomp__Pair,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_scomp__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_scomp__unfold,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__eq,axiom,
% 25.54/25.38 ! [V_n_2,V_m_2] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__eq__minimal,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 <=> ! [B_Q] :
% 25.54/25.38 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 25.54/25.38 => ? [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 25.54/25.38 & ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__trancl,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__than__def,axiom,
% 25.54/25.38 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acyclic__def,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.38 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl_Or__into__trancl,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__subset__Field2,axiom,
% 25.54/25.38 ! [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))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_r__into__trancl_H,axiom,
% 25.54/25.38 ! [V_r_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__empty,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__domain,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__range,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__trancl,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_r__r__into__trancl,axiom,
% 25.54/25.38 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_R_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__into__trancl2,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__trans,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__mono,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__unfold,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__subset__Sigma,axiom,
% 25.54/25.38 ! [V_A_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__Int__subset,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__insert,axiom,
% 25.54/25.38 ! [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)))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_reflcl__set__eq,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_r__into__rtrancl,axiom,
% 25.54/25.38 ! [V_r_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_IdI,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__into__rtrancl,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__rtrancl__absorb,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__trancl__absorb,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_reflcl__trancl,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__reflcl,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__unfold__right,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__unfold__left,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__r__diff__Id,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__Int__subset,axiom,
% 25.54/25.38 ! [V_r_2,V_s_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_r__comp__rtrancl__eq,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__idemp__self__comp,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__unfold,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__Un__subset,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__reflcl,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__Un__rtrancl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__reflcl__absorb,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__subset__rtrancl,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__subset,axiom,
% 25.54/25.38 ! [V_S_2,V_R_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__mono,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__closed__trancl,axiom,
% 25.54/25.38 ! [V_X_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__rtrancl__UnI,axiom,
% 25.54/25.38 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__trans,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__idemp,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__empty,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__rtrancl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__rtrancl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__rtrancl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__Id,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Id__O__R,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_R__O__Id,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pair__in__Id__conv,axiom,
% 25.54/25.38 ! [V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 25.54/25.38 <=> V_a_2 = V_b_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__eq__or__trancl,axiom,
% 25.54/25.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 <=> ( V_x_2 = V_y_2
% 25.54/25.38 | ( V_x_2 != V_y_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__into__trancl2,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtranclD,axiom,
% 25.54/25.38 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 => ( V_a_2 = V_b_2
% 25.54/25.38 | ( V_a_2 != V_b_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__into__trancl1,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__rtrancl__trancl,axiom,
% 25.54/25.38 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__trancl__trancl,axiom,
% 25.54/25.38 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__Id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__Id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__Id,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pair__leq__def,axiom,
% 25.54/25.38 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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Not__Domain__rtrancl,axiom,
% 25.54/25.38 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 <=> V_x_2 = V_y_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acc__downwards__aux,axiom,
% 25.54/25.38 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acc__downwards,axiom,
% 25.54/25.38 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__insert,axiom,
% 25.54/25.38 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 25.54/25.38 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acyclic__insert,axiom,
% 25.54/25.38 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.38 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__reflcl,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Id__def,axiom,
% 25.54/25.38 ! [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))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_irrefl__diff__Id,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pred__nat__trancl__eq__le,axiom,
% 25.54/25.38 ! [V_n_2,V_m_2] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__subset__Sigma__aux,axiom,
% 25.54/25.38 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => ( V_a_2 = V_b_2
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_irrefl__tranclI,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sequence__trans,axiom,
% 25.54/25.38 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 25.54/25.38 ( ! [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)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__converse,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__Id,axiom,
% 25.54/25.38 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__INTER,axiom,
% 25.54/25.38 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__UNION,axiom,
% 25.54/25.38 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__iff,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converseI,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converseD,axiom,
% 25.54/25.38 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__rel__comp,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__Un,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Field__converse,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__inv__image,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__converse,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__Int,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__converse,axiom,
% 25.54/25.38 ! [V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 25.54/25.38 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__Id__on,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acyclic__converse,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.38 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__converse,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.38 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__converse,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__converse__trancl,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.38 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_equiv__comp__eq,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.54/25.38 => 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 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__converse,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Domain__converse,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Range__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__converseD,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__converseI,axiom,
% 25.54/25.38 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__converseD,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__converseI,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__subset__eq,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 <=> 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))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_refl__on__comp__subset,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__equivI,axiom,
% 25.54/25.38 ! [V_A_2,V_r_2,T_b] :
% 25.54/25.38 ( 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
% 25.54/25.38 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 25.54/25.38 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__acyclic__wf__converse,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 25.54/25.38 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.38 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converse__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__INT__eq,axiom,
% 25.54/25.38 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 25.54/25.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 25.54/25.38 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_total__on__diff__Id,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__Id,axiom,
% 25.54/25.38 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__rel__comp,axiom,
% 25.54/25.38 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 25.54/25.38 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 25.54/25.38 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__subset,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 25.54/25.38 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__Id__on,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_total__on__empty,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_total__on__converse,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.38 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valuedD,axiom,
% 25.54/25.38 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
% 25.54/25.38 => V_y_2 = V_z_2 ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__def,axiom,
% 25.54/25.38 ! [V_r_2,T_c,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 25.54/25.38 <=> ! [B_x,B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 25.54/25.38 => ! [B_z] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 25.54/25.38 => B_y = B_z ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_total__on__def,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.38 => ! [B_xa] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 25.54/25.38 => ( B_x != B_xa
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__confluent,axiom,
% 25.54/25.38 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Image__Int__eq,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 25.54/25.38 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 25.54/25.38 ! [V_R_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_acyclicI,axiom,
% 25.54/25.38 ! [V_r_2,T_b] :
% 25.54/25.38 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 25.54/25.38 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_single__valued__rel__pow,axiom,
% 25.54/25.38 ! [V_n_2,V_R_2,T_b] :
% 25.54/25.38 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 25.54/25.38 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow__swap1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow__mult,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_wf__exp,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,T_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_comp__funpow,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__1,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__commute,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__power,axiom,
% 25.54/25.38 ! [V_R_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 <=> ? [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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__imp__rtrancl,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_relpow_Osimps_I2_J,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__add,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_relpow_Osimps_I1_J,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__0__E,axiom,
% 25.54/25.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),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)))
% 25.54/25.38 => V_x_2 = V_y_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__0__I,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__Suc__I2,axiom,
% 25.54/25.38 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__Suc__I,axiom,
% 25.54/25.38 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow__add,axiom,
% 25.54/25.38 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_trancl__power,axiom,
% 25.54/25.38 ! [V_R_2,V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 25.54/25.38 <=> ? [B_n] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 25.54/25.38 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_funpow__code__def,axiom,
% 25.54/25.38 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__E2,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => V_x_2 != V_z_2 )
% 25.54/25.38 => ~ ! [B_y,B_m] :
% 25.54/25.38 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__E,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => V_x_2 != V_z_2 )
% 25.54/25.38 => ~ ! [B_y,B_m] :
% 25.54/25.38 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__Un__separatorE,axiom,
% 25.54/25.38 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 25.54/25.38 => ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Qa_2))
% 25.54/25.38 => B_x = B_y ) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 25.54/25.38 ! [V_Qa_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_Pa_2),V_Qa_2))))
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2)))
% 25.54/25.38 => ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Qa_2))
% 25.54/25.38 => B_y = B_x ) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_Pa_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__Suc__D2,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 25.54/25.38 => ? [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__Suc__E,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 25.54/25.38 => ~ ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__pow__Suc__E2,axiom,
% 25.54/25.38 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 25.54/25.38 => ~ ! [B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tranclD,axiom,
% 25.54/25.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 25.54/25.38 => ? [B_z] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tranclD2,axiom,
% 25.54/25.38 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 25.54/25.38 => ? [B_z] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_IdE,axiom,
% 25.54/25.38 ! [V_p_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 25.54/25.38 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_transfer__nat__int__set__cong,axiom,
% 25.54/25.38 ! [V_P_H_2,V_Pa_2] :
% 25.54/25.38 ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 25.54/25.38 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.38 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 25.54/25.38 => hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_Pa_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_converseE,axiom,
% 25.54/25.38 ! [V_r_2,V_yx_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 25.54/25.38 => ~ ! [B_x,B_y] :
% 25.54/25.38 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rel__compE,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 25.54/25.38 => ~ ! [B_x,B_y,B_z] :
% 25.54/25.38 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_internal__split__def,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_internal__split__conv,axiom,
% 25.54/25.38 ! [V_b_2,V_a_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oof__frac__def,axiom,
% 25.54/25.38 ! [V_q,T_a,T_b] :
% 25.54/25.38 ( ( class_Rings_Oinverse(T_b)
% 25.54/25.38 & class_Rings_Oring__1(T_b) )
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oless__frac__def,axiom,
% 25.54/25.38 ! [V_r_2,V_q_2,T_b] :
% 25.54/25.38 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 25.54/25.38 ! [V_r_2,V_q_2,T_b] :
% 25.54/25.38 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Odenom__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Onum__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_bool_Osize_I2_J,axiom,
% 25.54/25.38 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_bool_Osize_I1_J,axiom,
% 25.54/25.38 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__less__ub,axiom,
% 25.54/25.38 ! [V_u_2,V_f_2] :
% 25.54/25.38 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lenlex__def,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexn__length,axiom,
% 25.54/25.38 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 25.54/25.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 25.54/25.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_neq__if__length__neq,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_a] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
% 25.54/25.38 => V_xs != V_ys ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lenlex__conv,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__sublist,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexn_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_impossible__Cons,axiom,
% 25.54/25.38 ! [V_x,V_ys,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
% 25.54/25.38 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_not__Cons__self,axiom,
% 25.54/25.38 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_not__Cons__self2,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Oinject,axiom,
% 25.54/25.38 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 25.54/25.38 <=> ( V_a_2 = V_a_H_2
% 25.54/25.38 & V_list_2 = V_list_H_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osize_I4_J,axiom,
% 25.54/25.38 ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__in__lex,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 25.54/25.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 25.54/25.38 | ( V_x_2 = V_y_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__Cons__def,axiom,
% 25.54/25.38 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pick_Osimps,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_i] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 25.54/25.38 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
% 25.54/25.38 => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select__weight__cons__zero,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__cons__cons,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 | ( V_a_2 = V_b_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__lex,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 & 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osize_I2_J,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__acc__listrel1I,axiom,
% 25.54/25.38 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 25.54/25.38 => ( 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))))
% 25.54/25.38 => 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)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__mono,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__converse,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1I2,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__eq__len,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__listrel1__converse,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__listrel1__Cons,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 & V_xs_2 = V_ys_2 )
% 25.54/25.38 | ( V_x_2 = V_y_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1I1,axiom,
% 25.54/25.38 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Cons,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__linear,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( ! [B_a,B_b] :
% 25.54/25.38 ( 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))
% 25.54/25.38 | B_a = B_b
% 25.54/25.38 | 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)) )
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 | V_x_2 = V_y_2
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__rtrancl__refl,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__mono,axiom,
% 25.54/25.38 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__eq__len,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__rtrancl__trans,axiom,
% 25.54/25.38 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__subset__listrel,axiom,
% 25.54/25.38 ! [V_r_H_2,V_r_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 25.54/25.38 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel_OCons,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrelp__listrel__eq,axiom,
% 25.54/25.38 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 25.54/25.38 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Cons1,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => ~ ! [B_y,B_ys] :
% 25.54/25.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrelp_OCons,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 25.54/25.38 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 25.54/25.38 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrelp_Oequations_I2_J,axiom,
% 25.54/25.38 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 25.54/25.38 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 25.54/25.38 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Cons2,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => ~ ! [B_x,B_xs] :
% 25.54/25.38 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__subset,axiom,
% 25.54/25.38 ! [V_A_2,V_r_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),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))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__UNIV,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__mono,axiom,
% 25.54/25.38 ! [V_B_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_equiv__listrel,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__refl__on,axiom,
% 25.54/25.38 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.38 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__in__lists__iff,axiom,
% 25.54/25.38 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__accD,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__accI,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => 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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__iff__nth,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 25.54/25.38 & ! [B_n] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__irreflexive,axiom,
% 25.54/25.38 ! [V_y_2,V_r_2,T_b] :
% 25.54/25.38 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_infinite__UNIV__listI,axiom,
% 25.54/25.38 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__eq__iff__nth__eq,axiom,
% 25.54/25.38 ! [T_b,V_ys_2,V_xs_2] :
% 25.54/25.38 ( V_xs_2 = V_ys_2
% 25.54/25.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 25.54/25.38 & ! [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__Cons__Suc,axiom,
% 25.54/25.38 ! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__Cons__0,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth_Osimps,axiom,
% 25.54/25.38 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__Cons_H,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_n] :
% 25.54/25.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 25.54/25.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__Cons__number__of,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_v] :
% 25.54/25.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = V_x )
% 25.54/25.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__take__index__conv,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 <=> ( ( 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)))
% 25.54/25.38 & 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 )
% 25.54/25.38 | ? [B_i] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__sublist,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__set,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__subset__Cons,axiom,
% 25.54/25.38 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__all,axiom,
% 25.54/25.38 ! [V_n,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 25.54/25.38 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__take__subset__set__take,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__take__subset,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__sublist__subset,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__take,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Suc__Cons,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__ConsD,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 25.54/25.38 => ( V_y_2 = V_x_2
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__sublistD,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__takeD,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_notin__set__sublistI,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__take,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__take,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__upt__eq__take,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_card__length,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_all__set__conv__all__nth,axiom,
% 25.54/25.38 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.38 ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.38 <=> ! [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__size__estimation,axiom,
% 25.54/25.38 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__size__estimation_H,axiom,
% 25.54/25.38 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__lists__conv__set,axiom,
% 25.54/25.38 ! [V_A_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__pos__if__in__set,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__conv__nth,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 <=> ? [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__mem,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__eq__set,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__conv__nth,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__lists__length__eq,axiom,
% 25.54/25.38 ! [V_n_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_finite__lists__length__le,axiom,
% 25.54/25.38 ! [V_n_2,V_A_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__iff__zip,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__zip,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__zip,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__zip,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(T_a,T_b))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__Cons__Cons,axiom,
% 25.54/25.38 ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__eq__iff__zip__eq,axiom,
% 25.54/25.38 ! [T_b,V_ys_2,V_xs_2] :
% 25.54/25.38 ( V_xs_2 = V_ys_2
% 25.54/25.38 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__zipE,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 25.54/25.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__zip__rightD,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__zip__leftD,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__same,axiom,
% 25.54/25.38 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 & V_a_2 = V_b_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__zip,axiom,
% 25.54/25.38 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_greaterThanLessThan__upto,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__setsum__nth,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 25.54/25.38 ! [V_ns_2] :
% 25.54/25.38 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 25.54/25.38 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_atLeastAtMost__upto,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__upto,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_elem__le__listsum__nat,axiom,
% 25.54/25.38 ! [V_ns,V_k] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__simps_I2_J,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_a)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_atLeastLessThan__upto,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_j_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_greaterThanAtMost__upto,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__list__def,axiom,
% 25.54/25.38 ! [V_l_2] :
% 25.54/25.38 ( c_List_Onat__list(V_l_2)
% 25.54/25.38 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__size__pointwise,axiom,
% 25.54/25.38 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 25.54/25.38 ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__update__nat,axiom,
% 25.54/25.38 ! [V_n,V_ns,V_k] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__take,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__beyond,axiom,
% 25.54/25.38 ! [V_x,V_i,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
% 25.54/25.38 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__list__update__neq,axiom,
% 25.54/25.38 ! [V_x,V_xs,T_a,V_j,V_i] :
% 25.54/25.38 ( V_i != V_j
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__id,axiom,
% 25.54/25.38 ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__list__update,axiom,
% 25.54/25.38 ! [V_x,V_xs,T_a,V_k] :
% 25.54/25.38 ( ( 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))
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( 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))
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__list__update,axiom,
% 25.54/25.38 ! [V_x,V_i,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__update,axiom,
% 25.54/25.38 ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_update__zip,axiom,
% 25.54/25.38 ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__overwrite,axiom,
% 25.54/25.38 ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__swap,axiom,
% 25.54/25.38 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 25.54/25.38 ( V_i != V_i_H
% 25.54/25.38 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__code_I3_J,axiom,
% 25.54/25.38 ! [V_y,V_i,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_i)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__code_I2_J,axiom,
% 25.54/25.38 ! [V_y,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_y) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__butlastD,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__update__subsetI,axiom,
% 25.54/25.38 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__update__subset__insert,axiom,
% 25.54/25.38 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__list__update__eq,axiom,
% 25.54/25.38 ! [V_x,V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__same__conv,axiom,
% 25.54/25.38 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 25.54/25.38 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__list__update,axiom,
% 25.54/25.38 ! [V_x,V_j,V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => ( ( V_i = V_j
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x )
% 25.54/25.38 & ( V_i != V_j
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__butlast,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__butlast,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__update__memI,axiom,
% 25.54/25.38 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__conv__take,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1__iff__update,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 <=> ? [B_y,B_n] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__list__update,axiom,
% 25.54/25.38 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__upto,axiom,
% 25.54/25.38 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__take,axiom,
% 25.54/25.38 ! [V_i,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__sublistI,axiom,
% 25.54/25.38 ! [V_I_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__zipI1,axiom,
% 25.54/25.38 ! [V_ys,T_b,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__zipI2,axiom,
% 25.54/25.38 ! [V_xs,T_b,V_ys,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 25.54/25.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__card,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_card__distinct,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__eq__iff__index__eq,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 25.54/25.38 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__conv__nth,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 <=> ! [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => ! [B_j] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => ( B_i != B_j
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Ocard_H__def,axiom,
% 25.54/25.38 ! [V_A_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__take__lemma,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_a,V_k] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => ( ! [B_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 25.54/25.38 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__remove1__eq,axiom,
% 25.54/25.38 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Cons__number__of,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_v] :
% 25.54/25.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists_ONil,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Nil2,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Nil1,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 25.54/25.38 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__butlast,axiom,
% 25.54/25.38 ! [T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__remove1,axiom,
% 25.54/25.38 ! [V_x,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct_Osimps_I1_J,axiom,
% 25.54/25.38 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast_Osimps_I1_J,axiom,
% 25.54/25.38 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_x,T_a,V_xs] :
% 25.54/25.38 ( ( V_xs = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 25.54/25.38 & ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_list_H,V_a_H,T_a] : c_List_Olist_ONil(T_a) != hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osimps_I3_J,axiom,
% 25.54/25.38 ! [V_list_H,V_a_H,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_a_H),V_list_H) != c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_y,V_x] :
% 25.54/25.38 ( ( V_x = V_y
% 25.54/25.38 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 25.54/25.38 & ( V_x != V_y
% 25.54/25.38 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upto__empty,axiom,
% 25.54/25.38 ! [V_i,V_j] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 25.54/25.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Nil,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__eq__Nil,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__0,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__nil,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1__commute,axiom,
% 25.54/25.38 ! [V_zs,V_y,V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Oremove1(T_a,V_y,V_zs)) = c_List_Oremove1(T_a,V_y,c_List_Oremove1(T_a,V_x,V_zs)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrelp_Oequations_I1_J,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrelp_ONil,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__Nil,axiom,
% 25.54/25.38 ! [V_ys,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Olist_ONil(T_a)),V_ys) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(tc_prod(T_a,T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__simps_I1_J,axiom,
% 25.54/25.38 ! [T_a] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_a)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__0__conv,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osize_I3_J,axiom,
% 25.54/25.38 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 25.54/25.38 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__empty2,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__empty,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osize_I1_J,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__code_I1_J,axiom,
% 25.54/25.38 ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__nonempty,axiom,
% 25.54/25.38 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__remove1,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 25.54/25.38 ( V_a_2 != V_b_2
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_notin__set__remove1,axiom,
% 25.54/25.38 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1__idem,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__empty,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__remove1__subset,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__greater__0__conv,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__1__Cons,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_not__listrel1__Nil,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_not__Nil__listrel1,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel_ONil,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__Nil__right,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nil2__notin__lex,axiom,
% 25.54/25.38 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nil__notin__lex,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Cons,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upto_Osimps,axiom,
% 25.54/25.38 ! [V_j,V_i] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 25.54/25.38 => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 25.54/25.38 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__singleton,axiom,
% 25.54/25.38 ! [V_x_2,T_b,V_A_2] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 25.54/25.38 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 25.54/25.38 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists__empty,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Cons_H,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_n] :
% 25.54/25.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upto__rec__number__of,axiom,
% 25.54/25.38 ! [V_n,V_m] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 25.54/25.38 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
% 25.54/25.38 => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel__Nil,axiom,
% 25.54/25.38 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__Cons__sing__Nil,axiom,
% 25.54/25.38 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__remove1,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upto_Opsimps,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2] :
% 25.54/25.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
% 25.54/25.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 25.54/25.38 => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 25.54/25.38 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select,axiom,
% 25.54/25.38 ! [V_s_2,T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listset_Osimps_I1_J,axiom,
% 25.54/25.38 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__Cons1,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osimps_I5_J,axiom,
% 25.54/25.38 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list_Osimps_I4_J,axiom,
% 25.54/25.38 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listset_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__Cons,axiom,
% 25.54/25.38 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sorted__list__of__set__remove,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upto_Opinduct,axiom,
% 25.54/25.38 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.54/25.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2)))
% 25.54/25.38 => ( ! [B_i,B_j] :
% 25.54/25.38 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_i),B_j)))
% 25.54/25.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 25.54/25.38 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint))),B_j)) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sorted__list__of__set__empty,axiom,
% 25.54/25.38 ! [T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_anamorph_Osimps,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 25.54/25.38 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__Cons,axiom,
% 25.54/25.38 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__eq__Cons__conv,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 25.54/25.38 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 25.54/25.38 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 25.54/25.38 | ? [B_ys_H] :
% 25.54/25.38 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 25.54/25.38 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__eq__append__conv,axiom,
% 25.54/25.38 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 25.54/25.38 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 25.54/25.38 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 25.54/25.38 | ? [B_ys_H] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 25.54/25.38 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append1__eq__conv,axiom,
% 25.54/25.38 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 25.54/25.38 <=> ( V_xs_2 = V_ys_2
% 25.54/25.38 & V_x_2 = V_y_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__Cons,axiom,
% 25.54/25.38 ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Cons__eq__appendI,axiom,
% 25.54/25.38 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 25.54/25.38 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 25.54/25.38 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__in__lists__conv,axiom,
% 25.54/25.38 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__eq__appendI,axiom,
% 25.54/25.38 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 25.54/25.38 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 25.54/25.38 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__same__eq,axiom,
% 25.54/25.38 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 25.54/25.38 <=> V_ys_2 = V_zs_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_same__append__eq,axiom,
% 25.54/25.38 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 25.54/25.38 <=> V_ys_2 = V_zs_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__eq__append__conv2,axiom,
% 25.54/25.38 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_ts_2)
% 25.54/25.38 <=> ? [B_us] :
% 25.54/25.38 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 25.54/25.38 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 25.54/25.38 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 25.54/25.38 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__assoc,axiom,
% 25.54/25.38 ! [V_zs,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__append,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_a] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_a)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_ys)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__append,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__append,axiom,
% 25.54/25.38 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
% 25.54/25.38 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
% 25.54/25.38 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__append,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__Nil,axiom,
% 25.54/25.38 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nil__is__append__conv,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 25.54/25.38 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 25.54/25.38 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__Nil2,axiom,
% 25.54/25.38 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 25.54/25.38
% 25.54/25.38 fof(fact_self__append__conv,axiom,
% 25.54/25.38 ! [V_ys_2,T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 25.54/25.38 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_self__append__conv2,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_ys_2] :
% 25.54/25.38 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__is__Nil__conv,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 25.54/25.38 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__self__conv,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 25.54/25.38 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__self__conv2,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_eq__Nil__appendI,axiom,
% 25.54/25.38 ! [T_a,V_ys,V_xs] :
% 25.54/25.38 ( V_xs = V_ys
% 25.54/25.38 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__append,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_ys] :
% 25.54/25.38 ( ( V_ys = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 25.54/25.38 & ( V_ys != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__append__length,axiom,
% 25.54/25.38 ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__append__length__plus,axiom,
% 25.54/25.38 ! [V_n,V_ys,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_ys),V_n) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__append,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__append1,axiom,
% 25.54/25.38 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__length,axiom,
% 25.54/25.38 ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1__append,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__butlast__appendI,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 25.54/25.38 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 25.54/25.38 => 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))))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__snoc,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__listrel1I,axiom,
% 25.54/25.38 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 & V_us_2 = V_vs_2 )
% 25.54/25.38 | ( V_xs_2 = V_ys_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__append__leftI,axiom,
% 25.54/25.38 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__append,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 25.54/25.38 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 25.54/25.38 & 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__append,axiom,
% 25.54/25.38 ! [V_ys,V_xs,T_a,V_n] :
% 25.54/25.38 ( ( 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)))
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( ~ 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)))
% 25.54/25.38 => 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))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__update__append,axiom,
% 25.54/25.38 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 25.54/25.38 ( ( 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)))
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( ~ 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)))
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sublist__append,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1I,axiom,
% 25.54/25.38 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => ( 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))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__append__left__rightI,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Suc__conv__app__nth,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_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)))
% 25.54/25.38 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 & V_x_2 = V_y_2 )
% 25.54/25.38 | ( V_xs_2 = V_ys_2
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listrel1E,axiom,
% 25.54/25.38 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 25.54/25.38 => ~ ! [B_x,B_y] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 25.54/25.38 => ! [B_us,B_vs] :
% 25.54/25.38 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 25.54/25.38 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__append__leftD,axiom,
% 25.54/25.38 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_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)))
% 25.54/25.38 => ( ! [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))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate1__def,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_upd__conv__take__nth__drop,axiom,
% 25.54/25.38 ! [V_a,V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__take__drop__id,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__1__Cons,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Suc__Cons,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__via__drop,axiom,
% 25.54/25.38 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__drop,axiom,
% 25.54/25.38 ! [V_i,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct1__rotate,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 25.54/25.38 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_butlast__drop,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__butlast,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__take,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__drop,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__drop,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__0,axiom,
% 25.54/25.38 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__zip,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__rotate1,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__drop,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__rotate1,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_in__set__dropD,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 25.54/25.38 ( 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))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__drop__subset,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Nil,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate1__is__Nil__conv,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__drop__subset__set__drop,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_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)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__eq__Nil,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__all,axiom,
% 25.54/25.38 ! [V_n,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
% 25.54/25.38 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__append,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__eq__conv__conj,axiom,
% 25.54/25.38 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 25.54/25.38 <=> ( 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)
% 25.54/25.38 & 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Cons,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Cons_H,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_n] :
% 25.54/25.38 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__drop,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_i,V_n] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__eq__append__conv__if,axiom,
% 25.54/25.38 ! [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] :
% 25.54/25.38 ( 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)
% 25.54/25.38 <=> ( ( 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)))
% 25.54/25.38 => ( 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)
% 25.54/25.38 & 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) ) )
% 25.54/25.38 & ( ~ 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)))
% 25.54/25.38 => ( 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
% 25.54/25.38 & 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 ) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__drop_H,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__simps,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_b,T_a] :
% 25.54/25.38 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 25.54/25.38 & 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Cons__number__of,axiom,
% 25.54/25.38 ! [V_xs,V_x,T_a,V_v] :
% 25.54/25.38 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__add,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_j,V_i] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate1__length01,axiom,
% 25.54/25.38 ! [V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 25.54/25.38 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__append1,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__append2,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_id__take__nth__drop,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_i] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__hd__drop,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__drop__conv__nth,axiom,
% 25.54/25.38 ! [V_n,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => ( 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)))
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd_Osimps,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__append2,axiom,
% 25.54/25.38 ! [V_ys,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__append,axiom,
% 25.54/25.38 ! [V_ys,T_a,V_xs] :
% 25.54/25.38 ( ( V_xs = c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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) )
% 25.54/25.38 & ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__in__set,axiom,
% 25.54/25.38 ! [T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__conv__nth,axiom,
% 25.54/25.38 ! [T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate1__hd__tl,axiom,
% 25.54/25.38 ! [T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__rotate__conv__nth,axiom,
% 25.54/25.38 ! [V_n,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__tl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl__drop,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl_Osimps_I2_J,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__tl,axiom,
% 25.54/25.38 ! [V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__rotate,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 25.54/25.38 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__rotate,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate0,axiom,
% 25.54/25.38 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__add,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__rotate,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__rotate,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl_Osimps_I1_J,axiom,
% 25.54/25.38 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__is__Nil__conv,axiom,
% 25.54/25.38 ! [V_xs_2,V_n_2,T_b] :
% 25.54/25.38 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate1__rotate__swap,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__def,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl__append2,axiom,
% 25.54/25.38 ! [V_ys,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__tl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__conv__mod,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__Suc,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__Suc,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl__append,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__id,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n] :
% 25.54/25.38 ( 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)
% 25.54/25.38 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__length01,axiom,
% 25.54/25.38 ! [V_n,V_xs,T_a] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 25.54/25.38 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__tl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_tl__take,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__Suc,axiom,
% 25.54/25.38 ! [V_n,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__drop__take,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fold1__set,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 25.54/25.38 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => 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)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sorted__list__of__set__insert,axiom,
% 25.54/25.38 ! [V_x_2,V_A_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__Nil,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__not__Nil,axiom,
% 25.54/25.38 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_remove1__insort,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_start__le__sum,axiom,
% 25.54/25.38 ! [V_ns_2,V_n_2,V_m_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__absorb0,axiom,
% 25.54/25.38 ! [V_zs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__key__left__comm,axiom,
% 25.54/25.38 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__assoc,axiom,
% 25.54/25.38 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Groups_Osemigroup__add(T_b)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__left__comm,axiom,
% 25.54/25.38 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fun__left__comm__insort,axiom,
% 25.54/25.38 ! [T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__insort,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__insort,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__Cons,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__key_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__key_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__append,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__foldl,axiom,
% 25.54/25.38 ! [T_b] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_b)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_sum__eq__0__conv,axiom,
% 25.54/25.38 ! [V_ns_2,V_m_2] :
% 25.54/25.38 ( 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)
% 25.54/25.38 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.38 & ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 25.54/25.38 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__insort,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 25.54/25.38 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 25.54/25.38 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sup__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Inf__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Sup__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Lattices_Olattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Inf__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Lattices_Olattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Min__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Max__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_SUPR__set__fold,axiom,
% 25.54/25.38 ! [V_f_2,V_xs_2,T_c,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_INFI__set__fold,axiom,
% 25.54/25.38 ! [V_f_2,V_xs_2,T_c,T_b] :
% 25.54/25.38 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_elem__le__sum,axiom,
% 25.54/25.38 ! [V_ns_2,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__insert__insort__key,axiom,
% 25.54/25.38 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 25.54/25.38 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__append__rightI,axiom,
% 25.54/25.38 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 25.54/25.38 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__insort__insert,axiom,
% 25.54/25.38 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__insert__triv,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__insort__insert,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__insert__key__triv,axiom,
% 25.54/25.38 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 25.54/25.38 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_insort__insert__insort,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.38 ( class_Orderings_Olinorder(T_b)
% 25.54/25.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lexord__Nil__left,axiom,
% 25.54/25.38 ! [V_r_2,V_y_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.38 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__list__update,axiom,
% 25.54/25.38 ! [V_x,V_k,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => ( ( 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))
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 25.54/25.38 & ( 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))
% 25.54/25.38 => 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) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__ConsL,axiom,
% 25.54/25.38 ! [V_x,T_a,V_xs] :
% 25.54/25.38 ( V_xs = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__ConsR,axiom,
% 25.54/25.38 ! [V_x,T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last_Osimps,axiom,
% 25.54/25.38 ! [V_x,T_a,V_xs] :
% 25.54/25.38 ( ( V_xs = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 25.54/25.38 & ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__appendL,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_ys] :
% 25.54/25.38 ( V_ys = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__appendR,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_ys] :
% 25.54/25.38 ( V_ys != c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__append,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_ys] :
% 25.54/25.38 ( ( V_ys = c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 25.54/25.38 & ( V_ys != c_List_Olist_ONil(T_a)
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__in__set,axiom,
% 25.54/25.38 ! [T_b,V_as_2] :
% 25.54/25.38 ( V_as_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__snoc,axiom,
% 25.54/25.38 ! [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 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__drop,axiom,
% 25.54/25.38 ! [V_xs,T_a,V_n] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_snoc__eq__iff__butlast,axiom,
% 25.54/25.38 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 25.54/25.38 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 25.54/25.38 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_append__butlast__last__id,axiom,
% 25.54/25.38 ! [T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__conv__nth,axiom,
% 25.54/25.38 ! [T_a,V_xs] :
% 25.54/25.38 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.38 => 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_lists_Osimps,axiom,
% 25.54/25.38 ! [V_A_2,V_a_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 25.54/25.38 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 25.54/25.38 | ? [B_a,B_l] :
% 25.54/25.38 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 25.54/25.38 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select__weigth__select,axiom,
% 25.54/25.38 ! [T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__mapI,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_last__map,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__size__map,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__map,axiom,
% 25.54/25.38 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Omap_Ocompositionality,axiom,
% 25.54/25.38 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__comp__map,axiom,
% 25.54/25.38 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Omap_Ocomp,axiom,
% 25.54/25.38 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Omap_Oid,axiom,
% 25.54/25.38 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_List_Omap_Oidentity,axiom,
% 25.54/25.38 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_drop__map,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_hd__map,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b,V_xs_2] :
% 25.54/25.38 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.38 => 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__append,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map_Osimps_I2_J,axiom,
% 25.54/25.38 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_set__map,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__butlast,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_take__map,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__ident,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__map__eq__map,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.38 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 25.54/25.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__injective,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 25.54/25.38 => V_xs_2 = V_ys_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__subtractf,axiom,
% 25.54/25.38 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Oab__group__add(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__addf,axiom,
% 25.54/25.38 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__const__mult,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,V_ca_2,T_c,T_b] :
% 25.54/25.38 ( class_Rings_Osemiring__0(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__mult__const,axiom,
% 25.54/25.38 ! [V_xs_2,V_ca_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( class_Rings_Osemiring__0(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_ca_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__0,axiom,
% 25.54/25.38 ! [V_xs_2,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Omonoid__add(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__eq__imp__length__eq,axiom,
% 25.54/25.38 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 25.54/25.38 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_length__map,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__eq__conv,axiom,
% 25.54/25.38 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 25.54/25.38 <=> ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 25.54/25.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__update,axiom,
% 25.54/25.38 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nil__is__map__conv,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map_Osimps_I1_J,axiom,
% 25.54/25.38 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__is__Nil__conv,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.38 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__same__conv__map,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__map2,axiom,
% 25.54/25.38 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__zip__map2,axiom,
% 25.54/25.38 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__zip__map,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__map1,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__map__map,axiom,
% 25.54/25.38 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__tl,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_rotate__map,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_foldl__map,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__map__eq__map,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 25.54/25.38 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 25.54/25.38 <=> V_xs_2 = V_ys_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__inj__on,axiom,
% 25.54/25.38 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.38 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 25.54/25.38 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 25.54/25.38 => V_xs_2 = V_ys_2 ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nth__map,axiom,
% 25.54/25.38 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__fun__upd,axiom,
% 25.54/25.38 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 25.54/25.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => 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) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_distinct__map,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 25.54/25.38 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 25.54/25.38 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__abs,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] :
% 25.54/25.38 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_uminus__listsum__map,axiom,
% 25.54/25.38 ! [V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( class_Groups_Oab__group__add(T_b)
% 25.54/25.38 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__on__mapI,axiom,
% 25.54/25.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 25.54/25.38 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__mapD,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 25.54/25.38 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_inj__map,axiom,
% 25.54/25.38 ! [V_f_2,T_c,T_b] :
% 25.54/25.38 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 25.54/25.38 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 25.54/25.38 ! [V_f_2,V_xs_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__triv,axiom,
% 25.54/25.38 ! [V_xs_2,V_r_2,T_c,T_b] :
% 25.54/25.38 ( class_Rings_Osemiring__1(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__map__remove1,axiom,
% 25.54/25.38 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 25.54/25.38 ! [V_f_2,V_A_2,T_b,T_c] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.38 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 25.54/25.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.38 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pick__same,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_l_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.38 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 25.54/25.38 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_times__code__numeral__code,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 25.54/25.38 ! [V_m_2,V_n_2] :
% 25.54/25.38 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 25.54/25.38 <=> V_n_2 = V_m_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zero__code__numeral__def,axiom,
% 25.54/25.38 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_one__code__numeral__def,axiom,
% 25.54/25.38 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__code__numeral__code,axiom,
% 25.54/25.38 ! [V_m_2,V_n_2] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.38 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.38 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 25.54/25.38 <=> V_x_2 = V_y_2 ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__fst__zip,axiom,
% 25.54/25.38 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.38 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_map__snd__zip,axiom,
% 25.54/25.38 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.38 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_number__of__code__numeral__def,axiom,
% 25.54/25.38 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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__map__fst__snd,axiom,
% 25.54/25.38 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 25.54/25.38
% 25.54/25.38 fof(fact_plus__code__numeral__code,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__eq__code__numeral__code,axiom,
% 25.54/25.38 ! [V_m_2,V_n_2] :
% 25.54/25.38 ( 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)))
% 25.54/25.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_subtract__code__numeral__code,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_pick__member,axiom,
% 25.54/25.38 ! [V_xs_2,T_b,V_i_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_zip__eq__conv,axiom,
% 25.54/25.38 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 25.54/25.38 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.38 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 25.54/25.38 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 25.54/25.38 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_list__size__conv__listsum,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_code__numeral__not__eq__zero,axiom,
% 25.54/25.38 ! [V_i_2] :
% 25.54/25.38 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.54/25.38 <=> 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)) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 25.54/25.38 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 25.54/25.38 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 25.54/25.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.38 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select__weight__member,axiom,
% 25.54/25.38 ! [V_s_2,V_xs_2,T_b] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select__weight__def,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_select__def,axiom,
% 25.54/25.38 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_listsum__mono,axiom,
% 25.54/25.38 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 25.54/25.38 ( ( class_Groups_Omonoid__add(T_c)
% 25.54/25.38 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 25.54/25.38 => ( ! [B_x] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 25.54/25.38 => 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)))) ) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_times__code__numeral__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of__of__nat,axiom,
% 25.54/25.38 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 25.54/25.38
% 25.54/25.38 fof(fact_of__nat__nat__of,axiom,
% 25.54/25.38 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of__inverse,axiom,
% 25.54/25.38 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 25.54/25.38
% 25.54/25.38 fof(fact_code__numeral_Onat__of__inject,axiom,
% 25.54/25.38 ! [V_y_2,V_x_2] :
% 25.54/25.38 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 25.54/25.38 <=> V_x_2 = V_y_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 25.54/25.38 ! [V_l_2,V_k_2] :
% 25.54/25.38 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 25.54/25.38 <=> V_k_2 = V_l_2 ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_type__definition__code__numeral,axiom,
% 25.54/25.38 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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__code__numeral__def,axiom,
% 25.54/25.38 ! [V_m_2,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of,axiom,
% 25.54/25.38 ! [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)))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of__number,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_int__of__def,axiom,
% 25.54/25.38 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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_less__eq__code__numeral__def,axiom,
% 25.54/25.38 ! [V_m_2,V_n_2] :
% 25.54/25.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 25.54/25.38 <=> 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))) ) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of__code,axiom,
% 25.54/25.38 ! [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)) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_nat__of__aux__def,axiom,
% 25.54/25.38 ! [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) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_Suc__code__numeral__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_minus__code__numeral__def,axiom,
% 25.54/25.38 ! [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))) ).
% 25.54/25.38
% 25.54/25.38 fof(fact_of__nat__inverse,axiom,
% 25.54/25.39 ! [V_y_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.39 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_plus__code__numeral__def,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_div__code__numeral__def,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_mod__code__numeral__def,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_code__numeral__decr,axiom,
% 25.54/25.39 ! [V_k] :
% 25.54/25.39 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition__set,axiom,
% 25.54/25.39 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 25.54/25.39 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition__P,axiom,
% 25.54/25.39 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Opartition(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_Pa_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lists__Int__eq,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lists__IntI,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp_ONil,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_append__in__listsp__conv,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 25.54/25.39 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 25.54/25.39 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp_Oequations_I2_J,axiom,
% 25.54/25.39 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 25.54/25.39 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 25.54/25.39 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp__infI,axiom,
% 25.54/25.39 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp__inf__eq,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp__conj__eq,axiom,
% 25.54/25.39 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 25.54/25.39 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__listsp__conv__set,axiom,
% 25.54/25.39 ! [V_xs_2,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp_Oequations_I1_J,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp__mono,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsp__lists__eq,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_product_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__def,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__map1,axiom,
% 25.54/25.39 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 25.54/25.39 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_Pa_2),V_f_2),V_as_2,V_bs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__map2,axiom,
% 25.54/25.39 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 25.54/25.39 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_Pa_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__Nil2,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 25.54/25.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__Nil,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 25.54/25.39 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__lengthD,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__eq,axiom,
% 25.54/25.39 ! [T_b,V_ys_2,V_xs_2] :
% 25.54/25.39 ( V_xs_2 = V_ys_2
% 25.54/25.39 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__takeI,axiom,
% 25.54/25.39 ! [V_n_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__Cons,axiom,
% 25.54/25.39 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 25.54/25.39 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__append,axiom,
% 25.54/25.39 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.39 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 25.54/25.39 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__appendI,axiom,
% 25.54/25.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 25.54/25.39 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_ca_2,V_d_2)
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__dropI,axiom,
% 25.54/25.39 ! [V_n_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_product_Osimps_I1_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__conv__all__nth,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
% 25.54/25.39 & ! [B_i] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__nthD,axiom,
% 25.54/25.39 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__nthD2,axiom,
% 25.54/25.39 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__update__cong,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__update__cong2,axiom,
% 25.54/25.39 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__product,axiom,
% 25.54/25.39 ! [V_ys,T_b,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_product__list__set,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublists__powset,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__sublists,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublists_Osimps_I1_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublists_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__set__sublists,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => 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)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__n__lists,axiom,
% 25.54/25.39 ! [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)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_enum__the__def,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__n__lists,axiom,
% 25.54/25.39 ! [V_n,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_n__lists_Osimps_I1_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_n__lists__Nil,axiom,
% 25.54/25.39 ! [T_a,V_n] :
% 25.54/25.39 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => 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))) )
% 25.54/25.39 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__n__lists,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__n__lists__elem,axiom,
% 25.54/25.39 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2I,axiom,
% 25.54/25.39 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 25.54/25.39 => ( 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)
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_all__nth__imp__all__set,axiom,
% 25.54/25.39 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_i] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 25.54/25.39 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 25.54/25.39 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__removeAll__inj__on,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__remdups,axiom,
% 25.54/25.39 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__remdups__leq,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__id__iff__distinct,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 25.54/25.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__removeAll,axiom,
% 25.54/25.39 ! [V_x,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__remdups__id,axiom,
% 25.54/25.39 ! [V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__remdups__eq,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( 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)
% 25.54/25.39 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__remdups,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__remdups,axiom,
% 25.54/25.39 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll__append,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs,T_a,V_y,V_x] :
% 25.54/25.39 ( ( V_x = V_y
% 25.54/25.39 => 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) )
% 25.54/25.39 & ( V_x != V_y
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups_Osimps_I1_J,axiom,
% 25.54/25.39 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__eq__nil__right__iff,axiom,
% 25.54/25.39 ! [V_x_2,T_b] :
% 25.54/25.39 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 25.54/25.39 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__eq__nil__iff,axiom,
% 25.54/25.39 ! [V_x_2,T_b] :
% 25.54/25.39 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__map__remdups,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remove1__remdups,axiom,
% 25.54/25.39 ! [V_x,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll__id,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__remove1__removeAll,axiom,
% 25.54/25.39 ! [V_x,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__remdups__card__conv,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__removeAll__inj,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__removeAll,axiom,
% 25.54/25.39 ! [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)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__remdups__concat,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__conv__foldl,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldl__conv__concat,axiom,
% 25.54/25.39 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sort__key__simps_I1_J,axiom,
% 25.54/25.39 ! [V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__sort,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__sort,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__sort,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 25.54/25.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat_Osimps_I1_J,axiom,
% 25.54/25.39 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs,V_x,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),V_x),c_List_Oconcat(T_a,V_xs)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Nil__eq__concat__conv,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] :
% 25.54/25.39 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 25.54/25.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__eq__Nil__conv,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] :
% 25.54/25.39 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 25.54/25.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__concat,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__concat,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__concat,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sort__key__simps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__append,axiom,
% 25.54/25.39 ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sort__foldl__insort,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__eq__concat__iff,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 25.54/25.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 25.54/25.39 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 25.54/25.39 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__injective,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 25.54/25.39 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 25.54/25.39 => V_xs_2 = V_ys_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__map__singleton,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_n__lists_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Osimps_I3_J,axiom,
% 25.54/25.39 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__aux__filter__head,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__concat,axiom,
% 25.54/25.39 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__sort,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__filter,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__filter__le,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sum__length__filter__compl,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__id__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__is__subset,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remove1__filter__not,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__remove1,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__filter,axiom,
% 25.54/25.39 ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Qa_2)),V_Pa_2)),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__insort__triv,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition__filter1,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition__filter__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_partition__filter2,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_Pa_2)),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__append,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Osimps_I1_J,axiom,
% 25.54/25.39 ! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__empty__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__filter__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2)),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll__filter__not__eq,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_removeAll__filter__not,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_remdups__filter,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__transpose,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_i_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__map__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__filter,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_Pa_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__filter__less,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__minus__filter__out,axiom,
% 25.54/25.39 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__in__sublist,axiom,
% 25.54/25.39 ! [V_s_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__empty,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__filter__conv__card,axiom,
% 25.54/25.39 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__aux__filter__tail,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Opsimps_I3_J,axiom,
% 25.54/25.39 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 25.54/25.39 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Opsimps_I2_J,axiom,
% 25.54/25.39 ! [V_xss_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 25.54/25.39 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublist__shift__lemma__Suc,axiom,
% 25.54/25.39 ! [V_is_2,V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_Pa_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pick__drop__zero,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_select__weigth__drop__zero,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose_Opsimps_I1_J,axiom,
% 25.54/25.39 ! [T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 25.54/25.39 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__max__length,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__aux__max,axiom,
% 25.54/25.39 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr__append,axiom,
% 25.54/25.39 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr_Osimps_I1_J,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr__conv__foldl,axiom,
% 25.54/25.39 ! [V_a_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Groups_Oab__semigroup__add(T_b)
% 25.54/25.39 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr__map,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldl__foldr1__lemma,axiom,
% 25.54/25.39 ! [V_xs_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Groups_Omonoid__add(T_b)
% 25.54/25.39 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldl__foldr1,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( class_Groups_Omonoid__add(T_b)
% 25.54/25.39 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__transpose,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublist__def,axiom,
% 25.54/25.39 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sublist__shift__lemma,axiom,
% 25.54/25.39 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__upt,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_atLeastLessThan__upt,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_i_2,V_j_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__0,axiom,
% 25.54/25.39 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__eq__Nil__conv,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2] :
% 25.54/25.39 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 25.54/25.39 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__conv__Nil,axiom,
% 25.54/25.39 ! [V_i,V_j] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 25.54/25.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__conv__Cons,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__rec,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_i),c_List_Oupt(hAPP(c_Nat_OSuc,V_i),V_j)) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__add__eq__append,axiom,
% 25.54/25.39 ! [V_k,V_j,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),c_List_Oupt(V_j,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__Suc,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__Suc__append,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_drop__upt,axiom,
% 25.54/25.39 ! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_hd__upt,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__list__of__set__range,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) = c_List_Oupt(V_m_2,V_n_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_take__upt,axiom,
% 25.54/25.39 ! [V_n,V_m,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
% 25.54/25.39 => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__upt,axiom,
% 25.54/25.39 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__upt,axiom,
% 25.54/25.39 ! [V_j,V_i] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_i) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__rec__number__of,axiom,
% 25.54/25.39 ! [V_n,V_m] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 25.54/25.39 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n))) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)))
% 25.54/25.39 => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_n)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_upt__eq__Cons__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 25.54/25.39 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 25.54/25.39 & V_i_2 = V_x_2
% 25.54/25.39 & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_j_2) = V_xs_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_last__upt,axiom,
% 25.54/25.39 ! [V_j,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => c_List_Olast(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__Suc__upt,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_atLeastAtMost__upt,axiom,
% 25.54/25.39 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_atLeast__upt,axiom,
% 25.54/25.39 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__upt,axiom,
% 25.54/25.39 ! [V_j,V_k,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_greaterThanAtMost__upt,axiom,
% 25.54/25.39 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_greaterThanLessThan__upt,axiom,
% 25.54/25.39 ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_atMost__upto,axiom,
% 25.54/25.39 ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__nth,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 25.54/25.39 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.39 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 25.54/25.39 ( class_Groups_Ocomm__monoid__add(T_b)
% 25.54/25.39 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__map__upt,axiom,
% 25.54/25.39 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__rectangle,axiom,
% 25.54/25.39 ! [V_n_2,T_b,V_xs_2] :
% 25.54/25.39 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 25.54/25.39 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.54/25.39 => ( ! [B_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 25.54/25.39 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_insort__key__remove1,axiom,
% 25.54/25.39 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 25.54/25.39 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 25.54/25.39 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted_ONil,axiom,
% 25.54/25.39 ! [T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__single,axiom,
% 25.54/25.39 ! [V_x,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__upt,axiom,
% 25.54/25.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__sort,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__insort__insert,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__tl,axiom,
% 25.54/25.39 ! [V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__remove1,axiom,
% 25.54/25.39 ! [V_a,V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__take,axiom,
% 25.54/25.39 ! [V_n,V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__upto,axiom,
% 25.54/25.39 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__drop,axiom,
% 25.54/25.39 ! [V_n,V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__insort,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 25.54/25.39 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__many,axiom,
% 25.54/25.39 ! [V_zs,V_y,V_x,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__many__eq,axiom,
% 25.54/25.39 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted_Oequations_I1_J,axiom,
% 25.54/25.39 ! [T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__butlast,axiom,
% 25.54/25.39 ! [V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__remdups,axiom,
% 25.54/25.39 ! [V_l,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__distinct__set__unique,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 25.54/25.39 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 25.54/25.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__sort__key,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__insort__insert__key,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__map__remove1,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__insort__key,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 25.54/25.39 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__map__same,axiom,
% 25.54/25.39 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__filter,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__same,axiom,
% 25.54/25.39 ! [V_xs_2,V_g_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__Cons,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 25.54/25.39 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__append,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 25.54/25.39 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ! [B_xa] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__insort,axiom,
% 25.54/25.39 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 25.54/25.39 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_c,V_Pa_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_Pa_2),V_xs_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted_Oequations_I2_J,axiom,
% 25.54/25.39 ! [V_a1_2,V_a2_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 25.54/25.39 <=> ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__list__of__set,axiom,
% 25.54/25.39 ! [V_A_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.39 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 25.54/25.39 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_insort__remove1,axiom,
% 25.54/25.39 ! [V_xs_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__equals__nth__mono,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 <=> ! [B_j] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => ! [B_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__nth__mono,axiom,
% 25.54/25.39 ! [V_j,V_i,V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__sorted__distinct__set__unique,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 25.54/25.39 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 25.54/25.39 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__column,axiom,
% 25.54/25.39 ! [V_i_2,V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__nth__transpose__sorted,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__on__rev,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__rev,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 25.54/25.39 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__append,axiom,
% 25.54/25.39 ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__singleton__conv,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 25.54/25.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_singleton__rev__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 25.54/25.39 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev_Osimps_I1_J,axiom,
% 25.54/25.39 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Nil__is__rev__conv,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 25.54/25.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__is__Nil__conv,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__concat,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__filter,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_zip__rev,axiom,
% 25.54/25.39 ! [V_ys,T_b,V_xs,T_a] :
% 25.54/25.39 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
% 25.54/25.39 => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__rev,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__rev1,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 25.54/25.39 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__rev,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 25.54/25.39 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 25.54/25.39 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__is__rev__conv,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 25.54/25.39 <=> V_xs_2 = V_ys_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__swap,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 25.54/25.39 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__rev__ident,axiom,
% 25.54/25.39 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsum__rev,axiom,
% 25.54/25.39 ! [V_xs,T_a] :
% 25.54/25.39 ( class_Groups_Ocomm__monoid__add(T_a)
% 25.54/25.39 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__rev,axiom,
% 25.54/25.39 ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr__foldl,axiom,
% 25.54/25.39 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldl__foldr,axiom,
% 25.54/25.39 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs,V_x,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__eq__Cons__iff,axiom,
% 25.54/25.39 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 25.54/25.39 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_last__rev,axiom,
% 25.54/25.39 ! [T_a,V_xs] :
% 25.54/25.39 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.39 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_hd__rev,axiom,
% 25.54/25.39 ! [T_a,V_xs] :
% 25.54/25.39 ( V_xs != c_List_Olist_ONil(T_a)
% 25.54/25.39 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__transpose,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__foldl__cons,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__take,axiom,
% 25.54/25.39 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__drop,axiom,
% 25.54/25.39 ! [V_xs,V_i,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i)),hAPP(c_List_Orev(T_a),V_xs)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rotate__rev,axiom,
% 25.54/25.39 ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Orev(T_a),hAPP(c_List_Orotate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))),V_xs)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__nth,axiom,
% 25.54/25.39 ! [V_xs,T_a,V_n] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_a),hAPP(c_List_Orev(T_a),V_xs)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__update,axiom,
% 25.54/25.39 ! [V_y,V_xs,T_a,V_k] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.39 => hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_y)) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(c_List_Orev(T_a),V_xs)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_k)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_y) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__rev__nth__mono,axiom,
% 25.54/25.39 ! [V_j,V_i,V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i))) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldr__max__sorted,axiom,
% 25.54/25.39 ! [V_y_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 25.54/25.39 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 25.54/25.39 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 25.54/25.39 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.39 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__transpose__sorted,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 25.54/25.39 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__column__length,axiom,
% 25.54/25.39 ! [V_i_2,V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpose__transpose,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 25.54/25.39 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 25.54/25.39 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__takeWhile,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__takeWhile__le,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__eq__all__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__takeWhileD,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_zip__takeWhile__fst,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_zip__takeWhile__snd,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__tail,axiom,
% 25.54/25.39 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__eq__take,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__takeWhile,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_return__list__def,axiom,
% 25.54/25.39 ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__append1,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__nth,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__length__takeWhile,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__not__last,axiom,
% 25.54/25.39 ! [T_b,V_xs_2] :
% 25.54/25.39 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 25.54/25.39 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 25.54/25.39 ! [V_l] :
% 25.54/25.39 ( c_List_Onat__list(V_l)
% 25.54/25.39 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_embed__list__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__neq__rev,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__neq__rev,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__dropWhile__id,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_hd__dropWhile,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__dropWhile,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__dropWhile__le,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__dropWhile,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__map,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__append1,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 25.54/25.39 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 25.54/25.39 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 25.54/25.39 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__eq__drop,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__nth,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listsum__map__filter,axiom,
% 25.54/25.39 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 25.54/25.39 ( class_Groups_Omonoid__add(T_c)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.39 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 25.54/25.39 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted__nth__monoI,axiom,
% 25.54/25.39 ! [V_xs,T_a] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_a)
% 25.54/25.39 => ( ! [B_i,B_j] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => 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))) ) )
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__eq__filter,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 25.54/25.39 ( ! [B_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 25.54/25.39 => ( ( 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)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__takeWhile__less__P__nth,axiom,
% 25.54/25.39 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 25.54/25.39 ( ! [B_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted_Osimps,axiom,
% 25.54/25.39 ! [V_a_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 25.54/25.39 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 25.54/25.39 | ? [B_xs,B_x] :
% 25.54/25.39 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 25.54/25.39 & ! [B_xa] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_List_Oinsert__def,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_not__in__set__insert,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_insert__remdups,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__insert,axiom,
% 25.54/25.39 ! [V_x,V_xs,T_a] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__insert,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_List_Oset__insert,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_insert__Nil,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__map__maps,axiom,
% 25.54/25.39 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_maps__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_maps__simps_I2_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_maps__simps_I1_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_distinct__concat,axiom,
% 25.54/25.39 ! [V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 25.54/25.39 => ( ! [B_ys] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 25.54/25.39 => ( ! [B_ys] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => ! [B_zs] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => ( B_ys != B_zs
% 25.54/25.39 => 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)) ) ) )
% 25.54/25.39 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measures__lesseq,axiom,
% 25.54/25.39 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_wf__measures,axiom,
% 25.54/25.39 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__measures_I1_J,axiom,
% 25.54/25.39 ! [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))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measures__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measures__less,axiom,
% 25.54/25.39 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__measures_I2_J,axiom,
% 25.54/25.39 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 25.54/25.39 <=> ( 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)))
% 25.54/25.39 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 25.54/25.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_foldl__apply,axiom,
% 25.54/25.39 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => 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)) )
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_order__fun_I2_J,axiom,
% 25.54/25.39 ! [V_g_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( ( class_Orderings_Oorder(T_c)
% 25.54/25.39 & class_Enum_Oenum(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.54/25.39 & 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)))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_enum__ex__prod__def,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b,T_c] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_c)
% 25.54/25.39 & class_Enum_Oenum(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 25.54/25.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_exists__code,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ( class_Enum_Oenum(T_b)
% 25.54/25.39 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.54/25.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_enum__ex,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ( class_Enum_Oenum(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 25.54/25.39 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_zip__obtain__same__length,axiom,
% 25.54/25.39 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 25.54/25.39 ( ( 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))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__not__random__dseq__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dropWhile__append2,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_ys_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all2__all__nthI,axiom,
% 25.54/25.39 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 25.54/25.39 ( 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)
% 25.54/25.39 => ( ! [B_n] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 25.54/25.39 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_finite__sorted__distinct__unique,axiom,
% 25.54/25.39 ! [V_A_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.39 => ? [B_x] :
% 25.54/25.39 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 25.54/25.39 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 25.54/25.39 & ! [B_y] :
% 25.54/25.39 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 25.54/25.39 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 25.54/25.39 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 25.54/25.39 => B_y = B_x ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_takeWhile__append2,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_Pa_2,V_ys_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_insort__is__Cons,axiom,
% 25.54/25.39 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_c)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__eq__Cons__iff,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 25.54/25.39 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 25.54/25.39 <=> ? [B_us,B_vs] :
% 25.54/25.39 ( 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))
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Cons__eq__filter__iff,axiom,
% 25.54/25.39 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)
% 25.54/25.39 <=> ? [B_us,B_vs] :
% 25.54/25.39 ( 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))
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 25.54/25.39 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_order__fun_I1_J,axiom,
% 25.54/25.39 ! [V_g_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( ( class_Orderings_Oorder(T_c)
% 25.54/25.39 & class_Enum_Oenum(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 25.54/25.39 <=> 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_enum__all,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ( class_Enum_Oenum(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 25.54/25.39 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_all__code,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ( class_Enum_Oenum(T_b)
% 25.54/25.39 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 25.54/25.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_enum__all__prod__def,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b,T_c] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_c)
% 25.54/25.39 & class_Enum_Oenum(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 25.54/25.39 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_Pa_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ball__nth,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b,V_n_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sorted_OCons,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( class_Orderings_Olinorder(T_b)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 25.54/25.39 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 25.54/25.39 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__length,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ? [B_n] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__conv__decomp,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 <=> ? [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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__simps_I2_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__append,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 25.54/25.39 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__iff,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__rev,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 25.54/25.39 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__simps_I1_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 25.54/25.39 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__conv__decomp__first,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 <=> ? [B_ys] :
% 25.54/25.39 ( ? [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))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__conv__decomp__last,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 <=> ? [B_ys,B_zs] :
% 25.54/25.39 ( 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))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__length,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ! [B_n] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measure__function__int,axiom,
% 25.54/25.39 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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__simps_I2_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__append,axiom,
% 25.54/25.39 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 25.54/25.39 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measure__size,axiom,
% 25.54/25.39 ! [T_b] :
% 25.54/25.39 ( class_Nat_Osize(T_b)
% 25.54/25.39 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_is__measure_Ointros,axiom,
% 25.54/25.39 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_is__measure_Oequations,axiom,
% 25.54/25.39 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_is__measure_Osimps,axiom,
% 25.54/25.39 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__iff,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measure__snd,axiom,
% 25.54/25.39 ! [T_c,V_f_2,T_b] :
% 25.54/25.39 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_measure__fst,axiom,
% 25.54/25.39 ! [T_c,V_f_2,T_b] :
% 25.54/25.39 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__rev,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 25.54/25.39 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__simps_I1_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 25.54/25.39 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Ball__set__list__all,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__iff__raw,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex1__simps_I2_J,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 25.54/25.39 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transfer__morphism__int__nat,axiom,
% 25.54/25.39 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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex1__simps_I1_J,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bool_Osize_I3_J,axiom,
% 25.54/25.39 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bool_Osize_I4_J,axiom,
% 25.54/25.39 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex1__iff,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.39 & ! [B_y] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 25.54/25.39 => B_y = B_x ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 25.54/25.39 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 25.54/25.39 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.39 => 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) )
% 25.54/25.39 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 25.54/25.39 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 25.54/25.39 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.39 => 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) )
% 25.54/25.39 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 25.54/25.39 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__empty__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_neg__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_neg__map__def,axiom,
% 25.54/25.39 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_neg__single__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__bind__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__map__def,axiom,
% 25.54/25.39 ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__single__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__splice,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_splice_Osimps_I3_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_splice__Nil2,axiom,
% 25.54/25.39 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 25.54/25.39
% 25.54/25.39 fof(fact_splice_Osimps_I1_J,axiom,
% 25.54/25.39 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 25.54/25.39
% 25.54/25.39 fof(fact_splice_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__single__def,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_acyclicP__converse,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 <=> 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_converse__meet,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_converse__join,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep__eq,axiom,
% 25.54/25.39 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep__conversep,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep__iff,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep_Oequations,axiom,
% 25.54/25.39 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep_Ointros,axiom,
% 25.54/25.39 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversepD,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep__noteq,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> V_x_2 != V_y_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_converse__pred__comp,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_conversep__converse__eq,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_,axiom,
% 25.54/25.39 ! [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)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_tl__replicate,axiom,
% 25.54/25.39 ! [V_x,T_a,V_n] :
% 25.54/25.39 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__length__filter,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_length__replicate,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__replicate__const,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__app__Cons__same,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__Suc,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rev__replicate,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_take__replicate,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_hd__replicate,axiom,
% 25.54/25.39 ! [V_x,T_a,V_n] :
% 25.54/25.39 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_drop__replicate,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_last__replicate,axiom,
% 25.54/25.39 ! [V_x,T_a,V_n] :
% 25.54/25.39 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_zip__replicate,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Ball__set__replicate,axiom,
% 25.54/25.39 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.54/25.39 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Bex__set__replicate,axiom,
% 25.54/25.39 ! [V_Pa_2,V_a_2,V_n_2,T_b] :
% 25.54/25.39 ( ? [B_x] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 25.54/25.39 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__eq__replicate,axiom,
% 25.54/25.39 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 25.54/25.39 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 25.54/25.39 <=> ( V_m_2 = V_n_2
% 25.54/25.39 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => V_x_2 = V_y_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nth__replicate,axiom,
% 25.54/25.39 ! [V_x,T_a,V_n,V_i] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 25.54/25.39 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_append__replicate__commute,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__add,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_filter__replicate,axiom,
% 25.54/25.39 ! [V_n_2,T_b,V_x_2,V_Pa_2] :
% 25.54/25.39 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 25.54/25.39 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_concat__replicate__trivial,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__empty,axiom,
% 25.54/25.39 ! [V_x_2,V_n_2,T_b] :
% 25.54/25.39 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 25.54/25.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_empty__replicate,axiom,
% 25.54/25.39 ! [V_x_2,V_n_2,T_b] :
% 25.54/25.39 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 25.54/25.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__0,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__replicate,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__replicate,axiom,
% 25.54/25.39 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 <=> ( V_x_2 = V_y_2
% 25.54/25.39 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_replicate__append__same,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_map__replicate__trivial,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__replicate,axiom,
% 25.54/25.39 ! [V_x_2,T_b,V_n_2] :
% 25.54/25.39 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__replicate__conv__if,axiom,
% 25.54/25.39 ! [V_x_2,T_b,V_n_2] :
% 25.54/25.39 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => 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)) )
% 25.54/25.39 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_set__replicate__Suc,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy__list_Osimps,axiom,
% 25.54/25.39 ! [V_d_2,T_b] :
% 25.54/25.39 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 25.54/25.39 => 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)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_eq__comp__r,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy__prod__def,axiom,
% 25.54/25.39 ! [V_d,T_b,T_a] :
% 25.54/25.39 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 25.54/25.39 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__union__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__01,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Oinject,axiom,
% 25.54/25.39 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 25.54/25.39 ( 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)
% 25.54/25.39 <=> ( V_a_2 = V_a_H_2
% 25.54/25.39 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_pos__union__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy_H_Osimps,axiom,
% 25.54/25.39 ! [V_i,V_d] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 25.54/25.39 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 25.54/25.39 => 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)))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy_H_Opsimps,axiom,
% 25.54/25.39 ! [V_i_2,V_d_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 25.54/25.39 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 25.54/25.39 => 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)))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy__int__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_small__lazy_H_Opinduct,axiom,
% 25.54/25.39 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( ! [B_d,B_i] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_size__code,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence__size__code,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_seq__case,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_yieldn__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_refl__on__INTER,axiom,
% 25.54/25.39 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.54/25.39 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_List_Omember__def,axiom,
% 25.54/25.39 ! [V_x_2,V_xs_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_member__rec_I2_J,axiom,
% 25.54/25.39 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_member__set,axiom,
% 25.54/25.39 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_member__rec_I1_J,axiom,
% 25.54/25.39 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> ( V_x_2 = V_y_2
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__set__member,axiom,
% 25.54/25.39 ! [V_xs_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex1__iff__raw,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.39 & ! [B_y] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 25.54/25.39 => B_y = B_x ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_setsum__UNION__zero,axiom,
% 25.54/25.39 ! [V_f_2,V_S_2,T_b,T_c] :
% 25.54/25.39 ( class_Groups_Ocomm__monoid__add(T_c)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 25.54/25.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 25.54/25.39 => ( ! [B_T1] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 25.54/25.39 => ! [B_T2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 25.54/25.39 => ( B_T1 != B_T2
% 25.54/25.39 => ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 25.54/25.39 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 25.54/25.39 => 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) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_THE__default__def,axiom,
% 25.54/25.39 ! [V_d_2,T_b,V_Pa_2] :
% 25.54/25.39 ( ( ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.39 & ! [B_y] :
% 25.54/25.39 ( hBOOL(hAPP(V_Pa_2,B_y))
% 25.54/25.39 => B_y = B_x ) )
% 25.54/25.39 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) )
% 25.54/25.39 & ( ~ ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(V_Pa_2,B_x))
% 25.54/25.39 & ! [B_y] :
% 25.54/25.39 ( hBOOL(hAPP(V_Pa_2,B_y))
% 25.54/25.39 => B_y = B_x ) )
% 25.54/25.39 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_INF2__I,axiom,
% 25.54/25.39 ! [T_d,T_c,V_ca_2,V_b_2,V_B_2,V_A_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) )
% 25.54/25.39 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_SUP2__E,axiom,
% 25.54/25.39 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2))
% 25.54/25.39 => ~ ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.39 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_finite__maxlen,axiom,
% 25.54/25.39 ! [V_M_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 25.54/25.39 => ? [B_n] :
% 25.54/25.39 ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__02,axiom,
% 25.54/25.39 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__iff__all__interval__int,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 25.54/25.39 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 25.54/25.39 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_all__interval__int__def,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Random_Osimps,axiom,
% 25.54/25.39 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 25.54/25.39 ( ( 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)))
% 25.54/25.39 => 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)) )
% 25.54/25.39 & ( ~ 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)))
% 25.54/25.39 => 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))))))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Random__Sequence_Oempty__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Random__Sequence_Osingle__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Random__Sequence_Omap__def,axiom,
% 25.54/25.39 ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_exE__realizer,axiom,
% 25.54/25.39 ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 25.54/25.39 => ( ! [B_x,B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 25.54/25.39 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 25.54/25.39 => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Image__Collect__split,axiom,
% 25.54/25.39 ! [V_A_2,V_Pa_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_Pa_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_Pa_2)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lexord__trans,axiom,
% 25.54/25.39 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
% 25.54/25.39 => ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__less__than,axiom,
% 25.54/25.39 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__lex__prod,axiom,
% 25.54/25.39 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_R1_2)
% 25.54/25.39 => ( c_Relation_Otrans(T_c,V_R2_2)
% 25.54/25.39 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__def,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 <=> ! [B_x,B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 25.54/25.39 => ! [B_z] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transD,axiom,
% 25.54/25.39 ! [V_ca_2,V_b_2,V_a_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_ca_2)),V_r_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_ca_2)),V_r_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Union__eq,axiom,
% 25.54/25.39 ! [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)))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__O__subset,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bex__UNIV,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ( ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_finite__Collect__bex,axiom,
% 25.54/25.39 ! [V_Qa_2,T_c,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.39 => ( 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_Qa_2)))))
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Qa_2),B_x)))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__converse,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.39 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bex__empty,axiom,
% 25.54/25.39 ! [V_Pa_2,T_b] :
% 25.54/25.39 ~ ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listrel__trans,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lexord__transI,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__finite__psubset,axiom,
% 25.54/25.39 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__Id__on,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__trancl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trancl__id,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__Id,axiom,
% 25.54/25.39 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__rtrancl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__Int,axiom,
% 25.54/25.39 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Otrans(T_b,V_s_2)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_SUPR__bool__eq,axiom,
% 25.54/25.39 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__reflclI,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__inv__image,axiom,
% 25.54/25.39 ! [V_f_2,T_c,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__iff__raw,axiom,
% 25.54/25.39 ! [V_xs_2,V_Pa_2,T_b] :
% 25.54/25.39 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 25.54/25.39 <=> ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Bex__set__list__ex,axiom,
% 25.54/25.39 ! [V_Pa_2,V_xs_2,T_b] :
% 25.54/25.39 ( ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_UN__eq,axiom,
% 25.54/25.39 ! [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))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_INT__eq,axiom,
% 25.54/25.39 ! [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))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Sup__apply,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.54/25.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.39 => 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)))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Sup__fun__def,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.54/25.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.39 => 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)))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Inf__apply,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.54/25.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.39 => 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)))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Inf__fun__def,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,T_c,T_b] :
% 25.54/25.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 25.54/25.39 => 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)))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_max__extp_Ointros,axiom,
% 25.54/25.39 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 25.54/25.39 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 25.54/25.39 => ? [B_xa] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 25.54/25.39 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 25.54/25.39 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transp__def,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Predicate_Otransp(T_b,V_r_2)
% 25.54/25.39 <=> 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_transpE,axiom,
% 25.54/25.39 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Predicate_Otransp(T_b,V_r_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivp__reflp__symp__transp,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 25.54/25.39 & c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivpI,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Predicate_Oreflp(T_b,V_R_2)
% 25.54/25.39 => ( c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 => ( c_Predicate_Otransp(T_b,V_R_2)
% 25.54/25.39 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sympE,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Predicate_Osymp(T_b,V_r_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivpE,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 25.54/25.39 => ( c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_max__extp_Osimps,axiom,
% 25.54/25.39 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 25.54/25.39 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 25.54/25.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 25.54/25.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 25.54/25.39 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 25.54/25.39 & ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 25.54/25.39 => ? [B_xa] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 25.54/25.39 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_trans__diff__Id,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Oantisym(T_b,V_r_2)
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__subset,axiom,
% 25.54/25.39 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 25.54/25.39 => ( c_Relation_Oantisym(T_b,V_s_2)
% 25.54/25.39 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__Id__on,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__Id,axiom,
% 25.54/25.39 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__empty,axiom,
% 25.54/25.39 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__converse,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.39 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisymD,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Oantisym(T_b,V_r_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( 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))
% 25.54/25.39 => V_a_2 = V_b_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__def,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Oantisym(T_b,V_r_2)
% 25.54/25.39 <=> ! [B_x,B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 25.54/25.39 => ( 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))
% 25.54/25.39 => B_x = B_y ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_antisym__reflcl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_fun__lub__def,axiom,
% 25.54/25.39 ! [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)))))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__trans__comp__subset,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__def,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 <=> ! [B_x,B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_symD,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__converse,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 25.54/25.39 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__conv__converse__eq,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_listrel__sym,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Id__on,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__trancl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Un,axiom,
% 25.54/25.39 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Osym(T_b,V_s_2)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Id,axiom,
% 25.54/25.39 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__rtrancl,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Int,axiom,
% 25.54/25.39 ! [V_s_2,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Osym(T_b,V_s_2)
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Un__converse,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__inv__image,axiom,
% 25.54/25.39 ! [V_f_2,T_c,V_r_2,T_b] :
% 25.54/25.39 ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_sym__Int__converse,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivE,axiom,
% 25.54/25.39 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.54/25.39 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.39 => ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivI,axiom,
% 25.54/25.39 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.39 => ( c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 => ( c_Relation_Otrans(T_b,V_r_2)
% 25.54/25.39 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equiv__def,axiom,
% 25.54/25.39 ! [V_r_2,V_A_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 25.54/25.39 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 25.54/25.39 & c_Relation_Osym(T_b,V_r_2)
% 25.54/25.39 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_symp__def,axiom,
% 25.54/25.39 ! [V_r_2,T_b] :
% 25.54/25.39 ( c_Predicate_Osymp(T_b,V_r_2)
% 25.54/25.39 <=> 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivp__refl__symp__transp,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 25.54/25.39 & c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivpI,axiom,
% 25.54/25.39 ! [T_b,V_R_2] :
% 25.54/25.39 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 25.54/25.39 => ( c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 => ( c_Predicate_Otransp(T_b,V_R_2)
% 25.54/25.39 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_equivp__implies__part__equivp,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivp__def,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 25.54/25.39 & ! [B_x,B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 25.54/25.39 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 25.54/25.39 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivp__symp,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivp__transp,axiom,
% 25.54/25.39 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivpE,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 25.54/25.39 => ( c_Predicate_Osymp(T_b,V_R_2)
% 25.54/25.39 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_part__equivp__typedef,axiom,
% 25.54/25.39 ! [V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 25.54/25.39 => ? [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))))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__iff,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 <=> 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__o__cancel,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_o__inv__o__cancel,axiom,
% 25.54/25.39 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__id,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_image__inv__into__cancel,axiom,
% 25.54/25.39 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_surj__iff__all,axiom,
% 25.54/25.39 ! [V_f_2,T_b,T_c] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> ! [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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_surj__f__inv__f,axiom,
% 25.54/25.39 ! [V_y_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_image__surj__f__inv__f,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_b,T_c] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__injective,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 25.54/25.39 ( 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)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 25.54/25.39 => V_x_2 = V_y_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__into,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_f__inv__into__f,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__f__f,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__f__eq,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 25.54/25.39 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 25.54/25.39 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__f__eq,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__f__f,axiom,
% 25.54/25.39 ! [V_x_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__def,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__imp__surj__inv,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_image__inv__f__f,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__image__comp,axiom,
% 25.54/25.39 ! [V_X_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_surj__imp__inj__inv,axiom,
% 25.54/25.39 ! [V_f_2,T_b,T_c] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__on__inv__into,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__image__cancel,axiom,
% 25.54/25.39 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__comp,axiom,
% 25.54/25.39 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 25.54/25.39 => ( 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))))
% 25.54/25.39 => 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) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_surj__iff,axiom,
% 25.54/25.39 ! [V_f_2,T_b,T_c] :
% 25.54/25.39 ( 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))
% 25.54/25.39 <=> 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__transfer,axiom,
% 25.54/25.39 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => ( ! [B_y] :
% 25.54/25.39 ( 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)))))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_fold__image__UN__disjoint,axiom,
% 25.54/25.39 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 25.54/25.39 ( class_Groups_Ocomm__monoid__mult(T_d)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 25.54/25.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 25.54/25.39 => ! [B_xa] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 25.54/25.39 => ( B_x != B_xa
% 25.54/25.39 => 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)) ) ) )
% 25.54/25.39 => 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) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nat__of__induct,axiom,
% 25.54/25.39 ! [V_Pa_2,V_y_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.39 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nat__of__cases,axiom,
% 25.54/25.39 ! [V_y_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.39 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_of__nat__induct,axiom,
% 25.54/25.39 ! [V_x_2,V_Pa_2] :
% 25.54/25.39 ( ! [B_y] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_of__nat__cases,axiom,
% 25.54/25.39 ! [V_x_2] :
% 25.54/25.39 ~ ! [B_y] :
% 25.54/25.39 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 25.54/25.39 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_beyond__def,axiom,
% 25.54/25.39 ! [V_l,V_k] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 25.54/25.39 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 25.54/25.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 25.54/25.39 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_beyond__zero,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__image__Collect__eq,axiom,
% 25.54/25.39 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_Pa_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curry__def,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2,V_ca_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_ca_2),V_x_2),V_y_2) = hAPP(V_ca_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curryI,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 25.54/25.39 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__id,axiom,
% 25.54/25.39 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__imp__bij__inv,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__inv__eq,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inv__into__inv__into__eq,axiom,
% 25.54/25.39 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__inv__into,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_o__inv__distrib,axiom,
% 25.54/25.39 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__image__INT,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__comp__iff2,axiom,
% 25.54/25.39 ! [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] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 25.54/25.39 <=> 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) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__comp,axiom,
% 25.54/25.39 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__comp__iff,axiom,
% 25.54/25.39 ! [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] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 25.54/25.39 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 25.54/25.39 <=> 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__trans,axiom,
% 25.54/25.39 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curryE,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 25.54/25.39 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curryD,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 25.54/25.39 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curry__conv,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_finite__vimage__iff,axiom,
% 25.54/25.39 ! [V_F_2,V_h_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 25.54/25.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__image__Compl__eq,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__is__inj,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__imp__inj__on,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__def,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inj__on__imp__bij__betw,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__imp__surj,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__is__surj,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__subset,axiom,
% 25.54/25.39 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.54/25.39 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 25.54/25.39 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__id,axiom,
% 25.54/25.39 ! [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))) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__id__iff,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 25.54/25.39 <=> V_A_2 = V_B_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__finite,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_BIJ,axiom,
% 25.54/25.39 ! [V_B_2,T_c,V_A_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 25.54/25.39 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 25.54/25.39 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__empty1,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)
% 25.54/25.39 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__empty2,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__same__card,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__the__inv__into,axiom,
% 25.54/25.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__combine,axiom,
% 25.54/25.39 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 25.54/25.39 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => 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)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__betw__Disj__Un,axiom,
% 25.54/25.39 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 25.54/25.39 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 25.54/25.39 => 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)) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__def,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 & 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bijI,axiom,
% 25.54/25.39 ! [V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 25.54/25.39 => ( 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))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_curry__split,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_split__curry,axiom,
% 25.54/25.39 ! [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 ).
% 25.54/25.39
% 25.54/25.39 fof(fact_vimage__subset__eq,axiom,
% 25.54/25.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( 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))
% 25.54/25.39 <=> 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bij__vimage__eq__inv__image,axiom,
% 25.54/25.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => 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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 25.54/25.39 ! [V_M_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 25.54/25.39 => ? [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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Cantor__Bernstein,axiom,
% 25.54/25.39 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_ex__bij__betw__nat__finite,axiom,
% 25.54/25.39 ! [V_M_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 25.54/25.39 => ? [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) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_ex__bij__betw__finite__nat,axiom,
% 25.54/25.39 ! [V_M_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 25.54/25.39 => ? [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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_refl__on__UNION,axiom,
% 25.54/25.39 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 25.54/25.39 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 25.54/25.39 => 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)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bex__reg__eqv,axiom,
% 25.54/25.39 ! [V_Pa_2,V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 => ( ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Respects__def,axiom,
% 25.54/25.39 ! [V_x_2,V_R_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_in__respects,axiom,
% 25.54/25.39 ! [V_R_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_bex__reg__right,axiom,
% 25.54/25.39 ! [V_Pa_2,V_Qa_2,V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(V_Qa_2,B_x))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 25.54/25.39 => ( ? [B_x1] : hBOOL(hAPP(V_Qa_2,B_x1))
% 25.54/25.39 => ? [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_babs__reg__eqv,axiom,
% 25.54/25.39 ! [V_Pa_2,T_c,V_R_2,T_b] :
% 25.54/25.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 25.54/25.39 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_Babs__def,axiom,
% 25.54/25.39 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 25.54/25.39 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_wf__weak__decr__stable,axiom,
% 25.54/25.39 ! [V_r_2,V_f_2,T_b] :
% 25.54/25.39 ( ! [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)))
% 25.54/25.39 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 25.54/25.39 => ? [B_i] :
% 25.54/25.39 ! [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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_INT__anti__mono,axiom,
% 25.54/25.39 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.39 => 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))) )
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_INT__greatest,axiom,
% 25.54/25.39 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 25.54/25.39 ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 25.54/25.39 => 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))) )
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_rtrancl__induct2,axiom,
% 25.54/25.39 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
% 25.54/25.39 => ( ! [B_a,B_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ! [B_aa,B_ba] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_converse__rtranclE2,axiom,
% 25.54/25.39 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( 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)
% 25.54/25.39 => ~ ! [B_a,B_b] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ~ 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_converse__rtrancl__induct2,axiom,
% 25.54/25.39 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
% 25.54/25.39 => ( ! [B_a,B_b,B_aa,B_ba] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
% 25.54/25.39 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_congruentI,axiom,
% 25.54/25.39 ! [T_c,V_f_2,V_r_2,T_b] :
% 25.54/25.39 ( ! [B_y,B_z] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 25.54/25.39 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_congruent2I_H,axiom,
% 25.54/25.39 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 25.54/25.39 ( ! [B_y1,B_z1] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => ! [B_y2,B_z2] :
% 25.54/25.39 ( 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))
% 25.54/25.39 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 25.54/25.39 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__03,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_all__interval__nat__def,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
% 25.54/25.39 <=> ! [B_x] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__04,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__all__iff__all__interval__nat,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 25.54/25.39 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 25.54/25.39 ! [V_j_2,V_i_2,V_Pa_2] :
% 25.54/25.39 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 25.54/25.39 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_Pa_2),V_i_2,V_j_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__05,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_folding__image_Ocong,axiom,
% 25.54/25.39 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 25.54/25.39 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 25.54/25.39 => ( ! [B_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 25.54/25.39 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 25.54/25.39 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__06,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact__07,axiom,
% 25.54/25.39 ! [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) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_New__DSequence_Opos__map__def,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_power__dvd__imp__le,axiom,
% 25.54/25.39 ! [V_n,V_m,V_i] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oorder__refl,axiom,
% 25.54/25.39 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__0__right,axiom,
% 25.54/25.39 ! [V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__1__left,axiom,
% 25.54/25.39 ! [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)) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__imp__le,axiom,
% 25.54/25.39 ! [V_n,V_k] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nat__mult__dvd__cancel1,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2,V_k_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__cancel,axiom,
% 25.54/25.39 ! [V_n,V_m,V_k] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_setprod__dvd__setprod__subset,axiom,
% 25.54/25.39 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 25.54/25.39 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 25.54/25.39 & class_Rings_Odvd(T_c) )
% 25.54/25.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 25.54/25.39 => 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inf__period_I4_J,axiom,
% 25.54/25.39 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 25.54/25.39 ( ( class_Rings_Ocomm__ring(T_b)
% 25.54/25.39 & class_Rings_Odvd(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 25.54/25.39 => ! [B_x,B_k] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_inf__period_I3_J,axiom,
% 25.54/25.39 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 25.54/25.39 ( ( class_Rings_Ocomm__ring(T_b)
% 25.54/25.39 & class_Rings_Odvd(T_b) )
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 25.54/25.39 => ! [B_x,B_k] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__div__eq__mult,axiom,
% 25.54/25.39 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_b)
% 25.54/25.39 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 25.54/25.39 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_ca_2
% 25.54/25.39 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__div__div__eq__mult,axiom,
% 25.54/25.39 ! [V_d_2,V_b_2,V_ca_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_b)
% 25.54/25.39 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.54/25.39 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_ca_2),V_d_2))
% 25.54/25.39 => ( 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_ca_2)
% 25.54/25.39 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 25.54/25.39 ! [V_n_2,V_m_2,V_k_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_div__mult__div__if__dvd,axiom,
% 25.54/25.39 ! [V_w,V_z,V_x,V_y,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 25.54/25.39 => 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)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__div__mult,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__div__mult__self,axiom,
% 25.54/25.39 ! [V_b,V_a,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_div__mult__swap,axiom,
% 25.54/25.39 ! [V_a,V_b,V_c,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__div__cancel,axiom,
% 25.54/25.39 ! [V_b,V_a,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => 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 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__right,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__left,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvdI,axiom,
% 25.54/25.39 ! [V_k,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Odvd(T_a)
% 25.54/25.39 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_mult__dvd__mono,axiom,
% 25.54/25.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 25.54/25.39 => 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult,axiom,
% 25.54/25.39 ! [V_b,V_c,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult2,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__triv__right,axiom,
% 25.54/25.39 ! [V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__triv__left,axiom,
% 25.54/25.39 ! [V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => 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))) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__cancel__left,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,V_ca_2,T_b] :
% 25.54/25.39 ( class_Rings_Oidom(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_ca_2),V_b_2)))
% 25.54/25.39 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mult__cancel__right,axiom,
% 25.54/25.39 ! [V_b_2,V_ca_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Rings_Oidom(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_ca_2)))
% 25.54/25.39 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_b)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_unity__coeff__ex,axiom,
% 25.54/25.39 ! [V_l_2,V_Pa_2,T_b] :
% 25.54/25.39 ( ( class_Rings_Odvd(T_b)
% 25.54/25.39 & class_Rings_Osemiring__0(T_b) )
% 25.54/25.39 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 25.54/25.39 <=> ? [B_x] :
% 25.54/25.39 ( 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))))
% 25.54/25.39 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_le__imp__power__dvd,axiom,
% 25.54/25.39 ! [V_a,V_n,V_m,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__power__le,axiom,
% 25.54/25.39 ! [V_m,V_n,V_y,V_x,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.54/25.39 => 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))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_power__le__dvd,axiom,
% 25.54/25.39 ! [V_m,V_b,V_n,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( 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))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 25.54/25.39 => 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)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 25.54/25.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2] :
% 25.54/25.39 ( 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_ca_2,V_d_2)))
% 25.54/25.39 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 25.54/25.39 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_ca_2),V_a_2))
% 25.54/25.39 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__diffD1,axiom,
% 25.54/25.39 ! [V_n,V_m,V_k] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__diffD,axiom,
% 25.54/25.39 ! [V_n,V_m,V_k] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_OlessThan__iff,axiom,
% 25.54/25.39 ! [V_k_2,V_i_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_OgreaterThan__iff,axiom,
% 25.54/25.39 ! [V_k_2,V_i_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_OatLeast__iff,axiom,
% 25.54/25.39 ! [V_k_2,V_i_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_OatMost__iff,axiom,
% 25.54/25.39 ! [V_k_2,V_i_2] :
% 25.54/25.39 ( 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)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_div__power,axiom,
% 25.54/25.39 ! [V_n,V_x,V_y,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 25.54/25.39 => 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)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__imp__mod__0,axiom,
% 25.54/25.39 ! [V_b,V_a,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__eq__mod__eq__0,axiom,
% 25.54/25.39 ! [V_b_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 25.54/25.39 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mod__iff,axiom,
% 25.54/25.39 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 25.54/25.39 => ( 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)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_mod__mod__cancel,axiom,
% 25.54/25.39 ! [V_a,V_b,V_c,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 25.54/25.39 => 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) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mod,axiom,
% 25.54/25.39 ! [V_n,V_m,V_k,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__mod__imp__dvd,axiom,
% 25.54/25.39 ! [V_n,V_m,V_k,T_a] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_one__dvd,axiom,
% 25.54/25.39 ! [V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__0__left,axiom,
% 25.54/25.39 ! [V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 25.54/25.39 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_div__dvd__div,axiom,
% 25.54/25.39 ! [V_ca_2,V_b_2,V_a_2,T_b] :
% 25.54/25.39 ( class_Divides_Osemiring__div(T_b)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_ca_2))
% 25.54/25.39 => ( 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_ca_2),V_a_2)))
% 25.54/25.39 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_ca_2)) ) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_nat__dvd__1__iff__1,axiom,
% 25.54/25.39 ! [V_m_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 25.54/25.39 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__power__same,axiom,
% 25.54/25.39 ! [V_n,V_y,V_x,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 25.54/25.39 => 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))) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__refl,axiom,
% 25.54/25.39 ! [V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__trans,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a,T_a] :
% 25.54/25.39 ( class_Rings_Ocomm__semiring__1(T_a)
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oeq__iff,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2] :
% 25.54/25.39 ( V_x_2 = V_y_2
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Ole__less,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 25.54/25.39 | V_x_2 = V_y_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oless__le,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2] :
% 25.54/25.39 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 25.54/25.39 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 & V_x_2 != V_y_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oneq__le__trans,axiom,
% 25.54/25.39 ! [V_b,V_a] :
% 25.54/25.39 ( V_a != V_b
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oeq__refl,axiom,
% 25.54/25.39 ! [V_y,V_x] :
% 25.54/25.39 ( V_x = V_y
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oantisym__conv,axiom,
% 25.54/25.39 ! [V_x_2,V_y_2] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 25.54/25.39 <=> V_x_2 = V_y_2 ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 25.54/25.39 ! [V_y,V_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 25.54/25.39 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 25.54/25.39 | V_x = V_y ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Ole__neq__trans,axiom,
% 25.54/25.39 ! [V_b,V_a] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 25.54/25.39 => ( V_a != V_b
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 25.54/25.39 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a] :
% 25.54/25.39 ( V_a = V_b
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 25.54/25.39 ! [V_c,V_b,V_a] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 25.54/25.39 => ( V_b = V_c
% 25.54/25.39 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd__antisym,axiom,
% 25.54/25.39 ! [V_n,V_m] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 25.54/25.39 => V_m = V_n ) ) ).
% 25.54/25.39
% 25.54/25.39 fof(fact_dvd_Oantisym,axiom,
% 25.54/25.39 ! [V_y,V_x] :
% 25.54/25.39 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 25.54/25.39 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 25.54/25.39 => V_x = V_y ) ) ).
% 25.54/25.39
% 25.54/25.39 %----Arity declarations (238)
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 25.54/25.39 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Obounded__lattice(T_1)
% 25.54/25.39 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 25.54/25.39 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Obounded__lattice(T_1)
% 25.54/25.39 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Obounded__lattice(T_1)
% 25.54/25.39 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Olattice(T_1)
% 25.54/25.39 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Olattice(T_1)
% 25.54/25.39 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Odistrib__lattice(T_1)
% 25.54/25.39 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Oboolean__algebra(T_1)
% 25.54/25.39 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Orderings_Opreorder,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Orderings_Opreorder(T_1)
% 25.54/25.39 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Finite__Set_Ofinite(T_2)
% 25.54/25.39 & class_Finite__Set_Ofinite(T_1) )
% 25.54/25.39 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Lattices_Olattice,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Lattices_Olattice(T_1)
% 25.54/25.39 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Orderings_Oorder,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Orderings_Oorder(T_1)
% 25.54/25.39 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Orderings_Otop,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Orderings_Otop(T_1)
% 25.54/25.39 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Orderings_Oord,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Orderings_Oord(T_1)
% 25.54/25.39 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Orderings_Obot,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Orderings_Obot(T_1)
% 25.54/25.39 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Groups_Ouminus,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Groups_Ouminus(T_1)
% 25.54/25.39 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Groups_Ominus,axiom,
% 25.54/25.39 ! [T_2,T_1] :
% 25.54/25.39 ( class_Groups_Ominus(T_1)
% 25.54/25.39 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_2)
% 25.54/25.39 & class_HOL_Oequal(T_1) )
% 25.54/25.39 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_fun__Enum_Oenum,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_2)
% 25.54/25.39 & class_Enum_Oenum(T_1) )
% 25.54/25.39 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Com__Ocom__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Com_Ocom) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Com_Ocom) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 25.54/25.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 25.54/25.39 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 25.54/25.39 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 25.54/25.39 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 25.54/25.39 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 25.54/25.39 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 25.54/25.39 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 25.54/25.39 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 25.54/25.39 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 25.54/25.39 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 25.54/25.39 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 25.54/25.39 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 25.54/25.39 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 25.54/25.39 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 25.54/25.39 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 25.54/25.39 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 25.54/25.39 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 25.54/25.39 class_Orderings_Opreorder(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 25.54/25.39 class_Orderings_Olinorder(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 25.54/25.39 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 25.54/25.39 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 25.54/25.39 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 25.54/25.39 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 25.54/25.39 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 25.54/25.39 class_Lattices_Olattice(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 25.54/25.39 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 25.54/25.39 class_Divides_Oring__div(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 25.54/25.39 class_Rings_Omult__zero(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 25.54/25.39 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 25.54/25.39 class_Orderings_Oorder(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 25.54/25.39 class_Int_Oring__char__0(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 25.54/25.39 class_Int_Onumber__ring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 25.54/25.39 class_Rings_Osemiring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 25.54/25.39 class_Orderings_Oord(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 25.54/25.39 class_Groups_Ouminus(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 25.54/25.39 class_Groups_Osgn__if(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 25.54/25.39 class_Groups_Oabs__if(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 25.54/25.39 class_Rings_Oring__1(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 25.54/25.39 class_Groups_Ominus(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Power_Opower,axiom,
% 25.54/25.39 class_Power_Opower(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 25.54/25.39 class_Groups_Ozero(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oring,axiom,
% 25.54/25.39 class_Rings_Oring(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 25.54/25.39 class_Rings_Oidom(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Int_Onumber,axiom,
% 25.54/25.39 class_Int_Onumber(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Groups_Oone,axiom,
% 25.54/25.39 class_Groups_Oone(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 25.54/25.39 class_Rings_Odvd(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Int__Oint__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Int_Oint) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 25.54/25.39 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 25.54/25.39 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 25.54/25.39 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 25.54/25.39 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 25.54/25.39 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 25.54/25.39 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 25.54/25.39 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 25.54/25.39 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 25.54/25.39 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 25.54/25.39 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 25.54/25.39 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 25.54/25.39 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 25.54/25.39 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 25.54/25.39 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 25.54/25.39 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 25.54/25.39 class_Lattices_Olattice(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 25.54/25.39 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 25.54/25.39 class_Orderings_Oorder(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 25.54/25.39 class_Rings_Osemiring(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 25.54/25.39 class_Orderings_Oord(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 25.54/25.39 class_Orderings_Obot(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 25.54/25.39 class_Groups_Ominus(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Power_Opower,axiom,
% 25.54/25.39 class_Power_Opower(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 25.54/25.39 class_Groups_Ozero(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 25.54/25.39 class_Int_Onumber(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 25.54/25.39 class_Groups_Oone(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 25.54/25.39 class_Rings_Odvd(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Nat_Onat) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 25.54/25.39 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 25.54/25.39 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 25.54/25.39 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 25.54/25.39 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 25.54/25.39 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 25.54/25.39 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 25.54/25.39 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 25.54/25.39 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 25.54/25.39 class_Lattices_Olattice(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 25.54/25.39 class_Orderings_Oorder(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 25.54/25.39 class_Orderings_Otop(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 25.54/25.39 class_Orderings_Oord(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 25.54/25.39 class_Orderings_Obot(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 25.54/25.39 class_Groups_Ouminus(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 25.54/25.39 class_Groups_Ominus(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 25.54/25.39 class_Enum_Oenum(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_HOL_Obool) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Com__Ostate__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Com_Ostate) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Com__Ostate__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Com_Ostate) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 25.54/25.39 ! [T_1] :
% 25.54/25.39 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 25.54/25.39 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_List__Olist__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_List__Olist__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Finite__Set_Ofinite(T_2)
% 25.54/25.39 & class_Finite__Set_Ofinite(T_1) )
% 25.54/25.39 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_sum__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_sum__Enum_Oenum,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_2)
% 25.54/25.39 & class_Enum_Oenum(T_1) )
% 25.54/25.39 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_sum__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 25.54/25.39 ! [T_1] :
% 25.54/25.39 ( class_Finite__Set_Ofinite(T_1)
% 25.54/25.39 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Option__Ooption__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 25.54/25.39 ! [T_1] :
% 25.54/25.39 ( class_Enum_Oenum(T_1)
% 25.54/25.39 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nitpick__Opair____box__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_HOL_Oequal(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 25.54/25.39 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 25.54/25.39 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Finite__Set_Ofinite(T_2)
% 25.54/25.39 & class_Finite__Set_Ofinite(T_1) )
% 25.54/25.39 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_prod__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_prod__Enum_Oenum,axiom,
% 25.54/25.39 ! [T_1,T_2] :
% 25.54/25.39 ( ( class_Enum_Oenum(T_2)
% 25.54/25.39 & class_Enum_Oenum(T_1) )
% 25.54/25.39 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_prod__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 25.54/25.39 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 25.54/25.39 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Product__Type_Ounit) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 25.54/25.39 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 25.54/25.39 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 25.54/25.39 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 25.54/25.39 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 25.54/25.39 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 25.54/25.39 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 25.54/25.39 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 25.54/25.39 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 25.54/25.39 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 25.54/25.39 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 25.54/25.39 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 25.54/25.39 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 25.54/25.39 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 25.54/25.39 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 25.54/25.39 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 25.54/25.39 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 25.54/25.39 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 25.54/25.39 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 25.54/25.39 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 25.54/25.39 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 25.54/25.39 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 25.54/25.39 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 25.54/25.39 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 25.54/25.39 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 25.54/25.39 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 25.54/25.39 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 25.54/25.39 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 25.54/25.39 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom,
% 25.54/25.39 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 25.54/25.39 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom,
% 25.54/25.39 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 25.54/25.39
% 25.54/25.39 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 25.54/25.39 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 25.54/25.39
% 25.54/25.39 %----Helper facts (20)
% 25.54/25.39 fof(help_c__COMBI__1,axiom,
% 25.54/25.39 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__COMBK__1,axiom,
% 25.54/25.39 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__COMBB__1,axiom,
% 25.54/25.39 ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__COMBC__1,axiom,
% 25.54/25.39 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__COMBS__1,axiom,
% 25.54/25.39 ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fequal__1,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 25.54/25.39 | V_x_2 = V_y_2 ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fequal__2,axiom,
% 25.54/25.39 ! [V_y_2,V_x_2] :
% 25.54/25.39 ( V_x_2 != V_y_2
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fFalse__1,axiom,
% 25.54/25.39 ~ hBOOL(c_fFalse) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fTrue__1,axiom,
% 25.54/25.39 hBOOL(c_fTrue) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fNot__1,axiom,
% 25.54/25.39 ! [V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 25.54/25.39 | ~ hBOOL(V_Pa_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fNot__2,axiom,
% 25.54/25.39 ! [V_Pa_2] :
% 25.54/25.39 ( ~ ~ hBOOL(V_Pa_2)
% 25.54/25.39 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fconj__1,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(V_Pa_2)
% 25.54/25.39 | ~ hBOOL(V_Qa_2)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fconj__2,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 25.54/25.39 | hBOOL(V_Pa_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fconj__3,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
% 25.54/25.39 | hBOOL(V_Qa_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fdisj__1,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(V_Pa_2)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fdisj__2,axiom,
% 25.54/25.39 ! [V_Pa_2,V_Qa_2] :
% 25.54/25.39 ( ~ hBOOL(V_Qa_2)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fdisj__3,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
% 25.54/25.39 | hBOOL(V_Pa_2)
% 25.54/25.39 | hBOOL(V_Qa_2) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fimplies__1,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( hBOOL(V_Pa_2)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fimplies__2,axiom,
% 25.54/25.39 ! [V_Pa_2,V_Qa_2] :
% 25.54/25.39 ( ~ hBOOL(V_Qa_2)
% 25.54/25.39 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ) ).
% 25.54/25.39
% 25.54/25.39 fof(help_c__fimplies__3,axiom,
% 25.54/25.39 ! [V_Qa_2,V_Pa_2] :
% 25.54/25.39 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
% 25.54/25.39 | ~ hBOOL(V_Pa_2)
% 25.54/25.39 | hBOOL(V_Qa_2) ) ).
% 25.54/25.39
% 25.54/25.39 %----Conjectures (2)
% 25.54/25.39 fof(conj_0,hypothesis,
% 25.54/25.39 ! [B_Z,B_s] :
% 25.54/25.39 ( v_Q_H(B_Z,B_s)
% 25.54/25.39 => v_Q(B_Z,B_s) ) ).
% 25.54/25.39
% 25.54/25.39 fof(conj_1,conjecture,
% 25.54/25.39 ! [B_Z,B_s] :
% 25.54/25.39 ( v_P(B_Z,B_s)
% 25.54/25.39 => ! [B_s_H] :
% 25.54/25.39 ( ! [B_Z_H] :
% 25.54/25.39 ( v_P(B_Z_H,B_s)
% 25.54/25.39 => v_Q_H(B_Z_H,B_s_H) )
% 25.54/25.39 => v_Q(B_Z,B_s_H) ) ) ).
% 25.54/25.39
% 25.54/25.39 %------------------------------------------------------------------------------
% 25.54/25.39 %-------------------------------------------
% 25.54/25.39 % Proof found
% 25.54/25.39 % SZS status Theorem for theBenchmark
% 25.54/25.39 % SZS output start Proof
% 25.54/25.40 %ClaNum:10480(EqnAxiom:3107)
% 25.54/25.40 %VarNum:80361(SingletonVarNum:23583)
% 25.54/25.40 %MaxLitNum:8
% 25.54/25.40 %MaxfuncDepth:13
% 25.54/25.40 %SharedTerms:1012
% 25.54/25.40 %goalClause: 3330 4667 4773
% 25.54/25.40 %singleGoalClaCount:2
% 25.54/25.40 [3111]P1(a180)
% 25.54/25.40 [3112]P2(a919)
% 25.54/25.40 [3113]P2(a920)
% 25.54/25.40 [3114]P2(a921)
% 25.54/25.40 [3115]P2(a924)
% 25.54/25.40 [3116]P2(a927)
% 25.54/25.40 [3117]P2(a1)
% 25.54/25.40 [3118]P2(a92)
% 25.54/25.40 [3119]P2(a315)
% 25.54/25.40 [3120]P3(a921)
% 25.54/25.40 [3121]P91(a921)
% 25.54/25.40 [3122]P91(a924)
% 25.54/25.40 [3123]P91(a1)
% 25.54/25.40 [3124]P91(a92)
% 25.54/25.40 [3125]P111(a921)
% 25.54/25.40 [3126]P92(a921)
% 25.54/25.40 [3127]P92(a924)
% 25.54/25.40 [3128]P108(a921)
% 25.54/25.40 [3129]P108(a924)
% 25.54/25.40 [3130]P108(a1)
% 25.54/25.40 [3131]P108(a92)
% 25.54/25.40 [3132]P109(a924)
% 25.54/25.40 [3133]P109(a1)
% 25.54/25.40 [3134]P109(a92)
% 25.54/25.40 [3135]P110(a921)
% 25.54/25.40 [3136]P110(a924)
% 25.54/25.40 [3137]P110(a1)
% 25.54/25.40 [3138]P110(a92)
% 25.54/25.40 [3139]P93(a921)
% 25.54/25.40 [3140]P93(a924)
% 25.54/25.40 [3141]P93(a1)
% 25.54/25.40 [3142]P58(a921)
% 25.54/25.40 [3143]P58(a924)
% 25.54/25.40 [3144]P58(a1)
% 25.54/25.40 [3145]P58(a92)
% 25.54/25.40 [3146]P94(a921)
% 25.54/25.40 [3147]P103(a921)
% 25.54/25.40 [3148]P103(a924)
% 25.54/25.40 [3149]P103(a1)
% 25.54/25.40 [3150]P104(a921)
% 25.54/25.40 [3151]P104(a924)
% 25.54/25.40 [3152]P104(a1)
% 25.54/25.40 [3153]P95(a921)
% 25.54/25.40 [3154]P102(a921)
% 25.54/25.40 [3155]P102(a924)
% 25.54/25.40 [3156]P102(a1)
% 25.54/25.40 [3157]P78(a1)
% 25.54/25.40 [3158]P59(a1)
% 25.54/25.40 [3159]P96(a921)
% 25.54/25.40 [3160]P68(a1)
% 25.54/25.40 [3161]P82(a921)
% 25.54/25.40 [3162]P82(a1)
% 25.54/25.40 [3163]P69(a924)
% 25.54/25.40 [3164]P69(a1)
% 25.54/25.40 [3165]P69(a92)
% 25.54/25.40 [3166]P112(a1)
% 25.54/25.40 [3167]P125(a1)
% 25.54/25.40 [3168]P113(a1)
% 25.54/25.40 [3169]P60(a921)
% 25.54/25.40 [3170]P60(a927)
% 25.54/25.40 [3171]P71(a924)
% 25.54/25.40 [3172]P71(a1)
% 25.54/25.40 [3173]P71(a92)
% 25.54/25.40 [3174]P72(a924)
% 25.54/25.40 [3175]P72(a1)
% 25.54/25.40 [3176]P72(a92)
% 25.54/25.40 [3177]P83(a924)
% 25.54/25.40 [3178]P83(a1)
% 25.54/25.40 [3179]P83(a92)
% 25.54/25.40 [3180]P70(a924)
% 25.54/25.40 [3181]P70(a1)
% 25.54/25.40 [3182]P70(a92)
% 25.54/25.40 [3183]P73(a924)
% 25.54/25.40 [3184]P73(a1)
% 25.54/25.40 [3185]P73(a92)
% 25.54/25.40 [3186]P74(a924)
% 25.54/25.40 [3187]P74(a1)
% 25.54/25.40 [3188]P74(a92)
% 25.54/25.40 [3189]P84(a924)
% 25.54/25.40 [3190]P84(a1)
% 25.54/25.40 [3191]P84(a92)
% 25.54/25.40 [3192]P85(a924)
% 25.54/25.40 [3193]P85(a1)
% 25.54/25.40 [3194]P85(a92)
% 25.54/25.40 [3195]P140(a924)
% 25.54/25.40 [3196]P140(a1)
% 25.54/25.40 [3197]P140(a92)
% 25.54/25.40 [3198]P114(a924)
% 25.54/25.40 [3199]P114(a1)
% 25.54/25.40 [3200]P114(a92)
% 25.54/25.40 [3201]P126(a1)
% 25.54/25.40 [3202]P115(a1)
% 25.54/25.40 [3203]P119(a924)
% 25.54/25.40 [3204]P119(a1)
% 25.54/25.40 [3205]P119(a92)
% 25.54/25.40 [3206]P144(a924)
% 25.54/25.40 [3207]P144(a1)
% 25.54/25.40 [3208]P79(a924)
% 25.54/25.40 [3209]P79(a1)
% 25.54/25.40 [3210]P79(a92)
% 25.54/25.40 [3211]P80(a924)
% 25.54/25.40 [3212]P80(a1)
% 25.54/25.40 [3213]P80(a92)
% 25.54/25.40 [3214]P127(a924)
% 25.54/25.40 [3215]P127(a1)
% 25.54/25.40 [3216]P127(a92)
% 25.54/25.40 [3217]P141(a1)
% 25.54/25.40 [3218]P130(a1)
% 25.54/25.40 [3219]P90(a924)
% 25.54/25.40 [3220]P90(a1)
% 25.54/25.40 [3221]P90(a92)
% 25.54/25.40 [3222]P81(a924)
% 25.54/25.40 [3223]P81(a1)
% 25.54/25.40 [3224]P81(a92)
% 25.54/25.40 [3225]P76(a1)
% 25.54/25.40 [3226]P133(a924)
% 25.54/25.40 [3227]P133(a1)
% 25.54/25.40 [3228]P133(a92)
% 25.54/25.40 [3229]P143(a1)
% 25.54/25.40 [3230]P134(a924)
% 25.54/25.40 [3231]P134(a1)
% 25.54/25.40 [3232]P134(a92)
% 25.54/25.40 [3233]P145(a924)
% 25.54/25.40 [3234]P145(a1)
% 25.54/25.40 [3235]P145(a92)
% 25.54/25.40 [3236]P87(a924)
% 25.54/25.40 [3237]P87(a1)
% 25.54/25.40 [3238]P87(a92)
% 25.54/25.40 [3239]P136(a924)
% 25.54/25.40 [3240]P136(a1)
% 25.54/25.40 [3241]P136(a92)
% 25.54/25.40 [3242]P138(a924)
% 25.54/25.40 [3243]P138(a1)
% 25.54/25.40 [3244]P138(a92)
% 25.54/25.40 [3245]P137(a924)
% 25.54/25.40 [3246]P137(a1)
% 25.54/25.40 [3247]P137(a92)
% 25.54/25.40 [3248]P128(a1)
% 25.54/25.40 [3249]P129(a1)
% 25.54/25.40 [3250]P123(a924)
% 25.54/25.40 [3251]P123(a1)
% 25.54/25.40 [3252]P123(a92)
% 25.54/25.40 [3253]P135(a924)
% 25.54/25.40 [3254]P135(a1)
% 25.54/25.40 [3255]P135(a92)
% 25.54/25.40 [3256]P131(a924)
% 25.54/25.40 [3257]P131(a1)
% 25.54/25.40 [3258]P131(a92)
% 25.54/25.40 [3259]P132(a1)
% 25.54/25.40 [3260]P142(a1)
% 25.54/25.40 [3261]P97(a1)
% 25.54/25.40 [3262]P88(a1)
% 25.54/25.40 [3263]P98(a1)
% 25.54/25.40 [3264]P99(a924)
% 25.54/25.40 [3265]P99(a1)
% 25.54/25.40 [3266]P99(a92)
% 25.54/25.40 [3267]P116(a924)
% 25.54/25.40 [3268]P116(a1)
% 25.54/25.40 [3269]P116(a92)
% 25.54/25.40 [3270]P146(a924)
% 25.54/25.40 [3271]P146(a1)
% 25.54/25.40 [3272]P146(a92)
% 25.54/25.40 [3273]P105(a924)
% 25.54/25.40 [3274]P105(a1)
% 25.54/25.40 [3275]P105(a92)
% 25.54/25.40 [3276]P61(a924)
% 25.54/25.40 [3277]P61(a1)
% 25.54/25.40 [3278]P61(a92)
% 25.54/25.40 [3279]P147(a924)
% 25.54/25.40 [3280]P147(a1)
% 25.54/25.40 [3281]P147(a92)
% 25.54/25.40 [3282]P62(a1)
% 25.54/25.40 [3283]P86(a1)
% 25.54/25.40 [3284]P139(a1)
% 25.54/25.40 [3285]P75(a1)
% 25.54/25.40 [3286]P77(a924)
% 25.54/25.40 [3287]P77(a1)
% 25.54/25.40 [3288]P77(a92)
% 25.54/25.40 [3289]P117(a924)
% 25.54/25.40 [3290]P89(a924)
% 25.54/25.40 [3291]P89(a1)
% 25.54/25.40 [3292]P89(a92)
% 25.54/25.40 [3293]P63(a921)
% 25.54/25.40 [3294]P63(a927)
% 25.54/25.40 [3295]P107(a919)
% 25.54/25.40 [3296]P107(a920)
% 25.54/25.40 [3297]P107(a921)
% 25.54/25.40 [3298]P107(a924)
% 25.54/25.40 [3299]P107(a927)
% 25.54/25.40 [3300]P107(a92)
% 25.54/25.40 [3301]P107(a315)
% 25.54/25.40 [3302]P106(a927)
% 25.54/25.40 [3303]P106(a1)
% 25.54/25.40 [3304]P120(a924)
% 25.54/25.40 [3305]P120(a1)
% 25.54/25.40 [3306]P120(a92)
% 25.54/25.40 [3307]P118(a1)
% 25.54/25.40 [3308]P101(a921)
% 25.54/25.40 [3327]P35(a924,a232)
% 25.54/25.40 [3328]P35(a924,a309)
% 25.54/25.40 [3329]P36(a924,a232)
% 25.54/25.40 [3330]P150(a316,a861)
% 25.54/25.40 [4662]~E(a90,a76)
% 25.54/25.40 [4663]~E(a90,a76)
% 25.54/25.40 [4664]~P25(a500)
% 25.54/25.40 [4665]~P1(a231)
% 25.54/25.40 [4667]~P151(a316,a863)
% 25.54/25.40 [3108]E(f2(a1),a76)
% 25.54/25.40 [3109]E(f3(a92),a4)
% 25.54/25.40 [3110]E(f93(a92),a5)
% 25.54/25.40 [3309]E(f181(a924),f2(a924))
% 25.54/25.40 [3310]E(f94(a924),f225(a924))
% 25.54/25.40 [3311]E(f103(a924),f226(a924))
% 25.54/25.40 [3312]E(f95(a1),f25(a1))
% 25.54/25.40 [3313]E(f77(a231),f2(a924))
% 25.54/25.40 [3314]E(f77(a180),f2(a924))
% 25.54/25.40 [3315]P4(f71(a1))
% 25.54/25.40 [3316]P4(f2(a1))
% 25.54/25.40 [3379]P35(f931(a924,a924),a26)
% 25.54/25.40 [3725]E(f311(a924,a924,a232,a232),a26)
% 25.54/25.40 [4666]~E(f71(a1),f2(a1))
% 25.54/25.40 [3317]E(f6(f2(a92)),f2(a924))
% 25.54/25.40 [3318]E(f104(f2(a924)),f2(a924))
% 25.54/25.40 [3332]E(f862(f72(a1),a76),a76)
% 25.54/25.40 [3335]E(f862(a105,f2(a924)),f71(a924))
% 25.54/25.40 [3336]E(f862(a97,f71(a1)),f71(a924))
% 25.54/25.40 [3337]E(f862(a5,f71(a924)),f71(a92))
% 25.54/25.40 [3338]E(f862(a97,f2(a1)),f2(a924))
% 25.54/25.40 [3339]E(f862(a5,f2(a924)),f2(a92))
% 25.54/25.40 [3340]E(f862(f96(a924),a76),f2(a924))
% 25.54/25.40 [3341]E(f862(f96(a1),a76),f2(a1))
% 25.54/25.40 [3342]E(f862(f96(a92),a76),f2(a92))
% 25.54/25.40 [3343]E(f862(a97,f2(a1)),f2(a924))
% 25.54/25.40 [3344]E(f862(f96(a924),a76),f2(a924))
% 25.54/25.40 [3345]E(f862(f182(a921),a231),f2(a924))
% 25.54/25.40 [3346]E(f862(f182(a921),a180),f2(a924))
% 25.54/25.40 [3352]E(f862(f72(a1),f71(a1)),a90)
% 25.54/25.40 [3357]E(f862(f93(a1),f71(a924)),f71(a1))
% 25.54/25.40 [3358]E(f862(f93(a1),f2(a924)),f2(a1))
% 25.54/25.40 [3359]E(f862(f72(a1),f2(a1)),f2(a1))
% 25.54/25.40 [3360]E(f862(f93(a1),f71(a924)),f71(a1))
% 25.54/25.40 [3361]E(f862(f93(a1),f2(a924)),f2(a1))
% 25.54/25.40 [3362]E(f862(f182(a924),f2(a924)),f2(a924))
% 25.54/25.40 [3363]E(f862(f182(a92),f2(a92)),f2(a924))
% 25.54/25.40 [3376]E(f862(a97,f71(a1)),f862(a105,f2(a924)))
% 25.54/25.40 [3377]E(f310(f931(a924,a924),a26),a27)
% 25.54/25.40 [3378]E(f312(f931(a924,a924),a26),a62)
% 25.54/25.40 [3405]E(f862(f274(a924),f2(a924)),f234(f932(a924,a921)))
% 25.54/25.40 [3406]E(f862(f292(a924),f2(a924)),f181(f932(a924,a921)))
% 25.54/25.40 [3415]P38(f181(f932(a1,a921)))
% 25.54/25.40 [3449]E(f862(f862(f3(a92),f2(a92)),f71(a92)),f2(a92))
% 25.54/25.40 [3494]E(f862(f862(f147(a1,a924),a97),f106(a1)),f106(a924))
% 25.54/25.40 [3528]P1(f862(f862(f228(a1),a90),f2(a1)))
% 25.54/25.40 [3552]P1(f862(f862(f227(a1),f2(a1)),f71(a1)))
% 25.54/25.40 [3553]P1(f862(f862(f227(a1),f2(a1)),f2(a1)))
% 25.54/25.40 [3554]P1(f862(f862(f228(a1),f2(a1)),f71(a1)))
% 25.54/25.40 [3756]E(f862(f862(f280(a924,a924,a924),a309),f299(a924,a309)),a232)
% 25.54/25.40 [3793]P39(a1,a924,a97,f862(f227(a1),f2(a1)))
% 25.54/25.40 [3797]E(f862(f862(f32(a924,f932(a924,a921)),f234(f932(a924,a921))),f293(a924)),f181(f932(a924,a921)))
% 25.54/25.40 [3798]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f294(a924)),f234(f932(a924,a921)))
% 25.54/25.40 [3799]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f274(a924)),f234(f932(a924,a921)))
% 25.54/25.40 [3800]E(f862(f862(f33(a924,f932(a924,a921)),f234(f932(a924,a921))),f292(a924)),f234(f932(a924,a921)))
% 25.54/25.40 [3815]P22(a924,a1,f93(a1),f234(f932(a924,a921)))
% 25.54/25.40 [3829]P39(a924,a1,f93(a1),f862(f18(a921,a924),a180))
% 25.54/25.40 [3963]E(f862(f66(a924,a92,a1,a5),a97),f96(a92))
% 25.54/25.40 [4182]P54(a92,a924,a22,a5,f234(f932(a924,a921)))
% 25.54/25.40 [4186]P54(a1,f932(f931(a924,a924),a921),a100,a82,a91)
% 25.54/25.40 [4441]E(f250(a1,a1,a1,a1,f25(a1),f72(a1)),a44)
% 25.54/25.40 [4676]~E(f862(f96(a1),a90),f862(f96(a1),a76))
% 25.54/25.40 [4677]~P1(f862(a186,f71(a1)))
% 25.54/25.40 [4678]~P1(f862(a186,f2(a1)))
% 25.54/25.40 [4705]~P1(f862(f862(f228(a1),a76),f2(a1)))
% 25.54/25.40 [3397]E(f862(f862(f3(a1),a90),a90),a76)
% 25.54/25.40 [3398]E(f862(f862(f73(a1),a76),a90),a90)
% 25.54/25.40 [3399]E(f862(f862(f73(a1),a76),a76),a76)
% 25.54/25.40 [3413]E(f862(f93(a1),f862(a105,f2(a924))),f71(a1))
% 25.54/25.40 [3479]E(f862(f28(a927),f234(f932(a927,a921))),f71(a924))
% 25.54/25.40 [3499]P1(f862(a186,f862(f96(a1),a90)))
% 25.54/25.40 [3500]P1(f862(f862(f84(a1),a90),a90))
% 25.54/25.40 [3501]P1(f862(f862(f84(a1),a76),a76))
% 25.54/25.40 [3502]P1(f862(f862(f227(a1),a90),a90))
% 25.54/25.40 [3503]P1(f862(f862(f227(a1),a90),a76))
% 25.54/25.40 [3504]P1(f862(f862(f227(a1),a76),a76))
% 25.54/25.40 [3505]P1(f862(f862(f228(a1),a90),a76))
% 25.54/25.40 [3562]E(f862(f862(f301(a924),f2(a924)),f181(f932(a924,a921))),f862(f294(a924),f2(a924)))
% 25.54/25.40 [3615]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),a76)))
% 25.54/25.40 [3627]E(f862(f302(a924,a924,a105),f234(f932(a924,a921))),f862(f293(a924),f2(a924)))
% 25.54/25.40 [3633]E(f862(f302(a1,a924,a97),f181(f932(a1,a921))),f181(f932(a924,a921)))
% 25.54/25.40 [3641]E(f862(f302(a924,a1,f93(a1)),f181(f932(a924,a921))),f181(f932(a1,a921)))
% 25.54/25.40 [3662]P6(f931(a924,a924),f234(f932(f931(a924,a924),a921)),a101)
% 25.54/25.40 [3970]E(f862(f66(a924,a1,a92,f93(a1)),a22),a24)
% 25.54/25.40 [4029]P35(a924,f862(f254(f931(a924,a924)),f862(f249(a924,a924,a921),f228(a924))))
% 25.54/25.40 [4694]~P1(f862(a186,f862(f96(a1),a76)))
% 25.54/25.40 [4695]~P1(f862(f862(f84(a1),a90),a76))
% 25.54/25.40 [4696]~P1(f862(f862(f84(a1),a76),a90))
% 25.54/25.40 [4697]~P1(f862(f862(f227(a1),a76),a90))
% 25.54/25.40 [4698]~P1(f862(f862(f228(a1),a90),a90))
% 25.54/25.40 [4699]~P1(f862(f862(f228(a1),a76),a90))
% 25.54/25.40 [4700]~P1(f862(f862(f228(a1),a76),a76))
% 25.54/25.40 [4709]~P1(f862(f54(a924),f234(f932(a924,a921))))
% 25.54/25.40 [4710]~P1(f862(f54(a1),f234(f932(a1,a921))))
% 25.54/25.40 [4609]E(f862(f249(a1,a1,a921),f862(f862(f10(f932(a1,a921),f932(a1,a921),a1),f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f228(a1),f2(a1))))),f862(f862(f9(a1,a1,f932(a1,a921)),f862(f862(f10(f932(a1,f932(a1,a921)),f932(a1,f932(a1,a921)),a1),f9(a1,a1,a921)),f862(f862(f10(f932(a1,a1),f932(a1,f932(a1,a921)),a1),f862(f10(a1,f932(a1,a921),a1),a317)),a210))),f71(a1)))),a206)
% 25.54/25.40 [3665]E(f862(f862(f3(a1),f862(f862(f73(a1),a90),a90)),a90),a90)
% 25.54/25.40 [3699]E(f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90),f862(f72(a1),a90))
% 25.54/25.40 [3738]E(f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90),f862(f862(f3(a1),a76),a90))
% 25.54/25.40 [3897]E(f862(f862(f53(f931(a924,a924)),f234(f932(f931(a924,a924),a921))),a101),a91)
% 25.54/25.40 [3925]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a924))
% 25.54/25.40 [3926]E(f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a1))
% 25.54/25.40 [3927]E(f862(f96(a92),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a92))
% 25.54/25.40 [3928]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(a924))
% 25.54/25.40 [3931]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(a105,f2(a924)))
% 25.54/25.40 [4308]E(f862(f862(f103(f932(f931(f931(a924,a924),f931(a924,a924)),a921)),a26),f299(f931(a924,a924),f181(f932(f931(f931(a924,a924),f931(a924,a924)),a921)))),a64)
% 25.54/25.40 [4374]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f71(a924)),f2(a924))),f181(f932(f931(a924,a924),a921))))),f71(a1))
% 25.54/25.40 [4375]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f2(a924)),f2(a924))),f181(f932(f931(a924,a924),a921))))),f2(a1))
% 25.54/25.40 [4388]E(f862(f254(f931(a924,a924)),f862(f249(a924,a924,a921),f862(f862(f10(a924,f932(a924,a921),a924),f862(f9(a924,a924,a921),a317)),a105))),a309)
% 25.54/25.40 [4359]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(a105,f862(a105,f2(a924))))
% 25.54/25.40 [4360]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(a105,f862(a105,f2(a924))))
% 25.54/25.40 [4363]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(f862(f73(a924),f71(a924)),f71(a924)))
% 25.54/25.40 [4364]E(f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),f862(f28(a921),f234(f932(a921,a921))))
% 25.54/25.40 [4427]P4(f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))
% 25.54/25.40 [4497]P24(f932(f931(a924,a924),a921),f862(f862(f244(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921),f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),a27),a63))
% 25.54/25.40 [4498]P24(f932(f931(a924,a924),a921),f862(f862(f244(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921),f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),a62),a65))
% 25.54/25.40 [4540]E(f862(f862(f103(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),f312(f931(a924,a924),a64)),f862(f862(f301(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),f181(f932(f931(a924,a924),a921)))),f181(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)))),a65)
% 25.54/25.40 [4541]E(f862(f862(f103(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)),f310(f931(a924,a924),a64)),f862(f862(f301(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),f181(f932(f931(a924,a924),a921)))),f181(f932(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a921)))),a63)
% 25.54/25.40 [4430]E(f862(a97,f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(a105,f2(a924))))
% 25.54/25.40 [4474]E(f862(a97,f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))
% 25.54/25.40 [4475]E(f862(f93(a1),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))
% 25.54/25.40 [4508]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.40 [4509]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)),f862(a105,f862(a105,f862(a105,f2(a924)))))
% 25.54/25.40 [4555]P4(f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)))
% 25.54/25.40 [4580]E(f862(a97,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)))
% 25.54/25.40 [4581]E(f862(f93(a1),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90)))
% 25.54/25.40 [4594]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))))
% 25.54/25.40 [3331]P5(x33311,a317)
% 25.54/25.40 [3726]P22(a924,a924,a105,x37261)
% 25.54/25.40 [3319]P2(f923(x33191))
% 25.54/25.40 [3320]P2(f928(x33201))
% 25.54/25.40 [3321]P2(f925(x33211))
% 25.54/25.40 [3322]P2(f926(x33221))
% 25.54/25.40 [3323]P107(f923(x33231))
% 25.54/25.40 [3324]P107(f928(x33241))
% 25.54/25.40 [3325]P107(f925(x33251))
% 25.54/25.40 [3326]P107(f926(x33261))
% 25.54/25.40 [3347]P35(a1,f98(x33471))
% 25.54/25.40 [3348]P35(a1,f99(x33481))
% 25.54/25.40 [3401]P35(f932(x34011,a921),f306(x34011))
% 25.54/25.40 [3402]P36(f932(x34021,a921),f306(x34021))
% 25.54/25.40 [3427]E(f235(x34271,x34271,a317),a317)
% 25.54/25.40 [3442]E(f38(a1,x34421,x34421),f2(a1))
% 25.54/25.40 [3496]P12(x34961,f932(x34961,a921),f301(x34961))
% 25.54/25.40 [4668]~E(f862(a105,x46681),x46681)
% 25.54/25.40 [4669]~E(f862(a105,x46691),x46691)
% 25.54/25.40 [4670]~E(f862(a105,x46701),f2(a924))
% 25.54/25.40 [4671]~E(f862(a105,x46711),f2(a924))
% 25.54/25.40 [4672]~E(f862(a105,x46721),f2(a924))
% 25.54/25.40 [4673]~E(f862(a105,x46731),f2(a924))
% 25.54/25.40 [4674]~E(f862(a105,x46741),f2(a924))
% 25.54/25.40 [4675]~E(f862(a105,x46751),f2(a924))
% 25.54/25.40 [3333]E(f862(f96(a1),x33331),x33331)
% 25.54/25.40 [3334]E(f862(f182(a924),x33341),x33341)
% 25.54/25.40 [3349]E(f862(a82,f320(x33491)),x33491)
% 25.54/25.40 [3350]E(f862(a5,f587(x33501)),x33501)
% 25.54/25.40 [3351]E(f233(x33511,f2(a92)),f2(a92))
% 25.54/25.40 [3364]E(f107(x33641,f106(x33641)),f106(x33641))
% 25.54/25.40 [3365]E(f145(x33651,f106(x33651)),f106(x33651))
% 25.54/25.40 [3373]E(f862(f160(x33731),f106(x33731)),f106(x33731))
% 25.54/25.40 [3374]E(f862(f164(x33741),f106(x33741)),f106(x33741))
% 25.54/25.40 [3375]E(f862(f161(x33751),f106(x33751)),f106(x33751))
% 25.54/25.40 [3380]E(f862(f96(a1),x33801),f862(f95(a1),x33801))
% 25.54/25.40 [3381]E(f862(a82,f862(a100,x33811)),x33811)
% 25.54/25.40 [3382]E(f862(a5,f862(a22,x33821)),x33821)
% 25.54/25.40 [3383]E(f862(a5,f862(a22,x33831)),x33831)
% 25.54/25.40 [3384]E(f862(a22,f862(a5,x33841)),x33841)
% 25.54/25.40 [3386]P4(f862(f93(a1),x33861))
% 25.54/25.40 [3395]E(f862(f182(f925(x33951)),f106(x33951)),f2(a924))
% 25.54/25.40 [3396]E(f862(f182(f926(x33961)),f112(x33961)),f2(a924))
% 25.54/25.40 [3418]E(f862(f862(f3(a924),x34181),f2(a924)),x34181)
% 25.54/25.40 [3419]E(f862(f862(f74(a924),x34191),f71(a924)),x34191)
% 25.54/25.40 [3420]E(f862(f862(f74(a1),x34201),f71(a1)),x34201)
% 25.54/25.40 [3421]E(f862(f862(f73(a924),x34211),f2(a924)),x34211)
% 25.54/25.40 [3422]E(f862(f862(f73(a1),x34221),f2(a1)),x34221)
% 25.54/25.40 [3423]E(f862(f862(f226(a924),x34231),f2(a924)),x34231)
% 25.54/25.40 [3424]E(f862(f862(f74(a924),x34241),f2(a924)),f2(a924))
% 25.54/25.40 [3425]E(f862(f862(f29(a1),x34251),f2(a1)),f2(a1))
% 25.54/25.40 [3426]E(f862(f862(f225(a924),x34261),f2(a924)),f2(a924))
% 25.54/25.40 [3433]E(f862(f165(x34331),f106(x34331)),f181(f932(x34331,a921)))
% 25.54/25.40 [3437]P1(f862(f130(x34371),f106(x34371)))
% 25.54/25.40 [3443]E(f862(f147(x34431,x34431),f7(x34431)),f25(f925(x34431)))
% 25.54/25.40 [3444]E(f862(f147(x34441,x34441),f25(x34441)),f25(f925(x34441)))
% 25.54/25.40 [3445]E(f38(a1,x34451,f2(a1)),x34451)
% 25.54/25.40 [3446]E(f862(f227(a924),f862(a105,x34461)),f862(f228(a924),x34461))
% 25.54/25.40 [3447]E(f862(f274(a924),f862(a105,x34471)),f862(f293(a924),x34471))
% 25.54/25.40 [3448]E(f862(f292(a924),f862(a105,x34481)),f862(f294(a924),x34481))
% 25.54/25.40 [3450]E(f38(a1,f2(a1),x34501),f2(a1))
% 25.54/25.40 [3464]E(f862(f862(f73(a924),x34641),f71(a924)),f862(a105,x34641))
% 25.54/25.40 [3473]E(f862(f295(a924,x34731),f2(a924)),f181(f932(a924,a921)))
% 25.54/25.40 [3485]E(f296(a924,f2(a924),x34851),f862(f294(a924),x34851))
% 25.54/25.40 [3531]E(f862(f862(f3(a924),f862(a105,x35311)),f71(a924)),x35311)
% 25.54/25.40 [3543]E(f40(f2(a1),x35431),f862(f862(f244(a1,a1),f2(a1)),f2(a1)))
% 25.54/25.40 [3547]E(f862(f862(f73(a924),f862(a22,x35471)),f2(a924)),f862(a22,x35471))
% 25.54/25.40 [3590]P1(f862(f862(f228(a924),x35901),f862(a105,x35901)))
% 25.54/25.40 [3602]P1(f862(f862(f228(a924),f2(a924)),f862(a105,x36021)))
% 25.54/25.40 [3613]E(f862(f862(f176(f925(x36131),f925(x36131)),f2(a924)),f160(x36131)),f25(f925(x36131)))
% 25.54/25.40 [3828]E(f86(x38281,x38281,f234(f932(x38281,a921)),f25(x38281)),f25(x38281))
% 25.54/25.40 [3884]E(f862(f862(f3(a92),f862(a5,f862(a105,f862(a22,x38841)))),f71(a92)),x38841)
% 25.54/25.40 [3954]P1(f862(f862(f227(a1),f862(f72(a1),f862(f93(a1),x39541))),f2(a1)))
% 25.54/25.40 [4097]P1(f862(f862(f228(a1),f862(f72(a1),f862(f93(a1),f862(a105,x40971)))),f2(a1)))
% 25.54/25.40 [4194]P23(x41941,x41941,f25(x41941),f234(f932(x41941,a921)),f234(f932(x41941,a921)))
% 25.54/25.40 [4683]~E(f234(f932(x46831,a921)),f181(f932(x46831,a921)))
% 25.54/25.40 [4706]~P1(f862(f862(f228(a924),x47061),f2(a924)))
% 25.54/25.40 [4707]~P1(f862(f862(f228(a924),x47071),f2(a924)))
% 25.54/25.40 [4708]~P1(f862(f862(f228(a924),x47081),f2(a924)))
% 25.54/25.40 [4719]~P1(f862(f862(f228(a1),f862(f93(a1),x47191)),f2(a1)))
% 25.54/25.40 [3385]E(f113(x33851,f112(f926(x33851))),f112(x33851))
% 25.54/25.40 [3400]E(f172(x34001,f106(f925(x34001))),f106(f925(x34001)))
% 25.54/25.40 [3403]E(f862(f862(f74(a1),a76),x34031),a76)
% 25.54/25.40 [3404]E(f862(f862(f73(a1),a76),x34041),x34041)
% 25.54/25.40 [3407]E(f862(a97,f862(f93(a1),x34071)),x34071)
% 25.54/25.40 [3408]E(f862(f862(f3(a1),x34081),a76),x34081)
% 25.54/25.40 [3409]E(f862(f862(f73(a1),x34091),a76),x34091)
% 25.54/25.40 [3412]E(f862(f862(f3(a924),x34121),x34121),f2(a924))
% 25.54/25.40 [3416]E(f862(f72(a1),f862(f72(a1),x34161)),x34161)
% 25.54/25.40 [3417]E(f862(f28(a924),f862(f292(a924),x34171)),x34171)
% 25.54/25.40 [3428]E(f862(f862(f74(a924),f71(a924)),x34281),x34281)
% 25.54/25.40 [3429]E(f862(f862(f74(a1),f71(a1)),x34291),x34291)
% 25.54/25.40 [3430]E(f862(f862(f73(a924),f2(a924)),x34301),x34301)
% 25.54/25.40 [3431]E(f862(f862(f73(a1),f2(a1)),x34311),x34311)
% 25.54/25.40 [3432]E(f862(f862(f226(a924),f2(a924)),x34321),x34321)
% 25.54/25.40 [3438]E(f862(f862(f3(a924),f2(a924)),x34381),f2(a924))
% 25.54/25.40 [3439]E(f862(f862(f74(a924),f2(a924)),x34391),f2(a924))
% 25.54/25.40 [3440]E(f862(f862(f29(a1),f2(a1)),x34401),f2(a1))
% 25.54/25.40 [3441]E(f862(f862(f225(a924),f2(a924)),x34411),f2(a924))
% 25.54/25.40 [3451]E(f121(x34511,f862(f72(a1),x34511)),f125(a1,x34511))
% 25.54/25.40 [3457]E(f862(f295(a924,f2(a924)),x34571),f862(f292(a924),x34571))
% 25.54/25.40 [3458]E(f862(f862(f74(a1),a90),x34581),f862(f72(a1),x34581))
% 25.54/25.40 [3465]E(f862(a97,f862(f96(a1),x34651)),f862(f96(a924),x34651))
% 25.54/25.40 [3466]E(f862(a97,f862(f96(a1),x34661)),f862(f96(a924),x34661))
% 25.54/25.40 [3467]E(f862(a22,f862(f96(a92),x34671)),f862(f96(a924),x34671))
% 25.54/25.40 [3468]E(f862(f28(a924),f862(f294(a924),x34681)),f862(a105,x34681))
% 25.54/25.40 [3477]E(f862(f862(f73(a924),f71(a924)),x34771),f862(a105,x34771))
% 25.54/25.40 [3481]E(f862(f95(a1),f862(f93(a1),x34811)),f862(f93(a1),x34811))
% 25.54/25.40 [3482]E(f862(f69(a1),f862(f93(a1),x34821)),f862(f93(a1),x34821))
% 25.54/25.40 [3486]E(f862(f28(x34861),f181(f932(x34861,a921))),f2(a924))
% 25.54/25.40 [3488]E(f862(f862(f29(a924),x34881),f862(a105,f2(a924))),x34881)
% 25.54/25.40 [3497]E(f38(a924,x34971,f862(a105,f2(a924))),f2(a924))
% 25.54/25.40 [3498]E(f38(a1,x34981,f862(f96(a1),a90)),f2(a1))
% 25.54/25.40 [3507]E(f862(f862(f73(a1),a90),x35071),f862(f862(f73(a1),x35071),a90))
% 25.54/25.40 [3514]E(f862(f862(f29(a1),x35141),f862(f96(a1),a90)),f862(f72(a1),x35141))
% 25.54/25.40 [3518]E(f132(a924,f862(f295(a924,x35181),f2(a924))),f106(a924))
% 25.54/25.40 [3519]E(f862(f862(f73(a1),x35191),f71(a1)),f862(f862(f3(a1),x35191),a90))
% 25.54/25.40 [3520]E(f862(f862(f3(a1),x35201),f71(a1)),f862(f862(f73(a1),x35201),a90))
% 25.54/25.40 [3524]P1(f862(f862(f84(a1),x35241),x35241))
% 25.54/25.40 [3525]P1(f862(f862(f227(a924),x35251),x35251))
% 25.54/25.40 [3526]P1(f862(f862(f227(a1),x35261),x35261))
% 25.54/25.40 [3527]P1(f862(f862(f278(a924),x35271),x35271))
% 25.54/25.40 [3532]E(f862(f72(a1),f862(f96(a1),x35321)),f862(f96(a1),f862(f72(a1),x35321)))
% 25.54/25.40 [3533]P1(f862(f54(a924),f862(f294(a924),x35331)))
% 25.54/25.40 [3534]P1(f862(f54(a924),f862(f292(a924),x35341)))
% 25.54/25.40 [3541]E(f154(x35411,f234(f932(x35411,a921))),f234(f932(f925(x35411),a921)))
% 25.54/25.40 [3545]P1(f862(f862(f227(a924),f2(a924)),x35451))
% 25.54/25.40 [3546]P1(f862(f862(f227(a924),f2(a924)),x35461))
% 25.54/25.40 [3556]E(f862(f862(f73(a924),f104(x35561)),f862(a105,f2(a924))),f104(f862(a105,x35561)))
% 25.54/25.40 [3557]E(f862(f254(x35571),f862(f18(a921,x35571),a231)),f181(f932(x35571,a921)))
% 25.54/25.40 [3558]E(f862(f254(x35581),f862(f18(a921,x35581),a180)),f234(f932(x35581,a921)))
% 25.54/25.40 [3561]E(f862(f862(f301(a924),x35611),f862(f292(a924),x35611)),f862(f292(a924),f862(a105,x35611)))
% 25.54/25.40 [3573]E(f862(f862(f73(a1),f71(a1)),f862(f93(a1),x35731)),f862(f93(a1),f862(a105,x35731)))
% 25.54/25.40 [3575]E(f862(f862(f144(f925(x35751)),f106(x35751)),f106(f925(x35751))),f47(x35751,f106(x35751)))
% 25.54/25.40 [3593]E(f181(f932(f931(x35931,x35931),a921)),f255(x35931,f181(f932(x35931,a921))))
% 25.54/25.40 [3594]E(f862(f300(x35941),f234(f932(x35941,a921))),f234(f932(f932(x35941,a921),a921)))
% 25.54/25.40 [3595]E(f862(f72(f932(x35951,a921)),f181(f932(x35951,a921))),f234(f932(x35951,a921)))
% 25.54/25.40 [3596]E(f862(f72(f932(x35961,a921)),f234(f932(x35961,a921))),f181(f932(x35961,a921)))
% 25.54/25.40 [3597]P1(f862(f54(x35971),f181(f932(x35971,a921))))
% 25.54/25.40 [3598]P1(f862(f54(x35981),f181(f932(x35981,a921))))
% 25.54/25.40 [3600]E(f862(f295(a924,x36001),f862(a105,x36001)),f862(f862(f301(a924),x36001),f181(f932(a924,a921))))
% 25.54/25.40 [3601]E(f78(f931(a924,a924),f41(x36011,f2(a924))),f862(f862(f244(a924,a924),f2(a924)),x36011))
% 25.54/25.40 [3614]E(f862(f862(f301(a924),f862(a105,x36141)),f862(f294(a924),x36141)),f862(f294(a924),f862(a105,x36141)))
% 25.54/25.40 [3618]P35(x36181,f181(f932(f931(x36181,x36181),a921)))
% 25.54/25.40 [3619]P37(x36191,f181(f932(f931(x36191,x36191),a921)))
% 25.54/25.40 [3621]P1(f862(f862(f227(a1),f2(a1)),f862(f93(a1),x36211)))
% 25.54/25.40 [3622]P1(f862(f862(f227(a1),f2(a1)),f862(f93(a1),x36221)))
% 25.54/25.40 [3629]E(f862(f862(f73(a924),f862(f182(a924),x36291)),f862(a105,f2(a924))),f862(f182(a924),f862(a105,x36291)))
% 25.54/25.40 [3675]P1(f862(f862(f321(a924),f587(x36751)),f234(f932(a924,a921))))
% 25.54/25.40 [3677]E(f862(f302(x36771,x36771,f25(x36771)),f234(f932(x36771,a921))),f234(f932(x36771,a921)))
% 25.54/25.40 [3719]P1(f862(f862(f321(x37191),f323(x37191)),f234(f932(x37191,a921))))
% 25.54/25.40 [3733]P38(f862(f302(a924,a1,f93(a1)),x37331))
% 25.54/25.40 [3771]P50(x37711,f181(f932(x37711,a921)),f181(f932(f931(x37711,x37711),a921)))
% 25.54/25.40 [3789]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f3(a1),x37891),f71(a1))),f43(f862(f96(a1),a90),x37891))
% 25.54/25.40 [3790]P1(f862(f862(f321(a924),f862(a22,x37901)),f234(f932(a924,a921))))
% 25.54/25.40 [3841]P57(x38411,f862(f18(f932(x38411,a921),x38411),f862(f18(a921,x38411),a231)))
% 25.54/25.40 [4023]E(f862(f135(f925(x40231),f925(x40231),f127(x40231),f106(x40231)),f106(f925(x40231))),f106(x40231))
% 25.54/25.40 [4041]P1(f862(f862(f321(f932(f931(a924,a924),a921)),f320(x40411)),a91))
% 25.54/25.40 [4066]P1(f862(f862(f321(f932(f931(a924,a924),a921)),f862(a100,x40661)),a91))
% 25.54/25.40 [4195]P22(x41951,f932(x41951,a921),f862(f862(f9(x41951,f932(x41951,a921),f932(x41951,a921)),f301(x41951)),f181(f932(x41951,a921))),f234(f932(x41951,a921)))
% 25.54/25.40 [4429]P54(f923(x44291),f932(f922(f930(a919,f932(x44291,f932(a920,a921))),f930(a920,x44291)),a921),f87(x44291),f85(x44291),f862(f254(f932(f922(f930(a919,f932(x44291,f932(a920,a921))),f930(a920,x44291)),a921)),f88(x44291)))
% 25.54/25.40 [4679]~E(f862(f862(f73(a1),x46791),x46791),a90)
% 25.54/25.40 [4680]~E(f862(f862(f73(a1),x46801),x46801),a90)
% 25.54/25.40 [4692]~E(f862(a5,f862(a105,f862(a22,x46921))),f2(a92))
% 25.54/25.40 [4693]~E(f862(a5,f862(a105,f862(a22,x46931))),f2(a92))
% 25.54/25.40 [4701]~P1(f862(a186,f862(f93(a1),x47011)))
% 25.54/25.40 [4703]~P1(f862(f862(f228(a924),x47031),x47031))
% 25.54/25.40 [4704]~P1(f862(f862(f228(a924),x47041),x47041))
% 25.54/25.40 [4712]~P1(f862(f862(f227(a924),f862(a105,x47121)),x47121))
% 25.54/25.40 [3548]E(f862(a97,f862(f72(a1),f862(f93(a1),x35481))),f2(a924))
% 25.54/25.40 [3551]E(f862(f862(f73(a1),f862(f72(a1),x35511)),x35511),f2(a1))
% 25.54/25.40 [3555]E(f862(f28(a1),f862(f295(a1,f2(a1)),x35551)),f862(a97,x35551))
% 25.54/25.40 [3566]E(f862(f862(f236(a924),f862(a105,f2(a924))),x35661),f862(a105,f2(a924)))
% 25.54/25.40 [3659]E(f862(f273(x36591),f181(f932(f931(x36591,x36591),a921))),f181(f932(x36591,a921)))
% 25.54/25.40 [3661]P1(f862(f54(a1),f862(f295(a1,f2(a1)),x36611)))
% 25.54/25.40 [3667]E(f31(f932(x36671,a921),f181(f932(f932(x36671,a921),a921))),f234(f932(x36671,a921)))
% 25.54/25.40 [3668]E(f31(f932(x36681,a921),f234(f932(f932(x36681,a921),a921))),f181(f932(x36681,a921)))
% 25.54/25.40 [3669]E(f30(f932(x36691,a921),f181(f932(f932(x36691,a921),a921))),f181(f932(x36691,a921)))
% 25.54/25.40 [3670]E(f30(f932(x36701,a921),f234(f932(f932(x36701,a921),a921))),f234(f932(x36701,a921)))
% 25.54/25.40 [3674]P1(f862(f862(f278(a924),f862(a105,f2(a924))),x36741))
% 25.54/25.40 [3715]E(f862(f862(f301(f925(x37151)),f106(x37151)),f181(f932(f925(x37151),a921))),f154(x37151,f181(f932(x37151,a921))))
% 25.54/25.40 [3716]E(f862(f862(f301(f925(x37161)),f106(x37161)),f181(f932(f925(x37161),a921))),f155(x37161,f106(f932(x37161,a921))))
% 25.54/25.40 [3742]E(f862(f862(f73(a1),f862(f72(a1),x37421)),f862(f72(a1),x37421)),f862(f72(a1),f862(f862(f73(a1),x37421),x37421)))
% 25.54/25.40 [3755]E(f862(f862(f73(a924),f6(x37551)),f862(a105,f2(a924))),f6(f862(a5,f862(a105,f862(a22,x37551)))))
% 25.54/25.40 [3780]E(f862(f28(a1),f862(f302(a924,a1,f93(a1)),x37801)),f862(f28(a924),x37801))
% 25.54/25.40 [3781]P1(f862(f862(f227(a924),x37811),f862(f862(f74(a924),x37811),x37811)))
% 25.54/25.40 [3819]E(f862(f302(a1,a924,a97),f296(a1,f2(a1),f862(f93(a1),x38191))),f862(f294(a924),x38191))
% 25.54/25.40 [3836]E(f862(f862(f29(a924),f862(a105,f2(a924))),f862(f96(a924),x38361)),f862(a97,f862(f862(f29(a1),f71(a1)),f862(f96(a1),x38361))))
% 25.54/25.40 [3838]E(f862(f165(a924),f132(a924,f862(f295(a924,f2(a924)),f862(a105,x38381)))),f862(f294(a924),x38381))
% 25.54/25.40 [3839]E(f862(f862(f73(a924),f862(f182(a92),x38391)),f862(a105,f2(a924))),f862(f182(a92),f862(a5,f862(a105,f862(a22,x38391)))))
% 25.54/25.40 [3857]P36(x38571,f299(x38571,f181(f932(f931(x38571,x38571),a921))))
% 25.54/25.40 [3858]P37(x38581,f299(x38581,f181(f932(f931(x38581,x38581),a921))))
% 25.54/25.40 [3859]P49(x38591,f299(x38591,f181(f932(f931(x38591,x38591),a921))))
% 25.54/25.40 [3860]E(f862(f302(a1,a924,a97),f862(f302(a924,a1,f93(a1)),x38601)),x38601)
% 25.54/25.40 [3890]E(f862(f862(f301(a924),f2(a924)),f862(f302(a924,a924,a105),f862(f292(a924),x38901))),f862(f292(a924),f862(a105,x38901)))
% 25.54/25.40 [3896]P52(x38961,x38961,f299(x38961,f181(f932(f931(x38961,x38961),a921))))
% 25.54/25.40 [3902]P1(f862(a186,f862(f72(a1),f862(f93(a1),f862(a105,x39021)))))
% 25.54/25.40 [3912]E(f862(f862(f3(f932(a924,a921)),f862(f274(a924),x39121)),f862(f862(f301(a924),x39121),f181(f932(a924,a921)))),f862(f274(a924),f862(a105,x39121)))
% 25.54/25.40 [3929]E(f862(f862(f73(a1),f862(f862(f3(a1),a76),x39291)),f862(f862(f3(a1),a76),x39291)),f862(f862(f3(a1),a76),f862(f862(f73(a1),x39291),x39291)))
% 25.54/25.40 [3932]P50(x39321,f234(f932(x39321,a921)),f299(x39321,f181(f932(f931(x39321,x39321),a921))))
% 25.54/25.40 [3943]E(f862(f862(f301(f932(x39431,a921)),f181(f932(x39431,a921))),f181(f932(f932(x39431,a921),a921))),f862(f300(x39431),f181(f932(x39431,a921))))
% 25.54/25.40 [3971]E(f862(f862(f3(f932(a924,a921)),f862(f293(a924),x39711)),f862(f862(f301(a924),f862(a105,x39711)),f181(f932(a924,a921)))),f862(f293(a924),f862(a105,x39711)))
% 25.54/25.40 [4078]E(f862(f96(a924),f862(f862(f73(a1),x40781),x40781)),f862(f862(f79(a924,a924),f862(f96(a924),x40781)),f862(f862(f20(a924,a924,a924),f73(a924)),f7(a924))))
% 25.54/25.40 [4450]P12(x44501,f932(x44501,a921),f862(f862(f10(f932(x44501,a921),f932(f932(x44501,a921),f932(x44501,a921)),x44501),f862(f9(f932(x44501,a921),f932(x44501,a921),f932(x44501,a921)),f3(f932(x44501,a921)))),f862(f862(f9(x44501,f932(x44501,a921),f932(x44501,a921)),f301(x44501)),f181(f932(x44501,a921)))))
% 25.54/25.40 [4539]E(f862(f254(f931(a1,a1)),f862(f249(a1,a1,a921),f862(f862(f10(f932(a1,a921),f932(a1,a921),a1),f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),x45391)))),f228(a1)))),f98(x45391))
% 25.54/25.40 [4572]E(f862(f254(f931(a1,a1)),f862(f249(a1,a1,a921),f862(f862(f20(a1,f932(a1,a921),f932(a1,a921)),f862(f862(f10(f932(a921,a921),f932(f932(a1,a921),f932(a1,a921)),a1),f10(a921,a921,a1)),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),x45721)))),f228(a1)))),f99(x45721))
% 25.54/25.40 [4625]E(f862(f254(f931(f932(x46251,a921),f932(x46251,a921))),f862(f249(f932(x46251,a921),f932(x46251,a921),a921),f862(f862(f9(f932(x46251,a921),f932(f932(x46251,a921),a921),f932(f932(x46251,a921),a921)),f862(f862(f10(f932(f932(x46251,a921),f932(a921,a921)),f932(f932(f932(x46251,a921),a921),f932(f932(x46251,a921),a921)),f932(x46251,a921)),f20(f932(x46251,a921),a921,a921)),f862(f862(f10(f932(f932(x46251,a921),a921),f932(f932(x46251,a921),f932(a921,a921)),f932(x46251,a921)),f862(f10(a921,f932(a921,a921),f932(x46251,a921)),a318)),f228(f932(x46251,a921))))),f54(x46251)))),f306(x46251))
% 25.54/25.40 [4716]~P1(f862(f54(f925(x47161)),f234(f932(f925(x47161),a921))))
% 25.54/25.40 [4721]~P1(f862(f862(f84(a1),a90),f862(f862(f73(a1),x47211),x47211)))
% 25.54/25.40 [4730]~P1(f862(f862(f227(a1),f2(a1)),f862(f72(a1),f862(f93(a1),f862(a105,x47301)))))
% 25.54/25.40 [3694]E(f862(f862(f3(a1),f862(f862(f73(a1),x36941),a90)),a90),x36941)
% 25.54/25.40 [3708]E(f862(f165(a924),f132(a924,f862(f295(a924,f2(a924)),x37081))),f862(f292(a924),x37081))
% 25.54/25.40 [3903]E(f862(f275(x39031,x39031),f299(x39031,f181(f932(f931(x39031,x39031),a921)))),f234(f932(x39031,a921)))
% 25.54/25.40 [3904]E(f862(f256(x39041,x39041),f299(x39041,f181(f932(f931(x39041,x39041),a921)))),f234(f932(x39041,a921)))
% 25.54/25.40 [3950]E(f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x39501)),x39501),f862(f862(f3(a1),f862(f862(f73(a1),x39501),x39501)),a90))
% 25.54/25.40 [3998]E(f862(f277(x39981,x39981),f299(x39981,f181(f932(f931(x39981,x39981),a921)))),f299(x39981,f181(f932(f931(x39981,x39981),a921))))
% 25.54/25.40 [4044]P1(f862(f862(f227(a924),x40441),f862(f862(f74(a924),x40441),f862(f862(f74(a924),x40441),x40441))))
% 25.54/25.40 [4132]E(f862(f862(f280(x41321,x41321,x41321),f181(f932(f931(x41321,x41321),a921))),f299(x41321,f181(f932(f931(x41321,x41321),a921)))),f181(f932(f931(x41321,x41321),a921)))
% 25.54/25.40 [4312]P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f227(a924)),x43121))))
% 25.54/25.40 [4313]P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),x43131))))
% 25.54/25.40 [4588]E(f862(f254(f931(x45881,x45881)),f862(f862(f10(f932(x45881,a921),a921,f931(x45881,x45881)),f80(x45881)),f862(f862(f9(f931(x45881,x45881),f932(x45881,f931(x45881,x45881)),f932(x45881,a921)),f862(f862(f10(f932(f931(x45881,x45881),a921),f932(f932(x45881,f931(x45881,x45881)),f932(x45881,a921)),f931(x45881,x45881)),f10(f931(x45881,x45881),a921,x45881)),a317)),f862(f862(f20(x45881,x45881,f931(x45881,x45881)),f244(x45881,x45881)),f7(x45881))))),f299(x45881,f181(f932(f931(x45881,x45881),a921))))
% 25.54/25.40 [4717]~E(f862(f862(f3(a1),f862(f862(f73(a1),x47171),x47171)),a90),a76)
% 25.54/25.40 [4718]~E(f862(f862(f3(a1),f862(f862(f73(a1),x47181),x47181)),a90),a76)
% 25.54/25.40 [4720]~E(f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x47201)),x47201),f2(a1))
% 25.54/25.40 [4727]~P1(f862(f862(f84(a1),f862(f862(f73(a1),x47271),x47271)),a90))
% 25.54/25.40 [4088]E(f862(f862(f73(a1),f862(f862(f3(a1),a90),x40881)),f862(f862(f3(a1),a90),x40881)),f862(f862(f3(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x40881),x40881)),a90)))
% 25.54/25.40 [4203]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),a90),x42031)),f862(f862(f3(a1),a90),x42031))),a90),f862(f862(f3(a1),a90),f862(f862(f73(a1),x42031),x42031)))
% 25.54/25.40 [4235]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x42351),a90)),f862(f862(f73(a1),x42351),a90))),a90),f862(f862(f73(a1),f862(f862(f73(a1),x42351),x42351)),a90))
% 25.54/25.40 [4273]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),a90),x42731)),f862(f862(f3(a1),a90),x42731))),a90),f862(f862(f3(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x42731),x42731)),a90)))
% 25.54/25.40 [4370]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x43701),f2(a924))),f181(f932(f931(a924,a924),a921))))),f862(f93(a1),x43701))
% 25.54/25.40 [4380]E(f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f324(x43801)),f522(x43801))),f181(f932(f931(a924,a924),a921))))),x43801)
% 25.54/25.40 [4413]E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x44131)),f862(f302(a924,a1,f93(a1)),f862(f254(a924),f862(f862(f10(a1,a921,a924),x44131),f93(a1)))))
% 25.54/25.40 [4458]P38(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x44581)))
% 25.54/25.40 [4478]P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x44781),f181(f932(f931(a924,a924),a921)))),a65))
% 25.54/25.40 [4483]E(f862(f302(a1,a924,a97),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),f862(f862(f10(a924,a921,a1),x44831),a97)))),f862(f254(a924),x44831))
% 25.54/25.40 [4640]E(f304(a924,f862(f862(f33(f931(a924,a924),f932(a924,a921)),f862(a100,x46401)),f862(f249(a924,a924,f932(a924,a921)),f862(f862(f9(a924,f932(a924,a921),f932(a924,f932(a924,a921))),f862(f862(f10(f932(a924,f932(f932(a924,a921),f932(a924,a921))),f932(f932(a924,a921),f932(a924,f932(a924,a921))),a924),f9(a924,f932(a924,a921),f932(a924,a921))),f862(f862(f10(f932(a924,a924),f932(a924,f932(f932(a924,a921),f932(a924,a921))),a924),f862(f10(a924,f932(f932(a924,a921),f932(a924,a921)),a924),f301(a924))),f3(a924)))),f181(f932(a924,a921)))))),f862(a97,x46401))
% 25.54/25.40 [4732]~P1(f862(f862(f84(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x47321),x47321)),a90)))
% 25.54/25.40 [4133]E(f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x41331),x41331)),a90)),a90),f862(f862(f73(a1),x41331),x41331))
% 25.54/25.40 [4183]E(f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x41831),x41831)),a90)),a90),f862(f862(f73(a1),f862(f862(f3(a1),x41831),a90)),f862(f862(f3(a1),x41831),a90)))
% 25.54/25.40 [4386]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),f862(f72(a1),x43861)),a90)),f862(f862(f73(a1),f862(f72(a1),x43861)),a90))),a90),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43861),x43861)),a90)))
% 25.54/25.40 [4740]~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x47401),x47401)),a90)),a76))
% 25.54/25.40 [4431]E(f862(f862(f73(a924),x44311),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(a105,x44311)))
% 25.54/25.40 [4432]E(f862(f862(f74(a924),x44321),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f73(a924),x44321),x44321))
% 25.54/25.40 [4433]E(f862(f862(f29(a924),f862(f862(f73(a924),x44331),x44331)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x44331)
% 25.54/25.40 [4511]E(f38(a924,f862(a105,f862(a105,x45111)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a924,x45111,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.40 [4654]E(f862(a82,f862(f862(f33(f931(a924,a924),f932(f931(a924,a924),a921)),f862(a100,x46541)),f862(f249(a924,a924,f932(f931(a924,a924),a921)),f862(f862(f10(f932(a924,f932(f931(a924,a924),a921)),f932(a924,f932(f931(a924,a924),a921)),a924),f862(f10(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921),a924),f276(f931(a924,a924),f931(a924,a924),a101))),f862(f862(f9(a924,f932(f931(a924,a924),a921),f932(a924,f932(f931(a924,a924),a921))),f862(f862(f10(f932(a924,f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f932(f932(f931(a924,a924),a921),f932(a924,f932(f931(a924,a924),a921))),a924),f9(a924,f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f10(f932(a924,f931(a924,a924)),f932(a924,f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),a924),f862(f10(f931(a924,a924),f932(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),a924),f301(f931(a924,a924)))),f862(f9(a924,a924,f931(a924,a924)),f244(a924,a924))))),f181(f932(f931(a924,a924),a921))))))),f862(f72(a1),x46541))
% 25.54/25.40 [4506]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x45061),f862(a105,f862(a105,x45061)))
% 25.54/25.40 [4507]E(f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x45071),f862(f862(f73(a924),x45071),x45071))
% 25.54/25.40 [4545]E(f862(f862(f29(a924),f862(a105,f862(a105,x45451))),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a105,f862(f862(f29(a924),x45451),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.40 [4595]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x45951),f862(a105,f862(a105,f862(a105,x45951))))
% 25.54/25.40 [4661]E(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f20(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f10(a1,a921,a1),f862(f227(a1),f2(a1))),f862(f862(f9(a1,a1,a1),f3(a1)),x46611))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f71(a1))))),f862(f862(f9(a1,a1,a1),f3(a1)),x46611))))),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))),f36(x46611))
% 25.54/25.40 [3367]P2(f930(x33671,x33672))
% 25.54/25.40 [3368]P2(f931(x33681,x33682))
% 25.54/25.40 [3369]P2(f929(x33691,x33692))
% 25.54/25.40 [3370]P107(f930(x33701,x33702))
% 25.54/25.40 [3371]P107(f931(x33711,x33712))
% 25.54/25.40 [3372]P107(f929(x33721,x33722))
% 25.54/25.40 [3389]P11(a1,f171(x33891,x33892))
% 25.54/25.40 [3390]P35(x33901,f146(x33901,x33902))
% 25.54/25.40 [3391]P36(x33911,f255(x33911,x33912))
% 25.54/25.40 [3392]P36(x33921,f299(x33921,x33922))
% 25.54/25.40 [3393]P37(x33931,f255(x33931,x33932))
% 25.54/25.40 [3394]P49(x33941,f255(x33941,x33942))
% 25.54/25.40 [3459]P29(x34591,x34592,f106(x34591))
% 25.54/25.40 [3492]P50(x34921,x34922,f255(x34921,x34922))
% 25.54/25.40 [3493]P52(x34931,x34931,f255(x34931,x34932))
% 25.54/25.40 [3758]P22(x37581,x37581,f7(x37581),x37582)
% 25.54/25.40 [3759]P22(x37591,x37591,f25(x37591),x37592)
% 25.54/25.40 [3766]P30(x37661,x37662,f106(x37661),f106(x37661))
% 25.54/25.40 [3767]P30(x37671,x37672,f106(x37671),f106(x37671))
% 25.54/25.40 [3774]P22(f925(x37741),f925(x37741),f161(x37741),x37742)
% 25.54/25.40 [4173]P23(x41731,x41731,f25(x41731),x41732,x41732)
% 25.54/25.40 [4688]~P31(x46881,x46882,f106(x46881))
% 25.54/25.40 [4689]~P33(x46891,x46892,f106(x46891))
% 25.54/25.40 [3353]E(f862(f254(x33531),x33532),x33532)
% 25.54/25.40 [3354]E(f862(f7(x33541),x33542),x33542)
% 25.54/25.40 [3355]E(f862(f25(x33551),x33552),x33552)
% 25.54/25.40 [3356]E(f862(f25(x33561),x33562),x33562)
% 25.54/25.40 [3366]E(f862(f184(x33661),x33662),f108(x33661))
% 25.54/25.40 [3387]E(f78(x33871,f862(a317,x33872)),x33872)
% 25.54/25.40 [3388]E(f83(x33881,f862(a317,x33882)),x33882)
% 25.54/25.40 [3410]E(f862(f85(x34101),f588(x34101,x34102)),x34102)
% 25.54/25.40 [3411]E(f862(f118(x34111,x34112),f112(x34111)),f2(a924))
% 25.54/25.40 [3414]E(f862(f129(x34141,x34142),f106(x34141)),f106(x34141))
% 25.54/25.40 [3434]E(f299(x34341,f299(x34341,x34342)),f299(x34341,x34342))
% 25.54/25.40 [3435]E(f145(x34351,f145(x34351,x34352)),f145(x34351,x34352))
% 25.54/25.40 [3454]E(f862(f862(f127(x34541),x34542),f106(x34541)),x34542)
% 25.54/25.40 [3460]E(f166(x34601,x34602,f106(x34601)),x34602)
% 25.54/25.40 [3461]E(f166(x34611,f106(x34611),x34612),x34612)
% 25.54/25.40 [3462]E(f109(x34621,f112(x34621),x34622),x34622)
% 25.54/25.40 [3463]E(f162(x34631,f2(a924),x34632),f106(x34631))
% 25.54/25.40 [3469]E(f862(f862(f168(x34691),x34692),f106(x34691)),f106(x34691))
% 25.54/25.40 [3470]E(f862(f862(f131(x34701),x34702),f106(x34701)),f106(x34701))
% 25.54/25.40 [3472]E(f148(x34721,x34722,f106(x34721)),f2(a924))
% 25.54/25.40 [3474]E(f163(x34741,x34742,f106(x34741)),f106(x34741))
% 25.54/25.40 [3475]E(f170(x34751,x34752,f106(x34751)),f106(x34751))
% 25.54/25.40 [3476]E(f169(x34761,f106(x34761),x34762),f106(x34761))
% 25.54/25.40 [3480]E(f862(f165(x34801),f145(x34801,x34802)),f862(f165(x34801),x34802))
% 25.54/25.40 [3483]E(f862(f275(x34831,x34831),f255(x34831,x34832)),x34832)
% 25.54/25.40 [3484]E(f862(f256(x34841,x34841),f255(x34841,x34842)),x34842)
% 25.54/25.40 [3491]E(f862(f277(x34911,x34911),f255(x34911,x34912)),f255(x34911,x34912))
% 25.54/25.40 [3506]E(f299(f925(x35061),f150(x35061,x35062)),f151(x35061,f299(x35061,x35062)))
% 25.54/25.40 [3508]P1(f862(f130(a1),f171(x35081,x35082)))
% 25.54/25.40 [3516]E(f862(f275(x35161,x35161),f299(x35161,x35162)),f234(f932(x35161,a921)))
% 25.54/25.40 [3517]E(f862(f256(x35171,x35171),f299(x35171,x35172)),f234(f932(x35171,a921)))
% 25.54/25.40 [3521]P1(f862(f130(x35211),f145(x35211,x35212)))
% 25.54/25.40 [3522]P1(f862(f153(x35221,x35222),f106(x35221)))
% 25.54/25.40 [3523]P1(f862(f153(x35231,x35232),f106(x35231)))
% 25.54/25.40 [3529]E(f862(f165(a1),f171(x35291,x35292)),f296(a1,x35291,x35292))
% 25.54/25.40 [3530]E(f862(f165(a1),f171(x35301,x35302)),f296(a1,x35301,x35302))
% 25.54/25.40 [3544]P53(x35441,f181(f932(x35441,a921)),x35442)
% 25.54/25.40 [3549]E(f862(f248(a1,a1),f39(x35491,x35492)),f38(a1,x35491,x35492))
% 25.54/25.40 [3550]E(f862(f295(a924,x35501),f862(a105,x35502)),f296(a924,x35501,x35502))
% 25.54/25.40 [3565]E(f862(f862(f144(x35651),x35652),f106(x35651)),f133(x35651,x35652,f106(x35651)))
% 25.54/25.40 [3577]E(f296(a924,f862(a105,x35771),x35772),f297(a924,x35771,x35772))
% 25.54/25.40 [3578]P50(x35781,f234(f932(x35781,a921)),f299(x35781,x35782))
% 25.54/25.40 [3640]E(f862(f862(f3(a924),x36401),f862(a105,x36402)),f862(f28(a924),f298(a924,x36402,x36401)))
% 25.54/25.40 [3695]E(f159(x36951,x36952,f106(x36951)),f862(f862(f244(f925(x36951),f925(x36951)),f106(x36951)),f106(x36951)))
% 25.54/25.40 [3713]E(f862(f249(x37131,x37132,f931(x37131,x37132)),f244(x37131,x37132)),f25(f931(x37131,x37132)))
% 25.54/25.40 [3717]P1(f862(f862(f321(f925(x37171)),f106(x37171)),f154(x37171,x37172)))
% 25.54/25.40 [3718]E(f862(f182(f925(x37181)),f107(x37181,x37182)),f862(f862(f3(a924),f862(f182(f925(x37181)),x37182)),f71(a924)))
% 25.54/25.40 [3727]P1(f862(f54(a924),f298(a924,x37271,x37272)))
% 25.54/25.40 [3728]P1(f862(f54(a924),f297(a924,x37281,x37282)))
% 25.54/25.40 [3729]P1(f862(f54(a924),f296(a924,x37291,x37292)))
% 25.54/25.40 [3730]P1(f862(f54(a1),f298(a1,x37301,x37302)))
% 25.54/25.40 [3731]P1(f862(f54(a1),f297(a1,x37311,x37312)))
% 25.54/25.40 [3732]P1(f862(f54(a1),f296(a1,x37321,x37322)))
% 25.54/25.40 [3835]E(f862(f302(a924,a924,a105),f296(a924,x38351,x38352)),f296(a924,f862(a105,x38351),f862(a105,x38352)))
% 25.54/25.40 [3854]E(f862(f862(f280(x38541,x38541,x38541),f299(x38541,x38542)),f299(x38541,x38542)),f299(x38541,x38542))
% 25.54/25.40 [3888]E(f862(f862(f244(a92,a92),f862(f862(f29(a92),x38881),x38882)),f38(a92,x38881,x38882)),f23(x38881,x38882))
% 25.54/25.40 [3889]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x38891),x38892)),f38(a1,x38891,x38892)),f39(x38891,x38892))
% 25.54/25.40 [3916]E(f862(f862(f244(a924,a924),f862(f862(f29(a924),x39161),x39162)),f38(a924,x39161,x39162)),f78(f931(a924,a924),f41(x39161,x39162)))
% 25.54/25.40 [3967]P1(f862(f862(f228(a924),f862(f862(f3(a924),x39671),x39672)),f862(a105,x39671)))
% 25.54/25.40 [4015]P36(x40151,f862(f862(f280(x40151,x40151,x40151),x40152),f299(x40151,x40152)))
% 25.54/25.40 [4055]E(f862(f862(f131(x40551),f862(f182(f925(x40551)),f170(x40551,x40552,f106(x40551)))),f106(x40551)),f106(x40551))
% 25.54/25.40 [4065]E(f862(f862(f73(a1),f862(f862(f74(a1),x40651),f862(f862(f29(a1),x40652),x40651))),f38(a1,x40652,x40651)),x40652)
% 25.54/25.40 [4069]E(f862(f862(f33(a924,f932(f931(f925(x40691),f925(x40691)),a921)),f234(f932(a924,a921))),f136(x40691,x40692)),f138(x40691,x40692))
% 25.54/25.40 [4148]E(f862(f129(x41481,f862(f862(f10(a921,a921,x41481),a314),f862(a317,x41482))),f106(x41481)),f106(x41481))
% 25.54/25.40 [4289]P1(f862(f862(f321(f931(f925(x42891),f925(x42891))),f862(f862(f244(f925(x42891),f925(x42891)),f106(x42891)),f106(x42891))),f151(x42891,x42892)))
% 25.54/25.40 [4398]E(f245(x43981,x43981,x43981,a317,f245(x43981,x43981,x43981,x43982,a317)),x43982)
% 25.54/25.40 [4442]E(f250(x44421,x44421,x44422,x44422,f25(x44421),f25(x44422)),f25(f931(x44421,x44422)))
% 25.54/25.40 [4443]E(f250(x44431,x44431,x44432,x44432,f7(x44431),f7(x44432)),f25(f931(x44431,x44432)))
% 25.54/25.40 [4444]E(f250(x44441,x44441,x44442,x44442,f25(x44441),f25(x44442)),f25(f931(x44441,x44442)))
% 25.54/25.40 [4445]E(f250(x44451,x44451,x44452,x44452,f25(x44451),f25(x44452)),f25(f931(x44451,x44452)))
% 25.54/25.40 [3452]E(f862(f85(x34521),f862(f87(x34521),x34522)),x34522)
% 25.54/25.40 [3453]E(f862(f161(x34531),f862(f161(x34531),x34532)),x34532)
% 25.54/25.40 [3455]E(f862(f862(f131(x34551),f2(a924)),x34552),x34552)
% 25.54/25.40 [3471]E(f862(f862(f168(x34711),f2(a924)),x34712),f106(x34711))
% 25.54/25.40 [3478]E(f862(f862(f127(x34781),f106(x34781)),x34782),x34782)
% 25.54/25.40 [3487]E(f30(f932(x34871,a921),f862(f300(x34871),x34872)),x34872)
% 25.54/25.40 [3489]E(f862(f165(x34891),f862(f160(x34891),x34892)),f862(f165(x34891),x34892))
% 25.54/25.40 [3490]E(f862(f165(x34901),f862(f161(x34901),x34902)),f862(f165(x34901),x34902))
% 25.54/25.40 [3495]E(f862(f862(f3(a92),x34951),x34952),f862(f862(a4,x34951),x34952))
% 25.54/25.40 [3510]E(f862(f862(f74(a924),x35101),x35102),f862(f862(f74(a924),x35102),x35101))
% 25.54/25.40 [3511]E(f862(f862(f74(a1),x35111),x35112),f862(f862(f74(a1),x35112),x35111))
% 25.54/25.40 [3512]E(f862(f862(f73(a924),x35121),x35122),f862(f862(f73(a924),x35122),x35121))
% 25.54/25.40 [3513]E(f862(f862(f73(a1),x35131),x35132),f862(f862(f73(a1),x35132),x35131))
% 25.54/25.40 [3536]E(f862(f862(f176(x35361,x35361),f2(a924)),x35362),f25(x35361))
% 25.54/25.40 [3537]E(f862(f182(f925(x35371)),f862(f160(x35371),x35372)),f862(f182(f925(x35371)),x35372))
% 25.54/25.40 [3538]E(f862(f182(f925(x35381)),f862(f161(x35381),x35382)),f862(f182(f925(x35381)),x35382))
% 25.54/25.40 [3539]E(f169(x35391,x35392,f181(f932(a924,a921))),f106(x35391))
% 25.54/25.40 [3540]E(f862(f862(f147(x35401,x35401),f7(x35401)),x35402),x35402)
% 25.54/25.40 [3542]E(f862(f243(a1,a1),f39(x35421,x35422)),f862(f862(f29(a1),x35421),x35422))
% 25.54/25.40 [3559]E(f862(f182(f925(x35591)),f145(x35591,x35592)),f862(f28(x35591),f862(f165(x35591),x35592)))
% 25.54/25.40 [3560]E(f862(f273(x35601),f862(f277(x35601,x35601),x35602)),f862(f273(x35601),x35602))
% 25.54/25.40 [3564]P1(f862(f54(x35641),f862(f165(x35641),x35642)))
% 25.54/25.40 [3571]E(f862(f862(f73(a1),x35711),f862(f72(a1),x35712)),f862(f862(f3(a1),x35711),x35712))
% 25.54/25.40 [3572]E(f862(f862(f73(a1),x35721),f862(f72(a1),x35722)),f862(f862(f3(a1),x35721),x35722))
% 25.54/25.40 [3579]E(f862(f302(x35791,x35791,f7(x35791)),x35792),x35792)
% 25.54/25.40 [3580]E(f862(f302(x35801,x35801,f25(x35801)),x35802),x35802)
% 25.54/25.40 [3581]E(f862(f303(x35811,x35811,f7(x35811)),x35812),x35812)
% 25.54/25.40 [3582]E(f862(f303(x35821,x35821,f25(x35821)),x35822),x35822)
% 25.54/25.40 [3583]P1(f862(f234(f932(x35831,a921)),x35832))
% 25.54/25.40 [3585]E(f862(f28(a924),f862(f295(a924,x35851),x35852)),f862(f862(f3(a924),x35852),x35851))
% 25.54/25.40 [3586]E(f862(f295(a924,f862(a105,x35861)),x35862),f298(a924,x35861,x35862))
% 25.54/25.40 [3599]E(f862(f862(f301(x35991),x35992),f181(f932(x35991,a921))),f862(f254(x35991),f862(a317,x35992)))
% 25.54/25.40 [3604]E(f299(x36041,f862(f277(x36041,x36041),x36042)),f862(f277(x36041,x36041),f299(x36041,x36042)))
% 25.54/25.40 [3609]E(f862(f862(f73(a924),f862(a105,x36091)),x36092),f862(f862(f73(a924),x36091),f862(a105,x36092)))
% 25.54/25.40 [3610]E(f862(f862(f3(a924),f862(a105,x36101)),f862(a105,x36102)),f862(f862(f3(a924),x36101),x36102))
% 25.54/25.40 [3616]E(f48(x36161,f2(a924),x36162),f862(f862(f144(f925(x36161)),f106(x36161)),f106(f925(x36161))))
% 25.54/25.40 [3617]E(f862(f28(a924),f297(a924,x36171,x36172)),f862(f862(f3(a924),x36172),x36171))
% 25.54/25.40 [3626]P35(x36261,f862(f862(f279(a924,x36261),a232),x36262))
% 25.54/25.40 [3628]P11(a924,f132(a924,f862(f295(a924,x36281),x36282)))
% 25.54/25.40 [3630]P1(f862(f54(a924),f862(f295(a924,x36301),x36302)))
% 25.54/25.40 [3631]P1(f862(f54(a1),f862(f295(a1,x36311),x36312)))
% 25.54/25.40 [3634]E(f862(f277(f925(x36341),f925(x36341)),f150(x36341,x36342)),f150(x36341,f862(f277(x36341,x36341),x36342)))
% 25.54/25.40 [3636]E(f862(f295(a1,x36361),f862(f862(f73(a1),x36362),f71(a1))),f296(a1,x36361,x36362))
% 25.54/25.40 [3639]E(f862(f862(f29(a1),f862(f72(a1),x36391)),f862(f72(a1),x36392)),f862(f862(f29(a1),x36391),x36392))
% 25.54/25.40 [3647]E(f862(f862(f176(f931(x36471,x36471),a921),f71(a924)),x36472),x36472)
% 25.54/25.40 [3649]E(f862(f862(f103(f932(x36491,a921)),x36492),f181(f932(x36491,a921))),x36492)
% 25.54/25.40 [3650]E(f862(f862(f94(f932(x36501,a921)),x36502),f234(f932(x36501,a921))),x36502)
% 25.54/25.40 [3651]E(f862(f862(f3(f932(x36511,a921)),x36512),f181(f932(x36511,a921))),x36512)
% 25.54/25.40 [3652]E(f862(f243(a924,a924),f78(f931(a924,a924),f41(x36521,x36522))),f862(f862(f29(a924),x36521),x36522))
% 25.54/25.40 [3658]E(f296(a1,f862(f862(f73(a1),x36581),f71(a1)),x36582),f297(a1,x36581,x36582))
% 25.54/25.40 [3663]E(f862(f248(a924,a924),f78(f931(a924,a924),f41(x36631,x36632))),f38(a924,x36631,x36632))
% 25.54/25.40 [3672]P1(f862(f862(f321(x36721),x36722),f234(f932(x36721,a921))))
% 25.54/25.40 [3673]P1(f862(f862(f321(x36731),x36732),f234(f932(x36731,a921))))
% 25.54/25.40 [3678]E(f862(f862(f3(a924),f862(a105,x36781)),x36782),f862(f28(a924),f296(a924,x36782,x36781)))
% 25.54/25.40 [3704]E(f862(f862(f103(f932(x37041,a921)),x37042),f234(f932(x37041,a921))),f234(f932(x37041,a921)))
% 25.54/25.40 [3705]E(f862(f862(f94(f932(x37051,a921)),x37052),f181(f932(x37051,a921))),f181(f932(x37051,a921)))
% 25.54/25.40 [3706]E(f862(f862(f3(f932(x37061,a921)),x37062),f234(f932(x37061,a921))),f181(f932(x37061,a921)))
% 25.54/25.40 [3721]E(f38(a1,f862(f93(a1),x37211),f862(f93(a1),x37212)),f862(f93(a1),f38(a924,x37211,x37212)))
% 25.54/25.40 [3722]E(f38(a1,f862(f72(a1),x37221),f862(f72(a1),x37222)),f862(f72(a1),f38(a1,x37221,x37222)))
% 25.54/25.40 [3723]E(f38(a1,f862(f93(a1),x37231),f862(f93(a1),x37232)),f862(f93(a1),f38(a924,x37231,x37232)))
% 25.54/25.40 [3734]E(f862(f182(f925(x37341)),f862(f164(x37341),x37342)),f862(f862(f3(a924),f862(f182(f925(x37341)),x37342)),f71(a924)))
% 25.54/25.40 [3760]E(f862(f862(f29(a1),f38(a1,x37601,x37602)),x37602),f2(a1))
% 25.54/25.40 [3769]E(f862(a5,f38(a924,f862(a22,x37691),f862(a22,x37692))),f38(a92,x37691,x37692))
% 25.54/25.40 [3802]E(f862(a5,f862(f862(f3(a924),f862(a22,x38021)),f862(a22,x38022))),f862(f862(f3(a92),x38021),x38022))
% 25.54/25.40 [3803]E(f862(a5,f862(f862(f74(a924),f862(a22,x38031)),f862(a22,x38032))),f862(f862(f74(a92),x38031),x38032))
% 25.54/25.40 [3804]E(f862(a5,f862(f862(f73(a924),f862(a22,x38041)),f862(a22,x38042))),f862(f862(f73(a92),x38041),x38042))
% 25.54/25.40 [3805]E(f862(a5,f862(f862(f29(a924),f862(a22,x38051)),f862(a22,x38052))),f862(f862(f29(a92),x38051),x38052))
% 25.54/25.40 [3813]E(f862(f302(a924,a924,a105),f862(f295(a924,x38131),x38132)),f862(f295(a924,f862(a105,x38131)),f862(a105,x38132)))
% 25.54/25.40 [3840]P1(f862(f41(x38401,x38402),f78(f931(a924,a924),f41(x38401,x38402))))
% 25.54/25.40 [3863]E(f38(a924,f862(a105,f38(a924,x38631,x38632)),x38632),f38(a924,f862(a105,x38631),x38632))
% 25.54/25.40 [3875]E(f862(f862(f32(f932(x38751,a921),f932(x38751,a921)),x38752),f7(f932(x38751,a921))),f31(f932(x38751,a921),x38752))
% 25.54/25.40 [3876]E(f862(f862(f33(f932(x38761,a921),f932(x38761,a921)),x38762),f7(f932(x38761,a921))),f30(f932(x38761,a921),x38762))
% 25.54/25.40 [3877]E(f862(f302(f925(x38771),f932(x38771,a921),f165(x38771)),f862(f165(f925(x38771)),f47(x38771,x38772))),f862(f300(x38771),f862(f165(x38771),x38772)))
% 25.54/25.40 [3881]P1(f862(f862(f321(f932(x38811,a921)),x38812),f862(f300(x38811),x38812)))
% 25.54/25.40 [3887]E(f38(a1,f862(f72(a1),f38(a1,x38871,x38872)),x38872),f38(a1,f862(f72(a1),x38871),x38872))
% 25.54/25.40 [3898]P1(f862(f862(f227(f932(x38981,a921)),x38982),f234(f932(x38981,a921))))
% 25.54/25.40 [3900]E(f862(f862(f280(x39001,x39001,x39001),f299(x39001,x39002)),f299(x39001,f299(x39001,x39002))),f299(x39001,x39002))
% 25.54/25.40 [3901]E(f862(f862(f103(f932(x39011,a921)),f862(f256(x39011,x39011),x39012)),f862(f275(x39011,x39011),x39012)),f862(f273(x39011),x39012))
% 25.54/25.40 [3922]E(f305(x39221,x39222,f234(f932(x39221,a921)),f234(f932(x39222,a921))),f234(f932(f930(x39221,x39222),a921)))
% 25.54/25.40 [3972]P1(f862(f862(f227(a924),f38(a924,x39721,x39722)),x39721))
% 25.54/25.40 [3996]P1(f862(f862(f227(a1),f862(f72(a1),f862(f93(a1),x39961))),f862(f93(a1),x39962)))
% 25.54/25.40 [4020]P1(f862(f862(f321(f932(x40201,a921)),f181(f932(x40201,a921))),f862(f300(x40201),x40202)))
% 25.54/25.40 [4025]E(f299(x40251,f862(f862(f280(x40251,x40251,x40251),x40252),f299(x40251,x40252))),f299(x40251,x40252))
% 25.54/25.40 [4027]E(f862(f862(f280(x40271,x40271,x40271),f299(x40271,x40272)),x40272),f862(f862(f280(x40271,x40271,x40271),x40272),f299(x40271,x40272)))
% 25.54/25.40 [4028]E(f862(f862(f280(x40281,x40281,x40281),f299(x40281,x40282)),x40282),f862(f862(f280(x40281,x40281,x40281),x40282),f299(x40281,x40282)))
% 25.54/25.40 [4030]E(f862(a97,f862(f862(f73(a1),f862(f862(f3(a1),x40301),x40302)),f71(a1))),f862(f28(a1),f296(a1,x40302,x40301)))
% 25.54/25.40 [4045]E(f862(f275(x40451,x40451),f862(f862(f280(x40451,x40451,x40451),x40452),f299(x40451,x40452))),f862(f275(x40451,x40451),x40452))
% 25.54/25.40 [4046]E(f862(f256(x40461,x40461),f862(f862(f280(x40461,x40461,x40461),x40462),f299(x40461,x40462))),f862(f256(x40461,x40461),x40462))
% 25.54/25.40 [4064]E(f862(f135(f925(x40641),f925(x40641),f127(x40641),f106(x40641)),f162(f925(x40641),x40642,f106(x40641))),f106(x40641))
% 25.54/25.40 [4073]P22(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x40731),x40732)
% 25.54/25.40 [4075]P11(a924,f862(f161(a924),f862(f862(f147(f925(x40751),a924),f182(f925(x40751))),f172(x40751,x40752))))
% 25.54/25.40 [4105]P49(x41051,f862(f862(f103(f932(f931(x41051,x41051),a921)),x41052),f862(f277(x41051,x41051),x41052)))
% 25.54/25.40 [4106]P49(x41061,f862(f862(f94(f932(f931(x41061,x41061),a921)),x41062),f862(f277(x41061,x41061),x41062)))
% 25.54/25.40 [4117]P1(f862(f862(f228(a1),f862(f72(a1),f862(f93(a1),f862(a105,x41171)))),f862(f93(a1),x41172)))
% 25.54/25.40 [4162]E(f862(f135(f925(x41621),x41621,f862(f9(x41621,f925(x41621),f925(x41621)),f144(x41621)),f106(x41621)),x41622),f862(f161(x41621),x41622))
% 25.54/25.40 [4210]P1(f862(f862(f227(f932(f931(f925(x42101),f925(x42101)),a921)),f151(x42101,x42102)),f299(f925(x42101),f150(x42101,x42102))))
% 25.54/25.40 [4239]P1(f862(f41(x42391,x42392),f862(f862(f244(a924,a924),f862(f862(f29(a924),x42391),x42392)),f38(a924,x42391,x42392))))
% 25.54/25.40 [4251]P1(f862(f862(f227(f932(f931(f925(x42511),f925(x42511)),a921)),f150(x42511,f299(x42511,x42512))),f299(f925(x42511),f150(x42511,x42512))))
% 25.54/25.40 [4468]E(f862(f862(f251(f931(a92,a92),a92,f931(a92,a92),f931(x44681,f931(a92,a92))),f259(f862(f158(a92),f862(f862(f147(f931(a92,x44681),a92),f243(a92,x44681)),x44682)))),f862(f862(f10(x44681,f932(f931(a92,a92),f931(x44681,f931(a92,a92))),a92),f244(x44681,f931(a92,a92))),f260(x44681,x44682))),f258(x44681,x44682))
% 25.54/25.40 [4524]P1(f862(f862(f321(f932(f922(f930(a919,f932(x45241,f932(a920,a921))),f930(a920,x45241)),a921)),f588(x45241,x45242)),f862(f254(f932(f922(f930(a919,f932(x45241,f932(a920,a921))),f930(a920,x45241)),a921)),f88(x45241))))
% 25.54/25.40 [4525]P1(f862(f862(f321(f932(f922(f930(a919,f932(x45251,f932(a920,a921))),f930(a920,x45251)),a921)),f862(f87(x45251),x45252)),f862(f254(f932(f922(f930(a919,f932(x45251,f932(a920,a921))),f930(a920,x45251)),a921)),f88(x45251))))
% 25.54/25.40 [4547]E(f216(a924,f931(x45471,f926(x45471)),f2(a924),f862(f249(x45471,f926(x45471),a924),f862(f18(f932(f926(x45471),a924),x45471),f862(f862(f9(f926(x45471),a924,a924),f862(f862(f10(a924,f932(a924,a924),f926(x45471)),f73(a924)),f182(f926(x45471)))),f71(a924)))),f862(f128(x45471),x45472)),f862(f182(f926(x45471)),x45472))
% 25.54/25.40 [4621]E(f38(a924,f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46211),f862(f96(a924),x46212)),f38(a924,f862(a105,f862(a105,f862(a105,x46211))),f862(f96(a924),x46212)))
% 25.54/25.40 [4634]E(f862(f862(f29(a924),f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46341)),f862(f96(a924),x46342)),f862(f862(f29(a924),f862(a105,f862(a105,f862(a105,x46341)))),f862(f96(a924),x46342)))
% 25.54/25.40 [4653]E(f862(f249(f932(f931(x46531,x46531),a921),f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f862(f862(f9(f932(f931(x46531,x46531),a921),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921))),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))))),f862(f862(f10(f932(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921))),f932(f932(f931(x46531,x46531),a921),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))))),f932(f931(x46531,x46531),a921)),f10(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))),f932(f931(x46531,x46531),a921))),f862(f862(f10(f932(f932(x46532,x46531),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f931(x46531,x46531),a921)),f20(f932(x46532,x46531),f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f862(f862(f10(f932(f932(x46532,x46531),f932(f931(x46532,x46532),a921)),f932(f932(x46532,x46531),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f932(f931(x46531,x46531),a921)),f862(f10(f932(f931(x46532,x46532),a921),f932(f932(f931(x46532,x46532),a921),f931(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921))),f932(x46532,x46531)),f244(f932(f931(x46532,x46532),a921),f932(f931(x46532,x46532),a921)))),f279(x46531,x46532))))),f279(x46531,x46532))),f67(x46531,x46532))
% 25.54/25.40 [4702]~E(f862(f300(x47021),x47022),f181(f932(f932(x47021,a921),a921)))
% 25.54/25.40 [4711]~P1(f862(f862(f165(x47111),f106(x47111)),x47112))
% 25.54/25.40 [4714]~P1(f862(f862(f321(x47141),x47142),f181(f932(x47141,a921))))
% 25.54/25.40 [4715]~P1(f862(f862(f321(x47151),x47152),f181(f932(x47151,a921))))
% 25.54/25.40 [4724]~P1(f862(f862(f228(f932(x47241,a921)),x47242),f181(f932(x47241,a921))))
% 25.54/25.40 [3588]E(f862(f862(f3(a924),x35881),f862(f862(f73(a924),x35881),x35882)),f2(a924))
% 25.54/25.40 [3591]E(f862(f862(f103(f932(x35911,a921)),x35912),x35912),x35912)
% 25.54/25.40 [3592]E(f862(f862(f94(f932(x35921,a921)),x35922),x35922),x35922)
% 25.54/25.40 [3620]E(f862(f862(f3(f932(x36201,a921)),x36202),x36202),f181(f932(x36201,a921)))
% 25.54/25.40 [3623]E(f862(f136(x36231,x36232),f2(a924)),f181(f932(f931(f925(x36231),f925(x36231)),a921)))
% 25.54/25.40 [3624]E(f862(f862(f73(a924),x36241),f862(a105,x36242)),f862(a105,f862(f862(f73(a924),x36241),x36242)))
% 25.54/25.40 [3635]E(f187(f862(f93(a1),x36351),f862(f93(a1),x36352)),f862(f93(a1),f862(f862(f3(a924),x36351),x36352)))
% 25.54/25.40 [3638]E(f862(f862(f29(a1),f862(f72(a1),x36381)),x36382),f862(f862(f29(a1),x36381),f862(f72(a1),x36382)))
% 25.54/25.40 [3642]E(f862(f28(a1),f862(f295(a1,x36421),x36422)),f862(a97,f862(f862(f3(a1),x36422),x36421)))
% 25.54/25.40 [3645]E(f862(f862(f73(a924),f862(a105,x36451)),x36452),f862(a105,f862(f862(f73(a924),x36451),x36452)))
% 25.54/25.40 [3648]E(f862(f72(f932(x36481,a921)),f862(f72(f932(x36481,a921)),x36482)),x36482)
% 25.54/25.40 [3660]E(f172(x36601,f862(f862(f144(f925(x36601)),f106(x36601)),x36602)),f172(x36601,x36602))
% 25.54/25.40 [3664]E(f862(f862(f73(a924),x36641),f862(f862(f74(a924),x36641),x36642)),f862(f862(f74(a924),x36641),f862(a105,x36642)))
% 25.54/25.40 [3671]E(f862(f862(a4,f862(a5,x36711)),f862(a5,x36712)),f862(a5,f862(f862(f3(a924),x36711),x36712)))
% 25.54/25.40 [3685]E(f862(f862(f236(a1),f862(f93(a1),x36851)),x36852),f862(f93(a1),f862(f862(f236(a924),x36851),x36852)))
% 25.54/25.40 [3686]E(f862(f862(f74(a1),f862(f72(a1),x36861)),x36862),f862(f72(a1),f862(f862(f74(a1),x36861),x36862)))
% 25.54/25.40 [3687]E(f862(f862(f236(a1),f862(f93(a1),x36871)),x36872),f862(f93(a1),f862(f862(f236(a924),x36871),x36872)))
% 25.54/25.40 [3688]E(f862(f862(f236(a1),f862(f93(a1),x36881)),x36882),f862(f93(a1),f862(f862(f236(a924),x36881),x36882)))
% 25.54/25.40 [3689]E(f862(f862(f74(a92),f862(a5,x36891)),f862(a5,x36892)),f862(a5,f862(f862(f74(a924),x36891),x36892)))
% 25.54/25.40 [3690]E(f862(f862(f73(a92),f862(a5,x36901)),f862(a5,x36902)),f862(a5,f862(f862(f73(a924),x36901),x36902)))
% 25.54/25.40 [3691]E(f862(f862(f225(a924),f862(a105,x36911)),f862(a105,x36912)),f862(a105,f862(f862(f225(a924),x36911),x36912)))
% 25.54/25.40 [3692]E(f862(f862(f226(a924),f862(a105,x36921)),f862(a105,x36922)),f862(a105,f862(f862(f226(a924),x36921),x36922)))
% 25.54/25.40 [3696]E(f862(f165(a924),f132(a924,f862(f295(a924,x36961),x36962))),f862(f295(a924,x36961),x36962))
% 25.54/25.40 [3697]E(f862(f165(a924),f132(a924,f862(f295(a924,x36971),x36972))),f862(f295(a924,x36971),x36972))
% 25.54/25.40 [3698]E(f304(x36981,f862(f862(f301(x36981),x36982),f181(f932(x36981,a921)))),x36982)
% 25.54/25.40 [3702]E(f862(f275(x37021,x37022),f181(f932(f931(x37021,x37022),a921))),f181(f932(x37022,a921)))
% 25.54/25.40 [3703]E(f862(f256(x37031,x37032),f181(f932(f931(x37031,x37032),a921))),f181(f932(x37031,a921)))
% 25.54/25.40 [3707]E(f862(a97,f862(f862(f3(a1),x37071),x37072)),f862(f28(a1),f297(a1,x37072,x37071)))
% 25.54/25.40 [3712]E(f862(f862(f73(a924),x37121),f862(f862(f74(a924),x37122),x37121)),f862(f862(f74(a924),f862(a105,x37122)),x37121))
% 25.54/25.40 [3714]E(f862(f862(f53(x37141),f181(f932(x37141,a921))),x37142),f181(f932(f932(x37141,a921),a921)))
% 25.54/25.40 [3724]E(f862(f182(f925(a924)),f132(a924,f862(f295(a924,x37241),x37242))),f862(f862(f3(a924),x37242),x37241))
% 25.54/25.40 [3739]E(f862(f862(f103(f932(x37391,a921)),f181(f932(x37391,a921))),x37392),x37392)
% 25.54/25.40 [3740]E(f862(f862(f94(f932(x37401,a921)),f234(f932(x37401,a921))),x37402),x37402)
% 25.54/25.40 [3741]E(f862(f862(f73(a1),f862(f72(a1),x37411)),f862(f72(a1),x37412)),f862(f72(a1),f862(f862(f73(a1),x37411),x37412)))
% 25.54/25.40 [3743]E(f862(f862(f74(a1),f862(f93(a1),x37431)),f862(f93(a1),x37432)),f862(f93(a1),f862(f862(f74(a924),x37431),x37432)))
% 25.54/25.40 [3744]E(f862(f862(f29(a1),f862(f93(a1),x37441)),f862(f93(a1),x37442)),f862(f93(a1),f862(f862(f29(a924),x37441),x37442)))
% 25.54/25.40 [3745]E(f862(f862(f74(a1),f862(f96(a1),x37451)),f862(f96(a1),x37452)),f862(f96(a1),f862(f862(f74(a1),x37451),x37452)))
% 25.54/25.40 [3746]E(f862(f862(f74(a1),f862(f93(a1),x37461)),f862(f93(a1),x37462)),f862(f93(a1),f862(f862(f74(a924),x37461),x37462)))
% 25.54/25.40 [3747]E(f862(f862(f74(a1),f862(f93(a1),x37471)),f862(f93(a1),x37472)),f862(f93(a1),f862(f862(f74(a924),x37471),x37472)))
% 25.54/25.40 [3748]E(f862(f862(f73(a1),f862(f96(a1),x37481)),f862(f96(a1),x37482)),f862(f96(a1),f862(f862(f73(a1),x37481),x37482)))
% 25.54/25.40 [3749]E(f862(f862(f73(a1),f862(f93(a1),x37491)),f862(f93(a1),x37492)),f862(f93(a1),f862(f862(f73(a924),x37491),x37492)))
% 25.54/25.40 [3750]E(f862(f862(f73(a1),f862(f93(a1),x37501)),f862(f93(a1),x37502)),f862(f93(a1),f862(f862(f73(a924),x37501),x37502)))
% 25.54/25.40 [3751]E(f862(f862(f29(a1),f862(f93(a1),x37511)),f862(f93(a1),x37512)),f862(f93(a1),f862(f862(f29(a924),x37511),x37512)))
% 25.54/25.40 [3770]E(f862(f862(f8(x37701,a924),f862(f18(a924,x37701),f71(a924))),x37702),f862(f28(x37701),x37702))
% 25.54/25.40 [3775]E(f862(f72(a1),f38(a1,f862(f72(a1),x37751),x37752)),f38(a1,x37751,f862(f72(a1),x37752)))
% 25.54/25.40 [3777]E(f862(f165(a1),f171(x37771,f862(f862(f3(a1),x37772),f71(a1)))),f862(f295(a1,x37771),x37772))
% 25.54/25.40 [3782]P1(f862(f862(f227(a924),x37821),f862(f862(f73(a924),x37822),x37821)))
% 25.54/25.40 [3783]P1(f862(f862(f227(a924),x37831),f862(f862(f73(a924),x37831),x37832)))
% 25.54/25.40 [3785]E(f862(f862(f103(f932(x37851,a921)),f234(f932(x37851,a921))),x37852),f234(f932(x37851,a921)))
% 25.54/25.40 [3786]E(f862(f862(f94(f932(x37861,a921)),f181(f932(x37861,a921))),x37862),f181(f932(x37861,a921)))
% 25.54/25.40 [3787]E(f862(f862(f3(f932(x37871,a921)),f181(f932(x37871,a921))),x37872),f181(f932(x37871,a921)))
% 25.54/25.40 [3794]E(f862(f862(f244(a1,a1),x37941),f862(f72(a1),x37942)),f862(a44,f862(f862(f244(a1,a1),x37941),x37942)))
% 25.54/25.40 [3795]E(f862(f295(a1,f862(f862(f73(a1),x37951),f71(a1))),x37952),f298(a1,x37951,x37952))
% 25.54/25.40 [3806]E(f862(f862(f74(a924),x38061),f862(f862(f29(a924),x38062),x38061)),f862(f862(f3(a924),x38062),f38(a924,x38062,x38061)))
% 25.54/25.40 [3807]E(f862(f862(f74(a1),x38071),f862(f862(f29(a1),x38072),x38071)),f862(f862(f3(a1),x38072),f38(a1,x38072,x38071)))
% 25.54/25.40 [3810]E(f862(f165(a1),f171(f862(f862(f73(a1),x38101),f71(a1)),x38102)),f297(a1,x38101,x38102))
% 25.54/25.40 [3814]P1(f862(f862(f227(f932(x38141,a921)),x38142),x38142))
% 25.54/25.40 [3817]E(f862(f862(f103(f932(x38171,a921)),x38172),f862(f72(f932(x38171,a921)),x38172)),f234(f932(x38171,a921)))
% 25.54/25.40 [3818]E(f862(f862(f94(f932(x38181,a921)),x38182),f862(f72(f932(x38181,a921)),x38182)),f181(f932(x38181,a921)))
% 25.54/25.40 [3826]E(f862(f862(f3(a924),f862(f862(f3(a924),x38261),f71(a924))),x38262),f862(f862(f3(a924),x38261),f862(a105,x38262)))
% 25.54/25.40 [3832]E(f862(f862(f3(f932(x38321,a921)),f234(f932(x38321,a921))),x38322),f862(f72(f932(x38321,a921)),x38322))
% 25.54/25.40 [3833]E(f862(f862(f3(a1),f862(f96(a1),x38331)),f862(f96(a1),x38332)),f862(f96(a1),f862(f862(f73(a1),x38331),f862(f72(a1),x38332))))
% 25.54/25.40 [3846]E(f862(f165(a924),f132(a924,f862(f295(a924,x38461),f862(a105,x38462)))),f296(a924,x38461,x38462))
% 25.54/25.40 [3861]E(f862(f182(f925(f925(x38611))),f47(x38611,x38612)),f862(f862(f236(a924),f862(a105,f862(a105,f2(a924)))),f862(f182(f925(x38611)),x38612)))
% 25.54/25.40 [3879]E(f862(f862(f176(f931(x38791,x38791),a921),f2(a924)),x38792),f299(x38791,f181(f932(f931(x38791,x38791),a921))))
% 25.54/25.40 [3883]P1(f862(f130(a924),f132(a924,f862(f295(a924,x38831),x38832))))
% 25.54/25.40 [3899]E(f862(f302(a1,a924,a97),f296(a1,f862(f93(a1),x38991),f862(f93(a1),x38992))),f296(a924,x38991,x38992))
% 25.54/25.40 [3908]E(f178(a924,f2(a924),f7(a924),f862(f862(f3(a924),x39081),x39082)),f862(f862(f3(a924),x39081),f862(a105,x39082)))
% 25.54/25.40 [3909]E(f862(a97,f862(f862(f3(a1),x39091),f862(f862(f73(a1),x39092),f71(a1)))),f862(f28(a1),f298(a1,x39092,x39091)))
% 25.54/25.40 [3944]E(f862(f862(f147(a924,a924),a105),f132(a924,f862(f295(a924,x39441),x39442))),f132(a924,f862(f295(a924,f862(a105,x39441)),f862(a105,x39442))))
% 25.54/25.40 [3952]E(f862(f165(a1),f171(f862(f862(f73(a1),x39521),f71(a1)),f862(f862(f3(a1),x39522),f71(a1)))),f298(a1,x39521,x39522))
% 25.54/25.40 [3964]P1(f862(f862(f227(f932(x39641,a921)),f181(f932(x39641,a921))),x39642))
% 25.54/25.40 [3968]E(f78(x39681,f862(f862(f9(x39681,x39681,a921),a317),x39682)),x39682)
% 25.54/25.40 [3969]E(f83(x39691,f862(f862(f9(x39691,x39691,a921),a317),x39692)),x39692)
% 25.54/25.40 [3973]E(f862(f165(a924),f132(a924,f862(f295(a924,f862(a105,x39731)),f862(a105,x39732)))),f297(a924,x39731,x39732))
% 25.54/25.40 [3999]E(f862(f862(f246(x39991,x39992),f234(f932(x39991,a921))),f862(f18(f932(x39992,a921),x39991),f234(f932(x39992,a921)))),f234(f932(f931(x39991,x39992),a921)))
% 25.54/25.40 [4032]E(f862(f254(x40321),f862(f862(f10(a921,a921,x40321),a314),x40322)),f862(f72(f932(x40321,a921)),f862(f254(x40321),x40322)))
% 25.54/25.40 [4035]E(f862(f254(x40351),f862(f862(f9(x40351,x40351,a921),a317),x40352)),f862(f862(f301(x40351),x40352),f181(f932(x40351,a921))))
% 25.54/25.40 [4042]E(f862(f862(f73(a1),f862(f862(f3(a1),x40421),x40422)),f862(f862(f3(a1),x40421),x40422)),f862(f862(f3(a1),f862(f862(f73(a1),x40421),x40421)),f862(f862(f73(a1),x40422),x40422)))
% 25.54/25.40 [4043]E(f862(f862(f73(a1),f862(f862(f73(a1),x40431),x40431)),f862(f862(f73(a1),x40432),x40432)),f862(f862(f73(a1),f862(f862(f73(a1),x40431),x40432)),f862(f862(f73(a1),x40431),x40432)))
% 25.54/25.40 [4059]P1(f862(f862(f227(a924),f862(f28(x40591),f862(f165(x40591),x40592))),f862(f182(f925(x40591)),x40592)))
% 25.54/25.40 [4060]P1(f862(f862(f227(a924),f862(f182(f925(x40601)),f145(x40601,x40602))),f862(f182(f925(x40601)),x40602)))
% 25.54/25.40 [4070]E(f862(f254(x40701),f862(f862(f9(x40701,f932(x40701,a921),a921),f321(x40701)),x40702)),x40702)
% 25.54/25.40 [4084]E(f862(f862(f168(x40841),f862(f862(f3(a924),f862(f182(f925(x40841)),x40842)),f71(a924))),x40842),f107(x40841,x40842))
% 25.54/25.40 [4104]E(f178(a924,f2(a924),f862(f862(f10(a924,a924,a924),a105),f862(f225(a924),x41041)),x41042),f862(f862(f225(a924),f862(a105,x41041)),x41042))
% 25.54/25.40 [4109]E(f30(f932(x41091,a921),f862(f302(f932(f931(x41091,x41091),a921),f932(x41091,a921),f273(x41091)),x41092)),f862(f273(x41091),f30(f932(f931(x41091,x41091),a921),x41092)))
% 25.54/25.40 [4110]E(f178(a924,f862(a105,x41101),f862(f862(f10(a924,a924,a924),a105),f862(f226(a924),x41101)),x41102),f862(f862(f226(a924),f862(a105,x41101)),x41102))
% 25.54/25.40 [4112]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),f862(f69(a1),x41121)),f862(f69(a1),x41122))),f38(a1,f862(f69(a1),x41121),f862(f69(a1),x41122))),f46(x41121,x41122))
% 25.54/25.40 [4135]P1(f862(f862(f227(f932(f932(x41351,a921),a921)),x41352),f862(f300(x41351),f30(f932(x41351,a921),x41352))))
% 25.54/25.40 [4167]E(f862(f862(f33(x41671,f932(x41671,a921)),x41672),f862(f862(f9(x41671,f932(x41671,a921),f932(x41671,a921)),f301(x41671)),f181(f932(x41671,a921)))),x41672)
% 25.54/25.40 [4168]E(f862(f862(f280(x41681,x41681,x41681),f862(f277(x41681,x41681),x41682)),f299(x41681,f862(f277(x41681,x41681),x41682))),f862(f277(x41681,x41681),f862(f862(f280(x41681,x41681,x41681),x41682),f299(x41681,x41682))))
% 25.54/25.40 [4231]E(f862(f165(x42311),f862(f135(f925(x42311),f925(x42311),f127(x42311),f106(x42311)),x42312)),f862(f862(f33(f925(x42311),f932(x42311,a921)),f862(f165(f925(x42311)),x42312)),f165(x42311)))
% 25.54/25.40 [4262]E(f862(f862(f103(f932(f931(x42621,x42621),a921)),f299(x42621,f181(f932(f931(x42621,x42621),a921)))),f862(f862(f280(x42621,x42621,x42621),f299(x42621,x42622)),x42622)),f299(x42621,x42622))
% 25.54/25.40 [4298]E(f862(f862(f174(x42981,x42981),x42982),x42982),f862(f862(f147(x42981,f931(x42981,x42981)),f862(f862(f20(x42981,x42981,f931(x42981,x42981)),f244(x42981,x42981)),f7(x42981))),x42982))
% 25.54/25.40 [4409]E(f862(f135(a924,f925(x44091),f862(f9(f925(x44091),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x44091)),f226(a924)),f182(f925(x44091)))),f2(a924)),f862(f161(f925(x44091)),x44092)),f862(f182(f925(f925(x44091))),f172(x44091,x44092)))
% 25.54/25.40 [4482]E(f862(f862(f279(f931(a924,f925(x44821)),f925(x44821)),f311(a924,f925(x44821),a232,f138(x44821,x44822))),f862(f862(f20(f925(x44821),f925(x44821),f931(a924,f925(x44821))),f862(f862(f10(a924,f932(f925(x44821),f931(a924,f925(x44821))),f925(x44821)),f244(a924,f925(x44821))),f182(f925(x44821)))),f7(f925(x44821)))),f139(x44821,x44822))
% 25.54/25.40 [4611]E(f862(f254(x46111),f862(f862(f10(f932(f932(x46111,a921),a921),a921,x46111),f81(f932(x46111,a921))),f862(f862(f10(f932(f932(x46111,a921),a921),f932(f932(x46111,a921),a921),x46111),f862(f20(f932(x46111,a921),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46111,a921)),a322),f862(f862(f9(f932(x46111,a921),f932(f932(x46111,a921),a921),a921),f321(f932(x46111,a921))),x46112)))),f321(x46111)))),f31(f932(x46111,a921),x46112))
% 25.54/25.40 [4612]E(f862(f254(x46121),f862(f862(f10(f932(f932(x46121,a921),a921),a921,x46121),f80(f932(x46121,a921))),f862(f862(f10(f932(f932(x46121,a921),a921),f932(f932(x46121,a921),a921),x46121),f862(f20(f932(x46121,a921),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46121,a921)),a318),f862(f862(f9(f932(x46121,a921),f932(f932(x46121,a921),a921),a921),f321(f932(x46121,a921))),x46122)))),f321(x46121)))),f30(f932(x46121,a921),x46122))
% 25.54/25.40 [4725]~P1(f862(f862(f228(a1),f862(f93(a1),x47251)),f862(f72(a1),f862(f93(a1),x47252))))
% 25.54/25.40 [4741]~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x47411),x47411)),a90)),f862(f862(f73(a1),x47412),x47412)))
% 25.54/25.40 [3710]E(f862(f862(f3(a924),f862(f862(f73(a924),x37101),x37102)),x37102),x37101)
% 25.54/25.40 [3711]E(f862(f862(f3(a924),f862(f862(f73(a924),x37111),x37112)),x37111),x37112)
% 25.54/25.40 [3776]E(f862(f862(f73(a924),f862(f862(f3(a924),x37761),x37762)),x37762),f862(f862(f226(a924),x37761),x37762))
% 25.54/25.40 [3886]E(f862(f862(f74(a924),f862(f862(f29(a924),x38861),x38862)),x38862),f862(f862(f3(a924),x38861),f38(a924,x38861,x38862)))
% 25.54/25.40 [3913]E(f862(f165(a924),f132(a924,f862(f295(a924,f862(a105,x39131)),x39132))),f298(a924,x39131,x39132))
% 25.54/25.40 [3921]E(f862(f93(a1),f209(f862(a97,f862(f69(a1),x39211)),f862(a97,f862(f69(a1),x39212)))),f862(f862(a210,x39211),x39212))
% 25.54/25.40 [3923]E(f862(f862(f103(f932(x39231,a921)),f862(f72(f932(x39231,a921)),x39232)),x39232),f234(f932(x39231,a921)))
% 25.54/25.40 [3924]E(f862(f862(f94(f932(x39241,a921)),f862(f72(f932(x39241,a921)),x39242)),x39242),f181(f932(x39241,a921)))
% 25.54/25.40 [3940]P1(f862(f862(f227(a924),f862(f862(f3(a924),x39401),x39402)),x39401))
% 25.54/25.40 [3941]P1(f862(f862(f227(a924),f862(f862(f29(a924),x39411),x39412)),x39411))
% 25.54/25.40 [3965]P1(f862(f862(f228(a924),x39651),f862(a105,f862(f862(f73(a924),x39652),x39651))))
% 25.54/25.40 [3966]P1(f862(f862(f228(a924),x39661),f862(a105,f862(f862(f73(a924),x39661),x39662))))
% 25.54/25.40 [3983]E(f862(f862(f74(a924),f862(a97,f862(f69(a1),x39831))),f862(a97,f862(f69(a1),x39832))),f862(a97,f862(f69(a1),f862(f862(f74(a1),x39831),x39832))))
% 25.54/25.40 [3993]E(f862(f862(f73(a1),f862(f862(f74(a1),x39931),x39932)),f862(f862(f74(a1),x39931),x39932)),f862(f862(f74(a1),f862(f862(f73(a1),x39931),x39931)),x39932))
% 25.54/25.40 [3995]P1(f862(f862(f227(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x39951)),x39952)))
% 25.54/25.40 [4063]E(f862(f276(f925(x40631),f925(x40631),f151(x40631,x40632)),f862(f862(f301(f925(x40631)),f106(x40631)),f181(f932(f925(x40631),a921)))),f862(f862(f301(f925(x40631)),f106(x40631)),f181(f932(f925(x40631),a921))))
% 25.54/25.40 [4082]E(f862(f862(f103(f932(f931(x40821,x40821),a921)),f299(x40821,x40822)),f299(x40821,f181(f932(f931(x40821,x40821),a921)))),f299(x40821,x40822))
% 25.54/25.40 [4094]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f73(a1),x40941),x40941))),f862(f96(a1),f862(f862(f73(a1),x40942),x40942))),f862(f862(f29(a1),f862(f96(a1),x40941)),f862(f96(a1),x40942)))
% 25.54/25.40 [4157]E(f862(f862(f236(a1),x41571),f862(f96(a924),f862(f862(f73(a1),x41572),x41572))),f862(f862(f79(a1,a1),f862(f862(f236(a1),x41571),f862(f96(a924),x41572))),f862(f862(f20(a1,a1,a1),f74(a1)),f7(a1))))
% 25.54/25.40 [4163]E(f862(f254(f932(x41631,a921)),f862(f862(f9(f932(x41631,a921),f932(x41631,a921),a921),f227(f932(x41631,a921))),x41632)),f862(f300(x41631),x41632))
% 25.54/25.40 [4179]E(f862(f862(f147(a1,a924),a97),f862(f862(f127(a1),f862(f862(f147(a924,a1),f93(a1)),x41791)),f862(f862(f147(a924,a1),f93(a1)),x41792))),f862(f862(f127(a924),x41791),x41792))
% 25.54/25.40 [4209]E(f862(f302(a1,a1,f862(f862(f9(a1,a1,a1),f73(a1)),x42091)),f862(f295(a1,f2(a1)),f862(f862(f3(a1),x42092),x42091))),f862(f295(a1,x42091),x42092))
% 25.54/25.40 [4211]P51(x42111,f862(f862(f3(f932(f931(x42111,x42111),a921)),x42112),f299(x42111,f181(f932(f931(x42111,x42111),a921)))))
% 25.54/25.40 [4229]E(f862(f182(f925(x42291)),f862(f135(f925(x42291),f925(x42291),f127(x42291),f106(x42291)),x42292)),f862(f158(a924),f862(f862(f147(f925(x42291),a924),f182(f925(x42291))),x42292)))
% 25.54/25.40 [4233]P50(x42331,f234(f932(x42331,a921)),f862(f862(f103(f932(f931(x42331,x42331),a921)),x42332),f299(x42331,f181(f932(f931(x42331,x42331),a921)))))
% 25.54/25.40 [4272]P1(f862(f862(f321(f931(x42721,x42721)),f862(f862(f244(x42721,x42721),x42722),x42722)),f299(x42721,f181(f932(f931(x42721,x42721),a921)))))
% 25.54/25.40 [4278]E(f178(a924,f2(a924),f862(f862(f10(a924,a924,a924),a105),f862(f862(f9(a924,a924,a924),f225(a924)),x42781)),x42782),f862(f862(f225(a924),x42782),f862(a105,x42781)))
% 25.54/25.40 [4281]E(f178(a924,f862(a105,x42811),f862(f862(f10(a924,a924,a924),a105),f862(f862(f9(a924,a924,a924),f226(a924)),x42811)),x42812),f862(f862(f226(a924),x42812),f862(a105,x42811)))
% 25.54/25.40 [4284]E(f862(f302(x42841,f925(x42841),f862(f862(f9(x42841,f925(x42841),f925(x42841)),f144(x42841)),f106(x42841))),x42842),f167(x42841,x42842,f862(f862(f301(f925(x42841)),f106(x42841)),f181(f932(f925(x42841),a921)))))
% 25.54/25.40 [4286]E(f862(f862(f103(f932(f931(x42861,x42861),a921)),f862(f862(f280(x42861,x42861,x42861),x42862),f299(x42861,x42862))),f299(x42861,f181(f932(f931(x42861,x42861),a921)))),f299(x42861,x42862))
% 25.54/25.40 [4293]P1(f862(f862(f227(f932(f931(x42931,x42931),a921)),f255(x42931,x42932)),f862(f862(f246(x42931,x42931),x42932),f862(f18(f932(x42931,a921),x42931),x42932))))
% 25.54/25.40 [4296]E(f862(f302(a1,a924,a97),f862(f862(f103(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x42961)),f862(f302(a924,a1,f93(a1)),x42962))),f862(f862(f103(f932(a924,a921)),x42961),x42962))
% 25.54/25.40 [4297]E(f862(f302(a1,a924,a97),f862(f862(f94(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x42971)),f862(f302(a924,a1,f93(a1)),x42972))),f862(f862(f94(f932(a924,a921)),x42971),x42972))
% 25.54/25.40 [4300]E(f862(f254(x43001),f862(f862(f10(a921,a921,x43001),a314),f862(f862(f9(x43001,f932(x43001,a921),a921),f321(x43001)),x43002))),f862(f72(f932(x43001,a921)),x43002))
% 25.54/25.40 [4327]E(f862(f135(f925(x43271),f925(x43271),f127(x43271),f106(x43271)),f862(f862(f147(f925(x43271),f925(x43271)),f161(x43271)),f862(f161(f925(x43271)),x43272))),f862(f161(x43271),f862(f135(f925(x43271),f925(x43271),f127(x43271),f106(x43271)),x43272)))
% 25.54/25.40 [4353]E(f862(f862(f33(a924,f932(f931(x43531,x43531),a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(f931(x43531,x43531),a921),f932(f931(x43531,x43531),a921)),f176(f931(x43531,x43531),a921)),x43532)),f299(x43531,x43532))
% 25.54/25.40 [4371]E(f78(x43711,f862(f862(f10(f932(x43711,a921),a921,x43711),f862(a317,x43712)),f862(f862(f9(x43711,f932(x43711,a921),f932(x43711,a921)),f301(x43711)),f181(f932(x43711,a921))))),f304(x43711,x43712))
% 25.54/25.40 [4379]E(f862(f182(f925(x43791)),f145(x43791,f862(f135(f925(x43791),f925(x43791),f127(x43791),f106(x43791)),x43792))),f862(f28(x43791),f862(f862(f33(f925(x43791),f932(x43791,a921)),f862(f165(f925(x43791)),x43792)),f165(x43791))))
% 25.54/25.40 [4393]E(f862(f862(f103(f932(f931(x43931,x43931),a921)),x43932),f862(f862(f280(x43931,x43931,x43931),f862(f862(f280(x43931,x43931,x43931),x43932),f299(x43931,x43932))),x43932)),f862(f862(f280(x43931,x43931,x43931),x43932),f299(x43931,x43932)))
% 25.54/25.40 [4417]P1(f862(f862(f227(f932(f931(x44171,x44171),a921)),f862(f862(f280(x44171,x44171,x44171),x44172),f299(x44171,x44172))),f862(f862(f246(x44171,x44171),f862(f273(x44171),x44172)),f862(f18(f932(x44171,a921),x44171),f862(f273(x44171),x44172)))))
% 25.54/25.40 [4459]E(f862(f254(f925(x44591)),f862(f862(f9(f925(x44591),f932(x44591,a921),a921),f862(f862(f10(f932(x44591,a921),f932(f932(x44591,a921),a921),f925(x44591)),f227(f932(x44591,a921))),f165(x44591))),x44592)),f154(x44591,x44592))
% 25.54/25.40 [4470]E(f862(f149(f925(x44701),x44701,f106(x44701),f862(f862(f10(f925(x44701),f932(f925(x44701),f925(x44701)),x44701),f862(f9(f925(x44701),f925(x44701),f925(x44701)),f127(x44701))),f862(f862(f9(x44701,f925(x44701),f925(x44701)),f144(x44701)),f106(x44701)))),x44702),f862(f160(x44701),x44702))
% 25.54/25.40 [4510]P22(f932(x45101,x45102),f932(f931(x45101,x45102),a921),f862(f862(f10(f932(f931(x45101,x45102),a921),f932(f931(x45101,x45102),a921),f932(x45101,x45102)),f254(f931(x45101,x45102))),f862(f862(f10(f932(x45101,f932(x45102,a921)),f932(f931(x45101,x45102),a921),f932(x45101,x45102)),f249(x45101,x45102,a921)),f862(f10(x45102,f932(x45102,a921),x45101),f862(f9(x45102,x45102,a921),a317)))),f234(f932(f932(x45101,x45102),a921)))
% 25.54/25.40 [4515]E(f38(a1,f862(f96(a1),f862(f862(f73(a1),x45151),x45151)),f862(f96(a1),f862(f862(f73(a1),x45152),x45152))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f96(a1),x45151),f862(f96(a1),x45152))))
% 25.54/25.40 [4561]E(f862(f862(f33(x45611,f932(f931(x45611,x45611),a921)),x45612),f862(f862(f9(x45611,f932(f931(x45611,x45611),a921),f932(f931(x45611,x45611),a921)),f862(f862(f10(f931(x45611,x45611),f932(f932(f931(x45611,x45611),a921),f932(f931(x45611,x45611),a921)),x45611),f301(f931(x45611,x45611))),f862(f862(f20(x45611,x45611,f931(x45611,x45611)),f244(x45611,x45611)),f7(x45611)))),f181(f932(f931(x45611,x45611),a921)))),f255(x45611,x45612))
% 25.54/25.40 [4569]E(f195(x45691,f862(f862(f244(a1,a1),f862(f72(a1),f862(f862(f66(f931(a1,a1),a1,x45691,f243(a1,a1)),f205(x45691)),x45692))),f862(f862(f66(f931(a1,a1),a1,x45691,f248(a1,a1)),f205(x45691)),x45692))),f220(x45691,x45692))
% 25.54/25.40 [4650]E(f862(f254(f932(x46501,a921)),f862(f862(f10(f932(f932(x46501,a921),a921),a921,f932(x46501,a921)),f80(f932(x46501,a921))),f862(f862(f9(f932(x46501,a921),f932(f932(x46501,a921),a921),f932(f932(x46501,a921),a921)),f862(f862(f10(f932(f932(x46501,a921),f932(a921,a921)),f932(f932(f932(x46501,a921),a921),f932(f932(x46501,a921),a921)),f932(x46501,a921)),f20(f932(x46501,a921),a921,a921)),f862(f862(f10(f932(f932(x46501,a921),a921),f932(f932(x46501,a921),f932(a921,a921)),f932(x46501,a921)),f862(f10(a921,f932(a921,a921),f932(x46501,a921)),a318)),f862(f862(f9(f932(x46501,a921),f932(f932(x46501,a921),f932(x46501,a921)),f932(f932(x46501,a921),a921)),f862(f862(f10(f932(f932(x46501,a921),a921),f932(f932(f932(x46501,a921),f932(x46501,a921)),f932(f932(x46501,a921),a921)),f932(x46501,a921)),f10(f932(x46501,a921),a921,f932(x46501,a921))),a317)),f72(f932(x46501,a921)))))),f862(f862(f10(f932(f932(x46501,a921),a921),a921,f932(x46501,a921)),f862(f321(f932(x46501,a921)),x46502)),f300(x46501))))),f862(f300(x46501),f862(f72(f932(x46501,a921)),x46502)))
% 25.54/25.40 [4722]~E(f862(f862(f73(a1),x47221),x47221),f862(f862(f3(a1),f862(f862(f73(a1),x47222),x47222)),a90))
% 25.54/25.40 [4723]~E(f862(f862(f73(a1),x47231),x47231),f862(f862(f3(a1),f862(f862(f73(a1),x47232),x47232)),a90))
% 25.54/25.40 [4728]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x47281),x47282)),x47282))
% 25.54/25.40 [4729]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x47291),x47292)),x47291))
% 25.54/25.40 [4000]E(f862(f862(f3(a924),x40001),f862(f862(f74(a924),f862(f862(f29(a924),x40001),x40002)),x40002)),f38(a924,x40001,x40002))
% 25.54/25.40 [4001]E(f862(f862(f3(a1),x40011),f862(f862(f74(a1),f862(f862(f29(a1),x40011),x40012)),x40012)),f38(a1,x40011,x40012))
% 25.54/25.40 [4033]E(f862(f862(f147(a924,x40331),f862(f157(x40331),x40332)),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x40331)),x40332)))),x40332)
% 25.54/25.40 [4090]E(f862(f276(x40901,x40901,f299(x40901,f181(f932(f931(x40901,x40901),a921)))),x40902),x40902)
% 25.54/25.40 [4214]E(f299(x42141,f862(f862(f103(f932(f931(x42141,x42141),a921)),x42142),f299(x42141,f181(f932(f931(x42141,x42141),a921))))),f299(x42141,x42142))
% 25.54/25.40 [4215]E(f299(x42151,f862(f862(f3(f932(f931(x42151,x42151),a921)),x42152),f299(x42151,f181(f932(f931(x42151,x42151),a921))))),f299(x42151,x42152))
% 25.54/25.40 [4265]E(f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x42651),x42651)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x42652),x42652)),a90)),f862(f862(f73(a1),f862(f862(f3(a1),x42651),x42652)),f862(f862(f3(a1),x42651),x42652)))
% 25.54/25.40 [4305]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x43051),x43052)),f862(f862(f73(a1),x43051),x43052))),a90),f862(f862(f73(a1),f862(f862(f73(a1),x43051),x43051)),f862(f862(f3(a1),f862(f862(f73(a1),x43052),x43052)),a90)))
% 25.54/25.40 [4330]E(f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43301),x43301)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x43302),x43302)),a90)),f862(f862(f73(a1),f862(f862(f73(a1),x43301),f862(f862(f3(a1),x43302),a90))),f862(f862(f73(a1),x43301),f862(f862(f3(a1),x43302),a90))))
% 25.54/25.40 [4341]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),x43411),x43412)),f862(f862(f3(a1),x43411),x43412))),a90),f862(f862(f3(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43411),x43411)),a90)),f862(f862(f73(a1),x43412),x43412)))
% 25.54/25.40 [4342]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f73(a1),x43421),x43422)),f862(f862(f73(a1),x43421),x43422))),a90),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43421),x43421)),a90)),f862(f862(f73(a1),x43422),x43422)))
% 25.54/25.40 [4390]E(f862(f93(a1),f862(f862(f29(a924),f862(f862(f74(a924),f862(a97,f862(f69(a1),x43901))),f862(a97,f862(f69(a1),x43902)))),f209(f862(a97,f862(f69(a1),x43901)),f862(a97,f862(f69(a1),x43902))))),f211(x43901,x43902))
% 25.54/25.40 [4436]E(f862(f862(f251(f931(a92,a92),a92,f931(a92,a92),f931(x44361,f931(a92,a92))),f259(f862(a5,f862(f182(f925(x44361)),x44362)))),f862(f862(f10(x44361,f932(f931(a92,a92),f931(x44361,f931(a92,a92))),a92),f244(x44361,f931(a92,a92))),f862(f862(f10(a924,x44361,a92),f862(f157(x44361),x44362)),a22))),f267(x44361,x44362))
% 25.54/25.40 [4516]E(f862(f135(a924,f925(x45161),f862(f9(f925(x45161),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x45161)),f226(a924)),f182(f925(x45161)))),f2(a924)),f862(f161(f925(x45161)),f172(x45161,x45162))),f862(f182(f925(f925(x45161))),f862(f129(f925(x45161),f862(f862(f10(a921,a921,f925(x45161)),a314),f862(f862(f9(f925(x45161),f925(x45161),a921),a317),f106(x45161)))),x45162)))
% 25.54/25.40 [4522]E(f862(f862(f33(a924,f932(x45221,a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(a924,f932(x45221,a921)),f932(x45221,a921)),f862(f862(f10(f932(a924,a921),f932(f932(a924,f932(x45221,a921)),f932(x45221,a921)),a924),f33(a924,f932(x45221,a921))),f295(a924,f2(a924)))),x45222)),f862(f862(f33(a924,f932(x45221,a921)),f234(f932(a924,a921))),x45222))
% 25.54/25.40 [4546]P1(f862(f54(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),x45461)),f862(f862(f9(a924,a924,a921),f228(a924)),x45462)))))
% 25.54/25.40 [4658]E(f862(f254(f931(f925(x46581),f925(x46581))),f862(f249(f925(x46581),f925(x46581),a921),f862(f862(f20(f925(x46581),f932(f925(x46581),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(a921,a921)),f932(f932(f925(x46581),a921),f932(f925(x46581),a921)),f925(x46581)),f20(f925(x46581),a921,a921)),f862(f862(f10(f932(f925(x46581),a921),f932(f925(x46581),f932(a921,a921)),f925(x46581)),f862(f10(a921,f932(a921,a921),f925(x46581)),a319)),f862(f862(f9(f925(x46581),f932(f925(x46581),a924),f932(f925(x46581),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x46581),a924),f932(f925(x46581),a921)),f925(x46581)),f10(a924,a921,f925(x46581))),f862(f862(f10(a924,f932(a924,a921),f925(x46581)),f228(a924)),f182(f925(x46581))))),f182(f925(x46581)))))),f862(f862(f20(f925(x46581),f932(f925(x46581),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(a921,a921)),f932(f932(f925(x46581),a921),f932(f925(x46581),a921)),f925(x46581)),f20(f925(x46581),a921,a921)),f862(f862(f10(f932(f925(x46581),a921),f932(f925(x46581),f932(a921,a921)),f925(x46581)),f862(f10(a921,f932(a921,a921),f925(x46581)),a318)),f862(f862(f9(f925(x46581),f932(f925(x46581),a924),f932(f925(x46581),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x46581),a924),f932(f925(x46581),a921)),f925(x46581)),f10(a924,a921,f925(x46581))),f862(f862(f10(a924,f932(a924,a921),f925(x46581)),a317),f182(f925(x46581))))),f182(f925(x46581)))))),f862(f862(f9(f925(x46581),f932(f931(f925(x46581),f925(x46581)),a921),f932(f925(x46581),a921)),f862(f862(f10(f932(f925(x46581),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921)),f932(f932(f931(f925(x46581),f925(x46581)),a921),f932(f925(x46581),a921)),f925(x46581)),f9(f925(x46581),f932(f931(f925(x46581),f925(x46581)),a921),a921)),f862(f862(f10(f932(f925(x46581),f931(f925(x46581),f925(x46581))),f932(f925(x46581),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921)),f925(x46581)),f862(f10(f931(f925(x46581),f925(x46581)),f932(f932(f931(f925(x46581),f925(x46581)),a921),a921),f925(x46581)),f321(f931(f925(x46581),f925(x46581))))),f244(f925(x46581),f925(x46581))))),f138(x46581,x46582)))))),f139(x46581,x46582))
% 25.54/25.40 [4734]~P1(f862(f862(f84(a1),f862(f862(f73(a1),x47341),x47341)),f862(f862(f3(a1),f862(f862(f73(a1),x47342),x47342)),a90)))
% 25.54/25.40 [4333]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),x43331),x43332)),f862(f862(f74(a1),x43331),x43332))),x43332),f862(f862(f74(a1),f862(f862(f3(a1),f862(f862(f73(a1),x43331),x43331)),a90)),x43332))
% 25.54/25.40 [4435]E(f862(a97,f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44351),x44352)),f181(f932(f931(a924,a924),a921)))))),f862(f862(f3(a924),x44351),x44352))
% 25.54/25.40 [4439]E(f862(f862(f280(x44391,x44391,x44391),f862(f862(f103(f932(f931(x44391,x44391),a921)),x44392),f299(x44391,f181(f932(f931(x44391,x44391),a921))))),f299(x44391,f862(f862(f103(f932(f931(x44391,x44391),a921)),x44392),f299(x44391,f181(f932(f931(x44391,x44391),a921)))))),f299(x44391,x44392))
% 25.54/25.40 [4476]E(f260(x44761,f862(f129(f931(a92,x44761),f862(f249(a92,x44761,a921),f862(f862(f10(a921,f932(x44761,a921),a92),f18(a921,x44761)),f862(f228(a92),f2(a92))))),x44762)),f260(x44761,x44762))
% 25.54/25.40 [4477]E(f258(x44771,f862(f129(f931(a92,x44771),f862(f249(a92,x44771,a921),f862(f862(f10(a921,f932(x44771,a921),a92),f18(a921,x44771)),f862(f228(a92),f2(a92))))),x44772)),f258(x44771,x44772))
% 25.54/25.40 [4479]E(f862(f72(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44791),x44792)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x44792),x44791)),f181(f932(f931(a924,a924),a921))))))
% 25.54/25.40 [4537]E(f862(f862(f279(f925(a924),x45371),f138(a924,a232)),f862(f862(f9(x45371,f925(f932(x45371,a924)),f925(a924)),f862(f862(f10(f932(f932(x45371,a924),a924),f932(f925(f932(x45371,a924)),f925(a924)),x45371),f147(f932(x45371,a924),a924)),f862(f9(f932(x45371,a924),x45371,a924),f7(f932(x45371,a924))))),x45372)),f146(x45371,x45372))
% 25.54/25.40 [4558]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45581),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f10(a924,a924,a1),f862(f225(a924),x45582)),a97)))),f862(f862(f225(a924),f862(a105,x45582)),f862(f96(a924),x45581)))
% 25.54/25.40 [4559]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45591),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f862(a105,x45592))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f10(a924,a924,a1),f862(f226(a924),x45592)),a97)))),f862(f862(f226(a924),f862(a105,x45592)),f862(f96(a924),x45591)))
% 25.54/25.40 [4579]E(f862(f135(f925(x45791),f925(x45791),f127(x45791),f106(x45791)),f862(f862(f147(f925(x45791),f925(x45791)),f149(f925(x45791),x45791,f106(x45791),f862(f862(f10(f925(x45791),f932(f925(x45791),f925(x45791)),x45791),f18(f925(x45791),f925(x45791))),f862(f862(f9(x45791,f925(x45791),f925(x45791)),f144(x45791)),f106(x45791))))),x45792)),f862(f862(f147(f925(x45791),x45791),f134(x45791)),f862(f129(f925(x45791),f862(f862(f10(a921,a921,f925(x45791)),a314),f862(f862(f9(f925(x45791),f925(x45791),a921),a317),f106(x45791)))),x45792)))
% 25.54/25.40 [4641]E(f862(f249(a1,a1,a921),f862(f862(f9(a1,f932(a1,a921),f932(a1,a921)),f862(f862(f10(f932(a1,f932(a921,a921)),f932(f932(a1,a921),f932(a1,a921)),a1),f20(a1,a921,a921)),f862(f862(f10(f932(a1,a921),f932(a1,f932(a921,a921)),a1),f862(f10(a921,f932(a921,a921),a1),a318)),f862(f862(f10(f932(a1,a1),f932(a1,a921),a1),f862(f10(a1,a921,a1),f862(a317,x46411))),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f74(a1),x46412)))))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),f862(a322,f862(f862(f228(a1),f2(a1)),x46412))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),f862(f862(f9(a1,a1,a921),f228(a1)),x46412))))),f862(f862(f10(a921,a921,a1),f862(a322,f862(a314,f862(f862(f228(a1),f2(a1)),x46412)))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f228(a1),x46412))),f862(f862(f9(a1,a1,a921),f227(a1)),f2(a1))))))),f42(x46411,x46412))
% 25.54/25.40 [4644]E(f862(f254(x46441),f862(f862(f10(f932(a924,a921),a921,x46441),f80(a924)),f862(f862(f9(x46441,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),x46441),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),x46441),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(x46441,f932(a924,x46441),f932(a924,a921)),f862(f862(f10(f932(x46441,a921),f932(f932(a924,x46441),f932(a924,a921)),x46441),f10(x46441,a921,a924)),a317)),f862(f157(x46441),x46442))))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x46441)),x46442))))),f862(f165(x46441),x46442))
% 25.54/25.40 [4449]E(f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),x44491),a90)),x44492)),f862(f862(f3(a1),f862(f862(f73(a1),x44491),a90)),x44492))),a90),f862(f862(f3(a1),f862(f862(f73(a1),x44491),x44491)),f862(f862(f3(a1),f862(f862(f73(a1),x44492),x44492)),a90)))
% 25.54/25.40 [4574]E(f862(f135(f925(f925(x45741)),f925(f925(x45741)),f127(f925(x45741)),f106(f925(x45741))),f862(f862(f147(f925(x45741),f925(f925(x45741))),f149(f925(f925(x45741)),x45741,f106(f925(x45741)),f862(f18(f932(f925(x45741),f925(f925(x45741))),x45741),f862(f862(f9(f925(x45741),f925(f925(x45741)),f925(f925(x45741))),f144(f925(x45741))),f106(f925(x45741)))))),x45742)),f862(f862(f147(f925(x45741),f925(x45741)),f164(x45741)),f862(f129(f925(x45741),f862(f862(f10(a921,a921,f925(x45741)),a314),f862(f862(f9(f925(x45741),f925(x45741),a921),a317),f106(x45741)))),x45742)))
% 25.54/25.40 [4584]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45841),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f225(a924)),a97)),x45842)))),f862(f862(f225(a924),f862(f96(a924),x45841)),f862(a105,x45842)))
% 25.54/25.40 [4585]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x45851),a90))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f862(a105,x45852))),f862(f862(f10(a924,a924,a1),a105),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f226(a924)),a97)),x45852)))),f862(f862(f226(a924),f862(f96(a924),x45851)),f862(a105,x45852)))
% 25.54/25.40 [4573]E(f862(f249(x45731,x45731,a921),f862(f862(f20(x45731,a921,f932(x45731,a921)),f862(f862(f10(f932(x45731,f932(a921,a921)),f932(a921,f932(x45731,a921)),x45731),f9(x45731,a921,a921)),f862(f862(f10(f932(x45731,a921),f932(x45731,f932(a921,a921)),x45731),f862(f10(a921,f932(a921,a921),x45731),a318)),a317))),x45732)),f255(x45731,x45732))
% 25.54/25.40 [4618]E(f862(f862(f29(a924),x46181),f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46182)),f862(f862(f29(a924),x46181),f862(a105,f862(a105,f862(a105,x46182)))))
% 25.54/25.40 [4619]E(f38(a924,x46191,f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46192)),f38(a924,x46191,f862(a105,f862(a105,f862(a105,x46192)))))
% 25.54/25.40 [4620]E(f38(a924,f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46201),x46202),f38(a924,f862(a105,f862(a105,f862(a105,x46201))),x46202))
% 25.54/25.40 [4632]E(f116(f862(x46321,f862(f862(f74(a92),f862(f96(a92),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46322))),f862(f193(x46321),x46322))
% 25.54/25.40 [4633]E(f862(f862(f29(a924),f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),x46331)),x46332),f862(f862(f29(a924),f862(a105,f862(a105,f862(a105,x46331)))),x46332))
% 25.54/25.40 [4686]~E(f119(x46861,x46862,x46863),f112(x46861))
% 25.54/25.40 [4687]~E(f119(x46871,x46872,x46873),f112(x46871))
% 25.54/25.40 [3436]E(f862(f185(x34361,x34362),x34363),f114(x34361,x34362))
% 25.54/25.40 [3456]E(f862(f192(x34561,x34562),x34563),f862(f122(x34561),x34562))
% 25.54/25.40 [3535]E(f862(f862(f147(x35351,x35352),x35353),f106(x35351)),f106(x35352))
% 25.54/25.40 [3574]E(f862(f177(x35741,x35742,x35743),f2(a924)),x35742)
% 25.54/25.40 [3576]E(f862(f862(f174(x35761,x35762),x35763),f106(x35762)),f106(f931(x35761,x35762)))
% 25.54/25.40 [3589]E(f862(f182(f925(x35891)),f162(x35891,x35892,x35893)),x35892)
% 25.54/25.40 [3608]E(f78(x36081,f55(x36081,x36082,x36083)),f862(f56(x36081,x36082),x36083))
% 25.54/25.40 [3612]E(f235(x36121,x36122,f235(x36122,x36121,x36123)),x36123)
% 25.54/25.40 [3632]E(f862(f161(x36321),f162(x36321,x36322,x36323)),f162(x36321,x36322,x36323))
% 25.54/25.40 [3657]E(f133(x36571,x36572,f145(x36571,x36573)),f145(x36571,f133(x36571,x36572,x36573)))
% 25.54/25.40 [3676]E(f862(f243(f925(x36761),f925(x36761)),f159(x36761,x36762,x36763)),f862(f129(x36761,x36762),x36763))
% 25.54/25.40 [3720]E(f862(f862(f144(x37201),x37202),f162(x37201,x37203,x37202)),f162(x37201,f862(a105,x37203),x37202))
% 25.54/25.40 [3752]E(f19(x37521,x37522,x37523,f2(a92)),x37522)
% 25.54/25.40 [3753]E(f178(x37531,x37532,x37533,f2(a924)),x37532)
% 25.54/25.40 [3754]E(f21(x37541,x37542,x37543,f2(a92)),x37542)
% 25.54/25.40 [3761]E(f156(x37611,x37612,x37613,f106(x37611)),f106(x37612))
% 25.54/25.40 [3762]E(f123(x37621,x37622,x37623,f112(x37621)),f112(x37622))
% 25.54/25.40 [3768]E(f862(f862(f157(x37681),f862(f862(f144(x37681),x37682),x37683)),f2(a924)),x37682)
% 25.54/25.40 [3796]E(f52(x37961,x37962,f106(x37961),x37963),f106(f931(x37961,x37962)))
% 25.54/25.40 [3816]P22(x38161,x38162,x38163,f181(f932(x38161,a921)))
% 25.54/25.40 [3917]E(f257(x39171,x39172,x39173),f862(f244(f932(a92,f932(a921,f928(f926(x39171)))),f931(a92,a92)),f34(x39171)))
% 25.54/25.40 [3974]E(f862(f66(x39741,x39742,x39741,x39743),f25(x39741)),x39743)
% 25.54/25.40 [4149]P1(f862(f862(f321(f931(x41491,x41491)),f862(f862(f244(x41491,x41491),x41492),x41492)),f299(x41491,x41493)))
% 25.54/25.40 [4735]~P1(f862(f862(f321(f931(f925(x47351),f925(x47351))),f862(f862(f244(f925(x47351),f925(x47351)),x47352),f106(x47351))),f138(x47351,x47353)))
% 25.54/25.40 [4736]~P1(f862(f862(f321(f931(f925(x47361),f925(x47361))),f862(f862(f244(f925(x47361),f925(x47361)),x47362),f106(x47361))),f140(x47361,x47363)))
% 25.54/25.40 [4737]~P1(f862(f862(f321(f931(f925(x47371),f925(x47371))),f862(f862(f244(f925(x47371),f925(x47371)),x47372),f106(x47371))),f150(x47371,x47373)))
% 25.54/25.40 [4738]~P1(f862(f862(f321(f931(f925(x47381),f925(x47381))),f862(f862(f244(f925(x47381),f925(x47381)),f106(x47381)),x47382)),f138(x47381,x47383)))
% 25.54/25.40 [4739]~P1(f862(f862(f321(f931(f925(x47391),f925(x47391))),f862(f862(f244(f925(x47391),f925(x47391)),f106(x47391)),x47392)),f150(x47391,x47393)))
% 25.54/25.40 [3509]E(f862(f862(f194(x35091),x35092),x35093),f195(x35091,f208(x35092,x35093)))
% 25.54/25.40 [3563]E(f862(f277(x35631,x35632),f862(f277(x35632,x35631),x35633)),x35633)
% 25.54/25.40 [3584]E(f862(f862(f174(x35841,x35842),f106(x35841)),x35843),f106(f931(x35841,x35842)))
% 25.54/25.40 [3587]E(f169(x35871,x35872,f862(f292(a924),x35873)),f862(f862(f168(x35871),x35873),x35872))
% 25.54/25.40 [3603]E(f862(f256(x36031,x36032),f862(f277(x36032,x36031),x36033)),f862(f275(x36032,x36031),x36033))
% 25.54/25.40 [3605]E(f145(x36051,f862(f129(x36051,x36052),x36053)),f862(f129(x36051,x36052),f145(x36051,x36053)))
% 25.54/25.40 [3606]E(f862(f275(x36061,x36062),f862(f277(x36062,x36061),x36063)),f862(f256(x36062,x36061),x36063))
% 25.54/25.40 [3607]E(f862(f256(x36071,x36072),f862(f277(x36072,x36071),x36073)),f862(f275(x36072,x36071),x36073))
% 25.54/25.40 [3625]E(f862(f129(x36251,x36252),f862(f161(x36251),x36253)),f862(f161(x36251),f862(f129(x36251,x36252),x36253)))
% 25.54/25.40 [3637]E(f862(f862(f131(x36371),x36372),f862(f164(x36371),x36373)),f862(f862(f131(x36371),f862(a105,x36372)),x36373))
% 25.54/25.40 [3653]E(f862(f302(x36531,x36532,x36533),f181(f932(x36531,a921))),f181(f932(x36532,a921)))
% 25.54/25.40 [3654]E(f862(f276(x36541,x36542,x36543),f181(f932(x36541,a921))),f181(f932(x36542,a921)))
% 25.54/25.40 [3655]E(f862(f303(x36551,x36552,x36553),f181(f932(x36552,a921))),f181(f932(x36551,a921)))
% 25.54/25.40 [3656]E(f862(f303(x36561,x36562,x36563),f234(f932(x36562,a921))),f234(f932(x36561,a921)))
% 25.54/25.40 [3682]E(f113(x36821,f119(f926(x36821),x36822,x36823)),f109(x36821,x36822,f113(x36821,x36823)))
% 25.54/25.40 [3683]E(f166(x36831,f862(f862(f144(x36831),x36832),x36833),f106(x36831)),f862(f862(f144(x36831),x36832),x36833))
% 25.54/25.40 [3684]E(f862(f862(f301(x36841),x36842),f862(f165(x36841),x36843)),f862(f165(x36841),f133(x36841,x36842,x36843)))
% 25.54/25.40 [3772]E(f862(f302(f931(x37721,x37722),x37722,f248(x37721,x37722)),x37723),f862(f275(x37721,x37722),x37723))
% 25.54/25.40 [3773]E(f862(f302(f931(x37731,x37732),x37731,f243(x37731,x37732)),x37733),f862(f256(x37731,x37732),x37733))
% 25.54/25.40 [3788]E(f862(f165(x37881),f162(x37881,f862(a105,x37882),x37883)),f862(f862(f301(x37881),x37883),f181(f932(x37881,a921))))
% 25.54/25.40 [3844]E(f862(f862(f244(x38441,x38442),f862(f243(x38441,x38442),x38443)),f862(f248(x38441,x38442),x38443)),x38443)
% 25.54/25.40 [3845]E(f862(f862(f244(x38451,x38452),f862(f243(x38451,x38452),x38453)),f862(f248(x38451,x38452),x38453)),x38453)
% 25.54/25.40 [3852]E(f862(f182(f926(x38521)),f119(x38521,x38522,x38523)),f862(f862(f73(a924),f862(f182(f926(x38521)),x38523)),f862(a105,f2(a924))))
% 25.54/25.40 [3853]E(f862(f862(f249(x38531,x38532,x38531),f18(x38531,x38532)),x38533),f862(f243(x38531,x38532),x38533))
% 25.54/25.40 [3979]E(f862(f66(x39791,x39791,x39792,f25(x39791)),x39793),x39793)
% 25.54/25.40 [3986]E(f862(f862(f127(x39861),f162(x39861,x39862,x39863)),f862(f862(f144(x39861),x39863),f106(x39861))),f862(f862(f144(x39861),x39863),f162(x39861,x39862,x39863)))
% 25.54/25.40 [4158]P1(f862(f862(f227(f932(x41581,a921)),f862(f165(x41581),f862(f129(x41581,x41582),x41583))),f862(f165(x41581),x41583)))
% 25.54/25.40 [4200]P1(f862(f862(f227(f932(x42001,a921)),f862(f165(x42001),f862(f862(f168(x42001),x42002),x42003))),f862(f165(x42001),x42003)))
% 25.54/25.40 [4201]P1(f862(f862(f227(f932(x42011,a921)),f862(f165(x42011),f862(f862(f131(x42011),x42012),x42013))),f862(f165(x42011),x42013)))
% 25.54/25.40 [4205]P1(f862(f862(f227(f932(x42051,a921)),f862(f165(x42051),f169(x42051,x42052,x42053))),f862(f165(x42051),x42052)))
% 25.54/25.40 [4206]P1(f862(f862(f227(f932(x42061,a921)),f862(f165(x42061),f163(x42061,x42062,x42063))),f862(f165(x42061),x42063)))
% 25.54/25.40 [4227]P22(f931(x42271,x42272),f931(x42272,x42271),f862(f249(x42271,x42272,f931(x42272,x42271)),f862(f9(x42272,x42271,f931(x42272,x42271)),f244(x42272,x42271))),x42273)
% 25.54/25.40 [4238]E(f862(f862(f862(f176(f925(x42381),f925(x42381)),f38(a924,x42382,f862(f182(f925(x42381)),x42383))),f160(x42381)),x42383),f862(f862(f862(f176(f925(x42381),f925(x42381)),x42382),f160(x42381)),x42383))
% 25.54/25.40 [4279]E(f862(f66(f925(x42791),f925(x42791),f925(x42791),f862(f862(f176(f925(x42791),f925(x42791)),x42792),f160(x42791))),f862(f862(f176(f925(x42791),f925(x42791)),x42793),f160(x42791))),f862(f862(f176(f925(x42791),f925(x42791)),f862(f862(f73(a924),x42792),x42793)),f160(x42791)))
% 25.54/25.40 [4282]P1(f862(f862(f321(f931(f925(x42821),f925(x42821))),f862(f862(f244(f925(x42821),f925(x42821)),x42822),x42822)),f151(x42821,f299(x42821,x42823))))
% 25.54/25.40 [4421]E(f78(f931(x44211,x44212),f862(f862(f20(f931(x44211,x44212),x44212,a921),f862(f862(f10(x44211,f932(x44212,a921),f931(x44211,x44212)),x44213),f243(x44211,x44212))),f248(x44211,x44212))),f78(f931(x44211,x44212),f862(f249(x44211,x44212,a921),x44213)))
% 25.54/25.40 [4422]E(f83(f931(x44221,x44222),f862(f862(f20(f931(x44221,x44222),x44222,a921),f862(f862(f10(x44221,f932(x44222,a921),f931(x44221,x44222)),x44223),f243(x44221,x44222))),f248(x44221,x44222))),f83(f931(x44221,x44222),f862(f249(x44221,x44222,a921),x44223)))
% 25.54/25.40 [4456]E(f862(f862(f279(f931(a924,x44561),x44561),f311(a924,x44561,a232,x44562)),f862(f862(f20(x44561,x44561,f931(a924,x44561)),f862(f862(f10(a924,f932(x44561,f931(a924,x44561)),x44561),f244(a924,x44561)),x44563)),f7(x44561))),f313(x44561,x44563,x44562))
% 25.54/25.40 [4518]E(f862(f250(x45181,x45181,x45182,x45182,f7(x45181),f7(x45182)),x45183),x45183)
% 25.54/25.40 [4593]E(f862(f135(f925(f925(x45931)),f925(f925(x45931)),f127(f925(x45931)),f106(f925(x45931))),f862(f862(f147(f925(x45931),f925(f925(x45931))),f862(f862(f9(f925(x45931),f925(x45931),f925(f925(x45931))),f862(f862(f10(f932(x45931,f925(x45931)),f932(f925(x45931),f925(f925(x45931))),f925(x45931)),f147(x45931,f925(x45931))),f862(f9(x45931,f925(x45931),f925(x45931)),f144(x45931)))),x45932)),f48(x45931,x45933,x45932))),f48(x45931,f862(a105,x45933),x45932))
% 25.54/25.40 [4649]E(f216(a924,f931(x46491,f926(x46491)),f2(a924),f862(f249(x46491,f926(x46491),a924),f862(f862(f9(x46491,a924,f932(f926(x46491),a924)),f862(f862(f10(f932(f926(x46491),f932(a924,a924)),f932(a924,f932(f926(x46491),a924)),x46491),f9(f926(x46491),a924,a924)),f862(f862(f10(f932(f926(x46491),a924),f932(f926(x46491),f932(a924,a924)),x46491),f862(f10(a924,f932(a924,a924),f926(x46491)),f73(a924))),f862(f862(f9(x46491,f932(f926(x46491),a924),f932(f926(x46491),a924)),f862(f862(f10(f932(a924,a924),f932(f932(f926(x46491),a924),f932(f926(x46491),a924)),x46491),f10(a924,a924,f926(x46491))),f862(f862(f10(a924,f932(a924,a924),x46491),f73(a924)),x46492))),f118(x46491,x46492))))),f71(a924))),f862(f128(x46491),x46493)),f862(f118(x46491,x46492),x46493))
% 25.54/25.40 [4657]E(f862(f862(f79(a1,x46571),f211(f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46572),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46573))),f862(f862(f20(a1,a1,x46571),f862(f862(f10(a1,f932(a1,x46571),a1),f194(x46571)),f862(f862(f20(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f73(a1)),f862(f862(f10(a1,a1,a1),f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x46571,f243(a1,a1)),f205(x46571)),x46572))),f862(f862(f9(a1,a1,a1),f29(a1)),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46572))))),f862(f862(f10(a1,a1,a1),f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x46571,f243(a1,a1)),f205(x46571)),x46573))),f862(f862(f9(a1,a1,a1),f29(a1)),f862(f862(f66(f931(a1,a1),a1,x46571,f248(a1,a1)),f205(x46571)),x46573)))))),f7(a1))),f223(x46571,x46572,x46573))
% 25.54/25.40 [4681]~E(f862(f862(f144(x46811),x46812),x46813),x46813)
% 25.54/25.40 [4682]~E(f862(f862(f144(x46821),x46822),x46823),x46823)
% 25.54/25.40 [4684]~E(f862(f862(f144(x46841),x46842),x46843),f106(x46841))
% 25.54/25.40 [4685]~E(f862(f862(f144(x46851),x46852),x46853),f106(x46851))
% 25.54/25.40 [4690]~E(f862(f862(f301(x46901),x46902),x46903),f181(f932(x46901,a921)))
% 25.54/25.40 [4691]~E(f862(f862(f301(x46911),x46912),x46913),f181(f932(x46911,a921)))
% 25.54/25.40 [4713]~E(f862(f302(x47131,f932(x47131,a921),x47132),x47133),f862(f300(x47131),x47133))
% 25.54/25.40 [3567]E(f862(f862(f152(x35671,f106(x35671)),x35672),x35673),f106(x35671))
% 25.54/25.40 [3568]E(f862(f862(f152(x35681,f106(x35681)),x35682),x35683),f106(x35681))
% 25.54/25.40 [3569]E(f862(f134(x35691),f862(f862(f144(x35691),x35692),x35693)),x35692)
% 25.54/25.40 [3570]E(f862(f164(x35701),f862(f862(f144(x35701),x35702),x35703)),x35703)
% 25.54/25.40 [3611]E(f862(f862(f131(x36111),f71(a924)),f862(f862(f144(x36111),x36112),x36113)),x36113)
% 25.54/25.40 [3643]E(f107(x36431,f862(f862(f131(x36431),x36432),x36433)),f862(f862(f131(x36431),x36432),f107(x36431,x36433)))
% 25.54/25.40 [3644]E(f107(x36441,f862(f862(f131(x36441),x36442),x36443)),f862(f862(f131(x36441),x36442),f107(x36441,x36443)))
% 25.54/25.40 [3646]E(f862(f862(f152(x36461,x36462),x36463),f862(f862(f157(x36461),x36462),x36463)),x36462)
% 25.54/25.40 [3666]E(f862(f862(f301(x36661),x36662),f862(f862(f301(x36661),x36662),x36663)),f862(f862(f301(x36661),x36662),x36663))
% 25.54/25.40 [3679]E(f862(f862(f301(x36791),x36792),f862(f165(x36791),x36793)),f862(f165(x36791),f862(f862(f144(x36791),x36792),x36793)))
% 25.54/25.40 [3680]E(f862(f862(f131(x36801),x36802),f862(f164(x36801),x36803)),f862(f164(x36801),f862(f862(f131(x36801),x36802),x36803)))
% 25.54/25.40 [3681]E(f862(f862(f131(x36811),x36812),f862(f164(x36811),x36813)),f862(f164(x36811),f862(f862(f131(x36811),x36812),x36813)))
% 25.54/25.40 [3693]E(f862(f862(f168(x36931),f71(a924)),f862(f862(f144(x36931),x36932),x36933)),f862(f862(f144(x36931),x36932),f106(x36931)))
% 25.54/25.40 [3737]E(f862(f56(x37371,x37372),f862(f862(f301(x37371),x37373),f181(f932(x37371,a921)))),x37373)
% 25.54/25.40 [3778]E(f862(f862(f73(a924),x37781),f862(f862(f73(a924),x37782),x37783)),f862(f862(f73(a924),x37782),f862(f862(f73(a924),x37781),x37783)))
% 25.54/25.40 [3779]E(f862(f862(f73(a1),x37791),f862(f862(f73(a1),x37792),x37793)),f862(f862(f73(a1),x37792),f862(f862(f73(a1),x37791),x37793)))
% 25.54/25.40 [3784]E(f862(f862(f246(x37841,x37842),f181(f932(x37841,a921))),x37843),f181(f932(f931(x37841,x37842),a921)))
% 25.54/25.40 [3808]E(f862(f862(f103(f932(x38081,a921)),x38082),x38083),f862(f862(f103(f932(x38081,a921)),x38083),x38082))
% 25.54/25.40 [3809]E(f862(f862(f94(f932(x38091,a921)),x38092),x38093),f862(f862(f94(f932(x38091,a921)),x38093),x38092))
% 25.54/25.40 [3811]E(f862(f862(f127(x38111),x38112),f862(f862(f144(x38111),x38113),f106(x38111))),f862(f160(x38111),f862(f862(f144(x38111),x38113),x38112)))
% 25.54/25.40 [3812]E(f862(f862(f127(x38121),f862(f161(x38121),x38122)),f862(f161(x38121),x38123)),f862(f161(x38121),f862(f862(f127(x38121),x38123),x38122)))
% 25.54/25.40 [3822]E(f862(f164(x38221),f862(f862(f168(x38221),f862(a105,x38222)),x38223)),f862(f862(f168(x38221),x38222),f862(f164(x38221),x38223)))
% 25.54/25.40 [3830]P1(f862(f862(f321(x38301),x38302),f862(f862(f301(x38301),x38302),x38303)))
% 25.54/25.40 [3834]E(f862(f862(f32(x38341,f932(x38342,a921)),f181(f932(x38341,a921))),x38343),f234(f932(x38342,a921)))
% 25.54/25.40 [3837]E(f862(f276(x38371,x38371,f255(x38371,x38372)),x38373),f862(f862(f94(f932(x38371,a921)),x38372),x38373))
% 25.54/25.40 [3851]E(f862(f182(f925(x38511)),f862(f862(f144(x38511),x38512),x38513)),f862(f862(f73(a924),f862(f182(f925(x38511)),x38513)),f862(a105,f2(a924))))
% 25.54/25.40 [3855]E(f107(x38551,f862(f862(f127(x38551),x38552),f862(f862(f144(x38551),x38553),f106(x38551)))),x38552)
% 25.54/25.40 [3856]E(f137(x38561,f862(f862(f127(x38561),x38562),f862(f862(f144(x38561),x38563),f106(x38561)))),x38563)
% 25.54/25.40 [3864]E(f862(f862(f127(x38641),f862(f862(f168(x38641),x38642),x38643)),f862(f862(f131(x38641),x38642),x38643)),x38643)
% 25.54/25.40 [3873]E(f862(f862(f3(a924),f862(f862(f73(a924),x38731),x38732)),f862(f862(f73(a924),x38733),x38732)),f862(f862(f3(a924),x38731),x38733))
% 25.54/25.40 [3874]E(f862(f862(f3(a924),f862(f862(f73(a924),x38741),x38742)),f862(f862(f73(a924),x38741),x38743)),f862(f862(f3(a924),x38742),x38743))
% 25.54/25.40 [3880]E(f862(f862(f127(x38801),f862(f161(x38801),x38802)),f862(f862(f144(x38801),x38803),f106(x38801))),f862(f161(x38801),f862(f862(f144(x38801),x38803),x38802)))
% 25.54/25.40 [3882]E(f862(f862(f73(a924),f862(f182(f925(x38821)),x38822)),f862(f182(f925(x38821)),x38823)),f862(f182(f925(x38821)),f862(f862(f127(x38821),x38822),x38823)))
% 25.54/25.40 [3885]E(f862(f862(f73(a924),f862(f182(f925(x38851)),x38852)),f862(f182(f925(x38851)),x38853)),f862(f182(f925(x38851)),f166(x38851,x38852,x38853)))
% 25.54/25.40 [3892]E(f862(f862(f103(f932(x38921,a921)),f862(f165(x38921),x38922)),f862(f165(x38921),x38923)),f862(f165(x38921),f862(f862(f127(x38921),x38922),x38923)))
% 25.54/25.40 [3893]E(f38(a924,f862(f862(f74(a924),x38931),x38932),f862(f862(f74(a924),x38931),x38933)),f862(f862(f74(a924),x38931),f38(a924,x38932,x38933)))
% 25.54/25.40 [3905]E(f862(f862(f168(x39051),f862(f862(f3(a924),x39052),f71(a924))),f862(f164(x39051),x39053)),f862(f164(x39051),f862(f862(f168(x39051),x39052),x39053)))
% 25.54/25.40 [3910]E(f862(f862(f94(f932(x39101,a921)),x39102),f862(f72(f932(x39101,a921)),x39103)),f862(f862(f3(f932(x39101,a921)),x39102),x39103))
% 25.54/25.40 [3911]E(f862(f862(f3(f932(x39111,a921)),x39112),f862(f72(f932(x39111,a921)),x39113)),f862(f862(f94(f932(x39111,a921)),x39112),x39113))
% 25.54/25.40 [3933]E(f862(f862(f246(x39331,x39332),x39333),f862(f18(f932(x39332,a921),x39331),f181(f932(x39332,a921)))),f181(f932(f931(x39331,x39332),a921)))
% 25.54/25.40 [3935]E(f862(f862(f3(a924),f862(f862(f74(a924),x39351),x39352)),f862(f862(f74(a924),x39351),x39353)),f862(f862(f74(a924),x39351),f862(f862(f3(a924),x39352),x39353)))
% 25.54/25.40 [3936]E(f862(f862(f73(a924),f862(f862(f74(a924),x39361),x39362)),f862(f862(f74(a924),x39361),x39363)),f862(f862(f74(a924),x39361),f862(f862(f73(a924),x39362),x39363)))
% 25.54/25.40 [3937]E(f862(f862(f3(a1),f862(f862(f74(a1),x39371),x39372)),f862(f862(f74(a1),x39371),x39373)),f862(f862(f74(a1),x39371),f862(f862(f3(a1),x39372),x39373)))
% 25.54/25.40 [3938]E(f862(f862(f73(a1),f862(f862(f74(a1),x39381),x39382)),f862(f862(f74(a1),x39381),x39383)),f862(f862(f74(a1),x39381),f862(f862(f73(a1),x39382),x39383)))
% 25.54/25.40 [3939]E(f862(f862(f74(a1),f862(f862(f236(a1),x39391),x39392)),f862(f862(f236(a1),x39391),x39393)),f862(f862(f236(a1),x39391),f862(f862(f73(a924),x39392),x39393)))
% 25.54/25.40 [3953]E(f862(f862(f33(x39531,f932(x39532,a921)),x39533),f862(f18(f932(x39532,a921),x39531),f181(f932(x39532,a921)))),f181(f932(x39532,a921)))
% 25.54/25.40 [3955]E(f38(a924,f862(f862(f74(a924),x39551),x39552),f862(f862(f74(a924),x39553),x39552)),f862(f862(f74(a924),f38(a924,x39551,x39553)),x39552))
% 25.54/25.40 [3959]E(f38(a1,f862(f862(f74(a1),x39591),f38(a1,x39592,x39593)),x39593),f38(a1,f862(f862(f74(a1),x39591),x39592),x39593))
% 25.54/25.40 [3960]E(f38(a1,f862(f862(f3(a1),x39601),f38(a1,x39602,x39603)),x39603),f38(a1,f862(f862(f3(a1),x39601),x39602),x39603))
% 25.54/25.40 [3961]E(f38(a1,f862(f862(f74(a1),x39611),f38(a1,x39612,x39613)),x39613),f38(a1,f862(f862(f74(a1),x39611),x39612),x39613))
% 25.54/25.40 [3962]P1(f862(f862(f227(f932(x39621,a921)),x39622),f862(f862(f301(x39621),x39623),x39622)))
% 25.54/25.40 [4037]E(f862(f862(f32(f932(x40371,a921),f932(x40371,a921)),x40372),f862(f103(f932(x40371,a921)),x40373)),f862(f862(f103(f932(x40371,a921)),x40373),f31(f932(x40371,a921),x40372)))
% 25.54/25.40 [4038]E(f862(f862(f33(f932(x40381,a921),f932(x40381,a921)),x40382),f862(f94(f932(x40381,a921)),x40383)),f862(f862(f94(f932(x40381,a921)),x40383),f30(f932(x40381,a921),x40382)))
% 25.54/25.40 [4050]E(f862(f165(x40501),f862(f862(f862(f176(f925(x40501),f925(x40501)),x40502),f160(x40501)),x40503)),f862(f165(x40501),x40503))
% 25.54/25.40 [4054]E(f862(f862(f168(x40541),f862(f182(f925(x40541)),f170(x40541,x40542,x40543))),x40543),f170(x40541,x40542,x40543))
% 25.54/25.40 [4058]E(f862(f182(f925(x40581)),f862(f862(f862(f176(f925(x40581),f925(x40581)),x40582),f160(x40581)),x40583)),f862(f182(f925(x40581)),x40583))
% 25.54/25.40 [4061]E(f862(f862(f249(x40611,x40612,x40612),f862(f18(f932(x40612,x40612),x40611),f7(x40612))),x40613),f862(f248(x40611,x40612),x40613))
% 25.54/25.40 [4067]E(f38(a1,f862(f862(f3(a1),f38(a1,x40671,x40672)),x40673),x40672),f38(a1,f862(f862(f3(a1),x40671),x40673),x40672))
% 25.54/25.40 [4068]E(f38(a1,f862(f862(f236(a1),f38(a1,x40681,x40682)),x40683),x40682),f38(a1,f862(f862(f236(a1),x40681),x40683),x40682))
% 25.54/25.40 [4071]E(f862(f862(f33(f932(f931(x40711,x40712),a921),f932(x40712,a921)),x40713),f275(x40711,x40712)),f862(f275(x40711,x40712),f30(f932(f931(x40711,x40712),a921),x40713)))
% 25.54/25.40 [4072]E(f862(f862(f33(f932(f931(x40721,x40722),a921),f932(x40721,a921)),x40723),f256(x40721,x40722)),f862(f256(x40721,x40722),f30(f932(f931(x40721,x40722),a921),x40723)))
% 25.54/25.40 [4095]E(f862(f66(x40951,x40951,x40951,x40952),f862(f862(f176(x40951,x40951),x40953),x40952)),f862(f862(f176(x40951,x40951),f862(a105,x40953)),x40952))
% 25.54/25.40 [4113]E(f862(f862(f131(x41131),f862(f862(f3(a924),f862(f182(f925(x41131)),x41132)),x41133)),f862(f161(x41131),x41132)),f862(f161(x41131),f862(f862(f168(x41131),x41133),x41132)))
% 25.54/25.40 [4114]E(f862(f862(f168(x41141),f862(f862(f3(a924),f862(f182(f925(x41141)),x41142)),x41143)),f862(f161(x41141),x41142)),f862(f161(x41141),f862(f862(f131(x41141),x41143),x41142)))
% 25.54/25.40 [4116]E(f862(f862(f73(a924),f862(f158(a924),f862(f862(f147(x41161,a924),x41162),x41163))),f862(f182(f925(x41161)),x41163)),f148(x41161,x41162,x41163))
% 25.54/25.40 [4129]E(f862(f862(f862(f176(f925(x41291),f925(x41291)),x41292),f160(x41291)),f862(f160(x41291),x41293)),f862(f160(x41291),f862(f862(f862(f176(f925(x41291),f925(x41291)),x41292),f160(x41291)),x41293)))
% 25.54/25.40 [4136]E(f862(f160(x41361),f862(f862(f862(f176(f925(x41361),f925(x41361)),x41362),f160(x41361)),x41363)),f862(f862(f862(f176(f925(x41361),f925(x41361)),f862(a105,x41362)),f160(x41361)),x41363))
% 25.54/25.40 [4150]P1(f862(f862(f227(a924),f862(f182(f925(x41501)),f862(f129(x41501,x41502),x41503))),f862(f182(f925(x41501)),x41503)))
% 25.54/25.40 [4166]E(f862(f862(f103(f932(f932(x41661,a921),a921)),f862(f300(x41661),x41662)),f862(f302(f932(x41661,a921),f932(x41661,a921),f862(f301(x41661),x41663)),f862(f300(x41661),x41662))),f862(f300(x41661),f862(f862(f301(x41661),x41663),x41662)))
% 25.54/25.40 [4197]P1(f862(f862(f227(a924),f862(f182(f925(x41971)),f170(x41971,x41972,x41973))),f862(f182(f925(x41971)),x41973)))
% 25.54/25.40 [4204]E(f862(f256(x42041,x42042),f862(f254(f931(x42041,x42042)),f862(f249(x42041,x42042,a921),x42043))),f862(f254(x42041),f862(f862(f10(f932(x42042,a921),a921,x42041),f80(x42042)),x42043)))
% 25.54/25.40 [4216]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x42161)),f296(a924,x42162,x42163)),f296(a924,f862(f862(f73(a924),x42162),x42161),f862(f862(f73(a924),x42163),x42161)))
% 25.54/25.40 [4230]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f73(a924)),x42301)),f862(f295(a924,x42302),x42303)),f862(f295(a924,f862(f862(f73(a924),x42302),x42301)),f862(f862(f73(a924),x42303),x42301)))
% 25.54/25.40 [4248]E(f862(f862(f174(x42481,x42482),f862(f862(f147(f931(x42481,x42482),x42481),f243(x42481,x42482)),x42483)),f862(f862(f147(f931(x42481,x42482),x42482),f248(x42481,x42482)),x42483)),x42483)
% 25.54/25.40 [4253]E(f862(f862(f73(a924),f862(f862(f74(a924),x42531),f38(a924,f862(f862(f29(a924),x42532),x42531),x42533))),f38(a924,x42532,x42531)),f38(a924,x42532,f862(f862(f74(a924),x42531),x42533)))
% 25.54/25.40 [4266]E(f862(f862(f127(x42661),x42662),f862(f135(f925(x42661),f925(x42661),f127(x42661),f106(x42661)),x42663)),f862(f135(f925(x42661),f925(x42661),f127(x42661),x42662),x42663))
% 25.54/25.40 [4287]P1(f862(f862(f321(f931(x42871,x42871)),f862(f862(f244(x42871,x42871),x42872),x42872)),f862(f862(f176(f931(x42871,x42871),a921),f2(a924)),x42873)))
% 25.54/25.40 [4292]E(f862(f254(x42921),f862(f862(f10(f932(x42922,a921),a921,x42921),f80(x42922)),f862(f9(x42922,x42921,a921),x42923))),f862(f275(x42922,x42921),f862(f254(f931(x42922,x42921)),f862(f249(x42922,x42921,a921),x42923))))
% 25.54/25.40 [4309]E(f862(f862(f103(f932(x43091,a921)),f862(f862(f33(a924,f932(x43091,a921)),f296(a924,f71(a924),x43092)),x43093)),f862(x43093,f2(a924))),f862(f862(f33(a924,f932(x43091,a921)),f862(f294(a924),x43092)),x43093))
% 25.54/25.40 [4324]E(f862(f135(f925(x43241),f925(x43241),f127(x43241),f106(x43241)),f862(f862(f147(f925(x43241),f925(x43241)),f129(x43241,x43242)),x43243)),f862(f129(x43241,x43242),f862(f135(f925(x43241),f925(x43241),f127(x43241),f106(x43241)),x43243)))
% 25.54/25.40 [4328]E(f862(f248(f925(x43281),f925(x43281)),f159(x43281,x43282,x43283)),f862(f129(x43281,f862(f66(a921,a921,x43281,a314),x43282)),x43283))
% 25.54/25.40 [4373]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),x43731),f862(f862(f29(a1),x43732),x43731))),f38(a1,x43732,x43731))),x43733),f862(f862(f73(a1),x43732),x43733))
% 25.54/25.40 [4410]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f74(a1),f862(f862(f29(a1),x44101),x44102)),x44102)),f38(a1,x44101,x44102))),x44103),f862(f862(f73(a1),x44101),x44103))
% 25.54/25.40 [4437]E(f78(f931(x44371,x44372),f862(f249(x44371,x44372,a921),f862(f862(f10(f932(x44372,f931(x44371,x44372)),f932(x44372,a921),x44371),f862(f10(f931(x44371,x44372),a921,x44372),x44373)),f244(x44371,x44372)))),f78(f931(x44371,x44372),x44373))
% 25.54/25.40 [4438]E(f83(f931(x44381,x44382),f862(f249(x44381,x44382,a921),f862(f862(f10(f932(x44382,f931(x44381,x44382)),f932(x44382,a921),x44381),f862(f10(f931(x44381,x44382),a921,x44382),x44383)),f244(x44381,x44382)))),f83(f931(x44381,x44382),x44383))
% 25.54/25.40 [4465]P1(f862(f862(f227(f932(x44651,a921)),f30(f932(x44651,a921),f862(f862(f94(f932(f932(x44651,a921),a921)),x44652),x44653))),f862(f862(f94(f932(x44651,a921)),f30(f932(x44651,a921),x44652)),f30(f932(x44651,a921),x44653))))
% 25.54/25.40 [4466]E(f862(f161(x44661),f862(f862(f862(f176(f925(x44661),f925(x44661)),f862(f862(f3(a924),f862(f182(f925(x44661)),x44662)),f38(a924,x44663,f862(f182(f925(x44661)),x44662)))),f160(x44661)),x44662)),f862(f862(f862(f176(f925(x44661),f925(x44661)),x44663),f160(x44661)),f862(f161(x44661),x44662)))
% 25.54/25.40 [4503]P1(f862(f862(f227(a924),f862(f182(f925(x45031)),f862(f862(f131(x45031),f862(f182(f925(x45031)),f170(x45031,x45032,x45033))),x45033))),f862(f182(f925(x45031)),x45033)))
% 25.54/25.40 [4726]~P1(f862(f55(x47261,x47262,f181(f932(x47261,a921))),x47263))
% 25.54/25.40 [4733]~P1(f862(f862(f321(f931(x47331,x47331)),f862(f862(f244(x47331,x47331),x47332),x47333)),f146(x47331,f106(f932(x47331,a924)))))
% 25.54/25.40 [3823]E(f862(f182(f925(x38231)),f862(f862(f168(x38231),x38232),x38233)),f862(f862(f225(a924),f862(f182(f925(x38231)),x38233)),x38232))
% 25.54/25.40 [3824]E(f862(f182(f925(x38241)),f862(f862(f131(x38241),x38242),x38243)),f862(f862(f3(a924),f862(f182(f925(x38241)),x38243)),x38242))
% 25.54/25.40 [3850]E(f862(f182(f925(f925(x38501))),f48(x38501,x38502,x38503)),f862(f862(f236(a924),f862(f182(f925(x38501)),x38503)),x38502))
% 25.54/25.40 [3866]E(f862(f862(f29(a924),f862(f862(f29(a924),x38661),x38662)),x38663),f862(f862(f29(a924),x38661),f862(f862(f74(a924),x38662),x38663)))
% 25.54/25.40 [3867]E(f862(f862(f3(a924),f862(f862(f3(a924),x38671),x38672)),x38673),f862(f862(f3(a924),x38671),f862(f862(f73(a924),x38672),x38673)))
% 25.54/25.40 [3868]E(f862(f862(f74(a924),f862(f862(f74(a924),x38681),x38682)),x38683),f862(f862(f74(a924),x38681),f862(f862(f74(a924),x38682),x38683)))
% 25.54/25.40 [3869]E(f862(f862(f74(a1),f862(f862(f74(a1),x38691),x38692)),x38693),f862(f862(f74(a1),x38691),f862(f862(f74(a1),x38692),x38693)))
% 25.54/25.40 [3870]E(f862(f862(f73(a924),f862(f862(f73(a924),x38701),x38702)),x38703),f862(f862(f73(a924),x38701),f862(f862(f73(a924),x38702),x38703)))
% 25.54/25.40 [3871]E(f862(f862(f73(a1),f862(f862(f73(a1),x38711),x38712)),x38713),f862(f862(f73(a1),x38711),f862(f862(f73(a1),x38712),x38713)))
% 25.54/25.40 [3872]E(f862(f862(f236(a1),f862(f862(f236(a1),x38721),x38722)),x38723),f862(f862(f236(a1),x38721),f862(f862(f74(a924),x38722),x38723)))
% 25.54/25.40 [3891]E(f155(x38911,f862(f862(f144(f932(x38911,a921)),x38912),x38913)),f167(x38911,x38912,f155(x38911,x38913)))
% 25.54/25.40 [3934]E(f862(f862(f3(a924),f862(f862(f3(a924),x39341),x39342)),x39343),f862(f862(f3(a924),f862(f862(f3(a924),x39341),x39343)),x39342))
% 25.54/25.40 [3942]E(f862(f862(f94(f932(x39421,a921)),x39422),f862(f862(f3(f932(x39421,a921)),x39423),x39422)),f181(f932(x39421,a921)))
% 25.54/25.40 [3946]E(f862(f862(f147(a924,x39461),f862(f18(x39461,a924),x39462)),f132(a924,f862(f295(a924,f2(a924)),x39463))),f162(x39461,x39463,x39462))
% 25.54/25.40 [3984]E(f31(f932(x39841,a921),f862(f862(f301(f932(x39841,a921)),x39842),x39843)),f862(f862(f94(f932(x39841,a921)),x39842),f31(f932(x39841,a921),x39843)))
% 25.54/25.40 [3985]E(f30(f932(x39851,a921),f862(f862(f301(f932(x39851,a921)),x39852),x39853)),f862(f862(f103(f932(x39851,a921)),x39852),f30(f932(x39851,a921),x39853)))
% 25.54/25.40 [3987]E(f162(x39871,f862(f182(f925(x39871)),f862(f129(x39871,f862(a317,x39872)),x39873)),x39872),f862(f129(x39871,f862(a317,x39872)),x39873))
% 25.54/25.40 [3989]E(f862(f862(f3(a924),f862(f862(f74(a924),x39891),x39892)),f862(f862(f74(a924),x39893),x39892)),f862(f862(f74(a924),f862(f862(f3(a924),x39891),x39893)),x39892))
% 25.54/25.40 [3990]E(f862(f862(f73(a924),f862(f862(f74(a924),x39901),x39902)),f862(f862(f74(a924),x39903),x39902)),f862(f862(f74(a924),f862(f862(f73(a924),x39901),x39903)),x39902))
% 25.54/25.40 [3991]E(f862(f862(f3(a1),f862(f862(f74(a1),x39911),x39912)),f862(f862(f74(a1),x39913),x39912)),f862(f862(f74(a1),f862(f862(f3(a1),x39911),x39913)),x39912))
% 25.54/25.40 [3992]E(f862(f862(f73(a1),f862(f862(f74(a1),x39921),x39922)),f862(f862(f74(a1),x39923),x39922)),f862(f862(f74(a1),f862(f862(f73(a1),x39921),x39923)),x39922))
% 25.54/25.40 [3994]E(f862(f862(f225(a924),f862(f862(f3(a924),x39941),x39942)),f862(f862(f3(a924),x39943),x39942)),f862(f862(f3(a924),f862(f862(f225(a924),x39941),x39943)),x39942))
% 25.54/25.40 [4014]E(f862(f862(f94(f932(f925(x40141),a921)),f153(x40141,x40142)),f153(x40141,x40143)),f153(x40141,f862(f862(f94(f932(x40141,a921)),x40142),x40143)))
% 25.54/25.40 [4017]E(f862(f862(f103(f932(x40171,a921)),x40172),f862(f862(f103(f932(x40171,a921)),x40172),x40173)),f862(f862(f103(f932(x40171,a921)),x40172),x40173))
% 25.54/25.40 [4018]E(f862(f862(f103(f932(x40181,a921)),x40182),f862(f862(f3(f932(x40181,a921)),x40183),x40182)),f862(f862(f103(f932(x40181,a921)),x40182),x40183))
% 25.54/25.40 [4019]E(f862(f862(f94(f932(x40191,a921)),x40192),f862(f862(f94(f932(x40191,a921)),x40192),x40193)),f862(f862(f94(f932(x40191,a921)),x40192),x40193))
% 25.54/25.40 [4031]E(f862(f862(f280(x40311,x40312,x40312),x40313),f299(x40312,f181(f932(f931(x40312,x40312),a921)))),x40313)
% 25.54/25.40 [4034]E(f862(f862(f103(f932(x40341,a921)),f862(f862(f301(x40341),x40342),f181(f932(x40341,a921)))),x40343),f862(f862(f301(x40341),x40342),x40343))
% 25.54/25.40 [4053]E(f862(f862(f3(a924),f862(f862(f3(a924),f862(a105,x40531)),x40532)),f862(a105,x40533)),f862(f862(f3(a924),f862(f862(f3(a924),x40531),x40532)),x40533))
% 25.54/25.40 [4080]E(f862(f862(f94(f932(f932(x40801,a921),a921)),f862(f300(x40801),x40802)),f862(f300(x40801),x40803)),f862(f300(x40801),f862(f862(f94(f932(x40801,a921)),x40802),x40803)))
% 25.54/25.40 [4083]E(f862(f862(f103(f932(x40831,a921)),f862(f72(f932(x40831,a921)),x40832)),x40833),f862(f72(f932(x40831,a921)),f862(f862(f3(f932(x40831,a921)),x40832),x40833)))
% 25.54/25.40 [4092]E(f862(f862(f301(x40921),x40922),f862(f862(f3(f932(x40921,a921)),x40923),f862(f862(f301(x40921),x40922),f181(f932(x40921,a921))))),f862(f862(f301(x40921),x40922),x40923))
% 25.54/25.40 [4102]P1(f862(f862(f227(f932(x41021,a921)),x41022),f862(f862(f103(f932(x41021,a921)),x41023),x41022)))
% 25.54/25.40 [4103]P1(f862(f862(f227(f932(x41031,a921)),x41032),f862(f862(f103(f932(x41031,a921)),x41032),x41033)))
% 25.54/25.40 [4107]E(f862(f862(f94(f932(x41071,a921)),f862(f72(f932(x41071,a921)),x41072)),f862(f72(f932(x41071,a921)),x41073)),f862(f72(f932(x41071,a921)),f862(f862(f103(f932(x41071,a921)),x41072),x41073)))
% 25.54/25.40 [4108]E(f862(f862(f103(f932(x41081,a921)),f862(f72(f932(x41081,a921)),x41082)),f862(f72(f932(x41081,a921)),x41083)),f862(f72(f932(x41081,a921)),f862(f862(f94(f932(x41081,a921)),x41082),x41083)))
% 25.54/25.40 [4122]P1(f862(f862(f227(f932(x41221,a921)),f862(f165(x41221),x41222)),f862(f165(x41221),f862(f862(f144(x41221),x41223),x41222))))
% 25.54/25.40 [4134]E(f862(f862(f103(f932(x41341,a921)),f862(f862(f3(f932(x41341,a921)),x41342),x41343)),f862(f862(f94(f932(x41341,a921)),x41342),x41343)),x41342)
% 25.54/25.40 [4184]E(f862(f862(f8(x41841,a1),f862(f862(f10(a924,a1,x41841),f93(a1)),x41842)),x41843),f862(f93(a1),f862(f862(f8(x41841,a924),x41842),x41843)))
% 25.54/25.40 [4185]E(f862(f862(f11(x41851,a1),f862(f862(f10(a924,a1,x41851),f93(a1)),x41852)),x41853),f862(f93(a1),f862(f862(f11(x41851,a924),x41852),x41853)))
% 25.54/25.40 [4232]E(f862(f862(f127(x42321),f170(x42321,x42322,x42323)),f862(f862(f131(x42321),f862(f182(f925(x42321)),f170(x42321,x42322,x42323))),x42323)),x42323)
% 25.54/25.40 [4236]E(f862(f72(f932(f931(x42361,x42362),a921)),f862(f862(f246(x42361,x42362),x42363),f862(f18(f932(x42362,a921),x42361),f234(f932(x42362,a921))))),f862(f862(f246(x42361,x42362),f862(f72(f932(x42361,a921)),x42363)),f862(f18(f932(x42362,a921),x42361),f234(f932(x42362,a921)))))
% 25.54/25.40 [4237]E(f862(f72(f932(f931(x42371,x42372),a921)),f862(f862(f246(x42371,x42372),f234(f932(x42371,a921))),f862(f18(f932(x42372,a921),x42371),x42373))),f862(f862(f246(x42371,x42372),f234(f932(x42371,a921))),f862(f18(f932(x42372,a921),x42371),f862(f72(f932(x42372,a921)),x42373))))
% 25.54/25.40 [4288]E(f862(f862(f33(f932(x42881,a921),f932(x42881,a921)),x42882),f862(f862(f9(f932(x42881,a921),f932(x42881,a921),f932(x42881,a921)),f94(f932(x42881,a921))),x42883)),f862(f862(f94(f932(x42881,a921)),f30(f932(x42881,a921),x42882)),x42883))
% 25.54/25.40 [4294]E(f862(f135(f925(x42941),f925(x42941),f127(x42941),f106(x42941)),f862(f862(f144(f925(x42941)),x42942),x42943)),f862(f862(f127(x42941),x42942),f862(f135(f925(x42941),f925(x42941),f127(x42941),f106(x42941)),x42943)))
% 25.54/25.40 [4315]E(f862(f862(f301(f932(x43151,a921)),f862(f276(x43151,x43151,x43152),f862(f862(f301(x43151),x43153),f181(f932(x43151,a921))))),f181(f932(f932(x43151,a921),a921))),f862(f862(f53(x43151),f862(f862(f301(x43151),x43153),f181(f932(x43151,a921)))),x43152))
% 25.54/25.40 [4325]E(f862(f862(f73(a924),f862(f862(f74(a924),x43251),f862(f862(f29(a924),x43252),x43253))),f862(f862(f29(a924),f862(f862(f74(a924),x43251),f38(a924,x43252,x43253))),x43253)),f862(f862(f29(a924),f862(f862(f74(a924),x43251),x43252)),x43253))
% 25.54/25.40 [4326]E(f862(f862(f73(a1),f862(f862(f74(a1),x43261),f862(f862(f29(a1),x43262),x43263))),f862(f862(f29(a1),f862(f862(f74(a1),x43261),f38(a1,x43262,x43263))),x43263)),f862(f862(f29(a1),f862(f862(f74(a1),x43261),x43262)),x43263))
% 25.54/25.40 [4358]E(f862(f862(f3(f932(x43581,a921)),f862(f165(x43581),x43582)),f862(f862(f301(x43581),x43583),f181(f932(x43581,a921)))),f862(f165(x43581),f862(f129(x43581,f862(f862(f10(a921,a921,x43581),a314),f862(a317,x43583))),x43582)))
% 25.54/25.40 [4408]E(f862(f862(f127(x44081),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),x44082)),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),x44083)),f862(f135(f925(x44081),f925(x44081),f127(x44081),f106(x44081)),f862(f862(f127(f925(x44081)),x44082),x44083)))
% 25.54/25.40 [4411]E(f862(f862(f244(f925(x44111),f925(x44111)),f862(f129(x44111,x44112),x44113)),f862(f129(x44111,f862(f66(a921,a921,x44111,a314),x44112)),x44113)),f159(x44111,x44112,x44113))
% 25.54/25.40 [4414]E(f862(f862(f73(a924),f862(f862(f73(a924),f862(f862(f29(a924),x44141),x44142)),f862(f862(f29(a924),x44143),x44142))),f862(f862(f29(a924),f862(f862(f73(a924),f38(a924,x44141,x44142)),f38(a924,x44143,x44142))),x44142)),f862(f862(f29(a924),f862(f862(f73(a924),x44141),x44143)),x44142))
% 25.54/25.40 [4415]E(f862(f862(f73(a1),f862(f862(f73(a1),f862(f862(f29(a1),x44151),x44152)),f862(f862(f29(a1),x44153),x44152))),f862(f862(f29(a1),f862(f862(f73(a1),f38(a1,x44151,x44152)),f38(a1,x44153,x44152))),x44152)),f862(f862(f29(a1),f862(f862(f73(a1),x44151),x44153)),x44152))
% 25.54/25.40 [4469]E(f862(f862(f94(f932(f925(x44691),a921)),f862(f862(f9(f925(x44691),f932(f925(x44691),a921),a921),f321(f925(x44691))),f154(x44691,x44692))),f862(f862(f9(f925(x44691),f932(f925(x44691),a921),a921),f321(f925(x44691))),f154(x44691,x44693))),f153(x44691,f862(f862(f94(f932(x44691,a921)),f862(f862(f9(x44691,f932(x44691,a921),a921),f321(x44691)),x44692)),f862(f862(f9(x44691,f932(x44691,a921),a921),f321(x44691)),x44693))))
% 25.54/25.40 [4480]E(f862(f254(x44801),f862(f862(f20(x44801,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44801),a319),f862(f862(f9(x44801,x44801,a921),a317),x44802))),f862(f862(f9(x44801,f932(x44801,a921),a921),f321(x44801)),x44803))),f862(f862(f301(x44801),x44802),x44803))
% 25.54/25.40 [4481]E(f862(f254(x44811),f862(f862(f20(x44811,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44811),a319),f862(f862(f9(x44811,x44811,a921),a317),x44812))),f862(f862(f9(x44811,f932(x44811,a921),a921),f321(x44811)),x44813))),f862(f862(f301(x44811),x44812),x44813))
% 25.54/25.40 [4501]E(f862(f862(f79(f925(f925(x45011)),f925(f925(x45011))),f47(x45011,x45012)),f862(f862(f20(f925(f925(x45011)),f925(f925(x45011)),f925(f925(x45011))),f862(f862(f10(f925(f925(x45011)),f932(f925(f925(x45011)),f925(f925(x45011))),f925(f925(x45011))),f127(f925(x45011))),f862(f147(f925(x45011),f925(x45011)),f862(f144(x45011),x45013)))),f7(f925(f925(x45011))))),f47(x45011,f862(f862(f144(x45011),x45013),x45012)))
% 25.54/25.40 [4504]E(f862(f254(x45041),f862(f862(f20(x45041,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45041),a319),f862(f862(f9(x45041,f932(x45041,a921),a921),f321(x45041)),x45042))),f862(f862(f9(x45041,f932(x45041,a921),a921),f321(x45041)),x45043))),f862(f862(f103(f932(x45041,a921)),x45042),x45043))
% 25.54/25.40 [4505]E(f862(f254(x45051),f862(f862(f20(x45051,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45051),a318),f862(f862(f9(x45051,f932(x45051,a921),a921),f321(x45051)),x45052))),f862(f862(f9(x45051,f932(x45051,a921),a921),f321(x45051)),x45053))),f862(f862(f94(f932(x45051,a921)),x45052),x45053))
% 25.54/25.40 [4596]E(f862(f862(f33(x45961,f932(f932(x45961,a921),a921)),x45962),f862(f862(f9(x45961,f932(f932(x45961,a921),a921),f932(f932(x45961,a921),a921)),f862(f862(f10(f932(x45961,a921),f932(f932(f932(x45961,a921),a921),f932(f932(x45961,a921),a921)),x45961),f301(f932(x45961,a921))),f862(f862(f10(f932(x45961,a921),f932(x45961,a921),x45961),f276(x45961,x45961,x45963)),f862(f862(f9(x45961,f932(x45961,a921),f932(x45961,a921)),f301(x45961)),f181(f932(x45961,a921)))))),f181(f932(f932(x45961,a921),a921)))),f862(f862(f53(x45961),x45962),x45963))
% 25.54/25.40 [4598]E(f862(f862(f194(x45981),f862(f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x45981,f243(a1,a1)),f205(x45981)),x45982)),f862(f862(f66(f931(a1,a1),a1,x45981,f243(a1,a1)),f205(x45981)),x45983))),f862(f862(f74(a1),f862(f862(f66(f931(a1,a1),a1,x45981,f248(a1,a1)),f205(x45981)),x45982)),f862(f862(f66(f931(a1,a1),a1,x45981,f248(a1,a1)),f205(x45981)),x45983))),f221(x45981,x45982,x45983))
% 25.54/25.40 [4601]E(f862(f254(f925(x46011)),f862(f862(f20(f925(x46011),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x46011)),a318),f862(f862(f9(f925(x46011),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46011)),a317),f182(f925(x46011)))),x46012))),f862(f862(f9(f925(x46011),f932(x46011,a921),a921),f862(f862(f10(f932(x46011,a921),f932(f932(x46011,a921),a921),f925(x46011)),f227(f932(x46011,a921))),f165(x46011))),f862(f165(x46011),x46013)))),f862(f165(f925(x46011)),f48(x46011,x46012,x46013)))
% 25.54/25.40 [4007]E(f38(a924,f862(f862(f73(a924),f862(f862(f74(a924),x40071),x40072)),x40073),x40072),f38(a924,x40073,x40072))
% 25.54/25.40 [4052]E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x40521),x40522)),x40523)),f862(f862(f131(a924),x40522),f132(a924,f862(f295(a924,x40521),x40523))))
% 25.54/25.40 [4091]E(f862(f862(f73(a1),f862(f93(a1),x40911)),f862(f862(f73(a1),f862(f93(a1),x40912)),x40913)),f862(f862(f73(a1),f862(f93(a1),f862(f862(f73(a924),x40911),x40912))),x40913))
% 25.54/25.40 [4098]E(f862(f862(f103(f932(x40981,a921)),f862(f862(f3(f932(x40981,a921)),x40982),x40983)),x40983),f862(f862(f103(f932(x40981,a921)),x40982),x40983))
% 25.54/25.40 [4099]E(f862(f862(f3(f932(x40991,a921)),f862(f862(f3(f932(x40991,a921)),x40992),x40993)),x40993),f862(f862(f3(f932(x40991,a921)),x40992),x40993))
% 25.54/25.40 [4123]E(f862(f862(f280(x41231,x41231,x41232),f299(x41231,f181(f932(f931(x41231,x41231),a921)))),x41233),x41233)
% 25.54/25.40 [4131]E(f862(f862(f103(f932(x41311,a921)),f862(f273(x41311),x41312)),f862(f273(x41311),x41313)),f862(f273(x41311),f862(f862(f103(f932(f931(x41311,x41311),a921)),x41312),x41313)))
% 25.54/25.40 [4141]E(f258(x41411,f862(f862(f144(f931(a92,x41411)),f862(f862(f244(a92,x41411),f2(a92)),x41412)),x41413)),f258(x41411,x41413))
% 25.54/25.40 [4143]E(f862(f862(f94(f932(x41431,a921)),f31(f932(x41431,a921),x41432)),f31(f932(x41431,a921),x41433)),f31(f932(x41431,a921),f862(f862(f103(f932(f932(x41431,a921),a921)),x41432),x41433)))
% 25.54/25.40 [4144]E(f862(f862(f103(f932(x41441,a921)),f30(f932(x41441,a921),x41442)),f30(f932(x41441,a921),x41443)),f30(f932(x41441,a921),f862(f862(f103(f932(f932(x41441,a921),a921)),x41442),x41443)))
% 25.54/25.40 [4181]E(f862(f862(f280(x41811,x41811,x41811),f862(f862(f176(f931(x41811,x41811),a921),x41812),x41813)),x41813),f862(f862(f176(f931(x41811,x41811),a921),f862(a105,x41812)),x41813))
% 25.54/25.40 [4224]P1(f862(f862(f227(f932(x42241,a921)),f862(f862(f94(f932(x42241,a921)),x42242),x42243)),x42243))
% 25.54/25.40 [4225]P1(f862(f862(f227(f932(x42251,a921)),f862(f862(f94(f932(x42251,a921)),x42252),x42253)),x42252))
% 25.54/25.40 [4226]P1(f862(f862(f227(f932(x42261,a921)),f862(f862(f3(f932(x42261,a921)),x42262),x42263)),x42262))
% 25.54/25.40 [4250]E(f299(x42501,f862(f862(f103(f932(f931(x42501,x42501),a921)),f299(x42501,x42502)),f299(x42501,x42503))),f299(x42501,f862(f862(f103(f932(f931(x42501,x42501),a921)),x42502),x42503)))
% 25.54/25.40 [4254]E(f30(f932(x42541,a921),f862(f862(f301(f932(x42541,a921)),x42542),f862(f862(f301(f932(x42541,a921)),x42543),f181(f932(f932(x42541,a921),a921))))),f862(f862(f103(f932(x42541,a921)),x42542),x42543))
% 25.54/25.40 [4255]E(f31(f932(x42551,a921),f862(f862(f301(f932(x42551,a921)),x42552),f862(f862(f301(f932(x42551,a921)),x42553),f181(f932(f932(x42551,a921),a921))))),f862(f862(f94(f932(x42551,a921)),x42552),x42553))
% 25.54/25.40 [4260]E(f862(f862(f280(x42601,x42601,x42601),f862(f862(f176(f931(x42601,x42601),a921),x42602),x42603)),x42603),f862(f862(f280(x42601,x42601,x42601),x42603),f862(f862(f176(f931(x42601,x42601),a921),x42602),x42603)))
% 25.54/25.40 [4329]E(f862(f862(f103(f932(x43291,a921)),f862(f254(x43291),f862(f862(f9(x43291,x43291,a921),a317),x43292))),x43293),f862(f862(f301(x43291),x43292),x43293))
% 25.54/25.40 [4331]E(f862(a97,f862(f862(f8(x43311,a1),f862(f862(f10(a924,a1,x43311),f93(a1)),x43312)),x43313)),f862(f862(f8(x43311,a924),x43312),x43313))
% 25.54/25.40 [4332]E(f862(a97,f862(f862(f11(x43321,a1),f862(f862(f10(a924,a1,x43321),f93(a1)),x43322)),x43323)),f862(f862(f11(x43321,a924),x43322),x43323))
% 25.54/25.40 [4405]E(f862(f149(f925(x44051),x44051,f862(f164(x44051),x44052),f862(f18(f932(f925(x44051),f925(x44051)),x44051),f862(f862(f9(f925(x44051),f925(x44051),f925(x44051)),f127(x44051)),x44052))),x44053),f862(f164(x44051),f862(f862(f127(x44051),x44053),x44052)))
% 25.54/25.40 [4434]P1(f862(f862(f227(f932(f932(x44341,a921),a921)),f862(f862(f103(f932(f932(x44341,a921),a921)),f862(f300(x44341),x44342)),f862(f300(x44341),x44343))),f862(f300(x44341),f862(f862(f103(f932(x44341,a921)),x44342),x44343))))
% 25.54/25.40 [4523]E(f862(f254(x45231),f862(f862(f20(x45231,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45231),a318),f862(f862(f9(x45231,f932(x45231,a921),a921),f321(x45231)),x45232))),f862(f862(f10(a921,a921,x45231),a314),f862(f862(f9(x45231,f932(x45231,a921),a921),f321(x45231)),x45233)))),f862(f862(f3(f932(x45231,a921)),x45232),x45233))
% 25.54/25.40 [4549]E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x45491)),x45492)))),f862(f862(f10(x45491,a921,a924),x45493),f862(f157(x45491),x45492))))),f862(f182(f925(x45491)),f862(f129(x45491,x45493),x45492)))
% 25.54/25.40 [4551]E(f862(f182(f925(x45511)),f169(x45511,x45512,x45513)),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x45511)),x45512)))),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x45513)))))
% 25.54/25.40 [4647]E(f862(f862(f94(f932(f931(f925(x46471),f925(x46471)),a921)),f862(f302(f931(f931(x46471,f925(x46471)),f931(x46471,f925(x46471))),f931(f925(x46471),f925(x46471)),f250(f931(x46471,f925(x46471)),f925(x46471),f931(x46471,f925(x46471)),f925(x46471),f862(f249(x46471,f925(x46471),f925(x46471)),f144(x46471)),f862(f249(x46471,f925(x46471),f925(x46471)),f144(x46471)))),f311(x46471,f925(x46471),x46472,f862(f136(x46471,x46472),x46473)))),f862(f254(f931(f925(x46471),f925(x46471))),f862(f249(f925(x46471),f925(x46471),a921),f862(f862(f9(f925(x46471),f932(f925(x46471),a921),f932(f925(x46471),a921)),f862(f862(f10(f932(a921,a921),f932(f932(f925(x46471),a921),f932(f925(x46471),a921)),f925(x46471)),f10(a921,a921,f925(x46471))),f862(f862(f10(a921,f932(a921,a921),f925(x46471)),a318),f862(f862(f9(f925(x46471),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46471)),a317),f182(f925(x46471)))),f862(a105,x46473))))),f862(f862(f9(f925(x46471),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x46471)),a317),f182(f925(x46471)))),f862(a105,x46473)))))),f862(f136(x46471,x46472),f862(a105,x46473)))
% 25.54/25.40 [4145]E(f38(a924,f862(a105,f862(f862(f73(a924),f862(f862(f74(a924),x41451),x41452)),x41453)),x41452),f38(a924,f862(a105,x41453),x41452))
% 25.54/25.40 [4391]E(f862(f254(x43911),f862(f862(f20(x43911,a921,a921),f862(f862(f10(a921,f932(a921,a921),x43911),a318),x43912)),x43913)),f862(f862(f94(f932(x43911,a921)),f862(f254(x43911),x43912)),f862(f254(x43911),x43913)))
% 25.54/25.40 [4392]E(f862(f254(x43921),f862(f862(f20(x43921,a921,a921),f862(f862(f10(a921,f932(a921,a921),x43921),a319),x43922)),x43923)),f862(f862(f103(f932(x43921,a921)),f862(f254(x43921),x43922)),f862(f254(x43921),x43923)))
% 25.54/25.40 [4394]E(f862(f862(f127(x43941),f862(f862(f131(x43941),f38(a924,x43942,f862(f182(f925(x43941)),x43943))),x43943)),f862(f862(f168(x43941),f38(a924,x43942,f862(f182(f925(x43941)),x43943))),x43943)),f862(f862(f862(f176(f925(x43941),f925(x43941)),x43942),f160(x43941)),x43943))
% 25.54/25.40 [4400]E(f862(f254(x44001),f862(f862(f20(x44001,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44001),a322),x44002)),x44003)),f862(f862(f103(f932(x44001,a921)),f862(f72(f932(x44001,a921)),f862(f254(x44001),x44002))),f862(f254(x44001),x44003)))
% 25.54/25.40 [4416]E(f862(f862(f73(a924),f862(f182(f925(x44161)),f862(f129(x44161,x44162),x44163))),f862(f182(f925(x44161)),f862(f129(x44161,f862(f862(f10(a921,a921,x44161),a314),x44162)),x44163))),f862(f182(f925(x44161)),x44163))
% 25.54/25.40 [4440]P1(f862(f862(f227(f932(x44401,a921)),f862(f862(f103(f932(x44401,a921)),f31(f932(x44401,a921),x44402)),f31(f932(x44401,a921),x44403))),f31(f932(x44401,a921),f862(f862(f94(f932(f932(x44401,a921),a921)),x44402),x44403))))
% 25.54/25.40 [4454]E(f862(f165(x44541),f862(f129(x44541,f862(f862(f10(a921,a921,x44541),a314),f862(f862(f9(x44541,x44541,a921),a317),x44542))),x44543)),f862(f862(f3(f932(x44541,a921)),f862(f165(x44541),x44543)),f862(f862(f301(x44541),x44542),f181(f932(x44541,a921)))))
% 25.54/25.40 [4463]P1(f862(f862(f227(f932(f931(x44631,x44631),a921)),f862(f862(f103(f932(f931(x44631,x44631),a921)),f299(x44631,x44632)),f299(x44631,x44633))),f299(x44631,f862(f862(f103(f932(f931(x44631,x44631),a921)),x44632),x44633))))
% 25.54/25.40 [4486]E(f862(f862(f74(a924),f862(a105,f862(a105,f2(a924)))),f862(f862(f8(a924,a924),f862(f862(f10(a924,a924,a924),f862(f73(a924),x44861)),f862(f862(f9(a924,a924,a924),f74(a924)),x44862))),f862(f292(a924),x44863))),f862(f862(f74(a924),x44863),f862(f862(f73(a924),x44861),f862(f862(f73(a924),x44861),f862(f862(f74(a924),f862(f862(f3(a924),x44863),f71(a924))),x44862)))))
% 25.54/25.40 [4496]E(f862(f254(x44961),f862(f862(f20(x44961,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44961),a318),f862(f862(f9(x44961,f932(x44961,a921),a921),f321(x44961)),f862(f165(x44961),x44962)))),x44963)),f862(f165(x44961),f862(f129(x44961,x44963),x44962)))
% 25.54/25.40 [4646]E(f862(f254(x46461),f862(f862(f10(f932(a924,a921),a921,x46461),f80(a924)),f862(f862(f9(x46461,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),x46461),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),x46461),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(x46461,f932(a924,x46461),f932(a924,a921)),f862(f862(f10(f932(x46461,a921),f932(f932(a924,x46461),f932(a924,a921)),x46461),f10(x46461,a921,a924)),a317)),f862(f157(x46461),x46462))))),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f182(f925(x46461)),x46462)))),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x46463))))),f862(f165(x46461),f169(x46461,x46462,x46463)))
% 25.54/25.40 [4538]E(f862(f254(x45381),f862(f862(f20(x45381,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45381),a322),f862(f862(f10(a921,a921,x45381),a314),f862(f862(f9(x45381,x45381,a921),a317),x45382)))),x45383)),f862(f862(f301(x45381),x45382),f862(f254(x45381),x45383)))
% 25.54/25.40 [4570]E(f862(f862(f147(f931(x45701,a924),x45701),f243(x45701,a924)),f862(f129(f931(x45701,a924),f862(f862(f9(f931(x45701,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x45701,a924)),f321(a924)),f248(x45701,a924))),x45702)),f862(f862(f174(x45701,a924),x45703),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x45701)),x45703)))))),f169(x45701,x45703,x45702))
% 25.54/25.40 [4597]E(f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f8(a924,a1),f862(f862(f10(a1,a1,a924),f862(f73(a1),x45971)),f862(f862(f9(a924,a1,a1),f862(f862(f10(a1,f932(a1,a1),a924),f74(a1)),f93(a1))),x45972))),f862(f292(a924),x45973))),f862(f862(f74(a1),f862(f93(a1),x45973)),f862(f862(f73(a1),x45971),f862(f862(f73(a1),x45971),f862(f862(f74(a1),f862(f93(a1),f862(f862(f3(a924),x45973),f71(a924)))),x45972)))))
% 25.54/25.40 [4639]E(f862(f254(f931(x46391,x46392)),f862(f249(x46391,x46392,a921),f862(f862(f9(x46391,f932(f931(x46392,x46391),a921),f932(x46392,a921)),f862(f862(f10(f932(x46392,f932(f932(f931(x46392,x46391),a921),a921)),f932(f932(f931(x46392,x46391),a921),f932(x46392,a921)),x46391),f9(x46392,f932(f931(x46392,x46391),a921),a921)),f862(f862(f10(f932(x46392,f931(x46392,x46391)),f932(x46392,f932(f932(f931(x46392,x46391),a921),a921)),x46391),f862(f10(f931(x46392,x46391),f932(f932(f931(x46392,x46391),a921),a921),x46392),f321(f931(x46392,x46391)))),f862(f9(x46392,x46391,f931(x46392,x46391)),f244(x46392,x46391))))),x46393))),f862(f277(x46392,x46391),x46393))
% 25.54/25.40 [4659]E(f862(f254(f925(x46591)),f862(f862(f10(f932(x46591,a921),a921,f925(x46591)),f80(x46591)),f862(f862(f10(f932(x46591,f932(f925(x46591),a921)),f932(x46591,a921),f925(x46591)),f862(f10(f932(f925(x46591),a921),a921,x46591),f80(f925(x46591)))),f862(f862(f9(f925(x46591),f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),a921))),f862(f862(f10(f932(x46591,f932(f932(f925(x46591),a921),f932(f925(x46591),a921))),f932(f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),a921))),f925(x46591)),f20(x46591,f932(f925(x46591),a921),f932(f925(x46591),a921))),f862(f862(f10(f932(x46591,f932(f925(x46591),f932(a921,a921))),f932(x46591,f932(f932(f925(x46591),a921),f932(f925(x46591),a921))),f925(x46591)),f862(f10(f932(f925(x46591),f932(a921,a921)),f932(f932(f925(x46591),a921),f932(f925(x46591),a921)),x46591),f20(f925(x46591),a921,a921))),f862(f862(f10(f932(x46591,f932(f925(x46591),a921)),f932(x46591,f932(f925(x46591),f932(a921,a921))),f925(x46591)),f862(f10(f932(f925(x46591),a921),f932(f925(x46591),f932(a921,a921)),x46591),f862(f10(a921,f932(a921,a921),f925(x46591)),a318))),f862(f862(f9(f925(x46591),f932(x46591,f932(f925(x46591),f925(x46591))),f932(x46591,f932(f925(x46591),a921))),f862(f862(f10(f932(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921)),f932(f932(x46591,f932(f925(x46591),f925(x46591))),f932(x46591,f932(f925(x46591),a921))),f925(x46591)),f10(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921),x46591)),f862(f862(f10(f932(f925(x46591),a921),f932(f932(f925(x46591),f925(x46591)),f932(f925(x46591),a921)),f925(x46591)),f10(f925(x46591),a921,f925(x46591))),a317))),f144(x46591)))))),f862(f862(f9(x46591,f932(f925(x46591),a921),f932(f925(x46591),a921)),f862(f862(f10(f932(a921,a921),f932(f932(f925(x46591),a921),f932(f925(x46591),a921)),x46591),f10(a921,a921,f925(x46591))),f862(f862(f10(a921,f932(a921,a921),x46591),a318),f862(f862(f9(x46591,f932(x46591,a921),a921),f321(x46591)),x46592)))),f862(f862(f9(f925(x46591),f932(f925(x46591),a921),a921),f321(f925(x46591))),x46593)))))),f167(x46591,x46592,x46593))
% 25.54/25.40 [4656]E(f862(f862(f79(a1,f931(a1,a1)),f862(f862(f3(a1),x46561),x46562)),f862(f862(f9(a1,f931(a1,a1),f931(a1,a1)),f862(f862(f20(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f227(a1),f2(a1)))),f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x46563)),f71(a1))))),f862(f862(f244(a1,a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x46563)),x46561))),f862(f36(x46562),f862(f862(f244(a1,a1),x46563),x46561)))
% 25.54/25.40 [3709]E(f109(x37091,f862(x37092,x37093),f862(x37094,x37093)),f862(f196(x37091,x37092,x37094),x37093))
% 25.54/25.40 [3763]E(f862(f862(f237(x37631,x37632,x37633),x37634),f2(a924)),x37632)
% 25.54/25.40 [3801]E(f178(x38011,x38012,x38013,f862(a105,x38014)),f862(x38013,x38014))
% 25.54/25.40 [3842]E(f163(x38421,x38422,f163(x38421,x38423,x38424)),f163(x38421,x38423,f163(x38421,x38422,x38424)))
% 25.54/25.40 [3843]E(f119(x38431,x38432,f109(x38431,x38433,x38434)),f109(x38431,f119(x38431,x38432,x38433),x38434))
% 25.54/25.40 [3975]E(f862(f149(x39751,x39752,x39753,x39754),f106(x39752)),x39753)
% 25.54/25.40 [3976]E(f862(f135(x39761,x39762,x39763,x39764),f106(x39762)),x39764)
% 25.54/25.40 [4013]E(f862(f182(f929(x40131,x40132)),f213(x40131,x40132,x40133,x40134)),f2(a924))
% 25.54/25.40 [4036]E(f862(f249(x40361,x40362,x40363),f247(x40361,x40362,x40363,x40364)),x40364)
% 25.54/25.40 [4079]E(f862(f862(f127(x40791),f162(x40791,x40792,x40793)),f162(x40791,x40794,x40793)),f862(f862(f127(x40791),f162(x40791,x40794,x40793)),f162(x40791,x40792,x40793)))
% 25.54/25.40 [4164]E(f862(f862(f251(x41641,x41642,x41643,f931(x41642,x41643)),x41644),f244(x41642,x41643)),x41644)
% 25.54/25.40 [4174]E(f120(x41741,x41742,x41743,x41744,f112(x41742)),x41743)
% 25.54/25.40 [4180]E(f68(x41801,x41802,x41803,x41804,f862(x41803,x41804)),x41803)
% 25.54/25.40 [4446]P40(x44461,x44462,x44463,x44464,f181(f932(x44461,a921)),x44464)
% 25.54/25.40 [4447]P40(x44471,x44472,x44473,x44474,f181(f932(x44471,a921)),x44474)
% 25.54/25.40 [3515]E(f862(f862(f18(x35151,x35152),x35153),x35154),x35153)
% 25.54/25.40 [3791]E(f163(x37911,x37912,f862(f129(x37911,x37913),x37914)),f862(f129(x37911,x37913),f163(x37911,x37912,x37914)))
% 25.54/25.40 [3825]E(f862(f862(f57(x38251,x38252,x38253),x38254),f181(f932(x38251,a921))),x38254)
% 25.54/25.40 [3849]E(f862(f862(f157(x38491),f862(f862(f144(x38491),x38492),x38493)),f862(a105,x38494)),f862(f862(f157(x38491),x38493),x38494))
% 25.54/25.40 [3915]E(f862(f862(x39151,x39152),f862(f177(x39153,x39154,x39151),x39152)),f862(f177(x39153,x39154,x39151),f862(a105,x39152)))
% 25.54/25.40 [3956]E(f247(x39561,x39562,x39563,f862(f249(x39561,x39562,x39563),x39564)),x39564)
% 25.54/25.40 [4011]E(f862(f862(f152(x40111,f862(f862(f144(x40111),x40112),x40113)),f2(a924)),x40114),f862(f862(f144(x40111),x40114),x40113))
% 25.54/25.40 [4021]E(f862(f862(f33(f932(x40211,a921),f932(x40212,a921)),x40213),f302(x40211,x40212,x40214)),f862(f302(x40211,x40212,x40214),f30(f932(x40211,a921),x40213)))
% 25.54/25.40 [4022]E(f862(f862(f33(f932(x40221,a921),f932(x40222,a921)),x40223),f303(x40222,x40221,x40224)),f862(f303(x40222,x40221,x40224),f30(f932(x40221,a921),x40223)))
% 25.54/25.40 [4047]E(f113(x40471,f123(x40472,f926(x40471),x40473,x40474)),f862(f111(x40472,x40471,x40474),x40473))
% 25.54/25.40 [4119]E(f862(f118(x41191,x41192),f119(x41191,x41193,x41194)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x41192,x41193)),f862(f118(x41191,x41192),x41194))),f862(a105,f2(a924))))
% 25.54/25.40 [4140]E(f862(f135(x41401,x41402,f862(f9(x41402,x41401,x41401),x41403),x41404),f862(f161(x41402),f106(x41402))),x41404)
% 25.54/25.40 [4244]E(f216(x42441,f931(x42442,f926(x42442)),x42443,f862(f249(x42442,f926(x42442),x42441),x42444),f862(f128(x42442),f112(x42442))),x42443)
% 25.54/25.40 [4376]E(f862(f249(x43761,x43762,x43763),f862(f862(f10(f932(x43762,f931(x43761,x43762)),f932(x43762,x43763),x43761),f862(f10(f931(x43761,x43762),x43763,x43762),x43764)),f244(x43761,x43762))),x43764)
% 25.54/25.40 [3700]E(f862(f248(x37001,x37002),f862(f862(f244(x37001,x37002),x37003),x37004)),x37004)
% 25.54/25.40 [3701]E(f862(f243(x37011,x37012),f862(f862(f244(x37011,x37012),x37013),x37014)),x37013)
% 25.54/25.40 [3735]E(f862(f182(f925(x37351)),f862(f862(f152(x37351,x37352),x37353),x37354)),f862(f182(f925(x37351)),x37352))
% 25.54/25.40 [3736]E(f862(f182(f925(x37361)),f862(f862(f147(x37362,x37361),x37363),x37364)),f862(f182(f925(x37362)),x37364))
% 25.54/25.40 [3757]E(f862(f862(f131(x37571),f862(a105,x37572)),f862(f862(f144(x37571),x37573),x37574)),f862(f862(f131(x37571),x37572),x37574))
% 25.54/25.40 [3820]E(f862(f862(f168(x38201),x38202),f162(x38201,x38203,x38204)),f162(x38201,f862(f862(f225(a924),x38202),x38203),x38204))
% 25.54/25.40 [3821]E(f862(f862(f131(x38211),x38212),f162(x38211,x38213,x38214)),f162(x38211,f862(f862(f3(a924),x38213),x38212),x38214))
% 25.54/25.40 [3827]E(f862(f862(f301(x38271),x38272),f862(f862(f301(x38271),x38273),x38274)),f862(f862(f301(x38271),x38273),f862(f862(f301(x38271),x38272),x38274)))
% 25.54/25.40 [3831]E(f862(f862(f147(x38311,x38312),x38313),f107(x38311,x38314)),f107(x38312,f862(f862(f147(x38311,x38312),x38313),x38314)))
% 25.54/25.40 [3847]E(f862(f161(x38471),f862(f862(f147(x38472,x38471),x38473),x38474)),f862(f862(f147(x38472,x38471),x38473),f862(f161(x38472),x38474)))
% 25.54/25.40 [3848]E(f862(f862(f147(x38481,x38482),x38483),f862(f164(x38481),x38484)),f862(f164(x38482),f862(f862(f147(x38481,x38482),x38483),x38484)))
% 25.54/25.40 [3862]E(f862(f862(f168(x38621),f862(a105,x38622)),f862(f862(f144(x38621),x38623),x38624)),f862(f862(f144(x38621),x38623),f862(f862(f168(x38621),x38622),x38624)))
% 25.54/25.40 [3865]E(f862(f165(x38651),f862(f862(f147(x38652,x38651),x38653),x38654)),f862(f302(x38652,x38651,x38653),f862(f165(x38652),x38654)))
% 25.54/25.40 [3878]E(f862(f862(f147(x38781,x38782),f862(f18(x38782,x38781),x38783)),x38784),f162(x38782,f862(f182(f925(x38781)),x38784),x38783))
% 25.54/25.40 [3914]E(f19(x39141,x39142,x39143,f862(a5,f862(a105,f862(a22,x39144)))),f862(x39143,x39144))
% 25.54/25.40 [3918]E(f862(f862(f127(x39181),f862(f129(x39181,x39182),x39183)),f862(f129(x39181,x39182),x39184)),f862(f129(x39181,x39182),f862(f862(f127(x39181),x39183),x39184)))
% 25.54/25.40 [3930]E(f145(x39301,f862(f862(f147(x39302,x39301),x39303),f145(x39302,x39304))),f145(x39301,f862(f862(f147(x39302,x39301),x39303),x39304)))
% 25.54/25.40 [3945]E(f862(f277(x39451,x39451),f862(f862(f279(x39452,x39451),x39453),x39454)),f862(f862(f279(x39452,x39451),f862(f277(x39452,x39452),x39453)),x39454))
% 25.54/25.40 [3957]E(f862(f862(f280(x39571,x39572,x39573),x39574),f181(f932(f931(x39572,x39573),a921))),f181(f932(f931(x39571,x39573),a921)))
% 25.54/25.40 [3958]E(f862(f862(f168(x39581),f862(f862(f3(a924),x39582),x39583)),f862(f862(f131(x39581),x39583),x39584)),f862(f862(f131(x39581),x39583),f862(f862(f168(x39581),x39582),x39584)))
% 25.54/25.40 [3977]E(f862(f862(f127(x39771),f162(x39771,x39772,x39773)),f162(x39771,x39774,x39773)),f162(x39771,f862(f862(f73(a924),x39772),x39774),x39773))
% 25.54/25.40 [3978]E(f862(f862(f862(f270(x39781),x39782),x39783),x39784),f862(f244(f932(a92,f932(a921,f928(f926(x39781)))),f931(a92,a92)),f862(f35(x39781),x39782)))
% 25.54/25.40 [4002]E(f31(f932(x40021,a921),f862(f302(x40022,f932(x40021,a921),x40023),x40024)),f862(f862(f32(x40022,f932(x40021,a921)),x40024),x40023))
% 25.54/25.40 [4003]E(f30(f932(x40031,a921),f862(f302(x40032,f932(x40031,a921),x40033),x40034)),f862(f862(f33(x40032,f932(x40031,a921)),x40034),x40033))
% 25.54/25.40 [4004]E(f31(f932(x40041,a921),f862(f302(x40042,f932(x40041,a921),x40043),x40044)),f862(f862(f32(x40042,f932(x40041,a921)),x40044),x40043))
% 25.54/25.40 [4005]E(f30(f932(x40051,a921),f862(f302(x40052,f932(x40051,a921),x40053),x40054)),f862(f862(f33(x40052,f932(x40051,a921)),x40054),x40053))
% 25.54/25.40 [4006]E(f862(f182(f925(f931(x40061,x40062))),f862(f862(f174(x40061,x40062),x40063),x40064)),f862(f862(f225(a924),f862(f182(f925(x40061)),x40063)),f862(f182(f925(x40062)),x40064)))
% 25.54/25.40 [4008]E(f862(f303(x40081,x40082,x40083),f862(f72(f932(x40082,a921)),x40084)),f862(f72(f932(x40081,a921)),f862(f303(x40081,x40082,x40083),x40084)))
% 25.54/25.40 [4057]E(f862(f303(x40571,x40572,x40573),f862(f254(x40572),x40574)),f862(f254(x40571),f862(f862(f10(x40572,a921,x40571),x40574),x40573)))
% 25.54/25.40 [4074]E(f862(f862(f157(x40741),f862(f862(f127(x40741),x40742),f862(f862(f144(x40741),x40743),x40744))),f862(f182(f925(x40741)),x40742)),x40743)
% 25.54/25.40 [4096]E(f862(f302(x40961,x40962,x40963),f862(f303(x40961,x40962,x40963),x40964)),f862(f862(f94(f932(x40962,a921)),x40964),f862(f302(x40961,x40962,x40963),f234(f932(x40961,a921)))))
% 25.54/25.40 [4115]P1(f862(f862(f321(x41151),f862(x41152,x41153)),f862(f302(x41154,x41151,x41152),f234(f932(x41154,a921)))))
% 25.54/25.40 [4124]E(f21(x41241,x41242,x41243,f862(a5,f862(a105,f862(a22,x41244)))),f862(f862(x41243,x41244),f21(x41241,x41242,x41243,x41244)))
% 25.54/25.40 [4128]E(f862(f862(f127(x41281),f162(x41281,x41282,x41283)),f862(f862(f144(x41281),x41283),x41284)),f862(f862(f144(x41281),x41283),f862(f862(f127(x41281),f162(x41281,x41282,x41283)),x41284)))
% 25.54/25.40 [4130]E(f862(f862(f246(x41301,x41302),f862(f165(x41301),x41303)),f862(f18(f932(x41302,a921),x41301),f862(f165(x41302),x41304))),f862(f165(f931(x41301,x41302)),f52(x41301,x41302,x41303,x41304)))
% 25.54/25.40 [4142]E(f148(x41421,x41422,f862(f862(f144(x41421),x41423),x41424)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x41422,x41423)),f148(x41421,x41422,x41424))),f862(a105,f2(a924))))
% 25.54/25.40 [4155]E(f178(f925(x41551),f862(f862(f144(x41551),x41552),x41553),f862(f862(f9(a924,f925(x41551),f925(x41551)),f131(x41551)),x41553),x41554),f862(f862(f131(x41551),x41554),f862(f862(f144(x41551),x41552),x41553)))
% 25.54/25.40 [4156]P22(x41561,f931(x41562,x41561),f556(x41563,x41564,x41562,x41561),f862(f862(f33(x41562,f932(x41561,a921)),x41564),x41563))
% 25.54/25.40 [4165]E(f862(f862(f3(f932(x41651,a921)),f862(f862(f3(f932(x41651,a921)),x41652),x41653)),f862(f862(f301(x41651),x41654),f181(f932(x41651,a921)))),f862(f862(f3(f932(x41651,a921)),x41652),f862(f862(f301(x41651),x41654),x41653)))
% 25.54/25.40 [4178]E(f862(f862(f176(f932(x41781,x41782),f932(x41781,x41782)),x41783),f66(x41782,x41782,x41781,x41784)),f66(x41782,x41782,x41781,f862(f862(f176(x41782,x41782),x41783),x41784)))
% 25.54/25.40 [4249]E(f862(f862(f862(f176(f925(x42491),f925(x42491)),x42492),f160(x42491)),f862(f862(f862(f176(f925(x42491),f925(x42491)),x42493),f160(x42491)),x42494)),f862(f862(f862(f176(f925(x42491),f925(x42491)),f862(f862(f73(a924),x42492),x42493)),f160(x42491)),x42494))
% 25.54/25.40 [4334]P1(f862(f862(f227(f932(x43341,a921)),f862(f165(x43341),f862(f862(f152(x43341,x43342),x43343),x43344))),f862(f862(f301(x43341),x43344),f862(f165(x43341),x43342))))
% 25.54/25.40 [4366]E(f862(f862(f33(f932(x43661,a921),f932(f931(x43661,x43662),a921)),x43663),f862(f862(f9(f932(x43661,a921),f932(x43661,f932(x43662,a921)),f932(f931(x43661,x43662),a921)),f246(x43661,x43662)),x43664)),f862(f862(f246(x43661,x43662),f30(f932(x43661,a921),x43663)),x43664))
% 25.54/25.40 [4404]E(f202(x44041,x44042,x44043,f862(f66(x44042,f932(a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x44042))))),x44041,f201(x44042)),x44044)),f203(x44041,x44042,x44044,x44043))
% 25.54/25.40 [4419]E(f198(x44191,x44192,x44193,f862(f66(x44192,f932(a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x44192)))))),x44191,f197(x44192)),x44194)),f199(x44191,x44192,x44194,x44193))
% 25.54/25.40 [4423]P1(f862(f59(x44231,x44232,x44233,x44234,f181(f932(x44231,a921))),x44234))
% 25.54/25.40 [4424]P1(f862(f59(x44241,x44242,x44243,x44244,f181(f932(x44241,a921))),x44244))
% 25.54/25.40 [4464]E(f862(f862(f33(x44641,f932(x44642,a921)),x44643),f862(f862(f9(x44641,f932(x44642,a921),f932(x44642,a921)),f862(f862(f10(x44642,f932(f932(x44642,a921),f932(x44642,a921)),x44641),f301(x44642)),x44644)),f181(f932(x44642,a921)))),f862(f302(x44641,x44642,x44644),x44643))
% 25.54/25.40 [4471]P1(f862(f862(f227(f932(x44711,a921)),f862(f275(x44712,x44711),f862(f862(f94(f932(f931(x44712,x44711),a921)),x44713),x44714))),f862(f862(f94(f932(x44711,a921)),f862(f275(x44712,x44711),x44713)),f862(f275(x44712,x44711),x44714))))
% 25.54/25.40 [4472]P1(f862(f862(f227(f932(x44721,a921)),f862(f256(x44721,x44722),f862(f862(f94(f932(f931(x44721,x44722),a921)),x44723),x44724))),f862(f862(f94(f932(x44721,a921)),f862(f256(x44721,x44722),x44723)),f862(f256(x44721,x44722),x44724))))
% 25.54/25.40 [4534]P1(f862(f862(f227(f932(f931(x45341,x45342),a921)),f862(f302(x45342,f931(x45341,x45342),f556(x45343,x45344,x45341,x45342)),f862(f862(f33(x45341,f932(x45342,a921)),x45344),x45343))),f862(f862(f246(x45341,x45342),x45344),x45343)))
% 25.54/25.40 [4535]E(f862(f111(x45351,f931(x45351,x45352),x45353),f862(f862(f10(f932(x45352,f926(f931(x45351,x45352))),f926(f931(x45351,x45352)),x45351),f111(x45352,f931(x45351,x45352),x45354)),f862(f862(f10(f932(x45352,f931(x45351,x45352)),f932(x45352,f926(f931(x45351,x45352))),x45351),f862(f10(f931(x45351,x45352),f926(f931(x45351,x45352)),x45352),f122(f931(x45351,x45352)))),f244(x45351,x45352)))),f124(x45351,x45352,x45353,x45354))
% 25.54/25.40 [4536]E(f268(x45361,x45362,x45363,f862(f66(x45362,f932(a92,f932(a92,f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x45362)))),f931(a92,a92))))),x45361,f270(x45362)),x45364)),f271(x45361,x45362,x45364,x45363))
% 25.54/25.40 [4576]E(f78(f931(x45761,x45762),f862(f249(x45761,x45762,a921),f862(f862(f9(x45761,f932(x45762,a921),f932(x45762,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45762,a921),f932(x45762,a921)),x45761),f10(a921,a921,x45762)),f862(f862(f10(a921,f932(a921,a921),x45761),a318),f862(a317,x45763)))),f862(a317,x45764)))),f862(f862(f244(x45761,x45762),x45763),x45764))
% 25.54/25.40 [4577]E(f83(f931(x45771,x45772),f862(f249(x45771,x45772,a921),f862(f862(f9(x45771,f932(x45772,a921),f932(x45772,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45772,a921),f932(x45772,a921)),x45771),f10(a921,a921,x45772)),f862(f862(f10(a921,f932(a921,a921),x45771),a318),f862(a317,x45773)))),f862(a317,x45774)))),f862(f862(f244(x45771,x45772),x45773),x45774))
% 25.54/25.40 [4648]E(f862(f862(f249(f925(x46481),f925(x46481),f931(f925(x46481),f925(x46481))),f862(f862(f20(f925(x46481),f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f932(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f925(x46481)),f20(f925(x46481),f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f925(x46481),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481)))),f925(x46481)),f862(f10(f931(f925(x46481),f925(x46481)),f932(f931(f925(x46481),f925(x46481)),f931(f925(x46481),f925(x46481))),f925(x46481)),f862(f89(f931(f925(x46481),f925(x46481))),f862(x46482,x46483)))),f862(f862(f10(f925(x46481),f932(f925(x46481),f931(f925(x46481),f925(x46481))),f925(x46481)),f244(f925(x46481),f925(x46481))),f862(f144(x46481),x46483))))),f862(f862(f9(f925(x46481),f932(f925(x46481),f925(x46481)),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f862(f862(f10(f932(f925(x46481),f931(f925(x46481),f925(x46481))),f932(f932(f925(x46481),f925(x46481)),f932(f925(x46481),f931(f925(x46481),f925(x46481)))),f925(x46481)),f10(f925(x46481),f931(f925(x46481),f925(x46481)),f925(x46481))),f244(f925(x46481),f925(x46481)))),f862(f144(x46481),x46483)))),f159(x46481,x46482,x46484)),f159(x46481,x46482,f862(f862(f144(x46481),x46483),x46484)))
% 25.54/25.40 [3894]E(f862(f862(f168(x38941),x38942),f862(f862(f168(x38941),x38943),x38944)),f862(f862(f168(x38941),f862(f862(f225(a924),x38942),x38943)),x38944))
% 25.54/25.40 [3895]E(f862(f862(f131(x38951),x38952),f862(f862(f131(x38951),x38953),x38954)),f862(f862(f131(x38951),f862(f862(f73(a924),x38952),x38953)),x38954))
% 25.54/25.40 [3906]E(f862(f862(f127(x39061),f862(f862(f144(x39061),x39062),x39063)),x39064),f862(f862(f144(x39061),x39062),f862(f862(f127(x39061),x39063),x39064)))
% 25.54/25.40 [3907]E(f862(f862(f127(x39071),f862(f862(f127(x39071),x39072),x39073)),x39074),f862(f862(f127(x39071),x39072),f862(f862(f127(x39071),x39073),x39074)))
% 25.54/25.40 [3988]E(f862(f862(f157(x39881),f862(f862(f144(x39881),x39882),x39883)),x39884),f178(x39881,x39882,f862(f157(x39881),x39883),x39884))
% 25.54/25.40 [3997]E(f862(f862(f176(x39971,x39971),x39972),f862(f862(f176(x39971,x39971),x39973),x39974)),f862(f862(f176(x39971,x39971),f862(f862(f74(a924),x39973),x39972)),x39974))
% 25.54/25.40 [4024]E(f862(f862(f103(f932(x40241,a921)),x40242),f862(f862(f301(x40241),x40243),x40244)),f862(f862(f301(x40241),x40243),f862(f862(f103(f932(x40241,a921)),x40242),x40244)))
% 25.54/25.40 [4039]E(f862(f862(f862(f176(x40391,x40391),x40392),x40393),f862(x40393,x40394)),f862(x40393,f862(f862(f862(f176(x40391,x40391),x40392),x40393),x40394)))
% 25.54/25.40 [4048]E(f862(f862(f280(x40481,x40482,x40483),f181(f932(f931(x40481,x40482),a921))),x40484),f181(f932(f931(x40481,x40483),a921)))
% 25.54/25.40 [4062]E(f862(f862(f103(f932(x40621,a921)),f862(f862(f301(x40621),x40622),x40623)),x40624),f862(f862(f301(x40621),x40622),f862(f862(f103(f932(x40621,a921)),x40623),x40624)))
% 25.54/25.40 [4081]E(f862(f28(f931(x40811,x40812)),f862(f862(f246(x40811,x40812),x40813),f862(f18(f932(x40812,a921),x40811),x40814))),f862(f862(f74(a924),f862(f28(x40811),x40813)),f862(f28(x40812),x40814)))
% 25.54/25.40 [4087]E(f862(f862(f94(f932(x40871,a921)),f862(f862(f301(x40871),x40872),x40873)),f862(f862(f301(x40871),x40872),x40874)),f862(f862(f301(x40871),x40872),f862(f862(f94(f932(x40871,a921)),x40873),x40874)))
% 25.54/25.40 [4100]E(f862(f862(f103(f932(x41001,a921)),x41002),f862(f862(f103(f932(x41001,a921)),x41003),x41004)),f862(f862(f103(f932(x41001,a921)),x41003),f862(f862(f103(f932(x41001,a921)),x41002),x41004)))
% 25.54/25.40 [4101]E(f862(f862(f94(f932(x41011,a921)),x41012),f862(f862(f94(f932(x41011,a921)),x41013),x41014)),f862(f862(f94(f932(x41011,a921)),x41013),f862(f862(f94(f932(x41011,a921)),x41012),x41014)))
% 25.54/25.40 [4111]E(f57(x41111,x41112,f862(f862(f10(x41112,f932(x41112,x41112),x41111),x41113),x41114)),f862(f58(x41112,x41111,x41113),x41114))
% 25.54/25.40 [4120]E(f172(x41201,f862(f862(f147(f925(x41202),f925(x41201)),f862(f147(x41202,x41201),x41203)),x41204)),f862(f862(f147(f925(x41202),f925(x41201)),f862(f147(x41202,x41201),x41203)),f172(x41202,x41204)))
% 25.54/25.40 [4138]E(f862(f135(f925(x41381),f925(x41381),f127(x41381),f106(x41381)),f862(f862(f147(x41382,f925(x41381)),x41383),x41384)),f156(x41382,x41381,x41383,x41384))
% 25.54/25.40 [4139]E(f862(f135(f925(x41391),f925(x41391),f127(x41391),f106(x41391)),f862(f862(f147(x41392,f925(x41391)),x41393),x41394)),f156(x41392,x41391,x41393,x41394))
% 25.54/25.40 [4196]E(f862(f66(x41961,x41961,x41961,f862(f862(f176(x41961,x41961),x41962),x41963)),f862(f862(f176(x41961,x41961),x41964),x41963)),f862(f862(f176(x41961,x41961),f862(f862(f73(a924),x41962),x41964)),x41963))
% 25.54/25.40 [4219]E(f862(f862(f94(f932(x42191,a921)),f862(f862(f103(f932(x42191,a921)),x42192),x42193)),f862(f862(f103(f932(x42191,a921)),x42192),x42194)),f862(f862(f103(f932(x42191,a921)),x42192),f862(f862(f94(f932(x42191,a921)),x42193),x42194)))
% 25.54/25.40 [4220]E(f862(f862(f103(f932(x42201,a921)),f862(f862(f94(f932(x42201,a921)),x42202),x42203)),f862(f862(f94(f932(x42201,a921)),x42202),x42204)),f862(f862(f94(f932(x42201,a921)),x42202),f862(f862(f103(f932(x42201,a921)),x42203),x42204)))
% 25.54/25.40 [4221]E(f862(f862(f3(f932(x42211,a921)),f862(f862(f94(f932(x42211,a921)),x42212),x42213)),f862(f862(f94(f932(x42211,a921)),x42212),x42214)),f862(f862(f94(f932(x42211,a921)),x42212),f862(f862(f3(f932(x42211,a921)),x42213),x42214)))
% 25.54/25.40 [4222]E(f862(f862(f94(f932(x42221,a921)),f862(f862(f3(f932(x42221,a921)),x42222),x42223)),f862(f862(f3(f932(x42221,a921)),x42222),x42224)),f862(f862(f3(f932(x42221,a921)),x42222),f862(f862(f103(f932(x42221,a921)),x42223),x42224)))
% 25.54/25.40 [4223]E(f862(f862(f103(f932(x42231,a921)),f862(f862(f3(f932(x42231,a921)),x42232),x42233)),f862(f862(f3(f932(x42231,a921)),x42232),x42234)),f862(f862(f3(f932(x42231,a921)),x42232),f862(f862(f94(f932(x42231,a921)),x42233),x42234)))
% 25.54/25.40 [4228]E(f862(f28(f931(x42281,x42282)),f862(f862(f246(x42281,x42282),f862(f862(f301(x42281),x42283),f181(f932(x42281,a921)))),f862(f18(f932(x42282,a921),x42281),x42284))),f862(f28(x42282),x42284))
% 25.54/25.40 [4263]E(f862(f862(f33(x42631,f932(x42632,a921)),x42633),f862(f862(f10(f932(x42632,a921),f932(x42632,a921),x42631),f72(f932(x42632,a921))),x42634)),f862(f72(f932(x42632,a921)),f862(f862(f32(x42631,f932(x42632,a921)),x42633),x42634)))
% 25.54/25.40 [4264]E(f862(f862(f32(x42641,f932(x42642,a921)),x42643),f862(f862(f10(f932(x42642,a921),f932(x42642,a921),x42641),f72(f932(x42642,a921))),x42644)),f862(f72(f932(x42642,a921)),f862(f862(f33(x42641,f932(x42642,a921)),x42643),x42644)))
% 25.54/25.40 [4280]E(f862(f862(f280(x42801,x42801,x42801),f862(f862(f176(f931(x42801,x42801),a921),x42802),x42803)),f862(f862(f176(f931(x42801,x42801),a921),x42804),x42803)),f862(f862(f176(f931(x42801,x42801),a921),f862(f862(f73(a924),x42802),x42804)),x42803))
% 25.54/25.40 [4310]E(f862(f862(f32(x43101,f932(f932(x43102,a921),a921)),x43103),f862(f862(f10(f932(x43102,a921),f932(f932(x43102,a921),a921),x43101),f300(x43102)),x43104)),f862(f300(x43102),f862(f862(f32(x43101,f932(x43102,a921)),x43103),x43104)))
% 25.54/25.40 [4337]E(f862(f862(f32(f932(x43371,a921),f932(x43372,a921)),x43373),f862(f862(f9(f932(x43371,a921),f932(x43371,f932(x43372,a921)),f932(x43372,a921)),f32(x43371,f932(x43372,a921))),x43374)),f862(f862(f32(x43371,f932(x43372,a921)),f30(f932(x43371,a921),x43373)),x43374))
% 25.54/25.40 [4338]E(f862(f862(f33(f932(x43381,a921),f932(x43382,a921)),x43383),f862(f862(f9(f932(x43381,a921),f932(x43381,f932(x43382,a921)),f932(x43382,a921)),f33(x43381,f932(x43382,a921))),x43384)),f862(f862(f33(x43381,f932(x43382,a921)),f30(f932(x43381,a921),x43383)),x43384))
% 25.54/25.40 [4339]E(f862(f862(f32(f932(x43391,a921),f932(x43392,a921)),x43393),f862(f862(f9(f932(x43391,a921),f932(x43391,f932(x43392,a921)),f932(x43392,a921)),f32(x43391,f932(x43392,a921))),x43394)),f862(f862(f32(x43391,f932(x43392,a921)),f30(f932(x43391,a921),x43393)),x43394))
% 25.54/25.40 [4340]E(f862(f862(f33(f932(x43401,a921),f932(x43402,a921)),x43403),f862(f862(f9(f932(x43401,a921),f932(x43401,f932(x43402,a921)),f932(x43402,a921)),f33(x43401,f932(x43402,a921))),x43404)),f862(f862(f33(x43401,f932(x43402,a921)),f30(f932(x43401,a921),x43403)),x43404))
% 25.54/25.40 [4345]E(f862(f862(f147(x43451,x43452),x43453),f862(f135(f925(x43451),f925(x43451),f127(x43451),f106(x43451)),x43454)),f862(f135(f925(x43452),f925(x43452),f127(x43452),f106(x43452)),f862(f862(f147(f925(x43451),f925(x43452)),f862(f147(x43451,x43452),x43453)),x43454)))
% 25.54/25.40 [4347]E(f178(f925(x43471),f106(x43471),f862(f862(f10(f925(x43471),f925(x43471),a924),f862(f144(x43471),x43472)),f862(f862(f9(a924,f925(x43471),f925(x43471)),f168(x43471)),x43473)),x43474),f862(f862(f168(x43471),x43474),f862(f862(f144(x43471),x43472),x43473)))
% 25.54/25.40 [4385]P1(f862(f862(f227(f932(x43851,a921)),f862(f302(x43852,x43851,x43853),f862(f303(x43852,x43851,x43853),x43854))),x43854))
% 25.54/25.40 [4387]E(f862(f302(f931(x43871,x43872),f931(x43872,x43871),f862(f249(x43871,x43872,f931(x43872,x43871)),f862(f9(x43872,x43871,f931(x43872,x43871)),f244(x43872,x43871)))),f862(f862(f246(x43871,x43872),x43873),f862(f18(f932(x43872,a921),x43871),x43874))),f862(f862(f246(x43872,x43871),x43874),f862(f18(f932(x43871,a921),x43872),x43873)))
% 25.54/25.40 [4396]E(f862(f862(f33(x43961,f932(x43962,a921)),x43963),f862(f862(f10(f932(x43961,a921),f932(x43962,a921),x43961),f276(x43961,x43962,x43964)),f862(f862(f9(x43961,f932(x43961,a921),f932(x43961,a921)),f301(x43961)),f181(f932(x43961,a921))))),f862(f276(x43961,x43962,x43964),x43963))
% 25.54/25.40 [4397]E(f862(f862(f33(x43971,f932(x43972,a921)),x43973),f862(f862(f10(f932(x43971,a921),f932(x43972,a921),x43971),f303(x43972,x43971,x43974)),f862(f862(f9(x43971,f932(x43971,a921),f932(x43971,a921)),f301(x43971)),f181(f932(x43971,a921))))),f862(f303(x43972,x43971,x43974),x43973))
% 25.54/25.40 [4473]E(f862(f862(f127(x44731),f862(f129(x44731,f862(f862(f10(a921,a921,x44731),a314),f862(a317,x44732))),x44733)),f862(f129(x44731,f862(f862(f10(a921,a921,x44731),a314),f862(a317,x44732))),x44734)),f862(f129(x44731,f862(f862(f10(a921,a921,x44731),a314),f862(a317,x44732))),f862(f862(f127(x44731),x44733),x44734)))
% 25.54/25.40 [4485]E(f862(f862(f103(f932(x44851,a921)),f862(f862(f103(f932(x44851,a921)),f862(f862(f94(f932(x44851,a921)),x44852),x44853)),f862(f862(f94(f932(x44851,a921)),x44853),x44854))),f862(f862(f94(f932(x44851,a921)),x44854),x44852)),f862(f862(f94(f932(x44851,a921)),f862(f862(f94(f932(x44851,a921)),f862(f862(f103(f932(x44851,a921)),x44852),x44853)),f862(f862(f103(f932(x44851,a921)),x44853),x44854))),f862(f862(f103(f932(x44851,a921)),x44854),x44852)))
% 25.54/25.40 [4550]E(f862(f135(f925(x45501),f925(x45501),f127(x45501),f106(x45501)),f862(f862(f147(x45502,f925(x45501)),f862(f862(f9(x45502,f925(x45501),f925(x45501)),f862(f862(f10(x45501,f932(f925(x45501),f925(x45501)),x45502),f144(x45501)),x45503)),f106(x45501))),x45504)),f862(f862(f147(x45502,x45501),x45503),x45504))
% 25.54/25.40 [4560]E(f862(f862(f79(a1,x45601),f862(f96(a1),f862(f862(f73(a1),x45602),a90))),f862(f862(f20(a1,x45601,x45601),f862(f862(f9(a1,x45601,f932(x45601,x45601)),f862(f862(f10(a921,f932(x45601,f932(x45601,x45601)),a1),f89(x45601)),a186)),x45603)),f862(f862(f10(a924,x45601,a1),x45604),a97))),f178(x45601,x45603,x45604,f862(f96(a924),x45602)))
% 25.54/25.40 [4591]E(f862(f254(x45911),f862(f862(f10(f932(x45912,a921),a921,x45911),f80(x45912)),f862(f862(f10(f932(x45912,a921),f932(x45912,a921),x45911),f862(f20(x45912,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45912),a318),f862(f862(f9(x45912,f932(x45912,a921),a921),f321(x45912)),x45913)))),f862(f9(x45912,x45911,a921),x45914)))),f862(f276(x45912,x45911,f862(f254(f931(x45912,x45911)),f862(f249(x45912,x45911,a921),x45914))),x45913))
% 25.54/25.40 [4731]~P1(f862(f862(f181(f932(x47311,f932(x47312,a921))),x47313),x47314))
% 25.54/25.40 [4051]E(f862(f862(f157(x40511),f862(f862(f127(x40511),x40512),x40513)),f862(f862(f73(a924),f862(f182(f925(x40511)),x40512)),x40514)),f862(f862(f157(x40511),x40513),x40514))
% 25.54/25.40 [4056]E(f862(f862(f131(x40561),x40562),f862(f862(f168(x40561),f862(f862(f73(a924),x40563),x40562)),x40564)),f862(f862(f168(x40561),x40563),f862(f862(f131(x40561),x40562),x40564)))
% 25.54/25.40 [4153]E(f862(f862(f103(f932(x41531,a921)),f862(f275(x41532,x41531),x41533)),f862(f275(x41532,x41531),x41534)),f862(f275(x41532,x41531),f862(f862(f103(f932(f931(x41532,x41531),a921)),x41533),x41534)))
% 25.54/25.40 [4154]E(f862(f862(f103(f932(x41541,a921)),f862(f256(x41541,x41542),x41543)),f862(f256(x41541,x41542),x41544)),f862(f256(x41541,x41542),f862(f862(f103(f932(f931(x41541,x41542),a921)),x41543),x41544)))
% 25.54/25.40 [4159]E(f862(f862(f103(f932(x41591,a921)),f862(f862(f103(f932(x41591,a921)),x41592),x41593)),x41594),f862(f862(f103(f932(x41591,a921)),x41592),f862(f862(f103(f932(x41591,a921)),x41593),x41594)))
% 25.54/25.40 [4160]E(f862(f862(f94(f932(x41601,a921)),f862(f862(f94(f932(x41601,a921)),x41602),x41603)),x41604),f862(f862(f94(f932(x41601,a921)),x41602),f862(f862(f94(f932(x41601,a921)),x41603),x41604)))
% 25.54/25.40 [4161]E(f862(f862(f3(f932(x41611,a921)),f862(f862(f94(f932(x41611,a921)),x41612),x41613)),x41614),f862(f862(f94(f932(x41611,a921)),x41612),f862(f862(f3(f932(x41611,a921)),x41613),x41614)))
% 25.54/25.40 [4198]E(f862(f862(f103(f932(f931(x41981,x41982),a921)),f862(f277(x41982,x41981),x41983)),f862(f277(x41982,x41981),x41984)),f862(f277(x41982,x41981),f862(f862(f103(f932(f931(x41982,x41981),a921)),x41983),x41984)))
% 25.54/25.40 [4199]E(f862(f862(f94(f932(f931(x41991,x41992),a921)),f862(f277(x41992,x41991),x41993)),f862(f277(x41992,x41991),x41994)),f862(f277(x41992,x41991),f862(f862(f94(f932(f931(x41992,x41991),a921)),x41993),x41994)))
% 25.54/25.40 [4212]E(f862(f862(f103(f932(x42121,f932(x42122,a921))),f235(x42122,x42121,x42123)),f235(x42122,x42121,x42124)),f235(x42122,x42121,f862(f862(f103(f932(x42122,f932(x42121,a921))),x42123),x42124)))
% 25.54/25.40 [4213]E(f862(f862(f94(f932(x42131,f932(x42132,a921))),f235(x42132,x42131,x42133)),f235(x42132,x42131,x42134)),f235(x42132,x42131,f862(f862(f94(f932(x42132,f932(x42131,a921))),x42133),x42134)))
% 25.54/25.40 [4267]E(f862(f862(f94(f932(x42671,a921)),f862(f862(f103(f932(x42671,a921)),x42672),x42673)),f862(f862(f103(f932(x42671,a921)),x42674),x42673)),f862(f862(f103(f932(x42671,a921)),f862(f862(f94(f932(x42671,a921)),x42672),x42674)),x42673))
% 25.54/25.40 [4268]E(f862(f862(f103(f932(x42681,a921)),f862(f862(f94(f932(x42681,a921)),x42682),x42683)),f862(f862(f94(f932(x42681,a921)),x42684),x42683)),f862(f862(f94(f932(x42681,a921)),f862(f862(f103(f932(x42681,a921)),x42682),x42684)),x42683))
% 25.54/25.40 [4269]E(f862(f862(f3(f932(x42691,a921)),f862(f862(f94(f932(x42691,a921)),x42692),x42693)),f862(f862(f94(f932(x42691,a921)),x42694),x42693)),f862(f862(f94(f932(x42691,a921)),f862(f862(f3(f932(x42691,a921)),x42692),x42694)),x42693))
% 25.54/25.40 [4270]E(f862(f862(f103(f932(x42701,a921)),f862(f862(f3(f932(x42701,a921)),x42702),x42703)),f862(f862(f3(f932(x42701,a921)),x42704),x42703)),f862(f862(f3(f932(x42701,a921)),f862(f862(f103(f932(x42701,a921)),x42702),x42704)),x42703))
% 25.54/25.40 [4271]E(f862(f862(f3(f932(x42711,a921)),f862(f862(f94(f932(x42711,a921)),x42712),x42713)),f862(f862(f94(f932(x42711,a921)),x42714),x42713)),f862(f862(f3(f932(x42711,a921)),f862(f862(f94(f932(x42711,a921)),x42712),x42713)),x42714))
% 25.54/25.40 [4283]E(f862(f862(f3(f932(x42831,a921)),f862(f862(f3(f932(x42831,a921)),x42832),f862(f862(f301(x42831),x42833),f181(f932(x42831,a921))))),x42834),f862(f862(f3(f932(x42831,a921)),x42832),f862(f862(f301(x42831),x42833),x42834)))
% 25.54/25.40 [4336]E(f862(f862(f103(f932(x43361,a921)),f862(f862(f301(x43361),x43362),f862(f862(f301(x43361),x43363),f181(f932(x43361,a921))))),f862(f273(x43361),x43364)),f862(f273(x43361),f862(f862(f301(f931(x43361,x43361)),f862(f862(f244(x43361,x43361),x43362),x43363)),x43364)))
% 25.54/25.40 [4361]E(f862(f862(f33(a924,f932(x43611,a921)),f862(f294(a924),x43612)),f862(f862(f10(a924,f932(x43611,a921),a924),x43613),f862(f862(f9(a924,a924,a924),f73(a924)),x43614))),f862(f862(f33(a924,f932(x43611,a921)),f296(a924,x43614,f862(f862(f73(a924),x43612),x43614))),x43613))
% 25.54/25.40 [4362]E(f167(x43621,f862(f276(x43621,x43621,x43622),f862(f862(f301(x43621),x43623),f181(f932(x43621,a921)))),f862(f276(f925(x43621),f925(x43621),f151(x43621,x43622)),f862(f862(f301(f925(x43621)),x43624),f181(f932(f925(x43621),a921))))),f862(f276(f925(x43621),f925(x43621),f151(x43621,x43622)),f862(f862(f301(f925(x43621)),f862(f862(f144(x43621),x43623),x43624)),f181(f932(f925(x43621),a921)))))
% 25.54/25.40 [4426]E(f862(f254(x44261),f862(f862(f9(x44261,f932(x44262,a921),a921),f862(f862(f10(x44262,f932(f932(x44262,a921),a921),x44261),f321(x44262)),x44263)),x44264)),f862(f303(x44261,x44262,x44263),x44264))
% 25.54/25.40 [4517]E(f862(f254(x45171),f862(f862(f9(x45171,f932(f931(x45172,x45171),a921),a921),f862(f862(f10(f931(x45172,x45171),f932(f932(f931(x45172,x45171),a921),a921),x45171),f321(f931(x45172,x45171))),f862(f244(x45172,x45171),x45173))),x45174)),f862(f276(x45172,x45171,x45174),f862(f862(f301(x45172),x45173),f181(f932(x45172,a921)))))
% 25.54/25.40 [4533]E(f862(f862(f147(f931(x45331,a924),x45331),f243(x45331,a924)),f862(f129(f931(x45331,a924),f862(f862(f10(a924,a921,f931(x45331,a924)),x45332),f862(f862(f10(a924,a924,f931(x45331,a924)),a105),f248(x45331,a924)))),f862(f862(f174(x45331,a924),x45333),x45334))),f862(f862(f147(f931(x45331,a924),x45331),f243(x45331,a924)),f862(f129(f931(x45331,a924),f862(f862(f10(a924,a921,f931(x45331,a924)),x45332),f248(x45331,a924))),f862(f862(f174(x45331,a924),x45333),f862(f862(f147(a924,a924),a105),x45334)))))
% 25.54/25.40 [4542]P1(f862(f862(f227(f932(f932(x45421,a921),a921)),f862(f862(f33(x45422,f932(f932(x45421,a921),a921)),x45423),f862(f862(f10(f932(x45421,a921),f932(f932(x45421,a921),a921),x45422),f300(x45421)),x45424))),f862(f300(x45421),f862(f862(f33(x45422,f932(x45421,a921)),x45423),x45424))))
% 25.54/25.40 [4583]E(f862(f862(f79(a1,x45831),f862(f96(a1),f862(f862(f73(a1),x45832),a90))),f862(f862(f20(a1,x45831,x45831),f862(f862(f9(a1,x45831,f932(x45831,x45831)),f862(f862(f10(a921,f932(x45831,f932(x45831,x45831)),a1),f89(x45831)),a186)),x45833)),f862(f862(f20(a1,x45831,x45831),f862(f862(f10(a924,f932(x45831,x45831),a1),x45834),a97)),f862(f862(f10(a924,x45831,a1),f177(x45831,x45833,x45834)),a97)))),f862(f177(x45831,x45833,x45834),f862(f96(a924),x45832)))
% 25.54/25.40 [4607]E(f862(f254(f931(x46071,x46072)),f862(f249(x46071,x46072,a921),f862(f862(f9(x46071,f932(x46072,a921),f932(x46072,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x46072,a921),f932(x46072,a921)),x46071),f10(a921,a921,x46072)),f862(f862(f10(a921,f932(a921,a921),x46071),a318),f862(f862(f9(x46071,f932(x46071,a921),a921),f321(x46071)),x46073)))),f862(f862(f9(x46072,f932(x46072,a921),a921),f321(x46072)),x46074)))),f222(x46071,x46072,x46073,x46074))
% 25.54/25.40 [4643]E(f862(f862(f33(x46431,f932(f931(x46431,x46432),a921)),x46433),f862(f862(f20(x46431,f932(x46432,f932(f931(x46431,x46432),a921)),f932(f931(x46431,x46432),a921)),f862(f862(f10(f932(x46432,a921),f932(f932(x46432,f932(f931(x46431,x46432),a921)),f932(f931(x46431,x46432),a921)),x46431),f33(x46432,f932(f931(x46431,x46432),a921))),x46434)),f862(f862(f9(x46431,f932(f931(x46431,x46432),a921),f932(x46432,f932(f931(x46431,x46432),a921))),f862(f862(f10(f932(x46432,f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),f932(f932(f931(x46431,x46432),a921),f932(x46432,f932(f931(x46431,x46432),a921))),x46431),f9(x46432,f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),f862(f862(f10(f932(x46432,f931(x46431,x46432)),f932(x46432,f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921))),x46431),f862(f10(f931(x46431,x46432),f932(f932(f931(x46431,x46432),a921),f932(f931(x46431,x46432),a921)),x46432),f301(f931(x46431,x46432)))),f244(x46431,x46432)))),f181(f932(f931(x46431,x46432),a921))))),f862(f862(f246(x46431,x46432),x46433),x46434))
% 25.54/25.40 [4207]E(f862(f862(f127(x42071),f862(f862(f168(x42071),x42072),x42073)),f862(f862(f168(x42071),f862(f862(f3(a924),x42072),f862(f182(f925(x42071)),x42073))),x42074)),f862(f862(f168(x42071),x42072),f862(f862(f127(x42071),x42073),x42074)))
% 25.54/25.40 [4208]E(f862(f862(f127(x42081),f862(f862(f131(x42081),x42082),x42083)),f862(f862(f131(x42081),f862(f862(f3(a924),x42082),f862(f182(f925(x42081)),x42083))),x42084)),f862(f862(f131(x42081),x42082),f862(f862(f127(x42081),x42083),x42084)))
% 25.54/25.40 [4257]E(f862(f862(f73(a924),f862(f862(f74(a924),x42571),x42572)),f862(f862(f73(a924),f862(f862(f74(a924),x42573),x42572)),x42574)),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f73(a924),x42571),x42573)),x42572)),x42574))
% 25.54/25.40 [4402]E(f83(x44021,f862(f862(f9(x44021,x44022,a921),f862(f862(f10(x44022,f932(x44022,a921),x44021),a317),x44023)),x44024)),f862(f86(x44021,x44022,f234(f932(x44021,a921)),x44023),x44024))
% 25.54/25.40 [4451]P1(f862(f862(f227(f932(x44511,a921)),f862(f862(f3(f932(x44511,a921)),f862(f275(x44512,x44511),x44513)),f862(f275(x44512,x44511),x44514))),f862(f275(x44512,x44511),f862(f862(f3(f932(f931(x44512,x44511),a921)),x44513),x44514))))
% 25.54/25.40 [4452]P1(f862(f862(f227(f932(x44521,a921)),f862(f862(f3(f932(x44521,a921)),f862(f256(x44521,x44522),x44523)),f862(f256(x44521,x44522),x44524))),f862(f256(x44521,x44522),f862(f862(f3(f932(f931(x44521,x44522),a921)),x44523),x44524))))
% 25.54/25.40 [4562]E(f862(f862(f73(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x45621),x45622)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x45623),x45624)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f862(f862(f73(a924),x45621),x45623)),f862(f862(f73(a924),x45622),x45624))),f181(f932(f931(a924,a924),a921))))))
% 25.54/25.40 [4602]E(f862(f862(f74(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x46021),x46022)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x46023),x46024)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f74(a924),x46021),x46023)),f862(f862(f74(a924),x46022),x46024))),f862(f862(f73(a924),f862(f862(f74(a924),x46021),x46024)),f862(f862(f74(a924),x46022),x46023)))),f181(f932(f931(a924,a924),a921))))))
% 25.54/25.40 [4623]E(f862(f254(x46231),f862(f862(f10(f932(x46232,a921),a921,x46231),f81(x46232)),f862(f862(f10(f932(x46232,a921),f932(x46232,a921),x46231),f862(f20(x46232,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46232),a322),f862(f862(f9(x46232,f932(x46232,a921),a921),f321(x46232)),x46233)))),f862(f862(f9(x46231,f932(x46232,f932(x46231,a921)),f932(x46232,a921)),f862(f862(f10(f932(f932(x46231,a921),a921),f932(f932(x46232,f932(x46231,a921)),f932(x46232,a921)),x46231),f10(f932(x46231,a921),a921,x46232)),f321(x46231))),x46234)))),f862(f862(f32(x46232,f932(x46231,a921)),x46233),x46234))
% 25.54/25.40 [4655]E(f862(f862(f280(x46551,x46551,x46551),f862(f862(f301(f931(x46551,x46551)),f862(f862(f244(x46551,x46551),x46552),x46553)),x46554)),f299(x46551,f862(f862(f301(f931(x46551,x46551)),f862(f862(f244(x46551,x46551),x46552),x46553)),x46554))),f862(f862(f103(f932(f931(x46551,x46551),a921)),f862(f862(f280(x46551,x46551,x46551),x46554),f299(x46551,x46554))),f862(f254(f931(x46551,x46551)),f862(f249(x46551,x46551,a921),f862(f862(f9(x46551,f932(x46551,a921),f932(x46551,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x46551,a921),f932(x46551,a921)),x46551),f10(a921,a921,x46551)),f862(f862(f10(a921,f932(a921,a921),x46551),a318),f862(f862(f9(x46551,f932(f931(x46551,x46551),a921),a921),f862(f862(f10(f931(x46551,x46551),f932(f932(f931(x46551,x46551),a921),a921),x46551),f321(f931(x46551,x46551))),f862(f862(f9(x46551,x46551,f931(x46551,x46551)),f244(x46551,x46551)),x46552))),f299(x46551,x46554))))),f862(f862(f9(x46551,f932(f931(x46551,x46551),a921),a921),f862(f862(f10(f931(x46551,x46551),f932(f932(f931(x46551,x46551),a921),a921),x46551),f321(f931(x46551,x46551))),f862(f244(x46551,x46551),x46553))),f299(x46551,x46554)))))))
% 25.54/25.40 [4453]E(f862(f129(x44531,f862(f862(f20(x44531,a921,a921),f862(f862(f10(a921,f932(a921,a921),x44531),a318),x44532)),x44533)),x44534),f862(f129(x44531,x44533),f862(f129(x44531,x44532),x44534)))
% 25.54/25.40 [4556]E(f862(f862(f127(x45561),f862(f862(f862(f89(f925(x45561)),f862(f862(f321(a924),f2(a924)),x45562)),f862(f862(f144(x45561),x45563),f106(x45561))),f106(x45561))),f169(x45561,x45564,f862(f254(a924),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x45562)))),f169(x45561,f862(f862(f144(x45561),x45563),x45564),x45562))
% 25.54/25.40 [4651]E(f862(f254(f931(x46511,x46512)),f862(f862(f10(f932(a924,a921),a921,f931(x46511,x46512)),f80(a924)),f862(f862(f9(f931(x46511,x46512),f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),f931(x46511,x46512)),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),f931(x46511,x46512)),f862(f10(a921,f932(a921,a921),a924),a318)),f862(f862(f9(f931(x46511,x46512),f932(a924,f931(x46511,x46512)),f932(a924,a921)),f862(f862(f10(f932(f931(x46511,x46512),a921),f932(f932(a924,f931(x46511,x46512)),f932(a924,a921)),f931(x46511,x46512)),f10(f931(x46511,x46512),a921,a924)),a317)),f862(f862(f20(a924,x46512,f931(x46511,x46512)),f862(f862(f10(x46511,f932(x46512,f931(x46511,x46512)),a924),f244(x46511,x46512)),f862(f157(x46511),x46513))),f862(f157(x46512),x46514)))))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(f862(f225(a924),f862(f182(f925(x46511)),x46513)),f862(f182(f925(x46512)),x46514)))))),f862(f165(f931(x46511,x46512)),f862(f862(f174(x46511,x46512),x46513),x46514)))
% 25.54/25.40 [4575]E(f862(f254(f931(x45751,x45752)),f862(f249(x45751,x45752,a921),f862(f862(f9(x45751,f932(x45752,a921),f932(x45752,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45752,a921),f932(x45752,a921)),x45751),f10(a921,a921,x45752)),f862(f862(f10(a921,f932(a921,a921),x45751),a318),x45753))),x45754))),f862(f862(f246(x45751,x45752),f862(f254(x45751),x45753)),f862(f18(f932(x45752,a921),x45751),f862(f254(x45752),x45754))))
% 25.54/25.40 [4578]E(f862(f254(f931(x45781,x45782)),f862(f249(x45781,x45782,a921),f862(f862(f20(x45781,f932(x45782,a921),f932(x45782,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x45782,a921),f932(x45782,a921)),x45781),f10(a921,a921,x45782)),f862(f862(f10(a921,f932(a921,a921),x45781),a318),x45783))),x45784))),f862(f862(f246(x45781,x45782),f862(f254(x45781),x45783)),f862(f862(f10(f932(x45782,a921),f932(x45782,a921),x45781),f254(x45782)),x45784)))
% 25.54/25.40 [4590]E(f862(f254(x45901),f862(f862(f10(f932(x45902,a921),a921,x45901),f81(x45902)),f862(f862(f10(f932(x45902,a921),f932(x45902,a921),x45901),f862(f20(x45902,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45902),a322),f862(f862(f9(x45902,f932(x45902,a921),a921),f321(x45902)),x45903)))),x45904))),f862(f862(f32(x45902,f932(x45901,a921)),x45903),f862(f862(f10(f932(x45901,a921),f932(x45901,a921),x45902),f254(x45901)),f862(f9(x45901,x45902,a921),x45904))))
% 25.54/25.40 [4635]E(f862(f862(f147(f931(x46351,a924),x46351),f243(x46351,a924)),f862(f129(f931(x46351,a924),f862(f862(f9(f931(x46351,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x46351,a924)),f321(a924)),f248(x46351,a924))),x46352)),f862(f862(f174(x46351,a924),x46353),f132(a924,f862(f295(a924,x46354),f862(f862(f73(a924),x46354),f862(f182(f925(x46351)),x46353))))))),f862(f862(f147(f931(x46351,a924),x46351),f243(x46351,a924)),f862(f129(f931(x46351,a924),f862(f862(f9(f931(x46351,a924),f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),f931(x46351,a924)),f321(a924)),f862(f862(f9(f931(x46351,a924),a924,a924),f862(f862(f10(a924,f932(a924,a924),f931(x46351,a924)),f73(a924)),f248(x46351,a924))),x46354))),x46352)),f862(f862(f174(x46351,a924),x46353),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(x46351)),x46353)))))))
% 25.54/25.40 [4636]E(f862(a105,f862(f862(f226(a924),f862(f182(f925(x46361)),x46362)),f862(f135(a924,f925(x46363),f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f226(a924)),f862(f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f3(a924)),f182(f925(x46363)))),f862(a105,f2(a924))))),f2(a924)),f862(f161(f925(x46363)),f862(f129(f925(x46363),f862(f862(f10(a921,a921,f925(x46363)),a314),f862(f862(f9(f925(x46363),f925(x46363),a921),a317),f106(x46363)))),x46364))))),f862(f862(f226(a924),f862(a105,f862(f182(f925(x46361)),x46362))),f862(f135(a924,f925(x46363),f862(f9(f925(x46363),a924,a924),f862(f862(f10(a924,f932(a924,a924),f925(x46363)),f226(a924)),f182(f925(x46363)))),f2(a924)),f862(f161(f925(x46363)),x46364))))
% 25.54/25.40 [4589]E(f862(f862(f127(x45891),f169(x45891,x45892,x45893)),f169(x45891,x45894,f862(f254(a924),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),f862(f862(f9(a924,a924,a924),f73(a924)),f862(f182(f925(x45891)),x45892)))),x45893)))),f169(x45891,f862(f862(f127(x45891),x45892),x45894),x45893))
% 25.54/25.40 [4637]E(f31(f932(x46371,a921),f862(f254(f932(x46371,a921)),f862(f862(f10(f932(x46372,a921),a921,f932(x46371,a921)),f80(x46372)),f862(f862(f10(f932(x46372,a921),f932(x46372,a921),f932(x46371,a921)),f862(f20(x46372,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46372),a318),f862(f862(f9(x46372,f932(x46372,a921),a921),f321(x46372)),x46373)))),f862(f862(f9(f932(x46371,a921),f932(x46372,f932(x46371,a921)),f932(x46372,a921)),f862(f862(f10(f932(f932(x46371,a921),a921),f932(f932(x46372,f932(x46371,a921)),f932(x46372,a921)),f932(x46371,a921)),f10(f932(x46371,a921),a921,x46372)),a317)),x46374))))),f862(f862(f32(x46372,f932(x46371,a921)),x46373),x46374))
% 25.54/25.40 [4638]E(f30(f932(x46381,a921),f862(f254(f932(x46381,a921)),f862(f862(f10(f932(x46382,a921),a921,f932(x46381,a921)),f80(x46382)),f862(f862(f10(f932(x46382,a921),f932(x46382,a921),f932(x46381,a921)),f862(f20(x46382,a921,a921),f862(f862(f10(a921,f932(a921,a921),x46382),a318),f862(f862(f9(x46382,f932(x46382,a921),a921),f321(x46382)),x46383)))),f862(f862(f9(f932(x46381,a921),f932(x46382,f932(x46381,a921)),f932(x46382,a921)),f862(f862(f10(f932(f932(x46381,a921),a921),f932(f932(x46382,f932(x46381,a921)),f932(x46382,a921)),f932(x46381,a921)),f10(f932(x46381,a921),a921,x46382)),a317)),x46384))))),f862(f862(f33(x46382,f932(x46381,a921)),x46383),x46384))
% 25.54/25.40 [4645]E(f862(f862(f144(f925(x46451)),f862(f862(f144(x46451),x46452),f862(f135(f925(x46451),f925(x46451),f127(x46451),f106(x46451)),f862(f862(f147(f925(x46451),f925(x46451)),f149(f925(x46451),x46451,f106(x46451),f862(f862(f10(f925(x46451),f932(f925(x46451),f925(x46451)),x46451),f18(f925(x46451),f925(x46451))),f862(f862(f9(x46451,f925(x46451),f925(x46451)),f144(x46451)),f106(x46451))))),x46453)))),f172(x46451,f862(f862(f144(f925(x46451)),x46454),f862(f135(f925(f925(x46451)),f925(f925(x46451)),f127(f925(x46451)),f106(f925(x46451))),f862(f862(f147(f925(x46451),f925(f925(x46451))),f149(f925(f925(x46451)),x46451,f106(f925(x46451)),f862(f18(f932(f925(x46451),f925(f925(x46451))),x46451),f862(f862(f9(f925(x46451),f925(f925(x46451)),f925(f925(x46451))),f144(f925(x46451))),f106(f925(x46451)))))),x46453))))),f172(x46451,f862(f862(f144(f925(x46451)),f862(f862(f144(x46451),x46452),x46454)),x46453)))
% 25.54/25.40 [4652]E(f862(f254(f931(x46521,x46521)),f862(f249(x46521,x46521,a921),f862(f862(f9(x46521,f932(f931(x46522,x46522),a921),f932(x46521,a921)),f862(f862(f10(f932(x46521,f932(f932(f931(x46522,x46522),a921),a921)),f932(f932(f931(x46522,x46522),a921),f932(x46521,a921)),x46521),f9(x46521,f932(f931(x46522,x46522),a921),a921)),f862(f862(f10(f932(x46521,f931(x46522,x46522)),f932(x46521,f932(f932(f931(x46522,x46522),a921),a921)),x46521),f862(f10(f931(x46522,x46522),f932(f932(f931(x46522,x46522),a921),a921),x46521),f321(f931(x46522,x46522)))),f862(f862(f9(x46521,f932(x46521,x46522),f932(x46521,f931(x46522,x46522))),f862(f862(f10(f932(x46522,f931(x46522,x46522)),f932(f932(x46521,x46522),f932(x46521,f931(x46522,x46522))),x46521),f10(x46522,f931(x46522,x46522),x46521)),f862(f862(f10(x46522,f932(x46522,f931(x46522,x46522)),x46521),f244(x46522,x46522)),x46523))),x46523)))),x46524))),f862(f862(f279(x46522,x46521),x46524),x46523))
% 25.54/25.40 [3792]E(f862(f862(f147(x37921,x37922),x37923),f162(x37921,x37924,x37925)),f162(x37922,x37924,f862(x37923,x37925)))
% 25.54/25.40 [4121]E(f123(x41211,x41212,x41213,f119(x41211,x41214,x41215)),f119(x41212,f862(x41213,x41214),f123(x41211,x41212,x41213,x41215)))
% 25.54/25.40 [4351]E(f862(f68(x43511,x43512,x43513,x43514,x43515),x43514),x43515)
% 25.54/25.40 [4403]E(f245(x44031,x44032,x44033,f235(x44032,x44031,x44034),f235(x44033,x44032,x44035)),f235(x44033,x44031,f245(x44033,x44032,x44031,x44035,x44034)))
% 25.54/25.40 [3980]E(f862(f862(f249(x39801,x39802,x39803),x39804),x39805),f862(f862(x39804,f862(f243(x39801,x39802),x39805)),f862(f248(x39801,x39802),x39805)))
% 25.54/25.40 [3981]E(f862(f862(f249(x39811,x39812,x39813),x39814),x39815),f862(f862(x39814,f862(f243(x39811,x39812),x39815)),f862(f248(x39811,x39812),x39815)))
% 25.54/25.40 [3982]E(f862(f862(f249(x39821,x39822,x39823),x39824),x39825),f862(f862(x39824,f862(f243(x39821,x39822),x39825)),f862(f248(x39821,x39822),x39825)))
% 25.54/25.40 [4016]E(f862(f862(f862(f58(x40161,x40162,x40163),x40164),x40165),f181(f932(x40162,a921))),x40165)
% 25.54/25.40 [4290]E(f862(f66(f925(x42901),f925(x42902),f925(x42903),f862(f147(x42901,x42902),x42904)),f862(f147(x42903,x42901),x42905)),f862(f147(x42903,x42902),f862(f66(x42901,x42902,x42903,x42904),x42905)))
% 25.54/25.40 [4291]E(f862(f66(f925(x42911),f925(x42912),f925(x42913),f862(f147(x42911,x42912),x42914)),f862(f147(x42913,x42911),x42915)),f862(f147(x42913,x42912),f862(f66(x42911,x42912,x42913,x42914),x42915)))
% 25.54/25.40 [4365]E(f78(x43651,f59(x43652,x43651,x43653,x43654,x43655)),f862(f862(f57(x43652,x43651,x43653),x43654),x43655))
% 25.54/25.40 [4399]E(f862(f862(f73(a924),f862(f862(f73(a924),f862(x43991,f862(f243(x43992,x43993),x43994))),f862(x43995,f862(f248(x43992,x43993),x43994)))),f862(a105,f2(a924))),f253(x43992,x43993,x43991,x43995,x43994))
% 25.54/25.40 [3919]E(f862(f862(f168(x39191),x39192),f862(f862(f147(x39193,x39191),x39194),x39195)),f862(f862(f147(x39193,x39191),x39194),f862(f862(f168(x39193),x39192),x39195)))
% 25.54/25.40 [3920]E(f862(f862(f131(x39201),x39202),f862(f862(f147(x39203,x39201),x39204),x39205)),f862(f862(f147(x39203,x39201),x39204),f862(f862(f131(x39203),x39202),x39205)))
% 25.54/25.40 [3951]E(f862(f862(f147(x39511,x39512),x39513),f862(f862(f144(x39511),x39514),x39515)),f862(f862(f144(x39512),f862(x39513,x39514)),f862(f862(f147(x39511,x39512),x39513),x39515)))
% 25.54/25.40 [4012]E(f862(f302(x40121,x40122,x40123),f862(f862(f301(x40121),x40124),x40125)),f862(f862(f301(x40122),f862(x40123,x40124)),f862(f302(x40121,x40122,x40123),x40125)))
% 25.54/25.40 [4040]E(f166(x40401,f862(f862(f144(x40401),x40402),x40403),f862(f862(f144(x40401),x40404),x40405)),f862(f862(f144(x40401),x40402),f862(f862(f144(x40401),x40404),f166(x40401,x40403,x40405))))
% 25.54/25.40 [4076]E(f862(f862(f174(x40761,x40762),f862(f862(f168(x40761),x40763),x40764)),f862(f862(f168(x40762),x40763),x40765)),f862(f862(f168(f931(x40761,x40762)),x40763),f862(f862(f174(x40761,x40762),x40764),x40765)))
% 25.54/25.40 [4077]E(f862(f862(f174(x40771,x40772),f862(f862(f131(x40771),x40773),x40774)),f862(f862(f131(x40772),x40773),x40775)),f862(f862(f131(f931(x40771,x40772)),x40773),f862(f862(f174(x40771,x40772),x40774),x40775)))
% 25.54/25.40 [4086]E(f862(f862(f152(x40861,f862(f862(f144(x40861),x40862),x40863)),f862(a105,x40864)),x40865),f862(f862(f144(x40861),x40862),f862(f862(f152(x40861,x40863),x40864),x40865)))
% 25.54/25.40 [4089]E(f862(f862(f127(x40891),f862(f862(f147(x40892,x40891),x40893),x40894)),f862(f862(f147(x40892,x40891),x40893),x40895)),f862(f862(f147(x40892,x40891),x40893),f862(f862(f127(x40892),x40894),x40895)))
% 25.54/25.40 [4093]E(f862(f862(x40931,x40932),f862(f862(f237(x40933,x40934,x40931),x40932),x40935)),f862(f862(f237(x40933,x40934,x40931),x40932),f862(a105,x40935)))
% 25.54/25.40 [4125]E(f156(x41251,x41252,x41253,f862(f862(f144(x41251),x41254),x41255)),f862(f862(f127(x41252),f862(x41253,x41254)),f156(x41251,x41252,x41253,x41255)))
% 25.54/25.40 [4137]E(f862(f862(f280(x41371,x41372,x41373),f862(f277(x41372,x41371),x41374)),f862(f277(x41373,x41372),x41375)),f862(f277(x41373,x41371),f862(f862(f280(x41373,x41372,x41371),x41375),x41374)))
% 25.54/25.40 [4169]E(f862(f862(f862(f176(f925(x41691),f925(x41691)),x41692),f160(x41691)),f862(f862(f147(x41693,x41691),x41694),x41695)),f862(f862(f147(x41693,x41691),x41694),f862(f862(f862(f176(f925(x41693),f925(x41693)),x41692),f160(x41693)),x41695)))
% 25.54/25.40 [4170]E(f862(f862(f251(x41701,x41702,x41701,x41703),f862(f244(x41702,x41701),x41704)),x41705),f862(x41705,x41704))
% 25.54/25.40 [4193]E(f148(x41931,x41932,f862(f862(f147(x41933,x41931),x41934),x41935)),f148(x41933,f862(f66(x41931,a924,x41933,x41932),x41934),x41935))
% 25.54/25.40 [4256]E(f170(f931(x42561,x42562),f862(f66(x42562,a921,f931(x42561,x42562),x42563),f248(x42561,x42562)),f862(f862(f174(x42561,x42562),x42564),x42565)),f862(f862(f174(x42561,x42562),x42564),f170(x42562,x42563,x42565)))
% 25.54/25.40 [4261]E(f862(f302(x42611,x42612,f862(f862(f10(x42613,x42612,x42611),x42614),x42615)),f234(f932(x42611,a921))),f862(f302(x42613,x42612,x42614),f862(f302(x42611,x42613,x42615),f234(f932(x42611,a921)))))
% 25.54/25.40 [4274]E(f170(f931(x42741,x42742),f862(f66(x42741,a921,f931(x42741,x42742),x42743),f243(x42741,x42742)),f862(f862(f174(x42741,x42742),x42744),x42745)),f862(f862(f174(x42741,x42742),f170(x42741,x42743,x42744)),x42745))
% 25.54/25.40 [4295]E(f862(f862(f103(f932(x42951,a921)),f862(f303(x42951,x42952,x42953),f862(f862(f301(x42952),x42954),f181(f932(x42952,a921))))),f862(f303(x42951,x42952,x42953),x42955)),f862(f303(x42951,x42952,x42953),f862(f862(f301(x42952),x42954),x42955)))
% 25.54/25.40 [4350]E(f862(f862(f127(f931(x43501,x43502)),f862(f862(f147(x43502,f931(x43501,x43502)),f862(f244(x43501,x43502),x43503)),x43504)),f52(x43501,x43502,x43505,x43504)),f52(x43501,x43502,f862(f862(f144(x43501),x43503),x43505),x43504))
% 25.54/25.40 [4352]E(f862(f862(f147(x43521,x43522),x43523),f170(x43521,f862(f66(x43522,a921,x43521,x43524),x43523),x43525)),f170(x43522,x43524,f862(f862(f147(x43521,x43522),x43523),x43525)))
% 25.54/25.40 [4357]E(f862(f135(x43571,x43572,f862(f9(x43572,x43571,x43571),f862(f9(x43571,x43572,x43571),x43573)),x43574),f862(f161(x43572),f862(f161(x43572),x43575))),f862(f135(x43571,x43572,x43573,x43574),x43575))
% 25.54/25.40 [4461]P1(f862(f862(f227(f932(x44611,a921)),f862(f302(x44612,x44611,x44613),f862(f862(f94(f932(x44612,a921)),x44614),x44615))),f862(f862(f94(f932(x44611,a921)),f862(f302(x44612,x44611,x44613),x44614)),f862(f302(x44612,x44611,x44613),x44615))))
% 25.54/25.40 [4462]P1(f862(f862(f227(f932(x44621,a921)),f862(f276(x44622,x44621,x44623),f862(f862(f94(f932(x44622,a921)),x44624),x44625))),f862(f862(f94(f932(x44621,a921)),f862(f276(x44622,x44621,x44623),x44624)),f862(f276(x44622,x44621,x44623),x44625))))
% 25.54/25.40 [4563]E(f862(f248(x45631,x45632),f862(f250(x45633,x45631,x45632,x45632,x45634,f25(x45632)),x45635)),f862(f248(x45633,x45632),x45635))
% 25.54/25.40 [4564]E(f862(f243(x45641,x45642),f862(f250(x45641,x45641,x45643,x45642,f25(x45641),x45644),x45645)),f862(f243(x45641,x45643),x45645))
% 25.54/25.40 [4567]E(f862(f243(x45671,x45672),f862(f250(x45673,x45671,x45672,x45672,x45674,f25(x45672)),x45675)),f862(x45674,f862(f243(x45673,x45672),x45675)))
% 25.54/25.40 [4568]E(f862(f248(x45681,x45682),f862(f250(x45681,x45681,x45683,x45682,f25(x45681),x45684),x45685)),f862(x45684,f862(f248(x45681,x45683),x45685)))
% 25.54/25.40 [3764]E(f862(f862(f862(f862(f197(x37641),x37642),x37643),x37644),x37645),f185(x37641,x37642))
% 25.54/25.40 [3765]E(f862(f862(f862(f862(f201(x37651),x37652),x37653),x37654),x37655),f192(x37651,x37652))
% 25.54/25.40 [4126]E(f862(f862(f32(x41261,f932(x41262,a921)),f862(f862(f301(x41261),x41263),x41264)),x41265),f862(f862(f94(f932(x41262,a921)),f862(x41265,x41263)),f862(f862(f32(x41261,f932(x41262,a921)),x41264),x41265)))
% 25.54/25.40 [4127]E(f862(f862(f33(x41271,f932(x41272,a921)),f862(f862(f301(x41271),x41273),x41274)),x41275),f862(f862(f103(f932(x41272,a921)),f862(x41275,x41273)),f862(f862(f33(x41271,f932(x41272,a921)),x41274),x41275)))
% 25.54/25.40 [4177]E(f862(f111(x41771,x41772,f862(x41773,x41774)),f862(f862(f9(x41771,a92,f926(x41772)),x41775),x41774)),f862(f190(x41771,x41772,x41773,x41775),x41774))
% 25.54/25.40 [4187]E(f862(f862(f103(f932(x41871,a921)),f862(f302(x41872,x41871,x41873),x41874)),f862(f302(x41872,x41871,x41873),x41875)),f862(f302(x41872,x41871,x41873),f862(f862(f103(f932(x41872,a921)),x41874),x41875)))
% 25.54/25.40 [4188]E(f862(f862(f103(f932(x41881,a921)),f862(f276(x41882,x41881,x41883),x41884)),f862(f276(x41882,x41881,x41883),x41885)),f862(f276(x41882,x41881,x41883),f862(f862(f103(f932(x41882,a921)),x41884),x41885)))
% 25.54/25.40 [4189]E(f862(f862(f103(f932(x41891,a921)),f862(f303(x41891,x41892,x41893),x41894)),f862(f303(x41891,x41892,x41893),x41895)),f862(f303(x41891,x41892,x41893),f862(f862(f103(f932(x41892,a921)),x41894),x41895)))
% 25.54/25.40 [4190]E(f862(f862(f94(f932(x41901,a921)),f862(f303(x41901,x41902,x41903),x41904)),f862(f303(x41901,x41902,x41903),x41905)),f862(f303(x41901,x41902,x41903),f862(f862(f94(f932(x41902,a921)),x41904),x41905)))
% 25.54/25.40 [4191]E(f862(f862(f3(f932(x41911,a921)),f862(f303(x41911,x41912,x41913),x41914)),f862(f303(x41911,x41912,x41913),x41915)),f862(f303(x41911,x41912,x41913),f862(f862(f3(f932(x41912,a921)),x41914),x41915)))
% 25.54/25.40 [4252]E(f862(f862(f152(x42521,f862(f862(f127(x42521),x42522),f862(f862(f144(x42521),x42523),x42524))),f862(f182(f925(x42521)),x42522)),x42525),f862(f862(f127(x42521),x42522),f862(f862(f144(x42521),x42525),x42524)))
% 25.54/25.40 [4258]E(f862(f862(f32(x42581,f932(x42582,a921)),x42583),f862(f862(f10(f932(x42582,a921),f932(x42582,a921),x42581),f862(f301(x42582),x42584)),x42585)),f862(f862(f301(x42582),x42584),f862(f862(f32(x42581,f932(x42582,a921)),x42583),x42585)))
% 25.54/25.40 [4259]E(f862(f862(f32(x42591,f932(x42592,a921)),x42593),f862(f862(f10(f932(x42592,a921),f932(x42592,a921),x42591),f862(f301(x42592),x42594)),x42595)),f862(f862(f301(x42592),x42594),f862(f862(f32(x42591,f932(x42592,a921)),x42593),x42595)))
% 25.54/25.40 [4367]E(f862(f862(f103(f932(f931(x43671,x43672),a921)),f862(f862(f246(x43671,x43672),x43673),f862(f18(f932(x43672,a921),x43671),x43674))),f862(f862(f246(x43671,x43672),x43675),f862(f18(f932(x43672,a921),x43671),x43674))),f862(f862(f246(x43671,x43672),f862(f862(f103(f932(x43671,a921)),x43673),x43675)),f862(f18(f932(x43672,a921),x43671),x43674)))
% 25.54/25.40 [4368]E(f862(f862(f94(f932(f931(x43681,x43682),a921)),f862(f862(f246(x43681,x43682),x43683),f862(f18(f932(x43682,a921),x43681),x43684))),f862(f862(f246(x43681,x43682),x43685),f862(f18(f932(x43682,a921),x43681),x43684))),f862(f862(f246(x43681,x43682),f862(f862(f94(f932(x43681,a921)),x43683),x43685)),f862(f18(f932(x43682,a921),x43681),x43684)))
% 25.54/25.40 [4369]E(f862(f862(f3(f932(f931(x43691,x43692),a921)),f862(f862(f246(x43691,x43692),x43693),f862(f18(f932(x43692,a921),x43691),x43694))),f862(f862(f246(x43691,x43692),x43695),f862(f18(f932(x43692,a921),x43691),x43694))),f862(f862(f246(x43691,x43692),f862(f862(f3(f932(x43691,a921)),x43693),x43695)),f862(f18(f932(x43692,a921),x43691),x43694)))
% 25.54/25.40 [4412]E(f862(f862(f147(x44121,x44122),x44123),f862(f129(x44121,f862(f66(x44122,a921,x44121,x44124),x44123)),x44125)),f862(f129(x44122,x44124),f862(f862(f147(x44121,x44122),x44123),x44125)))
% 25.54/25.40 [4418]E(f862(f182(f925(x44181)),f862(f129(x44181,x44182),f862(f862(f147(x44183,x44181),x44184),x44185))),f862(f182(f925(x44183)),f862(f129(x44183,f862(f66(x44181,a921,x44183,x44182),x44184)),x44185)))
% 25.54/25.40 [4628]E(f862(f149(f925(f931(x46281,x46282)),x46282,f106(f931(x46281,x46282)),f862(f862(f9(x46282,f932(f925(x46282),f925(f931(x46281,x46282))),f932(f925(x46282),f925(f931(x46281,x46282)))),f862(f862(f10(f932(f925(f931(x46281,x46282)),f925(f931(x46281,x46282))),f932(f932(f925(x46282),f925(f931(x46281,x46282))),f932(f925(x46282),f925(f931(x46281,x46282)))),x46282),f10(f925(f931(x46281,x46282)),f925(f931(x46281,x46282)),f925(x46282))),f862(f862(f10(f931(x46281,x46282),f932(f925(f931(x46281,x46282)),f925(f931(x46281,x46282))),x46282),f144(f931(x46281,x46282))),f862(f244(x46281,x46282),x46283)))),f862(f174(x46281,x46282),x46284))),x46285),f862(f862(f174(x46281,x46282),f862(f862(f144(x46281),x46283),x46284)),x46285))
% 25.54/25.40 [4118]E(f862(f862(f152(x41181,f862(f862(f152(x41181,x41182),x41183),x41184)),x41183),x41185),f862(f862(f152(x41181,x41182),x41183),x41185))
% 25.54/25.40 [4171]E(f862(f275(x41711,x41712),f862(f862(f301(f931(x41711,x41712)),f862(f862(f244(x41711,x41712),x41713),x41714)),x41715)),f862(f862(f301(x41712),x41714),f862(f275(x41711,x41712),x41715)))
% 25.54/25.40 [4172]E(f862(f256(x41721,x41722),f862(f862(f301(f931(x41721,x41722)),f862(f862(f244(x41721,x41722),x41723),x41724)),x41725)),f862(f862(f301(x41721),x41723),f862(f256(x41721,x41722),x41725)))
% 25.54/25.40 [4217]E(f115(x42171,x42172,f862(x42173,x42174),f862(f862(f9(x42171,a92,f926(f928(x42172))),x42175),x42174)),f862(f188(x42171,x42172,x42173,x42175),x42174))
% 25.54/25.40 [4245]E(f862(f862(f103(f932(f931(x42451,x42452),a921)),f862(f862(f246(x42451,x42452),x42453),x42454)),f862(f862(f246(x42451,x42452),x42455),x42454)),f862(f862(f246(x42451,x42452),f862(f862(f103(f932(x42451,a921)),x42453),x42455)),x42454))
% 25.54/25.40 [4246]E(f862(f862(f94(f932(f931(x42461,x42462),a921)),f862(f862(f246(x42461,x42462),x42463),x42464)),f862(f862(f246(x42461,x42462),x42465),x42464)),f862(f862(f246(x42461,x42462),f862(f862(f94(f932(x42461,a921)),x42463),x42465)),x42464))
% 25.54/25.40 [4247]E(f862(f862(f3(f932(f931(x42471,x42472),a921)),f862(f862(f246(x42471,x42472),x42473),x42474)),f862(f862(f246(x42471,x42472),x42475),x42474)),f862(f862(f246(x42471,x42472),f862(f862(f3(f932(x42471,a921)),x42473),x42475)),x42474))
% 25.54/25.40 [4306]E(f862(f862(f94(f932(x43061,a921)),f862(f862(f32(x43062,f932(x43061,a921)),x43063),x43064)),f862(f862(f32(x43062,f932(x43061,a921)),x43065),x43064)),f862(f862(f32(x43062,f932(x43061,a921)),f862(f862(f103(f932(x43062,a921)),x43063),x43065)),x43064))
% 25.54/25.40 [4307]E(f862(f862(f103(f932(x43071,a921)),f862(f862(f33(x43072,f932(x43071,a921)),x43073),x43074)),f862(f862(f33(x43072,f932(x43071,a921)),x43075),x43074)),f862(f862(f33(x43072,f932(x43071,a921)),f862(f862(f103(f932(x43072,a921)),x43073),x43075)),x43074))
% 25.54/25.40 [4316]E(f862(f862(f32(x43161,f932(x43162,a921)),x43163),f862(f862(f10(f932(x43162,a921),f932(x43162,a921),x43161),f862(f103(f932(x43162,a921)),x43164)),x43165)),f862(f862(f103(f932(x43162,a921)),x43164),f862(f862(f32(x43161,f932(x43162,a921)),x43163),x43165)))
% 25.54/25.40 [4317]E(f862(f862(f32(x43171,f932(x43172,a921)),x43173),f862(f862(f10(f932(x43172,a921),f932(x43172,a921),x43171),f862(f103(f932(x43172,a921)),x43174)),x43175)),f862(f862(f103(f932(x43172,a921)),x43174),f862(f862(f32(x43171,f932(x43172,a921)),x43173),x43175)))
% 25.54/25.40 [4318]E(f862(f862(f33(x43181,f932(x43182,a921)),x43183),f862(f862(f10(f932(x43182,a921),f932(x43182,a921),x43181),f862(f94(f932(x43182,a921)),x43184)),x43185)),f862(f862(f94(f932(x43182,a921)),x43184),f862(f862(f33(x43181,f932(x43182,a921)),x43183),x43185)))
% 25.54/25.40 [4319]E(f862(f862(f33(x43191,f932(x43192,a921)),x43193),f862(f862(f10(f932(x43192,a921),f932(x43192,a921),x43191),f862(f94(f932(x43192,a921)),x43194)),x43195)),f862(f862(f94(f932(x43192,a921)),x43194),f862(f862(f33(x43191,f932(x43192,a921)),x43193),x43195)))
% 25.54/25.40 [4320]E(f862(f862(f33(x43201,f932(x43202,a921)),x43203),f862(f862(f10(f932(x43202,a921),f932(x43202,a921),x43201),f862(f3(f932(x43202,a921)),x43204)),x43205)),f862(f862(f3(f932(x43202,a921)),x43204),f862(f862(f32(x43201,f932(x43202,a921)),x43203),x43205)))
% 25.54/25.40 [4321]E(f862(f862(f32(x43211,f932(x43212,a921)),x43213),f862(f862(f10(f932(x43212,a921),f932(x43212,a921),x43211),f862(f103(f932(x43212,a921)),x43214)),x43215)),f862(f862(f103(f932(x43212,a921)),x43214),f862(f862(f32(x43211,f932(x43212,a921)),x43213),x43215)))
% 25.54/25.40 [4322]E(f862(f862(f33(x43221,f932(x43222,a921)),x43223),f862(f862(f10(f932(x43222,a921),f932(x43222,a921),x43221),f862(f94(f932(x43222,a921)),x43224)),x43225)),f862(f862(f94(f932(x43222,a921)),x43224),f862(f862(f33(x43221,f932(x43222,a921)),x43223),x43225)))
% 25.54/25.40 [4323]E(f862(f862(f33(x43231,f932(x43232,a921)),x43233),f862(f862(f10(f932(x43232,a921),f932(x43232,a921),x43231),f862(f3(f932(x43232,a921)),x43234)),x43235)),f862(f862(f3(f932(x43232,a921)),x43234),f862(f862(f32(x43231,f932(x43232,a921)),x43233),x43235)))
% 25.54/25.40 [4377]E(f178(f925(x43771),f862(f862(f144(x43771),x43772),x43773),f862(f862(f10(f925(x43771),f925(x43771),a924),f862(f144(x43771),x43774)),f862(f862(f9(a924,x43771,f925(x43771)),f152(x43771,x43773)),x43772)),x43775),f862(f862(f152(x43771,f862(f862(f144(x43771),x43774),x43773)),x43775),x43772))
% 25.54/25.40 [4381]E(f862(f862(f32(x43811,f932(f931(x43812,x43813),a921)),x43814),f862(f862(f10(f932(f931(x43813,x43812),a921),f932(f931(x43812,x43813),a921),x43811),f277(x43813,x43812)),x43815)),f862(f277(x43813,x43812),f862(f862(f32(x43811,f932(f931(x43813,x43812),a921)),x43814),x43815)))
% 25.54/25.40 [4382]E(f862(f862(f33(x43821,f932(f931(x43822,x43823),a921)),x43824),f862(f862(f10(f932(f931(x43823,x43822),a921),f932(f931(x43822,x43823),a921),x43821),f277(x43823,x43822)),x43825)),f862(f277(x43823,x43822),f862(f862(f33(x43821,f932(f931(x43823,x43822),a921)),x43824),x43825)))
% 25.54/25.40 [4484]P1(f862(f862(f227(f932(x44841,a921)),f862(f862(f3(f932(x44841,a921)),f862(f302(x44842,x44841,x44843),x44844)),f862(f302(x44842,x44841,x44843),x44845))),f862(f302(x44842,x44841,x44843),f862(f862(f3(f932(x44842,a921)),x44844),x44845))))
% 25.54/25.40 [4631]E(f862(f149(f925(f931(x46311,x46312)),x46311,f106(f931(x46311,x46312)),f862(f862(f9(x46311,f932(f925(x46311),f925(f931(x46311,x46312))),f932(f925(x46311),f925(f931(x46311,x46312)))),f862(f862(f10(f932(f925(f931(x46311,x46312)),f925(f931(x46311,x46312))),f932(f932(f925(x46311),f925(f931(x46311,x46312))),f932(f925(x46311),f925(f931(x46311,x46312)))),x46311),f10(f925(f931(x46311,x46312)),f925(f931(x46311,x46312)),f925(x46311))),f862(f862(f10(f931(x46311,x46312),f932(f925(f931(x46311,x46312)),f925(f931(x46311,x46312))),x46311),f144(f931(x46311,x46312))),f862(f862(f9(x46311,x46312,f931(x46311,x46312)),f244(x46311,x46312)),x46313)))),f862(f862(f9(f925(x46311),f925(x46312),f925(f931(x46311,x46312))),f174(x46311,x46312)),x46314))),x46315),f862(f862(f174(x46311,x46312),x46315),f862(f862(f144(x46312),x46313),x46314)))
% 25.54/25.40 [4346]E(f862(f862(f103(f932(x43461,a921)),f862(f276(x43462,x43461,x43463),x43464)),f862(f276(x43462,x43461,x43465),x43464)),f862(f276(x43462,x43461,f862(f862(f103(f932(f931(x43462,x43461),a921)),x43463),x43465)),x43464))
% 25.54/25.40 [4383]E(f862(f862(f127(f931(x43831,x43832)),f862(f862(f174(x43831,x43832),x43833),f862(f862(f168(x43832),f862(f182(f925(x43831)),x43833)),x43834))),f862(f862(f174(x43831,x43832),x43835),f862(f862(f131(x43832),f862(f182(f925(x43831)),x43833)),x43834))),f862(f862(f174(x43831,x43832),f862(f862(f127(x43831),x43833),x43835)),x43834))
% 25.54/25.40 [4487]E(f862(f862(f246(x44871,x44872),x44873),f862(f862(f20(x44871,f932(x44872,a921),f932(x44872,a921)),f862(f862(f10(f932(x44872,a921),f932(f932(x44872,a921),f932(x44872,a921)),x44871),f103(f932(x44872,a921))),x44874)),x44875)),f862(f862(f103(f932(f931(x44871,x44872),a921)),f862(f862(f246(x44871,x44872),x44873),x44874)),f862(f862(f246(x44871,x44872),x44873),x44875)))
% 25.54/25.40 [4488]E(f862(f862(f246(x44881,x44882),x44883),f862(f862(f20(x44881,f932(x44882,a921),f932(x44882,a921)),f862(f862(f10(f932(x44882,a921),f932(f932(x44882,a921),f932(x44882,a921)),x44881),f94(f932(x44882,a921))),x44884)),x44885)),f862(f862(f94(f932(f931(x44881,x44882),a921)),f862(f862(f246(x44881,x44882),x44883),x44884)),f862(f862(f246(x44881,x44882),x44883),x44885)))
% 25.54/25.40 [4489]E(f862(f862(f246(x44891,x44892),x44893),f862(f862(f20(x44891,f932(x44892,a921),f932(x44892,a921)),f862(f862(f10(f932(x44892,a921),f932(f932(x44892,a921),f932(x44892,a921)),x44891),f3(f932(x44892,a921))),x44894)),x44895)),f862(f862(f3(f932(f931(x44891,x44892),a921)),f862(f862(f246(x44891,x44892),x44893),x44894)),f862(f862(f246(x44891,x44892),x44893),x44895)))
% 25.54/25.40 [4490]E(f862(f862(f32(x44901,f932(x44902,a921)),x44903),f862(f862(f9(x44901,f932(x44902,a921),f932(x44902,a921)),f862(f862(f10(f932(x44902,a921),f932(f932(x44902,a921),f932(x44902,a921)),x44901),f103(f932(x44902,a921))),x44904)),x44905)),f862(f862(f103(f932(x44902,a921)),f862(f862(f32(x44901,f932(x44902,a921)),x44903),x44904)),x44905))
% 25.54/25.40 [4491]E(f862(f862(f33(x44911,f932(x44912,a921)),x44913),f862(f862(f9(x44911,f932(x44912,a921),f932(x44912,a921)),f862(f862(f10(f932(x44912,a921),f932(f932(x44912,a921),f932(x44912,a921)),x44911),f94(f932(x44912,a921))),x44914)),x44915)),f862(f862(f94(f932(x44912,a921)),f862(f862(f33(x44911,f932(x44912,a921)),x44913),x44914)),x44915))
% 25.54/25.40 [4492]E(f862(f862(f33(x44921,f932(x44922,a921)),x44923),f862(f862(f9(x44921,f932(x44922,a921),f932(x44922,a921)),f862(f862(f10(f932(x44922,a921),f932(f932(x44922,a921),f932(x44922,a921)),x44921),f3(f932(x44922,a921))),x44924)),x44925)),f862(f862(f3(f932(x44922,a921)),f862(f862(f33(x44921,f932(x44922,a921)),x44923),x44924)),x44925))
% 25.54/25.40 [4493]E(f862(f862(f32(x44931,f932(x44932,a921)),x44933),f862(f862(f9(x44931,f932(x44932,a921),f932(x44932,a921)),f862(f862(f10(f932(x44932,a921),f932(f932(x44932,a921),f932(x44932,a921)),x44931),f103(f932(x44932,a921))),x44934)),x44935)),f862(f862(f103(f932(x44932,a921)),f862(f862(f32(x44931,f932(x44932,a921)),x44933),x44934)),x44935))
% 25.54/25.40 [4494]E(f862(f862(f33(x44941,f932(x44942,a921)),x44943),f862(f862(f9(x44941,f932(x44942,a921),f932(x44942,a921)),f862(f862(f10(f932(x44942,a921),f932(f932(x44942,a921),f932(x44942,a921)),x44941),f94(f932(x44942,a921))),x44944)),x44945)),f862(f862(f94(f932(x44942,a921)),f862(f862(f33(x44941,f932(x44942,a921)),x44943),x44944)),x44945))
% 25.54/25.40 [4495]E(f862(f862(f33(x44951,f932(x44952,a921)),x44953),f862(f862(f9(x44951,f932(x44952,a921),f932(x44952,a921)),f862(f862(f10(f932(x44952,a921),f932(f932(x44952,a921),f932(x44952,a921)),x44951),f3(f932(x44952,a921))),x44954)),x44955)),f862(f862(f3(f932(x44952,a921)),f862(f862(f33(x44951,f932(x44952,a921)),x44953),x44954)),x44955))
% 25.54/25.40 [4499]E(f862(f862(f32(x44991,f932(x44992,a921)),x44993),f862(f862(f20(x44991,f932(x44992,a921),f932(x44992,a921)),f862(f862(f10(f932(x44992,a921),f932(f932(x44992,a921),f932(x44992,a921)),x44991),f94(f932(x44992,a921))),x44994)),x44995)),f862(f862(f94(f932(x44992,a921)),f862(f862(f32(x44991,f932(x44992,a921)),x44993),x44994)),f862(f862(f32(x44991,f932(x44992,a921)),x44993),x44995)))
% 25.54/25.40 [4500]E(f862(f862(f33(x45001,f932(x45002,a921)),x45003),f862(f862(f20(x45001,f932(x45002,a921),f932(x45002,a921)),f862(f862(f10(f932(x45002,a921),f932(f932(x45002,a921),f932(x45002,a921)),x45001),f103(f932(x45002,a921))),x45004)),x45005)),f862(f862(f103(f932(x45002,a921)),f862(f862(f33(x45001,f932(x45002,a921)),x45003),x45004)),f862(f862(f33(x45001,f932(x45002,a921)),x45003),x45005)))
% 25.54/25.40 [4513]E(f862(f862(f32(x45131,f932(x45132,a921)),x45133),f862(f862(f20(x45131,f932(x45132,a921),f932(x45132,a921)),f862(f862(f10(f932(x45132,a921),f932(f932(x45132,a921),f932(x45132,a921)),x45131),f94(f932(x45132,a921))),x45134)),x45135)),f862(f862(f94(f932(x45132,a921)),f31(f932(x45132,a921),f862(f302(x45131,f932(x45132,a921),x45134),x45133))),f31(f932(x45132,a921),f862(f302(x45131,f932(x45132,a921),x45135),x45133))))
% 25.54/25.40 [4514]E(f862(f862(f33(x45141,f932(x45142,a921)),x45143),f862(f862(f20(x45141,f932(x45142,a921),f932(x45142,a921)),f862(f862(f10(f932(x45142,a921),f932(f932(x45142,a921),f932(x45142,a921)),x45141),f103(f932(x45142,a921))),x45144)),x45145)),f862(f862(f103(f932(x45142,a921)),f30(f932(x45142,a921),f862(f302(x45141,f932(x45142,a921),x45144),x45143))),f30(f932(x45142,a921),f862(f302(x45141,f932(x45142,a921),x45145),x45143))))
% 25.54/25.40 [4552]E(f862(f862(f131(x45521),f862(f182(f925(x45521)),f170(x45521,x45522,f862(f862(f147(x45523,x45521),x45524),x45525)))),f862(f862(f147(x45523,x45521),x45524),x45525)),f862(f862(f147(x45523,x45521),x45524),f862(f862(f131(x45523),f862(f182(f925(x45523)),f170(x45523,f862(f66(x45521,a921,x45523,x45522),x45524),x45525))),x45525)))
% 25.54/25.40 [4425]E(f862(f862(f127(f931(x44251,x44252)),f862(f862(f174(x44251,x44252),f862(f862(f168(x44251),f862(f182(f925(x44252)),x44253)),x44254)),x44253)),f862(f862(f174(x44251,x44252),f862(f862(f131(x44251),f862(f182(f925(x44252)),x44253)),x44254)),x44255)),f862(f862(f174(x44251,x44252),x44254),f862(f862(f127(x44252),x44253),x44255)))
% 25.54/25.40 [4543]E(f78(x45431,f862(f862(f20(x45431,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45431),a318),f862(f862(f9(x45431,f932(x45431,a921),a921),f321(x45431)),x45432))),f862(f862(f9(x45431,x45433,a921),f862(f862(f10(x45433,f932(x45433,a921),x45431),a317),x45434)),x45435))),f862(f70(x45431,x45433,x45432,x45434),x45435))
% 25.54/25.40 [4544]E(f83(x45441,f862(f862(f20(x45441,a921,a921),f862(f862(f10(a921,f932(a921,a921),x45441),a318),f862(f862(f9(x45441,f932(x45441,a921),a921),f321(x45441)),x45442))),f862(f862(f9(x45441,x45443,a921),f862(f862(f10(x45443,f932(x45443,a921),x45441),a317),x45444)),x45445))),f862(f86(x45441,x45443,x45442,x45444),x45445))
% 25.54/25.40 [4592]E(f862(f862(f79(a1,x45921),f862(f96(a1),f862(f862(f73(a1),x45922),a90))),f862(f862(f20(a1,x45921,x45921),f862(f862(f9(a1,x45921,f932(x45921,x45921)),f862(f862(f10(a921,f932(x45921,f932(x45921,x45921)),a1),f89(x45921)),a186)),f178(x45921,x45923,x45924,x45925))),f862(f862(f10(a924,x45921,a1),x45924),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x45925)))),f178(x45921,x45923,x45924,f862(f862(f73(a924),f862(f96(a924),x45922)),x45925)))
% 25.54/25.40 [4627]E(f862(f862(f79(a1,x46271),f862(f96(a1),f862(f862(f73(a1),x46272),a90))),f862(f862(f20(a1,x46271,x46271),f862(f862(f9(a1,x46271,f932(x46271,x46271)),f862(f862(f10(a921,f932(x46271,f932(x46271,x46271)),a1),f89(x46271)),a186)),f862(f177(x46271,x46273,x46274),x46275))),f862(f862(f20(a1,x46271,x46271),f862(f862(f10(a924,f932(x46271,x46271),a1),x46274),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x46275))),f862(f862(f10(a924,x46271,a1),f177(x46271,x46273,x46274)),f862(f862(f9(a1,a924,a924),f862(f862(f10(a924,f932(a924,a924),a1),f73(a924)),a97)),x46275))))),f862(f177(x46271,x46273,x46274),f862(f862(f73(a924),f862(f96(a924),x46272)),x46275)))
% 25.54/25.40 [4660]E(f862(f254(f931(x46601,x46602)),f862(f249(x46601,x46602,a921),f862(f862(f10(f932(x46602,f932(x46603,a921)),f932(x46602,a921),x46601),f862(f10(f932(x46603,a921),a921,x46602),f80(x46603))),f862(f862(f9(x46601,f932(x46602,f932(x46603,a921)),f932(x46602,f932(x46603,a921))),f862(f862(f10(f932(f932(x46603,a921),f932(x46603,a921)),f932(f932(x46602,f932(x46603,a921)),f932(x46602,f932(x46603,a921))),x46601),f10(f932(x46603,a921),f932(x46603,a921),x46602)),f862(f862(f10(f932(x46603,f932(a921,a921)),f932(f932(x46603,a921),f932(x46603,a921)),x46601),f20(x46603,a921,a921)),f862(f862(f10(f932(x46603,a921),f932(x46603,f932(a921,a921)),x46601),f862(f10(a921,f932(a921,a921),x46603),a318)),f862(f862(f9(x46601,f932(f931(x46601,x46603),a921),f932(x46603,a921)),f862(f862(f10(f932(x46603,f932(f932(f931(x46601,x46603),a921),a921)),f932(f932(f931(x46601,x46603),a921),f932(x46603,a921)),x46601),f9(x46603,f932(f931(x46601,x46603),a921),a921)),f862(f862(f10(f932(x46603,f931(x46601,x46603)),f932(x46603,f932(f932(f931(x46601,x46603),a921),a921)),x46601),f862(f10(f931(x46601,x46603),f932(f932(f931(x46601,x46603),a921),a921),x46603),f321(f931(x46601,x46603)))),f244(x46601,x46603)))),x46604))))),f862(f862(f9(x46602,f932(f931(x46603,x46602),a921),f932(x46603,a921)),f862(f862(f10(f932(x46603,f932(f932(f931(x46603,x46602),a921),a921)),f932(f932(f931(x46603,x46602),a921),f932(x46603,a921)),x46602),f9(x46603,f932(f931(x46603,x46602),a921),a921)),f862(f862(f10(f932(x46603,f931(x46603,x46602)),f932(x46603,f932(f932(f931(x46603,x46602),a921),a921)),x46602),f862(f10(f931(x46603,x46602),f932(f932(f931(x46603,x46602),a921),a921),x46603),f321(f931(x46603,x46602)))),f862(f9(x46603,x46602,f931(x46603,x46602)),f244(x46603,x46602))))),x46605))))),f862(f862(f280(x46601,x46603,x46602),x46604),x46605))
% 25.54/25.40 [4275]E(f217(x42751,x42752,x42753,x42754,f213(x42751,x42752,x42755,x42756)),f862(f862(x42754,x42755),x42756))
% 25.54/25.40 [4276]E(f218(x42761,x42762,x42763,x42764,f213(x42761,x42762,x42765,x42766)),f862(f862(x42764,x42765),x42766))
% 25.54/25.41 [4401]E(f120(x44011,x44012,x44013,x44014,f119(x44012,x44015,x44016)),f862(f862(f862(x44014,x44015),x44016),f120(x44011,x44012,x44013,x44014,x44016)))
% 25.54/25.41 [4420]E(f68(x44201,x44202,f68(x44201,x44202,x44203,x44204,x44205),x44204,x44206),f68(x44201,x44202,x44203,x44204,x44206))
% 25.54/25.41 [4531]E(f862(f66(f931(x45311,x45312),x45312,f931(x45313,x45314),f248(x45311,x45312)),f250(x45313,x45311,x45314,x45312,x45315,x45316)),f862(f66(x45314,x45312,f931(x45313,x45314),x45316),f248(x45313,x45314)))
% 25.54/25.41 [4532]E(f862(f66(f931(x45321,x45322),x45321,f931(x45323,x45324),f243(x45321,x45322)),f250(x45323,x45321,x45324,x45322,x45325,x45326)),f862(f66(x45323,x45321,f931(x45323,x45324),x45325),f243(x45323,x45324)))
% 25.54/25.41 [4146]E(f862(f862(f66(x41461,x41462,x41463,x41464),x41465),x41466),f862(x41464,f862(x41465,x41466)))
% 25.54/25.41 [4147]E(f862(f862(f66(x41471,x41472,x41473,x41474),x41475),x41476),f862(x41474,f862(x41475,x41476)))
% 25.54/25.41 [4285]E(f216(x42851,f931(x42852,f926(x42852)),x42853,f862(f249(x42852,f926(x42852),x42851),x42854),f862(f128(x42852),f119(x42852,x42855,x42856))),f862(f862(x42854,x42855),x42856))
% 25.54/25.41 [4335]E(f219(x43351,x43352,x43353,x43354,f213(x43351,x43352,x43355,x43356)),f862(f862(f73(a924),f862(f862(f73(a924),f862(x43353,x43355)),f862(x43354,x43356))),f862(a105,f2(a924))))
% 25.54/25.41 [3947]E(f862(f862(f249(x39471,x39472,x39473),x39474),f862(f862(f244(x39471,x39472),x39475),x39476)),f862(f862(x39474,x39475),x39476))
% 25.54/25.41 [3948]E(f862(f862(f249(x39481,x39482,x39483),x39484),f862(f862(f244(x39481,x39482),x39485),x39486)),f862(f862(x39484,x39485),x39486))
% 25.54/25.41 [3949]E(f862(f862(f249(x39491,x39492,x39493),x39494),f862(f862(f244(x39491,x39492),x39495),x39496)),f862(f862(x39494,x39495),x39496))
% 25.54/25.41 [4009]E(f862(f862(f862(f10(x40091,x40092,x40093),x40094),x40095),x40096),f862(x40094,f862(x40095,x40096)))
% 25.54/25.41 [4010]E(f862(f862(f862(f9(x40101,x40102,x40103),x40104),x40105),x40106),f862(f862(x40104,x40106),x40105))
% 25.54/25.41 [4026]E(f862(f862(f862(f20(x40261,x40262,x40263),x40264),x40265),x40266),f862(f862(x40264,x40266),f862(x40265,x40266)))
% 25.54/25.41 [4049]E(f862(f149(x40491,x40492,x40493,x40494),f862(f862(f144(x40492),x40495),x40496)),f862(f862(x40494,x40495),x40496))
% 25.54/25.41 [4085]E(f162(f931(x40851,x40852),f862(f862(f225(a924),x40853),x40854),f862(f862(f244(x40851,x40852),x40855),x40856)),f862(f862(f174(x40851,x40852),f162(x40851,x40853,x40855)),f162(x40852,x40854,x40856)))
% 25.54/25.41 [4151]E(f862(f862(f144(f931(x41511,x41512)),f862(f862(f244(x41511,x41512),x41513),x41514)),f862(f862(f174(x41511,x41512),x41515),x41516)),f862(f862(f174(x41511,x41512),f862(f862(f144(x41511),x41513),x41515)),f862(f862(f144(x41512),x41514),x41516)))
% 25.54/25.41 [4152]E(f862(f862(f147(x41521,x41522),x41523),f862(f862(f152(x41521,x41524),x41525),x41526)),f862(f862(f152(x41522,f862(f862(f147(x41521,x41522),x41523),x41524)),x41525),f862(x41523,x41526)))
% 25.54/25.41 [4175]E(f862(f862(f247(x41751,x41752,x41753,x41754),x41755),x41756),f862(x41754,f862(f862(f244(x41751,x41752),x41755),x41756)))
% 25.54/25.41 [4176]E(f862(f862(f247(x41761,x41762,x41763,x41764),x41765),x41766),f862(x41764,f862(f862(f244(x41761,x41762),x41765),x41766)))
% 25.54/25.41 [4192]E(f862(f135(x41921,x41922,x41923,x41924),f862(f862(f144(x41922),x41925),x41926)),f862(f135(x41921,x41922,x41923,f862(f862(x41923,x41924),x41925)),x41926))
% 25.54/25.41 [4218]E(f252(x42181,x42182,x42183,x42184,f862(f862(f244(x42181,x42182),x42185),x42186)),f862(f862(x42184,x42185),x42186))
% 25.54/25.41 [4299]E(f862(f862(f33(x42991,f932(x42992,a921)),x42993),f862(f66(x42994,f932(x42992,a921),x42991,x42995),x42996)),f862(f862(f33(x42994,f932(x42992,a921)),f862(f302(x42991,x42994,x42996),x42993)),x42995))
% 25.54/25.41 [4348]E(f862(f862(f147(x43481,x43482),x43483),f862(f862(f147(x43484,x43481),x43485),x43486)),f862(f862(f147(x43484,x43482),f862(f66(x43481,x43482,x43484,x43483),x43485)),x43486))
% 25.54/25.41 [4349]E(f862(f862(f147(x43491,x43492),x43493),f862(f862(f147(x43494,x43491),x43495),x43496)),f862(f862(f147(x43494,x43492),f862(f66(x43491,x43492,x43494,x43493),x43495)),x43496))
% 25.54/25.41 [4355]E(f862(f302(x43551,x43552,f862(f66(x43553,x43552,x43551,x43554),x43555)),x43556),f862(f302(x43553,x43552,x43554),f862(f302(x43551,x43553,x43555),x43556)))
% 25.54/25.41 [4356]E(f862(f303(x43561,x43562,f862(f66(x43563,x43562,x43561,x43564),x43565)),x43566),f862(f303(x43561,x43563,x43565),f862(f303(x43563,x43562,x43564),x43566)))
% 25.54/25.41 [4384]E(f862(f135(x43841,x43842,x43843,f862(f135(x43841,x43842,x43843,x43844),x43845)),x43846),f862(f135(x43841,x43842,x43843,x43844),f862(f862(f127(x43842),x43845),x43846)))
% 25.54/25.41 [4519]E(f862(f250(x45191,x45191,x45192,x45193,f25(x45191),x45194),f862(f862(f244(x45191,x45192),x45195),x45196)),f862(f862(f244(x45191,x45193),x45195),f862(x45194,x45196)))
% 25.54/25.41 [4520]E(f862(f250(x45201,x45202,x45203,x45203,x45204,f25(x45203)),f862(f862(f244(x45201,x45203),x45205),x45206)),f862(f862(f244(x45202,x45203),f862(x45204,x45205)),x45206))
% 25.54/25.41 [4610]E(f862(f862(f147(f931(x46101,x46102),f931(x46101,x46103)),f862(f249(x46101,x46102,f931(x46101,x46103)),f862(f862(f9(x46101,f932(x46102,x46103),f932(x46102,f931(x46101,x46103))),f862(f862(f10(f932(x46103,f931(x46101,x46103)),f932(f932(x46102,x46103),f932(x46102,f931(x46101,x46103))),x46101),f10(x46103,f931(x46101,x46103),x46102)),f244(x46101,x46103))),x46104))),f862(f862(f174(x46101,x46102),x46105),x46106)),f862(f862(f174(x46101,x46103),x46105),f862(f862(f147(x46102,x46103),x46104),x46106)))
% 25.54/25.41 [4202]E(f862(f862(f66(x42021,x42022,x42023,f862(f18(x42022,x42021),x42024)),x42025),x42026),x42024)
% 25.54/25.41 [4234]E(f862(f302(x42341,x42342,x42343),f862(f302(x42344,x42341,x42345),x42346)),f862(f302(x42344,x42342,f862(f862(f10(x42341,x42342,x42344),x42343),x42345)),x42346))
% 25.54/25.41 [4240]E(f862(f862(f32(x42401,f932(x42402,a921)),f862(f302(x42403,x42401,x42404),x42405)),x42406),f862(f862(f32(x42403,f932(x42402,a921)),x42405),f862(f862(f10(x42401,f932(x42402,a921),x42403),x42406),x42404)))
% 25.54/25.41 [4241]E(f862(f862(f33(x42411,f932(x42412,a921)),f862(f302(x42413,x42411,x42414),x42415)),x42416),f862(f862(f33(x42413,f932(x42412,a921)),x42415),f862(f862(f10(x42411,f932(x42412,a921),x42413),x42416),x42414)))
% 25.54/25.41 [4242]E(f862(f862(f32(x42421,f932(x42422,a921)),x42423),f862(f862(f10(x42424,f932(x42422,a921),x42421),x42425),x42426)),f862(f862(f32(x42424,f932(x42422,a921)),f862(f302(x42421,x42424,x42426),x42423)),x42425))
% 25.54/25.41 [4243]E(f862(f862(f33(x42431,f932(x42432,a921)),x42433),f862(f862(f10(x42434,f932(x42432,a921),x42431),x42435),x42436)),f862(f862(f33(x42434,f932(x42432,a921)),f862(f302(x42431,x42434,x42436),x42433)),x42435))
% 25.54/25.41 [4301]E(f862(f862(f33(x43011,f932(x43012,a921)),x43013),f862(f862(f10(f932(x43014,a921),f932(x43012,a921),x43011),f302(x43014,x43012,x43015)),x43016)),f862(f302(x43014,x43012,x43015),f862(f862(f33(x43011,f932(x43014,a921)),x43013),x43016)))
% 25.54/25.41 [4302]E(f862(f862(f33(x43021,f932(x43022,a921)),x43023),f862(f862(f10(f932(x43024,a921),f932(x43022,a921),x43021),f276(x43024,x43022,x43025)),x43026)),f862(f276(x43024,x43022,x43025),f862(f862(f33(x43021,f932(x43024,a921)),x43023),x43026)))
% 25.54/25.41 [4303]E(f862(f862(f32(x43031,f932(x43032,a921)),x43033),f862(f862(f10(f932(x43034,a921),f932(x43032,a921),x43031),f303(x43032,x43034,x43035)),x43036)),f862(f303(x43032,x43034,x43035),f862(f862(f32(x43031,f932(x43034,a921)),x43033),x43036)))
% 25.54/25.41 [4304]E(f862(f862(f33(x43041,f932(x43042,a921)),x43043),f862(f862(f10(f932(x43044,a921),f932(x43042,a921),x43041),f303(x43042,x43044,x43045)),x43046)),f862(f303(x43042,x43044,x43045),f862(f862(f33(x43041,f932(x43044,a921)),x43043),x43046)))
% 25.54/25.41 [4389]E(f862(f135(x43891,x43892,f862(f9(x43892,x43891,x43891),x43893),x43894),f862(f161(x43892),f862(f862(f144(x43892),x43895),x43896))),f862(f862(x43893,x43895),f862(f135(x43891,x43892,f862(f9(x43892,x43891,x43891),x43893),x43894),f862(f161(x43892),x43896))))
% 25.54/25.41 [4448]E(f862(f862(f20(f931(x44481,x44482),x44482,x44483),f862(f862(f10(x44484,f932(x44482,x44483),f931(x44481,x44482)),x44485),f862(f862(f10(x44481,x44484,f931(x44481,x44482)),x44486),f243(x44481,x44482)))),f248(x44481,x44482)),f862(f249(x44481,x44482,x44483),f862(f862(f10(x44484,f932(x44482,x44483),x44481),x44485),x44486)))
% 25.54/25.41 [4455]E(f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),x44554),f862(f161(x44552),x44555))),f862(f161(x44552),x44556)),f862(f135(x44551,x44552,f862(f9(x44552,x44551,x44551),x44553),x44554),f862(f161(x44552),f862(f862(f127(x44552),x44556),x44555))))
% 25.54/25.41 [4457]E(f862(f862(f147(f931(x44571,x44572),f931(x44573,x44572)),f862(f249(x44571,x44572,f931(x44573,x44572)),f862(f862(f10(x44573,f932(x44572,f931(x44573,x44572)),x44571),f244(x44573,x44572)),x44574))),f862(f862(f174(x44571,x44572),x44575),x44576)),f862(f862(f174(x44573,x44572),f862(f862(f147(x44571,x44573),x44574),x44575)),x44576))
% 25.54/25.41 [4502]P1(f862(f862(f227(f932(x45021,a921)),f862(f276(x45022,x45021,x45023),f862(f862(f32(x45024,f932(x45022,a921)),x45025),x45026))),f862(f862(f32(x45024,f932(x45021,a921)),x45025),f862(f862(f10(f932(x45022,a921),f932(x45021,a921),x45024),f276(x45022,x45021,x45023)),x45026))))
% 25.54/25.41 [4314]E(f862(f862(f174(x43141,x43142),f862(f862(f152(x43141,x43143),x43144),f862(f243(x43141,x43142),x43145))),f862(f862(f152(x43142,x43146),x43144),f862(f248(x43141,x43142),x43145))),f862(f862(f152(f931(x43141,x43142),f862(f862(f174(x43141,x43142),x43143),x43146)),x43144),x43145))
% 25.54/25.41 [4372]E(f862(f862(f103(f932(f931(x43721,x43722),a921)),f862(f862(f280(x43721,x43723,x43722),x43724),x43725)),f862(f862(f280(x43721,x43723,x43722),x43724),x43726)),f862(f862(f280(x43721,x43723,x43722),x43724),f862(f862(f103(f932(f931(x43723,x43722),a921)),x43725),x43726)))
% 25.54/25.41 [4467]E(f862(f862(f301(f931(x44671,x44672)),f862(f862(f244(x44671,x44672),x44673),x44674)),f862(f862(f103(f932(f931(x44671,x44672),a921)),f862(f862(f246(x44671,x44672),x44675),f862(f18(f932(x44672,a921),x44671),f862(f862(f301(x44672),x44674),x44676)))),f862(f862(f246(x44671,x44672),f862(f862(f301(x44671),x44673),x44675)),f862(f18(f932(x44672,a921),x44671),x44676)))),f862(f862(f246(x44671,x44672),f862(f862(f301(x44671),x44673),x44675)),f862(f18(f932(x44672,a921),x44671),f862(f862(f301(x44672),x44674),x44676))))
% 25.54/25.41 [4548]E(f862(f862(f94(f932(x45481,a921)),f862(f303(x45481,x45482,f862(f66(f931(x45482,x45483),x45482,x45481,f243(x45482,x45483)),x45484)),x45485)),f862(f303(x45481,x45483,f862(f66(f931(x45482,x45483),x45483,x45481,f248(x45482,x45483)),x45484)),x45486)),f862(f303(x45481,f931(x45482,x45483),x45484),f862(f862(f246(x45482,x45483),x45485),f862(f18(f932(x45483,a921),x45482),x45486))))
% 25.54/25.41 [4395]E(f862(f862(f103(f932(f931(x43951,x43952),a921)),f862(f862(f280(x43951,x43953,x43952),x43954),x43955)),f862(f862(f280(x43951,x43953,x43952),x43956),x43955)),f862(f862(f280(x43951,x43953,x43952),f862(f862(f103(f932(f931(x43951,x43953),a921)),x43954),x43956)),x43955))
% 25.54/25.41 [4526]E(f862(f862(f32(x45261,f932(x45262,a921)),x45263),f862(f862(f9(x45261,f932(x45264,f932(x45262,a921)),f932(x45262,a921)),f862(f862(f10(f932(x45264,a921),f932(f932(x45264,f932(x45262,a921)),f932(x45262,a921)),x45261),f32(x45264,f932(x45262,a921))),x45265)),x45266)),f862(f862(f32(x45264,f932(x45262,a921)),f862(f862(f33(x45261,f932(x45264,a921)),x45263),x45265)),x45266))
% 25.54/25.41 [4527]E(f862(f862(f33(x45271,f932(x45272,a921)),x45273),f862(f862(f9(x45271,f932(x45274,f932(x45272,a921)),f932(x45272,a921)),f862(f862(f10(f932(x45274,a921),f932(f932(x45274,f932(x45272,a921)),f932(x45272,a921)),x45271),f33(x45274,f932(x45272,a921))),x45275)),x45276)),f862(f862(f33(x45274,f932(x45272,a921)),f862(f862(f33(x45271,f932(x45274,a921)),x45273),x45275)),x45276))
% 25.54/25.41 [4528]E(f862(f862(f33(x45281,f932(x45282,a921)),x45283),f862(f862(f9(x45281,f932(x45284,f932(x45282,a921)),f932(x45282,a921)),f862(f862(f10(f932(x45284,a921),f932(f932(x45284,f932(x45282,a921)),f932(x45282,a921)),x45281),f33(x45284,f932(x45282,a921))),x45285)),x45286)),f862(f862(f33(x45284,f932(x45282,a921)),f862(f862(f33(x45281,f932(x45284,a921)),x45283),x45285)),x45286))
% 25.54/25.41 [4529]E(f862(f862(f32(x45291,f932(x45292,a921)),x45293),f862(f862(f9(x45291,f932(x45294,f932(x45292,a921)),f932(x45292,a921)),f862(f862(f10(f932(x45294,a921),f932(f932(x45294,f932(x45292,a921)),f932(x45292,a921)),x45291),f32(x45294,f932(x45292,a921))),x45295)),x45296)),f862(f862(f32(x45294,f932(x45292,a921)),f862(f862(f33(x45291,f932(x45294,a921)),x45293),x45295)),x45296))
% 25.54/25.41 [4530]E(f862(f862(f33(x45301,f932(x45302,a921)),x45303),f862(f862(f9(x45301,f932(x45304,f932(x45302,a921)),f932(x45302,a921)),f862(f862(f10(f932(x45304,a921),f932(f932(x45304,f932(x45302,a921)),f932(x45302,a921)),x45301),f33(x45304,f932(x45302,a921))),x45305)),x45306)),f862(f862(f33(x45304,f932(x45302,a921)),f862(f862(f33(x45301,f932(x45304,a921)),x45303),x45305)),x45306))
% 25.54/25.41 [4582]E(f862(f249(x45821,x45822,f931(x45823,x45824)),f862(f862(f9(x45821,f932(x45822,x45824),f932(x45822,f931(x45823,x45824))),f862(f862(f10(f932(x45824,f931(x45823,x45824)),f932(f932(x45822,x45824),f932(x45822,f931(x45823,x45824))),x45821),f10(x45824,f931(x45823,x45824),x45822)),f862(f862(f10(x45823,f932(x45824,f931(x45823,x45824)),x45821),f244(x45823,x45824)),x45825))),x45826)),f250(x45821,x45823,x45822,x45824,x45825,x45826))
% 25.54/25.41 [4605]E(f862(f302(x46051,x46052,f862(f862(f20(x46051,x46052,x46052),f862(f862(f20(x46051,x46052,f932(x46052,x46052)),f862(f862(f10(a921,f932(x46052,f932(x46052,x46052)),x46051),f89(x46052)),x46053)),x46054)),x46055)),x46056),f862(f862(f103(f932(x46052,a921)),f862(f302(x46051,x46052,x46054),f862(f862(f94(f932(x46051,a921)),x46056),f862(f254(x46051),x46053)))),f862(f302(x46051,x46052,x46055),f862(f862(f94(f932(x46051,a921)),x46056),f862(f254(x46051),f862(f862(f10(a921,a921,x46051),a314),x46053))))))
% 25.54/25.41 [4617]E(f862(f302(x46171,f931(x46172,x46173),f862(f862(f20(x46171,x46173,f931(x46172,x46173)),f862(f862(f10(x46172,f932(x46173,f931(x46172,x46173)),x46171),f244(x46172,x46173)),x46174)),x46175)),x46176),f862(f862(f246(x46172,x46173),f862(f302(x46171,x46172,x46174),x46176)),f862(f862(f10(f932(x46171,a921),f932(x46173,a921),x46172),f302(x46171,x46173,x46175)),f862(f862(f9(x46172,f932(x46171,a921),f932(x46171,a921)),f862(f862(f10(f932(x46171,a921),f932(f932(x46171,a921),f932(x46171,a921)),x46172),f94(f932(x46171,a921))),f862(f862(f10(f932(x46172,a921),f932(x46171,a921),x46172),f303(x46171,x46172,x46174)),f862(f862(f9(x46172,f932(x46172,a921),f932(x46172,a921)),f301(x46172)),f181(f932(x46172,a921)))))),x46176))))
% 25.54/25.41 [4642]E(f238(x46421,x46422,x46423,x46424,x46425,x46426),f862(x46424,f862(f254(x46421),f862(f862(f10(f932(f932(x46423,x46421),a921),a921,x46421),f80(f932(x46423,x46421))),f862(f862(f10(f932(f932(x46423,x46421),a921),f932(f932(x46423,x46421),a921),x46421),f862(f20(f932(x46423,x46421),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x46423,x46421)),a318),f862(f862(f9(f932(x46423,x46421),f932(f932(x46423,x46421),a921),a921),f321(f932(x46423,x46421))),x46425)))),f862(f862(f9(x46421,f932(f932(x46423,x46421),x46421),f932(f932(x46423,x46421),a921)),f862(f862(f10(f932(x46421,a921),f932(f932(f932(x46423,x46421),x46421),f932(f932(x46423,x46421),a921)),x46421),f10(x46421,a921,f932(x46423,x46421))),a317)),f862(f862(f9(f932(x46423,x46421),x46423,x46421),f7(f932(x46423,x46421))),x46426)))))))
% 25.54/25.41 [4428]E(f862(f66(x44281,x44282,x44283,x44284),f68(x44283,x44281,x44285,x44286,x44287)),f68(x44283,x44282,f862(f66(x44281,x44282,x44283,x44284),x44285),x44286,f862(x44284,x44287)))
% 25.54/25.41 [4565]E(f862(f248(x45651,x45652),f862(f250(x45653,x45651,x45654,x45652,x45655,x45656),x45657)),f862(x45656,f862(f248(x45653,x45654),x45657)))
% 25.54/25.41 [4566]E(f862(f243(x45661,x45662),f862(f250(x45663,x45661,x45664,x45662,x45665,x45666),x45667)),f862(x45665,f862(f243(x45663,x45664),x45667)))
% 25.54/25.41 [4277]E(f862(f862(f174(x42771,x42772),f862(f862(f152(x42771,x42773),x42774),x42775)),f862(f862(f152(x42772,x42776),x42774),x42777)),f862(f862(f152(f931(x42771,x42772),f862(f862(f174(x42771,x42772),x42773),x42776)),x42774),f862(f862(f244(x42771,x42772),x42775),x42777)))
% 25.54/25.41 [4343]E(f862(f862(f862(f251(x43431,x43432,x43433,x43434),x43435),x43436),x43437),f862(f862(f249(x43432,x43433,x43434),x43436),f862(x43435,x43437)))
% 25.54/25.41 [4344]E(f862(f862(f862(f251(x43441,x43442,x43443,x43444),x43445),x43446),x43447),f862(f862(f249(x43442,x43443,x43444),x43446),f862(x43445,x43447)))
% 25.54/25.41 [4354]E(f862(f862(f862(f251(x43541,x43542,x43543,x43544),x43545),x43546),x43547),f862(f862(x43546,f862(f243(x43542,x43543),f862(x43545,x43547))),f862(f248(x43542,x43543),f862(x43545,x43547))))
% 25.54/25.41 [4406]E(f862(f66(x44061,x44062,x44063,x44064),f862(f66(x44065,x44061,x44063,x44066),x44067)),f862(f66(x44065,x44062,x44063,f862(f66(x44061,x44062,x44065,x44064),x44066)),x44067))
% 25.54/25.41 [4586]E(f862(f250(x45861,x45862,x45863,x45863,x45864,f25(x45863)),f862(f250(x45861,x45861,x45865,x45863,f25(x45861),x45866),x45867)),f862(f862(f244(x45862,x45863),f862(x45864,f862(f243(x45861,x45865),x45867))),f862(x45866,f862(f248(x45861,x45865),x45867))))
% 25.54/25.41 [4587]E(f862(f250(x45871,x45871,x45872,x45873,f25(x45871),x45874),f862(f250(x45875,x45871,x45872,x45872,x45876,f25(x45872)),x45877)),f862(f862(f244(x45871,x45873),f862(x45876,f862(f243(x45875,x45872),x45877))),f862(x45874,f862(f248(x45875,x45872),x45877))))
% 25.54/25.41 [4603]E(f862(f250(x46031,x46032,x46033,x46033,x46034,f25(x46033)),f862(f250(x46035,x46031,x46033,x46033,x46036,f25(x46033)),x46037)),f862(f250(x46035,x46032,x46033,x46033,f862(f66(x46031,x46032,x46035,x46034),x46036),f25(x46033)),x46037))
% 25.54/25.41 [4604]E(f862(f250(x46041,x46041,x46042,x46043,f25(x46041),x46044),f862(f250(x46041,x46041,x46045,x46042,f25(x46041),x46046),x46047)),f862(f250(x46041,x46041,x46045,x46043,f25(x46041),f862(f66(x46042,x46043,x46045,x46044),x46046)),x46047))
% 25.54/25.41 [4614]E(f862(f250(x46141,x46142,x46143,x46143,x46144,f25(x46143)),f862(f250(x46141,x46141,x46145,x46143,f25(x46141),x46146),x46147)),f862(f250(x46142,x46142,x46145,x46143,f25(x46142),x46146),f862(f250(x46141,x46142,x46145,x46145,x46144,f25(x46145)),x46147)))
% 25.54/25.41 [4311]E(f862(f862(f280(x43111,x43112,x43113),f862(f862(f280(x43111,x43114,x43112),x43115),x43116)),x43117),f862(f862(f280(x43111,x43114,x43113),x43115),f862(f862(f280(x43114,x43112,x43113),x43116),x43117)))
% 25.54/25.41 [4378]E(f862(f862(f249(x43781,x43782,x43783),f862(f66(x43784,f932(x43782,x43783),x43781,x43785),x43786)),x43787),f862(f862(x43785,f862(x43786,f862(f243(x43781,x43782),x43787))),f862(f248(x43781,x43782),x43787)))
% 25.54/25.41 [4460]E(f862(f135(x44601,x44602,f862(f9(x44602,x44601,x44601),x44603),x44604),f862(f161(x44602),f862(f862(f147(x44605,x44602),x44606),x44607))),f862(f135(x44601,x44605,f862(f9(x44605,x44601,x44601),f862(f66(x44602,f932(x44601,x44601),x44605,x44603),x44606)),x44604),f862(f161(x44605),x44607)))
% 25.54/25.41 [4407]E(f862(f862(f33(x44071,f932(f931(x44072,x44073),a921)),x44074),f862(f862(f10(f932(f931(x44075,x44073),a921),f932(f931(x44072,x44073),a921),x44071),f862(f280(x44072,x44075,x44073),x44076)),x44077)),f862(f862(f280(x44072,x44075,x44073),x44076),f862(f862(f33(x44071,f932(f931(x44075,x44073),a921)),x44074),x44077)))
% 25.54/25.41 [4553]E(f862(f862(f33(x45531,f932(f931(x45532,x45533),a921)),x45534),f862(f862(f9(x45531,f932(f931(x45535,x45533),a921),f932(f931(x45532,x45533),a921)),f862(f862(f10(f932(f931(x45532,x45535),a921),f932(f932(f931(x45535,x45533),a921),f932(f931(x45532,x45533),a921)),x45531),f280(x45532,x45535,x45533)),x45536)),x45537)),f862(f862(f280(x45532,x45535,x45533),f862(f862(f33(x45531,f932(f931(x45532,x45535),a921)),x45534),x45536)),x45537))
% 25.54/25.41 [4554]E(f862(f135(x45541,x45542,f862(f862(f9(x45541,f932(x45542,x45543),f932(x45542,x45541)),f862(f862(f10(f932(x45543,x45541),f932(f932(x45542,x45543),f932(x45542,x45541)),x45541),f10(x45543,x45541,x45542)),x45544)),x45545),x45546),x45547),f862(f135(x45541,x45543,x45544,x45546),f862(f862(f147(x45542,x45543),x45545),x45547)))
% 25.54/25.41 [4615]E(f862(f862(f32(x46151,f932(x46152,a921)),x46153),f862(f862(f10(f932(x46154,f932(x46152,a921)),f932(x46152,a921),x46151),f862(f32(x46154,f932(x46152,a921)),x46155)),f862(f862(f9(x46151,f932(x46154,f932(x46152,a921)),f932(x46154,f932(x46152,a921))),f862(f862(f10(f932(f932(x46152,a921),f932(x46152,a921)),f932(f932(x46154,f932(x46152,a921)),f932(x46154,f932(x46152,a921))),x46151),f10(f932(x46152,a921),f932(x46152,a921),x46154)),f862(f862(f10(f932(x46152,a921),f932(f932(x46152,a921),f932(x46152,a921)),x46151),f103(f932(x46152,a921))),x46156))),x46157))),f862(f862(f103(f932(x46152,a921)),f862(f862(f32(x46151,f932(x46152,a921)),x46153),x46156)),f862(f862(f32(x46154,f932(x46152,a921)),x46155),x46157)))
% 25.54/25.41 [4616]E(f862(f862(f33(x46161,f932(x46162,a921)),x46163),f862(f862(f10(f932(x46164,f932(x46162,a921)),f932(x46162,a921),x46161),f862(f33(x46164,f932(x46162,a921)),x46165)),f862(f862(f9(x46161,f932(x46164,f932(x46162,a921)),f932(x46164,f932(x46162,a921))),f862(f862(f10(f932(f932(x46162,a921),f932(x46162,a921)),f932(f932(x46164,f932(x46162,a921)),f932(x46164,f932(x46162,a921))),x46161),f10(f932(x46162,a921),f932(x46162,a921),x46164)),f862(f862(f10(f932(x46162,a921),f932(f932(x46162,a921),f932(x46162,a921)),x46161),f94(f932(x46162,a921))),x46166))),x46167))),f862(f862(f94(f932(x46162,a921)),f862(f862(f33(x46161,f932(x46162,a921)),x46163),x46166)),f862(f862(f33(x46164,f932(x46162,a921)),x46165),x46167)))
% 25.54/25.41 [4608]E(f190(x46081,x46082,f862(f862(f862(x46083,x46084),x46085),x46086),f862(f862(f9(x46081,f931(a92,a92),f932(a92,f926(x46082))),f862(f862(f9(x46081,a92,f932(f931(a92,a92),f932(a92,f926(x46082)))),f862(f862(f9(x46081,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x46082))))),x46087),x46084)),x46085)),x46086)),f862(f862(f862(f202(x46081,x46082,x46083,x46087),x46084),x46085),x46086))
% 25.54/25.41 [4622]E(f191(x46221,x46222,f862(f862(f862(x46223,x46224),x46225),x46226),f862(f862(f9(x46221,f931(a92,a92),f932(a92,f926(x46222))),f862(f862(f9(x46221,a92,f932(f931(a92,a92),f932(a92,f926(x46222)))),f862(f862(f9(x46221,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(x46222))))),x46227),x46224)),x46225)),x46226)),f204(x46221,x46222,x46223,x46227,x46224,x46225,x46226))
% 25.54/25.41 [4613]E(f188(x46131,x46132,f862(f862(f862(x46133,x46134),x46135),x46136),f862(f862(f9(x46131,f931(a92,a92),f932(a92,f926(f928(x46132)))),f862(f862(f9(x46131,a92,f932(f931(a92,a92),f932(a92,f926(f928(x46132))))),f862(f862(f9(x46131,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x46132)))))),x46137),x46134)),x46135)),x46136)),f862(f862(f862(f198(x46131,x46132,x46133,x46137),x46134),x46135),x46136))
% 25.54/25.41 [4624]E(f189(x46241,x46242,f862(f862(f862(x46243,x46244),x46245),x46246),f862(f862(f9(x46241,f931(a92,a92),f932(a92,f926(f928(x46242)))),f862(f862(f9(x46241,a92,f932(f931(a92,a92),f932(a92,f926(f928(x46242))))),f862(f862(f9(x46241,a92,f932(a92,f932(f931(a92,a92),f932(a92,f926(f928(x46242)))))),x46247),x46244)),x46245)),x46246)),f200(x46241,x46242,x46243,x46247,x46244,x46245,x46246))
% 25.54/25.41 [4521]E(f862(f250(x45211,x45212,x45213,x45214,x45215,x45216),f862(f862(f244(x45211,x45213),x45217),x45218)),f862(f862(f244(x45212,x45214),f862(x45215,x45217)),f862(x45216,x45218)))
% 25.54/25.41 [4626]E(f862(f862(f147(f931(x46261,x46262),f931(x46263,x46264)),f862(f249(x46261,x46262,f931(x46263,x46264)),f862(f862(f9(x46261,f932(x46262,x46264),f932(x46262,f931(x46263,x46264))),f862(f862(f10(f932(x46264,f931(x46263,x46264)),f932(f932(x46262,x46264),f932(x46262,f931(x46263,x46264))),x46261),f10(x46264,f931(x46263,x46264),x46262)),f862(f862(f10(x46263,f932(x46264,f931(x46263,x46264)),x46261),f244(x46263,x46264)),x46265))),x46266))),f862(f862(f174(x46261,x46262),x46267),x46268)),f862(f862(f174(x46263,x46264),f862(f862(f147(x46261,x46263),x46265),x46267)),f862(f862(f147(x46262,x46264),x46266),x46268)))
% 25.54/25.41 [4629]E(f862(f862(f147(f931(x46291,x46292),x46293),f862(f249(x46291,x46292,x46293),f862(f862(f10(f932(x46292,f931(x46291,x46294)),f932(x46292,x46293),x46291),f862(f10(f931(x46291,x46294),x46293,x46292),x46295)),f862(f862(f9(x46291,f932(x46292,x46294),f932(x46292,f931(x46291,x46294))),f862(f862(f10(f932(x46294,f931(x46291,x46294)),f932(f932(x46292,x46294),f932(x46292,f931(x46291,x46294))),x46291),f10(x46294,f931(x46291,x46294),x46292)),f244(x46291,x46294))),x46296)))),f862(f862(f174(x46291,x46292),x46297),x46298)),f862(f862(f147(f931(x46291,x46294),x46293),x46295),f862(f862(f174(x46291,x46294),x46297),f862(f862(f147(x46292,x46294),x46296),x46298))))
% 25.54/25.41 [4557]E(f862(f862(f147(f931(x45571,x45572),x45573),f862(f249(x45571,x45572,x45573),f862(f862(f10(f932(x45572,f931(x45574,x45572)),f932(x45572,x45573),x45571),f862(f10(f931(x45574,x45572),x45573,x45572),x45575)),f862(f862(f10(x45574,f932(x45572,f931(x45574,x45572)),x45571),f244(x45574,x45572)),x45576)))),f862(f862(f174(x45571,x45572),x45577),x45578)),f862(f862(f147(f931(x45574,x45572),x45573),x45575),f862(f862(f174(x45574,x45572),f862(f862(f147(x45571,x45574),x45576),x45577)),x45578)))
% 25.54/25.41 [4512]E(f862(f862(f249(x45121,x45122,x45123),f862(f862(f10(f932(x45122,f931(x45124,x45125)),f932(x45122,x45123),x45121),f862(f10(f931(x45124,x45125),x45123,x45122),f862(f249(x45124,x45125,x45123),x45126))),x45127)),x45128),f862(f862(f249(x45124,x45125,x45123),x45126),f862(f862(f249(x45121,x45122,f931(x45124,x45125)),x45127),x45128)))
% 25.54/25.41 [4630]E(f862(f862(f33(f931(x46301,x46302),f932(f931(x46303,x46304),a921)),f862(f862(f246(x46301,x46302),x46305),f862(f18(f932(x46302,a921),x46301),x46306))),f862(f249(x46301,x46302,f932(f931(x46303,x46304),a921)),f862(f862(f9(x46301,f932(x46302,f932(x46303,f932(x46304,a921))),f932(x46302,f932(f931(x46303,x46304),a921))),f862(f862(f10(f932(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921)),f932(f932(x46302,f932(x46303,f932(x46304,a921))),f932(x46302,f932(f931(x46303,x46304),a921))),x46301),f10(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921),x46302)),f862(f862(f10(f932(x46303,a921),f932(f932(x46303,f932(x46304,a921)),f932(f931(x46303,x46304),a921)),x46301),f246(x46303,x46304)),x46307))),f862(f862(f10(f932(x46304,a921),f932(x46303,f932(x46304,a921)),x46302),f18(f932(x46304,a921),x46303)),x46308)))),f862(f862(f246(x46303,x46304),f862(f862(f33(x46301,f932(x46303,a921)),x46305),x46307)),f862(f18(f932(x46304,a921),x46303),f862(f862(f33(x46302,f932(x46304,a921)),x46306),x46308))))
% 25.54/25.41 [4571]E(f862(f862(f251(x45711,x45712,x45713,x45714),f862(f862(f251(x45711,x45715,x45716,f931(x45712,x45713)),x45717),x45718)),x45719),f862(f862(f251(x45711,x45715,x45716,x45714),x45717),f862(f862(f9(x45715,f932(x45712,f932(x45713,x45714)),f932(x45716,x45714)),f862(f862(f10(f932(x45716,f931(x45712,x45713)),f932(f932(x45712,f932(x45713,x45714)),f932(x45716,x45714)),x45715),f251(x45716,x45712,x45713,x45714)),x45718)),x45719)))
% 25.54/25.41 [4599]E(f862(f66(f931(x45991,x45992),f931(x45993,x45994),f931(x45995,x45996),f250(x45991,x45993,x45992,x45994,x45997,x45998)),f250(x45995,x45991,x45996,x45992,x45999,x459910)),f250(x45995,x45993,x45996,x45994,f862(f66(x45991,x45993,x45995,x45997),x45999),f862(f66(x45992,x45994,x45996,x45998),x459910)))
% 25.54/25.41 [4600]E(f862(f66(f931(x46001,x46002),f931(x46003,x46004),f931(x46005,x46006),f250(x46001,x46003,x46002,x46004,x46007,x46008)),f250(x46005,x46001,x46006,x46002,x46009,x460010)),f250(x46005,x46003,x46006,x46004,f862(f66(x46001,x46003,x46005,x46007),x46009),f862(f66(x46002,x46004,x46006,x46008),x460010)))
% 25.54/25.41 [4606]E(f862(f250(x46061,x46062,x46063,x46064,x46065,x46066),f862(f250(x46067,x46061,x46068,x46063,x46069,x460610),x460611)),f862(f250(x46067,x46062,x46068,x46064,f862(f66(x46061,x46062,x46067,x46065),x46069),f862(f66(x46063,x46064,x46068,x46066),x460610)),x460611))
% 25.54/25.41 [4773]~P150(x47731,a861)+P152(x47731,a863)
% 25.54/25.41 [4742]~P2(x47421)+E(f84(x47421),a317)
% 25.54/25.41 [4743]~P2(x47431)+E(f84(x47431),a317)
% 25.54/25.41 [4744]~P60(x47441)+P60(f928(x47441))
% 25.54/25.41 [4745]~P63(x47451)+P63(f928(x47451))
% 25.54/25.41 [4746]~P106(x47461)+P106(f925(x47461))
% 25.54/25.41 [4748]~P145(x47481)+~E(f71(x47481),f2(x47481))
% 25.54/25.41 [4749]~P145(x47491)+~E(f71(x47491),f2(x47491))
% 25.54/25.41 [4751]~E(x47511,f2(a92))+E(f862(a24,x47511),f2(a1))
% 25.54/25.41 [4752]~E(x47521,f2(a1))+E(f75(a1,x47521),f2(a1))
% 25.54/25.41 [4758]~P147(x47581)+P26(x47581,f2(x47581))
% 25.54/25.41 [4759]~P109(x47591)+P11(x47591,f106(x47591))
% 25.54/25.41 [4760]~P109(x47601)+P11(x47601,f106(x47601))
% 25.54/25.41 [4769]P1(x47691)+P1(f862(a314,x47691))
% 25.54/25.41 [4825]~P147(x48251)+~P26(x48251,f71(x48251))
% 25.54/25.41 [4863]~P1(x48631)+~P1(f862(a314,x48631))
% 25.54/25.41 [4884]E(f862(a97,x48841),f2(a924))+~P1(f862(a186,x48841))
% 25.54/25.41 [4951]~P69(x49511)+P14(x49511,x49511,f74(x49511))
% 25.54/25.41 [4952]~P103(x49521)+P12(x49521,x49521,f103(x49521))
% 25.54/25.41 [4953]~P104(x49531)+P12(x49531,x49531,f94(x49531))
% 25.54/25.41 [4954]~P100(x49541)+P12(x49541,x49541,f74(x49541))
% 25.54/25.41 [4955]~P109(x49551)+P12(x49551,x49551,f225(x49551))
% 25.54/25.41 [4956]~P109(x49561)+P12(x49561,x49561,f226(x49561))
% 25.54/25.41 [4755]~E(x47551,f2(a924))+E(f862(f93(a1),x47551),f2(a1))
% 25.54/25.41 [4761]~P98(x47611)+E(f862(f96(x47611),a76),f2(x47611))
% 25.54/25.41 [4762]~P98(x47621)+E(f862(f96(x47621),a76),f2(x47621))
% 25.54/25.41 [4765]~E(f656(x47651),f2(a924))+E(f862(f158(a924),x47651),f2(a924))
% 25.54/25.41 [4766]~P108(x47661)+E(f229(x47661,f227(x47661)),f225(x47661))
% 25.54/25.41 [4767]~P108(x47671)+E(f230(x47671,f227(x47671)),f226(x47671))
% 25.54/25.41 [4768]~P88(x47681)+E(f75(x47681,f2(x47681)),f2(x47681))
% 25.54/25.41 [4778]~P147(x47781)+E(f862(f93(x47781),f71(a924)),f71(x47781))
% 25.54/25.41 [4779]~P147(x47791)+E(f862(f93(x47791),f2(a924)),f2(x47791))
% 25.54/25.41 [4780]~P142(x47801)+E(f862(f95(x47801),f71(a1)),f71(x47801))
% 25.54/25.41 [4781]~P142(x47811)+E(f862(f95(x47811),f2(a1)),f2(x47811))
% 25.54/25.41 [4782]E(x47821,f2(a924))+~E(f862(f93(a1),x47821),f2(a1))
% 25.54/25.41 [4819]~P96(x48191)+E(f862(f72(x48191),f181(x48191)),f234(x48191))
% 25.54/25.41 [4820]~P96(x48201)+E(f862(f72(x48201),f234(x48201)),f181(x48201))
% 25.54/25.41 [4821]~P68(x48211)+E(f862(f72(x48211),f2(x48211)),f2(x48211))
% 25.54/25.41 [4822]~P112(x48221)+E(f862(f69(x48221),f71(x48221)),f71(x48221))
% 25.54/25.41 [4823]~P86(x48231)+E(f862(f69(x48231),f2(x48231)),f2(x48231))
% 25.54/25.41 [4824]~P81(x48241)+E(f862(f158(x48241),f106(x48241)),f2(x48241))
% 25.54/25.41 [4842]~P34(x48421)+P38(f862(f165(a1),x48421))
% 25.54/25.41 [4867]~P98(x48671)+E(f862(f72(x48671),f71(x48671)),f862(f96(x48671),a90))
% 25.54/25.41 [4868]~P98(x48681)+E(f862(f72(x48681),f71(x48681)),f862(f96(x48681),a90))
% 25.54/25.41 [4883]~P98(x48831)+P26(x48831,f862(f96(x48831),a76))
% 25.54/25.41 [4909]P34(x49091)+~P38(f862(f165(a1),x49091))
% 25.54/25.41 [4957]E(f862(f93(a1),f862(a97,x49571)),x49571)+P1(f862(a186,x49571))
% 25.54/25.41 [5027]~P116(x50271)+E(f237(x50271,f71(x50271),f74(x50271)),f236(x50271))
% 25.54/25.41 [5060]~P98(x50601)+~P26(x50601,f862(f96(x50601),a90))
% 25.54/25.41 [5155]~E(x51551,f2(a924))+P1(f862(f862(f227(a924),x51551),f2(a924)))
% 25.54/25.41 [5156]~E(x51561,f71(a924))+P1(f862(f862(f278(a924),x51561),f71(a924)))
% 25.54/25.41 [5215]E(f862(f69(a1),x52151),x52151)+P1(f862(f862(f228(a1),x52151),f2(a1)))
% 25.54/25.41 [5233]~E(f862(a97,x52331),f2(a924))+P1(f862(f862(f227(a1),x52331),f2(a1)))
% 25.54/25.41 [5299]~P1(f862(a186,x52991))+P1(f862(f862(f228(a1),x52991),f2(a1)))
% 25.54/25.41 [5339]~P142(x53391)+P1(f862(f862(f321(x53391),f71(x53391)),f102(x53391)))
% 25.54/25.41 [5340]~P147(x53401)+P1(f862(f862(f321(x53401),f71(x53401)),f179(x53401)))
% 25.54/25.41 [5341]~P142(x53411)+P1(f862(f862(f321(x53411),f2(x53411)),f102(x53411)))
% 25.54/25.41 [5342]~P147(x53421)+P1(f862(f862(f321(x53421),f2(x53421)),f179(x53421)))
% 25.54/25.41 [5343]~P127(x53431)+P1(f862(f862(f227(x53431),f2(x53431)),f71(x53431)))
% 25.54/25.41 [5344]~P127(x53441)+P1(f862(f862(f228(x53441),f2(x53441)),f71(x53441)))
% 25.54/25.41 [5398]E(x53981,f71(a924))+~P1(f862(f862(f278(a924),x53981),f71(a924)))
% 25.54/25.41 [5399]E(x53991,f2(a924))+~P1(f862(f862(f227(a924),x53991),f2(a924)))
% 25.54/25.41 [5441]E(f862(a97,x54411),f2(a924))+~P1(f862(f862(f227(a1),x54411),f2(a1)))
% 25.54/25.41 [5442]E(f862(a97,x54421),f2(a924))+~P1(f862(f862(f227(a1),x54421),f2(a1)))
% 25.54/25.41 [5498]P1(f862(a186,x54981))+~P1(f862(f862(f228(a1),x54981),f2(a1)))
% 25.54/25.41 [5505]~P109(x55051)+P14(x55051,f925(x55051),f141(x55051,x55051,f7(x55051)))
% 25.54/25.41 [5523]P38(x55231)+~P1(f862(f862(f227(a1),f2(a1)),f424(x55231)))
% 25.54/25.41 [5528]E(f862(f69(a1),x55281),f862(f72(a1),x55281))+~P1(f862(f862(f228(a1),x55281),f2(a1)))
% 25.54/25.41 [5701]~P127(x57011)+~P1(f862(f862(f227(x57011),f71(x57011)),f2(x57011)))
% 25.54/25.41 [5702]~P127(x57021)+~P1(f862(f862(f228(x57021),f71(x57021)),f2(x57021)))
% 25.54/25.41 [5718]~E(x57181,f2(a924))+P1(f862(f862(f227(a1),f862(f93(a1),x57181)),f2(a1)))
% 25.54/25.41 [5719]~E(x57191,f2(a1))+P1(f862(f862(f228(a1),f862(f69(a1),x57191)),f71(a1)))
% 25.54/25.41 [5843]~P81(x58431)+E(f135(x58431,x58431,f73(x58431),f2(x58431)),f158(x58431))
% 25.54/25.41 [6026]~P105(x60261)+P22(a924,x60261,f93(x60261),f234(f932(a924,a921)))
% 25.54/25.41 [6229]E(x62291,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x62291)),f2(a1)))
% 25.54/25.41 [6230]E(x62301,f2(a1))+~P1(f862(f862(f228(a1),f862(f69(a1),x62301)),f71(a1)))
% 25.54/25.41 [7030]~P1(f862(f862(f228(a1),x70301),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x70301),x70301)),f2(a1)))
% 25.54/25.41 [7593]P1(f862(f862(f228(a1),x75931),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75931),x75931)),f2(a1)))
% 25.54/25.41 [8144]E(x81441,f862(a5,f2(a924)))+P1(f862(f862(f228(a924),f862(f862(f3(a924),f862(a22,x81441)),f862(a105,f2(a924)))),f862(a22,x81441)))
% 25.54/25.41 [8920]~P1(f862(f862(f228(a1),x89201),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89201),x89201)),a90)),f2(a1)))
% 25.54/25.41 [9017]~P1(f862(f862(f228(a1),x90171),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x90171)),x90171)),f2(a1)))
% 25.54/25.41 [9339]P1(f862(f862(f228(a1),x93391),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93391),x93391)),a90)),f2(a1)))
% 25.54/25.41 [9401]P1(f862(f862(f228(a1),x94011),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f73(a1),f71(a1)),x94011)),x94011)),f2(a1)))
% 25.54/25.41 [4857]~E(a76,x48571)+E(f862(f862(f73(a1),x48571),x48571),a76)
% 25.54/25.41 [4858]~E(x48581,a76)+E(f862(f862(f73(a1),x48581),x48581),a76)
% 25.54/25.41 [4869]E(x48691,f2(a1))+E(f862(f862(f29(a1),x48691),x48691),f71(a1))
% 25.54/25.41 [5004]E(x50041,a76)+~E(f862(f862(f73(a1),x50041),x50041),a76)
% 25.54/25.41 [5005]E(a76,x50051)+~E(f862(f862(f73(a1),x50051),x50051),a76)
% 25.54/25.41 [5007]~P98(x50071)+E(f862(f95(x50071),f862(f96(a1),a90)),f862(f96(x50071),a90))
% 25.54/25.41 [5017]~P3(x50171)+E(f31(x50171,f181(f932(x50171,a921))),f234(x50171))
% 25.54/25.41 [5018]~P3(x50181)+E(f31(x50181,f234(f932(x50181,a921))),f181(x50181))
% 25.54/25.41 [5019]~P3(x50191)+E(f30(x50191,f181(f932(x50191,a921))),f181(x50191))
% 25.54/25.41 [5020]~P3(x50201)+E(f30(x50201,f234(f932(x50201,a921))),f234(x50201))
% 25.54/25.41 [5021]~P109(x50211)+E(f132(x50211,f181(f932(x50211,a921))),f106(x50211))
% 25.54/25.41 [5167]E(x51671,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),x51671))
% 25.54/25.41 [5168]E(x51681,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),x51681))
% 25.54/25.41 [5189]~P4(x51891)+P1(f862(f862(f227(a1),f2(a1)),x51891))
% 25.54/25.41 [5223]~E(f862(f96(a924),x52231),f2(a924))+P1(f862(f862(f227(a1),x52231),a76))
% 25.54/25.41 [5224]~E(f862(f96(a924),x52241),f2(a924))+P1(f862(f862(f227(a1),x52241),a76))
% 25.54/25.41 [5229]P38(x52291)+P1(f862(f862(f321(a1),f424(x52291)),x52291))
% 25.54/25.41 [5230]E(x52301,f862(a5,f2(a924)))+P1(f862(f862(f227(a92),f71(a92)),x52301))
% 25.54/25.41 [5271]P1(f862(a186,x52711))+P1(f862(f862(f227(a1),f2(a1)),x52711))
% 25.54/25.41 [5321]E(f862(f93(a1),f862(a97,x53211)),f2(a1))+P1(f862(f862(f227(a1),f2(a1)),x53211))
% 25.54/25.41 [5364]~P60(x53641)+P1(f862(f54(x53641),f234(f932(x53641,a921))))
% 25.54/25.41 [5378]E(f862(f93(a1),f862(f96(a924),x53781)),f862(f96(a1),x53781))+P1(f862(a186,f862(f96(a1),x53781)))
% 25.54/25.41 [5381]~E(x53811,f2(a924))+P1(f862(f862(f228(a924),x53811),f862(a105,f2(a924))))
% 25.54/25.41 [5404]E(f862(f96(a924),x54041),f2(a924))+~P1(f862(f862(f227(a1),x54041),a76))
% 25.54/25.41 [5405]E(f862(f96(a924),x54051),f2(a924))+~P1(f862(a186,f862(f96(a1),x54051)))
% 25.54/25.41 [5406]E(f862(f96(a924),x54061),f2(a924))+~P1(f862(f862(f227(a1),x54061),a76))
% 25.54/25.41 [5439]P4(x54391)+~P1(f862(f862(f227(a1),f2(a1)),x54391))
% 25.54/25.41 [5452]~E(x54521,f2(a924))+~P1(f862(f862(f228(a924),f2(a924)),x54521))
% 25.54/25.41 [5508]E(f862(a105,f328(x55081)),x55081)+~P1(f862(f862(f228(a924),f2(a924)),x55081))
% 25.54/25.41 [5517]E(f862(a105,f862(f96(a924),x55171)),f71(a924))+~P1(f862(a186,f862(f96(a1),x55171)))
% 25.54/25.41 [5524]E(f862(f93(a1),f432(x55241)),x55241)+~P1(f862(f862(f228(a1),f2(a1)),x55241))
% 25.54/25.41 [5531]~E(x55311,f862(a5,f2(a924)))+~P1(f862(f862(f227(a92),f71(a92)),x55311))
% 25.54/25.41 [5538]E(f862(f93(a1),f862(f96(a924),x55381)),f2(a1))+~P1(f862(a186,f862(f96(a1),x55381)))
% 25.54/25.41 [5565]E(f862(f158(a924),x55651),f2(a924))+P1(f862(f862(f321(a924),f656(x55651)),f862(f165(a924),x55651)))
% 25.54/25.41 [5585]E(f862(f93(a1),f862(a97,x55851)),x55851)+~P1(f862(f862(f227(a1),f2(a1)),x55851))
% 25.54/25.41 [5586]E(f862(f93(a1),f862(a97,x55861)),x55861)+~P1(f862(f862(f227(a1),f2(a1)),x55861))
% 25.54/25.41 [5594]~P1(f862(a186,x55941))+~P1(f862(f862(f227(a1),f2(a1)),x55941))
% 25.54/25.41 [5694]E(f862(f862(f73(a924),f71(a924)),f862(f96(a924),x56941)),f71(a924))+~P1(f862(f862(f228(a1),x56941),a76))
% 25.54/25.41 [5762]E(x57621,f2(a924))+~P1(f862(f862(f228(a924),x57621),f862(a105,f2(a924))))
% 25.54/25.41 [5802]E(f862(f862(f3(a924),f862(f96(a924),x58021)),f71(a924)),f2(a924))+~P1(f862(f862(f227(a1),x58021),a76))
% 25.54/25.41 [5803]E(f862(f862(f73(a924),f862(f96(a924),x58031)),f71(a924)),f71(a924))+~P1(f862(f862(f228(a1),x58031),a76))
% 25.54/25.41 [5815]~P38(x58151)+E(f862(f28(a924),f862(f302(a1,a924,a97),x58151)),f862(f28(a1),x58151))
% 25.54/25.41 [5844]~P109(x58441)+E(f229(x58441,f862(f9(x58441,x58441,a921),f227(x58441))),f226(x58441))
% 25.54/25.41 [5845]~P109(x58451)+E(f230(x58451,f862(f9(x58451,x58451,a921),f227(x58451))),f225(x58451))
% 25.54/25.41 [5855]E(f38(a924,f862(a105,f2(a924)),f862(f96(a924),x58551)),f862(a105,f2(a924)))+~P1(f862(a186,f862(f96(a1),x58551)))
% 25.54/25.41 [5864]~P1(f862(f862(f228(a1),f2(a1)),x58641))+P1(f862(f862(f227(a1),f71(a1)),x58641))
% 25.54/25.41 [5865]P1(f862(f862(f228(a1),f2(a1)),x58651))+~P1(f862(f862(f227(a1),f71(a1)),x58651))
% 25.54/25.41 [5875]E(f862(a105,f862(f862(f3(a924),x58751),f71(a924))),x58751)+~P1(f862(f862(f228(a924),f2(a924)),x58751))
% 25.54/25.41 [5876]E(f862(a105,f862(f862(f3(a924),x58761),f71(a924))),x58761)+~P1(f862(f862(f228(a924),f2(a924)),x58761))
% 25.54/25.41 [5932]P1(f862(f862(f228(a924),f2(a924)),f432(x59321)))+~P1(f862(f862(f228(a1),f2(a1)),x59321))
% 25.54/25.41 [5993]E(f38(a1,f862(f96(a1),a90),x59931),f862(f862(f3(a1),x59931),f71(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x59931))
% 25.54/25.41 [6039]~P1(f862(f862(f228(a1),a76),x60391))+P1(f862(f862(f228(a924),f2(a924)),f862(f96(a924),x60391)))
% 25.54/25.41 [6044]E(f862(a22,f814(x60441)),x60441)+~P1(f862(f862(f321(a924),x60441),f234(f932(a924,a921))))
% 25.54/25.41 [6097]P1(f862(f862(f228(a924),f2(a924)),f862(a97,x60971)))+~P1(f862(f862(f228(a1),f2(a1)),x60971))
% 25.54/25.41 [6116]E(f862(a22,f862(a5,x61161)),x61161)+~P1(f862(f862(f321(a924),x61161),f234(f932(a924,a921))))
% 25.54/25.41 [6147]~P1(f862(f862(f228(a924),f2(a924)),x61471))+P1(f862(f862(f228(a1),f2(a1)),f862(f93(a1),x61471)))
% 25.54/25.41 [6182]~P1(f862(f862(f228(a924),f2(a924)),f862(a97,x61821)))+P1(f862(f862(f228(a1),f2(a1)),x61821))
% 25.54/25.41 [6196]~P38(x61961)+E(f862(f302(a924,a1,f93(a1)),f862(f302(a1,a924,a97),x61961)),x61961)
% 25.54/25.41 [6209]P1(f862(f862(f228(a1),a76),x62091))+~P1(f862(f862(f228(a924),f2(a924)),f862(f96(a924),x62091)))
% 25.54/25.41 [6265]P1(f862(f862(f228(a924),f2(a924)),x62651))+~P1(f862(f862(f228(a1),f2(a1)),f862(f93(a1),x62651)))
% 25.54/25.41 [6300]E(f172(x63001,f106(f925(x63001))),f106(f925(x63001)))+~P1(f862(f307(f925(f925(x63001)),f173(x63001)),f106(f925(x63001))))
% 25.54/25.41 [6380]E(f862(f302(a924,a1,f93(a1)),f862(f292(a924),f862(a97,x63801))),f862(f295(a1,f2(a1)),x63801))+~P1(f862(f862(f227(a1),f2(a1)),x63801))
% 25.54/25.41 [6397]~P127(x63971)+P1(f862(f862(f228(x63971),f2(x63971)),f862(f862(f73(x63971),f71(x63971)),f71(x63971))))
% 25.54/25.41 [6446]P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(a97,x64461)))+~P1(f862(f862(f228(a1),f71(a1)),x64461))
% 25.54/25.41 [6546]E(x65461,f2(a1))+P1(f862(f42(f2(a1),x65461),f862(f862(f244(a1,a1),f2(a1)),f2(a1))))
% 25.54/25.41 [6717]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(a97,x67171)))+P1(f862(f862(f228(a1),f71(a1)),x67171))
% 25.54/25.41 [6765]E(f862(a105,f862(f862(f3(a924),f862(f96(a924),x67651)),f71(a924))),f862(f96(a924),x67651))+~P1(f862(f862(f228(a924),f2(a924)),f862(f96(a924),x67651)))
% 25.54/25.41 [7142]~P117(x71421)+P35(x71421,f862(f254(f931(x71421,x71421)),f862(f249(x71421,x71421,a921),f228(x71421))))
% 25.54/25.41 [5749]E(f862(f96(a924),f862(f862(f3(a1),x57491),a90)),f862(a105,f862(f96(a924),x57491)))+P1(f862(a186,f862(f96(a1),x57491)))
% 25.54/25.41 [5765]~P34(x57651)+E(f862(f862(f147(a924,a1),f93(a1)),f862(f862(f147(a1,a924),a97),x57651)),x57651)
% 25.54/25.41 [5882]E(f862(f72(a1),f862(f93(a1),f862(a105,f419(x58821)))),x58821)+~P1(f862(f862(f228(a1),x58821),f2(a1)))
% 25.54/25.41 [5892]E(f862(f862(f73(a924),f71(a924)),f862(f96(a924),x58921)),f862(f96(a924),f862(f862(f3(a1),x58921),a90)))+P1(f862(f862(f228(a1),x58921),a76))
% 25.54/25.41 [5934]E(f862(f862(f29(a1),f862(f96(a1),a90)),x59341),f862(f96(a1),a90))+~P1(f862(f862(f228(a1),f2(a1)),x59341))
% 25.54/25.41 [6035]E(f862(f862(f3(a924),f862(f96(a924),x60351)),f71(a924)),f862(f96(a924),f862(f862(f73(a1),x60351),a90)))+P1(f862(f862(f227(a1),x60351),a76))
% 25.54/25.41 [6036]E(f862(f862(f73(a924),f862(f96(a924),x60361)),f71(a924)),f862(f96(a924),f862(f862(f3(a1),x60361),a90)))+P1(f862(f862(f228(a1),x60361),a76))
% 25.54/25.41 [6082]E(f862(a97,f862(f862(f73(a1),f71(a1)),x60821)),f862(a105,f862(a97,x60821)))+~P1(f862(f862(f227(a1),f2(a1)),x60821))
% 25.54/25.41 [6118]E(f862(a105,f862(f862(f3(a924),x61181),f862(a105,f2(a924)))),x61181)+~P1(f862(f862(f228(a924),f2(a924)),x61181))
% 25.54/25.41 [6330]E(f38(a924,f862(a105,f2(a924)),f862(f96(a924),x63301)),f862(a97,f38(a1,f71(a1),f862(f96(a1),x63301))))+P1(f862(a186,f862(f96(a1),x63301)))
% 25.54/25.41 [6372]~P1(f862(f862(f84(a1),a76),x63721))+P1(f862(f862(f84(a1),a76),f862(f862(f73(a1),x63721),x63721)))
% 25.54/25.41 [6373]~P1(f862(f862(f228(a1),a90),x63731))+P1(f862(f862(f227(a1),a90),f862(f862(f73(a1),x63731),x63731)))
% 25.54/25.41 [6374]~P1(f862(f862(f227(a1),a76),x63741))+P1(f862(f862(f227(a1),a76),f862(f862(f73(a1),x63741),x63741)))
% 25.54/25.41 [6375]~P1(f862(f862(f228(a1),a90),x63751))+P1(f862(f862(f228(a1),a90),f862(f862(f73(a1),x63751),x63751)))
% 25.54/25.41 [6376]~P1(f862(f862(f228(a1),a76),x63761))+P1(f862(f862(f228(a1),a76),f862(f862(f73(a1),x63761),x63761)))
% 25.54/25.41 [6560]~P1(f862(f54(x65601),f234(f932(x65601,a921))))+P1(f862(f54(f928(x65601)),f234(f932(f928(x65601),a921))))
% 25.54/25.41 [6647]~P1(f862(f862(f227(a1),f2(a1)),x66471))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f73(a1),f71(a1)),x66471)))
% 25.54/25.41 [6654]E(f862(f243(a1,a1),f40(f71(a1),f862(f96(a1),x66541))),f862(f862(f29(a1),f71(a1)),f862(f96(a1),x66541)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x66541)))
% 25.54/25.41 [6676]E(f862(f248(a1,a1),f40(f71(a1),f862(f96(a1),x66761))),f38(a1,f71(a1),f862(f96(a1),x66761)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x66761)))
% 25.54/25.41 [6688]P1(f862(f54(x66881),f234(f932(x66881,a921))))+~P1(f862(f54(f928(x66881)),f234(f932(f928(x66881),a921))))
% 25.54/25.41 [6718]P1(f862(f862(f84(a1),a76),x67181))+~P1(f862(f862(f84(a1),a76),f862(f862(f73(a1),x67181),x67181)))
% 25.54/25.41 [6719]P1(f862(f862(f227(a1),a76),x67191))+~P1(f862(f862(f227(a1),a76),f862(f862(f73(a1),x67191),x67191)))
% 25.54/25.41 [6720]P1(f862(f862(f228(a1),a90),x67201))+~P1(f862(f862(f227(a1),a90),f862(f862(f73(a1),x67201),x67201)))
% 25.54/25.41 [6721]P1(f862(f862(f228(a1),a90),x67211))+~P1(f862(f862(f228(a1),a90),f862(f862(f73(a1),x67211),x67211)))
% 25.54/25.41 [6722]P1(f862(f862(f228(a1),a76),x67221))+~P1(f862(f862(f228(a1),a76),f862(f862(f73(a1),x67221),x67221)))
% 25.54/25.41 [6908]~P1(f862(f54(a924),x69081))+P1(f862(f54(a1),f862(f302(a924,a1,f93(a1)),x69081)))
% 25.54/25.41 [7034]~P1(f862(f54(x70341),f234(f932(x70341,a921))))+P1(f862(f862(f228(a924),f2(a924)),f862(f28(x70341),f234(f932(x70341,a921)))))
% 25.54/25.41 [7631]P1(f862(f54(a924),x76311))+~P1(f862(f54(a1),f862(f302(a924,a1,f93(a1)),x76311)))
% 25.54/25.41 [5670]~E(a90,x56701)+E(f862(f862(f3(a1),f862(f862(f73(a1),x56701),x56701)),a90),a90)
% 25.54/25.41 [5671]~E(x56711,a90)+E(f862(f862(f3(a1),f862(f862(f73(a1),x56711),x56711)),a90),a90)
% 25.54/25.41 [6204]E(x62041,a90)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x62041),x62041)),a90),a90)
% 25.54/25.41 [6205]E(a90,x62051)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x62051),x62051)),a90),a90)
% 25.54/25.41 [6616]~E(f862(f96(a924),x66161),f2(a924))+P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x66161),a90))))
% 25.54/25.41 [6963]~P1(f862(a186,f862(f96(a1),x69631)))+P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x69631),x69631))))
% 25.54/25.41 [6964]~P1(f862(f862(f84(a1),x69641),a76))+P1(f862(f862(f84(a1),f862(f862(f73(a1),x69641),x69641)),a76))
% 25.54/25.41 [6965]~P1(f862(f862(f227(a1),x69651),a90))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x69651),x69651)),a90))
% 25.54/25.41 [6966]~P1(f862(f862(f227(a1),x69661),a76))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x69661),x69661)),a76))
% 25.54/25.41 [6967]~P1(f862(f862(f227(a1),x69671),a90))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69671),x69671)),a90))
% 25.54/25.41 [6968]~P1(f862(f862(f228(a1),x69681),a76))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69681),x69681)),a76))
% 25.54/25.41 [7289]E(f862(f96(a924),x72891),f2(a924))+~P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x72891),a90))))
% 25.54/25.41 [7545]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x75451)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f73(a1),x75451),x75451))))
% 25.54/25.41 [7546]P1(f862(a186,f862(f96(a1),x75461)))+~P1(f862(a186,f862(f96(a1),f862(f862(f73(a1),x75461),x75461))))
% 25.54/25.41 [7547]P1(f862(f862(f84(a1),x75471),a76))+~P1(f862(f862(f84(a1),f862(f862(f73(a1),x75471),x75471)),a76))
% 25.54/25.41 [7548]P1(f862(f862(f227(a1),x75481),a90))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x75481),x75481)),a90))
% 25.54/25.41 [7549]P1(f862(f862(f227(a1),x75491),a90))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75491),x75491)),a90))
% 25.54/25.41 [7550]P1(f862(f862(f227(a1),x75501),a76))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x75501),x75501)),a76))
% 25.54/25.41 [7551]P1(f862(f862(f228(a1),x75511),a76))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75511),x75511)),a76))
% 25.54/25.41 [7912]E(f862(a100,f567(x79121)),x79121)+~P1(f862(f862(f321(f932(f931(a924,a924),a921)),x79121),a91))
% 25.54/25.41 [6532]~P98(x65321)+E(f862(f96(x65321),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(x65321))
% 25.54/25.41 [6533]~P98(x65331)+E(f862(f96(x65331),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f71(x65331))
% 25.54/25.41 [7014]~P1(f862(a186,f862(f96(a1),x70141)))+E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x70141),x70141)),a90)),f2(a924))
% 25.54/25.41 [8088]~P1(f862(f862(f228(a1),f862(f96(a1),x80881)),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f43(f862(f72(a1),f71(a1)),f862(f72(a1),f862(f96(a1),x80881))))),f862(f862(f29(a1),f71(a1)),f862(f96(a1),x80881)))
% 25.54/25.41 [8102]~P1(f862(f862(f228(a1),f862(f96(a1),x81021)),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f43(f862(f72(a1),f71(a1)),f862(f72(a1),f862(f96(a1),x81021))))),f38(a1,f71(a1),f862(f96(a1),x81021)))
% 25.54/25.41 [8151]~P1(f862(f862(f84(a1),a90),x81511))+P1(f862(f862(f84(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81511),x81511)),a90)))
% 25.54/25.41 [8152]~P1(f862(f862(f227(a1),a90),x81521))+P1(f862(f862(f227(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81521),x81521)),a90)))
% 25.54/25.41 [8153]~P1(f862(f862(f227(a1),a76),x81531))+P1(f862(f862(f227(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x81531),x81531)),a90)))
% 25.54/25.41 [8154]~P1(f862(f862(f228(a1),a90),x81541))+P1(f862(f862(f228(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x81541),x81541)),a90)))
% 25.54/25.41 [8155]~P1(f862(f862(f227(a1),a76),x81551))+P1(f862(f862(f228(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x81551),x81551)),a90)))
% 25.54/25.41 [8457]~P98(x84571)+~P26(x84571,f862(f96(x84571),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))
% 25.54/25.41 [8641]P1(f862(f862(f84(a1),a90),x86411))+~P1(f862(f862(f84(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86411),x86411)),a90)))
% 25.54/25.41 [8642]P1(f862(f862(f227(a1),a90),x86421))+~P1(f862(f862(f227(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86421),x86421)),a90)))
% 25.54/25.41 [8643]P1(f862(f862(f227(a1),a76),x86431))+~P1(f862(f862(f227(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x86431),x86431)),a90)))
% 25.54/25.41 [8644]P1(f862(f862(f227(a1),a76),x86441))+~P1(f862(f862(f228(a1),a76),f862(f862(f3(a1),f862(f862(f73(a1),x86441),x86441)),a90)))
% 25.54/25.41 [8645]P1(f862(f862(f228(a1),a90),x86451))+~P1(f862(f862(f228(a1),a90),f862(f862(f3(a1),f862(f862(f73(a1),x86451),x86451)),a90)))
% 25.54/25.41 [8967]E(f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x89671),x89671)),a90)),f862(f862(f79(a924,a924),f862(f96(a924),x89671)),f862(f862(f10(a924,a924,a924),a105),f862(f862(f20(a924,a924,a924),f73(a924)),f7(a924)))))+P1(f862(a186,f862(f96(a1),x89671)))
% 25.54/25.41 [9830]E(x98301,f181(f932(f931(a924,a924),a921)))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x98301),f181(f932(f931(a924,a924),a921)))),a62))
% 25.54/25.41 [8893]~P1(f862(a186,f862(f96(a1),x88931)))+P1(f862(a186,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88931),x88931)),a90))))
% 25.54/25.41 [8894]~P1(f862(f862(f84(a1),x88941),a90))+P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88941),x88941)),a90)),a90))
% 25.54/25.41 [8895]~P1(f862(f862(f227(a1),x88951),a90))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88951),x88951)),a90)),a90))
% 25.54/25.41 [8896]~P1(f862(f862(f228(a1),x88961),a76))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88961),x88961)),a90)),a76))
% 25.54/25.41 [8897]~P1(f862(f862(f228(a1),x88971),a90))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88971),x88971)),a90)),a90))
% 25.54/25.41 [8898]~P1(f862(f862(f228(a1),x88981),a76))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x88981),x88981)),a90)),a76))
% 25.54/25.41 [9008]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x90081)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x90081),x90081)),a90))))
% 25.54/25.41 [9168]~P98(x91681)+E(f862(f862(f73(x91681),f71(x91681)),f71(x91681)),f862(f96(x91681),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))
% 25.54/25.41 [9322]P1(f862(a186,f862(f96(a1),x93221)))+~P1(f862(a186,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93221),x93221)),a90))))
% 25.54/25.41 [9323]P1(f862(f862(f84(a1),x93231),a90))+~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93231),x93231)),a90)),a90))
% 25.54/25.41 [9324]P1(f862(f862(f227(a1),x93241),a90))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93241),x93241)),a90)),a90))
% 25.54/25.41 [9325]P1(f862(f862(f228(a1),x93251),a90))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93251),x93251)),a90)),a90))
% 25.54/25.41 [9326]P1(f862(f862(f228(a1),x93261),a76))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93261),x93261)),a90)),a76))
% 25.54/25.41 [9327]P1(f862(f862(f228(a1),x93271),a76))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93271),x93271)),a90)),a76))
% 25.54/25.41 [9875]~P1(f862(f54(f931(a924,a924)),x98751))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),x98751)),a63))
% 25.54/25.41 [9658]~P147(x96581)+E(f862(f862(f236(x96581),f71(x96581)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96581))
% 25.54/25.41 [9659]~P147(x96591)+E(f862(f862(f236(x96591),f2(x96591)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(x96591))
% 25.54/25.41 [10104]~P1(f862(f862(f228(a924),f71(a924)),x101041))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f29(a924),x101041),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10110]~P1(f862(f862(f228(a924),f2(a924)),x101101))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f29(a924),f862(f862(f73(a924),x101101),f71(a924))),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10148]~E(f38(a924,x101481,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(a924))+P1(f862(f862(f228(a924),f2(a924)),f38(a924,x101481,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10167]E(f38(a924,x101671,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(a924))+~P1(f862(f862(f228(a924),f2(a924)),f38(a924,x101671,f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [4786]~P35(x47861,x47862)+P55(x47861,x47862)
% 25.54/25.41 [4787]~P41(x47871,x47872)+P55(x47871,x47872)
% 25.54/25.41 [4788]~P5(x47881,x47882)+P46(x47881,x47882)
% 25.54/25.41 [4789]~P5(x47891,x47892)+P46(x47891,x47892)
% 25.54/25.41 [4790]~P5(x47901,x47902)+P47(x47901,x47902)
% 25.54/25.41 [4791]~P5(x47911,x47912)+P47(x47911,x47912)
% 25.54/25.41 [4792]~P13(x47921,x47922)+P47(x47921,x47922)
% 25.54/25.41 [4793]~P13(x47931,x47932)+P47(x47931,x47932)
% 25.54/25.41 [4794]~P5(x47941,x47942)+P48(x47941,x47942)
% 25.54/25.41 [4795]~P5(x47951,x47952)+P48(x47951,x47952)
% 25.54/25.41 [4796]~P13(x47961,x47962)+P48(x47961,x47962)
% 25.54/25.41 [4797]~P13(x47971,x47972)+P48(x47971,x47972)
% 25.54/25.41 [4798]~P5(x47981,x47982)+P13(x47981,x47982)
% 25.54/25.41 [4799]~P152(x47991,x47992)+P151(x47991,x47992)
% 25.54/25.41 [4747]~E(x47471,x47472)+E(f261(x47471,x47472),f71(a92))
% 25.54/25.41 [4750]E(f209(x47501,x47502),x47501)+~E(x47502,f2(a924))
% 25.54/25.41 [4756]~E(x47562,f106(x47561))+E(f145(x47561,x47562),f106(x47561))
% 25.54/25.41 [4757]~E(x47572,f106(x47571))+E(f145(x47571,x47572),f106(x47571))
% 25.54/25.41 [4776]~E(f145(x47762,x47761),f106(x47762))+E(x47761,f106(x47762))
% 25.54/25.41 [4777]~E(f145(x47772,x47771),f106(x47772))+E(x47771,f106(x47772))
% 25.54/25.41 [4803]~P3(x48032)+P3(f932(x48031,x48032))
% 25.54/25.41 [4804]~P91(x48042)+P91(f932(x48041,x48042))
% 25.54/25.41 [4805]~P111(x48052)+P111(f932(x48051,x48052))
% 25.54/25.41 [4806]~P92(x48062)+P92(f932(x48061,x48062))
% 25.54/25.41 [4807]~P108(x48072)+P108(f932(x48071,x48072))
% 25.54/25.41 [4808]~P110(x48082)+P110(f932(x48081,x48082))
% 25.54/25.41 [4809]~P93(x48092)+P93(f932(x48091,x48092))
% 25.54/25.41 [4810]~P58(x48102)+P58(f932(x48101,x48102))
% 25.54/25.41 [4811]~P101(x48112)+P94(f932(x48111,x48112))
% 25.54/25.41 [4812]~P93(x48122)+P103(f932(x48121,x48122))
% 25.54/25.41 [4813]~P93(x48132)+P104(f932(x48131,x48132))
% 25.54/25.41 [4814]~P101(x48142)+P95(f932(x48141,x48142))
% 25.54/25.41 [4815]~P102(x48152)+P102(f932(x48151,x48152))
% 25.54/25.41 [4816]~P96(x48162)+P96(f932(x48161,x48162))
% 25.54/25.41 [4817]~P82(x48172)+P82(f932(x48171,x48172))
% 25.54/25.41 [4818]~P101(x48182)+P101(f932(x48181,x48182))
% 25.54/25.41 [4830]E(x48301,x48302)+~E(f862(a105,x48301),f862(a105,x48302))
% 25.54/25.41 [4831]E(x48311,x48312)+~E(f862(a105,x48311),f862(a105,x48312))
% 25.54/25.41 [4832]E(x48321,x48322)+~E(f862(a100,x48321),f862(a100,x48322))
% 25.54/25.41 [4833]E(x48331,x48332)+~E(f862(a5,x48331),f862(a5,x48332))
% 25.54/25.41 [4834]E(x48341,x48342)+~E(f862(a22,x48341),f862(a22,x48342))
% 25.54/25.41 [4835]E(x48351,x48352)+~E(f862(a22,x48351),f862(a22,x48352))
% 25.54/25.41 [4885]P37(x48851,x48852)+~E(f712(x48852,x48851),f713(x48852,x48851))
% 25.54/25.41 [4915]~P55(x49151,x49152)+P37(x49151,f299(x49151,x49152))
% 25.54/25.41 [4916]~P49(x49161,x49162)+P49(x49161,f299(x49161,x49162))
% 25.54/25.41 [4930]~P61(x49301)+E(f38(x49301,x49302,x49302),f2(x49301))
% 25.54/25.41 [4964]~P35(x49641,x49642)+P35(f925(x49641),f139(x49641,x49642))
% 25.54/25.41 [4965]~P35(x49651,x49652)+P35(f925(x49651),f138(x49651,x49652))
% 25.54/25.41 [4966]~P36(x49661,x49662)+P36(f925(x49661),f140(x49661,x49662))
% 25.54/25.41 [4967]~P36(x49671,x49672)+P36(f925(x49671),f151(x49671,x49672))
% 25.54/25.41 [4968]~P49(x49681,x49682)+P49(f925(x49681),f151(x49681,x49682))
% 25.54/25.41 [5065]~P35(x50651,x50652)+P35(f932(x50651,a921),f310(x50651,x50652))
% 25.54/25.41 [5066]~P35(x50661,x50662)+P35(f932(x50661,a921),f312(x50661,x50662))
% 25.54/25.41 [5198]~P4(x51981)+P38(f296(a1,x51981,x51982))
% 25.54/25.41 [5302]~P35(x53021,x53022)+P57(x53021,f60(x53021,x53021,x53022))
% 25.54/25.41 [5809]~P78(x58091)+P22(x58091,x58091,f72(x58091),x58092)
% 25.54/25.41 [4770]~E(x47702,f106(x47701))+E(f862(f161(x47701),x47702),f106(x47701))
% 25.54/25.41 [4771]~E(x47712,f106(x47711))+E(f862(f160(x47711),x47712),f106(x47711))
% 25.54/25.41 [4772]~E(x47722,f106(x47721))+E(f862(f161(x47721),x47722),f106(x47721))
% 25.54/25.41 [4837]E(x48371,f862(a97,x48372))+~E(f862(f93(a1),x48371),x48372)
% 25.54/25.41 [4839]E(x48391,f106(x48392))+~E(f862(f161(x48392),x48391),f106(x48392))
% 25.54/25.41 [4840]E(x48401,f106(x48402))+~E(f862(f160(x48402),x48401),f106(x48402))
% 25.54/25.41 [4841]E(x48411,f106(x48412))+~E(f862(f161(x48412),x48411),f106(x48412))
% 25.54/25.41 [4854]~P98(x48541)+E(f862(f96(x48541),x48542),f862(f95(x48541),x48542))
% 25.54/25.41 [4861]~P60(x48611)+P1(f862(f54(x48611),x48612))
% 25.54/25.41 [4862]~P60(x48621)+P1(f862(f54(x48621),x48622))
% 25.54/25.41 [4870]~E(f672(x48702,x48701),f106(x48701))+E(f172(x48701,x48702),f106(f925(x48701)))
% 25.54/25.41 [4879]~E(x48792,f106(x48791))+E(f862(f165(x48791),x48792),f181(f932(x48791,a921)))
% 25.54/25.41 [4880]~E(x48802,f106(x48801))+E(f181(f932(x48801,a921)),f862(f165(x48801),x48802))
% 25.54/25.41 [4881]E(x48811,x48812)+~E(f862(f93(a1),x48811),f862(f93(a1),x48812))
% 25.54/25.41 [4882]E(x48821,x48822)+~E(f862(f93(a1),x48821),f862(f93(a1),x48822))
% 25.54/25.41 [4886]E(f207(x48861,x48862),f2(a924))+P1(f862(f54(x48861),x48862))
% 25.54/25.41 [4904]~P112(x49041)+E(f75(x49041,f75(x49041,x49042)),f75(x49041,x49042))
% 25.54/25.41 [4918]~P119(x49181)+E(f862(f862(f236(x49181),x49182),f71(a924)),x49182)
% 25.54/25.41 [4919]~P80(x49191)+E(f862(f862(f236(x49191),x49192),f71(a924)),x49192)
% 25.54/25.41 [4920]~P49(x49201,x49202)+E(f862(f277(x49201,x49201),x49202),x49202)
% 25.54/25.41 [4924]E(x49241,x49242)+E(f261(x49241,x49242),f862(f862(f73(a92),x49242),f71(a92)))
% 25.54/25.41 [4925]E(f862(f28(x49251),x49252),f2(a924))+P1(f862(f54(x49251),x49252))
% 25.54/25.41 [4926]E(f862(f28(x49261),x49262),f2(a924))+P1(f862(f54(x49261),x49262))
% 25.54/25.41 [4927]E(f862(f28(x49271),x49272),f2(a924))+P1(f862(f54(x49271),x49272))
% 25.54/25.41 [4931]~E(f145(x49311,x49312),x49312)+P1(f862(f130(x49311),x49312))
% 25.54/25.41 [4934]~P95(x49341)+E(f862(f862(f103(x49341),x49342),f181(x49341)),x49342)
% 25.54/25.41 [4935]~P94(x49351)+E(f862(f862(f94(x49351),x49352),f234(x49351)),x49352)
% 25.54/25.41 [4936]~P68(x49361)+E(f862(f862(f3(x49361),x49362),f2(x49361)),x49362)
% 25.54/25.41 [4937]~P71(x49371)+E(f862(f862(f74(x49371),x49372),f71(x49371)),x49372)
% 25.54/25.41 [4938]~P119(x49381)+E(f862(f862(f74(x49381),x49382),f71(x49381)),x49382)
% 25.54/25.41 [4939]~P80(x49391)+E(f862(f862(f74(x49391),x49392),f71(x49391)),x49392)
% 25.54/25.41 [4940]~P72(x49401)+E(f862(f862(f73(x49401),x49402),f2(x49401)),x49402)
% 25.54/25.41 [4941]~P119(x49411)+E(f862(f862(f73(x49411),x49412),f2(x49411)),x49412)
% 25.54/25.41 [4942]~P81(x49421)+E(f862(f862(f73(x49421),x49422),f2(x49421)),x49422)
% 25.54/25.41 [4943]~P121(x49431)+E(f862(f862(f281(x49431),x49432),f71(x49431)),x49432)
% 25.54/25.41 [4944]~P61(x49441)+E(f862(f862(f29(x49441),x49442),f71(x49441)),x49442)
% 25.54/25.41 [4945]~P119(x49451)+E(f862(f862(f236(x49451),x49452),f2(a924)),f71(x49451))
% 25.54/25.41 [4946]~P116(x49461)+E(f862(f862(f236(x49461),x49462),f2(a924)),f71(x49461))
% 25.54/25.41 [4947]~E(x49472,f181(f932(x49471,a921)))+E(f862(f28(x49471),x49472),f2(a924))
% 25.54/25.41 [4958]~P61(x49581)+E(f38(x49581,x49582,f2(x49581)),x49582)
% 25.54/25.41 [4969]~P94(x49691)+E(f862(f862(f103(x49691),x49692),f234(x49691)),f234(x49691))
% 25.54/25.41 [4970]~P95(x49701)+E(f862(f862(f94(x49701),x49702),f181(x49701)),f181(x49701))
% 25.54/25.41 [4971]~P119(x49711)+E(f862(f862(f74(x49711),x49712),f2(x49711)),f2(x49711))
% 25.54/25.41 [4972]~P134(x49721)+E(f862(f862(f74(x49721),x49722),f2(x49721)),f2(x49721))
% 25.54/25.41 [4973]~P122(x49731)+E(f862(f862(f281(x49731),x49732),f2(x49731)),f2(x49731))
% 25.54/25.41 [4974]~P61(x49741)+E(f862(f862(f29(x49741),x49742),f2(x49741)),f2(x49741))
% 25.54/25.41 [4976]~P61(x49761)+E(f38(x49761,x49762,f71(x49761)),f2(x49761))
% 25.54/25.41 [4977]~P61(x49771)+E(f38(x49771,f2(x49771),x49772),f2(x49771))
% 25.54/25.41 [5006]E(x50061,f2(a924))+E(f48(x50062,x50061,f106(x50062)),f106(f925(x50062)))
% 25.54/25.41 [5029]P49(x50291,x50292)+~E(f862(f277(x50291,x50291),x50292),x50292)
% 25.54/25.41 [5030]P35(x50301,x50302)+~E(f589(x50302,x50301),f181(f932(x50301,a921)))
% 25.54/25.41 [5031]E(x50311,f106(x50312))+~E(f862(f165(x50312),x50311),f181(f932(x50312,a921)))
% 25.54/25.41 [5032]E(x50321,f106(x50322))+~E(f181(f932(x50322,a921)),f862(f165(x50322),x50321))
% 25.54/25.41 [5035]~E(x50351,x50352)+P1(f862(f862(a317,x50351),x50352))
% 25.54/25.41 [5045]P1(x50451)+P1(f862(f862(a322,x50451),x50452))
% 25.54/25.41 [5046]E(x50461,f106(x50462))+E(f862(f862(f157(x50462),x50461),f2(a924)),f862(f134(x50462),x50461))
% 25.54/25.41 [5048]E(f145(x50481,x50482),x50482)+~P1(f862(f130(x50481),x50482))
% 25.54/25.41 [5049]E(f145(x50491,x50492),x50492)+~P1(f862(f130(x50491),x50492))
% 25.54/25.41 [5056]~P1(x50562)+P1(f862(f862(a322,x50561),x50562))
% 25.54/25.41 [5057]~P1(x50572)+P1(f862(f862(a319,x50571),x50572))
% 25.54/25.41 [5058]~P1(x50581)+P1(f862(f862(a319,x50581),x50582))
% 25.54/25.41 [5068]~E(f673(x50682,x50681),f677(x50682,x50681))+P1(f862(f130(x50681),x50682))
% 25.54/25.41 [5075]E(f862(f254(x50751),x50752),f181(f932(x50751,a921)))+P1(f862(x50752,f325(x50752)))
% 25.54/25.41 [5076]E(f181(f932(x50761,a921)),f862(f254(x50761),x50762))+P1(f862(x50762,f326(x50762)))
% 25.54/25.41 [5149]~P112(x51491)+E(f862(f862(f74(x51491),x51492),f75(x51491,x51492)),f862(f69(x51491),x51492))
% 25.54/25.41 [5160]~E(x51601,f2(a1))+E(f39(x51601,x51602),f862(f862(f244(a1,a1),f2(a1)),f2(a1)))
% 25.54/25.41 [5161]~E(x51611,f2(a1))+E(f39(x51611,x51612),f862(f862(f244(a1,a1),f2(a1)),f2(a1)))
% 25.54/25.41 [5194]~P55(x51941,x51942)+P55(x51941,f862(f277(x51941,x51941),x51942))
% 25.54/25.41 [5195]~P36(x51951,x51952)+P36(x51951,f862(f277(x51951,x51951),x51952))
% 25.54/25.41 [5196]~P37(x51961,x51962)+P37(x51961,f862(f277(x51961,x51961),x51962))
% 25.54/25.41 [5197]~P49(x51971,x51972)+P49(x51971,f862(f277(x51971,x51971),x51972))
% 25.54/25.41 [5220]E(x52201,x52202)+~P1(f862(f862(a317,x52201),x52202))
% 25.54/25.41 [5231]P1(x52311)+~P1(f862(f862(a318,x52312),x52311))
% 25.54/25.41 [5232]P1(x52321)+~P1(f862(f862(a318,x52321),x52322))
% 25.54/25.41 [5237]~P111(x52371)+P1(f862(f862(f227(x52371),x52372),f234(x52371)))
% 25.54/25.41 [5238]~P119(x52381)+P1(f862(f862(f278(x52381),x52382),f2(x52381)))
% 25.54/25.41 [5242]E(x52421,x52422)+~E(f862(x52421,f431(x52422,x52421)),f862(x52422,f431(x52422,x52421)))
% 25.54/25.41 [5273]E(x52731,f2(a924))+E(f209(x52731,f38(a924,x52732,x52731)),f209(x52732,x52731))
% 25.54/25.41 [5278]~P109(x52781)+P11(x52781,f862(f862(f144(x52781),x52782),f106(x52781)))
% 25.54/25.41 [5280]E(x52801,f2(a1))+P1(f862(f42(x52802,x52801),f39(x52802,x52801)))
% 25.54/25.41 [5297]~P13(x52972,x52971)+P1(f862(f862(x52971,f806(x52971)),f806(x52971)))
% 25.54/25.41 [5300]~E(x53001,x53002)+P1(f862(f862(f228(a924),x53001),f862(a105,x53002)))
% 25.54/25.41 [5310]~E(x53101,f2(a924))+P1(f862(f862(f228(a924),x53101),f862(a105,x53102)))
% 25.54/25.41 [5320]P1(f862(x53201,x53202))+P1(f862(f862(f227(a1),f2(a1)),f425(x53201)))
% 25.54/25.41 [5384]E(f862(f862(f301(x53842),f745(x53842,x53841)),f788(x53842,x53841)),x53841)+E(x53841,f181(f932(x53842,a921)))
% 25.54/25.41 [5385]P55(x53851,x53852)+~P55(x53851,f862(f277(x53851,x53851),x53852))
% 25.54/25.41 [5386]P36(x53861,x53862)+~P36(x53861,f862(f277(x53861,x53861),x53862))
% 25.54/25.41 [5387]P37(x53871,x53872)+~P37(x53871,f862(f277(x53871,x53871),x53872))
% 25.54/25.41 [5388]P49(x53881,x53882)+~P49(x53881,f862(f277(x53881,x53881),x53882))
% 25.54/25.41 [5391]~E(f38(a924,x53912,x53911),f2(a924))+E(f862(f862(f74(a924),x53911),f427(x53911,x53912)),x53912)
% 25.54/25.41 [5392]~E(f38(a1,x53922,x53921),f2(a1))+E(f862(f862(f74(a1),x53921),f415(x53921,x53922)),x53922)
% 25.54/25.41 [5397]~E(x53971,f862(a105,x53972))+P1(f862(f862(f227(a924),x53971),f862(a105,x53972)))
% 25.54/25.41 [5419]~P1(f862(x54191,x54192))+P1(f862(f862(f227(a1),f2(a1)),f414(x54191)))
% 25.54/25.41 [5430]E(f862(f862(f3(a924),f862(a97,x54301)),f862(a97,x54302)),f862(a97,x54301))+~P1(f862(a186,x54302))
% 25.54/25.41 [5454]E(f264(x54541,x54542),f71(a92))+~P1(f862(f862(f227(a92),x54541),f71(a92)))
% 25.54/25.41 [5551]E(f862(f862(f157(x55511),x55512),f673(x55512,x55511)),f862(f862(f157(x55511),x55512),f677(x55512,x55511)))+P1(f862(f130(x55511),x55512))
% 25.54/25.41 [5595]~P1(f862(x55951,f83(x55952,x55951)))+P1(f862(x55951,f606(x55952,x55951)))
% 25.54/25.41 [5660]P57(x56601,x56602)+~P1(f862(f307(x56601,x56602),f557(x56602,x56601)))
% 25.54/25.41 [5806]~P13(x58062,x58061)+P1(f862(f862(x58061,f807(x58061,x58062)),f807(x58061,x58062)))
% 25.54/25.41 [5807]~P13(x58072,x58071)+P1(f862(f862(x58071,f810(x58071,x58072)),f810(x58071,x58072)))
% 25.54/25.41 [5816]~E(f862(a105,f38(a924,x58161,x58162)),x58162)+E(f38(a924,f862(a105,x58161),x58162),f2(a924))
% 25.54/25.41 [5871]P35(x58711,x58712)+P1(f862(f862(f321(x58711),f609(x58712,x58711)),f610(x58712,x58711)))
% 25.54/25.41 [5878]~P98(x58781)+P1(f862(f862(f321(x58781),f862(f96(x58781),x58782)),f102(x58781)))
% 25.54/25.41 [5879]~P142(x58791)+P1(f862(f862(f321(x58791),f862(f93(x58791),x58792)),f102(x58791)))
% 25.54/25.41 [5880]~P147(x58801)+P1(f862(f862(f321(x58801),f862(f93(x58801),x58802)),f179(x58801)))
% 25.54/25.41 [5881]~P142(x58811)+P1(f862(f862(f321(x58811),f862(f95(x58811),x58812)),f102(x58811)))
% 25.54/25.41 [6024]~P36(x60241,x60242)+E(f862(f862(f280(x60241,x60241,x60241),x60242),f299(x60241,x60242)),x60242)
% 25.54/25.41 [6038]E(f862(a105,f38(a924,x60381,x60382)),x60382)+E(f38(a924,f862(a105,x60381),x60382),f862(a105,f38(a924,x60381,x60382)))
% 25.54/25.41 [6458]P35(x64581,x64582)+~P1(f862(f862(f321(x64581),f545(x64582,x64581)),f308(x64581,x64582)))
% 25.54/25.41 [6496]~P127(x64961)+~P1(f862(f862(f228(x64961),f862(f93(x64961),x64962)),f2(x64961)))
% 25.54/25.41 [6497]~P86(x64971)+~P1(f862(f862(f228(x64971),f862(f69(x64971),x64972)),f2(x64971)))
% 25.54/25.41 [6529]E(x65291,f181(f932(x65292,a921)))+~P1(f862(f862(f321(x65292),f745(x65292,x65291)),f788(x65292,x65291)))
% 25.54/25.41 [6587]P1(f862(f862(f228(a1),x65871),f38(a1,x65872,x65871)))+~P1(f862(f862(f228(a1),x65871),f2(a1)))
% 25.54/25.41 [6588]P1(f862(f862(f228(a1),x65881),f38(a1,x65882,x65881)))+~P1(f862(f862(f228(a1),x65881),f2(a1)))
% 25.54/25.41 [6690]E(f862(f862(f301(a924),f862(a105,x66901)),f296(a924,x66902,x66901)),f296(a924,x66902,f862(a105,x66901)))+~P1(f862(f862(f227(a924),x66902),f862(a105,x66901)))
% 25.54/25.41 [6779]~P109(x67791)+P11(x67791,f143(x67791,x67791,f7(x67791),x67792))
% 25.54/25.41 [6906]E(f862(f160(x69061),x69062),x69062)+~P1(f862(f862(f227(a924),f862(f182(f925(x69061)),x69062)),f71(a924)))
% 25.54/25.41 [6925]~P86(x69251)+P1(f862(f862(f227(x69251),f862(f72(x69251),f862(f69(x69251),x69252))),f2(x69251)))
% 25.54/25.41 [6959]~P35(x69591,x69592)+P35(x69591,f862(f862(f280(x69591,x69591,x69591),x69592),f299(x69591,x69592)))
% 25.54/25.41 [6960]~P49(x69601,x69602)+P49(x69601,f862(f862(f280(x69601,x69601,x69601),x69602),f299(x69601,x69602)))
% 25.54/25.41 [7182]~P1(f862(f862(f228(a1),x71822),f2(a1)))+P1(f862(f862(f227(a1),f38(a1,x71821,x71822)),f2(a1)))
% 25.54/25.41 [7183]~P1(f862(f862(f228(a1),x71832),f2(a1)))+P1(f862(f862(f227(a1),f38(a1,x71831,x71832)),f2(a1)))
% 25.54/25.41 [7587]~P147(x75871)+E(f183(x75871,f862(f862(f9(x75871,x75871,x75871),f73(x75871)),f71(x75871)),x75872,f2(x75871)),f862(f93(x75871),x75872))
% 25.54/25.41 [7617]~P129(x76171)+~P1(f862(f862(f228(x76171),f862(f862(f74(x76171),x76172),x76172)),f2(x76171)))
% 25.54/25.41 [10256]~P112(x102561)+~P1(f862(f862(f228(x102561),f862(f862(f236(x102561),x102562),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102561)))
% 25.54/25.41 [4838]~E(x48382,f106(x48381))+E(f862(f182(f925(x48381)),x48382),f2(a924))
% 25.54/25.41 [4871]~E(x48711,f2(a924))+E(f862(f862(f73(a924),x48711),x48712),x48712)
% 25.54/25.41 [4872]~E(x48722,f2(a924))+E(f862(f862(f74(a924),x48721),x48722),f2(a924))
% 25.54/25.41 [4873]~E(x48731,f2(a924))+E(f862(f862(f74(a924),x48731),x48732),f2(a924))
% 25.54/25.41 [4874]~E(x48741,f2(a924))+E(f862(f862(f74(a924),x48741),x48742),f2(a924))
% 25.54/25.41 [4875]~E(x48752,f2(a924))+E(f862(f862(f236(a924),x48751),x48752),f71(a924))
% 25.54/25.41 [4876]~E(x48762,f2(a1))+E(f862(f862(f29(a1),x48761),x48762),f2(a1))
% 25.54/25.41 [4887]E(x48871,f106(x48872))+~E(f862(f182(f925(x48872)),x48871),f2(a924))
% 25.54/25.41 [4888]~P93(x48881)+E(f862(f862(f103(x48881),x48882),x48882),x48882)
% 25.54/25.41 [4889]~P103(x48891)+E(f862(f862(f103(x48891),x48892),x48892),x48892)
% 25.54/25.41 [4890]~P103(x48901)+E(f862(f862(f103(x48901),x48902),x48902),x48902)
% 25.54/25.41 [4891]~P93(x48911)+E(f862(f862(f94(x48911),x48912),x48912),x48912)
% 25.54/25.41 [4892]~P104(x48921)+E(f862(f862(f94(x48921),x48922),x48922),x48922)
% 25.54/25.41 [4893]~P104(x48931)+E(f862(f862(f94(x48931),x48932),x48932),x48932)
% 25.54/25.41 [4894]~P100(x48941)+E(f862(f862(f74(x48941),x48942),x48942),x48942)
% 25.54/25.41 [4895]~P100(x48951)+E(f862(f862(f74(x48951),x48952),x48952),x48952)
% 25.54/25.41 [4896]~P109(x48961)+E(f862(f862(f225(x48961),x48962),x48962),x48962)
% 25.54/25.41 [4897]~P109(x48971)+E(f862(f862(f225(x48971),x48972),x48972),x48972)
% 25.54/25.41 [4898]~P109(x48981)+E(f862(f862(f226(x48981),x48982),x48982),x48982)
% 25.54/25.41 [4899]~P109(x48991)+E(f862(f862(f226(x48991),x48992),x48992),x48992)
% 25.54/25.41 [4917]~P68(x49171)+E(f862(f862(f3(x49171),x49172),x49172),f2(x49171))
% 25.54/25.41 [4932]~P96(x49321)+E(f862(f72(x49321),f862(f72(x49321),x49322)),x49322)
% 25.54/25.41 [4933]~P68(x49331)+E(f862(f72(x49331),f862(f72(x49331),x49332)),x49332)
% 25.54/25.41 [4950]~E(x49502,f2(a924))+E(f862(f862(f236(a924),x49501),x49502),f862(a105,f2(a924)))
% 25.54/25.41 [4985]~P95(x49851)+E(f862(f862(f103(x49851),f181(x49851)),x49852),x49852)
% 25.54/25.41 [4986]~P94(x49861)+E(f862(f862(f94(x49861),f234(x49861)),x49862),x49862)
% 25.54/25.41 [4987]~P71(x49871)+E(f862(f862(f74(x49871),f71(x49871)),x49872),x49872)
% 25.54/25.41 [4988]~P119(x49881)+E(f862(f862(f74(x49881),f71(x49881)),x49882),x49882)
% 25.54/25.41 [4989]~P80(x49891)+E(f862(f862(f74(x49891),f71(x49891)),x49892),x49892)
% 25.54/25.41 [4990]~P72(x49901)+E(f862(f862(f73(x49901),f2(x49901)),x49902),x49902)
% 25.54/25.41 [4991]~P119(x49911)+E(f862(f862(f73(x49911),f2(x49911)),x49912),x49912)
% 25.54/25.41 [4992]~P81(x49921)+E(f862(f862(f73(x49921),f2(x49921)),x49922),x49922)
% 25.54/25.41 [5010]~P94(x50101)+E(f862(f862(f103(x50101),f234(x50101)),x50102),f234(x50101))
% 25.54/25.41 [5011]~P95(x50111)+E(f862(f862(f94(x50111),f181(x50111)),x50112),f181(x50111))
% 25.54/25.41 [5012]~P119(x50121)+E(f862(f862(f74(x50121),f2(x50121)),x50122),f2(x50121))
% 25.54/25.41 [5013]~P134(x50131)+E(f862(f862(f74(x50131),f2(x50131)),x50132),f2(x50131))
% 25.54/25.41 [5014]~P121(x50141)+E(f862(f862(f281(x50141),f2(x50141)),x50142),f2(x50141))
% 25.54/25.41 [5015]~P80(x50151)+E(f862(f862(f236(x50151),f71(x50151)),x50152),f71(x50151))
% 25.54/25.41 [5016]~P61(x50161)+E(f862(f862(f29(x50161),f2(x50161)),x50162),f2(x50161))
% 25.54/25.41 [5024]E(x50241,f106(x50242))+E(f137(x50242,f862(f161(x50242),x50241)),f862(f134(x50242),x50241))
% 25.54/25.41 [5025]E(x50251,f106(x50252))+E(f862(f134(x50252),f862(f161(x50252),x50251)),f137(x50252,x50251))
% 25.54/25.41 [5026]E(x50261,f2(a924))+~E(f862(f862(f73(a924),x50262),x50261),x50262)
% 25.54/25.41 [5033]~P98(x50331)+E(f862(f95(x50331),f862(f96(a1),x50332)),f862(f96(x50331),x50332))
% 25.54/25.41 [5034]~P142(x50341)+E(f862(f95(x50341),f862(f93(a1),x50342)),f862(f93(x50341),x50342))
% 25.54/25.41 [5039]E(x50391,f71(a924))+~E(f862(f862(f74(a924),x50392),x50391),f71(a924))
% 25.54/25.41 [5040]E(x50401,f71(a924))+~E(f862(f862(f74(a924),x50401),x50402),f71(a924))
% 25.54/25.41 [5041]E(x50411,f71(a924))+~E(f862(f862(f74(a924),x50412),x50411),f71(a924))
% 25.54/25.41 [5042]E(x50421,f71(a924))+~E(f862(f862(f74(a924),x50421),x50422),f71(a924))
% 25.54/25.41 [5043]E(x50431,f2(a924))+~E(f862(f862(f73(a924),x50432),x50431),f2(a924))
% 25.54/25.41 [5044]E(x50441,f2(a924))+~E(f862(f862(f73(a924),x50441),x50442),f2(a924))
% 25.54/25.41 [5061]~P86(x50611)+E(f862(f69(x50611),f862(f72(x50611),x50612)),f862(f69(x50611),x50612))
% 25.54/25.41 [5062]~P112(x50621)+E(f862(f69(x50621),f862(f93(x50621),x50622)),f862(f93(x50621),x50622))
% 25.54/25.41 [5063]~P86(x50631)+E(f862(f69(x50631),f862(f69(x50631),x50632)),f862(f69(x50631),x50632))
% 25.54/25.41 [5064]~P72(x50641)+E(f862(f158(x50641),f862(f161(x50641),x50642)),f862(f158(x50641),x50642))
% 25.54/25.41 [5069]~E(x50691,f862(a105,f2(a924)))+E(f862(f862(f236(a924),x50691),x50692),f862(a105,f2(a924)))
% 25.54/25.41 [5078]~P68(x50781)+E(f862(f862(f3(x50781),f2(x50781)),x50782),f862(f72(x50781),x50782))
% 25.54/25.41 [5079]~E(x50792,f2(a924))+E(f132(a924,f862(f295(a924,x50791),x50792)),f106(a924))
% 25.54/25.41 [5088]~P98(x50881)+E(f862(f862(f73(x50881),x50882),f862(f96(x50881),a76)),x50882)
% 25.54/25.41 [5089]E(x50891,f2(a1))+E(f40(f862(f69(a1),x50892),f862(f69(a1),x50891)),f46(x50892,x50891))
% 25.54/25.41 [5103]~E(x51031,x51032)+P1(f862(f862(f227(a924),x51031),x51032))
% 25.54/25.41 [5104]~E(x51041,x51042)+P1(f862(f862(f227(a924),x51041),x51042))
% 25.54/25.41 [5105]~E(x51051,x51052)+P1(f862(f862(f227(a924),x51051),x51052))
% 25.54/25.41 [5106]~E(x51061,x51062)+P1(f862(f862(f278(a924),x51061),x51062))
% 25.54/25.41 [5107]~E(x51071,x51072)+P1(f862(f862(f278(a924),x51071),x51072))
% 25.54/25.41 [5108]~E(x51081,x51082)+P1(f862(f862(f278(a924),x51081),x51082))
% 25.54/25.41 [5109]~E(x51091,x51092)+P1(f862(f862(f278(a924),x51091),x51092))
% 25.54/25.41 [5116]~E(x51161,f2(a92))+E(f862(f862(f73(a924),f862(a22,x51161)),x51162),x51162)
% 25.54/25.41 [5117]~E(f862(f93(a1),x51171),f862(f96(a1),x51172))+E(x51171,f862(a97,f862(f96(a1),x51172)))
% 25.54/25.41 [5130]~P4(x51301)+P4(f862(f862(f236(a1),x51301),x51302))
% 25.54/25.41 [5131]~P96(x51311)+E(f862(f862(f103(x51311),x51312),f862(f72(x51311),x51312)),f234(x51311))
% 25.54/25.41 [5132]~P96(x51321)+E(f862(f862(f94(x51321),x51322),f862(f72(x51321),x51322)),f181(x51321))
% 25.54/25.41 [5133]~P68(x51331)+E(f862(f862(f73(x51331),x51332),f862(f72(x51331),x51332)),f2(x51331))
% 25.54/25.41 [5158]E(x51581,f2(a924))+~E(f862(f72(a1),f862(f93(a1),x51582)),f862(f93(a1),x51581))
% 25.54/25.41 [5159]E(x51591,f2(a924))+~E(f862(f72(a1),f862(f93(a1),x51591)),f862(f93(a1),x51592))
% 25.54/25.41 [5169]E(f187(x51691,x51692),f2(a1))+P1(f862(f862(f227(a1),x51692),x51691))
% 25.54/25.41 [5170]E(f171(x51701,x51702),f106(a1))+P1(f862(f862(f227(a1),x51701),x51702))
% 25.54/25.41 [5171]E(f233(x51711,x51712),f2(a92))+P1(f862(f862(f228(a92),x51711),x51712))
% 25.54/25.41 [5184]E(x51841,f862(a105,f2(a924)))+~E(f862(f862(f74(a924),x51842),x51841),f862(a105,f2(a924)))
% 25.54/25.41 [5185]E(x51851,f862(a105,f2(a924)))+~E(f862(f862(f74(a924),x51851),x51852),f862(a105,f2(a924)))
% 25.54/25.41 [5186]~P2(x51861)+P1(f862(f862(f84(x51861),x51862),x51862))
% 25.54/25.41 [5187]~P91(x51871)+P1(f862(f862(f227(x51871),x51872),x51872))
% 25.54/25.41 [5188]~P119(x51881)+P1(f862(f862(f278(x51881),x51882),x51882))
% 25.54/25.41 [5191]~P98(x51911)+E(f862(f862(f74(x51911),x51912),f862(f96(x51911),a90)),f862(f72(x51911),x51912))
% 25.54/25.41 [5211]~P98(x52111)+E(f862(f72(x52111),f862(f96(x52111),x52112)),f862(f96(x52111),f862(f72(a1),x52112)))
% 25.54/25.41 [5212]~P98(x52121)+E(f862(f72(x52121),f862(f96(x52121),x52122)),f862(f96(x52121),f862(f72(a1),x52122)))
% 25.54/25.41 [5213]~P142(x52131)+E(f862(f72(x52131),f862(f95(x52131),x52132)),f862(f95(x52131),f862(f72(a1),x52132)))
% 25.54/25.41 [5243]~E(x52431,f862(a105,x52432))+P1(f862(f862(f228(a924),f2(a924)),x52431))
% 25.54/25.41 [5261]~P109(x52611)+E(f862(f72(f932(x52611,a921)),f862(f293(x52611),x52612)),f862(f294(x52611),x52612))
% 25.54/25.41 [5262]~P109(x52621)+E(f862(f72(f932(x52621,a921)),f862(f294(x52621),x52622)),f862(f293(x52621),x52622))
% 25.54/25.41 [5263]~P109(x52631)+E(f862(f72(f932(x52631,a921)),f862(f274(x52631),x52632)),f862(f292(x52631),x52632))
% 25.54/25.41 [5264]~P109(x52641)+E(f862(f72(f932(x52641,a921)),f862(f292(x52641),x52642)),f862(f274(x52641),x52642))
% 25.54/25.41 [5272]~E(f862(f93(a1),x52722),x52721)+P1(f862(f862(f227(a1),f2(a1)),x52721))
% 25.54/25.41 [5279]~E(x52792,f2(a1))+E(f46(x52791,x52792),f862(f862(f244(a1,a1),f2(a1)),f862(f69(a1),x52791)))
% 25.54/25.41 [5281]~P92(x52811)+P1(f862(f862(f227(x52811),f181(x52811)),x52812))
% 25.54/25.41 [5282]~P119(x52821)+P1(f862(f862(f278(x52821),f71(x52821)),x52822))
% 25.54/25.41 [5315]E(x53151,x53152)+~E(f862(f862(f73(a1),x53151),x53151),f862(f862(f73(a1),x53152),x53152))
% 25.54/25.41 [5319]~P1(f862(x53191,x53192))+P1(f862(x53191,f862(a97,f414(x53191))))
% 25.54/25.41 [5345]~P112(x53451)+E(f862(f862(f74(x53451),f75(x53451,x53452)),f862(f69(x53451),x53452)),x53452)
% 25.54/25.41 [5352]~E(x53522,f2(a924))+E(f78(f931(a924,a924),f41(x53521,x53522)),f862(f862(f244(a924,a924),f2(a924)),x53521))
% 25.54/25.41 [5353]~E(x53531,x53532)+~P1(f862(f862(f228(a924),x53531),x53532))
% 25.54/25.41 [5354]~E(x53541,x53542)+~P1(f862(f862(f228(a924),x53541),x53542))
% 25.54/25.41 [5355]~E(x53551,x53552)+~P1(f862(f862(f228(a924),x53551),x53552))
% 25.54/25.41 [5356]~E(x53561,x53562)+~P1(f862(f862(f228(a924),x53561),x53562))
% 25.54/25.41 [5357]~E(x53571,x53572)+~P1(f862(f862(f228(a924),x53571),x53572))
% 25.54/25.41 [5358]~E(x53581,x53582)+~P1(f862(f862(f228(a1),x53581),x53582))
% 25.54/25.41 [5361]~P147(x53611)+E(f862(f862(f73(x53611),f71(x53611)),f862(f93(x53611),x53612)),f862(f93(x53611),f862(a105,x53612)))
% 25.54/25.41 [5365]~E(x53651,f2(a924))+~P1(f862(f862(f228(a924),x53652),x53651))
% 25.54/25.41 [5379]E(f145(x53791,x53792),x53792)+~E(f862(f182(f925(x53791)),f145(x53791,x53792)),f862(f182(f925(x53791)),x53792))
% 25.54/25.41 [5380]E(f862(f28(x53801),f862(f165(x53801),x53802)),f862(f182(f925(x53801)),x53802))+~P1(f862(f130(x53801),x53802))
% 25.54/25.41 [5396]~P1(f862(x53961,f357(x53961)))+P1(f862(x53961,f862(f93(a1),x53962)))
% 25.54/25.41 [5407]E(f233(x54071,x54072),x54072)+~P1(f862(f862(f228(a92),x54071),x54072))
% 25.54/25.41 [5409]E(f264(x54091,x54092),f71(a92))+~P1(f862(f862(f228(a92),x54092),x54091))
% 25.54/25.41 [5410]E(f171(x54101,x54102),f106(a1))+~P1(f862(f862(f228(a1),x54102),x54101))
% 25.54/25.41 [5411]E(f121(x54111,x54112),f108(a1))+~P1(f862(f862(f228(a1),x54111),x54112))
% 25.54/25.41 [5413]~P110(x54131)+E(f296(x54131,x54132,x54132),f862(f862(f301(x54131),x54132),f181(f932(x54131,a921))))
% 25.54/25.41 [5433]~E(f862(f862(f3(a1),x54331),x54332),f2(a1))+P1(f862(f862(f84(a1),x54331),x54332))
% 25.54/25.41 [5434]~E(f862(f862(f3(a924),x54341),x54342),f2(a924))+P1(f862(f862(f227(a924),x54341),x54342))
% 25.54/25.41 [5451]~E(x54512,f2(a924))+E(f48(x54511,x54512,f106(x54511)),f862(f862(f144(f925(x54511)),f106(x54511)),f106(f925(x54511))))
% 25.54/25.41 [5455]~P91(x54551)+~P1(f862(f862(f228(x54551),x54552),x54552))
% 25.54/25.41 [5456]~E(f38(a1,x54561,x54562),f2(a1))+E(f38(a1,x54561,f862(f72(a1),x54562)),f2(a1))
% 25.54/25.41 [5457]~E(f38(a1,x54571,x54572),f2(a1))+E(f38(a1,x54571,f862(f72(a1),x54572)),f2(a1))
% 25.54/25.41 [5458]~E(f38(a1,x54581,x54582),f2(a1))+E(f38(a1,f862(f72(a1),x54581),x54582),f2(a1))
% 25.54/25.41 [5459]~E(f38(a1,x54591,x54592),f2(a1))+E(f38(a1,f862(f72(a1),x54591),x54592),f2(a1))
% 25.54/25.41 [5467]E(f862(f295(a924,x54671),f862(a105,x54672)),f181(f932(a924,a921)))+P1(f862(f862(f227(a924),x54671),x54672))
% 25.54/25.41 [5490]E(f132(a924,f862(f295(a924,x54901),x54902)),f106(a924))+P1(f862(f862(f228(a924),x54901),x54902))
% 25.54/25.41 [5495]~E(f862(f28(x54951),f862(f165(x54951),x54952)),f862(f182(f925(x54951)),x54952))+P1(f862(f130(x54951),x54952))
% 25.54/25.41 [5499]~P1(f862(f130(x54991),x54992))+P1(f862(f130(x54991),f862(f160(x54991),x54992)))
% 25.54/25.41 [5500]~P1(f862(f130(x55001),x55002))+P1(f862(f130(x55001),f862(f164(x55001),x55002)))
% 25.54/25.41 [5501]~P1(f862(f130(x55011),x55012))+P1(f862(f130(x55011),f862(f161(x55011),x55012)))
% 25.54/25.41 [5509]P1(f862(x55091,x55092))+~P1(f862(x55091,f862(a97,f425(x55091))))
% 25.54/25.41 [5510]P1(f862(f862(f227(a924),x55102),x55101))+P1(f862(f862(f227(a924),x55101),x55102))
% 25.54/25.41 [5511]P1(f862(f862(f227(a1),x55112),x55111))+P1(f862(f862(f227(a1),x55111),x55112))
% 25.54/25.41 [5515]~P86(x55151)+P1(f862(f862(f227(x55151),x55152),f862(f69(x55151),x55152)))
% 25.54/25.41 [5518]P1(f862(x55181,f358(x55181)))+~P1(f862(x55181,f862(f93(a1),x55182)))
% 25.54/25.41 [5541]E(f862(f862(f3(a924),x55411),x55412),f2(a924))+~P1(f862(f862(f227(a924),x55411),x55412))
% 25.54/25.41 [5542]E(f862(f862(f3(a924),x55421),x55422),f2(a924))+~P1(f862(f862(f227(a924),x55421),x55422))
% 25.54/25.41 [5543]E(f862(f862(f3(a1),x55431),x55432),f2(a1))+~P1(f862(f862(f84(a1),x55431),x55432))
% 25.54/25.41 [5544]E(f862(f862(f29(a924),x55441),x55442),f2(a924))+~P1(f862(f862(f228(a924),x55441),x55442))
% 25.54/25.41 [5562]E(f38(a924,x55621,x55622),x55621)+~P1(f862(f862(f228(a924),x55621),x55622))
% 25.54/25.41 [5563]E(f38(a924,x55631,x55632),x55631)+~P1(f862(f862(f228(a924),x55631),x55632))
% 25.54/25.41 [5571]E(f38(a1,x55711,f862(f72(a1),x55712)),f282(x55711,x55712))+P1(f862(f862(f227(a1),f2(a1)),x55712))
% 25.54/25.41 [5583]E(f862(f862(f3(a1),x55831),x55832),f187(x55831,x55832))+~P1(f862(f862(f227(a1),x55832),x55831))
% 25.54/25.41 [5584]E(f862(f862(f3(a1),x55841),x55842),f187(x55841,x55842))+~P1(f862(f862(f227(a1),x55842),x55841))
% 25.54/25.41 [5604]P1(f862(f862(f227(a1),f2(a1)),f357(x56041)))+P1(f862(x56041,f862(f93(a1),x56042)))
% 25.54/25.41 [5616]~P127(x56161)+P1(f862(f862(f227(x56161),f2(x56161)),f862(f93(x56161),x56162)))
% 25.54/25.41 [5617]~P127(x56171)+P1(f862(f862(f227(x56171),f2(x56171)),f862(f93(x56171),x56172)))
% 25.54/25.41 [5618]~P86(x56181)+P1(f862(f862(f227(x56181),f2(x56181)),f862(f69(x56181),x56182)))
% 25.54/25.41 [5646]E(f862(f862(f73(a924),x56461),f864(x56462,x56461)),x56462)+~P1(f862(f862(f227(a924),x56461),x56462))
% 25.54/25.41 [5658]~E(f862(f93(a1),x56582),f862(f96(a1),x56581))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x56581)))
% 25.54/25.41 [5661]E(f296(a1,x56611,x56612),f181(f932(a1,a921)))+~P1(f862(f862(f228(a1),x56612),x56611))
% 25.54/25.41 [5664]~P112(x56641)+E(f862(f862(f74(x56641),f862(f69(x56641),x56642)),f862(f69(x56641),x56642)),f862(f862(f74(x56641),x56642),x56642))
% 25.54/25.41 [5669]E(f132(a924,f862(f295(a924,x56691),f862(a105,x56692))),f106(a924))+P1(f862(f862(f227(a924),x56691),x56692))
% 25.54/25.41 [5672]E(f862(f862(f29(a1),x56721),x56722),f283(x56721,x56722))+~P1(f862(f862(f227(a1),f2(a1)),x56722))
% 25.54/25.41 [5692]P1(f862(f130(x56921),x56922))+~P1(f862(f130(x56921),f862(f160(x56921),x56922)))
% 25.54/25.41 [5693]P1(f862(f130(x56931),x56932))+~P1(f862(f130(x56931),f862(f161(x56931),x56932)))
% 25.54/25.41 [5720]P1(f862(f54(a924),x57201))+P1(f862(f862(f321(a924),f865(x57201,x57202)),x57201))
% 25.54/25.41 [5721]P1(f862(f54(a924),x57211))+P1(f862(f862(f321(a924),f912(x57211,x57212)),x57211))
% 25.54/25.41 [5724]P1(f862(f862(f228(a924),x57242),f862(a105,x57241)))+P1(f862(f862(f228(a924),x57241),x57242))
% 25.54/25.41 [5725]E(f38(a1,x57251,x57252),f282(x57251,x57252))+~P1(f862(f862(f227(a1),f2(a1)),x57252))
% 25.54/25.41 [5728]E(f132(a924,f862(f295(a924,x57281),x57282)),f106(a924))+~P1(f862(f862(f227(a924),x57282),x57281))
% 25.54/25.41 [5729]E(f132(a924,f862(f295(a924,x57291),x57292)),f106(a924))+~P1(f862(f862(f227(a924),x57292),x57291))
% 25.54/25.41 [5730]~P78(x57301)+E(f862(f302(x57301,x57301,f72(x57301)),f862(f293(x57301),x57302)),f862(f292(x57301),f862(f72(x57301),x57302)))
% 25.54/25.41 [5731]~P78(x57311)+E(f862(f302(x57311,x57311,f72(x57311)),f862(f294(x57311),x57312)),f862(f274(x57311),f862(f72(x57311),x57312)))
% 25.54/25.41 [5732]~P78(x57321)+E(f862(f302(x57321,x57321,f72(x57321)),f862(f274(x57321),x57322)),f862(f294(x57321),f862(f72(x57321),x57322)))
% 25.54/25.41 [5733]~P78(x57331)+E(f862(f302(x57331,x57331,f72(x57331)),f862(f292(x57331),x57332)),f862(f293(x57331),f862(f72(x57331),x57332)))
% 25.54/25.41 [5744]E(x57441,f181(f932(x57442,a921)))+P1(f862(f862(f321(x57442),f359(x57441,x57442)),x57441))
% 25.54/25.41 [5745]E(x57451,f181(f932(x57452,a921)))+P1(f862(f862(f321(x57452),f570(x57451,x57452)),x57451))
% 25.54/25.41 [5746]E(x57461,f181(f932(x57462,a921)))+P1(f862(f862(f321(x57462),f395(x57461,x57462)),x57461))
% 25.54/25.41 [5753]~P1(f862(f862(f228(a924),x57531),x57532))+P1(f862(f862(f227(a924),x57531),x57532))
% 25.54/25.41 [5754]~P1(f862(f862(f228(a924),x57541),x57542))+P1(f862(f862(f227(a924),x57541),x57542))
% 25.54/25.41 [5755]~P1(f862(f862(f228(a924),x57551),x57552))+P1(f862(f862(f227(a924),x57551),x57552))
% 25.54/25.41 [5756]~P1(f862(f862(f228(a924),x57561),x57562))+P1(f862(f862(f227(a924),x57561),x57562))
% 25.54/25.41 [5757]~P1(f862(f862(f228(a924),x57571),x57572))+P1(f862(f862(f227(a924),x57571),x57572))
% 25.54/25.41 [5758]~P1(f862(f862(f228(a1),x57581),x57582))+P1(f862(f862(f227(a1),x57581),x57582))
% 25.54/25.41 [5775]E(f40(x57751,x57752),f862(f862(f244(a1,a1),f2(a1)),x57751))+~P1(f862(f862(f228(a1),x57751),x57752))
% 25.54/25.41 [5777]E(f208(f862(f72(a1),x57771),f862(f72(a1),x57772)),f208(x57771,x57772))+~P1(f862(f862(f228(a1),x57772),f2(a1)))
% 25.54/25.41 [5788]E(x57881,x57882)+~E(f862(a5,f862(a105,f862(a22,x57881))),f862(a5,f862(a105,f862(a22,x57882))))
% 25.54/25.41 [5793]E(f40(x57931,x57932),f862(f862(f244(a1,a1),f2(a1)),x57931))+~P1(f862(f862(f227(a1),x57932),f2(a1)))
% 25.54/25.41 [5822]E(f38(a924,f862(f96(a924),x58221),f862(f96(a924),x58222)),f2(a924))+~P1(f862(a186,f862(f96(a1),x58221)))
% 25.54/25.41 [5836]P1(f862(f862(f227(a1),f2(a1)),f358(x58361)))+~P1(f862(x58361,f862(f93(a1),x58362)))
% 25.54/25.41 [5869]P38(f296(a1,x58691,x58692))+~P1(f862(f862(f227(a1),f2(a1)),x58691))
% 25.54/25.41 [5874]~P1(f862(f54(x58741),x58742))+P1(f862(f54(f932(x58741,a921)),f862(f300(x58741),x58742)))
% 25.54/25.41 [5887]E(f862(f862(f73(a1),x58871),f862(f93(a1),f409(x58872,x58871))),x58872)+~P1(f862(f862(f227(a1),x58871),x58872))
% 25.54/25.41 [5895]P1(f862(f862(f227(a924),x58951),x58952))+P1(f862(f862(f227(a924),f862(a105,x58952)),x58951))
% 25.54/25.41 [5939]E(f862(f862(f29(a924),f862(f96(a924),x59391)),f862(f96(a924),x59392)),f2(a924))+~P1(f862(a186,f862(f96(a1),x59391)))
% 25.54/25.41 [5940]E(f862(f862(f74(a924),f862(f96(a924),x59401)),f862(f96(a924),x59402)),f2(a924))+~P1(f862(f862(f228(a1),x59401),a76))
% 25.54/25.41 [5941]P1(f862(f862(f227(a924),x59411),f862(a105,x59412)))+~P1(f862(f862(f227(a924),x59411),x59412))
% 25.54/25.41 [5942]P1(f862(f862(f227(a924),x59421),f862(a105,x59422)))+~P1(f862(f862(f227(a924),x59421),x59422))
% 25.54/25.41 [5943]P1(f862(f862(f228(a924),x59431),f862(a105,x59432)))+~P1(f862(f862(f227(a924),x59431),x59432))
% 25.54/25.41 [5944]P1(f862(f862(f228(a924),x59441),f862(a105,x59442)))+~P1(f862(f862(f227(a924),x59441),x59442))
% 25.54/25.41 [5945]P1(f862(f862(f228(a924),x59451),f862(a105,x59452)))+~P1(f862(f862(f228(a924),x59451),x59452))
% 25.54/25.41 [5946]P1(f862(f862(f228(a924),x59461),f862(a105,x59462)))+~P1(f862(f862(f228(a924),x59461),x59462))
% 25.54/25.41 [5949]~E(x59491,x59492)+P1(f862(f862(f228(a1),x59491),f862(f862(f73(a1),x59492),f71(a1))))
% 25.54/25.41 [5952]E(f38(a1,x59521,x59522),f2(a1))+E(f862(f862(f3(a1),x59522),f38(a1,x59521,x59522)),f38(a1,f862(f72(a1),x59521),x59522))
% 25.54/25.41 [5961]E(x59611,f106(x59612))+P1(f862(f862(f321(x59612),f137(x59612,x59611)),f862(f165(x59612),x59611)))
% 25.54/25.41 [5972]E(f78(f931(a924,a924),f41(x59721,x59722)),f862(f862(f244(a924,a924),f2(a924)),x59721))+~P1(f862(f862(f228(a924),x59721),x59722))
% 25.54/25.41 [5973]E(f78(f931(a924,a924),f41(x59731,x59732)),f862(f862(f244(a924,a924),f2(a924)),x59731))+~P1(f862(f862(f228(a924),x59731),x59732))
% 25.54/25.41 [6017]E(f862(f862(f3(a924),f862(f96(a924),x60171)),f862(f96(a924),x60172)),f862(f96(a924),x60171))+~P1(f862(f862(f228(a1),x60172),a76))
% 25.54/25.41 [6018]E(f862(f862(f73(a924),f862(f96(a924),x60181)),f862(f96(a924),x60182)),f862(f96(a924),x60182))+~P1(f862(f862(f228(a1),x60181),a76))
% 25.54/25.41 [6025]E(f862(a105,f862(f862(f73(a924),x60251),f332(x60252,x60251))),x60252)+~P1(f862(f862(f228(a924),x60251),x60252))
% 25.54/25.41 [6049]P1(f862(x60491,x60492))+~P1(f862(x60491,f862(a82,f578(x60492,x60491))))
% 25.54/25.41 [6050]P1(f862(x60501,x60502))+~P1(f862(x60501,f862(a5,f823(x60502,x60501))))
% 25.54/25.41 [6059]~P1(f862(f862(f228(a924),x60591),f862(a105,x60592)))+P1(f862(f862(f227(a924),x60591),x60592))
% 25.54/25.41 [6096]P1(f862(x60961,x60962))+P1(f862(f862(f321(a924),f823(x60962,x60961)),f234(f932(a924,a921))))
% 25.54/25.41 [6109]E(f862(f862(f301(a924),x61091),f862(f295(a924,x61092),x61091)),f862(f295(a924,x61092),f862(a105,x61091)))+~P1(f862(f862(f227(a924),x61092),x61091))
% 25.54/25.41 [6111]E(x61111,f106(x61112))+E(f862(f862(f127(x61112),f107(x61112,x61111)),f862(f862(f144(x61112),f137(x61112,x61111)),f106(x61112))),x61111)
% 25.54/25.41 [6127]P1(f862(f54(x61271),x61272))+~P1(f862(f862(f228(a924),f2(a924)),f862(f28(x61271),x61272)))
% 25.54/25.41 [6128]P1(f862(f54(x61281),x61282))+~P1(f862(f862(f228(a924),f2(a924)),f862(f28(x61281),x61282)))
% 25.54/25.41 [6132]~E(x61321,f181(f932(x61322,a921)))+~P1(f862(f862(f228(a924),f2(a924)),f862(f28(x61322),x61321)))
% 25.54/25.41 [6142]~P1(f862(f862(f228(a924),x61421),x61422))+P1(f862(f862(f227(a924),f862(a105,x61421)),x61422))
% 25.54/25.41 [6143]~P1(f862(f862(f228(a924),x61431),x61432))+P1(f862(f862(f227(a924),f862(a105,x61431)),x61432))
% 25.54/25.41 [6144]~P1(f862(f862(f228(a924),x61441),x61442))+P1(f862(f862(f227(a924),f862(a105,x61441)),x61442))
% 25.54/25.41 [6148]~P109(x61481)+E(f143(x61481,x61481,f7(x61481),f145(x61481,x61482)),f132(x61481,f862(f165(x61481),x61482)))
% 25.54/25.41 [6151]E(x61511,f106(x61512))+P1(f862(f862(f321(x61512),f862(f134(x61512),x61511)),f862(f165(x61512),x61511)))
% 25.54/25.41 [6157]~P127(x61571)+P1(f862(f862(f228(x61571),x61572),f862(f862(f73(x61571),x61572),f71(x61571))))
% 25.54/25.41 [6159]~P86(x61591)+P1(f862(f862(f227(x61591),f862(f72(x61591),x61592)),f862(f69(x61591),x61592)))
% 25.54/25.41 [6189]P1(f862(f54(a924),x61891))+~P1(f862(f862(f227(a924),f865(x61891,x61892)),x61892))
% 25.54/25.41 [6190]P1(f862(f54(a924),x61901))+~P1(f862(f862(f228(a924),f912(x61901,x61902)),x61902))
% 25.54/25.41 [6193]~P1(f862(f54(f931(x61931,x61931)),x61932))+P1(f862(f54(x61931),f862(f273(x61931),x61932)))
% 25.54/25.41 [6215]E(f234(f932(x62151,a921)),x62152)+~P1(f862(f862(f321(x62151),f528(x62152,x62151)),x62152))
% 25.54/25.41 [6247]E(f171(f862(f96(a1),x62471),f862(f96(a1),x62472)),f106(a1))+P1(f862(f862(f227(a1),f862(f96(a1),x62471)),f862(f96(a1),x62472)))
% 25.54/25.41 [6249]~P1(f862(f862(f228(a924),x62492),f862(a105,x62491)))+~P1(f862(f862(f228(a924),x62491),x62492))
% 25.54/25.41 [6250]~P110(x62501)+E(f862(f862(f94(f932(x62501,a921)),f862(f294(x62501),x62502)),f862(f274(x62501),x62502)),f862(f862(f301(x62501),x62502),f181(f932(x62501,a921))))
% 25.54/25.41 [6252]E(f862(f862(f236(a924),f862(f96(a924),x62521)),f862(f96(a924),x62522)),f862(f862(f236(a924),f2(a924)),f862(f96(a924),x62522)))+~P1(f862(a186,f862(f96(a1),x62521)))
% 25.54/25.41 [6262]P1(f862(f54(x62621),x62622))+~P1(f862(f54(f932(x62621,a921)),f862(f300(x62621),x62622)))
% 25.54/25.41 [6284]P1(f862(f862(f227(a924),f862(a105,x62841)),f862(a105,x62842)))+~P1(f862(f862(f227(a924),x62841),x62842))
% 25.54/25.41 [6285]P1(f862(f862(f227(a924),f862(a22,x62851)),f862(a22,x62852)))+~P1(f862(f862(f227(a92),x62851),x62852))
% 25.54/25.41 [6286]P1(f862(f862(f227(a92),f862(a5,x62861)),f862(a5,x62862)))+~P1(f862(f862(f227(a924),x62861),x62862))
% 25.54/25.41 [6287]P1(f862(f862(f228(a924),f862(a105,x62871)),f862(a105,x62872)))+~P1(f862(f862(f228(a924),x62871),x62872))
% 25.54/25.41 [6288]P1(f862(f862(f228(a924),f862(a105,x62881)),f862(a105,x62882)))+~P1(f862(f862(f228(a924),x62881),x62882))
% 25.54/25.41 [6289]P1(f862(f862(f228(a924),f862(a22,x62891)),f862(a22,x62892)))+~P1(f862(f862(f228(a92),x62891),x62892))
% 25.54/25.41 [6290]P1(f862(f862(f228(a92),f862(a5,x62901)),f862(a5,x62902)))+~P1(f862(f862(f228(a924),x62901),x62902))
% 25.54/25.41 [6295]E(x62951,x62952)+~E(f862(f302(a924,a1,f93(a1)),x62951),f862(f302(a924,a1,f93(a1)),x62952))
% 25.54/25.41 [6311]P1(f862(f862(f227(a924),x63111),x63112))+~P1(f862(f862(f227(a924),f862(a105,x63111)),x63112))
% 25.54/25.41 [6312]P1(f862(f862(f228(a924),x63121),x63122))+~P1(f862(f862(f227(a924),f862(a105,x63121)),x63122))
% 25.54/25.41 [6313]P1(f862(f862(f228(a924),x63131),x63132))+~P1(f862(f862(f227(a924),f862(a105,x63131)),x63132))
% 25.54/25.41 [6314]P1(f862(f862(f228(a924),x63141),x63142))+~P1(f862(f862(f227(a924),f862(a105,x63141)),x63142))
% 25.54/25.41 [6315]P1(f862(f862(f228(a924),x63151),x63152))+~P1(f862(f862(f228(a924),f862(a105,x63151)),x63152))
% 25.54/25.41 [6333]E(f38(a1,x63331,x63332),f2(a1))+E(f862(f862(f3(a1),f38(a1,x63331,x63332)),x63332),f38(a1,x63331,f862(f72(a1),x63332)))
% 25.54/25.41 [6400]E(f862(f28(f932(x64001,a921)),f862(f300(x64001),x64002)),f862(f862(f236(a924),f862(a105,f862(a105,f2(a924)))),f862(f28(x64001),x64002)))+~P1(f862(f54(x64001),x64002))
% 25.54/25.41 [6403]E(x64031,f106(x64032))+E(f862(f862(f157(x64032),x64031),f862(f862(f3(a924),f862(f182(f925(x64032)),x64031)),f71(a924))),f137(x64032,x64031))
% 25.54/25.41 [6425]E(x64251,f106(x64252))+E(f862(f862(f127(x64252),f862(f164(x64252),x64251)),f862(f862(f144(x64252),f862(f134(x64252),x64251)),f106(x64252))),f862(f160(x64252),x64251))
% 25.54/25.41 [6426]~P1(f862(f181(f932(x64261,a921)),x64262))+P1(f862(f862(f321(x64261),x64262),f181(f932(x64261,a921))))
% 25.54/25.41 [6455]~P1(f862(f54(x64551),f30(f932(x64551,a921),x64552)))+P1(f862(f54(f932(x64551,a921)),x64552))
% 25.54/25.41 [6477]P1(f862(f862(f227(a924),f862(f96(a924),x64771)),f862(f96(a924),x64772)))+~P1(f862(f862(f227(a1),x64771),a76))
% 25.54/25.41 [6498]~P1(f862(f862(f228(a1),x64981),x64982))+P1(f862(f862(f227(a1),x64981),f862(f862(f3(a1),x64982),f71(a1))))
% 25.54/25.41 [6499]~P1(f862(f862(f227(a1),x64991),x64992))+P1(f862(f862(f228(a1),x64991),f862(f862(f73(a1),x64992),f71(a1))))
% 25.54/25.41 [6500]~P1(f862(f862(f228(a1),x65001),x65002))+P1(f862(f862(f228(a1),x65001),f862(f862(f73(a1),x65002),f71(a1))))
% 25.54/25.41 [6502]~P1(f862(f862(f84(a1),x65021),x65022))+P1(f862(f862(f84(a1),f862(f96(a1),x65021)),f862(f96(a1),x65022)))
% 25.54/25.41 [6503]~P1(f862(f862(f227(a1),x65031),x65032))+P1(f862(f862(f227(a924),f862(f96(a924),x65031)),f862(f96(a924),x65032)))
% 25.54/25.41 [6504]~P1(f862(f862(f227(a1),x65041),x65042))+P1(f862(f862(f227(a1),f862(f96(a1),x65041)),f862(f96(a1),x65042)))
% 25.54/25.41 [6505]~P1(f862(f862(f227(a924),x65051),x65052))+P1(f862(f862(f227(a1),f862(f93(a1),x65051)),f862(f93(a1),x65052)))
% 25.54/25.41 [6506]~P1(f862(f862(f227(a924),x65061),x65062))+P1(f862(f862(f227(a1),f862(f93(a1),x65061)),f862(f93(a1),x65062)))
% 25.54/25.41 [6507]~P1(f862(f862(f228(a1),x65071),x65072))+P1(f862(f862(f228(a1),f862(f96(a1),x65071)),f862(f96(a1),x65072)))
% 25.54/25.41 [6508]~P1(f862(f862(f228(a924),x65081),x65082))+P1(f862(f862(f228(a1),f862(f93(a1),x65081)),f862(f93(a1),x65082)))
% 25.54/25.41 [6509]~P1(f862(f862(f228(a924),x65091),x65092))+P1(f862(f862(f228(a1),f862(f93(a1),x65091)),f862(f93(a1),x65092)))
% 25.54/25.41 [6516]~E(x65162,f181(f932(x65161,a921)))+P1(f862(f862(f227(f932(x65161,a921)),x65162),f181(f932(x65161,a921))))
% 25.54/25.41 [6530]~P1(f862(f862(f227(a924),x65301),x65302))+~P1(f862(f862(f227(a924),f862(a105,x65302)),x65301))
% 25.54/25.41 [6573]~P1(f862(f862(f227(a924),f862(a105,x65731)),f862(a105,x65732)))+P1(f862(f862(f227(a924),x65731),x65732))
% 25.54/25.41 [6574]~P1(f862(f862(f227(a92),f862(a5,x65741)),f862(a5,x65742)))+P1(f862(f862(f227(a924),x65741),x65742))
% 25.54/25.41 [6575]~P1(f862(f862(f227(a924),f862(a22,x65751)),f862(a22,x65752)))+P1(f862(f862(f227(a92),x65751),x65752))
% 25.54/25.41 [6576]~P1(f862(f862(f228(a924),f862(a105,x65761)),f862(a105,x65762)))+P1(f862(f862(f228(a924),x65761),x65762))
% 25.54/25.41 [6577]~P1(f862(f862(f228(a924),f862(a105,x65771)),f862(a105,x65772)))+P1(f862(f862(f228(a924),x65771),x65772))
% 25.54/25.41 [6578]~P1(f862(f862(f228(a92),f862(a5,x65781)),f862(a5,x65782)))+P1(f862(f862(f228(a924),x65781),x65782))
% 25.54/25.41 [6579]~P1(f862(f862(f228(a924),f862(a97,x65791)),f862(a97,x65792)))+P1(f862(f862(f228(a1),x65791),x65792))
% 25.54/25.41 [6580]~P1(f862(f862(f228(a924),f862(a22,x65801)),f862(a22,x65802)))+P1(f862(f862(f228(a92),x65801),x65802))
% 25.54/25.41 [6597]~P1(f862(f862(f278(a924),x65972),x65971))+P1(f862(f862(f321(a924),x65971),f284(a924,f278(a924),x65972)))
% 25.54/25.41 [6598]~P1(f862(f862(f278(a924),x65981),x65982))+P1(f862(f862(f321(a924),x65981),f286(a924,f278(a924),x65982)))
% 25.54/25.41 [6602]~P1(f862(f862(f321(x66021),x66022),f181(f932(x66021,a921))))+P1(f862(f181(f932(x66021,a921)),x66022))
% 25.54/25.41 [6622]~P1(f862(f862(f228(a924),f862(a97,x66222)),f862(a97,x66221)))+P1(f862(f862(f228(a1),f2(a1)),x66221))
% 25.54/25.41 [6652]P1(f862(f862(f227(a1),f2(a1)),f38(a1,x66521,x66522)))+~P1(f862(f862(f228(a1),f2(a1)),x66522))
% 25.54/25.41 [6653]P1(f862(f862(f227(a1),f2(a1)),f38(a1,x66531,x66532)))+~P1(f862(f862(f228(a1),f2(a1)),x66532))
% 25.54/25.41 [6813]P35(x68131,x68132)+~E(f862(f862(f280(x68131,x68131,x68131),x68132),x68132),f181(f932(f931(x68131,x68131),a921)))
% 25.54/25.41 [6825]~P35(x68251,x68252)+P35(x68251,f862(f862(f280(x68251,x68251,x68251),x68252),x68252))
% 25.54/25.41 [6836]P1(f862(f862(f227(a1),x68361),x68362))+~P1(f862(f862(f228(a1),x68361),f862(f862(f73(a1),x68362),f71(a1))))
% 25.54/25.41 [6837]P1(f862(f862(f228(a1),x68371),x68372))+~P1(f862(f862(f227(a1),x68371),f862(f862(f3(a1),x68372),f71(a1))))
% 25.54/25.41 [6839]P1(f862(f862(f84(a1),x68391),x68392))+~P1(f862(f862(f84(a1),f862(f96(a1),x68391)),f862(f96(a1),x68392)))
% 25.54/25.41 [6840]P1(f862(f862(f227(a924),x68401),x68402))+~P1(f862(f862(f227(a1),f862(f93(a1),x68401)),f862(f93(a1),x68402)))
% 25.54/25.41 [6841]P1(f862(f862(f227(a924),x68411),x68412))+~P1(f862(f862(f227(a1),f862(f93(a1),x68411)),f862(f93(a1),x68412)))
% 25.54/25.41 [6842]P1(f862(f862(f227(a1),x68421),x68422))+~P1(f862(f862(f227(a1),f862(f96(a1),x68421)),f862(f96(a1),x68422)))
% 25.54/25.41 [6843]P1(f862(f862(f228(a924),x68431),x68432))+~P1(f862(f862(f228(a1),f862(f93(a1),x68431)),f862(f93(a1),x68432)))
% 25.54/25.41 [6844]P1(f862(f862(f228(a924),x68441),x68442))+~P1(f862(f862(f228(a1),f862(f93(a1),x68441)),f862(f93(a1),x68442)))
% 25.54/25.41 [6845]P1(f862(f862(f228(a1),x68451),x68452))+~P1(f862(f862(f228(a924),f862(f96(a924),x68451)),f862(f96(a924),x68452)))
% 25.54/25.41 [6846]P1(f862(f862(f228(a1),x68461),x68462))+~P1(f862(f862(f228(a1),f862(f96(a1),x68461)),f862(f96(a1),x68462)))
% 25.54/25.41 [6939]P1(f862(f862(f278(a924),x69391),x69392))+~P1(f862(f862(f321(a924),x69392),f284(a924,f278(a924),x69391)))
% 25.54/25.41 [6940]P1(f862(f862(f278(a924),x69401),x69402))+~P1(f862(f862(f321(a924),x69401),f286(a924,f278(a924),x69402)))
% 25.54/25.41 [6941]~E(f702(x69412,x69411),f106(x69411))+E(f862(f135(f925(x69411),f925(x69411),f127(x69411),f106(x69411)),x69412),f106(x69411))
% 25.54/25.41 [6942]~E(f708(x69422,x69421),f106(x69421))+E(f862(f135(f925(x69421),f925(x69421),f127(x69421),f106(x69421)),x69422),f106(x69421))
% 25.54/25.41 [6946]~P3(x69461)+E(f862(f135(x69461,x69461,f94(x69461),f234(x69461)),x69462),f31(x69461,f862(f165(x69461),x69462)))
% 25.54/25.41 [6947]~P3(x69471)+E(f862(f135(x69471,x69471,f103(x69471),f181(x69471)),x69472),f30(x69471,f862(f165(x69471),x69472)))
% 25.54/25.41 [6961]E(x69611,f2(a92))+E(f862(f862(f73(a924),f862(a22,f862(f862(f3(a92),x69611),f71(a92)))),f862(a105,x69612)),f862(f862(f73(a924),f862(a22,x69611)),x69612))
% 25.54/25.41 [7011]P1(f862(f862(f228(a1),f862(f862(f3(a1),x70111),x70112)),f2(a1)))+~P1(f862(f862(f228(a1),x70111),x70112))
% 25.54/25.41 [7036]~P109(x70361)+E(f862(f862(f103(f932(x70361,a921)),f862(f862(f301(x70361),x70362),f181(f932(x70361,a921)))),f862(f293(x70361),x70362)),f862(f274(x70361),x70362))
% 25.54/25.41 [7112]~P57(x71121,x71122)+P35(x71121,f862(f254(f931(x71121,x71121)),f862(f249(x71121,x71121,a921),x71122)))
% 25.54/25.41 [7113]~P57(x71131,x71132)+P55(x71131,f862(f254(f931(x71131,x71131)),f862(f249(x71131,x71131,a921),x71132)))
% 25.54/25.41 [7114]~P47(x71141,x71142)+P36(x71141,f862(f254(f931(x71141,x71141)),f862(f249(x71141,x71141,a921),x71142)))
% 25.54/25.41 [7115]~P48(x71151,x71152)+P49(x71151,f862(f254(f931(x71151,x71151)),f862(f249(x71151,x71151,a921),x71152)))
% 25.54/25.41 [7116]E(x71161,f181(f932(x71162,a921)))+~P1(f862(f862(f227(f932(x71162,a921)),x71161),f181(f932(x71162,a921))))
% 25.54/25.41 [7198]~P1(f862(f862(f228(a924),f2(a924)),x71982))+P1(f862(f862(f227(a924),f38(a924,x71981,x71982)),x71982))
% 25.54/25.41 [7199]~P1(f862(f862(f227(a1),f2(a1)),x71991))+P1(f862(f862(f227(a1),f38(a1,x71991,x71992)),x71991))
% 25.54/25.41 [7200]~P1(f862(f862(f228(a924),f2(a924)),x72002))+P1(f862(f862(f228(a924),f38(a924,x72001,x72002)),x72002))
% 25.54/25.41 [7201]~P1(f862(f862(f228(a1),f2(a1)),x72012))+P1(f862(f862(f228(a1),f38(a1,x72011,x72012)),x72012))
% 25.54/25.41 [7202]~P1(f862(f862(f228(a1),f2(a1)),x72022))+P1(f862(f862(f228(a1),f38(a1,x72021,x72022)),x72022))
% 25.54/25.41 [7279]~P110(x72791)+E(f862(f862(f3(f932(x72791,a921)),f862(f862(f301(x72791),x72792),f181(f932(x72791,a921)))),f862(f292(x72791),x72792)),f862(f862(f301(x72791),x72792),f181(f932(x72791,a921))))
% 25.54/25.41 [7354]~P46(x73541,x73542)+P50(x73541,f234(f932(x73541,a921)),f862(f254(f931(x73541,x73541)),f862(f249(x73541,x73541,a921),x73542)))
% 25.54/25.41 [7355]P1(f862(x73551,x73552))+P1(f862(f862(f321(f932(f931(a924,a924),a921)),f578(x73552,x73551)),a91))
% 25.54/25.41 [7399]E(f862(f862(f127(a924),f132(a924,f862(f295(a924,x73991),x73992))),f862(f862(f144(a924),x73992),f106(a924))),f132(a924,f862(f295(a924,x73991),f862(a105,x73992))))+~P1(f862(f862(f227(a924),x73991),x73992))
% 25.54/25.41 [7400]E(f862(f862(f127(a924),f132(a924,f862(f295(a924,x74001),x74002))),f862(f862(f144(a924),x74002),f106(a924))),f132(a924,f862(f295(a924,x74001),f862(a105,x74002))))+~P1(f862(f862(f227(a924),x74001),x74002))
% 25.54/25.41 [7555]E(x75551,f2(a924))+~E(f862(f135(a924,a924,f73(a924),x75551),x75552),f2(a924))
% 25.54/25.41 [7579]~P1(f862(f862(f228(a1),f862(f862(f3(a1),x75791),x75792)),f2(a1)))+P1(f862(f862(f228(a1),x75791),x75792))
% 25.54/25.41 [7609]P35(x76091,x76092)+~P35(x76091,f862(f862(f280(x76091,x76091,x76091),x76092),x76092))
% 25.54/25.41 [7634]~P1(f862(f862(f227(a924),f862(a105,x76341)),x76342))+P1(f178(a921,a231,f862(f227(a924),x76341),x76342))
% 25.54/25.41 [7789]P22(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x77891),x77892)+P1(f862(f862(f321(a924),f592(x77891,x77892)),x77892))
% 25.54/25.41 [7846]E(f862(f862(f862(f58(a924,x78461,f73(a924)),f862(f18(a924,x78461),f71(a924))),f2(a924)),x78462),f862(f28(x78461),x78462))+~P1(f862(f54(x78461),x78462))
% 25.54/25.41 [7847]E(f862(f862(f862(f58(a924,x78471,f73(a924)),f862(f18(a924,x78471),f71(a924))),f2(a924)),x78472),f862(f28(x78471),x78472))+~P1(f862(f54(x78471),x78472))
% 25.54/25.41 [7889]P22(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x78891),x78892)+~P1(f862(f862(f227(a924),x78891),f592(x78891,x78892)))
% 25.54/25.41 [7944]P35(x79441,x79442)+P1(f862(f862(f227(f932(x79441,a921)),f589(x79442,x79441)),f862(f276(x79441,x79441,x79442),f589(x79442,x79441))))
% 25.54/25.41 [7949]P57(x79491,x79492)+~P35(x79491,f862(f254(f931(x79491,x79491)),f862(f249(x79491,x79491,a921),x79492)))
% 25.54/25.41 [7950]P47(x79501,x79502)+~P36(x79501,f862(f254(f931(x79501,x79501)),f862(f249(x79501,x79501,a921),x79502)))
% 25.54/25.41 [7951]P48(x79511,x79512)+~P49(x79511,f862(f254(f931(x79511,x79511)),f862(f249(x79511,x79511,a921),x79512)))
% 25.54/25.41 [8019]P1(f862(f862(f227(a924),f862(a105,x80191)),x80192))+~P1(f178(a921,a231,f862(f227(a924),x80191),x80192))
% 25.54/25.41 [8076]P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x80761),x80762)),f299(a924,a309)))+~P1(f862(f862(f227(a924),x80761),x80762))
% 25.54/25.41 [8175]P46(x81751,x81752)+~P50(x81751,f234(f932(x81751,a921)),f862(f254(f931(x81751,x81751)),f862(f249(x81751,x81751,a921),x81752)))
% 25.54/25.41 [8231]~P1(f862(f130(x82311),x82312))+P1(f862(f130(f932(x82311,a921)),f862(f862(f147(f925(x82311),f932(x82311,a921)),f165(x82311)),f47(x82311,x82312))))
% 25.54/25.41 [8435]~P35(x84351,f862(f277(x84351,x84351),x84352))+P35(x84351,f862(f277(x84351,x84351),f862(f862(f280(x84351,x84351,x84351),x84352),f299(x84351,x84352))))
% 25.54/25.41 [8533]P23(x85331,a924,f826(x85332,x85331),x85332,f862(f295(a924,f2(a924)),f862(f28(x85331),x85332)))+~P1(f862(f54(x85331),x85332))
% 25.54/25.41 [8534]P23(a924,x85341,f827(x85342,x85341),f862(f295(a924,f2(a924)),f862(f28(x85341),x85342)),x85342)+~P1(f862(f54(x85341),x85342))
% 25.54/25.41 [8551]P23(a924,x85511,f828(x85512,x85511),f296(a924,f71(a924),f862(f28(x85511),x85512)),x85512)+~P1(f862(f54(x85511),x85512))
% 25.54/25.41 [8561]P1(f862(f54(f931(x85611,x85611)),f862(f862(f280(x85611,x85611,x85611),x85612),f299(x85611,x85612))))+~P1(f862(f54(f931(x85611,x85611)),x85612))
% 25.54/25.41 [8588]E(x85881,f2(a1))+P1(f862(f42(x85882,x85881),f862(f862(f244(a1,a1),f862(f862(f29(a1),x85882),x85881)),f38(a1,x85882,x85881))))
% 25.54/25.41 [8602]~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x86021),x86022)),f299(a924,a309)))+P1(f862(f862(f227(a924),x86021),x86022))
% 25.54/25.41 [8619]~P81(x86191)+E(f862(f135(x86191,x86191,f862(f9(x86191,x86191,x86191),f73(x86191)),f2(x86191)),f862(f161(x86191),x86192)),f862(f135(x86191,x86191,f73(x86191),f2(x86191)),x86192))
% 25.54/25.41 [8793]~P109(x87931)+E(f862(f135(f925(x87931),x87931,f862(f9(x87931,f925(x87931),f925(x87931)),f141(x87931,x87931,f7(x87931))),f106(x87931)),x87932),f143(x87931,x87931,f7(x87931),x87932))
% 25.54/25.41 [8905]~P55(x89051,f862(f254(f931(x89051,x89051)),f862(f249(x89051,x89051,a921),x89052)))+P55(x89051,f862(f254(f931(x89051,x89051)),f862(f249(x89051,x89051,a921),f235(x89051,x89051,x89052))))
% 25.54/25.41 [8919]P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x89191),x89192)),f862(f862(f280(a924,a924,a924),a309),f299(a924,a309))))+~P1(f862(f862(f228(a924),x89191),x89192))
% 25.54/25.41 [8965]~P1(f862(f54(f931(x89651,x89651)),f862(f862(f280(x89651,x89651,x89651),x89652),f299(x89651,x89652))))+P1(f862(f54(f931(x89651,x89651)),x89652))
% 25.54/25.41 [9023]~P55(x90231,f862(f254(f931(x90231,x90231)),f862(f249(x90231,x90231,a921),f235(x90231,x90231,x90232))))+P55(x90231,f862(f254(f931(x90231,x90231)),f862(f249(x90231,x90231,a921),x90232)))
% 25.54/25.41 [9222]P55(x92221,x92222)+P1(f862(f862(f321(f931(x92221,x92221)),f862(f862(f244(x92221,x92221),f621(x92222,x92221)),f621(x92222,x92221))),f862(f862(f280(x92221,x92221,x92221),x92222),f299(x92221,x92222))))
% 25.54/25.41 [9223]P55(x92231,x92232)+P1(f862(f862(f321(f931(x92231,x92231)),f862(f862(f244(x92231,x92231),f630(x92232,x92231)),f630(x92232,x92231))),f862(f862(f280(x92231,x92231,x92231),x92232),f299(x92231,x92232))))
% 25.54/25.41 [9342]~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x93421),x93422)),f862(f862(f280(a924,a924,a924),a309),f299(a924,a309))))+P1(f862(f862(f228(a924),x93421),x93422))
% 25.54/25.41 [10091]E(f862(f87(x100911),f879(x100912,x100911)),x100912)+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x100911,f932(a920,a921))),f930(a920,x100911)),a921)),x100912),f862(f254(f932(f922(f930(a919,f932(x100911,f932(a920,a921))),f930(a920,x100911)),a921)),f88(x100911))))
% 25.54/25.41 [10092]E(f862(f87(x100921),f862(f85(x100921),x100922)),x100922)+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x100921,f932(a920,a921))),f930(a920,x100921)),a921)),x100922),f862(f254(f932(f922(f930(a919,f932(x100921,f932(a920,a921))),f930(a920,x100921)),a921)),f88(x100921))))
% 25.54/25.41 [5257]~P98(x52571)+E(f862(f862(f73(x52571),f862(f96(x52571),a76)),x52572),x52572)
% 25.54/25.41 [5287]~P96(x52871)+E(f862(f862(f103(x52871),f862(f72(x52871),x52872)),x52872),f234(x52871))
% 25.54/25.41 [5288]~P96(x52881)+E(f862(f862(f94(x52881),f862(f72(x52881),x52882)),x52882),f181(x52881))
% 25.54/25.41 [5289]~P59(x52891)+E(f862(f862(f73(x52891),f862(f72(x52891),x52892)),x52892),f2(x52891))
% 25.54/25.41 [5290]~P68(x52901)+E(f862(f862(f73(x52901),f862(f72(x52901),x52902)),x52902),f2(x52901))
% 25.54/25.41 [5323]~P98(x53231)+E(f862(f862(f74(x53231),f862(f96(x53231),a90)),x53232),f862(f72(x53231),x53232))
% 25.54/25.41 [5482]~P115(x54821)+E(f862(f862(f74(x54821),f862(f72(x54821),f71(x54821))),x54822),f862(f72(x54821),x54822))
% 25.54/25.41 [5527]E(f862(f69(a1),x55271),f71(a1))+~E(f862(f69(a1),f862(f862(f74(a1),x55271),x55272)),f71(a1))
% 25.54/25.41 [5620]~P98(x56201)+E(f862(f862(f73(x56201),f71(x56201)),f862(f96(x56201),x56202)),f862(f96(x56201),f862(f862(f3(a1),x56202),a90)))
% 25.54/25.41 [5673]~P3(x56731)+E(f31(x56731,f862(f862(f301(x56731),x56732),f181(f932(x56731,a921)))),x56732)
% 25.54/25.41 [5674]~P3(x56741)+E(f30(x56741,f862(f862(f301(x56741),x56742),f181(f932(x56741,a921)))),x56742)
% 25.54/25.41 [5675]~P93(x56751)+E(f12(x56751,f862(f862(f301(x56751),x56752),f181(f932(x56751,a921)))),x56752)
% 25.54/25.41 [5676]~P93(x56761)+E(f15(x56761,f862(f862(f301(x56761),x56762),f181(f932(x56761,a921)))),x56762)
% 25.54/25.41 [5677]~P109(x56771)+E(f16(x56771,f862(f862(f301(x56771),x56772),f181(f932(x56771,a921)))),x56772)
% 25.54/25.41 [5678]~P109(x56781)+E(f17(x56781,f862(f862(f301(x56781),x56782),f181(f932(x56781,a921)))),x56782)
% 25.54/25.41 [5700]E(f862(f862(f73(a924),x57001),f862(f862(f3(a924),x57002),x57001)),x57002)+P1(f862(f862(f228(a924),x57002),x57001))
% 25.54/25.41 [5739]E(x57391,f106(x57392))+P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x57392)),x57391)))
% 25.54/25.41 [5866]~P109(x58661)+E(f13(x58661,f225(x58661),f862(f862(f301(x58661),x58662),f181(f932(x58661,a921)))),x58662)
% 25.54/25.41 [5867]~P109(x58671)+E(f14(x58671,f226(x58671),f862(f862(f301(x58671),x58672),f181(f932(x58671,a921)))),x58672)
% 25.54/25.41 [5928]E(f862(f862(f3(a924),x59281),f862(f862(f3(a924),x59281),x59282)),x59282)+~P1(f862(f862(f227(a924),x59282),x59281))
% 25.54/25.41 [5929]E(f862(f862(f73(a924),x59291),f862(f862(f3(a924),x59292),x59291)),x59292)+~P1(f862(f862(f227(a924),x59291),x59292))
% 25.54/25.41 [5950]E(f38(a924,f862(f862(f3(a924),x59501),x59502),x59502),f38(a924,x59501,x59502))+P1(f862(f862(f228(a924),x59501),x59502))
% 25.54/25.41 [5951]E(f38(a924,f862(f862(f3(a924),x59511),x59512),x59512),f38(a924,x59511,x59512))+P1(f862(f862(f228(a924),x59511),x59512))
% 25.54/25.41 [5962]E(f862(f72(a1),f862(f862(f29(a1),x59621),f862(f72(a1),x59622))),f283(x59621,x59622))+P1(f862(f862(f227(a1),f2(a1)),x59622))
% 25.54/25.41 [5964]~E(x59642,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x59641),x59642)))
% 25.54/25.41 [6027]~P98(x60271)+E(f862(f862(f73(x60271),f862(f72(x60271),f71(x60271))),f862(f96(x60271),x60272)),f862(f96(x60271),f862(f862(f73(a1),x60272),a90)))
% 25.54/25.41 [6029]E(f862(f862(f236(a924),f862(f96(a924),x60291)),x60292),f862(f862(f236(a924),f2(a924)),x60292))+~P1(f862(a186,f862(f96(a1),x60291)))
% 25.54/25.41 [6136]E(f862(f134(a924),f132(a924,f862(f295(a924,x61361),x61362))),x61361)+~P1(f862(f862(f228(a924),x61361),x61362))
% 25.54/25.41 [6152]E(f862(f862(f74(a924),f862(f96(a924),x61521)),f862(f96(a924),x61522)),f862(f96(a924),f862(f862(f74(a1),x61521),x61522)))+P1(f862(f862(f228(a1),x61521),a76))
% 25.54/25.41 [6158]~P129(x61581)+P1(f862(f862(f227(x61581),f2(x61581)),f862(f862(f74(x61581),x61582),x61582)))
% 25.54/25.41 [6170]E(f862(f862(f3(a924),f862(a105,x61701)),x61702),f862(a105,f862(f862(f3(a924),x61701),x61702)))+~P1(f862(f862(f227(a924),x61702),x61701))
% 25.54/25.41 [6173]E(f38(a924,f862(f862(f3(a924),x61731),x61732),x61732),f38(a924,x61731,x61732))+~P1(f862(f862(f227(a924),x61732),x61731))
% 25.54/25.41 [6224]E(f862(f862(f236(a924),f862(a97,x62241)),x62242),f862(a97,f862(f862(f236(a1),x62241),x62242)))+~P1(f862(f862(f227(a1),f2(a1)),x62241))
% 25.54/25.41 [6225]E(f862(f862(f236(a924),f862(a97,x62251)),x62252),f862(a97,f862(f862(f236(a1),x62251),x62252)))+~P1(f862(f862(f227(a1),f2(a1)),x62251))
% 25.54/25.41 [6243]P1(f862(f130(x62431),x62432))+P1(f862(f862(f228(a924),f673(x62432,x62431)),f862(f182(f925(x62431)),x62432)))
% 25.54/25.41 [6244]P1(f862(f130(x62441),x62442))+P1(f862(f862(f228(a924),f677(x62442,x62441)),f862(f182(f925(x62441)),x62442)))
% 25.54/25.41 [6256]~E(x62561,f106(x62562))+~P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x62562)),x62561)))
% 25.54/25.41 [6267]E(f137(a924,f132(a924,f862(f295(a924,x62671),x62672))),f862(f862(f3(a924),x62672),f71(a924)))+~P1(f862(f862(f228(a924),x62671),x62672))
% 25.54/25.41 [6270]E(f862(f862(f73(a1),x62701),f862(f93(a1),f862(a105,f411(x62702,x62701)))),x62702)+~P1(f862(f862(f228(a1),x62701),x62702))
% 25.54/25.41 [6277]E(x62771,f2(a924))+E(f862(f862(f74(a924),x62772),f862(f862(f236(a924),x62772),f862(f862(f3(a924),x62771),f71(a924)))),f862(f862(f236(a924),x62772),x62771))
% 25.54/25.41 [6305]E(f862(f862(f74(a924),f862(a97,x63051)),f862(a97,x63052)),f862(a97,f862(f862(f74(a1),x63051),x63052)))+~P1(f862(f862(f227(a1),f2(a1)),x63051))
% 25.54/25.41 [6306]E(f862(f862(f29(a924),f862(a97,x63061)),f862(a97,x63062)),f862(a97,f862(f862(f29(a1),x63061),x63062)))+~P1(f862(f862(f227(a1),f2(a1)),x63061))
% 25.54/25.41 [6320]~P119(x63201)+E(f862(f862(f73(x63201),x63202),x63202),f862(f862(f74(x63201),f862(f862(f73(x63201),f71(x63201)),f71(x63201))),x63202))
% 25.54/25.41 [6342]E(f862(f862(f3(a1),f862(f93(a1),x63421)),f862(f93(a1),x63422)),f862(f93(a1),f862(f862(f3(a924),x63421),x63422)))+~P1(f862(f862(f227(a924),x63422),x63421))
% 25.54/25.41 [6344]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x63441),x63442)),f43(x63441,x63442))+~P1(f862(f862(f227(a1),x63442),f2(a1)))
% 25.54/25.41 [6377]E(f172(x63771,x63772),f106(f925(x63771)))+P1(f862(f862(f321(f925(x63771)),f672(x63772,x63771)),f862(f165(f925(x63771)),x63772)))
% 25.54/25.41 [6387]E(f109(a1,f862(f122(a1),x63871),f121(x63872,f862(f862(f73(a1),x63871),f71(a1)))),f121(x63872,x63871))+P1(f862(f862(f228(a1),x63872),x63871))
% 25.54/25.41 [6461]E(f862(f862(f144(a1),x64611),f171(f862(f862(f73(a1),x64611),f71(a1)),x64612)),f171(x64611,x64612))+~P1(f862(f862(f227(a1),x64611),x64612))
% 25.54/25.41 [6501]~P1(f862(f862(f228(a924),x65012),x65011))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f3(a924),x65011),x65012)))
% 25.54/25.41 [6535]~P1(f862(f862(f228(a924),x65351),f862(a97,x65352)))+P1(f862(f862(f228(a1),f862(f93(a1),x65351)),x65352))
% 25.54/25.41 [6564]~P109(x65641)+E(f862(f862(f103(f932(x65641,a921)),f862(f292(x65641),x65642)),f862(f862(f301(x65641),x65642),f181(f932(x65641,a921)))),f862(f294(x65641),x65642))
% 25.54/25.41 [6565]~P1(f862(f862(f227(a1),f2(a1)),x65651))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f236(a1),x65651),x65652)))
% 25.54/25.41 [6566]~P1(f862(f862(f228(a924),f2(a924)),x65662))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f73(a924),x65661),x65662)))
% 25.54/25.41 [6567]~P1(f862(f862(f228(a924),f2(a924)),x65671))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f73(a924),x65671),x65672)))
% 25.54/25.41 [6568]~P1(f862(f862(f228(a924),f2(a924)),x65681))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x65681),x65682)))
% 25.54/25.41 [6596]~E(f862(x65961,f2(a924)),f2(a924))+E(f862(f862(f8(a924,a924),x65961),f296(a924,f862(a105,f2(a924)),x65962)),f862(f862(f8(a924,a924),x65961),f296(a924,f2(a924),x65962)))
% 25.54/25.41 [6661]~P98(x66611)+E(f862(f862(f74(x66611),f862(f862(f73(x66611),f71(x66611)),f71(x66611))),f862(f96(x66611),x66612)),f862(f96(x66611),f862(f862(f73(a1),x66612),x66612)))
% 25.54/25.41 [6678]E(f862(f862(f301(a1),x66781),f296(a1,f862(f862(f73(a1),x66781),f71(a1)),x66782)),f296(a1,x66781,x66782))+P1(f862(f862(f228(a1),x66782),x66781))
% 25.54/25.41 [6679]P1(f862(f862(f228(a924),x66791),f862(a97,x66792)))+~P1(f862(f862(f228(a1),f862(f93(a1),x66791)),x66792))
% 25.54/25.41 [6781]E(f862(a97,f862(f862(f236(a1),f862(f96(a1),x67811)),f862(f96(a924),x67812))),f862(f862(f236(a924),f862(f96(a924),x67811)),f862(f96(a924),x67812)))+P1(f862(a186,f862(f96(a1),x67811)))
% 25.54/25.41 [6782]E(f862(a97,f862(f862(f29(a1),f862(f96(a1),x67821)),f862(f96(a1),x67822))),f862(f862(f29(a924),f862(f96(a924),x67821)),f862(f96(a924),x67822)))+P1(f862(a186,f862(f96(a1),x67821)))
% 25.54/25.41 [6838]P1(f862(f862(f228(a924),x68381),x68382))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f3(a924),x68382),x68381)))
% 25.54/25.41 [6882]P1(f862(f862(f228(a924),f2(a924)),x68821))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x68822),x68821)))
% 25.54/25.41 [6883]P1(f862(f862(f228(a924),f2(a924)),x68831))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x68831),x68832)))
% 25.54/25.41 [6899]E(f132(a924,f862(f295(a924,f862(f96(a924),x68991)),f862(f96(a924),x68992))),f106(a924))+P1(f862(f862(f228(a924),f862(f96(a924),x68991)),f862(f96(a924),x68992)))
% 25.54/25.41 [6901]~P1(f862(f862(f227(a1),x69011),f2(a1)))+E(f862(f862(f74(a924),f862(a97,f862(f72(a1),x69011))),f862(a97,f862(f72(a1),x69012))),f862(a97,f862(f862(f74(a1),x69011),x69012)))
% 25.54/25.41 [6958]~E(x69582,f181(f932(x69581,a921)))+P1(f862(f862(f227(f932(x69581,a921)),x69582),f862(f72(f932(x69581,a921)),x69582)))
% 25.54/25.41 [7021]~P98(x70211)+E(f862(f862(f73(x70211),f862(f862(f73(x70211),f2(x70211)),f862(f96(x70211),x70212))),f862(f96(x70211),x70212)),f862(f96(x70211),f862(f862(f73(a1),x70212),x70212)))
% 25.54/25.41 [7076]~P1(f862(f862(f228(a1),x70761),x70762))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x70761),f71(a1))),x70762))
% 25.54/25.41 [7077]~P1(f862(f862(f228(a1),x70771),x70772))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x70771),f71(a1))),x70772))
% 25.54/25.41 [7143]E(x71431,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x71432)),f862(f72(a1),f862(f93(a1),x71431))))
% 25.54/25.41 [7144]E(x71441,f2(a924))+~P1(f862(f862(f227(a1),f862(f93(a1),x71441)),f862(f72(a1),f862(f93(a1),x71442))))
% 25.54/25.41 [7246]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x72461),x72462)),f43(x72461,x72462))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x72461),x72462)))
% 25.54/25.41 [7291]~P24(x72911,x72912)+P35(x72911,f862(f243(f932(f931(x72911,x72911),a921),f932(f931(x72911,x72911),a921)),x72912))
% 25.54/25.41 [7310]~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x73101))+P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f236(a924),x73101),x73102)))
% 25.54/25.41 [7480]~P1(f862(f862(f84(a1),x74801),x74802))+P1(f862(f862(f84(a1),f862(f862(f73(a1),x74801),x74801)),f862(f862(f73(a1),x74802),x74802)))
% 25.54/25.41 [7491]~P1(f862(f862(f227(a1),x74911),x74912))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x74911),x74911)),f862(f862(f73(a1),x74912),x74912)))
% 25.54/25.41 [7492]~P1(f862(f862(f227(a1),x74921),x74922))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x74921),x74921)),f862(f862(f73(a1),x74922),x74922)))
% 25.54/25.41 [7496]~P1(f862(f862(f228(a1),x74961),x74962))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x74961),x74961)),f862(f862(f73(a1),x74962),x74962)))
% 25.54/25.41 [7497]~P1(f862(f862(f228(a1),x74971),x74972))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x74971),x74971)),f862(f862(f73(a1),x74972),x74972)))
% 25.54/25.41 [7556]~P1(f862(f862(f228(a924),f2(a924)),x75561))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x75561),f862(a105,x75562))),x75561))
% 25.54/25.41 [7591]P1(f862(f862(f227(a924),f862(a105,f2(a924))),x75911))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x75912),x75911)))
% 25.54/25.41 [7592]P1(f862(f862(f227(a924),f862(a105,f2(a924))),x75921))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x75921),x75922)))
% 25.54/25.41 [7596]P1(f862(f862(f227(a924),f862(f862(f157(a924),x75961),x75962)),f862(f158(a924),x75961)))+~P1(f862(f862(f228(a924),x75962),f862(f182(f925(a924)),x75961)))
% 25.54/25.41 [7633]P1(f862(f862(f228(a1),x76331),x76332))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x76331),f71(a1))),x76332))
% 25.54/25.41 [7642]~P1(f862(f862(f321(a924),x76421),x76422))+P1(f862(f862(f321(a1),f862(f93(a1),x76421)),f862(f302(a924,a1,f93(a1)),x76422)))
% 25.54/25.41 [7674]P1(f862(f54(x76741),f234(f932(x76741,a921))))+~P1(f862(f54(f932(x76742,x76741)),f234(f932(f932(x76742,x76741),a921))))
% 25.54/25.41 [7675]P1(f862(f54(x76751),f234(f932(x76751,a921))))+~P1(f862(f54(f930(x76752,x76751)),f234(f932(f930(x76752,x76751),a921))))
% 25.54/25.41 [7676]P1(f862(f54(x76761),f234(f932(x76761,a921))))+~P1(f862(f54(f930(x76761,x76762)),f234(f932(f930(x76761,x76762),a921))))
% 25.54/25.41 [7715]E(x77151,f181(f932(x77152,a921)))+~P1(f862(f862(f227(f932(x77152,a921)),x77151),f862(f72(f932(x77152,a921)),x77151)))
% 25.54/25.41 [7857]E(f862(f135(f925(x78571),f925(x78571),f127(x78571),f106(x78571)),x78572),f106(x78571))+P1(f862(f862(f321(f925(x78571)),f702(x78572,x78571)),f862(f165(f925(x78571)),x78572)))
% 25.54/25.41 [7858]E(f862(f135(f925(x78581),f925(x78581),f127(x78581),f106(x78581)),x78582),f106(x78581))+P1(f862(f862(f321(f925(x78581)),f708(x78582,x78581)),f862(f165(f925(x78581)),x78582)))
% 25.54/25.41 [7995]E(f172(x79951,f862(f862(f144(f925(x79951)),f106(x79951)),x79952)),f172(x79951,x79952))+~P1(f862(f307(f925(f925(x79951)),f173(x79951)),f862(f862(f144(f925(x79951)),f106(x79951)),x79952)))
% 25.54/25.41 [8092]P1(f862(f862(f84(a1),x80921),x80922))+~P1(f862(f862(f84(a1),f862(f862(f73(a1),x80921),x80921)),f862(f862(f73(a1),x80922),x80922)))
% 25.54/25.41 [8094]P1(f862(f862(f227(a1),x80941),x80942))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x80941),x80941)),f862(f862(f73(a1),x80942),x80942)))
% 25.54/25.41 [8095]P1(f862(f862(f227(a1),x80951),x80952))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x80951),x80951)),f862(f862(f73(a1),x80952),x80952)))
% 25.54/25.41 [8099]P1(f862(f862(f228(a1),x80991),x80992))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x80991),x80991)),f862(f862(f73(a1),x80992),x80992)))
% 25.54/25.41 [8100]P1(f862(f862(f228(a1),x81001),x81002))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x81001),x81001)),f862(f862(f73(a1),x81002),x81002)))
% 25.54/25.41 [8195]~P119(x81951)+E(f862(f862(f74(x81951),f862(f862(f73(x81951),f71(x81951)),f71(x81951))),f862(f862(f8(a924,x81951),f93(x81951)),f296(a924,f71(a924),x81952))),f862(f862(f74(x81951),f862(f93(x81951),x81952)),f862(f862(f73(x81951),f862(f93(x81951),x81952)),f71(x81951))))
% 25.54/25.41 [8230]E(f862(f862(f144(a1),f862(f96(a1),x82301)),f171(f862(f862(f73(a1),f862(f96(a1),x82301)),f71(a1)),f862(f96(a1),x82302))),f171(f862(f96(a1),x82301),f862(f96(a1),x82302)))+~P1(f862(f862(f227(a1),f862(f96(a1),x82301)),f862(f96(a1),x82302)))
% 25.54/25.41 [8245]P1(f862(f862(f321(a924),x82451),x82452))+~P1(f862(f862(f321(a1),f862(f93(a1),x82451)),f862(f302(a924,a1,f93(a1)),x82452)))
% 25.54/25.41 [8407]~P1(f862(f54(x84071),x84072))+E(f862(f302(a924,x84071,f548(x84072,x84071)),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),f542(x84072,x84071)))),x84072)
% 25.54/25.41 [8688]P51(x86881,x86882)+P1(f862(f862(f321(f931(x86881,x86881)),f862(f862(f244(x86881,x86881),f513(x86882,x86881)),f513(x86882,x86881))),x86882))
% 25.54/25.41 [8689]P36(x86891,x86892)+P1(f862(f862(f321(f931(x86891,x86891)),f862(f862(f244(x86891,x86891),f794(x86892,x86891)),f797(x86892,x86891))),x86892))
% 25.54/25.41 [8690]P36(x86901,x86902)+P1(f862(f862(f321(f931(x86901,x86901)),f862(f862(f244(x86901,x86901),f797(x86902,x86901)),f798(x86902,x86901))),x86902))
% 25.54/25.41 [8691]P37(x86911,x86912)+P1(f862(f862(f321(f931(x86911,x86911)),f862(f862(f244(x86911,x86911),f713(x86912,x86911)),f712(x86912,x86911))),x86912))
% 25.54/25.41 [8692]P37(x86921,x86922)+P1(f862(f862(f321(f931(x86921,x86921)),f862(f862(f244(x86921,x86921),f712(x86922,x86921)),f713(x86922,x86921))),x86922))
% 25.54/25.41 [8693]P49(x86931,x86932)+P1(f862(f862(f321(f931(x86931,x86931)),f862(f862(f244(x86931,x86931),f808(x86932,x86931)),f809(x86932,x86931))),x86932))
% 25.54/25.41 [8836]~P98(x88361)+E(f862(f862(f3(x88361),f71(x88361)),f862(f96(x88361),x88362)),f862(f96(x88361),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x88362))))
% 25.54/25.41 [8961]~P1(f862(f862(f227(f932(a924,a921)),x89611),x89612))+P1(f862(f862(f227(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x89611)),f862(f302(a924,a1,f93(a1)),x89612)))
% 25.54/25.41 [8962]~P1(f862(f862(f228(f932(a924,a921)),x89621),x89622))+P1(f862(f862(f228(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x89621)),f862(f302(a924,a1,f93(a1)),x89622)))
% 25.54/25.41 [8995]~P1(f862(f862(f228(a1),x89951),x89952))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89951),x89951)),a90)),f862(f862(f73(a1),x89952),x89952)))
% 25.54/25.41 [8996]~P1(f862(f862(f228(a1),x89961),x89962))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89961),x89961)),a90)),f862(f862(f73(a1),x89962),x89962)))
% 25.54/25.41 [8997]~P1(f862(f862(f228(a1),x89971),x89972))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89971),x89971)),a90)),f862(f862(f73(a1),x89972),x89972)))
% 25.54/25.41 [8998]~P1(f862(f862(f228(a1),x89981),x89982))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x89981),x89981)),a90)),f862(f862(f73(a1),x89982),x89982)))
% 25.54/25.41 [9073]~P1(f862(f862(f321(a924),x90731),f862(f165(a924),x90732)))+P1(f862(f862(f227(a924),x90731),f862(f135(a924,a924,f73(a924),f2(a924)),x90732)))
% 25.54/25.41 [9162]P43(x91621,x91622)+~P1(f862(f862(f321(f931(x91621,x91621)),f862(f862(f244(x91621,x91621),f493(x91622,x91621)),f493(x91622,x91621))),x91622))
% 25.54/25.41 [9163]P36(x91631,x91632)+~P1(f862(f862(f321(f931(x91631,x91631)),f862(f862(f244(x91631,x91631),f794(x91632,x91631)),f798(x91632,x91631))),x91632))
% 25.54/25.41 [9164]P49(x91641,x91642)+~P1(f862(f862(f321(f931(x91641,x91641)),f862(f862(f244(x91641,x91641),f809(x91642,x91641)),f808(x91642,x91641))),x91642))
% 25.54/25.41 [9304]~P1(f862(f862(f227(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x93041)),f862(f302(a924,a1,f93(a1)),x93042)))+P1(f862(f862(f227(f932(a924,a921)),x93041),x93042))
% 25.54/25.41 [9305]~P1(f862(f862(f228(f932(a1,a921)),f862(f302(a924,a1,f93(a1)),x93051)),f862(f302(a924,a1,f93(a1)),x93052)))+P1(f862(f862(f228(f932(a924,a921)),x93051),x93052))
% 25.54/25.41 [9390]P1(f862(f862(f228(a1),x93901),x93902))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93901),x93901)),a90)),f862(f862(f73(a1),x93902),x93902)))
% 25.54/25.41 [9391]P1(f862(f862(f228(a1),x93911),x93912))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93911),x93911)),a90)),f862(f862(f73(a1),x93912),x93912)))
% 25.54/25.41 [9392]P1(f862(f862(f228(a1),x93921),x93922))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93921),x93921)),a90)),f862(f862(f73(a1),x93922),x93922)))
% 25.54/25.41 [9393]P1(f862(f862(f228(a1),x93931),x93932))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x93931),x93931)),a90)),f862(f862(f73(a1),x93932),x93932)))
% 25.54/25.41 [10276]~P106(x102761)+E(f109(f925(x102761),f862(f122(f925(x102761)),f106(x102761)),f862(f862(f862(f89(f926(f925(x102761))),f862(f862(f228(a1),f2(a1)),x102762)),f862(f111(f931(x102761,f925(x102761)),f925(x102761),f124(x102761,f925(x102761),f125(x102761,f862(f862(f3(a1),x102762),f71(a1))),f125(f925(x102761),f862(f862(f3(a1),x102762),f71(a1))))),f862(f249(x102761,f925(x102761),f926(f925(x102761))),f862(f862(f10(f932(f925(x102761),f925(x102761)),f932(f925(x102761),f926(f925(x102761))),x102761),f862(f10(f925(x102761),f926(f925(x102761)),f925(x102761)),f122(f925(x102761)))),f144(x102761))))),f108(f925(x102761)))),f125(f925(x102761),x102762))
% 25.54/25.41 [10298]~P1(f862(f54(x102981),x102982))+E(f862(f182(f925(x102981)),f83(f925(x102981),f862(f862(f20(f925(x102981),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x102981)),a318),f862(f862(f9(f925(x102981),f932(x102981,a921),a921),f862(f862(f10(f932(x102981,a921),f932(f932(x102981,a921),a921),f925(x102981)),a317),f165(x102981))),x102982))),f130(x102981)))),f207(x102981,x102982))
% 25.54/25.41 [6266]E(f862(f862(f73(a924),f862(f862(f3(a924),x62661),x62662)),x62662),x62661)+~P1(f862(f862(f227(a924),x62662),x62661))
% 25.54/25.41 [6338]E(f862(f862(f29(a924),f862(f862(f74(a924),x63381),x63382)),x63382),x63381)+~P1(f862(f862(f228(a924),f2(a924)),x63382))
% 25.54/25.41 [6339]E(f862(f862(f29(a924),f862(f862(f74(a924),x63391),x63392)),x63391),x63392)+~P1(f862(f862(f228(a924),f2(a924)),x63391))
% 25.54/25.41 [6343]~P72(x63431)+E(f862(f862(f8(a924,x63431),f862(f157(x63431),x63432)),f862(f295(a924,f2(a924)),f862(f182(f925(x63431)),x63432))),f862(f158(x63431),x63432))
% 25.54/25.41 [6453]E(f38(a924,f862(a105,f862(f862(f74(a924),x64531),x64532)),x64531),f71(a924))+~P1(f862(f862(f228(a924),f71(a924)),x64531))
% 25.54/25.41 [6459]E(f862(a105,f862(f862(f73(a924),f862(f96(a924),x64591)),x64592)),f862(f862(f73(a924),f71(a924)),x64592))+~P1(f862(a186,f862(f96(a1),x64591)))
% 25.54/25.41 [6488]E(f862(a97,f862(f862(f236(a1),f862(f96(a1),x64881)),x64882)),f862(f862(f236(a924),f862(f96(a924),x64881)),x64882))+P1(f862(a186,f862(f96(a1),x64881)))
% 25.54/25.41 [6734]E(f862(f862(f3(a924),x67341),f862(f96(a924),f862(f862(f73(a1),x67342),a90))),f862(f862(f3(a924),f862(a105,x67341)),f862(f96(a924),x67342)))+~P1(f862(f862(f228(a1),a76),x67342))
% 25.54/25.41 [6812]E(x68121,f2(a924))+E(f862(a105,f862(f862(f73(a924),f862(f862(f3(a924),x68121),f71(a924))),x68122)),f862(f862(f73(a924),x68121),x68122))
% 25.54/25.41 [6852]E(x68521,f2(a1))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x68521)),x68522)))
% 25.54/25.41 [6867]~E(x68672,f2(a924))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x68671)),x68672)))
% 25.54/25.41 [6904]E(x69041,f2(a924))+E(f862(f862(f73(a924),x69042),f862(f862(f74(a924),f862(f862(f3(a924),x69041),f71(a924))),x69042)),f862(f862(f74(a924),x69041),x69042))
% 25.54/25.41 [6951]~P1(f862(f862(f227(a1),x69511),x69512))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x69511),a90)),x69512))
% 25.54/25.41 [7080]E(f862(f862(f144(a924),x70801),f132(a924,f862(f295(a924,f862(a105,x70801)),x70802))),f132(a924,f862(f295(a924,x70801),x70802)))+~P1(f862(f862(f228(a924),x70801),x70802))
% 25.54/25.41 [7081]E(f862(f862(f144(a924),x70811),f132(a924,f862(f295(a924,f862(a105,x70811)),x70812))),f132(a924,f862(f295(a924,x70811),x70812)))+~P1(f862(f862(f228(a924),x70811),x70812))
% 25.54/25.41 [7282]E(x72821,x72822)+~E(f862(f862(f3(a1),f862(f862(f73(a1),x72821),x72821)),a90),f862(f862(f3(a1),f862(f862(f73(a1),x72822),x72822)),a90))
% 25.54/25.41 [7285]E(x72851,f106(x72852))+E(f258(x72852,f862(f862(f147(x72852,f931(a92,x72852)),f862(f244(a92,x72852),f71(a92))),x72851)),f267(x72852,x72851))
% 25.54/25.41 [7525]P1(f862(f862(f227(a1),x75251),x75252))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x75251),a90)),x75252))
% 25.54/25.41 [7997]~P1(f862(f862(f228(a924),x79971),x79972))+P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x79971),x79972)),a232))
% 25.54/25.41 [8222]~P1(f862(f862(f228(a92),f2(a92)),x82221))+P1(f862(f862(f228(a92),f862(f243(a92,f931(a92,a92)),f862(f259(x82221),x82222))),x82221))
% 25.54/25.41 [8488]~P36(x84881,x84882)+P36(x84881,f862(f862(f103(f932(f931(x84881,x84881),a921)),x84882),f299(x84881,f181(f932(f931(x84881,x84881),a921)))))
% 25.54/25.41 [8489]~P37(x84891,x84892)+P37(x84891,f862(f862(f103(f932(f931(x84891,x84891),a921)),x84892),f299(x84891,f181(f932(f931(x84891,x84891),a921)))))
% 25.54/25.41 [8537]~P86(x85371)+P1(f862(f862(f227(x85371),f862(f69(x85371),f862(f158(x85371),x85372))),f862(f158(x85371),f862(f862(f147(x85371,x85371),f69(x85371)),x85372))))
% 25.54/25.41 [8563]P1(f862(f862(f228(a924),x85631),x85632))+~P1(f862(f862(f321(f931(a924,a924)),f862(f862(f244(a924,a924),x85631),x85632)),a232))
% 25.54/25.41 [8713]E(f862(f862(f244(x87131,x87131),f646(x87132,x87131)),f646(x87132,x87131)),x87132)+~P1(f862(f862(f321(f931(x87131,x87131)),x87132),f299(x87131,f181(f932(f931(x87131,x87131),a921)))))
% 25.54/25.41 [8758]E(f862(f295(a924,x87581),f862(f862(f73(a924),x87581),f862(f28(a924),x87582))),x87582)+~P1(f862(f862(f227(f932(a924,a921)),x87582),f862(f295(a924,x87581),f862(f862(f73(a924),x87581),f862(f28(a924),x87582)))))
% 25.54/25.41 [8779]E(f862(f862(f144(a924),f862(f96(a924),x87791)),f132(a924,f862(f295(a924,f862(a105,f862(f96(a924),x87791))),f862(f96(a924),x87792)))),f132(a924,f862(f295(a924,f862(f96(a924),x87791)),f862(f96(a924),x87792))))+~P1(f862(f862(f228(a924),f862(f96(a924),x87791)),f862(f96(a924),x87792)))
% 25.54/25.41 [8989]P37(x89891,x89892)+~P37(x89891,f862(f862(f103(f932(f931(x89891,x89891),a921)),x89892),f299(x89891,f181(f932(f931(x89891,x89891),a921)))))
% 25.54/25.41 [9117]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x91171),x91171)),a90))),f862(f96(a1),f862(f862(f73(a1),x91172),x91172))),f862(f862(f29(a1),f862(f96(a1),x91171)),f862(f96(a1),x91172)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x91172)))
% 25.54/25.41 [9207]~P36(x92071,x92072)+P1(f862(f862(f227(f932(f931(x92071,x92071),a921)),f862(f862(f280(x92071,x92071,x92071),x92072),x92072)),x92072))
% 25.54/25.41 [9233]E(f170(f925(x92331),f862(f862(f10(a921,a921,f925(x92331)),a314),f862(f862(f9(f925(x92331),f925(x92331),a921),a317),f106(x92331))),x92332),f172(x92331,f172(x92331,x92332)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x92331),a924),f182(f925(x92331))),x92332)))
% 25.54/25.41 [9236]E(f862(f862(f29(a1),f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92361),x92361)),a90))),f862(f96(a1),f862(f862(f73(a1),x92362),x92362))),f862(f862(f29(a1),f862(f862(f73(a1),f862(f96(a1),x92361)),f71(a1))),f862(f96(a1),x92362)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x92362)))
% 25.54/25.41 [10082]P1(f862(a186,x100822))+E(f862(f862(f79(a1,a924),f862(f862(f3(a1),x100821),x100822)),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),a97)),f862(f862(f3(a924),f862(a97,x100821)),f862(a97,x100822)))
% 25.54/25.41 [10090]E(f862(f862(f79(a1,a924),f862(f96(a1),f862(f862(f73(a1),x100901),f862(f72(a1),x100902)))),f862(f862(f20(a1,a924,a924),f862(f862(f9(a1,a924,f932(a924,a924)),f862(f862(f10(a921,f932(a924,f932(a924,a924)),a1),f89(a924)),a186)),f2(a924))),a97)),f862(f862(f3(a924),f862(f96(a924),x100901)),f862(f96(a924),x100902)))+P1(f862(f862(f228(a1),x100902),a76))
% 25.54/25.41 [10093]~P24(x100931,x100932)+P1(f862(f862(f227(f932(f931(x100931,x100931),a921)),f862(f862(f280(x100931,x100931,x100931),f862(f243(f932(f931(x100931,x100931),a921),f932(f931(x100931,x100931),a921)),x100932)),f862(f248(f932(f931(x100931,x100931),a921),f932(f931(x100931,x100931),a921)),x100932))),f862(f243(f932(f931(x100931,x100931),a921),f932(f931(x100931,x100931),a921)),x100932)))
% 25.54/25.41 [10149]~E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x101491))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x101492))))),f2(a924))+~P1(f862(f862(f321(a924),f2(a924)),x101491))
% 25.54/25.41 [10205]E(f38(a1,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x102051),x102051)),a90)),f862(f96(a1),f862(f862(f73(a1),x102052),x102052))),f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f96(a1),x102051),f862(f96(a1),x102052)))),f71(a1)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x102052)))
% 25.54/25.41 [10214]E(f38(a1,f862(f96(a1),f862(f862(f3(a1),f862(f862(f73(a1),x102141),x102141)),a90)),f862(f96(a1),f862(f862(f73(a1),x102142),x102142))),f862(f862(f3(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f862(f73(a1),f862(f96(a1),x102141)),f71(a1)),f862(f96(a1),x102142)))),f71(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x102142)))
% 25.54/25.41 [10265]~P3(x102651)+E(f30(x102651,f862(f254(x102651),f862(f862(f10(f932(x102651,a921),a921,x102651),f81(x102651)),f862(f862(f10(f932(x102651,a921),f932(x102651,a921),x102651),f862(f20(x102651,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102651),a322),f862(f862(f9(x102651,f932(x102651,a921),a921),f321(x102651)),x102652)))),f227(x102651))))),f31(x102651,x102652))
% 25.54/25.41 [10291]~P35(x102911,x102912)+P57(x102911,f862(f862(f9(x102911,f932(f931(x102911,x102911),a921),f932(x102911,a921)),f862(f862(f10(f932(x102911,f932(f932(f931(x102911,x102911),a921),a921)),f932(f932(f931(x102911,x102911),a921),f932(x102911,a921)),x102911),f9(x102911,f932(f931(x102911,x102911),a921),a921)),f862(f862(f10(f932(x102911,f931(x102911,x102911)),f932(x102911,f932(f932(f931(x102911,x102911),a921),a921)),x102911),f862(f10(f931(x102911,x102911),f932(f932(f931(x102911,x102911),a921),a921),x102911),f321(f931(x102911,x102911)))),f244(x102911,x102911)))),x102912))
% 25.54/25.41 [10292]~P6(x102921,f234(f932(x102921,a921)),x102922)+P5(x102921,f862(f862(f9(x102921,f932(f931(x102921,x102921),a921),f932(x102921,a921)),f862(f862(f10(f932(x102921,f932(f932(f931(x102921,x102921),a921),a921)),f932(f932(f931(x102921,x102921),a921),f932(x102921,a921)),x102921),f9(x102921,f932(f931(x102921,x102921),a921),a921)),f862(f862(f10(f932(x102921,f931(x102921,x102921)),f932(x102921,f932(f932(f931(x102921,x102921),a921),a921)),x102921),f862(f10(f931(x102921,x102921),f932(f932(f931(x102921,x102921),a921),a921),x102921),f321(f931(x102921,x102921)))),f244(x102921,x102921)))),x102922))
% 25.54/25.41 [10335]P35(x103351,x103352)+~P57(x103351,f862(f862(f9(x103351,f932(f931(x103351,x103351),a921),f932(x103351,a921)),f862(f862(f10(f932(x103351,f932(f932(f931(x103351,x103351),a921),a921)),f932(f932(f931(x103351,x103351),a921),f932(x103351,a921)),x103351),f9(x103351,f932(f931(x103351,x103351),a921),a921)),f862(f862(f10(f932(x103351,f931(x103351,x103351)),f932(x103351,f932(f932(f931(x103351,x103351),a921),a921)),x103351),f862(f10(f931(x103351,x103351),f932(f932(f931(x103351,x103351),a921),a921),x103351),f321(f931(x103351,x103351)))),f244(x103351,x103351)))),x103352))
% 25.54/25.41 [10336]P6(x103361,f234(f932(x103361,a921)),x103362)+~P5(x103361,f862(f862(f9(x103361,f932(f931(x103361,x103361),a921),f932(x103361,a921)),f862(f862(f10(f932(x103361,f932(f932(f931(x103361,x103361),a921),a921)),f932(f932(f931(x103361,x103361),a921),f932(x103361,a921)),x103361),f9(x103361,f932(f931(x103361,x103361),a921),a921)),f862(f862(f10(f932(x103361,f931(x103361,x103361)),f932(x103361,f932(f932(f931(x103361,x103361),a921),a921)),x103361),f862(f10(f931(x103361,x103361),f932(f932(f931(x103361,x103361),a921),a921),x103361),f321(f931(x103361,x103361)))),f244(x103361,x103361)))),x103362))
% 25.54/25.41 [7471]E(f862(f862(f73(a924),f862(f96(a924),f862(f862(f3(a1),x74711),a90))),x74712),f862(a105,f862(f862(f73(a924),f862(f96(a924),x74711)),x74712)))+P1(f862(a186,f862(f96(a1),x74711)))
% 25.54/25.41 [7915]~P98(x79151)+E(f862(f862(f73(x79151),f862(f862(f73(x79151),f71(x79151)),f862(f96(x79151),x79152))),f862(f96(x79151),x79152)),f862(f96(x79151),f862(f862(f3(a1),f862(f862(f73(a1),x79152),x79152)),a90)))
% 25.54/25.41 [8564]~P1(f862(f862(f227(a1),x85641),x85642))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x85641),x85641)),f862(f862(f3(a1),f862(f862(f73(a1),x85642),x85642)),a90)))
% 25.54/25.41 [8565]~P1(f862(f862(f227(a1),x85651),x85652))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x85651),x85651)),f862(f862(f3(a1),f862(f862(f73(a1),x85652),x85652)),a90)))
% 25.54/25.41 [8566]~P1(f862(f862(f227(a1),x85661),x85662))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x85661),x85661)),f862(f862(f3(a1),f862(f862(f73(a1),x85662),x85662)),a90)))
% 25.54/25.41 [8567]~P1(f862(f862(f227(a1),x85671),x85672))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x85671),x85671)),f862(f862(f3(a1),f862(f862(f73(a1),x85672),x85672)),a90)))
% 25.54/25.41 [8999]P1(f862(f862(f227(a1),x89991),x89992))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x89991),x89991)),f862(f862(f3(a1),f862(f862(f73(a1),x89992),x89992)),a90)))
% 25.54/25.41 [9000]P1(f862(f862(f227(a1),x90001),x90002))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x90001),x90001)),f862(f862(f3(a1),f862(f862(f73(a1),x90002),x90002)),a90)))
% 25.54/25.41 [9001]P1(f862(f862(f227(a1),x90011),x90012))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x90011),x90011)),f862(f862(f3(a1),f862(f862(f73(a1),x90012),x90012)),a90)))
% 25.54/25.41 [9002]P1(f862(f862(f227(a1),x90021),x90022))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),x90021),x90021)),f862(f862(f3(a1),f862(f862(f73(a1),x90022),x90022)),a90)))
% 25.54/25.41 [9291]~P1(f862(f862(f84(a1),x92911),x92912))+P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92911),x92911)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92912),x92912)),a90)))
% 25.54/25.41 [9292]~P1(f862(f862(f227(a1),x92921),x92922))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92921),x92921)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92922),x92922)),a90)))
% 25.54/25.41 [9293]~P1(f862(f862(f227(a1),x92931),x92932))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92931),x92931)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92932),x92932)),a90)))
% 25.54/25.41 [9294]~P1(f862(f862(f228(a1),x92941),x92942))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92941),x92941)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92942),x92942)),a90)))
% 25.54/25.41 [9295]~P1(f862(f862(f228(a1),x92951),x92952))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x92951),x92951)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x92952),x92952)),a90)))
% 25.54/25.41 [9564]P1(f862(f862(f84(a1),x95641),x95642))+~P1(f862(f862(f84(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95641),x95641)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95642),x95642)),a90)))
% 25.54/25.41 [9565]P1(f862(f862(f227(a1),x95651),x95652))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95651),x95651)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95652),x95652)),a90)))
% 25.54/25.41 [9566]P1(f862(f862(f227(a1),x95661),x95662))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95661),x95661)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95662),x95662)),a90)))
% 25.54/25.41 [9567]P1(f862(f862(f228(a1),x95671),x95672))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95671),x95671)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95672),x95672)),a90)))
% 25.54/25.41 [9568]P1(f862(f862(f228(a1),x95681),x95682))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),x95681),x95681)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),x95682),x95682)),a90)))
% 25.54/25.41 [9602]~P1(f862(f54(x96021),x96022))+P1(f862(f54(f932(x96021,a921)),f862(f254(f932(x96021,a921)),f862(f862(f9(f932(x96021,a921),f932(x96021,a921),a921),f227(f932(x96021,a921))),x96022))))
% 25.54/25.41 [9653]~E(f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x96531),f181(f932(f931(a924,a924),a921)))),f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x96532),f181(f932(f931(a924,a924),a921)))))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x96531),x96532)),a101))
% 25.54/25.41 [9741]E(f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x97411),f181(f932(f931(a924,a924),a921)))),f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),x97412),f181(f932(f931(a924,a924),a921)))))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x97411),x97412)),a101))
% 25.54/25.41 [9777]P1(f862(f862(f227(a1),f2(a1)),f649(x97771,x97772)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97771)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97772)))
% 25.54/25.41 [10273]~P3(x102731)+E(f31(x102731,f862(f254(x102731),f862(f862(f10(f932(x102731,a921),a921,x102731),f81(x102731)),f862(f862(f10(f932(x102731,a921),f932(x102731,a921),x102731),f862(f20(x102731,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102731),a322),f862(f862(f9(x102731,f932(x102731,a921),a921),f321(x102731)),x102732)))),f862(f9(x102731,x102731,a921),f227(x102731)))))),f30(x102731,x102732))
% 25.54/25.41 [10297]P1(f862(f862(f321(a924),f2(a924)),x102971))+E(f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x102971))),f862(f862(f9(a924,a924,a921),f228(a924)),x102972)))),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x102971))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x102972))))))
% 25.54/25.41 [10355]P1(f862(f862(f278(a924),x103551),x103552))+~P1(f862(f862(f321(a924),x103552),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103551)))
% 25.54/25.41 [10356]P1(f862(f862(f278(a924),x103561),x103562))+~P1(f862(f862(f321(a924),x103561),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103562)))
% 25.54/25.41 [10357]~P1(f862(f862(f278(a924),x103571),x103572))+~P1(f862(f862(f321(a924),x103572),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103571)))
% 25.54/25.41 [10358]~P1(f862(f862(f278(a924),x103581),x103582))+~P1(f862(f862(f321(a924),x103581),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103582)))
% 25.54/25.41 [7783]~P98(x77831)+E(f862(f862(f74(x77831),x77832),f862(f96(x77831),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x77832)
% 25.54/25.41 [8046]~P98(x80461)+E(f862(f862(f73(x80461),f862(f96(x80461),x80462)),f71(x80461)),f862(f96(x80461),f862(f862(f73(a1),x80462),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))
% 25.54/25.41 [8193]P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x81932)))+E(f862(f862(f236(a1),x81931),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x81932),x81932)),a90))),f71(a1))
% 25.54/25.41 [9629]~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x96292)))+E(f862(f862(f236(a1),x96291),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x96292),x96292)),a90))),f862(f862(f79(a1,a1),f862(f862(f236(a1),x96291),f862(f96(a924),x96292))),f862(f862(f20(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f74(a1)),f862(f74(a1),x96291))),f7(a1))))
% 25.54/25.41 [10000]~P1(f862(f862(f227(a924),f651(x100002,x100001)),f862(x100001,f651(x100002,x100001))))+P1(f862(f54(a924),f862(f254(a924),f862(f862(f9(a924,a924,a921),f862(f862(f10(a924,f932(a924,a921),a924),f227(a924)),x100001)),x100002))))
% 25.54/25.41 [10139]~P1(f862(f862(f227(a924),f862(f96(a924),x101391)),f862(a105,x101392)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101391),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f227(a924)),a97)),x101392))))
% 25.54/25.41 [10140]~P1(f862(f862(f228(a924),f862(f96(a924),x101401)),f862(a105,x101402)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101401),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f228(a924)),a97)),x101402))))
% 25.54/25.41 [10189]P1(f862(f862(f227(a924),f862(f96(a924),x101891)),f862(a105,x101892)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101891),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f227(a924)),a97)),x101892))))
% 25.54/25.41 [10190]P1(f862(f862(f228(a924),f862(f96(a924),x101901)),f862(a105,x101902)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x101901),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),f228(a924)),a97)),x101902))))
% 25.54/25.41 [10220]~P1(f862(f862(f227(a924),f862(a105,x102202)),f862(f96(a924),x102201)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102201),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f227(a924),x102202)),a97)))))
% 25.54/25.41 [10221]~P1(f862(f862(f228(a924),f862(a105,x102212)),f862(f96(a924),x102211)))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102211),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f228(a924),x102212)),a97)))))
% 25.54/25.41 [10263]P1(f862(f862(f227(a924),f862(a105,x102631)),f862(f96(a924),x102632)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102632),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f227(a924),x102631)),a97)))))
% 25.54/25.41 [10264]P1(f862(f862(f228(a924),f862(a105,x102641)),f862(f96(a924),x102642)))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102642),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f10(a924,a921,a1),f862(f228(a924),x102641)),a97)))))
% 25.54/25.41 [10345]~P1(f862(f862(f321(a924),f2(a924)),x103451))+E(f862(a105,f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f862(f862(f10(a924,f932(f932(a924,a921),a921),a924),f321(a924)),a105)),x103451))),f862(f862(f9(a924,a924,a921),f228(a924)),x103452))))),f862(f28(a924),f862(f254(a924),f862(f862(f20(a924,a921,a921),f862(f862(f10(a921,f932(a921,a921),a924),a318),f862(f862(f9(a924,f932(a924,a921),a921),f321(a924)),x103451))),f862(f862(f9(a924,a924,a921),f228(a924)),f862(a105,x103452))))))
% 25.54/25.41 [8740]~P98(x87401)+E(f862(f862(f74(x87401),f862(f96(x87401),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x87402),x87402)
% 25.54/25.41 [8802]~P98(x88021)+E(f862(f862(f73(x88021),f71(x88021)),f862(f96(x88021),x88022)),f862(f96(x88021),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x88022)))
% 25.54/25.41 [8864]~P98(x88641)+E(f862(f862(f3(x88641),f862(f96(x88641),x88642)),f71(x88641)),f862(f96(x88641),f862(f862(f73(a1),x88642),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9019]~P1(f862(f862(f228(a924),f862(f96(a924),a76)),x90192))+E(f862(f862(f3(a924),x90191),f862(f862(f3(a924),x90192),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f3(a924),f862(a105,x90191)),x90192))
% 25.54/25.41 [9671]~P119(x96711)+E(f862(f862(f74(x96711),x96712),x96712),f862(f862(f236(x96711),x96712),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9672]~P80(x96721)+E(f862(f862(f236(x96721),x96722),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f74(x96721),x96722),x96722))
% 25.54/25.41 [9674]~P98(x96741)+E(f862(f862(f74(x96741),x96742),f862(f96(x96741),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f73(x96741),x96742),x96742))
% 25.54/25.41 [9917]~P142(x99171)+E(f862(f862(f236(x99171),f862(f72(x99171),x99172)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x99171),x99172),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9918]~P112(x99181)+E(f862(f862(f236(x99181),f862(f69(x99181),x99182)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x99181),x99182),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9914]~P98(x99141)+E(f862(f862(f74(x99141),f862(f96(x99141),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x99142),f862(f862(f73(x99141),x99142),x99142))
% 25.54/25.41 [10034]~P112(x100341)+E(f862(f69(x100341),f862(f862(f236(x100341),x100342),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x100341),x100342),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [10101]~P112(x101011)+P1(f862(f862(f227(x101011),f2(x101011)),f862(f862(f236(x101011),x101012),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10254]~E(f862(a105,x102542),f862(f96(a924),x102541))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102541),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x102542)))))
% 25.54/25.41 [10255]~E(f862(f96(a924),x102551),f862(a105,x102552))+P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x102551),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x102552)))))
% 25.54/25.41 [10300]E(f862(a105,x103001),f862(f96(a924),x103002))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x103002),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x103001)))))
% 25.54/25.41 [10301]E(f862(f96(a924),x103011),f862(a105,x103012))+~P1(f862(f862(f79(a1,a921),f862(f96(a1),f862(f862(f73(a1),x103011),a90))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a322),f862(f862(f10(a921,a921,a1),a314),a186))),f862(f862(f9(a1,a924,a921),f862(f862(f10(a924,f932(a924,a921),a1),a317),a97)),x103012)))))
% 25.54/25.41 [10346]~P13(x103461,x103462)+P1(f862(f862(f321(f932(x103461,a921)),f817(x103462,x103461)),f862(f862(f10(f932(x103461,a921),a921,f932(x103461,a921)),f80(x103461)),f862(f862(f10(f932(x103461,a921),f932(x103461,a921),f932(x103461,a921)),f862(f20(x103461,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103461),a318),f862(f862(f20(x103461,x103461,a921),x103462),f7(x103461))))),f862(f862(f9(f932(x103461,a921),f932(x103461,f932(x103461,a921)),f932(x103461,a921)),f862(f862(f10(f932(f932(x103461,a921),a921),f932(f932(x103461,f932(x103461,a921)),f932(x103461,a921)),f932(x103461,a921)),f10(f932(x103461,a921),a921,x103461)),a317)),x103462)))))
% 25.54/25.41 [10098]~P98(x100981)+E(f862(f862(f236(x100981),f862(f96(x100981),a90)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x100982)),f71(x100981))
% 25.54/25.41 [10099]~P142(x100991)+E(f862(f862(f236(x100991),f862(f72(x100991),f71(x100991))),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x100992)),f71(x100991))
% 25.54/25.41 [10103]~P80(x101031)+E(f862(f862(f236(x101031),x101032),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),a90))),f862(f862(f74(x101031),f862(f862(f74(x101031),x101032),x101032)),x101032))
% 25.54/25.41 [10280]~P1(f862(f862(f227(a1),f2(a1)),x102802))+E(f38(a1,f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102801)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102802)),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,x102801,x102802))))
% 25.54/25.41 [10303]~P1(f862(f862(f227(a1),f2(a1)),x103032))+E(f862(f862(f29(a1),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103031))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103032)),f862(f862(f29(a1),x103031),x103032))
% 25.54/25.41 [10305]~P1(f862(f862(f227(a1),x103052),f2(a1)))+E(f862(f862(f29(a1),f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103051))),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103052)),f862(f862(f29(a1),f862(f862(f73(a1),x103051),f71(a1))),x103052))
% 25.54/25.41 [10306]~P1(f862(f862(f227(a1),x103062),f2(a1)))+E(f38(a1,f862(f862(f73(a1),f71(a1)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103061)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103062)),f862(f862(f3(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f38(a1,f862(f862(f73(a1),x103061),f71(a1)),x103062))),f71(a1)))
% 25.54/25.41 [10180]~P98(x101801)+E(f862(f862(f236(x101801),f862(f96(x101801),a90)),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101802))),f862(f96(x101801),a90))
% 25.54/25.41 [10182]~P142(x101821)+E(f862(f862(f236(x101821),f862(f72(x101821),f71(x101821))),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101822))),f862(f72(x101821),f71(x101821)))
% 25.54/25.41 [5118]P36(x51181,x51182)+~P6(x51181,x51183,x51182)
% 25.54/25.41 [5119]P36(x51191,x51192)+~P6(x51191,x51193,x51192)
% 25.54/25.41 [5120]P49(x51201,x51202)+~P6(x51201,x51203,x51202)
% 25.54/25.41 [5121]P49(x51211,x51212)+~P6(x51211,x51213,x51212)
% 25.54/25.41 [5295]~P6(x52951,x52952,x52953)+P50(x52951,x52952,x52953)
% 25.54/25.41 [5296]~P6(x52961,x52962,x52963)+P50(x52961,x52962,x52963)
% 25.54/25.41 [8260]~E(x82602,x82603)+P32(x82601,x82601,a317,x82602,x82603)
% 25.54/25.41 [8815]E(x88151,x88152)+~P32(x88153,x88153,a317,x88151,x88152)
% 25.54/25.41 [4921]E(f162(x49211,x49212,x49213),f106(x49211))+~E(x49212,f2(a924))
% 25.54/25.41 [4922]E(f162(x49221,x49222,x49223),f106(x49221))+~E(x49222,f2(a924))
% 25.54/25.41 [5090]~E(f162(x50902,x50901,x50903),f106(x50902))+E(x50901,f2(a924))
% 25.54/25.41 [5091]~E(f162(x50912,x50911,x50913),f106(x50912))+E(x50911,f2(a924))
% 25.54/25.41 [5301]~P35(x53011,x53013)+P35(x53011,f313(x53011,x53012,x53013))
% 25.54/25.41 [5412]~P27(x54121,x54122,x54123)+P29(a1,x54121,f171(x54122,x54123))
% 25.54/25.41 [5480]P27(x54801,x54802,x54803)+~P29(a1,x54801,f171(x54802,x54803))
% 25.54/25.41 [5552]~P6(x55521,x55522,x55523)+P6(f925(x55521),f154(x55521,x55522),f151(x55521,x55523))
% 25.54/25.41 [5553]~P50(x55531,x55532,x55533)+P50(f925(x55531),f154(x55531,x55532),f151(x55531,x55533))
% 25.54/25.41 [5666]P52(x56661,x56662,x56663)+~E(f607(x56663,x56662,x56661),f608(x56663,x56662,x56661))
% 25.54/25.41 [5667]P53(x56671,x56672,x56673)+~E(f625(x56673,x56672,x56671),f626(x56673,x56672,x56671))
% 25.54/25.41 [8266]~E(x82662,x82663)+P23(x82661,x82661,f25(x82661),x82662,x82663)
% 25.54/25.41 [8823]E(x88231,x88232)+~P23(x88233,x88233,f25(x88233),x88231,x88232)
% 25.54/25.41 [4877]~E(f862(f161(x48772),x48771),x48773)+E(x48771,f862(f161(x48772),x48773))
% 25.54/25.41 [4878]~E(x48782,f862(f161(x48781),x48783))+E(f862(f161(x48781),x48782),x48783)
% 25.54/25.41 [4928]E(x49281,x49282)+~E(f862(f87(x49283),x49281),f862(f87(x49283),x49282))
% 25.54/25.41 [4929]E(x49291,x49292)+~E(f862(f161(x49293),x49291),f862(f161(x49293),x49292))
% 25.54/25.41 [5145]~P5(x51453,x51451)+P1(f862(f862(x51451,x51452),x51452))
% 25.54/25.41 [5146]~P46(x51463,x51461)+P1(f862(f862(x51461,x51462),x51462))
% 25.54/25.41 [5147]~P57(x51471,x51472)+P1(f862(f307(x51471,x51472),x51473))
% 25.54/25.41 [5148]~P57(x51481,x51482)+P1(f862(f307(x51481,x51482),x51483))
% 25.54/25.41 [5216]~P35(x52161,x52162)+P35(f925(x52161),f862(f136(x52161,x52162),x52163))
% 25.54/25.41 [5221]~P1(f862(x52212,x52213))+~E(f862(f254(x52211),x52212),f181(f932(x52211,a921)))
% 25.54/25.41 [5222]~P1(f862(x52222,x52223))+~E(f181(f932(x52221,a921)),f862(f254(x52221),x52222))
% 25.54/25.41 [5234]E(x52341,f2(a924))+E(f137(x52342,f162(x52342,x52341,x52343)),x52343)
% 25.54/25.41 [5250]~P1(f862(x52501,x52503))+P1(f862(x52501,f83(x52502,x52501)))
% 25.54/25.41 [5251]~P1(f862(x52511,x52513))+P1(f862(x52511,f83(x52512,x52511)))
% 25.54/25.41 [5252]~P1(f862(x52521,x52523))+P1(f862(x52521,f83(x52522,x52521)))
% 25.54/25.41 [5253]~P1(f862(x52531,x52533))+P1(f862(x52531,f83(x52532,x52531)))
% 25.54/25.41 [5254]~P1(f862(x52541,x52543))+P1(f862(x52541,f743(x52541,x52542)))
% 25.54/25.41 [5266]E(x52661,f2(a924))+E(f862(f134(x52662),f162(x52662,x52661,x52663)),x52663)
% 25.54/25.41 [5372]~E(x53722,x53723)+P1(f862(f862(f321(x53721),x53722),f862(a317,x53723)))
% 25.54/25.41 [5389]~E(x53892,f2(a924))+E(f862(f165(x53891),f162(x53891,x53892,x53893)),f181(f932(x53891,a921)))
% 25.54/25.41 [5435]E(f862(f161(x54351),x54352),f862(f862(f144(x54351),x54353),f106(x54351)))+~E(x54352,f862(f862(f144(x54351),x54353),f106(x54351)))
% 25.54/25.41 [5436]~E(x54363,f862(f862(f144(x54361),x54362),f106(x54361)))+E(f862(f862(f144(x54361),x54362),f106(x54361)),f862(f161(x54361),x54363))
% 25.54/25.41 [5476]~P31(x54761,x54762,x54763)+P31(x54761,x54762,f862(f161(x54761),x54763))
% 25.54/25.41 [5477]~P29(x54771,x54772,x54773)+P29(x54771,x54772,f862(f161(x54771),x54773))
% 25.54/25.41 [5481]E(f862(f28(x54811),f327(x54812,x54813,x54811)),x54812)+~E(f862(f28(x54811),x54813),f862(a105,x54812))
% 25.54/25.41 [5487]~P35(x54871,x54873)+P1(f862(f862(f321(x54871),x54872),f308(x54871,x54873)))
% 25.54/25.41 [5488]~P35(x54881,x54883)+P1(f862(f862(f321(x54881),x54882),f308(x54881,x54883)))
% 25.54/25.41 [5492]~E(f862(f161(x54922),x54921),f862(f862(f144(x54922),x54923),f106(x54922)))+E(x54921,f862(f862(f144(x54922),x54923),f106(x54922)))
% 25.54/25.41 [5493]~E(f862(f862(f144(x54932),x54933),f106(x54932)),f862(f161(x54932),x54931))+E(x54931,f862(f862(f144(x54932),x54933),f106(x54932)))
% 25.54/25.41 [5516]E(f78(f931(a924,a924),f41(x55161,x55162)),x55163)+~P1(f862(f41(x55161,x55162),x55163))
% 25.54/25.41 [5556]P31(x55561,x55562,x55563)+~P31(x55561,x55562,f862(f161(x55561),x55563))
% 25.54/25.41 [5557]P29(x55571,x55572,x55573)+~P29(x55571,x55572,f862(f161(x55571),x55573))
% 25.54/25.41 [5596]P1(f862(f862(x55961,x55962),x55962))+~P1(f862(f262(x55963,x55961),x55962))
% 25.54/25.41 [5597]~P1(f862(f862(x55972,x55973),x55973))+P1(f862(f262(x55971,x55972),x55973))
% 25.54/25.41 [5619]~E(x56192,f106(x56191))+P1(f862(f862(f321(f925(x56191)),x56192),f154(x56191,x56193)))
% 25.54/25.41 [5629]~P50(x56291,x56292,x56293)+P50(x56291,x56292,f862(f277(x56291,x56291),x56293))
% 25.54/25.41 [5630]~P53(x56301,x56302,x56303)+P53(x56301,x56302,f862(f277(x56301,x56301),x56303))
% 25.54/25.41 [5647]~P61(x56471)+E(f38(x56471,f38(x56471,x56472,x56473),x56473),f38(x56471,x56472,x56473))
% 25.54/25.41 [5751]E(x57511,x57512)+~P1(f862(f862(f321(x57513),x57511),f862(a317,x57512)))
% 25.54/25.41 [5798]~P147(x57981)+E(f183(x57981,x57982,f2(a924),x57983),x57983)
% 25.54/25.41 [5820]P50(x58201,x58202,x58203)+~P50(x58201,x58202,f862(f277(x58201,x58201),x58203))
% 25.54/25.41 [5821]P53(x58211,x58212,x58213)+~P53(x58211,x58212,f862(f277(x58211,x58211),x58213))
% 25.54/25.41 [5825]~P109(x58252)+E(f143(x58251,x58252,x58253,f106(x58251)),f106(x58251))
% 25.54/25.41 [5837]E(f163(x58371,x58372,f145(x58371,x58373)),f145(x58371,f163(x58371,x58372,x58373)))+~P1(f862(f130(x58371),x58373))
% 25.54/25.41 [5936]~P1(f862(f862(x59363,x59362),x59362))+P1(f862(f862(f321(x59361),x59362),f262(x59361,x59363)))
% 25.54/25.41 [5938]E(f862(f129(x59381,x59382),x59383),f106(x59381))+P1(f862(x59382,f678(x59383,x59382,x59381)))
% 25.54/25.41 [6006]E(f61(x60061,x60062,x60063),x60062)+P1(f862(x60063,f744(x60062,x60061,x60063)))
% 25.54/25.41 [6102]~P1(f862(f130(x61021),x61022))+P1(f862(f130(x61021),f169(x61021,x61022,x61023)))
% 25.54/25.41 [6103]~P1(f862(f130(x61031),x61033))+P1(f862(f130(x61031),f163(x61031,x61032,x61033)))
% 25.54/25.41 [6104]~P1(f862(f130(x61041),x61043))+P1(f862(f130(x61041),f170(x61041,x61042,x61043)))
% 25.54/25.41 [6105]~P1(f862(f130(x61051),x61053))+P1(f862(f130(x61051),f133(x61051,x61052,x61053)))
% 25.54/25.41 [6106]~P148(x61061,x61063,x61062)+P1(f862(x61061,f38(a1,x61062,x61063)))
% 25.54/25.41 [6122]~P31(x61223,x61221,x61222)+P1(f862(x61221,f757(x61222,x61221,x61223)))
% 25.54/25.41 [6123]~P33(x61233,x61231,x61232)+P1(f862(x61231,f764(x61232,x61231,x61233)))
% 25.54/25.41 [6124]~P33(x61243,x61241,x61242)+P1(f862(x61241,f775(x61242,x61241,x61243)))
% 25.54/25.41 [6125]~P31(x61253,x61251,x61252)+P1(f862(x61251,f799(x61252,x61251,x61253)))
% 25.54/25.41 [6126]~P31(x61263,x61261,x61262)+P1(f862(x61261,f801(x61261,x61262,x61263)))
% 25.54/25.41 [6131]P1(f862(f862(x61311,x61312),x61312))+~P1(f862(f862(f321(x61313),x61312),f262(x61313,x61311)))
% 25.54/25.41 [6146]E(f862(f129(x61461,x61462),x61463),f170(x61461,x61462,x61463))+P1(f862(x61462,f728(x61463,x61462,x61461)))
% 25.54/25.41 [6185]~P1(f862(f130(x61851),x61853))+P1(f862(f130(f925(x61851)),f48(x61851,x61852,x61853)))
% 25.54/25.41 [6219]~P110(x62191)+E(f862(f862(f94(f932(x62191,a921)),f862(f294(x62191),x62192)),f298(x62191,x62192,x62193)),f181(f932(x62191,a921)))
% 25.54/25.41 [6220]~P110(x62201)+E(f862(f862(f94(f932(x62201,a921)),f862(f294(x62201),x62202)),f297(x62201,x62202,x62203)),f181(f932(x62201,a921)))
% 25.54/25.41 [6221]~P110(x62211)+E(f862(f862(f94(f932(x62211,a921)),f862(f292(x62211),x62212)),f296(x62211,x62212,x62213)),f181(f932(x62211,a921)))
% 25.54/25.41 [6449]E(f862(f129(x64491,x64492),x64493),x64493)+~P1(f862(x64492,f679(x64493,x64492,x64491)))
% 25.54/25.41 [6451]E(f862(f862(f301(x64511),f351(x64512,x64513,x64511)),f327(x64512,x64513,x64511)),x64513)+~E(f862(f28(x64511),x64513),f862(a105,x64512))
% 25.54/25.41 [6466]P148(x64661,x64662,x64663)+~P1(f862(x64661,f38(a1,x64663,x64662)))
% 25.54/25.41 [6517]P29(x65171,x65172,x65173)+~P1(f862(x65172,f765(x65173,x65172,x65171)))
% 25.54/25.41 [6518]P29(x65181,x65182,x65183)+~P1(f862(x65182,f771(x65182,x65183,x65181)))
% 25.54/25.41 [6519]P29(x65191,x65192,x65193)+~P1(f862(x65192,f774(x65193,x65192,x65191)))
% 25.54/25.41 [6520]P27(x65201,x65202,x65203)+~P1(f862(x65201,f793(x65203,x65202,x65201)))
% 25.54/25.41 [6521]P28(x65211,x65212,x65213)+~P1(f862(x65211,f833(x65213,x65212,x65211)))
% 25.54/25.41 [6523]E(f170(x65231,x65232,x65233),x65233)+~P1(f862(x65232,f723(x65233,x65232,x65231)))
% 25.54/25.41 [6605]~P1(f862(x66052,f590(x66053,x66052,x66051)))+P1(f862(f240(x66051,x66052),x66053))
% 25.54/25.41 [6606]~P1(f862(x66062,f680(x66063,x66062,x66061)))+P1(f862(f153(x66061,x66062),x66063))
% 25.54/25.41 [6853]~P1(f862(f307(x68531,x68532),f448(x68533,x68532,x68531)))+P1(f862(f307(x68531,x68532),x68533))
% 25.54/25.41 [6854]~P1(f862(f307(x68541,x68542),f497(x68543,x68542,x68541)))+P1(f862(f307(x68541,x68542),x68543))
% 25.54/25.41 [7472]~P61(x74721)+E(f862(f862(f73(x74721),f862(f862(f74(x74721),x74722),f862(f862(f29(x74721),x74723),x74722))),f38(x74721,x74723,x74722)),x74723)
% 25.54/25.41 [7503]P27(x75031,x75032,x75033)+P1(f862(f862(f321(a1),f793(x75033,x75032,x75031)),f296(a1,x75032,x75033)))
% 25.54/25.41 [7936]E(f862(f862(f244(x79361,x79361),f536(x79362,x79363,x79361)),f536(x79362,x79363,x79361)),x79363)+~P1(f862(f862(f321(f931(x79361,x79361)),x79363),f255(x79361,x79362)))
% 25.54/25.41 [8054]~P1(f862(f862(f321(x80541),f547(x80543,x80542,x80541)),f308(x80541,x80543)))+P1(f862(f862(f321(x80541),x80542),f308(x80541,x80543)))
% 25.54/25.41 [8055]~P1(f862(f862(f321(x80551),f612(x80553,x80552,x80551)),f308(x80551,x80553)))+P1(f862(f862(f321(x80551),x80552),f308(x80551,x80553)))
% 25.54/25.41 [8056]~P1(f862(f862(f321(x80561),f614(x80563,x80562,x80561)),f308(x80561,x80563)))+P1(f862(f862(f321(x80561),x80562),f308(x80561,x80563)))
% 25.54/25.41 [8150]P31(a1,x81501,f171(x81502,x81503))+P27(f862(f66(a921,a921,a1,a314),x81501),x81502,x81503)
% 25.54/25.41 [8240]~P61(x82401)+E(f862(f862(f73(x82401),f862(f862(f74(x82401),f862(f862(f29(x82401),x82402),x82403)),x82403)),f38(x82401,x82402,x82403)),x82402)
% 25.54/25.41 [8241]~P61(x82411)+E(f862(f862(f73(x82411),f862(f862(f74(x82411),f862(f862(f29(x82411),x82412),x82413)),x82413)),f38(x82411,x82412,x82413)),x82412)
% 25.54/25.41 [8288]~E(f862(f28(x82881),x82882),f862(a105,x82883))+~P1(f862(f862(f321(x82881),f351(x82883,x82882,x82881)),f327(x82883,x82882,x82881)))
% 25.54/25.41 [8732]~P31(a1,x87321,f171(x87322,x87323))+~P27(f862(f66(a921,a921,a1,a314),x87321),x87322,x87323)
% 25.54/25.41 [8921]P1(f862(f862(f227(f932(f931(x89211,x89211),a921)),f299(x89211,x89212)),f299(x89211,x89213)))+~P1(f862(f862(f227(f932(f931(x89211,x89211),a921)),x89212),f299(x89211,x89213)))
% 25.54/25.41 [9059]~P23(x90591,x90592,x90593,f234(f932(x90591,a921)),f234(f932(x90592,a921)))+P22(x90591,x90592,x90593,f234(f932(x90591,a921)))
% 25.54/25.41 [9060]~P23(x90601,x90602,x90603,f234(f932(x90601,a921)),f234(f932(x90602,a921)))+P22(x90601,x90602,x90603,f234(f932(x90601,a921)))
% 25.54/25.41 [9203]E(x92031,f106(x92032))+~P1(f862(f862(f321(f931(f925(x92032),f925(x92032))),f862(f862(f244(f925(x92032),f925(x92032)),x92031),f106(x92032))),f151(x92032,x92033)))
% 25.54/25.41 [9227]E(x92271,f106(x92272))+~P1(f862(f862(f321(f931(f925(x92272),f925(x92272))),f862(f862(f244(f925(x92272),f925(x92272)),f106(x92272)),x92271)),f151(x92272,x92273)))
% 25.54/25.41 [9354]E(f862(f862(f144(x93541),f697(x93542,x93543,x93541)),f698(x93542,x93543,x93541)),x93543)+~P1(f862(f862(f321(f931(f925(x93541),f925(x93541))),f862(f862(f244(f925(x93541),f925(x93541)),f106(x93541)),x93543)),f140(x93541,x93542)))
% 25.54/25.41 [9595]~P129(x95951)+~P1(f862(f862(f228(x95951),f862(f862(f73(x95951),f862(f862(f74(x95951),x95952),x95952)),f862(f862(f74(x95951),x95953),x95953))),f2(x95951)))
% 25.54/25.41 [9646]P1(f862(f54(x96461),x96462))+~P1(f862(f862(f321(f931(f932(x96461,a921),f932(x96461,a921))),f862(f862(f244(f932(x96461,a921),f932(x96461,a921)),x96463),x96462)),f306(x96461)))
% 25.54/25.41 [9943]~P44(x99431,x99432,x99433)+P1(f862(f862(f227(a1),f862(f862(f66(f931(a1,a1),a1,x99431,f243(a1,a1)),f205(x99431)),f223(x99431,x99432,f220(x99431,x99433)))),f2(a1)))
% 25.54/25.41 [9944]~P45(x99441,x99442,x99443)+P1(f862(f862(f228(a1),f862(f862(f66(f931(a1,a1),a1,x99441,f243(a1,a1)),f205(x99441)),f223(x99441,x99442,f220(x99441,x99443)))),f2(a1)))
% 25.54/25.41 [10064]P45(x100641,x100642,x100643)+~P1(f862(f862(f228(a1),f862(f862(f66(f931(a1,a1),a1,x100641,f243(a1,a1)),f205(x100641)),f223(x100641,x100642,f220(x100641,x100643)))),f2(a1)))
% 25.54/25.41 [10065]P44(x100651,x100652,x100653)+~P1(f862(f862(f227(a1),f862(f862(f66(f931(a1,a1),a1,x100651,f243(a1,a1)),f205(x100651)),f223(x100651,x100652,f220(x100651,x100653)))),f2(a1)))
% 25.54/25.41 [10408]~P112(x104081)+~P1(f862(f862(f228(x104081),f862(f862(f73(x104081),f862(f862(f236(x104081),x104082),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104081),x104083),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104081)))
% 25.54/25.41 [4905]~E(x49053,f106(x49051))+E(f862(f862(f127(x49051),x49052),x49053),x49052)
% 25.54/25.41 [4906]~E(x49062,f106(x49061))+E(f862(f862(f127(x49061),x49062),x49063),x49063)
% 25.54/25.41 [4907]~E(x49073,f106(x49071))+E(f862(f862(f127(x49071),x49072),x49073),x49072)
% 25.54/25.41 [4908]~E(x49082,f106(x49081))+E(f862(f862(f127(x49081),x49082),x49083),x49083)
% 25.54/25.41 [4914]~E(x49142,f2(a924))+E(f862(f862(f168(x49141),x49142),x49143),f106(x49141))
% 25.54/25.41 [4923]~E(x49233,f106(x49231))+E(f862(f862(f168(x49231),x49232),x49233),f106(x49231))
% 25.54/25.41 [4963]~E(x49631,x49633)+E(x49631,f862(f862(f127(x49632),f106(x49632)),x49633))
% 25.54/25.41 [5053]~P92(x50532)+E(f862(f181(f932(x50531,x50532)),x50533),f181(x50532))
% 25.54/25.41 [5054]~P92(x50542)+E(f862(f181(f932(x50541,x50542)),x50543),f181(x50542))
% 25.54/25.41 [5055]~P111(x50552)+E(f862(f234(f932(x50551,x50552)),x50553),f234(x50552))
% 25.54/25.41 [5071]E(x50711,f106(x50712))+~E(f862(f862(f127(x50712),x50711),x50713),x50713)
% 25.54/25.41 [5072]E(x50721,f106(x50722))+~E(f862(f862(f127(x50722),x50723),x50721),x50723)
% 25.54/25.41 [5073]E(x50731,f106(x50732))+~E(f862(f862(f127(x50732),x50733),x50731),x50733)
% 25.54/25.41 [5074]E(x50741,f106(x50742))+~E(f862(f862(f127(x50742),x50741),x50743),x50743)
% 25.54/25.41 [5080]E(x50801,f106(x50802))+~E(f862(f862(f127(x50802),x50803),x50801),f106(x50802))
% 25.54/25.41 [5081]E(x50811,f106(x50812))+~E(f862(f862(f127(x50812),x50811),x50813),f106(x50812))
% 25.54/25.41 [5082]E(x50821,f106(x50822))+~E(f862(f862(f127(x50822),x50823),x50821),f106(x50822))
% 25.54/25.41 [5083]E(x50831,f106(x50832))+~E(f862(f862(f127(x50832),x50831),x50833),f106(x50832))
% 25.54/25.41 [5112]~E(x51122,f2(a924))+E(f862(f862(f74(a924),x51121),x51122),f862(f862(f74(a924),x51123),x51122))
% 25.54/25.41 [5113]~E(x51131,f2(a924))+E(f862(f862(f74(a924),x51131),x51132),f862(f862(f74(a924),x51131),x51133))
% 25.54/25.41 [5114]~E(x51141,f2(a924))+E(f862(f862(f74(a924),x51141),x51142),f862(f862(f74(a924),x51141),x51143))
% 25.54/25.41 [5172]~P93(x51721)+E(f862(f862(f103(x51721),x51722),x51723),f862(f862(f103(x51721),x51723),x51722))
% 25.54/25.41 [5173]~P103(x51731)+E(f862(f862(f103(x51731),x51732),x51733),f862(f862(f103(x51731),x51733),x51732))
% 25.54/25.41 [5174]~P103(x51741)+E(f862(f862(f103(x51741),x51742),x51743),f862(f862(f103(x51741),x51743),x51742))
% 25.54/25.41 [5175]~P93(x51751)+E(f862(f862(f94(x51751),x51752),x51753),f862(f862(f94(x51751),x51753),x51752))
% 25.54/25.41 [5176]~P104(x51761)+E(f862(f862(f94(x51761),x51762),x51763),f862(f862(f94(x51761),x51763),x51762))
% 25.54/25.41 [5177]~P104(x51771)+E(f862(f862(f94(x51771),x51772),x51773),f862(f862(f94(x51771),x51773),x51772))
% 25.54/25.41 [5178]~P119(x51781)+E(f862(f862(f74(x51781),x51782),x51783),f862(f862(f74(x51781),x51783),x51782))
% 25.54/25.41 [5179]~P119(x51791)+E(f862(f862(f73(x51791),x51792),x51793),f862(f862(f73(x51791),x51793),x51792))
% 25.54/25.41 [5180]~P109(x51801)+E(f862(f862(f225(x51801),x51802),x51803),f862(f862(f225(x51801),x51803),x51802))
% 25.54/25.41 [5181]~P109(x51811)+E(f862(f862(f225(x51811),x51812),x51813),f862(f862(f225(x51811),x51813),x51812))
% 25.54/25.41 [5182]~P109(x51821)+E(f862(f862(f226(x51821),x51822),x51823),f862(f862(f226(x51821),x51823),x51822))
% 25.54/25.41 [5183]~P109(x51831)+E(f862(f862(f226(x51831),x51832),x51833),f862(f862(f226(x51831),x51833),x51832))
% 25.54/25.41 [5248]E(f38(a924,x52481,x52482),f2(a924))+~E(x52481,f862(f862(f74(a924),x52482),x52483))
% 25.54/25.41 [5249]E(f38(a1,x52491,x52492),f2(a1))+~E(x52491,f862(f862(f74(a1),x52492),x52493))
% 25.54/25.41 [5313]E(x53131,x53132)+~E(f862(f862(f73(a924),x53133),x53131),f862(f862(f73(a924),x53133),x53132))
% 25.54/25.41 [5314]E(x53141,x53142)+~E(f862(f862(f73(a924),x53141),x53143),f862(f862(f73(a924),x53142),x53143))
% 25.54/25.41 [5324]~P96(x53241)+E(f862(f862(f94(x53241),x53242),f862(f72(x53241),x53243)),f862(f862(f3(x53241),x53242),x53243))
% 25.54/25.41 [5325]~P59(x53251)+E(f862(f862(f73(x53251),x53252),f862(f72(x53251),x53253)),f862(f862(f3(x53251),x53252),x53253))
% 25.54/25.41 [5326]~P68(x53261)+E(f862(f862(f73(x53261),x53262),f862(f72(x53261),x53263)),f862(f862(f3(x53261),x53262),x53263))
% 25.54/25.41 [5327]~P115(x53271)+E(f862(f862(f73(x53271),x53272),f862(f72(x53271),x53273)),f862(f862(f3(x53271),x53272),x53273))
% 25.54/25.41 [5328]~P68(x53281)+E(f862(f862(f3(x53281),x53282),f862(f72(x53281),x53283)),f862(f862(f73(x53281),x53282),x53283))
% 25.54/25.41 [5366]~P1(f862(x53663,x53662))+P1(f862(f862(f321(x53661),x53662),x53663))
% 25.54/25.41 [5367]~P72(x53672)+E(f862(f862(f8(x53671,x53672),x53673),f181(f932(x53671,a921))),f2(x53672))
% 25.54/25.41 [5368]~P72(x53682)+E(f862(f862(f8(x53681,x53682),x53683),f181(f932(x53681,a921))),f2(x53682))
% 25.54/25.41 [5369]~P71(x53692)+E(f862(f862(f11(x53691,x53692),x53693),f181(f932(x53691,a921))),f71(x53692))
% 25.54/25.41 [5370]~P71(x53702)+E(f862(f862(f11(x53701,x53702),x53703),f181(f932(x53701,a921))),f71(x53702))
% 25.54/25.41 [5424]~E(x54242,f862(f862(f73(a924),x54241),x54243))+P1(f862(f862(f227(a924),x54241),x54242))
% 25.54/25.41 [5427]~E(x54272,f181(f932(x54271,a921)))+E(f862(f862(f53(x54271),x54272),x54273),f181(f932(f932(x54271,a921),a921)))
% 25.54/25.41 [5428]~E(x54282,f181(f932(x54281,a921)))+E(f181(f932(f932(x54281,a921),a921)),f862(f862(f53(x54281),x54282),x54283))
% 25.54/25.41 [5496]~E(f862(f275(x54962,x54963),x54961),f181(f932(x54963,a921)))+E(x54961,f181(f932(f931(x54962,x54963),a921)))
% 25.54/25.41 [5497]~E(f862(f256(x54972,x54973),x54971),f181(f932(x54972,a921)))+E(x54971,f181(f932(f931(x54972,x54973),a921)))
% 25.54/25.41 [5529]E(f862(f275(x55291,x55292),x55293),f181(f932(x55292,a921)))+~E(x55293,f181(f932(f931(x55291,x55292),a921)))
% 25.54/25.41 [5530]E(f862(f256(x55301,x55302),x55303),f181(f932(x55301,a921)))+~E(x55303,f181(f932(f931(x55301,x55302),a921)))
% 25.54/25.41 [5533]E(f266(x55331,x55332,x55333),f862(f862(f3(a92),x55332),x55333))+P1(f862(f862(f228(a92),x55332),x55333))
% 25.54/25.41 [5550]P1(f862(x55501,x55502))+~P1(f862(f862(f321(x55503),x55502),x55501))
% 25.54/25.41 [5589]E(x55891,x55892)+~E(f862(f72(f932(x55893,a921)),x55891),f862(f72(f932(x55893,a921)),x55892))
% 25.54/25.41 [5598]~E(x55981,f181(f932(x55982,a921)))+~P1(f862(f862(f321(x55982),x55983),x55981))
% 25.54/25.41 [5599]~E(x55991,f181(f932(x55992,a921)))+~P1(f862(f862(f321(x55992),x55993),x55991))
% 25.54/25.41 [5600]~E(x56001,f181(f932(x56002,a921)))+~P1(f862(f862(f321(x56002),x56003),x56001))
% 25.54/25.41 [5631]~E(x56312,f862(f862(f73(a1),x56311),f862(f93(a1),x56313)))+P1(f862(f862(f227(a1),x56311),x56312))
% 25.54/25.41 [5645]E(f862(f862(f301(x56451),x56452),x56453),x56453)+~P1(f862(f862(f321(x56451),x56452),x56453))
% 25.54/25.41 [5656]E(x56561,f181(f932(x56562,a921)))+~E(f862(f862(f53(x56562),x56561),x56563),f181(f932(f932(x56562,a921),a921)))
% 25.54/25.41 [5657]E(x56571,f181(f932(x56572,a921)))+~E(f181(f932(f932(x56572,a921),a921)),f862(f862(f53(x56572),x56571),x56573))
% 25.54/25.41 [5663]~P125(x56631)+E(f862(f862(f74(x56631),f862(f72(x56631),x56632)),f862(f72(x56631),x56633)),f862(f862(f74(x56631),x56632),x56633))
% 25.54/25.41 [5665]~P64(x56651)+E(f862(f862(f281(x56651),f862(f72(x56651),x56652)),f862(f72(x56651),x56653)),f862(f862(f281(x56651),x56652),x56653))
% 25.54/25.41 [5695]~P1(f862(x56953,x56952))+P1(f862(f862(f321(x56951),x56952),f862(f254(x56951),x56953)))
% 25.54/25.41 [5696]~P1(f862(x56963,x56962))+P1(f862(f862(f321(x56961),x56962),f862(f254(x56961),x56963)))
% 25.54/25.41 [5722]E(x57221,f2(a924))+E(f862(f165(x57222),f162(x57222,x57221,x57223)),f862(f862(f301(x57222),x57223),f181(f932(x57222,a921))))
% 25.54/25.41 [5723]E(x57231,f2(a924))+E(f862(f165(x57232),f162(x57232,x57231,x57233)),f862(f862(f301(x57232),x57233),f181(f932(x57232,a921))))
% 25.54/25.41 [5743]E(f163(x57431,x57432,x57433),x57433)+P1(f862(f862(f321(x57431),x57432),f862(f165(x57431),x57433)))
% 25.54/25.41 [5829]~P1(f862(f130(x58291),x58293))+P1(f862(f130(x58291),f862(f129(x58291,x58292),x58293)))
% 25.54/25.41 [5872]~P61(x58721)+E(f862(f862(f29(x58721),f38(x58721,x58722,x58723)),x58723),f2(x58721))
% 25.54/25.41 [5891]E(f169(x58911,f862(f862(f144(x58911),x58912),f106(x58911)),x58913),f106(x58911))+P1(f862(f862(f321(a924),f2(a924)),x58913))
% 25.54/25.41 [5897]E(x58971,f2(a924))+E(f862(f164(x58972),f162(x58972,x58971,x58973)),f162(x58972,f862(f862(f3(a924),x58971),f71(a924)),x58973))
% 25.54/25.41 [5947]E(f862(f862(f144(x59471),x59472),x59473),f133(x59471,x59472,x59473))+P1(f862(f862(f321(x59471),x59472),f862(f165(x59471),x59473)))
% 25.54/25.41 [5948]E(f862(f862(f144(x59481),x59482),x59483),f133(x59481,x59482,x59483))+P1(f862(f862(f321(x59481),x59482),f862(f165(x59481),x59483)))
% 25.54/25.41 [5957]E(x59571,x59572)+~E(f862(f862(f74(a924),f862(a105,x59573)),x59571),f862(f862(f74(a924),f862(a105,x59573)),x59572))
% 25.54/25.41 [5958]~E(x59582,f862(f862(f73(a1),x59581),f862(f93(a1),f862(a105,x59583))))+P1(f862(f862(f228(a1),x59581),x59582))
% 25.54/25.41 [6028]~P28(x60281,x60282,x60283)+P29(a924,x60281,f132(a924,f862(f295(a924,x60282),x60283)))
% 25.54/25.41 [6081]~E(x60813,f106(x60811))+E(f862(f862(f862(f176(f925(x60811),f925(x60811)),x60812),f160(x60811)),x60813),f106(x60811))
% 25.54/25.41 [6083]P1(f862(x60831,x60832))+~P1(f862(f862(f321(x60833),x60832),f862(f254(x60833),x60831)))
% 25.54/25.41 [6084]P1(f862(x60841,x60842))+~P1(f862(f862(f321(x60843),x60842),f862(f254(x60843),x60841)))
% 25.54/25.41 [6085]P1(f862(x60851,x60852))+~P1(f862(f862(f321(x60853),x60852),f862(f254(x60853),x60851)))
% 25.54/25.41 [6117]E(x61171,x61172)+~E(f862(f862(f301(x61173),x61171),f181(f932(x61173,a921))),f862(f862(f301(x61173),x61172),f181(f932(x61173,a921))))
% 25.54/25.41 [6133]~P110(x61331)+E(f862(f862(f94(f932(x61331,a921)),f862(f292(x61331),x61332)),f862(f295(x61331,x61332),x61333)),f181(f932(x61331,a921)))
% 25.54/25.41 [6171]E(f133(x61711,x61712,x61713),x61713)+~P1(f862(f862(f321(x61711),x61712),f862(f165(x61711),x61713)))
% 25.54/25.41 [6172]E(f133(x61721,x61722,x61723),x61723)+~P1(f862(f862(f321(x61721),x61722),f862(f165(x61721),x61723)))
% 25.54/25.41 [6192]~P78(x61921)+E(f862(f302(x61921,x61921,f72(x61921)),f862(f295(x61921,x61922),x61923)),f297(x61921,f862(f72(x61921),x61923),f862(f72(x61921),x61922)))
% 25.54/25.41 [6197]P1(f862(f862(f321(x61971),x61972),f862(f165(x61971),x61973)))+~P1(f862(f862(f165(x61971),x61973),x61972))
% 25.54/25.41 [6198]P1(f862(f862(f321(x61981),x61982),f862(f165(x61981),x61983)))+~P1(f862(f862(f165(x61981),x61983),x61982))
% 25.54/25.41 [6203]E(f862(f182(f925(x62031)),f163(x62031,x62032,x62033)),f862(f182(f925(x62031)),x62033))+P1(f862(f862(f321(x62031),x62032),f862(f165(x62031),x62033)))
% 25.54/25.41 [6222]P1(f862(x62221,x62222))+~P1(f862(f862(f321(x62223),x62222),f181(f932(x62223,a921))))
% 25.54/25.41 [6223]~P1(f862(x62232,x62233))+P1(f862(f862(f321(x62231),f743(x62232,x62231)),f234(f932(x62231,a921))))
% 25.54/25.41 [6255]~P110(x62551)+E(f862(f862(f94(f932(x62551,a921)),f862(f295(x62551,x62552),x62553)),f862(f274(x62551),x62553)),f181(f932(x62551,a921)))
% 25.54/25.41 [6275]~P78(x62751)+E(f862(f302(x62751,x62751,f72(x62751)),f298(x62751,x62752,x62753)),f298(x62751,f862(f72(x62751),x62753),f862(f72(x62751),x62752)))
% 25.54/25.41 [6276]~P78(x62761)+E(f862(f302(x62761,x62761,f72(x62761)),f296(x62761,x62762,x62763)),f296(x62761,f862(f72(x62761),x62763),f862(f72(x62761),x62762)))
% 25.54/25.41 [6281]~P1(f862(x62811,x62812))+~P1(f862(f862(f321(x62813),x62812),f181(f932(x62813,a921))))
% 25.54/25.41 [6335]~P1(f862(f862(f321(x63351),x63353),f862(f165(x63351),x63352)))+P1(f862(f862(f165(x63351),x63352),x63353))
% 25.54/25.41 [6336]~P1(f862(f862(f321(x63361),x63363),f862(f165(x63361),x63362)))+P1(f862(f862(f165(x63361),x63362),x63363))
% 25.54/25.41 [6340]E(f169(x63401,f862(f862(f144(x63401),x63402),f106(x63401)),x63403),f862(f862(f144(x63401),x63402),f106(x63401)))+~P1(f862(f862(f321(a924),f2(a924)),x63403))
% 25.54/25.41 [6345]P28(x63451,x63452,x63453)+~P29(a924,x63451,f132(a924,f862(f295(a924,x63452),x63453)))
% 25.54/25.41 [6348]~P78(x63481)+E(f862(f302(x63481,x63481,f72(x63481)),f297(x63481,x63482,x63483)),f862(f295(x63481,f862(f72(x63481),x63483)),f862(f72(x63481),x63482)))
% 25.54/25.41 [6368]~P62(x63681)+E(f38(x63681,f862(f72(x63681),f38(x63681,x63682,x63683)),x63683),f38(x63681,f862(f72(x63681),x63682),x63683))
% 25.54/25.41 [6464]~P1(f862(f54(f931(x64642,x64641)),x64643))+P1(f862(f54(x64641),f862(f275(x64642,x64641),x64643)))
% 25.54/25.41 [6465]~P1(f862(f54(f931(x64651,x64652)),x64653))+P1(f862(f54(x64651),f862(f256(x64651,x64652),x64653)))
% 25.54/25.41 [6470]~P110(x64701)+E(f862(f862(f94(f932(x64701,a921)),f298(x64701,x64702,x64703)),f862(f274(x64701),x64703)),f181(f932(x64701,a921)))
% 25.54/25.41 [6471]~P110(x64711)+E(f862(f862(f94(f932(x64711,a921)),f297(x64711,x64712,x64713)),f862(f293(x64711),x64713)),f181(f932(x64711,a921)))
% 25.54/25.41 [6472]~P110(x64721)+E(f862(f862(f94(f932(x64721,a921)),f296(x64721,x64722,x64723)),f862(f293(x64721),x64723)),f181(f932(x64721,a921)))
% 25.54/25.41 [6544]E(f862(f862(f157(x65441),x65442),f668(x65442,x65443,x65441)),x65443)+~P1(f862(f862(f321(x65441),x65443),f862(f165(x65441),x65442)))
% 25.54/25.41 [6689]E(x66891,f106(x66892))+~E(f862(f862(f862(f176(f925(x66892),f925(x66892)),x66893),f160(x66892)),x66891),f106(x66892))
% 25.54/25.41 [6792]~P1(f862(f54(f931(x67922,x67921)),x67923))+P1(f862(f54(f931(x67921,x67922)),f862(f277(x67922,x67921),x67923)))
% 25.54/25.41 [6943]P53(x69431,x69432,x69433)+P1(f862(f862(f321(x69431),f626(x69433,x69432,x69431)),x69432))
% 25.54/25.41 [6944]P53(x69441,x69442,x69443)+P1(f862(f862(f321(x69441),f625(x69443,x69442,x69441)),x69442))
% 25.54/25.41 [6954]P1(f862(f307(x69541,x69542),x69543))+P1(f862(f862(x69542,f448(x69543,x69542,x69541)),x69543))
% 25.54/25.41 [6955]P1(f862(f307(x69551,x69552),x69553))+P1(f862(f862(x69552,f497(x69553,x69552,x69551)),x69553))
% 25.54/25.41 [6987]E(f862(f182(f925(x69871)),f163(x69871,x69872,x69873)),f862(f862(f3(a924),f862(f182(f925(x69871)),x69873)),f71(a924)))+~P1(f862(f862(f321(x69871),x69872),f862(f165(x69871),x69873)))
% 25.54/25.41 [7026]P1(f862(f240(x70261,x70262),x70263))+P1(f862(f862(f321(x70261),f590(x70263,x70262,x70261)),x70263))
% 25.54/25.41 [7035]~P1(f862(f54(f931(x70352,x70351)),f862(f277(x70351,x70352),x70353)))+P1(f862(f54(f931(x70351,x70352)),x70353))
% 25.54/25.41 [7093]~P1(f862(f862(f321(x70931),x70932),f862(f165(x70931),f107(x70931,x70933))))+P1(f862(f862(f321(x70931),x70932),f862(f165(x70931),x70933)))
% 25.54/25.41 [7127]E(f862(f129(x71271,x71272),x71273),x71273)+P1(f862(f862(f321(x71271),f679(x71273,x71272,x71271)),f862(f165(x71271),x71273)))
% 25.54/25.41 [7141]E(f862(f129(x71411,x71412),x71413),f106(x71411))+P1(f862(f862(f321(x71411),f678(x71413,x71412,x71411)),f862(f165(x71411),x71413)))
% 25.54/25.41 [7166]P29(x71661,x71662,x71663)+P1(f862(f862(f321(x71661),f765(x71663,x71662,x71661)),f862(f165(x71661),x71663)))
% 25.54/25.41 [7167]P29(x71671,x71672,x71673)+P1(f862(f862(f321(x71671),f774(x71673,x71672,x71671)),f862(f165(x71671),x71673)))
% 25.54/25.41 [7168]P29(x71681,x71682,x71683)+P1(f862(f862(f321(x71681),f771(x71682,x71683,x71681)),f862(f165(x71681),x71683)))
% 25.54/25.41 [7171]E(f170(x71711,x71712,x71713),x71713)+P1(f862(f862(f321(x71711),f723(x71713,x71712,x71711)),f862(f165(x71711),x71713)))
% 25.54/25.41 [7247]P1(f862(f153(x72471,x72472),x72473))+P1(f862(f862(f321(x72471),f680(x72473,x72472,x72471)),f862(f165(x72471),x72473)))
% 25.54/25.41 [7256]~P31(x72561,x72563,x72562)+P1(f862(f862(f321(x72561),f757(x72562,x72563,x72561)),f862(f165(x72561),x72562)))
% 25.54/25.41 [7257]~P33(x72571,x72573,x72572)+P1(f862(f862(f321(x72571),f764(x72572,x72573,x72571)),f862(f165(x72571),x72572)))
% 25.54/25.41 [7258]~P33(x72581,x72583,x72582)+P1(f862(f862(f321(x72581),f775(x72582,x72583,x72581)),f862(f165(x72581),x72582)))
% 25.54/25.41 [7259]~P31(x72591,x72593,x72592)+P1(f862(f862(f321(x72591),f799(x72592,x72593,x72591)),f862(f165(x72591),x72592)))
% 25.54/25.41 [7260]~P31(x72601,x72602,x72603)+P1(f862(f862(f321(x72601),f801(x72602,x72603,x72601)),f862(f165(x72601),x72603)))
% 25.54/25.41 [7295]P1(f862(f862(f321(x72951),x72952),f449(x72953,x72952,x72951)))+~P1(f862(f862(f321(x72951),x72952),f30(f932(x72951,a921),x72953)))
% 25.54/25.41 [7296]~P72(x72961)+E(f862(f862(f73(x72961),f862(f862(f8(a924,x72961),x72962),f862(f292(a924),x72963))),f862(x72962,x72963)),f862(f862(f8(a924,x72961),x72962),f862(f292(a924),f862(a105,x72963))))
% 25.54/25.41 [7308]P28(x73081,x73082,x73083)+P1(f862(f862(f321(a924),f833(x73083,x73082,x73081)),f862(f295(a924,x73082),x73083)))
% 25.54/25.41 [7388]~P31(x73882,x73881,x73883)+P1(f862(x73881,f862(f862(f157(x73882),x73883),f760(x73883,x73881,x73882))))
% 25.54/25.41 [7401]~P1(f862(f862(f321(x74011),x74012),f447(x74012,x74013,x74011)))+P1(f862(f862(f321(x74011),x74012),f31(f932(x74011,a921),x74013)))
% 25.54/25.41 [7434]~P72(x74341)+E(f862(f862(f73(x74341),f862(f862(f8(a924,x74341),x74342),f862(f294(a924),x74343))),f862(x74342,f862(a105,x74343))),f862(f862(f8(a924,x74341),x74342),f862(f294(a924),f862(a105,x74343))))
% 25.54/25.41 [7440]P1(f862(x74401,f529(x74402,x74403,x74401)))+P1(f862(f862(f227(f932(x74402,a921)),f862(f254(x74402),x74401)),f862(f254(x74402),x74403)))
% 25.54/25.41 [7577]P1(f862(f862(f321(f925(x75771)),x75772),f154(x75771,x75773)))+P1(f862(f862(f321(x75771),f669(x75773,x75772,x75771)),f862(f165(x75771),x75772)))
% 25.54/25.41 [7594]~P1(f862(f862(f321(f925(x75941)),x75942),f154(x75941,f308(x75941,x75943))))+P1(f862(f862(f321(f925(x75941)),x75942),f308(f925(x75941),f150(x75941,x75943))))
% 25.54/25.41 [7618]~P1(f862(f862(f321(f925(x76181)),x76182),f308(f925(x76181),f150(x76181,x76183))))+P1(f862(f862(f321(f925(x76181)),x76182),f154(x76181,f308(x76181,x76183))))
% 25.54/25.41 [7650]E(f862(f862(f862(f176(f925(x76501),f925(x76501)),x76502),f160(x76501)),x76503),x76503)+~P1(f862(f862(f227(a924),f862(f182(f925(x76501)),x76503)),f71(a924)))
% 25.54/25.41 [7682]P1(f862(x76821,x76822))+~P1(f862(x76821,f862(f85(x76823),f546(x76822,x76821,x76823))))
% 25.54/25.41 [7684]E(f862(f862(f127(x76841),f762(x76842,x76843,x76841)),f862(f862(f144(x76841),x76843),f763(x76842,x76843,x76841))),x76842)+~P1(f862(f862(f321(x76841),x76843),f862(f165(x76841),x76842)))
% 25.54/25.41 [7685]E(f862(f862(f127(x76851),f767(x76852,x76853,x76851)),f862(f862(f144(x76851),x76853),f768(x76852,x76853,x76851))),x76852)+~P1(f862(f862(f321(x76851),x76853),f862(f165(x76851),x76852)))
% 25.54/25.41 [7686]E(f862(f862(f127(x76861),f769(x76862,x76863,x76861)),f862(f862(f144(x76861),x76863),f770(x76862,x76863,x76861))),x76862)+~P1(f862(f862(f321(x76861),x76863),f862(f165(x76861),x76862)))
% 25.54/25.41 [7706]~P22(x77061,x77062,x77063,f234(f932(x77061,a921)))+P22(f925(x77061),f925(x77062),f862(f147(x77061,x77062),x77063),f234(f932(f925(x77061),a921)))
% 25.54/25.41 [7707]~P22(x77071,x77072,x77073,f234(f932(x77071,a921)))+P22(f925(x77071),f925(x77072),f862(f147(x77071,x77072),x77073),f234(f932(f925(x77071),a921)))
% 25.54/25.41 [7745]~P1(f862(x77453,f529(x77451,x77453,x77452)))+P1(f862(f862(f227(f932(x77451,a921)),f862(f254(x77451),x77452)),f862(f254(x77451),x77453)))
% 25.54/25.41 [7859]E(x78591,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x78592)),x78593)),f862(f248(a924,a924),x78592)))+~P1(f862(f41(x78591,x78593),x78592))
% 25.54/25.41 [7866]P22(x78661,x78662,x78663,f234(f932(x78661,a921)))+~P22(f925(x78661),f925(x78662),f862(f147(x78661,x78662),x78663),f234(f932(f925(x78661),a921)))
% 25.54/25.41 [7867]P22(x78671,x78672,x78673,f234(f932(x78671,a921)))+~P22(f925(x78671),f925(x78672),f862(f147(x78671,x78672),x78673),f234(f932(f925(x78671),a921)))
% 25.54/25.41 [7911]P1(f862(f862(f321(f932(x79111,a921)),f447(x79112,x79113,x79111)),x79113))+P1(f862(f862(f321(x79111),x79112),f31(f932(x79111,a921),x79113)))
% 25.54/25.41 [8001]P1(f862(f862(f321(f925(x80011)),x80012),f154(x80011,x80013)))+~P1(f862(f862(f321(x80011),f669(x80013,x80012,x80011)),x80013))
% 25.54/25.41 [8104]P29(x81041,x81042,x81043)+~P1(f862(x81042,f862(f862(f157(x81041),x81043),f766(x81043,x81042,x81041))))
% 25.54/25.41 [8129]E(x81291,x81292)+~E(f862(f862(f9(x81293,f932(x81293,a921),a921),f321(x81293)),x81291),f862(f862(f9(x81293,f932(x81293,a921),a921),f321(x81293)),x81292))
% 25.54/25.41 [8137]~P1(f862(f862(f321(f931(x81371,x81371)),x81373),f255(x81371,x81372)))+P1(f862(f862(f321(x81371),f536(x81372,x81373,x81371)),x81372))
% 25.54/25.41 [8139]~P1(f862(f862(f321(x81391),x81393),f30(f932(x81391,a921),x81392)))+P1(f862(f862(f321(f932(x81391,a921)),f449(x81392,x81393,x81391)),x81392))
% 25.54/25.41 [8197]P1(f862(f862(f227(f932(x81971,a921)),x81972),f31(f932(x81971,a921),x81973)))+P1(f862(f862(f321(f932(x81971,a921)),f467(x81972,x81973,x81971)),x81973))
% 25.54/25.41 [8261]P22(x82611,x82612,f86(x82612,x82611,f234(f932(x82612,a921)),x82613),f234(f932(x82611,a921)))+~E(f862(f302(x82612,x82611,x82613),f234(f932(x82612,a921))),f234(f932(x82611,a921)))
% 25.54/25.41 [8287]~P1(f862(f862(f227(f932(x82871,a921)),x82872),f467(x82872,x82873,x82871)))+P1(f862(f862(f227(f932(x82871,a921)),x82872),f31(f932(x82871,a921),x82873)))
% 25.54/25.41 [8317]~P1(f862(f862(f321(x83171),x83172),f862(f165(x83171),f767(x83173,x83172,x83171))))+~P1(f862(f862(f321(x83171),x83172),f862(f165(x83171),x83173)))
% 25.54/25.41 [8318]~P1(f862(f862(f321(x83181),x83182),f862(f165(x83181),f770(x83183,x83182,x83181))))+~P1(f862(f862(f321(x83181),x83182),f862(f165(x83181),x83183)))
% 25.54/25.41 [8347]P28(f862(f66(a921,a921,a924,a314),x83471),x83472,x83473)+P31(a924,x83471,f132(a924,f862(f295(a924,x83472),x83473)))
% 25.54/25.41 [8508]E(x85081,f106(x85082))+P1(f862(f862(f321(x85082),f862(f243(x85082,f931(a92,a92)),f862(f267(x85082,x85081),x85083))),f862(f165(x85082),x85081)))
% 25.54/25.41 [8608]~P70(x86081)+E(f862(f135(x86081,x86081,f862(f9(x86081,x86081,x86081),f73(x86081)),x86082),f862(f161(x86081),x86083)),f862(f135(x86081,x86081,f73(x86081),x86082),x86083))
% 25.54/25.41 [8803]~P22(x88032,x88031,x88033,f234(f932(x88032,a921)))+E(f862(f302(x88031,x88032,f86(x88032,x88031,f234(f932(x88032,a921)),x88033)),f234(f932(x88031,a921))),f234(f932(x88032,a921)))
% 25.54/25.41 [8873]~P28(f862(f66(a921,a921,a924,a314),x88731),x88732,x88733)+~P31(a924,x88731,f132(a924,f862(f295(a924,x88732),x88733)))
% 25.54/25.41 [9015]~P23(x90151,x90152,x90153,f234(f932(x90151,a921)),f234(f932(x90152,a921)))+E(f862(f302(x90151,x90152,x90153),f234(f932(x90151,a921))),f234(f932(x90152,a921)))
% 25.54/25.41 [9016]~P23(x90161,x90162,x90163,f234(f932(x90161,a921)),f234(f932(x90162,a921)))+E(f862(f302(x90161,x90162,x90163),f234(f932(x90161,a921))),f234(f932(x90162,a921)))
% 25.54/25.41 [9123]~P109(x91231)+E(f862(f165(x91231),f142(x91231,x91231,f7(x91231),x91232,x91233)),f862(f862(f301(x91231),x91232),f862(f165(x91231),x91233)))
% 25.54/25.41 [9132]~E(f862(x91323,f862(f86(x91321,x91322,f234(f932(x91321,a921)),x91323),f816(x91323,x91322,x91321))),f816(x91323,x91322,x91321))+E(f862(f302(x91321,x91322,x91323),f234(f932(x91321,a921))),f234(f932(x91322,a921)))
% 25.54/25.41 [9134]P1(f862(f862(f228(a924),f2(a924)),f631(x91341,x91342,x91343)))+~P1(f862(f862(f321(f931(x91343,x91343)),x91342),f862(f862(f280(x91343,x91343,x91343),x91341),f299(x91343,x91341))))
% 25.54/25.41 [9412]~P55(x94121,x94122)+~P1(f862(f862(f321(f931(x94121,x94121)),f862(f862(f244(x94121,x94121),x94123),x94123)),f862(f862(f280(x94121,x94121,x94121),x94122),f299(x94121,x94122))))
% 25.54/25.41 [9514]~P23(x95142,x95141,x95143,f234(f932(x95142,a921)),f234(f932(x95141,a921)))+P23(x95141,x95142,f86(x95142,x95141,f234(f932(x95142,a921)),x95143),f234(f932(x95141,a921)),f234(f932(x95142,a921)))
% 25.54/25.41 [9548]~E(f862(f862(f94(f932(f931(x95481,x95481),a921)),f862(f277(x95481,x95481),x95482)),f299(x95481,x95482)),f181(f932(f931(x95481,x95481),a921)))+~P1(f862(f862(f321(f931(x95481,x95481)),f862(f862(f244(x95481,x95481),x95483),x95483)),f862(f862(f280(x95481,x95481,x95481),x95482),f299(x95481,x95482))))
% 25.54/25.41 [9734]~P1(f862(f54(x97341),x97342))+P1(f862(f862(f227(a924),f862(f28(x97341),f862(f862(f3(f932(x97341,a921)),x97342),f862(f862(f301(x97341),x97343),f181(f932(x97341,a921)))))),f862(f28(x97341),x97342)))
% 25.54/25.41 [10003]P1(f862(x100031,x100032))+P1(f862(f862(f321(f932(f922(f930(a919,f932(x100033,f932(a920,a921))),f930(a920,x100033)),a921)),f546(x100032,x100031,x100033)),f862(f254(f932(f922(f930(a919,f932(x100033,f932(a920,a921))),f930(a920,x100033)),a921)),f88(x100033))))
% 25.54/25.41 [5235]~E(x52353,f106(x52351))+E(f137(x52351,f862(f862(f144(x52351),x52352),x52353)),x52352)
% 25.54/25.41 [5236]~E(x52363,f106(x52361))+E(f137(x52361,f862(f862(f144(x52361),x52362),x52363)),x52362)
% 25.54/25.41 [5245]~E(x52453,f106(x52451))+E(f107(x52451,f862(f862(f144(x52451),x52452),x52453)),f106(x52451))
% 25.54/25.41 [5274]E(x52741,f106(x52742))+E(f137(x52742,f862(f862(f144(x52742),x52743),x52741)),f137(x52742,x52741))
% 25.54/25.41 [5275]E(x52751,f106(x52752))+E(f137(x52752,f862(f862(f144(x52752),x52753),x52751)),f137(x52752,x52751))
% 25.54/25.41 [5276]E(x52761,f106(x52762))+E(f137(x52762,f862(f862(f127(x52762),x52763),x52761)),f137(x52762,x52761))
% 25.54/25.41 [5277]E(x52771,f106(x52772))+E(f137(x52772,f862(f862(f127(x52772),x52773),x52771)),f137(x52772,x52771))
% 25.54/25.41 [5283]~E(x52833,f106(x52831))+E(f107(x52831,f862(f862(f127(x52831),x52832),x52833)),f107(x52831,x52832))
% 25.54/25.41 [5284]~E(x52843,f106(x52841))+E(f137(x52841,f862(f862(f127(x52841),x52842),x52843)),f137(x52841,x52842))
% 25.54/25.41 [5285]~E(x52853,f106(x52851))+E(f137(x52851,f862(f862(f127(x52851),x52852),x52853)),f137(x52851,x52852))
% 25.54/25.41 [5317]E(x53171,f106(x53172))+E(f862(f134(x53172),f862(f862(f127(x53172),x53171),x53173)),f862(f134(x53172),x53171))
% 25.54/25.41 [5318]E(x53181,f106(x53182))+E(f862(f134(x53182),f862(f862(f127(x53182),x53181),x53183)),f862(f134(x53182),x53181))
% 25.54/25.41 [5346]~E(x53462,f106(x53461))+E(f862(f134(x53461),f862(f862(f127(x53461),x53462),x53463)),f862(f134(x53461),x53463))
% 25.54/25.41 [5382]~E(x53822,x53823)+P1(f862(f862(f84(f923(x53821)),x53822),x53823))
% 25.54/25.41 [5400]~P93(x54001)+E(f862(f862(f103(x54001),x54002),f862(f862(f94(x54001),x54002),x54003)),x54002)
% 25.54/25.41 [5401]~P93(x54011)+E(f862(f862(f94(x54011),x54012),f862(f862(f103(x54011),x54012),x54013)),x54012)
% 25.54/25.41 [5402]~P109(x54021)+E(f862(f862(f225(x54021),x54022),f862(f862(f226(x54021),x54022),x54023)),x54022)
% 25.54/25.41 [5403]~P109(x54031)+E(f862(f862(f226(x54031),x54032),f862(f862(f225(x54031),x54032),x54033)),x54032)
% 25.54/25.41 [5422]~P61(x54221)+E(f38(x54221,f862(f862(f74(x54221),x54222),x54223),x54223),f2(x54221))
% 25.54/25.41 [5423]~P61(x54231)+E(f38(x54231,f862(f862(f74(x54231),x54232),x54233),x54232),f2(x54231))
% 25.54/25.41 [5491]~P59(x54911)+E(f862(f72(x54911),f862(f862(f3(x54911),x54912),x54913)),f862(f862(f3(x54911),x54913),x54912))
% 25.54/25.41 [5554]E(x55541,f106(x55542))+E(f107(x55542,f862(f862(f144(x55542),x55543),x55541)),f862(f862(f144(x55542),x55543),f107(x55542,x55541)))
% 25.54/25.41 [5555]E(x55551,f106(x55552))+E(f107(x55552,f862(f862(f127(x55552),x55553),x55551)),f862(f862(f127(x55552),x55553),f107(x55552,x55551)))
% 25.54/25.41 [5558]~P3(x55581)+E(f31(x55581,f862(f862(f301(x55581),x55582),x55583)),f862(f862(f94(x55581),x55582),f31(x55581,x55583)))
% 25.54/25.41 [5559]~P3(x55591)+E(f30(x55591,f862(f862(f301(x55591),x55592),x55593)),f862(f862(f103(x55591),x55592),f30(x55591,x55593)))
% 25.54/25.41 [5605]~P93(x56051)+E(f862(f862(f103(x56051),x56052),f862(f862(f103(x56051),x56052),x56053)),f862(f862(f103(x56051),x56052),x56053))
% 25.54/25.41 [5606]~P103(x56061)+E(f862(f862(f103(x56061),x56062),f862(f862(f103(x56061),x56062),x56063)),f862(f862(f103(x56061),x56062),x56063))
% 25.54/25.41 [5607]~P103(x56071)+E(f862(f862(f103(x56071),x56072),f862(f862(f103(x56071),x56072),x56073)),f862(f862(f103(x56071),x56072),x56073))
% 25.54/25.41 [5608]~P93(x56081)+E(f862(f862(f94(x56081),x56082),f862(f862(f94(x56081),x56082),x56083)),f862(f862(f94(x56081),x56082),x56083))
% 25.54/25.41 [5609]~P104(x56091)+E(f862(f862(f94(x56091),x56092),f862(f862(f94(x56091),x56092),x56093)),f862(f862(f94(x56091),x56092),x56093))
% 25.54/25.41 [5610]~P104(x56101)+E(f862(f862(f94(x56101),x56102),f862(f862(f94(x56101),x56102),x56103)),f862(f862(f94(x56101),x56102),x56103))
% 25.54/25.41 [5611]~P100(x56111)+E(f862(f862(f74(x56111),x56112),f862(f862(f74(x56111),x56112),x56113)),f862(f862(f74(x56111),x56112),x56113))
% 25.54/25.41 [5612]~P109(x56121)+E(f862(f862(f225(x56121),x56122),f862(f862(f225(x56121),x56122),x56123)),f862(f862(f225(x56121),x56122),x56123))
% 25.54/25.41 [5613]~P109(x56131)+E(f862(f862(f225(x56131),x56132),f862(f862(f225(x56131),x56132),x56133)),f862(f862(f225(x56131),x56132),x56133))
% 25.54/25.41 [5614]~P109(x56141)+E(f862(f862(f226(x56141),x56142),f862(f862(f226(x56141),x56142),x56143)),f862(f862(f226(x56141),x56142),x56143))
% 25.54/25.41 [5615]~P109(x56151)+E(f862(f862(f226(x56151),x56152),f862(f862(f226(x56151),x56152),x56153)),f862(f862(f226(x56151),x56152),x56153))
% 25.54/25.41 [5622]~P61(x56221)+E(f38(x56221,f862(f862(f73(x56221),x56222),x56223),x56223),f38(x56221,x56222,x56223))
% 25.54/25.41 [5623]~P61(x56231)+E(f38(x56231,f862(f862(f73(x56231),x56232),x56233),x56232),f38(x56231,x56233,x56232))
% 25.54/25.41 [5632]~P125(x56321)+E(f862(f862(f74(x56321),x56322),f862(f72(x56321),x56323)),f862(f72(x56321),f862(f862(f74(x56321),x56322),x56323)))
% 25.54/25.41 [5633]~P64(x56331)+E(f862(f862(f281(x56331),x56332),f862(f72(x56331),x56333)),f862(f72(x56331),f862(f862(f281(x56331),x56332),x56333)))
% 25.54/25.41 [5634]~P81(x56341)+E(f862(f862(f73(x56341),x56342),f862(f158(x56341),x56343)),f862(f158(x56341),f862(f862(f144(x56341),x56342),x56343)))
% 25.54/25.41 [5662]~P125(x56621)+E(f862(f862(f74(x56621),f862(f72(x56621),x56622)),x56623),f862(f862(f74(x56621),x56622),f862(f72(x56621),x56623)))
% 25.54/25.41 [5668]~P6(x56681,x56682,x56683)+E(f30(f932(x56681,a921),f862(f862(f53(x56681),x56682),x56683)),x56682)
% 25.54/25.41 [5734]~P119(x57341)+E(f862(f862(f74(x57341),x57342),f862(f862(f236(x57341),x57342),x57343)),f862(f862(f236(x57341),x57342),f862(a105,x57343)))
% 25.54/25.41 [5735]~P116(x57351)+E(f862(f862(f74(x57351),x57352),f862(f862(f236(x57351),x57352),x57353)),f862(f862(f236(x57351),x57352),f862(a105,x57353)))
% 25.54/25.41 [5736]~P119(x57361)+E(f862(f862(f74(x57361),x57362),f862(f862(f236(x57361),x57362),x57363)),f862(f862(f236(x57361),x57362),f862(a105,x57363)))
% 25.54/25.41 [5747]~P68(x57471)+E(f862(f862(f73(x57471),f862(f72(x57471),x57472)),f862(f862(f73(x57471),x57472),x57473)),x57473)
% 25.54/25.41 [5770]~P147(x57701)+E(f862(f862(f236(x57701),f862(f93(x57701),x57702)),x57703),f862(f93(x57701),f862(f862(f236(a924),x57702),x57703)))
% 25.54/25.41 [5771]~P142(x57711)+E(f862(f862(f236(x57711),f862(f95(x57711),x57712)),x57713),f862(f95(x57711),f862(f862(f236(a1),x57712),x57713)))
% 25.54/25.41 [5772]E(x57721,x57722)+~P1(f862(f862(f84(f923(x57723)),x57721),x57722))
% 25.54/25.41 [5778]~P86(x57781)+E(f862(f69(x57781),f862(f862(f3(x57781),x57782),x57783)),f862(f69(x57781),f862(f862(f3(x57781),x57783),x57782)))
% 25.54/25.41 [5780]~P112(x57801)+E(f862(f862(f74(x57801),f75(x57801,x57802)),f75(x57801,x57803)),f75(x57801,f862(f862(f74(x57801),x57802),x57803)))
% 25.54/25.41 [5784]E(x57841,f106(x57842))+E(f862(f862(f127(x57842),f862(f164(x57842),x57841)),x57843),f862(f164(x57842),f862(f862(f127(x57842),x57841),x57843)))
% 25.54/25.41 [5789]~E(x57892,f862(a105,f862(f862(f73(a924),x57891),x57893)))+P1(f862(f862(f228(a924),x57891),x57892))
% 25.54/25.41 [5790]~P125(x57901)+E(f862(f862(f74(x57901),f862(f72(x57901),x57902)),x57903),f862(f72(x57901),f862(f862(f74(x57901),x57902),x57903)))
% 25.54/25.41 [5791]~P121(x57911)+E(f862(f862(f281(x57911),f862(f72(x57911),x57912)),x57913),f862(f72(x57911),f862(f862(f281(x57911),x57912),x57913)))
% 25.54/25.41 [5792]~P112(x57921)+E(f862(f862(f236(x57921),f862(f69(x57921),x57922)),x57923),f862(f69(x57921),f862(f862(f236(x57921),x57922),x57923)))
% 25.54/25.41 [5890]E(f627(x58901,x58902,x58903),f657(x58901,x58902,x58903))+E(f862(f862(f94(f932(x58903,a921)),x58902),x58901),f181(f932(x58903,a921)))
% 25.54/25.41 [5905]~P72(x59052)+E(f862(f862(f8(x59051,x59052),f862(f18(x59052,x59051),f2(x59052))),x59053),f2(x59052))
% 25.54/25.41 [5906]~P71(x59062)+E(f862(f862(f11(x59061,x59062),f862(f18(x59062,x59061),f71(x59062))),x59063),f71(x59062))
% 25.54/25.41 [5908]~P98(x59081)+E(f862(f862(f3(x59081),f862(f96(x59081),x59082)),f862(f96(x59081),x59083)),f862(f96(x59081),f862(f862(f3(a1),x59082),x59083)))
% 25.54/25.41 [5909]~P98(x59091)+E(f862(f862(f74(x59091),f862(f96(x59091),x59092)),f862(f96(x59091),x59093)),f862(f96(x59091),f862(f862(f74(a1),x59092),x59093)))
% 25.54/25.41 [5910]~P98(x59101)+E(f862(f862(f73(x59101),f862(f96(x59101),x59102)),f862(f96(x59101),x59103)),f862(f96(x59101),f862(f862(f73(a1),x59102),x59103)))
% 25.54/25.41 [5911]~P147(x59111)+E(f862(f862(f74(x59111),f862(f93(x59111),x59112)),f862(f93(x59111),x59113)),f862(f93(x59111),f862(f862(f74(a924),x59112),x59113)))
% 25.54/25.41 [5912]~P147(x59121)+E(f862(f862(f73(x59121),f862(f93(x59121),x59122)),f862(f93(x59121),x59123)),f862(f93(x59121),f862(f862(f73(a924),x59122),x59123)))
% 25.54/25.41 [5913]~P142(x59131)+E(f862(f862(f3(x59131),f862(f95(x59131),x59132)),f862(f95(x59131),x59133)),f862(f95(x59131),f862(f862(f3(a1),x59132),x59133)))
% 25.54/25.41 [5914]~P142(x59141)+E(f862(f862(f74(x59141),f862(f95(x59141),x59142)),f862(f95(x59141),x59143)),f862(f95(x59141),f862(f862(f74(a1),x59142),x59143)))
% 25.54/25.41 [5915]~P142(x59151)+E(f862(f862(f73(x59151),f862(f95(x59151),x59152)),f862(f95(x59151),x59153)),f862(f95(x59151),f862(f862(f73(a1),x59152),x59153)))
% 25.54/25.41 [5916]~P98(x59161)+E(f862(f862(f74(x59161),f862(f96(x59161),x59162)),f862(f96(x59161),x59163)),f862(f96(x59161),f862(f862(f74(a1),x59162),x59163)))
% 25.54/25.41 [5917]~P98(x59171)+E(f862(f862(f73(x59171),f862(f96(x59171),x59172)),f862(f96(x59171),x59173)),f862(f96(x59171),f862(f862(f73(a1),x59172),x59173)))
% 25.54/25.41 [5965]~E(x59653,x59652)+P1(f862(f862(f227(f932(x59651,a921)),x59652),x59653))
% 25.54/25.41 [5966]~E(x59662,x59663)+P1(f862(f862(f227(f932(x59661,a921)),x59662),x59663))
% 25.54/25.41 [5967]~E(x59672,x59673)+P1(f862(f862(f227(f932(x59671,a921)),x59672),x59673))
% 25.54/25.41 [5968]~E(x59682,x59683)+P1(f862(f862(f227(f932(x59681,a921)),x59682),x59683))
% 25.54/25.41 [5969]~E(x59692,x59693)+P1(f862(f862(f227(f932(x59691,a921)),x59692),x59693))
% 25.54/25.41 [5970]~E(x59702,x59703)+P1(f862(f862(f227(f932(x59701,a921)),x59702),x59703))
% 25.54/25.41 [5971]~E(x59712,x59713)+P1(f862(f862(f227(f932(x59711,a921)),x59712),x59713))
% 25.54/25.41 [5976]~P96(x59761)+E(f862(f862(f94(x59761),f862(f72(x59761),x59762)),f862(f72(x59761),x59763)),f862(f72(x59761),f862(f862(f103(x59761),x59762),x59763)))
% 25.54/25.41 [5977]~P96(x59771)+E(f862(f862(f103(x59771),f862(f72(x59771),x59772)),f862(f72(x59771),x59773)),f862(f72(x59771),f862(f862(f94(x59771),x59772),x59773)))
% 25.54/25.41 [5978]~P68(x59781)+E(f862(f862(f73(x59781),f862(f72(x59781),x59782)),f862(f72(x59781),x59783)),f862(f72(x59781),f862(f862(f73(x59781),x59783),x59782)))
% 25.54/25.41 [5979]~P59(x59791)+E(f862(f862(f73(x59791),f862(f72(x59791),x59792)),f862(f72(x59791),x59793)),f862(f72(x59791),f862(f862(f73(x59791),x59792),x59793)))
% 25.54/25.41 [5980]~P76(x59801)+E(f862(f862(f226(x59801),f862(f72(x59801),x59802)),f862(f72(x59801),x59803)),f862(f72(x59801),f862(f862(f225(x59801),x59802),x59803)))
% 25.54/25.41 [5981]~P76(x59811)+E(f862(f862(f225(x59811),f862(f72(x59811),x59812)),f862(f72(x59811),x59813)),f862(f72(x59811),f862(f862(f226(x59811),x59812),x59813)))
% 25.54/25.41 [5982]~P112(x59821)+E(f862(f862(f74(x59821),f862(f69(x59821),x59822)),f862(f69(x59821),x59823)),f862(f69(x59821),f862(f862(f74(x59821),x59822),x59823)))
% 25.54/25.41 [5983]~P66(x59831)+E(f862(f862(f281(x59831),f862(f69(x59831),x59832)),f862(f69(x59831),x59833)),f862(f69(x59831),f862(f862(f281(x59831),x59832),x59833)))
% 25.54/25.41 [5984]~P81(x59841)+E(f862(f862(f73(x59841),f862(f158(x59841),x59842)),f862(f158(x59841),x59843)),f862(f158(x59841),f862(f862(f127(x59841),x59842),x59843)))
% 25.54/25.41 [5985]E(x59851,f181(f932(x59852,a921)))+~E(f862(f862(f103(f932(x59852,a921)),x59853),x59851),f181(f932(x59852,a921)))
% 25.54/25.41 [5986]E(x59861,f181(f932(x59862,a921)))+~E(f862(f862(f103(f932(x59862,a921)),x59861),x59863),f181(f932(x59862,a921)))
% 25.54/25.41 [5987]~P149(x59871,x59873,x59872)+P1(f862(x59871,f862(f862(f29(a1),x59872),x59873)))
% 25.54/25.41 [6051]~P1(f862(f54(x60511),x60513))+P1(f862(f54(x60511),f862(f862(f301(x60511),x60512),x60513)))
% 25.54/25.41 [6052]~P1(f862(f54(x60521),x60523))+P1(f862(f54(x60521),f862(f862(f301(x60521),x60522),x60523)))
% 25.54/25.41 [6053]~P1(f862(f130(x60531),x60533))+P1(f862(f130(x60531),f862(f862(f168(x60531),x60532),x60533)))
% 25.54/25.41 [6054]~P1(f862(f130(x60541),x60543))+P1(f862(f130(x60541),f862(f862(f131(x60541),x60542),x60543)))
% 25.54/25.41 [6086]~P93(x60861)+P1(f862(f862(f227(x60861),x60862),f862(f862(f103(x60861),x60863),x60862)))
% 25.54/25.41 [6087]~P103(x60871)+P1(f862(f862(f227(x60871),x60872),f862(f862(f103(x60871),x60873),x60872)))
% 25.54/25.41 [6088]~P93(x60881)+P1(f862(f862(f227(x60881),x60882),f862(f862(f103(x60881),x60882),x60883)))
% 25.54/25.41 [6089]~P103(x60891)+P1(f862(f862(f227(x60891),x60892),f862(f862(f103(x60891),x60892),x60893)))
% 25.54/25.41 [6090]~P109(x60901)+P1(f862(f862(f227(x60901),x60902),f862(f862(f226(x60901),x60903),x60902)))
% 25.54/25.41 [6091]~P109(x60911)+P1(f862(f862(f227(x60911),x60912),f862(f862(f226(x60911),x60912),x60913)))
% 25.54/25.41 [6092]~P119(x60921)+P1(f862(f862(f278(x60921),x60922),f862(f862(f74(x60921),x60923),x60922)))
% 25.54/25.41 [6093]~P119(x60931)+P1(f862(f862(f278(x60931),x60932),f862(f862(f74(x60931),x60932),x60933)))
% 25.54/25.41 [6107]~E(x61071,f2(a924))+E(f862(f862(f29(a924),f862(f862(f74(a924),x61071),x61072)),f862(f862(f74(a924),x61071),x61073)),f2(a924))
% 25.54/25.41 [6187]~P98(x61871)+E(f862(f862(f3(x61871),f862(f96(x61871),x61872)),f862(f96(x61871),x61873)),f862(f96(x61871),f862(f862(f73(a1),x61872),f862(f72(a1),x61873))))
% 25.54/25.41 [6245]E(x62451,f2(a924))+E(f862(f862(f29(a924),f862(f862(f74(a924),x62451),x62452)),f862(f862(f74(a924),x62451),x62453)),f862(f862(f29(a924),x62452),x62453))
% 25.54/25.41 [6273]E(f145(x62731,f862(f862(f144(x62731),x62732),x62733)),f862(f862(f144(x62731),x62732),f145(x62731,x62733)))+P1(f862(f862(f321(x62731),x62732),f862(f165(x62731),x62733)))
% 25.54/25.41 [6309]P149(x63091,x63092,x63093)+~P1(f862(x63091,f862(f862(f29(a1),x63093),x63092)))
% 25.54/25.41 [6382]E(x63821,f106(x63822))+E(f862(f862(f144(x63822),f862(f134(x63822),x63821)),f862(f862(f168(x63822),x63823),f862(f164(x63822),x63821))),f862(f862(f168(x63822),f862(a105,x63823)),x63821))
% 25.54/25.41 [6390]E(f862(f862(f3(f932(x63901,a921)),x63902),x63903),x63902)+~E(f862(f862(f94(f932(x63901,a921)),x63902),x63903),f181(f932(x63901,a921)))
% 25.54/25.41 [6404]E(f145(x64041,f862(f862(f144(x64041),x64042),x64043)),f145(x64041,x64043))+~P1(f862(f862(f321(x64041),x64042),f862(f165(x64041),x64043)))
% 25.54/25.41 [6433]~P1(f862(f862(f227(a924),x64331),x64333))+P1(f862(f862(f227(a924),x64331),f862(f862(f73(a924),x64332),x64333)))
% 25.54/25.41 [6434]~P1(f862(f862(f227(a924),x64341),x64343))+P1(f862(f862(f227(a924),x64341),f862(f862(f73(a924),x64342),x64343)))
% 25.54/25.41 [6435]~P1(f862(f862(f227(a924),x64351),x64352))+P1(f862(f862(f227(a924),x64351),f862(f862(f73(a924),x64352),x64353)))
% 25.54/25.41 [6436]~P1(f862(f862(f227(a924),x64361),x64362))+P1(f862(f862(f227(a924),x64361),f862(f862(f73(a924),x64362),x64363)))
% 25.54/25.41 [6437]~P1(f862(f862(f228(a924),x64371),x64373))+P1(f862(f862(f228(a924),x64371),f862(f862(f73(a924),x64372),x64373)))
% 25.54/25.41 [6438]~P1(f862(f862(f228(a924),x64381),x64383))+P1(f862(f862(f228(a924),x64381),f862(f862(f73(a924),x64382),x64383)))
% 25.54/25.41 [6439]~P1(f862(f862(f228(a924),x64391),x64392))+P1(f862(f862(f228(a924),x64391),f862(f862(f73(a924),x64392),x64393)))
% 25.54/25.41 [6440]~P1(f862(f862(f228(a924),x64401),x64402))+P1(f862(f862(f228(a924),x64401),f862(f862(f73(a924),x64402),x64403)))
% 25.54/25.41 [6478]P1(f862(f54(x64781),x64782))+~P1(f862(f54(x64781),f862(f862(f301(x64781),x64783),x64782)))
% 25.54/25.41 [6479]P1(f862(f130(x64791),x64792))+~P1(f862(f130(x64791),f862(f862(f144(x64791),x64793),x64792)))
% 25.54/25.41 [6480]P1(f862(f130(x64801),x64802))+~P1(f862(f130(x64801),f862(f862(f127(x64801),x64803),x64802)))
% 25.54/25.41 [6481]P1(f862(f130(x64811),x64812))+~P1(f862(f130(x64811),f862(f862(f127(x64811),x64812),x64813)))
% 25.54/25.41 [6534]~P119(x65341)+E(f862(f862(f73(x65341),x65342),f862(f862(f74(x65341),x65343),x65342)),f862(f862(f74(x65341),f862(f862(f73(x65341),x65343),f71(x65341))),x65342))
% 25.54/25.41 [6581]~E(x65811,x65812)+~P1(f862(f862(f228(f932(x65813,a921)),x65811),x65812))
% 25.54/25.41 [6626]P1(f862(f862(f321(x66261),x66262),x66263))+P1(f862(f862(f321(x66261),x66262),f862(f72(f932(x66261,a921)),x66263)))
% 25.54/25.41 [6627]P1(f862(f862(f321(x66271),x66272),x66273))+P1(f862(f862(f321(x66271),x66272),f862(f72(f932(x66271,a921)),x66273)))
% 25.54/25.41 [6633]E(f137(x66331,f862(f862(f131(x66331),x66332),x66333)),f137(x66331,x66333))+~P1(f862(f862(f228(a924),x66332),f862(f182(f925(x66331)),x66333)))
% 25.54/25.41 [6634]E(f862(f862(f168(x66341),x66342),f107(x66341,x66343)),f862(f862(f168(x66341),x66342),x66343))+~P1(f862(f862(f228(a924),x66342),f862(f182(f925(x66341)),x66343)))
% 25.54/25.41 [6691]E(f862(f862(f862(f176(f925(x66911),f925(x66911)),x66912),f160(x66911)),x66913),x66913)+~E(f38(a924,x66912,f862(f182(f925(x66911)),x66913)),f2(a924))
% 25.54/25.41 [6698]~P6(x66981,x66983,x66982)+E(f862(f862(f280(x66981,x66981,x66981),f862(f277(x66981,x66981),x66982)),x66982),x66982)
% 25.54/25.41 [6741]~E(f862(f862(f103(f932(x67411,a921)),x67412),x67413),x67413)+P1(f862(f862(f227(f932(x67411,a921)),x67412),x67413))
% 25.54/25.41 [6746]~P52(x67461,x67461,x67463)+P52(x67461,x67461,f862(f862(f176(f931(x67461,x67461),a921),x67462),x67463))
% 25.54/25.41 [6749]~P1(f862(f862(f321(x67491),x67493),f862(f165(x67491),x67492)))+P1(f862(f862(f228(a924),f2(a924)),f862(f182(f925(x67491)),x67492)))
% 25.54/25.41 [6764]~E(x67642,x67643)+P1(f862(f862(f321(x67641),x67642),f862(f862(f301(x67641),x67643),f181(f932(x67641,a921)))))
% 25.54/25.41 [6775]~P86(x67751)+E(f862(f69(x67751),f862(f862(f73(x67751),f862(f69(x67751),x67752)),f862(f69(x67751),x67753))),f862(f862(f73(x67751),f862(f69(x67751),x67752)),f862(f69(x67751),x67753)))
% 25.54/25.41 [6785]E(f862(f862(f29(a924),f862(f862(f74(a924),x67851),x67852)),f862(f862(f74(a924),x67851),x67853)),f862(f862(f29(a924),x67852),x67853))+~P1(f862(f862(f228(a924),f2(a924)),x67851))
% 25.54/25.41 [6921]~P1(f862(f54(x69211),x69213))+E(f862(f862(f57(x69211,f932(x69211,a921),f301(x69211)),x69212),x69213),f862(f862(f103(f932(x69211,a921)),x69213),x69212))
% 25.54/25.41 [6980]E(f862(f862(f103(f932(x69801,a921)),x69802),x69803),x69802)+~P1(f862(f862(f227(f932(x69801,a921)),x69803),x69802))
% 25.54/25.41 [6981]E(f862(f862(f103(f932(x69811,a921)),x69812),x69813),x69813)+~P1(f862(f862(f227(f932(x69811,a921)),x69812),x69813))
% 25.54/25.41 [6982]E(f862(f862(f103(f932(x69821,a921)),x69822),x69823),x69823)+~P1(f862(f862(f227(f932(x69821,a921)),x69822),x69823))
% 25.54/25.41 [6983]E(f862(f862(f94(f932(x69831,a921)),x69832),x69833),x69833)+~P1(f862(f862(f227(f932(x69831,a921)),x69833),x69832))
% 25.54/25.41 [6984]E(f862(f862(f94(f932(x69841,a921)),x69842),x69843),x69842)+~P1(f862(f862(f227(f932(x69841,a921)),x69842),x69843))
% 25.54/25.41 [7033]~P1(f862(f130(x70331),x70332))+E(f862(f862(f3(f932(x70331,a921)),f862(f165(x70331),x70332)),f862(f862(f301(x70331),x70333),f181(f932(x70331,a921)))),f862(f165(x70331),f163(x70331,x70333,x70332)))
% 25.54/25.41 [7088]P35(x70881,x70882)+~P35(x70881,f862(f862(f176(f931(x70881,x70881),a921),x70883),x70882))
% 25.54/25.41 [7104]~E(x71041,f2(a924))+P1(f862(f862(f278(a924),f862(f862(f74(a924),x71041),x71042)),f862(f862(f74(a924),x71041),x71043)))
% 25.54/25.41 [7153]P1(f862(f42(x71531,x71532),f862(a44,x71533)))+~P1(f862(f42(f862(f72(a1),x71531),f862(f72(a1),x71532)),x71533))
% 25.54/25.41 [7158]E(f862(f862(f3(f932(x71581,a921)),f862(f862(f301(x71581),x71582),x71583)),f862(f862(f301(x71581),x71582),f181(f932(x71581,a921)))),x71583)+P1(f862(f862(f321(x71581),x71582),x71583))
% 25.54/25.41 [7181]E(f862(f862(f94(f932(x71811,a921)),f862(f165(x71811),x71812)),f862(f165(x71811),x71813)),f181(f932(x71811,a921)))+~P1(f862(f130(x71811),f862(f862(f127(x71811),x71812),x71813)))
% 25.54/25.41 [7196]~P1(f862(f862(f321(x71961),x71962),f862(f165(x71961),x71963)))+~P1(f862(f130(x71961),f862(f862(f144(x71961),x71962),x71963)))
% 25.54/25.41 [7267]P29(x72671,x72672,x72673)+P1(f862(f862(f228(a924),f766(x72673,x72672,x72671)),f862(f182(f925(x72671)),x72673)))
% 25.54/25.41 [7277]E(f862(f862(f94(f932(x72771,a921)),x72772),x72773),f181(f932(x72771,a921)))+P1(f862(f862(f321(x72771),f627(x72773,x72772,x72771)),x72772))
% 25.54/25.41 [7278]E(f862(f862(f94(f932(x72781,a921)),x72782),x72783),f181(f932(x72781,a921)))+P1(f862(f862(f321(x72781),f657(x72783,x72782,x72781)),x72783))
% 25.54/25.41 [7281]E(f107(x72811,f862(f862(f168(x72811),x72812),x72813)),f862(f862(f168(x72811),f862(f862(f3(a924),x72812),f71(a924))),x72813))+~P1(f862(f862(f227(a924),x72812),f862(f182(f925(x72811)),x72813)))
% 25.54/25.41 [7341]~P31(x73413,x73412,x73411)+P1(f862(f862(f228(a924),f760(x73411,x73412,x73413)),f862(f182(f925(x73413)),x73411)))
% 25.54/25.41 [7361]P1(f862(f862(f228(a924),f2(a924)),x73611))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x73612),x73611)),f862(f862(f74(a924),x73613),x73611)))
% 25.54/25.41 [7362]P1(f862(f862(f228(a924),f2(a924)),x73621))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x73621),x73622)),f862(f862(f74(a924),x73621),x73623)))
% 25.54/25.41 [7363]~P1(f862(f862(f321(x73631),x73632),x73633))+~P1(f862(f862(f321(x73631),x73632),f862(f72(f932(x73631,a921)),x73633)))
% 25.54/25.41 [7364]~P1(f862(f862(f321(x73641),x73642),x73643))+~P1(f862(f862(f321(x73641),x73642),f862(f72(f932(x73641,a921)),x73643)))
% 25.54/25.41 [7365]~P1(f862(f862(f321(x73651),x73652),x73653))+~P1(f862(f862(f321(x73651),x73652),f862(f72(f932(x73651,a921)),x73653)))
% 25.54/25.41 [7369]~P1(f862(f862(f228(f932(x73691,a921)),x73692),x73693))+P1(f862(f862(f227(f932(x73691,a921)),x73692),x73693))
% 25.54/25.41 [7370]~P1(f862(f862(f228(f932(x73701,a921)),x73702),x73703))+P1(f862(f862(f227(f932(x73701,a921)),x73702),x73703))
% 25.54/25.41 [7371]~P1(f862(f862(f228(f932(x73711,a921)),x73712),x73713))+P1(f862(f862(f227(f932(x73711,a921)),x73712),x73713))
% 25.54/25.41 [7481]~P1(f862(f862(f227(a924),x74813),x74812))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x74811),x74812)),f862(f862(f3(a924),x74811),x74813)))
% 25.54/25.41 [7482]~P1(f862(f862(f227(a924),x74821),x74823))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x74821),x74822)),f862(f862(f3(a924),x74823),x74822)))
% 25.54/25.41 [7483]~P1(f862(f862(f227(a924),x74832),x74833))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74831),x74832)),f862(f862(f74(a924),x74831),x74833)))
% 25.54/25.41 [7484]~P1(f862(f862(f227(a924),x74842),x74843))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74841),x74842)),f862(f862(f74(a924),x74841),x74843)))
% 25.54/25.41 [7485]~P1(f862(f862(f227(a924),x74851),x74853))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74851),x74852)),f862(f862(f74(a924),x74853),x74852)))
% 25.54/25.41 [7486]~P1(f862(f862(f227(a924),x74861),x74863))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x74861),x74862)),f862(f862(f74(a924),x74863),x74862)))
% 25.54/25.41 [7487]~P1(f862(f862(f227(a924),x74872),x74873))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x74871),x74872)),f862(f862(f73(a924),x74871),x74873)))
% 25.54/25.41 [7488]~P1(f862(f862(f227(a924),x74881),x74883))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x74881),x74882)),f862(f862(f73(a924),x74883),x74882)))
% 25.54/25.41 [7489]~P1(f862(f862(f227(a924),x74891),x74893))+P1(f862(f862(f227(a924),f862(f862(f29(a924),x74891),x74892)),f862(f862(f29(a924),x74893),x74892)))
% 25.54/25.41 [7490]~P1(f862(f862(f227(a1),x74902),x74903))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x74901),x74902)),f862(f862(f73(a1),x74901),x74903)))
% 25.54/25.41 [7493]~P1(f862(f862(f228(a924),x74932),x74933))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x74931),x74932)),f862(f862(f73(a924),x74931),x74933)))
% 25.54/25.41 [7494]~P1(f862(f862(f228(a924),x74941),x74943))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x74941),x74942)),f862(f862(f73(a924),x74943),x74942)))
% 25.54/25.41 [7495]~P1(f862(f862(f228(a1),x74951),x74953))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x74951),x74952)),f862(f862(f73(a1),x74953),x74952)))
% 25.54/25.41 [7498]~P1(f862(f862(f278(a924),x74982),x74983))+P1(f862(f862(f278(a924),f862(f862(f74(a924),x74981),x74982)),f862(f862(f74(a924),x74981),x74983)))
% 25.54/25.41 [7575]E(x75751,x75752)+~P1(f862(f862(f321(x75753),x75751),f862(f862(f301(x75753),x75752),f181(f932(x75753,a921)))))
% 25.54/25.41 [7576]E(x75761,x75762)+~P1(f862(f862(f321(x75763),x75761),f862(f862(f301(x75763),x75762),f181(f932(x75763,a921)))))
% 25.54/25.41 [7578]~E(f862(f862(f94(f932(x75781,a921)),x75782),x75783),f181(f932(x75781,a921)))+P1(f862(f862(f227(f932(x75781,a921)),x75782),f862(f72(f932(x75781,a921)),x75783)))
% 25.54/25.41 [7582]P1(f862(f862(f321(f932(x75821,a921)),x75822),f862(f300(x75821),x75823)))+~P1(f862(f862(f227(f932(x75821,a921)),x75822),x75823))
% 25.54/25.41 [7583]P1(f862(f862(f321(f932(x75831,a921)),x75832),f862(f300(x75831),x75833)))+~P1(f862(f862(f227(f932(x75831,a921)),x75832),x75833))
% 25.54/25.41 [7590]P1(f862(f862(f321(x75901),f523(x75902,x75903,x75901)),x75903))+P1(f862(f862(f227(f932(x75901,a921)),x75903),x75902))
% 25.54/25.41 [7635]E(f862(f862(f144(x76351),f862(f862(f157(x76351),x76352),x76353)),f862(f862(f131(x76351),f862(a105,x76353)),x76352)),f862(f862(f131(x76351),x76353),x76352))+~P1(f862(f862(f228(a924),x76353),f862(f182(f925(x76351)),x76352)))
% 25.54/25.41 [7660]P1(f862(f862(f321(f931(x76601,x76601)),x76602),f299(x76601,x76603)))+~P1(f862(f862(f321(f931(x76601,x76601)),x76602),x76603))
% 25.54/25.41 [7668]~P1(f862(f862(f321(f932(x76681,a921)),x76682),f862(f300(x76681),x76683)))+P1(f862(f862(f227(f932(x76681,a921)),x76682),x76683))
% 25.54/25.41 [7669]~P1(f862(f862(f321(f932(x76691,a921)),x76692),f862(f300(x76691),x76693)))+P1(f862(f862(f227(f932(x76691,a921)),x76692),x76693))
% 25.54/25.41 [7713]P1(f862(f862(f227(f932(x77131,a921)),x77132),f30(f932(x77131,a921),x77133)))+~P1(f862(f862(f321(f932(x77131,a921)),x77132),x77133))
% 25.54/25.41 [7738]~P142(x77381)+E(f862(f862(f74(x77381),f862(f862(f236(x77381),f862(f72(x77381),f71(x77381))),x77382)),f862(f862(f236(x77381),x77383),x77382)),f862(f862(f236(x77381),f862(f72(x77381),x77383)),x77382))
% 25.54/25.41 [7761]E(f862(f862(f157(x77611),x77612),f862(f862(f3(a924),f862(f182(f925(x77611)),x77612)),f862(a105,x77613))),f862(f862(f157(x77611),f862(f161(x77611),x77612)),x77613))+~P1(f862(f862(f228(a924),x77613),f862(f182(f925(x77611)),x77612)))
% 25.54/25.41 [7778]~E(f862(f862(f94(f932(x77781,a921)),f682(x77783,x77782,x77781)),x77783),f181(f932(x77781,a921)))+E(f862(f862(f94(f932(x77781,a921)),f30(f932(x77781,a921),x77782)),x77783),f181(f932(x77781,a921)))
% 25.54/25.41 [7842]~P1(f862(f862(f321(x78423),x78422),f862(f165(x78423),x78421)))+P1(f862(f862(f228(a924),f668(x78421,x78422,x78423)),f862(f182(f925(x78423)),x78421)))
% 25.54/25.41 [7850]P1(f862(f862(f321(x78501),f862(f862(f157(x78501),x78502),x78503)),f862(f165(x78501),x78502)))+~P1(f862(f862(f228(a924),x78503),f862(f182(f925(x78501)),x78502)))
% 25.54/25.41 [7947]~P1(f862(x79472,f725(x79473,x79472,x79471)))+E(f862(f862(f131(x79471),f862(f182(f925(x79471)),f170(x79471,x79472,x79473))),x79473),f106(x79471))
% 25.54/25.41 [7960]P1(f862(f862(f227(f932(f925(x79601),a921)),f154(x79601,x79602)),f154(x79601,x79603)))+~P1(f862(f862(f227(f932(x79601,a921)),x79602),x79603))
% 25.54/25.41 [7961]P1(f862(f862(f227(f932(f925(x79611),a921)),f153(x79611,x79612)),f153(x79611,x79613)))+~P1(f862(f862(f227(f932(x79611,a921)),x79612),x79613))
% 25.54/25.41 [7987]E(f862(f862(f94(f932(x79871,a921)),f30(f932(x79871,a921),x79872)),x79873),f181(f932(x79871,a921)))+P1(f862(f862(f321(f932(x79871,a921)),f682(x79873,x79872,x79871)),x79872))
% 25.54/25.41 [7989]~P1(f862(f862(f321(f932(x79891,a921)),x79893),x79892))+P1(f862(f862(f227(f932(x79891,a921)),f31(f932(x79891,a921),x79892)),x79893))
% 25.54/25.41 [7991]E(f862(f862(f94(f932(x79911,a921)),x79912),x79913),f181(f932(x79911,a921)))+~P1(f862(f862(f227(f932(x79911,a921)),x79912),f862(f72(f932(x79911,a921)),x79913)))
% 25.54/25.41 [8041]E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f158(a924),x80411)),x80412)),f862(f862(f157(a924),x80411),x80413)),f862(f158(a924),f862(f862(f152(a924,x80411),x80413),x80412)))+~P1(f862(f862(f228(a924),x80413),f862(f182(f925(a924)),x80411)))
% 25.54/25.41 [8093]P1(f862(f862(f227(a924),x80931),x80932))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x80933),x80931)),f862(f862(f73(a924),x80933),x80932)))
% 25.54/25.41 [8096]P1(f862(f862(f228(a924),x80961),x80962))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x80963),x80961)),f862(f862(f73(a924),x80963),x80962)))
% 25.54/25.41 [8097]P1(f862(f862(f228(a924),x80971),x80972))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x80973),x80971)),f862(f862(f74(a924),x80973),x80972)))
% 25.54/25.41 [8098]P1(f862(f862(f228(a924),x80981),x80982))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x80981),x80983)),f862(f862(f74(a924),x80982),x80983)))
% 25.54/25.41 [8127]P1(f862(f862(f228(a924),f2(a924)),x81271))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x81272),x81271)),f862(f862(f74(a924),x81273),x81271)))
% 25.54/25.41 [8128]P1(f862(f862(f228(a924),f2(a924)),x81281))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x81281),x81282)),f862(f862(f74(a924),x81281),x81283)))
% 25.54/25.41 [8167]~P1(f862(f862(f321(x81671),f523(x81673,x81672,x81671)),x81673))+P1(f862(f862(f227(f932(x81671,a921)),x81672),x81673))
% 25.54/25.41 [8204]E(f239(x82041,x82042,x82043),x82042)+~P1(f862(f862(f227(f932(x82041,a921)),x82043),f862(f862(f301(x82041),x82042),f181(f932(x82041,a921)))))
% 25.54/25.41 [8254]~P1(f862(f130(x82541),x82543))+E(f862(f129(x82541,f862(f862(f10(a921,a921,x82541),a314),f862(a317,x82542))),x82543),f163(x82541,x82542,x82543))
% 25.54/25.41 [8279]E(f862(f862(f131(x82791),f862(f182(f925(x82791)),f170(x82791,x82792,x82793))),x82793),f106(x82791))+P1(f862(f862(f321(x82791),f725(x82793,x82792,x82791)),f862(f165(x82791),x82793)))
% 25.54/25.41 [8283]E(f862(f862(f127(x82831),f862(f862(f168(x82831),x82832),x82833)),f862(f862(f144(x82831),f862(f862(f157(x82831),x82833),x82832)),f106(x82831))),f862(f862(f168(x82831),f862(a105,x82832)),x82833))+~P1(f862(f862(f228(a924),x82832),f862(f182(f925(x82831)),x82833)))
% 25.54/25.41 [8352]E(f862(f129(x83521,f862(f862(f10(a921,a921,x83521),a314),f862(a317,x83522))),x83523),x83523)+P1(f862(f862(f321(x83521),x83522),f862(f165(x83521),x83523)))
% 25.54/25.41 [8358]P1(f862(f862(f227(f932(f932(x83581,a921),a921)),f240(x83581,x83582)),f240(x83581,x83583)))+~P1(f862(f862(f227(f932(x83581,a921)),x83582),x83583))
% 25.54/25.41 [8377]P1(f862(f862(f321(f932(x83771,a921)),f490(x83772,x83773,x83771)),x83773))+P1(f862(f862(f227(f932(x83771,a921)),f30(f932(x83771,a921),x83773)),x83772))
% 25.54/25.41 [8398]~P1(f862(f130(x83981),x83983))+P1(f862(f130(x83981),f862(f862(f862(f176(f925(x83981),f925(x83981)),x83982),f160(x83981)),x83983)))
% 25.54/25.41 [8403]~P1(f862(f862(f227(a924),x84032),x84033))+P1(f862(f862(f227(a924),f862(f862(f74(a924),f862(a105,x84031)),x84032)),f862(f862(f74(a924),f862(a105,x84031)),x84033)))
% 25.54/25.41 [8404]~P1(f862(f862(f228(a924),x84042),x84043))+P1(f862(f862(f228(a924),f862(f862(f74(a924),f862(a105,x84041)),x84042)),f862(f862(f74(a924),f862(a105,x84041)),x84043)))
% 25.54/25.41 [8424]P1(f862(f862(f227(f932(f932(x84241,a921),a921)),f862(f300(x84241),x84242)),f862(f300(x84241),x84243)))+~P1(f862(f862(f227(f932(x84241,a921)),x84242),x84243))
% 25.54/25.41 [8493]~E(f862(f302(x84931,x84932,x84933),f234(f932(x84931,a921))),f234(f932(x84932,a921)))+E(f862(f66(x84931,x84932,x84932,x84933),f86(x84931,x84932,f234(f932(x84931,a921)),x84933)),f25(x84932))
% 25.54/25.41 [8586]~P1(f862(f862(f227(f932(x85861,a921)),x85863),x85862))+P1(f862(f862(f227(f932(x85861,a921)),f862(f72(f932(x85861,a921)),x85862)),f862(f72(f932(x85861,a921)),x85863)))
% 25.54/25.41 [8587]~P1(f862(f862(f227(f932(x85871,a921)),x85873),x85872))+P1(f862(f862(f227(f932(x85871,a921)),f862(f72(f932(x85871,a921)),x85872)),f862(f72(f932(x85871,a921)),x85873)))
% 25.54/25.41 [8622]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x86221)),f862(f295(a924,x86222),x86223)),f862(f295(a924,f862(f862(f3(a924),x86222),x86221)),f862(f862(f3(a924),x86223),x86221)))+~P1(f862(f862(f228(a924),x86221),x86223))
% 25.54/25.41 [8649]~P81(x86491)+E(f862(f862(f73(x86491),x86492),f862(f135(x86491,x86491,f73(x86491),f2(x86491)),x86493)),f862(f135(x86491,x86491,f73(x86491),x86492),x86493))
% 25.54/25.41 [8704]~P1(f862(f862(f227(f932(x87041,a921)),f490(x87043,x87042,x87041)),x87043))+P1(f862(f862(f227(f932(x87041,a921)),f30(f932(x87041,a921),x87042)),x87043))
% 25.54/25.41 [8726]~P86(x87261)+P1(f862(f862(f227(x87261),f862(f69(x87261),f862(f862(f3(x87261),x87262),x87263))),f862(f862(f73(x87261),f862(f69(x87261),x87262)),f862(f69(x87261),x87263))))
% 25.54/25.41 [8727]~P86(x87271)+P1(f862(f862(f227(x87271),f862(f69(x87271),f862(f862(f73(x87271),x87272),x87273))),f862(f862(f73(x87271),f862(f69(x87271),x87272)),f862(f69(x87271),x87273))))
% 25.54/25.41 [8738]E(f862(f862(f73(a1),f862(f862(f74(a1),x87381),f38(a1,f862(f862(f29(a1),x87382),x87381),x87383))),f38(a1,x87382,x87381)),f38(a1,x87382,f862(f862(f74(a1),x87381),x87383)))+~P1(f862(f862(f228(a1),f2(a1)),x87383))
% 25.54/25.41 [8744]E(f862(f862(f127(x87441),f862(f862(f168(x87441),x87442),x87443)),f862(f862(f144(x87441),f862(f134(x87441),f862(f862(f131(x87441),x87442),x87443))),f106(x87441))),f862(f862(f168(x87441),f862(a105,x87442)),x87443))+~P1(f862(f862(f228(a924),x87442),f862(f182(f925(x87441)),x87443)))
% 25.54/25.41 [8765]E(f862(f260(x87651,f862(f862(f147(x87651,f931(a92,x87651)),f862(f244(a92,x87651),f71(a92))),x87652)),f862(a5,x87653)),f862(f862(f157(x87651),x87652),x87653))+~P1(f862(f862(f228(a924),x87653),f862(f182(f925(x87651)),x87652)))
% 25.54/25.41 [8833]P1(f862(f862(f321(f931(x88331,x88331)),x88332),f862(f862(f280(x88331,x88331,x88331),x88333),f299(x88331,x88333))))+~P1(f862(f862(f321(f931(x88331,x88331)),x88332),x88333))
% 25.54/25.41 [8844]E(f862(f302(x88441,x88442,x88443),f234(f932(x88441,a921))),f234(f932(x88442,a921)))+~E(f862(f66(x88441,x88442,x88442,x88443),f86(x88441,x88442,f234(f932(x88441,a921)),x88443)),f25(x88442))
% 25.54/25.41 [8853]P1(f862(f862(f227(a924),x88531),x88532))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),f862(a105,x88533)),x88531)),f862(f862(f74(a924),f862(a105,x88533)),x88532)))
% 25.54/25.41 [8854]P1(f862(f862(f228(a924),x88541),x88542))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),f862(a105,x88543)),x88541)),f862(f862(f74(a924),f862(a105,x88543)),x88542)))
% 25.54/25.41 [8869]P1(f862(f862(f227(f932(x88691,a921)),x88692),x88693))+~P1(f862(f862(f227(f932(x88691,a921)),f862(f72(f932(x88691,a921)),x88693)),f862(f72(f932(x88691,a921)),x88692)))
% 25.54/25.41 [8892]P1(f862(f130(x88921),x88922))+~P1(f862(f130(x88921),f862(f862(f862(f176(f925(x88921),f925(x88921)),x88923),f160(x88921)),x88922)))
% 25.54/25.41 [8966]E(f862(f276(x89661,x89661,f299(x89661,x89662)),x89663),x89663)+~P1(f862(f862(f227(f932(x89661,a921)),f862(f276(x89661,x89661,x89662),x89663)),x89663))
% 25.54/25.41 [9014]~P109(x90141)+P11(x90141,f862(f129(x90141,f862(f862(f9(x90141,x90141,a921),a317),f862(x90142,x90143))),x90143))
% 25.54/25.41 [9021]~P1(f862(f862(f227(a924),x90211),x90212))+P1(f862(f862(f227(a924),x90211),f862(f135(a924,a924,f73(a924),x90212),x90213)))
% 25.54/25.41 [9109]~P1(f862(f862(f321(f931(x91091,x91091)),x91092),f299(x91091,x91093)))+P1(f862(f862(f321(f931(x91091,x91091)),x91092),f862(f862(f176(f931(x91091,x91091),a921),f629(x91093,x91092,x91091)),x91093)))
% 25.54/25.41 [9190]~P81(x91901)+E(f862(f862(f73(x91901),x91902),f862(f135(x91901,x91901,f862(f9(x91901,x91901,x91901),f73(x91901)),f2(x91901)),f862(f161(x91901),x91903))),f862(f135(x91901,x91901,f73(x91901),x91902),x91903))
% 25.54/25.41 [9308]~P23(x93082,x93081,x93083,f234(f932(x93082,a921)),f234(f932(x93081,a921)))+E(f86(x93081,x93082,f234(f932(x93081,a921)),f86(x93082,x93081,f234(f932(x93082,a921)),x93083)),x93083)
% 25.54/25.41 [9463]P52(x94631,x94632,x94633)+P1(f862(f862(f321(f931(x94631,x94632)),f862(f862(f244(x94631,x94632),f623(x94633,x94632,x94631)),f608(x94633,x94632,x94631))),x94633))
% 25.54/25.41 [9464]P52(x94641,x94642,x94643)+P1(f862(f862(f321(f931(x94641,x94642)),f862(f862(f244(x94641,x94642),f623(x94643,x94642,x94641)),f607(x94643,x94642,x94641))),x94643))
% 25.54/25.41 [9532]~P1(f862(f862(f321(f931(x95321,x95321)),x95322),f862(f862(f280(x95321,x95321,x95321),x95323),f299(x95321,x95323))))+P1(f862(f862(f321(f931(x95321,x95321)),x95322),f862(f862(f176(f931(x95321,x95321),a921),f631(x95323,x95322,x95321)),x95323)))
% 25.54/25.41 [9533]~P1(f862(x95331,f862(f862(f157(x95332),x95333),f862(f182(f925(x95332)),f170(x95332,x95331,x95333)))))+~P1(f862(f862(f228(a924),f862(f182(f925(x95332)),f170(x95332,x95331,x95333))),f862(f182(f925(x95332)),x95333)))
% 25.54/25.41 [9627]~P1(f862(f862(f227(f932(x96271,a921)),x96272),x96273))+P1(f862(f862(f227(f932(x96271,a921)),f862(f862(f9(x96271,f932(x96271,a921),a921),f321(x96271)),x96272)),f862(f862(f9(x96271,f932(x96271,a921),a921),f321(x96271)),x96273)))
% 25.54/25.41 [9686]~P1(f862(f862(f321(f931(f932(x96861,a921),f932(x96861,a921))),f862(f862(f244(f932(x96861,a921),f932(x96861,a921)),x96862),x96863)),f306(x96861)))+P1(f862(f862(f228(f932(x96861,a921)),x96862),x96863))
% 25.54/25.41 [9710]P53(x97101,x97102,x97103)+~P1(f862(f862(f321(f931(x97101,x97101)),f862(f862(f244(x97101,x97101),f626(x97103,x97102,x97101)),f625(x97103,x97102,x97101))),x97103))
% 25.54/25.41 [9711]P53(x97111,x97112,x97113)+~P1(f862(f862(f321(f931(x97111,x97111)),f862(f862(f244(x97111,x97111),f625(x97113,x97112,x97111)),f626(x97113,x97112,x97111))),x97113))
% 25.54/25.41 [9748]~P1(f862(f862(f321(f931(f925(x97481),f925(x97481))),f862(f862(f244(f925(x97481),f925(x97481)),x97482),x97482)),f140(x97481,x97483)))+P1(f862(f862(f321(f931(x97481,x97481)),f862(f862(f244(x97481,x97481),f664(x97482,x97483,x97481)),f664(x97482,x97483,x97481))),x97483))
% 25.54/25.41 [9798]P1(f862(f862(f227(f932(x97981,a921)),x97982),x97983))+~P1(f862(f862(f227(f932(x97981,a921)),f862(f862(f9(x97981,f932(x97981,a921),a921),f321(x97981)),x97982)),f862(f862(f9(x97981,f932(x97981,a921),a921),f321(x97981)),x97983)))
% 25.54/25.41 [9879]E(f862(f862(f3(a924),f862(f862(f8(a924,a924),x98791),f862(f292(a924),x98792))),f862(f862(f8(a924,a924),x98793),f862(f292(a924),x98792))),f862(f862(f8(a924,a924),f862(f862(f20(a924,a924,a924),f862(f862(f10(a924,f932(a924,a924),a924),f3(a924)),x98791)),x98793)),f862(f292(a924),x98792)))+~P1(f862(f862(f227(a924),f862(x98793,f515(x98792,x98791,x98793))),f862(x98791,f515(x98792,x98791,x98793))))
% 25.54/25.41 [5826]~P68(x58261)+E(f862(f862(f3(x58261),f862(f862(f73(x58261),x58262),x58263)),x58263),x58262)
% 25.54/25.41 [5827]~P68(x58271)+E(f862(f862(f73(x58271),f862(f862(f3(x58271),x58272),x58273)),x58273),x58272)
% 25.54/25.41 [6061]~P68(x60611)+E(f862(f862(f73(x60611),x60612),f862(f862(f73(x60611),f862(f72(x60611),x60612)),x60613)),x60613)
% 25.54/25.41 [6149]~P80(x61491)+E(f862(f862(f74(x61491),f862(f862(f236(x61491),x61492),x61493)),x61492),f862(f862(f236(x61491),x61492),f862(a105,x61493)))
% 25.54/25.41 [6150]~P119(x61501)+E(f862(f862(f74(x61501),f862(f862(f236(x61501),x61502),x61503)),x61502),f862(f862(f236(x61501),x61502),f862(a105,x61503)))
% 25.54/25.41 [6365]~P112(x63651)+E(f862(f69(x63651),f862(f862(f236(x63651),f862(f72(x63651),x63652)),x63653)),f862(f69(x63651),f862(f862(f236(x63651),x63652),x63653)))
% 25.54/25.41 [6416]~P80(x64161)+E(f862(f862(f74(x64161),f862(f862(f236(x64161),x64162),x64163)),x64162),f862(f862(f74(x64161),x64162),f862(f862(f236(x64161),x64162),x64163)))
% 25.54/25.41 [6469]E(f862(f862(f3(a92),f862(f862(f73(a92),x64691),x64692)),x64693),f266(x64691,x64692,x64693))+~P1(f862(f862(f228(a92),x64692),x64693))
% 25.54/25.41 [6493]~E(f862(f862(f131(x64931),x64933),x64932),f106(x64931))+P1(f862(f862(f227(a924),f862(f182(f925(x64931)),x64932)),x64933))
% 25.54/25.41 [6632]E(f862(f862(f74(a924),f862(f96(a924),x66321)),f862(f862(f74(a924),f862(f96(a924),x66322)),x66323)),f2(a924))+~P1(f862(f862(f228(a1),x66321),a76))
% 25.54/25.41 [6648]~P64(x66481)+E(f862(f862(f236(x66481),f862(f862(f281(x66481),f71(x66481)),x66482)),x66483),f862(f862(f281(x66481),f71(x66481)),f862(f862(f236(x66481),x66482),x66483)))
% 25.54/25.41 [6728]E(f862(f862(f3(a924),f862(f862(f73(a924),x67281),x67282)),x67283),f862(f862(f3(a924),x67281),f862(f862(f3(a924),x67283),x67282)))+~P1(f862(f862(f227(a924),x67282),x67283))
% 25.54/25.41 [6729]E(f862(f862(f3(a924),f862(f862(f73(a924),x67291),x67292)),x67293),f862(f862(f73(a924),x67291),f862(f862(f3(a924),x67292),x67293)))+~P1(f862(f862(f227(a924),x67293),x67292))
% 25.54/25.41 [6730]E(f862(f862(f3(a924),f862(f862(f73(a924),x67301),x67302)),x67303),f862(f862(f73(a924),x67301),f862(f862(f3(a924),x67302),x67303)))+~P1(f862(f862(f227(a924),x67303),x67302))
% 25.54/25.41 [6766]~P93(x67661)+P1(f862(f862(f227(x67661),f862(f862(f94(x67661),x67662),x67663)),x67663))
% 25.54/25.41 [6767]~P104(x67671)+P1(f862(f862(f227(x67671),f862(f862(f94(x67671),x67672),x67673)),x67673))
% 25.54/25.41 [6768]~P93(x67681)+P1(f862(f862(f227(x67681),f862(f862(f94(x67681),x67682),x67683)),x67682))
% 25.54/25.41 [6769]~P104(x67691)+P1(f862(f862(f227(x67691),f862(f862(f94(x67691),x67692),x67693)),x67692))
% 25.54/25.41 [6770]~P109(x67701)+P1(f862(f862(f227(x67701),f862(f862(f225(x67701),x67702),x67703)),x67703))
% 25.54/25.41 [6771]~P109(x67711)+P1(f862(f862(f227(x67711),f862(f862(f225(x67711),x67712),x67713)),x67712))
% 25.54/25.41 [6784]E(f862(f862(f29(a1),f862(f862(f29(a1),x67841),x67842)),x67843),f862(f862(f29(a1),x67841),f862(f862(f74(a1),x67842),x67843)))+~P1(f862(f862(f228(a1),f2(a1)),x67843))
% 25.54/25.41 [6834]~P119(x68341)+E(f862(f862(f73(x68341),f862(f862(f74(x68341),x68342),x68343)),x68343),f862(f862(f74(x68341),f862(f862(f73(x68341),x68342),f71(x68341))),x68343))
% 25.54/25.41 [6835]~P98(x68351)+E(f862(f862(f74(x68351),f862(f72(x68351),f862(f96(x68351),x68352))),x68353),f862(f862(f74(x68351),f862(f96(x68351),f862(f72(a1),x68352))),x68353))
% 25.54/25.41 [6907]~P81(x69071)+E(f862(f158(x69071),f862(f862(f147(x69072,x69071),f862(f18(x69071,x69072),f2(x69071))),x69073)),f2(x69071))
% 25.54/25.41 [6922]E(f862(f862(f73(a924),f862(f96(a924),x69221)),f862(f862(f73(a924),f862(f96(a924),x69222)),x69223)),f862(f862(f73(a924),f862(f96(a924),x69222)),x69223))+~P1(f862(a186,f862(f96(a1),x69221)))
% 25.54/25.41 [6937]~P3(x69371)+E(f31(x69371,f862(f862(f301(x69371),x69372),f862(f862(f301(x69371),x69373),f181(f932(x69371,a921))))),f862(f862(f94(x69371),x69372),x69373))
% 25.54/25.41 [6938]~P3(x69381)+E(f30(x69381,f862(f862(f301(x69381),x69382),f862(f862(f301(x69381),x69383),f181(f932(x69381,a921))))),f862(f862(f103(x69381),x69382),x69383))
% 25.54/25.41 [6962]E(f862(f862(f168(x69621),x69622),x69623),x69623)+~P1(f862(f862(f227(a924),f862(f182(f925(x69621)),x69623)),x69622))
% 25.54/25.41 [6974]E(f862(f862(f131(x69741),x69742),x69743),f106(x69741))+~P1(f862(f862(f227(a924),f862(f182(f925(x69741)),x69743)),x69742))
% 25.54/25.41 [6975]E(f862(f862(f131(x69751),x69752),x69753),f106(x69751))+~P1(f862(f862(f227(a924),f862(f182(f925(x69751)),x69753)),x69752))
% 25.54/25.41 [6985]E(f862(f862(f73(a924),f862(f862(f3(a924),x69851),x69852)),x69853),f862(f862(f3(a924),f862(f862(f73(a924),x69851),x69853)),x69852))+~P1(f862(f862(f227(a924),x69852),x69851))
% 25.54/25.41 [6986]E(f862(f862(f73(a924),f862(f862(f3(a924),x69861),x69862)),x69863),f862(f862(f3(a924),f862(f862(f73(a924),x69861),x69863)),x69862))+~P1(f862(f862(f227(a924),x69862),x69861))
% 25.54/25.41 [7000]~P1(f862(f862(f228(a924),x70001),x70003))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x70001),x70002)),x70003))
% 25.54/25.41 [7027]~P109(x70271)+E(f163(x70271,x70272,f862(f862(f141(x70271,x70271,f7(x70271)),x70272),x70273)),x70273)
% 25.54/25.41 [7117]E(f862(f862(f3(a924),f862(f862(f73(a924),x71171),x71172)),f862(a105,x71173)),f862(f862(f3(a924),x71171),f862(a105,f862(f862(f3(a924),x71173),x71172))))+~P1(f862(f862(f227(a924),x71172),x71173))
% 25.54/25.41 [7118]~P112(x71181)+P1(f862(f862(f227(x71181),f2(x71181)),f862(f862(f236(x71181),f862(f69(x71181),x71182)),x71183)))
% 25.54/25.41 [7207]~P1(f862(f54(x72071),x72073))+P1(f862(f54(x72071),f862(f862(f94(f932(x72071,a921)),x72072),x72073)))
% 25.54/25.41 [7208]~P1(f862(f54(x72081),x72082))+P1(f862(f54(x72081),f862(f862(f94(f932(x72081,a921)),x72082),x72083)))
% 25.54/25.41 [7209]~P1(f862(f54(x72091),x72092))+P1(f862(f54(x72091),f862(f862(f3(f932(x72091,a921)),x72092),x72093)))
% 25.54/25.41 [7351]~P35(x73511,x73513)+P35(x73511,f862(f862(f94(f932(f931(x73511,x73511),a921)),x73512),x73513))
% 25.54/25.41 [7352]~P35(x73521,x73522)+P35(x73521,f862(f862(f94(f932(f931(x73521,x73521),a921)),x73522),x73523))
% 25.54/25.41 [7476]~P93(x74761)+E(f12(x74761,f862(f165(x74761),f862(f862(f144(x74761),x74762),x74763))),f862(f135(x74761,x74761,f94(x74761),x74762),x74763))
% 25.54/25.41 [7477]~P93(x74771)+E(f15(x74771,f862(f165(x74771),f862(f862(f144(x74771),x74772),x74773))),f862(f135(x74771,x74771,f103(x74771),x74772),x74773))
% 25.54/25.41 [7478]~P109(x74781)+E(f16(x74781,f862(f165(x74781),f862(f862(f144(x74781),x74782),x74783))),f862(f135(x74781,x74781,f225(x74781),x74782),x74783))
% 25.54/25.41 [7479]~P109(x74791)+E(f17(x74791,f862(f165(x74791),f862(f862(f144(x74791),x74792),x74793))),f862(f135(x74791,x74791,f226(x74791),x74792),x74793))
% 25.54/25.41 [7544]~P1(f862(f54(x75441),x75442))+P1(f862(f862(f227(a924),f862(f28(x75441),x75442)),f862(f28(x75441),f862(f862(f301(x75441),x75443),x75442))))
% 25.54/25.41 [7552]E(f862(f862(f103(f932(a924,a921)),f862(f295(a924,x75521),x75522)),f862(f295(a924,x75522),f862(f862(f73(a924),x75522),x75523))),f862(f295(a924,x75521),f862(f862(f73(a924),x75522),x75523)))+~P1(f862(f862(f227(a924),x75521),x75522))
% 25.54/25.41 [7559]P1(f862(f862(f227(a924),x75591),x75592))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75593),x75591)),x75592))
% 25.54/25.41 [7560]P1(f862(f862(f227(a924),x75601),x75602))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75601),x75603)),x75602))
% 25.54/25.41 [7561]P1(f862(f862(f227(a924),x75611),x75612))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75613),x75611)),x75612))
% 25.54/25.41 [7562]P1(f862(f862(f227(a924),x75621),x75622))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x75621),x75623)),x75622))
% 25.54/25.41 [7563]P1(f862(f862(f228(a924),x75631),x75632))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x75631),x75633)),x75632))
% 25.54/25.41 [7603]~P109(x76031)+E(f13(x76031,f225(x76031),f862(f165(x76031),f862(f862(f144(x76031),x76032),x76033))),f862(f135(x76031,x76031,f225(x76031),x76032),x76033))
% 25.54/25.41 [7604]~P109(x76041)+E(f14(x76041,f226(x76041),f862(f165(x76041),f862(f862(f144(x76041),x76042),x76043))),f862(f135(x76041,x76041,f226(x76041),x76042),x76043))
% 25.54/25.41 [7608]~E(x76082,f181(f932(f931(x76081,x76081),a921)))+P1(f862(f862(f227(f932(f931(x76081,x76081),a921)),x76082),x76083))
% 25.54/25.41 [7708]E(f862(f862(f103(f932(x77081,a921)),x77082),f862(f862(f3(f932(x77081,a921)),x77083),x77082)),x77083)+~P1(f862(f862(f227(f932(x77081,a921)),x77082),x77083))
% 25.54/25.41 [7709]~P1(f862(f862(f227(a924),x77091),f862(f862(f73(a924),x77093),x77092)))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x77091),x77092)),x77093))
% 25.54/25.41 [7710]~P1(f862(f862(f228(a924),x77101),f862(f862(f3(a924),x77103),x77102)))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x77101),x77102)),x77103))
% 25.54/25.41 [7768]E(x77681,f106(x77682))+E(f862(f134(x77682),f862(f862(f862(f176(f925(x77682),f925(x77682)),x77683),f160(x77682)),x77681)),f862(f862(f157(x77682),x77681),f38(a924,x77683,f862(f182(f925(x77682)),x77681))))
% 25.54/25.41 [7777]E(f862(f862(f301(x77771),x77772),f862(f862(f3(f932(x77771,a921)),x77773),f862(f862(f301(x77771),x77772),f181(f932(x77771,a921))))),x77773)+~P1(f862(f862(f321(x77771),x77772),x77773))
% 25.54/25.41 [7938]P1(f862(f862(f227(a924),x79381),f862(f862(f73(a924),x79382),x79383)))+~P1(f862(f862(f227(a924),f862(f862(f3(a924),x79381),x79383)),x79382))
% 25.54/25.41 [7939]P1(f862(f862(f228(a924),x79391),f862(f862(f3(a924),x79392),x79393)))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x79391),x79393)),x79392))
% 25.54/25.41 [7964]P1(f862(f54(x79641),x79642))+~P1(f862(f54(x79641),f862(f862(f103(f932(x79641,a921)),x79643),x79642)))
% 25.54/25.41 [7965]P1(f862(f54(x79651),x79652))+~P1(f862(f54(x79651),f862(f862(f103(f932(x79651,a921)),x79652),x79653)))
% 25.54/25.41 [8040]~P43(x80401,x80403)+P1(f862(f862(f321(f931(x80401,x80401)),f862(f862(f244(x80401,x80401),x80402),x80402)),x80403))
% 25.54/25.41 [8176]E(f862(f862(f157(a924),f132(a924,f862(f295(a924,x81761),x81762))),x81763),f862(f862(f73(a924),x81761),x81763))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),x81761),x81763)),x81762))
% 25.54/25.41 [8243]E(f862(f862(f168(a924),x82431),f132(a924,f862(f295(a924,x82432),x82433))),f132(a924,f862(f295(a924,x82432),f862(f862(f73(a924),x82432),x82431))))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x82432),x82431)),x82433))
% 25.54/25.41 [8302]~P98(x83021)+E(f862(f862(f236(x83021),x83022),f862(f96(a924),f862(f862(f73(a1),x83023),x83023))),f862(f862(f79(x83021,x83021),f862(f862(f236(x83021),x83022),f862(f96(a924),x83023))),f862(f862(f20(x83021,x83021,x83021),f74(x83021)),f7(x83021))))
% 25.54/25.41 [8568]E(f862(f862(f127(x85681),f862(f862(f168(x85681),x85682),x85683)),f862(f862(f144(x85681),f862(f862(f157(x85681),x85683),x85682)),f862(f862(f131(x85681),f862(a105,x85682)),x85683))),x85683)+~P1(f862(f862(f228(a924),x85682),f862(f182(f925(x85681)),x85683)))
% 25.54/25.41 [8575]P1(f862(f862(f227(f932(x85751,a921)),f307(x85751,x85752)),f307(x85751,x85753)))+~P1(f862(f862(f227(f932(x85751,f932(x85751,a921))),x85753),x85752))
% 25.54/25.41 [8576]~P53(x85761,x85762,x85763)+P53(x85761,x85762,f862(f862(f3(f932(f931(x85761,x85761),a921)),x85763),f299(x85761,f181(f932(f931(x85761,x85761),a921)))))
% 25.54/25.41 [8595]P1(f862(f862(f227(f932(x85951,a921)),f308(x85951,x85952)),f308(x85951,x85953)))+~P1(f862(f862(f227(f932(f931(x85951,x85951),a921)),x85953),x85952))
% 25.54/25.41 [8601]~P1(f862(f862(f228(f932(x86011,a921)),x86013),x86012))+P1(f862(f862(f321(x86011),f772(x86012,x86013,x86011)),f862(f862(f3(f932(x86011,a921)),x86012),x86013)))
% 25.54/25.41 [8603]~P129(x86031)+P1(f862(f862(f227(x86031),f2(x86031)),f862(f862(f73(x86031),f862(f862(f74(x86031),x86032),x86032)),f862(f862(f74(x86031),x86033),x86033))))
% 25.54/25.41 [8632]~P98(x86321)+E(f862(f862(f236(x86321),f862(f96(x86321),x86322)),f862(f96(a924),f862(f862(f73(a1),x86323),x86323))),f862(f862(f79(x86321,x86321),f862(f862(f236(x86321),f862(f96(x86321),x86322)),f862(f96(a924),x86323))),f862(f862(f20(x86321,x86321,x86321),f74(x86321)),f7(x86321))))
% 25.54/25.41 [8637]P1(f862(f862(f227(f932(x86371,a921)),f862(f273(x86371),x86372)),f862(f273(x86371),x86373)))+~P1(f862(f862(f227(f932(f931(x86371,x86371),a921)),x86372),x86373))
% 25.54/25.41 [8667]~P51(x86671,x86672)+~P1(f862(f862(f321(f931(x86671,x86671)),f862(f862(f244(x86671,x86671),x86673),x86673)),x86672))
% 25.54/25.41 [8668]~P35(x86681,x86682)+~P1(f862(f862(f321(f931(x86681,x86681)),f862(f862(f244(x86681,x86681),x86683),x86683)),x86682))
% 25.54/25.41 [8669]~P35(x86691,x86692)+~P1(f862(f862(f321(f931(x86691,x86691)),f862(f862(f244(x86691,x86691),x86693),x86693)),x86692))
% 25.54/25.41 [8710]~E(x87102,x87103)+P1(f862(f862(f321(f931(x87101,x87101)),f862(f862(f244(x87101,x87101),x87102),x87103)),f299(x87101,f181(f932(f931(x87101,x87101),a921)))))
% 25.54/25.41 [8728]P1(f862(f862(f227(f932(x87281,a921)),f31(f932(x87281,a921),x87282)),f31(f932(x87281,a921),x87283)))+~P1(f862(f862(f227(f932(f932(x87281,a921),a921)),x87283),x87282))
% 25.54/25.41 [8729]P1(f862(f862(f227(f932(x87291,a921)),f30(f932(x87291,a921),x87292)),f30(f932(x87291,a921),x87293)))+~P1(f862(f862(f227(f932(f932(x87291,a921),a921)),x87292),x87293))
% 25.54/25.41 [8784]~P6(x87841,x87843,x87842)+P1(f862(f862(f227(f932(f931(x87841,x87841),a921)),x87842),f862(f862(f246(x87841,x87841),x87843),f862(f18(f932(x87841,a921),x87841),x87843))))
% 25.54/25.41 [8785]~P50(x87851,x87853,x87852)+P1(f862(f862(f227(f932(f931(x87851,x87851),a921)),x87852),f862(f862(f246(x87851,x87851),x87853),f862(f18(f932(x87851,a921),x87851),x87853))))
% 25.54/25.41 [8834]~P86(x88341)+P1(f862(f862(f227(x88341),f862(f862(f3(x88341),f862(f69(x88341),x88342)),f862(f69(x88341),x88343))),f862(f69(x88341),f862(f862(f3(x88341),x88343),x88342))))
% 25.54/25.41 [8835]~P86(x88351)+P1(f862(f862(f227(x88351),f862(f862(f3(x88351),f862(f69(x88351),x88352)),f862(f69(x88351),x88353))),f862(f69(x88351),f862(f862(f3(x88351),x88352),x88353))))
% 25.54/25.41 [8867]P1(f862(f862(f227(f932(f931(x88671,x88671),a921)),f299(x88671,x88672)),f299(x88671,x88673)))+~P1(f862(f862(f227(f932(f931(x88671,x88671),a921)),x88672),x88673))
% 25.54/25.41 [8978]~P22(x89782,x89781,x89783,f234(f932(x89782,a921)))+E(f862(f66(x89781,x89782,x89782,f86(x89782,x89781,f234(f932(x89782,a921)),x89783)),x89783),f25(x89782))
% 25.54/25.41 [8979]~P22(x89792,x89791,x89793,f234(f932(x89792,a921)))+E(f862(f66(x89791,x89792,x89792,f86(x89792,x89791,f234(f932(x89792,a921)),x89793)),x89793),f25(x89792))
% 25.54/25.41 [9041]P53(x90411,x90412,x90413)+~P53(x90411,x90412,f862(f862(f3(f932(f931(x90411,x90411),a921)),x90413),f299(x90411,f181(f932(f931(x90411,x90411),a921)))))
% 25.54/25.41 [9061]P1(f862(f862(f227(f932(f931(f925(x90611),f925(x90611)),a921)),f150(x90611,x90612)),f150(x90611,x90613)))+~P1(f862(f862(f227(f932(f931(x90611,x90611),a921)),x90612),x90613))
% 25.54/25.41 [9062]P1(f862(f862(f227(f932(f931(f925(x90621),f925(x90621)),a921)),f151(x90621,x90622)),f151(x90621,x90623)))+~P1(f862(f862(f227(f932(f931(x90621,x90621),a921)),x90622),x90623))
% 25.54/25.41 [9083]~P50(x90831,x90833,x90832)+P1(f862(f862(f227(f932(f931(x90831,x90831),a921)),x90832),f862(f862(f280(x90831,x90831,x90831),f862(f277(x90831,x90831),x90832)),x90832)))
% 25.54/25.41 [9118]~P1(f862(f130(x91181),x91183))+P1(f862(f130(x91181),f862(f862(f131(x91181),f862(f182(f925(x91181)),f170(x91181,x91182,x91183))),x91183)))
% 25.54/25.41 [9135]~P1(f862(f130(x91351),x91352))+E(f862(f129(x91351,f862(f862(f9(x91351,f932(x91351,a921),a921),f321(x91351)),f862(f165(x91351),f169(x91351,x91352,x91353)))),x91352),f169(x91351,x91352,x91353))
% 25.54/25.41 [9188]E(x91881,x91882)+~P1(f862(f862(f321(f931(x91883,x91883)),f862(f862(f244(x91883,x91883),x91881),x91882)),f299(x91883,f181(f932(f931(x91883,x91883),a921)))))
% 25.54/25.41 [9270]P1(f862(f862(f321(x92701),x92702),f308(x92701,x92703)))+P1(f862(f862(f321(f931(x92701,x92701)),f862(f862(f244(x92701,x92701),f547(x92703,x92702,x92701)),x92702)),x92703))
% 25.54/25.41 [9271]P1(f862(f862(f321(x92711),x92712),f308(x92711,x92713)))+P1(f862(f862(f321(f931(x92711,x92711)),f862(f862(f244(x92711,x92711),f612(x92713,x92712,x92711)),x92712)),x92713))
% 25.54/25.41 [9272]P1(f862(f862(f321(x92721),x92722),f308(x92721,x92723)))+P1(f862(f862(f321(f931(x92721,x92721)),f862(f862(f244(x92721,x92721),f614(x92723,x92722,x92721)),x92722)),x92723))
% 25.54/25.41 [9309]P22(x93091,x93092,x93093,f234(f932(x93091,a921)))+~E(f862(f66(x93092,x93091,x93091,f86(x93091,x93092,f234(f932(x93091,a921)),x93093)),x93093),f25(x93091))
% 25.54/25.41 [9363]~P1(f862(f862(f321(f925(x93631)),x93633),f154(x93631,x93632)))+P1(f862(f153(x93631,f862(f862(f9(x93631,f932(x93631,a921),a921),f321(x93631)),x93632)),x93633))
% 25.54/25.41 [9386]P1(f862(x93863,x93862))+E(f862(f254(x93861),f862(f862(f20(x93861,a921,a921),f862(f862(f10(a921,f932(a921,a921),x93861),a318),f862(a317,x93862))),x93863)),f181(f932(x93861,a921)))
% 25.54/25.41 [9403]~P86(x94031)+P1(f862(f862(f227(x94031),f862(f69(x94031),f862(f862(f3(x94031),f862(f69(x94031),x94032)),f862(f69(x94031),x94033)))),f862(f69(x94031),f862(f862(f3(x94031),x94032),x94033))))
% 25.54/25.41 [9417]~P1(f862(x94173,x94172))+E(f862(f254(x94171),f862(f862(f20(x94171,a921,a921),f862(f862(f10(a921,f932(a921,a921),x94171),a318),f862(a317,x94172))),x94173)),f862(f862(f301(x94171),x94172),f181(f932(x94171,a921))))
% 25.54/25.41 [9426]~P1(f862(f862(f321(f932(x94261,a921)),x94263),f862(f300(x94261),x94262)))+P1(f862(f240(x94261,f862(f862(f9(x94261,f932(x94261,a921),a921),f321(x94261)),x94262)),x94263))
% 25.54/25.41 [9462]P35(x94621,x94622)+P1(f862(f862(f321(f931(x94621,x94621)),f862(f862(f244(x94621,x94621),f862(f553(x94622,x94621),f862(a105,x94623))),f862(f553(x94622,x94621),x94623))),x94622))
% 25.54/25.41 [9558]~P1(f862(f130(x95581),x95583))+P1(f862(f130(x95581),f862(f129(x95581,f862(f862(f10(a921,a921,x95581),a314),f862(a317,x95582))),x95583)))
% 25.54/25.41 [9604]P1(f862(f862(f321(f925(x96041)),x96042),f154(x96041,x96043)))+~P1(f862(f153(x96041,f862(f862(f9(x96041,f932(x96041,a921),a921),f321(x96041)),x96043)),x96042))
% 25.54/25.41 [9619]P1(f862(f862(f321(f932(x96191,a921)),x96192),f862(f300(x96191),x96193)))+~P1(f862(f240(x96191,f862(f862(f9(x96191,f932(x96191,a921),a921),f321(x96191)),x96193)),x96192))
% 25.54/25.41 [9681]P1(f862(f862(f321(x96811),f862(f260(x96811,x96812),x96813)),f862(f165(x96811),f862(f862(f147(f931(a92,x96811),x96811),f248(a92,x96811)),x96812))))+~P1(f862(f862(f228(a92),x96813),f862(f158(a92),f862(f862(f147(f931(a92,x96811),a92),f243(a92,x96811)),x96812))))
% 25.54/25.41 [9727]P1(f862(f862(f227(f932(f931(f925(x97271),f925(x97271)),a921)),f151(x97271,x97272)),f862(f862(f246(f925(x97271),f925(x97271)),f154(x97271,x97273)),f862(f18(f932(f925(x97271),a921),f925(x97271)),f154(x97271,x97273)))))+~P1(f862(f862(f227(f932(f931(x97271,x97271),a921)),x97272),f862(f862(f246(x97271,x97271),x97273),f862(f18(f932(x97271,a921),x97271),x97273))))
% 25.54/25.41 [9751]P1(f862(f862(f321(x97511),f862(f243(x97511,f931(a92,a92)),f862(f258(x97511,x97512),x97513))),f862(f165(x97511),f862(f862(f147(f931(a92,x97511),x97511),f248(a92,x97511)),x97512))))+~P1(f862(f862(f228(a92),f2(a92)),f862(f158(a92),f862(f862(f147(f931(a92,x97511),a92),f243(a92,x97511)),x97512))))
% 25.54/25.41 [9766]~P1(f862(f862(f227(f932(f931(x97661,x97661),a921)),x97662),f862(f862(f246(x97661,x97661),x97663),f862(f18(f932(x97661,a921),x97661),x97663))))+P1(f862(f862(f227(f932(f931(x97661,x97661),a921)),f862(f862(f280(x97661,x97661,x97661),x97662),f299(x97661,x97662))),f862(f862(f246(x97661,x97661),x97663),f862(f18(f932(x97661,a921),x97661),x97663))))
% 25.54/25.41 [10067]~P35(x100671,x100672)+~P1(f862(f862(f321(f931(x100671,x100671)),f862(f862(f244(x100671,x100671),f862(x100673,f862(a105,f554(x100672,x100671,x100673)))),f862(x100673,f554(x100672,x100671,x100673)))),x100672))
% 25.54/25.41 [10068]~P35(x100681,x100682)+~P1(f862(f862(f321(f931(x100681,x100681)),f862(f862(f244(x100681,x100681),f862(x100683,f862(a105,f618(x100683,x100682,x100681)))),f862(x100683,f618(x100683,x100682,x100681)))),x100682))
% 25.54/25.41 [10314]P1(f862(f862(f227(f932(f931(f932(x103141,a921),f932(x103141,a921)),a921)),f862(f862(f280(f932(x103141,a921),f932(x103141,a921),f932(x103141,a921)),f310(x103141,x103142)),f862(f862(f103(f932(f931(f932(x103141,a921),f932(x103141,a921)),a921)),f310(x103141,x103143)),f862(f862(f301(f931(f932(x103141,a921),f932(x103141,a921))),f862(f862(f244(f932(x103141,a921),f932(x103141,a921)),f181(f932(x103141,a921))),f181(f932(x103141,a921)))),f181(f932(f931(f932(x103141,a921),f932(x103141,a921)),a921)))))),f310(x103141,x103142)))+~P1(f862(f862(f227(f932(f931(x103141,x103141),a921)),f862(f862(f280(x103141,x103141,x103141),x103142),x103143)),x103142))
% 25.54/25.41 [10315]P1(f862(f862(f227(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)),f862(f862(f280(f932(x103151,a921),f932(x103151,a921),f932(x103151,a921)),f312(x103151,x103152)),f862(f862(f103(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)),f312(x103151,x103153)),f862(f862(f301(f931(f932(x103151,a921),f932(x103151,a921))),f862(f862(f244(f932(x103151,a921),f932(x103151,a921)),f181(f932(x103151,a921))),f181(f932(x103151,a921)))),f181(f932(f931(f932(x103151,a921),f932(x103151,a921)),a921)))))),f312(x103151,x103152)))+~P1(f862(f862(f227(f932(f931(x103151,x103151),a921)),f862(f862(f280(x103151,x103151,x103151),x103152),x103153)),x103152))
% 25.54/25.41 [7475]~P1(f862(f862(f227(a924),x74752),x74751))+E(f862(f862(f3(a924),f862(a105,f862(f862(f3(a924),x74751),x74752))),x74753),f862(f862(f3(a924),f862(a105,x74751)),f862(f862(f73(a924),x74752),x74753)))
% 25.54/25.41 [7516]~P61(x75161)+E(f862(f862(f73(x75161),f38(x75161,x75162,x75163)),f862(f862(f74(x75161),f862(f862(f29(x75161),x75162),x75163)),x75163)),x75162)
% 25.54/25.41 [7714]E(f862(f862(f74(a924),f862(f96(a924),x77141)),f862(f862(f74(a924),f862(f96(a924),x77142)),x77143)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f74(a1),x77141),x77142))),x77143))+P1(f862(f862(f228(a1),x77141),a76))
% 25.54/25.41 [8185]~P1(f862(f862(f227(a924),x81853),x81852))+P1(f862(f862(f227(a924),x81851),f862(f862(f3(a924),f862(f862(f73(a924),x81852),x81851)),x81853)))
% 25.54/25.41 [8389]~P1(f862(f862(f227(a924),x83891),x83892))+E(f862(f862(f127(a924),f132(a924,f862(f295(a924,x83891),x83892))),f132(a924,f862(f295(a924,x83892),f862(f862(f73(a924),x83892),x83893)))),f132(a924,f862(f295(a924,x83891),f862(f862(f73(a924),x83892),x83893))))
% 25.54/25.41 [8646]~P1(f862(f54(x86461),x86462))+E(f862(a105,f862(f28(x86461),f862(f862(f3(f932(x86461,a921)),x86462),f862(f862(f301(x86461),x86463),f181(f932(x86461,a921)))))),f862(f28(x86461),f862(f862(f301(x86461),x86463),x86462)))
% 25.54/25.41 [8685]~P1(f862(f54(x86851),x86852))+E(f862(f862(f73(a924),f71(a924)),f862(f28(x86851),f862(f862(f3(f932(x86851,a921)),x86852),f862(f862(f301(x86851),x86853),f181(f932(x86851,a921)))))),f862(f28(x86851),f862(f862(f301(x86851),x86853),x86852)))
% 25.54/25.41 [8876]E(f862(f862(f3(a924),f862(f28(x88761),x88762)),f862(f28(x88761),f862(f862(f94(f932(x88761,a921)),x88762),x88763))),f862(f28(x88761),f862(f862(f3(f932(x88761,a921)),x88762),x88763)))+~P1(f862(f54(x88761),f862(f862(f94(f932(x88761,a921)),x88762),x88763)))
% 25.54/25.41 [9130]~P4(f862(x91302,f505(x91302,x91303,x91301)))+E(f862(f93(a1),f862(f862(f8(x91301,a924),f862(f862(f10(a1,a924,x91301),a97),x91302)),x91303)),f862(f862(f8(x91301,a1),x91302),x91303))
% 25.54/25.41 [9131]~P4(f862(x91312,f506(x91312,x91313,x91311)))+E(f862(f93(a1),f862(f862(f11(x91311,a924),f862(f862(f10(a1,a924,x91311),a97),x91312)),x91313)),f862(f862(f11(x91311,a1),x91312),x91313))
% 25.54/25.41 [9171]~P1(f862(f54(x91711),x91713))+P1(f862(f862(f227(a924),f862(f862(f3(a924),f862(f28(x91711),x91712)),f862(f28(x91711),x91713))),f862(f28(x91711),f862(f862(f3(f932(x91711,a921)),x91712),x91713))))
% 25.54/25.41 [9198]P1(f862(f862(f321(x91981),f505(x91982,x91983,x91981)),x91983))+E(f862(f93(a1),f862(f862(f8(x91981,a924),f862(f862(f10(a1,a924,x91981),a97),x91982)),x91983)),f862(f862(f8(x91981,a1),x91982),x91983))
% 25.54/25.41 [9199]P1(f862(f862(f321(x91991),f506(x91992,x91993,x91991)),x91993))+E(f862(f93(a1),f862(f862(f11(x91991,a924),f862(f862(f10(a1,a924,x91991),a97),x91992)),x91993)),f862(f862(f11(x91991,a1),x91992),x91993))
% 25.54/25.41 [9262]E(f78(x92621,f862(f862(f9(x92621,f932(x92621,a921),a921),f321(x92621)),f862(f862(f3(f932(x92621,a921)),x92622),f862(f862(f301(x92621),x92623),f181(f932(x92621,a921)))))),f239(x92621,x92623,x92622))+P1(f862(f862(f227(f932(x92621,a921)),x92622),f862(f862(f301(x92621),x92623),f181(f932(x92621,a921)))))
% 25.54/25.41 [9620]E(f862(f862(f147(f925(x96201),x96201),f862(f862(f9(f925(x96201),a924,x96201),f157(x96201)),x96202)),f862(f129(f925(x96201),f862(f862(f10(a924,a921,f925(x96201)),f862(f228(a924),x96202)),f182(f925(x96201)))),x96203)),f862(f862(f157(f925(x96201)),f172(x96201,x96203)),x96202))+~P1(f862(f862(f228(a924),x96202),f862(f182(f925(f925(x96201))),f172(x96201,x96203))))
% 25.54/25.41 [9701]E(f862(f129(x97011,x97012),x97013),f170(x97011,x97012,x97013))+P1(f862(f862(f321(x97011),f728(x97013,x97012,x97011)),f862(f165(x97011),f862(f862(f131(x97011),f862(f182(f925(x97011)),f170(x97011,x97012,x97013))),x97013))))
% 25.54/25.41 [9839]E(f862(f862(f131(x98391),f862(f182(f925(x98391)),f170(x98391,x98392,x98393))),x98393),f106(x98391))+~P1(f862(x98392,f862(f134(x98391),f862(f862(f131(x98391),f862(f182(f925(x98391)),f170(x98391,x98392,x98393))),x98393))))
% 25.54/25.41 [9932]~P1(f862(f862(f321(f931(x99321,x99321)),x99322),f299(x99321,x99323)))+P1(f862(f862(f321(f931(x99321,x99321)),x99322),f862(f862(f33(a924,f932(f931(x99321,x99321),a921)),f234(f932(a924,a921))),f862(f862(f9(a924,f932(f931(x99321,x99321),a921),f932(f931(x99321,x99321),a921)),f176(f931(x99321,x99321),a921)),x99323))))
% 25.54/25.41 [9993]~P1(f862(f862(f227(f932(x99931,a921)),f862(f862(f33(a924,f932(x99931,a921)),f862(f295(a924,f2(a924)),f517(x99933,x99932,x99931))),x99932)),x99933))+P1(f862(f862(f227(f932(x99931,a921)),f862(f862(f33(a924,f932(x99931,a921)),f234(f932(a924,a921))),x99932)),x99933))
% 25.54/25.41 [10040]~P1(f862(f862(f228(a1),f2(a1)),x100403))+P1(f862(f862(f228(a1),x100401),f862(f862(f73(a1),x100402),f862(f862(f74(a1),f862(f862(f73(a1),f862(f69(a1),f862(f862(f3(a1),x100402),x100401))),f71(a1))),x100403))))
% 25.54/25.41 [10054]~P35(x100541,f862(f862(f103(f932(f931(x100541,x100541),a921)),x100542),x100543))+P35(x100541,f862(f862(f103(f932(f931(x100541,x100541),a921)),f862(f862(f103(f932(f931(x100541,x100541),a921)),f862(f862(f280(x100541,x100541,x100541),x100542),x100542)),f862(f862(f280(x100541,x100541,x100541),x100543),x100542))),x100543))
% 25.54/25.41 [10132]P35(x101321,f862(f862(f103(f932(f931(x101321,x101321),a921)),x101322),x101323))+~P35(x101321,f862(f862(f103(f932(f931(x101321,x101321),a921)),f862(f862(f103(f932(f931(x101321,x101321),a921)),f862(f862(f280(x101321,x101321,x101321),x101322),x101322)),f862(f862(f280(x101321,x101321,x101321),x101323),x101322))),x101323))
% 25.54/25.41 [9704]~P142(x97041)+E(f862(f95(x97041),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x97042),x97043)),f181(f932(f931(a924,a924),a921)))))),f862(f862(f3(x97041),f862(f93(x97041),x97042)),f862(f93(x97041),x97043)))
% 25.54/25.41 [9786]P1(f862(x97863,x97862))+E(f862(f254(x97861),f862(f862(f20(x97861,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97861),a318),f862(f862(f9(x97861,x97861,a921),a317),x97862))),x97863)),f181(f932(x97861,a921)))
% 25.54/25.41 [9788]~P1(f862(x97883,x97882))+E(f862(f254(x97881),f862(f862(f20(x97881,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97881),a318),f862(f862(f9(x97881,x97881,a921),a317),x97882))),x97883)),f862(f862(f301(x97881),x97882),f181(f932(x97881,a921))))
% 25.54/25.41 [10020]E(x100201,x100202)+P1(f862(f862(f235(x100203,x100203,f862(f862(f10(f932(x100203,a921),f932(x100203,a921),x100203),f862(f10(a921,a921,x100203),a314)),a317)),x100201),x100202))
% 25.54/25.41 [10112]~E(x101121,x101122)+~P1(f862(f862(f235(x101123,x101123,f862(f862(f10(f932(x101123,a921),f932(x101123,a921),x101123),f862(f10(a921,a921,x101123),a314)),a317)),x101121),x101122))
% 25.54/25.41 [10124]~P1(f862(f54(x101241),x101243))+E(f862(f862(f57(x101241,f932(x101241,a921),f862(f862(f10(f932(x101241,a921),f932(f932(x101241,a921),f932(x101241,a921)),x101241),f862(f9(f932(x101241,a921),f932(x101241,a921),f932(x101241,a921)),f3(f932(x101241,a921)))),f862(f862(f9(x101241,f932(x101241,a921),f932(x101241,a921)),f301(x101241)),f181(f932(x101241,a921))))),x101242),x101243),f862(f862(f3(f932(x101241,a921)),x101242),x101243))
% 25.54/25.41 [10154]~P1(f862(f862(f228(a1),f2(a1)),x101543))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x101541),f862(f862(f74(a1),f862(f862(f73(a1),f862(f69(a1),f862(f862(f3(a1),x101541),x101542))),f71(a1))),x101543))),x101542))
% 25.54/25.41 [10404]~P1(f862(f862(f321(x104041),x104043),f308(x104041,x104042)))+P1(f862(f307(x104041,f862(f862(f9(x104041,f932(f931(x104041,x104041),a921),f932(x104041,a921)),f862(f862(f10(f932(x104041,f932(f932(f931(x104041,x104041),a921),a921)),f932(f932(f931(x104041,x104041),a921),f932(x104041,a921)),x104041),f9(x104041,f932(f931(x104041,x104041),a921),a921)),f862(f862(f10(f932(x104041,f931(x104041,x104041)),f932(x104041,f932(f932(f931(x104041,x104041),a921),a921)),x104041),f862(f10(f931(x104041,x104041),f932(f932(f931(x104041,x104041),a921),a921),x104041),f321(f931(x104041,x104041)))),f244(x104041,x104041)))),x104042)),x104043))
% 25.54/25.41 [10417]P1(f862(f862(f321(x104171),x104172),f308(x104171,x104173)))+~P1(f862(f307(x104171,f862(f862(f9(x104171,f932(f931(x104171,x104171),a921),f932(x104171,a921)),f862(f862(f10(f932(x104171,f932(f932(f931(x104171,x104171),a921),a921)),f932(f932(f931(x104171,x104171),a921),f932(x104171,a921)),x104171),f9(x104171,f932(f931(x104171,x104171),a921),a921)),f862(f862(f10(f932(x104171,f931(x104171,x104171)),f932(x104171,f932(f932(f931(x104171,x104171),a921),a921)),x104171),f862(f10(f931(x104171,x104171),f932(f932(f931(x104171,x104171),a921),a921),x104171),f321(f931(x104171,x104171)))),f244(x104171,x104171)))),x104173)),x104172))
% 25.54/25.41 [9991]~P1(f862(f54(x99911),f862(f254(x99911),x99913)))+P1(f862(f54(x99911),f862(f254(x99911),f862(f862(f20(x99911,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99911),a318),x99912)),x99913))))
% 25.54/25.41 [9992]~P1(f862(f54(x99921),f862(f254(x99921),x99922)))+P1(f862(f54(x99921),f862(f254(x99921),f862(f862(f20(x99921,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99921),a318),x99922)),x99923))))
% 25.54/25.41 [10088]P1(f862(f54(x100881),f862(f254(x100881),x100882)))+~P1(f862(f54(x100881),f862(f254(x100881),f862(f862(f20(x100881,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100881),a319),x100883)),x100882))))
% 25.54/25.41 [10089]P1(f862(f54(x100891),f862(f254(x100891),x100892)))+~P1(f862(f54(x100891),f862(f254(x100891),f862(f862(f20(x100891,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100891),a319),x100892)),x100893))))
% 25.54/25.41 [10383]~P1(f862(f54(x103831),x103832))+P1(f862(f54(f925(x103831)),f862(f254(f925(x103831)),f862(f862(f20(f925(x103831),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103831)),a318),f862(f862(f9(f925(x103831),f932(x103831,a921),a921),f862(f862(f10(f932(x103831,a921),f932(f932(x103831,a921),a921),f925(x103831)),f227(f932(x103831,a921))),f165(x103831))),x103832))),f862(f862(f9(f925(x103831),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x103831)),a317),f182(f925(x103831)))),x103833)))))
% 25.54/25.41 [10384]~P1(f862(f54(x103841),x103842))+P1(f862(f54(f925(x103841)),f862(f254(f925(x103841)),f862(f862(f20(f925(x103841),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103841)),a318),f862(f862(f9(f925(x103841),f932(x103841,a921),a921),f862(f862(f10(f932(x103841,a921),f932(f932(x103841,a921),a921),f925(x103841)),f227(f932(x103841,a921))),f165(x103841))),x103842))),f862(f862(f9(f925(x103841),a924,a921),f862(f862(f10(a924,f932(a924,a921),f925(x103841)),f227(a924)),f182(f925(x103841)))),x103843)))))
% 25.54/25.41 [10105]~P119(x101051)+E(f862(f862(f236(x101051),x101052),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101053)),f862(f862(f74(x101051),f862(f862(f236(x101051),x101052),x101053)),f862(f862(f236(x101051),x101052),x101053)))
% 25.54/25.41 [10135]~P80(x101351)+E(f862(f862(f236(x101351),f862(f862(f236(x101351),x101352),x101353)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x101351),x101352),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101353)))
% 25.54/25.41 [10181]~P142(x101811)+E(f862(f862(f236(x101811),f862(f72(x101811),x101812)),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101813)),f862(f862(f236(x101811),x101812),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101813)))
% 25.54/25.41 [10322]~P112(x103221)+P1(f862(f862(f227(x103221),f2(x103221)),f862(f862(f73(x103221),f862(f862(f236(x103221),x103222),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103221),x103223),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))))
% 25.54/25.41 [10191]~P119(x101911)+E(f862(f862(f236(x101911),x101912),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101913))),f862(f862(f74(x101911),x101912),f862(f862(f74(x101911),f862(f862(f236(x101911),x101912),x101913)),f862(f862(f236(x101911),x101912),x101913))))
% 25.54/25.41 [10242]~P80(x102421)+E(f862(f862(f74(x102421),x102422),f862(f862(f236(x102421),f862(f862(f236(x102421),x102422),x102423)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102421),x102422),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102423))))
% 25.54/25.41 [10279]~P112(x102791)+P1(f862(f862(f227(x102791),f2(x102791)),f862(f862(f236(x102791),x102792),f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x102793))))
% 25.54/25.41 [10359]~P98(x103591)+E(f862(f862(f3(x103591),f862(f862(f73(x103591),f862(f862(f236(x103591),x103592),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103591),x103593),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(f862(f74(x103591),f862(f862(f74(x103591),f862(f96(x103591),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103592)),x103593)),f862(f862(f236(x103591),f862(f862(f3(x103591),x103592),x103593)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [10360]~P98(x103601)+E(f862(f862(f73(x103601),f862(f862(f73(x103601),f862(f862(f236(x103601),x103602),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103601),x103603),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(f862(f74(x103601),f862(f862(f74(x103601),f862(f96(x103601),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103602)),x103603)),f862(f862(f236(x103601),f862(f862(f73(x103601),x103602),x103603)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [7981]P22(x79811,x79812,x79813,x79814)+~E(f537(x79814,x79813,x79812,x79811),f538(x79814,x79813,x79812,x79811))
% 25.54/25.41 [8277]P32(x82771,x82772,x82773,x82774,f106(x82772))+~E(x82774,f106(x82771))
% 25.54/25.41 [8278]P32(x82781,x82782,x82783,f106(x82781),x82784)+~E(x82784,f106(x82782))
% 25.54/25.41 [8824]~P32(x88242,x88243,x88244,x88241,f106(x88243))+E(x88241,f106(x88242))
% 25.54/25.41 [8825]~P32(x88253,x88252,x88254,f106(x88253),x88251)+E(x88251,f106(x88252))
% 25.54/25.41 [5241]~P15(x52413,x52411,x52414)+E(f862(f862(x52411,x52412),x52412),x52412)
% 25.54/25.41 [5489]P1(f862(x54892,x54894))+E(f862(f129(x54891,x54892),f162(x54891,x54893,x54894)),f106(x54891))
% 25.54/25.41 [5525]~E(x55254,f181(f932(x55251,a921)))+E(f862(f302(x55251,x55252,x55253),x55254),f181(f932(x55252,a921)))
% 25.54/25.41 [5526]~E(x55264,f181(f932(x55261,a921)))+E(f862(f302(x55261,x55262,x55263),x55264),f181(f932(x55262,a921)))
% 25.54/25.41 [5776]~P1(f862(x57762,x57764))+E(f862(f129(x57761,x57762),f162(x57761,x57763,x57764)),f162(x57761,x57763,x57764))
% 25.54/25.41 [5804]~E(f862(f302(x58042,x58043,x58044),x58041),f181(f932(x58043,a921)))+E(x58041,f181(f932(x58042,a921)))
% 25.54/25.41 [5805]~E(f862(f302(x58052,x58053,x58054),x58051),f181(f932(x58053,a921)))+E(x58051,f181(f932(x58052,a921)))
% 25.54/25.41 [5992]~P5(x59921,x59923)+E(f263(x59921,x59922,f262(x59921,x59923),x59924),x59924)
% 25.54/25.41 [6108]~P109(x61082)+E(f862(f862(f141(x61081,x61082,x61083),x61084),f106(x61081)),f862(f862(f144(x61081),x61084),f106(x61081)))
% 25.54/25.41 [6463]~E(x64631,f181(f932(x64632,a921)))+~P1(f862(f55(x64632,x64633,x64631),x64634))
% 25.54/25.41 [6484]~P56(x64841,x64843,x64844,x64842)+P1(f862(f54(x64841),x64842))
% 25.54/25.41 [6485]~P56(x64851,x64853,x64854,x64852)+P1(f862(f54(x64851),x64852))
% 25.54/25.41 [6486]~P56(x64861,x64863,x64862,x64864)+P1(f862(f54(x64861),x64862))
% 25.54/25.41 [6487]~P56(x64871,x64873,x64872,x64874)+P1(f862(f54(x64871),x64872))
% 25.54/25.41 [6494]~P56(x64942,x64943,x64944,x64941)+~E(x64941,f181(f932(x64942,a921)))
% 25.54/25.41 [6495]~P56(x64952,x64953,x64954,x64951)+~E(x64951,f181(f932(x64952,a921)))
% 25.54/25.41 [6528]~P110(x65281)+E(f862(f862(f94(f932(x65281,a921)),f862(f295(x65281,x65282),x65283)),f296(x65281,x65283,x65284)),f181(f932(x65281,a921)))
% 25.54/25.41 [6556]~P1(f862(f862(x65563,x65564),x65562))+P1(f862(f862(f321(x65561),x65562),f284(x65561,x65563,x65564)))
% 25.54/25.41 [6557]~P1(f862(f862(x65573,x65574),x65572))+P1(f862(f862(f321(x65571),x65572),f285(x65571,x65573,x65574)))
% 25.54/25.41 [6558]~P1(f862(f862(x65583,x65582),x65584))+P1(f862(f862(f321(x65581),x65582),f286(x65581,x65583,x65584)))
% 25.54/25.41 [6559]~P1(f862(f862(x65593,x65592),x65594))+P1(f862(f862(f321(x65591),x65592),f289(x65591,x65593,x65594)))
% 25.54/25.41 [6702]~P110(x67021)+E(f862(f862(f94(f932(x67021,a921)),f298(x67021,x67022,x67023)),f296(x67021,x67023,x67024)),f181(f932(x67021,a921)))
% 25.54/25.41 [6703]~P110(x67031)+E(f862(f862(f94(f932(x67031,a921)),f297(x67031,x67032,x67033)),f298(x67031,x67033,x67034)),f181(f932(x67031,a921)))
% 25.54/25.41 [6704]~P110(x67041)+E(f862(f862(f94(f932(x67041,a921)),f297(x67041,x67042,x67043)),f297(x67041,x67043,x67044)),f181(f932(x67041,a921)))
% 25.54/25.41 [6705]~P110(x67051)+E(f862(f862(f94(f932(x67051,a921)),f296(x67051,x67052,x67053)),f298(x67051,x67053,x67054)),f181(f932(x67051,a921)))
% 25.54/25.41 [6706]~P110(x67061)+E(f862(f862(f94(f932(x67061,a921)),f296(x67061,x67062,x67063)),f297(x67061,x67063,x67064)),f181(f932(x67061,a921)))
% 25.54/25.41 [6744]P1(f862(f862(x67441,x67442),f561(x67442,x67441)))+~P1(f862(f241(x67443,x67444,x67441),x67442))
% 25.54/25.41 [6821]~P109(x68212)+E(f862(f165(x68211),f143(x68211,x68212,x68213,x68214)),f862(f165(x68211),x68214))
% 25.54/25.41 [6872]~P147(x68721)+E(f183(x68721,x68722,f862(a105,x68723),x68724),f183(x68721,x68722,x68723,f862(x68722,x68724)))
% 25.54/25.41 [6931]~P1(f862(f862(f321(x69314),x69313),f284(x69314,x69311,x69312)))+P1(f862(f862(x69311,x69312),x69313))
% 25.54/25.41 [6932]~P1(f862(f862(f321(x69324),x69323),f285(x69324,x69321,x69322)))+P1(f862(f862(x69321,x69322),x69323))
% 25.54/25.41 [6933]~P1(f862(f862(f321(x69334),x69332),f286(x69334,x69331,x69333)))+P1(f862(f862(x69331,x69332),x69333))
% 25.54/25.41 [6934]~P1(f862(f862(f321(x69344),x69342),f289(x69344,x69341,x69343)))+P1(f862(f862(x69341,x69342),x69343))
% 25.54/25.41 [7012]E(f862(f28(f930(x70121,x70122)),f305(x70121,x70122,x70123,x70124)),f2(a924))+P1(f862(f54(x70122),x70124))
% 25.54/25.41 [7013]E(f862(f28(f930(x70131,x70132)),f305(x70131,x70132,x70133,x70134)),f2(a924))+P1(f862(f54(x70131),x70133))
% 25.54/25.41 [7215]~P12(x72154,x72151,x72152)+E(f862(f66(x72151,x72151,x72151,f862(x72152,x72153)),f862(x72152,x72153)),f862(x72152,x72153))
% 25.54/25.41 [7460]E(f269(x74601,x74602,x74603,x74604),f862(f244(f932(a92,f932(a921,f928(f926(x74601)))),f931(a92,a92)),f34(x74601)))+~P1(f862(f862(f227(a92),x74603),f2(a92)))
% 25.54/25.41 [8106]~E(x81062,x81063)+P1(f862(f862(f321(f931(x81061,x81061)),f862(f862(f244(x81061,x81061),x81062),x81063)),f299(x81061,x81064)))
% 25.54/25.41 [8135]~P22(x81351,x81352,x81353,f234(f932(x81351,a921)))+E(f862(f70(x81351,x81352,f234(f932(x81351,a921)),x81353),f862(x81353,x81354)),x81354)
% 25.54/25.41 [8136]~P22(x81361,x81362,x81363,f234(f932(x81361,a921)))+E(f862(f86(x81361,x81362,f234(f932(x81361,a921)),x81363),f862(x81363,x81364)),x81364)
% 25.54/25.41 [8226]~P1(f862(f862(f321(f925(x82261)),f862(f862(f144(x82261),x82264),x82262)),f154(x82261,x82263)))+P1(f862(f862(f321(f925(x82261)),x82262),f154(x82261,x82263)))
% 25.54/25.41 [8227]~P1(f862(f862(f321(f925(x82271)),f862(f862(f127(x82271),x82274),x82272)),f154(x82271,x82273)))+P1(f862(f862(f321(f925(x82271)),x82272),f154(x82271,x82273)))
% 25.54/25.41 [8228]~P1(f862(f862(f321(f925(x82281)),f862(f862(f127(x82281),x82282),x82284)),f154(x82281,x82283)))+P1(f862(f862(f321(f925(x82281)),x82282),f154(x82281,x82283)))
% 25.54/25.41 [8239]~P109(x82391)+P11(x82391,f862(f862(f147(x82392,x82391),x82393),f143(x82392,x82391,x82393,x82394)))
% 25.54/25.41 [8346]P22(x83464,x83463,x83461,x83462)+E(f862(x83461,f537(x83462,x83461,x83463,x83464)),f862(x83461,f538(x83462,x83461,x83463,x83464)))
% 25.54/25.41 [8453]~P22(x84532,x84531,x84534,x84533)+P22(x84531,x84532,f70(x84532,x84531,x84533,x84534),f862(f302(x84532,x84531,x84534),x84533))
% 25.54/25.41 [8593]P35(f931(x85932,x85934),f272(x85932,x85934,x85931,x85933))+P1(f862(x85931,f558(x85932,x85933,x85934,x85931)))
% 25.54/25.41 [8711]E(x87111,x87112)+~P1(f862(f862(f321(f931(x87113,x87113)),f862(f862(f244(x87113,x87113),x87111),x87112)),f255(x87113,x87114)))
% 25.54/25.41 [8774]~P1(f862(f54(f930(x87743,x87741)),f305(x87743,x87741,x87744,x87742)))+P1(f862(f54(x87741),x87742))
% 25.54/25.41 [8775]~P1(f862(f54(f930(x87751,x87753)),f305(x87751,x87753,x87752,x87754)))+P1(f862(f54(x87751),x87752))
% 25.54/25.41 [8776]~P1(f862(f54(f930(x87763,x87761)),f305(x87763,x87761,x87764,x87762)))+P1(f862(f54(x87761),x87762))
% 25.54/25.41 [8777]~P1(f862(f54(f930(x87771,x87773)),f305(x87771,x87773,x87772,x87774)))+P1(f862(f54(x87771),x87772))
% 25.54/25.41 [8786]~P22(x87861,x87862,x87863,x87864)+P23(x87861,x87862,x87863,x87864,f862(f302(x87861,x87862,x87863),x87864))
% 25.54/25.41 [8787]P9(x87871,x87872,x87873,x87874)+~E(f862(x87874,f834(x87872,x87874,x87873,x87871)),f862(x87874,f835(x87872,x87874,x87873,x87871)))
% 25.54/25.41 [8877]~P23(x88772,x88773,x88774,x88771,f181(f932(x88773,a921)))+E(x88771,f181(f932(x88772,a921)))
% 25.54/25.41 [8878]~P23(x88783,x88782,x88784,f181(f932(x88783,a921)),x88781)+E(x88781,f181(f932(x88782,a921)))
% 25.54/25.41 [8971]P35(f931(x89711,x89712),f272(x89711,x89712,x89713,x89714))+~P35(x89712,f862(x89714,f558(x89711,x89714,x89712,x89713)))
% 25.54/25.41 [9537]E(f862(f862(f152(x95371,x95372),f675(x95373,x95374,x95372,x95371)),f676(x95373,x95374,x95372,x95371)),x95374)+~P1(f862(f862(f321(f931(f925(x95371),f925(x95371))),f862(f862(f244(f925(x95371),f925(x95371)),x95372),x95374)),f150(x95371,x95373)))
% 25.54/25.41 [9543]~P1(f862(f862(f321(f931(f925(x95431),f925(x95431))),f862(f862(f244(f925(x95431),f925(x95431)),x95432),x95433)),f138(x95431,x95434)))+P1(f862(f862(f321(f931(f925(x95431),f925(x95431))),f862(f862(f244(f925(x95431),f925(x95431)),x95432),x95433)),f140(x95431,x95434)))
% 25.54/25.41 [9656]P1(f862(f54(x96561),x96562))+~P1(f862(f862(f321(f931(f932(x96561,a921),f932(x96561,a921))),f862(f862(f244(f932(x96561,a921),f932(x96561,a921)),x96563),x96562)),f310(x96561,x96564)))
% 25.54/25.41 [9657]P1(f862(f54(x96571),x96572))+~P1(f862(f862(f321(f931(f932(x96571,a921),f932(x96571,a921))),f862(f862(f244(f932(x96571,a921),f932(x96571,a921)),x96572),x96573)),f310(x96571,x96574)))
% 25.54/25.41 [9660]~E(x96601,f181(f932(x96602,a921)))+~P1(f862(f862(f321(f931(f932(x96602,a921),f932(x96602,a921))),f862(f862(f244(f932(x96602,a921),f932(x96602,a921)),x96603),x96601)),f310(x96602,x96604)))
% 25.54/25.41 [10290]P9(x102901,x102902,x102903,x102904)+~P1(f862(f862(f249(x102901,x102901,a921),f862(f862(f9(x102901,f932(x102901,x102902),f932(x102901,a921)),f862(f862(f10(f932(x102902,a921),f932(f932(x102901,x102902),f932(x102901,a921)),x102901),f10(x102902,a921,x102901)),f862(f862(f10(x102902,f932(x102902,a921),x102901),a317),x102904))),x102904)),f593(x102904,x102903,x102902,x102901)))
% 25.54/25.41 [5136]~E(x51364,f106(x51361))+E(f862(f862(f147(x51361,x51362),x51363),x51364),f106(x51362))
% 25.54/25.41 [5137]~E(x51372,f106(x51371))+E(f862(f862(f152(x51371,x51372),x51373),x51374),f106(x51371))
% 25.54/25.41 [5138]~E(x51384,f106(x51381))+E(f862(f862(f147(x51381,x51382),x51383),x51384),f106(x51382))
% 25.54/25.41 [5373]E(x53731,f106(x53732))+~E(f862(f862(f147(x53732,x53733),x53734),x53731),f106(x53733))
% 25.54/25.41 [5374]E(x53741,f106(x53742))+~E(f862(f862(f147(x53742,x53743),x53744),x53741),f106(x53743))
% 25.54/25.41 [5375]E(x53751,f106(x53752))+~E(f862(f862(f152(x53752,x53751),x53753),x53754),f106(x53752))
% 25.54/25.41 [5414]E(x54141,x54142)+~E(f862(f862(f127(x54143),x54144),x54141),f862(f862(f127(x54143),x54144),x54142))
% 25.54/25.41 [5415]E(x54151,x54152)+~E(f862(f862(f127(x54153),x54151),x54154),f862(f862(f127(x54153),x54152),x54154))
% 25.54/25.41 [5564]P1(f862(x55643,x55642))+E(f163(x55641,x55642,f862(f129(x55641,x55643),x55644)),f862(f129(x55641,x55643),x55644))
% 25.54/25.41 [5566]~P1(f862(x55662,x55663))+P31(x55661,x55662,f862(f862(f144(x55661),x55663),x55664))
% 25.54/25.41 [5576]E(x55761,x55762)+~E(f132(a924,f862(f295(a924,x55761),x55763)),f862(f862(f144(a924),x55762),x55764))
% 25.54/25.41 [5625]~P24(x56252,x56253)+P24(x56251,f862(f862(f67(x56252,x56251),x56253),x56254))
% 25.54/25.41 [5626]~P35(x56262,x56263)+P35(x56261,f862(f862(f279(x56262,x56261),x56263),x56264))
% 25.54/25.41 [5627]~P36(x56272,x56273)+P36(x56271,f862(f862(f279(x56272,x56271),x56273),x56274))
% 25.54/25.41 [5628]~P49(x56282,x56283)+P49(x56281,f862(f862(f279(x56282,x56281),x56283),x56284))
% 25.54/25.41 [5759]~P31(x57591,x57592,x57594)+P31(x57591,x57592,f862(f862(f144(x57591),x57593),x57594))
% 25.54/25.41 [5760]~P31(x57601,x57602,x57604)+P31(x57601,x57602,f862(f862(f127(x57601),x57603),x57604))
% 25.54/25.41 [5761]~P31(x57611,x57612,x57613)+P31(x57611,x57612,f862(f862(f127(x57611),x57613),x57614))
% 25.54/25.41 [5848]~E(x58481,f106(x58482))+~E(f862(f862(f127(x58482),x58483),f862(f862(f144(x58482),x58484),f106(x58482))),x58481)
% 25.54/25.41 [5873]~P29(x58733,x58731,f862(f862(f144(x58733),x58732),x58734))+P1(f862(x58731,x58732))
% 25.54/25.41 [5883]E(f107(x58831,x58832),x58833)+~E(f862(f862(f127(x58831),x58833),f862(f862(f144(x58831),x58834),f106(x58831))),x58832)
% 25.54/25.41 [5884]E(f137(x58841,x58842),x58843)+~E(f862(f862(f127(x58841),x58844),f862(f862(f144(x58841),x58843),f106(x58841))),x58842)
% 25.54/25.41 [5994]~E(f132(a924,f862(f295(a924,x59941),x59942)),f862(f862(f144(a924),x59943),x59944))+P1(f862(f862(f228(a924),x59941),x59942))
% 25.54/25.41 [6012]P29(x60121,x60122,x60123)+~P29(x60121,x60122,f862(f862(f144(x60121),x60124),x60123))
% 25.54/25.41 [6013]P29(x60131,x60132,x60133)+~P29(x60131,x60132,f862(f862(f127(x60131),x60134),x60133))
% 25.54/25.41 [6014]P29(x60141,x60142,x60143)+~P29(x60141,x60142,f862(f862(f127(x60141),x60143),x60144))
% 25.54/25.41 [6098]~E(f862(f96(a924),x60984),f2(a924))+E(f862(f862(f157(x60981),f862(f862(f144(x60981),x60982),x60983)),f862(f96(a924),x60984)),x60982)
% 25.54/25.41 [6210]E(x62101,f862(f862(f127(x62102),f862(f161(x62102),x62103)),f862(f862(f144(x62102),x62104),f106(x62102))))+~E(f862(f161(x62102),x62101),f862(f862(f144(x62102),x62104),x62103))
% 25.54/25.41 [6385]~P110(x63851)+E(f862(f862(f94(f932(x63851,a921)),f862(f295(x63851,x63852),x63853)),f862(f295(x63851,x63853),x63854)),f181(f932(x63851,a921)))
% 25.54/25.41 [6396]E(f862(f862(f157(x63961),f162(x63961,x63962,x63963)),x63964),x63963)+~P1(f862(f862(f228(a924),x63964),x63962))
% 25.54/25.41 [6423]~P72(x64231)+E(f862(f158(x64231),f862(f862(f147(a1,x64231),x64232),f171(x64233,x64234))),f862(f862(f8(a1,x64231),x64232),f862(f165(a1),f171(x64233,x64234))))
% 25.54/25.41 [6424]~P72(x64241)+E(f862(f862(f8(a1,x64241),x64242),f862(f165(a1),f171(x64243,x64244))),f862(f158(x64241),f862(f862(f147(a1,x64241),x64242),f171(x64243,x64244))))
% 25.54/25.41 [6569]~E(x65692,f862(f862(f127(x65691),f862(f161(x65691),x65694)),f862(f862(f144(x65691),x65693),f106(x65691))))+E(f862(f161(x65691),x65692),f862(f862(f144(x65691),x65693),x65694))
% 25.54/25.41 [6585]~P17(x65852,x65853,x65854,x65851)+E(f862(x65851,f181(f932(x65852,a921))),f25(x65853))
% 25.54/25.41 [6613]~P110(x66131)+E(f862(f862(f94(f932(x66131,a921)),f298(x66131,x66132,x66133)),f862(f295(x66131,x66133),x66134)),f181(f932(x66131,a921)))
% 25.54/25.41 [6822]E(x68221,f181(f932(x68222,a921)))+~E(f305(x68223,x68222,x68224,x68221),f181(f932(f930(x68223,x68222),a921)))
% 25.54/25.41 [6823]E(x68231,f181(f932(x68232,a921)))+~E(f305(x68232,x68233,x68231,x68234),f181(f932(f930(x68232,x68233),a921)))
% 25.54/25.41 [6892]~P109(x68922)+E(f862(f182(f925(x68921)),f143(x68921,x68922,x68923,x68924)),f862(f182(f925(x68921)),x68924))
% 25.54/25.41 [6903]~P1(f862(f242(x69033,x69034,x69031),x69032))+P1(f862(f862(x69031,f562(x69032,x69031)),x69032))
% 25.54/25.41 [6927]E(f862(f96(a924),x69271),f2(a924))+E(f862(f862(f157(x69272),f862(f862(f144(x69272),x69273),x69274)),f862(f96(a924),x69271)),f862(f862(f157(x69272),x69274),f862(f862(f3(a924),f862(f96(a924),x69271)),f71(a924))))
% 25.54/25.41 [6945]~P1(f862(f54(x69452),x69454))+P1(f862(f54(x69451),f862(f302(x69452,x69451,x69453),x69454)))
% 25.54/25.41 [7177]~P22(x71772,x71771,x71773,x71774)+E(f862(f28(x71771),f862(f302(x71772,x71771,x71773),x71774)),f862(f28(x71772),x71774))
% 25.54/25.41 [7195]E(f862(f302(x71951,x71952,x71953),f862(f303(x71951,x71952,x71953),x71954)),x71954)+~E(f862(f302(x71951,x71952,x71953),f234(f932(x71951,a921))),f234(f932(x71952,a921)))
% 25.54/25.41 [7616]~P22(x76161,x76162,x76163,f234(f932(x76161,a921)))+E(f862(f303(x76161,x76162,x76163),f862(f302(x76161,x76162,x76163),x76164)),x76164)
% 25.54/25.41 [7899]E(x78991,x78992)+~P1(f862(f862(f321(x78993),x78991),f862(f165(x78993),f162(x78993,x78994,x78992))))
% 25.54/25.41 [7908]~E(x79081,f2(a924))+~P1(f862(f862(f321(x79082),x79083),f862(f165(x79082),f162(x79082,x79081,x79084))))
% 25.54/25.41 [7941]P1(f862(x79411,x79412))+~P1(f862(f862(f321(x79413),x79412),f862(f165(x79413),f170(x79413,x79411,x79414))))
% 25.54/25.41 [8051]~P1(f862(f862(f321(f925(x80511)),f862(f862(f144(x80511),x80512),x80514)),f154(x80511,x80513)))+P1(f862(f862(f321(x80511),x80512),x80513))
% 25.54/25.41 [8181]~P1(f862(f862(f321(x81811),x81812),f862(f165(x81811),f169(x81811,x81813,x81814))))+P1(f862(f862(f321(x81811),x81812),f862(f165(x81811),x81813)))
% 25.54/25.41 [8182]~P1(f862(f862(f321(x81821),x81822),f862(f165(x81821),f169(x81821,x81823,x81824))))+P1(f862(f862(f321(x81821),x81822),f862(f165(x81821),x81823)))
% 25.54/25.41 [8183]~P1(f862(f862(f321(x81831),x81832),f862(f165(x81831),f163(x81831,x81834,x81833))))+P1(f862(f862(f321(x81831),x81832),f862(f165(x81831),x81833)))
% 25.54/25.41 [8184]~P1(f862(f862(f321(x81841),x81842),f862(f165(x81841),f170(x81841,x81844,x81843))))+P1(f862(f862(f321(x81841),x81842),f862(f165(x81841),x81843)))
% 25.54/25.41 [8194]E(f862(f182(f925(x81941)),x81942),x81943)+~P1(f862(f862(f321(f925(x81941)),x81942),f862(f165(f925(x81941)),f48(x81941,x81943,x81944))))
% 25.54/25.41 [8291]P1(f862(x82913,x82912))+E(f862(f129(x82911,f862(f862(f10(a921,a921,x82911),a314),f862(a317,x82912))),f862(f129(x82911,x82913),x82914)),f862(f129(x82911,x82913),x82914))
% 25.54/25.41 [8405]E(f862(f862(f157(x84051),f170(x84051,x84052,x84053)),x84054),f862(f862(f157(x84051),x84053),x84054))+~P1(f862(f862(f228(a924),x84054),f862(f182(f925(x84051)),f170(x84051,x84052,x84053))))
% 25.54/25.41 [8491]~P72(x84911)+E(f862(f862(f8(a924,x84911),f862(f862(f10(a924,x84911,a924),x84912),a105)),f862(f295(a924,x84913),x84914)),f862(f862(f8(a924,x84911),x84912),f862(f295(a924,f862(a105,x84913)),f862(a105,x84914))))
% 25.54/25.41 [8500]~P72(x85001)+E(f862(f862(f8(a924,x85001),f862(f862(f10(a924,x85001,a924),x85002),a105)),f296(a924,x85003,x85004)),f862(f862(f8(a924,x85001),x85002),f296(a924,f862(a105,x85003),f862(a105,x85004))))
% 25.54/25.41 [8630]~P22(x86301,x86303,x86304,f234(f932(x86301,a921)))+P22(x86301,f932(x86302,x86303),f862(f862(f10(x86303,f932(x86302,x86303),x86301),f18(x86303,x86302)),x86304),f234(f932(x86301,a921)))
% 25.54/25.41 [8717]~P22(x87172,x87171,x87174,x87173)+E(f862(f302(x87171,x87172,f70(x87172,x87171,x87173,x87174)),f862(f302(x87172,x87171,x87174),x87173)),x87173)
% 25.54/25.41 [8778]~P1(f862(f862(f321(f931(x87781,x87781)),f862(f862(f244(x87781,x87781),x87782),x87784)),f255(x87781,x87783)))+P1(f862(f862(f321(x87781),x87782),x87783))
% 25.54/25.41 [8901]~P22(x89012,x89011,x89013,f234(f932(x89012,a921)))+E(f862(f302(x89011,x89012,f86(x89012,x89011,f234(f932(x89012,a921)),x89013)),f862(f302(x89012,x89011,x89013),x89014)),x89014)
% 25.54/25.41 [8902]~P22(x89022,x89021,x89023,f234(f932(x89022,a921)))+E(f862(f302(x89021,x89022,f86(x89022,x89021,f234(f932(x89022,a921)),x89023)),f862(f302(x89022,x89021,x89023),x89024)),x89024)
% 25.54/25.41 [8977]~P23(x89771,x89772,x89773,x89774,f234(f932(x89772,a921)))+E(f862(f302(x89771,x89772,x89773),f234(f932(x89771,a921))),f234(f932(x89772,a921)))
% 25.54/25.41 [9010]~E(f862(f862(f8(x90101,a924),x90104),x90103),f862(a105,x90102))+P1(f862(f862(f321(x90101),f373(x90102,x90103,x90104,x90101)),x90103))
% 25.54/25.41 [9032]~E(f862(f862(f8(x90324,a924),x90321),x90323),f862(a105,x90322))+P1(f862(f862(f228(a924),f2(a924)),f862(x90321,f373(x90322,x90323,x90321,x90324))))
% 25.54/25.41 [9044]~P1(f862(f54(x90442),x90444))+P1(f862(f862(f227(a924),f862(f28(x90441),f862(f302(x90442,x90441,x90443),x90444))),f862(f28(x90442),x90444)))
% 25.54/25.41 [9045]E(f862(f862(f244(x90451,x90452),f647(x90453,x90454,x90452,x90451)),f648(x90453,x90454,x90452,x90451)),x90454)+~P1(f862(f862(f321(f931(x90451,x90452)),x90454),f862(f277(x90452,x90451),x90453)))
% 25.54/25.41 [9053]P22(x90531,x90532,x90533,x90534)+P1(f862(f862(f321(x90531),f537(x90534,x90533,x90532,x90531)),x90534))
% 25.54/25.41 [9054]P22(x90541,x90542,x90543,x90544)+P1(f862(f862(f321(x90541),f538(x90544,x90543,x90542,x90541)),x90544))
% 25.54/25.41 [9122]P9(x91221,x91222,x91223,x91224)+P1(f862(f862(f321(f931(x91221,x91221)),f593(x91224,x91223,x91222,x91221)),x91223))
% 25.54/25.41 [9176]P1(f862(x91761,x91762))+~P1(f862(x91761,f862(f862(f244(x91763,x91764),f495(x91764,x91763,x91761)),f496(x91764,x91763,x91761))))
% 25.54/25.41 [9193]E(f862(f182(f925(x91931)),x91932),f862(f182(f925(x91931)),x91933))+~P1(f862(f862(f321(f931(f925(x91931),f925(x91931))),f862(f862(f244(f925(x91931),f925(x91931)),x91932),x91933)),f138(x91931,x91934)))
% 25.54/25.41 [9194]E(f862(f182(f925(x91941)),x91942),f862(f182(f925(x91941)),x91943))+~P1(f862(f862(f321(f931(f925(x91941),f925(x91941))),f862(f862(f244(f925(x91941),f925(x91941)),x91942),x91943)),f150(x91941,x91944)))
% 25.54/25.41 [9195]E(f862(f182(f925(x91951)),x91952),f862(f182(f925(x91951)),x91953))+~P1(f862(f862(f321(f931(f925(x91951),f925(x91951))),f862(f862(f244(f925(x91951),f925(x91951)),x91952),x91953)),f151(x91951,x91954)))
% 25.54/25.41 [9196]E(f862(f182(f925(x91961)),x91962),f862(f182(f925(x91961)),x91963))+~P1(f862(f862(f321(f931(f925(x91961),f925(x91961))),f862(f862(f244(f925(x91961),f925(x91961)),x91962),x91963)),f151(x91961,x91964)))
% 25.54/25.41 [9197]E(f862(f182(f925(x91971)),x91972),f862(f182(f925(x91971)),x91973))+~P1(f862(f862(f321(f931(f925(x91971),f925(x91971))),f862(f862(f244(f925(x91971),f925(x91971)),x91972),x91973)),f151(x91971,x91974)))
% 25.54/25.41 [9266]P1(f862(f862(f227(a924),f148(x92661,x92662,x92663)),f148(x92661,x92664,x92663)))+P1(f862(f862(f321(x92661),f674(x92664,x92662,x92663,x92661)),f862(f165(x92661),x92663)))
% 25.54/25.41 [9269]E(f862(f182(f925(x92691)),x92692),f862(f182(f925(x92691)),x92693))+~P1(f862(f862(f321(f931(f925(x92691),f925(x92691))),f862(f862(f244(f925(x92691),f925(x92691)),x92692),x92693)),f299(f925(x92691),f150(x92691,x92694))))
% 25.54/25.41 [9389]P1(f862(f862(f278(a924),x93891),x93892))+P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x93891,x93892)),f287(a924,f278(a924),x93893,x93894)))
% 25.54/25.41 [9508]~P22(x95081,x95082,x95083,x95084)+~P1(f862(f862(f228(a924),f862(f28(x95082),f862(f302(x95081,x95082,x95083),x95084))),f862(f28(x95081),x95084)))
% 25.54/25.41 [9556]~P1(f862(f862(f321(f931(f925(x95561),f925(x95561))),f862(f862(f244(f925(x95561),f925(x95561)),x95562),x95563)),f150(x95561,x95564)))+P1(f862(f862(f321(f931(f925(x95561),f925(x95561))),f862(f862(f244(f925(x95561),f925(x95561)),x95562),x95563)),f151(x95561,f299(x95561,x95564))))
% 25.54/25.41 [9560]~P1(f862(f862(f321(f931(f925(x95601),f925(x95601))),f862(f862(f244(f925(x95601),f925(x95601)),x95602),x95603)),f151(x95601,x95604)))+P1(f862(f862(f321(f931(f925(x95601),f925(x95601))),f862(f862(f244(f925(x95601),f925(x95601)),x95602),x95603)),f299(f925(x95601),f150(x95601,x95604))))
% 25.54/25.41 [9577]P1(f862(f862(f321(f931(x95771,x95771)),f862(f862(f244(x95771,x95771),x95772),x95773)),f299(x95771,x95774)))+~P1(f862(f862(f321(f931(x95771,x95771)),f862(f862(f244(x95771,x95771),x95772),x95773)),f862(f862(f280(x95771,x95771,x95771),x95774),f299(x95771,x95774))))
% 25.54/25.41 [9767]E(f862(f862(f127(x97671),f690(x97672,x97673,x97674,x97671)),f862(f862(f144(x97671),f691(x97672,x97673,x97674,x97671)),f693(x97672,x97673,x97674,x97671))),x97674)+~P1(f862(f862(f321(f931(f925(x97671),f925(x97671))),f862(f862(f244(f925(x97671),f925(x97671)),x97674),x97673)),f150(x97671,x97672)))
% 25.54/25.41 [9768]E(f862(f862(f127(x97681),f690(x97682,x97683,x97684,x97681)),f862(f862(f144(x97681),f692(x97682,x97683,x97684,x97681)),f693(x97682,x97683,x97684,x97681))),x97683)+~P1(f862(f862(f321(f931(f925(x97681),f925(x97681))),f862(f862(f244(f925(x97681),f925(x97681)),x97684),x97683)),f150(x97681,x97682)))
% 25.54/25.41 [9846]P1(f862(f862(f321(f931(x98461,x98461)),f862(f862(f244(x98461,x98461),x98462),f645(x98463,x98464,x98462,x98461))),f299(x98461,x98463)))+~P1(f862(f862(f321(f931(x98461,x98461)),f862(f862(f244(x98461,x98461),x98462),x98464)),f862(f862(f280(x98461,x98461,x98461),x98463),f299(x98461,x98463))))
% 25.54/25.41 [9915]P1(f862(f862(f227(a924),f148(x99151,x99152,x99153)),f148(x99151,x99154,x99153)))+~P1(f862(f862(f228(a924),f862(x99152,f674(x99154,x99152,x99153,x99151))),f862(x99154,f674(x99154,x99152,x99153,x99151))))
% 25.54/25.41 [9987]P1(f862(f862(f321(f931(x99871,x99871)),f862(f862(f244(x99871,x99871),f637(x99872,x99873,x99874,x99871)),x99873)),f299(x99871,x99872)))+~P1(f862(f862(f321(f931(x99871,x99871)),f862(f862(f244(x99871,x99871),x99874),x99873)),f862(f862(f280(x99871,x99871,x99871),x99872),f299(x99871,x99872))))
% 25.54/25.41 [5395]~E(x53952,x53953)+E(f163(x53951,x53952,f862(f862(f144(x53951),x53953),x53954)),x53954)
% 25.54/25.41 [5408]~E(x54082,f2(a924))+E(f862(f862(f168(x54081),x54082),f862(f862(f144(x54081),x54083),x54084)),f106(x54081))
% 25.54/25.41 [5519]P1(f862(x55192,x55193))+E(f170(x55191,x55192,f862(f862(f144(x55191),x55193),x55194)),f106(x55191))
% 25.54/25.41 [5587]~P82(x55872)+E(f862(f862(f72(f932(x55871,x55872)),x55873),x55874),f862(f72(x55872),f862(x55873,x55874)))
% 25.54/25.41 [5588]~P82(x55882)+E(f862(f862(f72(f932(x55881,x55882)),x55883),x55884),f862(f72(x55882),f862(x55883,x55884)))
% 25.54/25.41 [5601]~E(x56012,f2(a924))+E(f862(f862(f131(x56011),x56012),f862(f862(f144(x56011),x56013),x56014)),f862(f862(f144(x56011),x56013),x56014))
% 25.54/25.41 [5602]P1(f862(x56022,x56023))+E(f862(f129(x56021,x56022),f862(f862(f144(x56021),x56023),x56024)),f862(f129(x56021,x56022),x56024))
% 25.54/25.41 [5741]~E(x57412,x57414)+P1(f862(f862(f862(f301(x57411),x57412),x57413),x57414))
% 25.54/25.41 [5750]E(x57501,f106(x57502))+E(f137(x57503,f862(f862(f147(x57502,x57503),x57504),x57501)),f862(x57504,f137(x57502,x57501)))
% 25.54/25.41 [5764]~E(x57641,f56(x57642,x57644))+E(f862(x57641,f862(f862(f301(x57642),x57643),f181(f932(x57642,a921)))),x57643)
% 25.54/25.41 [5781]~E(f862(f96(a924),x57812),f2(a924))+E(f862(f862(f168(x57811),f862(f96(a924),x57812)),f862(f862(f144(x57811),x57813),x57814)),f106(x57811))
% 25.54/25.41 [5800]E(x58001,f106(x58002))+E(f862(f134(x58003),f862(f862(f147(x58002,x58003),x58004),x58001)),f862(x58004,f862(f134(x58002),x58001)))
% 25.54/25.41 [5903]~P1(f862(x59033,x59034))+P1(f862(f862(f862(f301(x59031),x59032),x59033),x59034))
% 25.54/25.41 [6015]~E(f862(f96(a924),x60152),f2(a924))+E(f862(f862(f131(x60151),f862(f96(a924),x60152)),f862(f862(f144(x60151),x60153),x60154)),f862(f862(f144(x60151),x60153),x60154))
% 25.54/25.41 [6031]~P16(x60312,x60314,x60311)+E(f862(x60311,f862(f862(f301(x60312),x60313),f181(f932(x60312,a921)))),x60313)
% 25.54/25.41 [6056]~E(x60562,x60563)+P1(f862(f862(f321(x60561),x60562),f862(f862(f301(x60561),x60563),x60564)))
% 25.54/25.41 [6057]~E(x60572,x60573)+P1(f862(f862(f321(x60571),x60572),f862(f862(f301(x60571),x60573),x60574)))
% 25.54/25.41 [6062]~P93(x60621)+E(f862(f862(f103(x60621),x60622),f862(f862(f103(x60621),x60623),x60624)),f862(f862(f103(x60621),x60623),f862(f862(f103(x60621),x60622),x60624)))
% 25.54/25.41 [6063]~P103(x60631)+E(f862(f862(f103(x60631),x60632),f862(f862(f103(x60631),x60633),x60634)),f862(f862(f103(x60631),x60633),f862(f862(f103(x60631),x60632),x60634)))
% 25.54/25.41 [6064]~P103(x60641)+E(f862(f862(f103(x60641),x60642),f862(f862(f103(x60641),x60643),x60644)),f862(f862(f103(x60641),x60643),f862(f862(f103(x60641),x60642),x60644)))
% 25.54/25.41 [6065]~P93(x60651)+E(f862(f862(f94(x60651),x60652),f862(f862(f94(x60651),x60653),x60654)),f862(f862(f94(x60651),x60653),f862(f862(f94(x60651),x60652),x60654)))
% 25.54/25.41 [6066]~P104(x60661)+E(f862(f862(f94(x60661),x60662),f862(f862(f94(x60661),x60663),x60664)),f862(f862(f94(x60661),x60663),f862(f862(f94(x60661),x60662),x60664)))
% 25.54/25.41 [6067]~P104(x60671)+E(f862(f862(f94(x60671),x60672),f862(f862(f94(x60671),x60673),x60674)),f862(f862(f94(x60671),x60673),f862(f862(f94(x60671),x60672),x60674)))
% 25.54/25.41 [6068]~P119(x60681)+E(f862(f862(f74(x60681),x60682),f862(f862(f74(x60681),x60683),x60684)),f862(f862(f74(x60681),x60683),f862(f862(f74(x60681),x60682),x60684)))
% 25.54/25.41 [6069]~P119(x60691)+E(f862(f862(f73(x60691),x60692),f862(f862(f73(x60691),x60693),x60694)),f862(f862(f73(x60691),x60693),f862(f862(f73(x60691),x60692),x60694)))
% 25.54/25.41 [6070]~P109(x60701)+E(f862(f862(f225(x60701),x60702),f862(f862(f225(x60701),x60703),x60704)),f862(f862(f225(x60701),x60703),f862(f862(f225(x60701),x60702),x60704)))
% 25.54/25.41 [6071]~P109(x60711)+E(f862(f862(f225(x60711),x60712),f862(f862(f225(x60711),x60713),x60714)),f862(f862(f225(x60711),x60713),f862(f862(f225(x60711),x60712),x60714)))
% 25.54/25.41 [6072]~P109(x60721)+E(f862(f862(f226(x60721),x60722),f862(f862(f226(x60721),x60723),x60724)),f862(f862(f226(x60721),x60723),f862(f862(f226(x60721),x60722),x60724)))
% 25.54/25.41 [6073]~P109(x60731)+E(f862(f862(f226(x60731),x60732),f862(f862(f226(x60731),x60733),x60734)),f862(f862(f226(x60731),x60733),f862(f862(f226(x60731),x60732),x60734)))
% 25.54/25.41 [6080]E(x60801,x60802)+E(f163(x60803,x60801,f862(f862(f144(x60803),x60802),x60804)),f862(f862(f144(x60803),x60802),f163(x60803,x60801,x60804)))
% 25.54/25.41 [6095]~P1(f862(x60952,x60953))+E(f862(f129(x60951,x60952),f862(f862(f144(x60951),x60953),x60954)),f862(f862(f144(x60951),x60953),f862(f129(x60951,x60952),x60954)))
% 25.54/25.41 [6186]~E(x61864,f181(f932(x61861,a921)))+E(f862(f302(x61861,x61862,f862(f18(x61862,x61861),x61863)),x61864),f181(f932(x61862,a921)))
% 25.54/25.41 [6231]~P1(f862(x62312,x62313))+E(f170(x62311,x62312,f862(f862(f144(x62311),x62313),x62314)),f862(f862(f144(x62311),x62313),f170(x62311,x62312,x62314)))
% 25.54/25.41 [6293]E(x62931,f181(f932(x62932,a921)))+E(f862(f862(f32(x62932,f932(x62933,a921)),x62931),f862(f18(f932(x62933,a921),x62932),x62934)),x62934)
% 25.54/25.41 [6294]E(x62941,f181(f932(x62942,a921)))+E(f862(f862(f33(x62942,f932(x62943,a921)),x62941),f862(f18(f932(x62943,a921),x62942),x62944)),x62944)
% 25.54/25.41 [6303]~E(x63034,f181(f932(x63032,a921)))+E(f862(f862(f246(x63031,x63032),x63033),f862(f18(f932(x63032,a921),x63031),x63034)),f181(f932(f931(x63031,x63032),a921)))
% 25.54/25.41 [6304]~E(x63043,f181(f932(x63041,a921)))+E(f862(f862(f246(x63041,x63042),x63043),f862(f18(f932(x63042,a921),x63041),x63044)),f181(f932(f931(x63041,x63042),a921)))
% 25.54/25.41 [6356]E(x63561,f2(a924))+E(f862(f862(f131(x63562),x63561),f862(f862(f144(x63562),x63563),x63564)),f862(f862(f131(x63562),f862(f862(f3(a924),x63561),f71(a924))),x63564))
% 25.54/25.41 [6378]E(x63781,f181(f932(x63782,a921)))+E(f862(f302(x63782,x63783,f862(f18(x63783,x63782),x63784)),x63781),f862(f862(f301(x63783),x63784),f181(f932(x63783,a921))))
% 25.54/25.41 [6381]E(f862(f303(x63811,x63812,f862(f18(x63812,x63811),x63813)),x63814),f181(f932(x63811,a921)))+P1(f862(f862(f321(x63812),x63813),x63814))
% 25.54/25.41 [6447]~E(x64473,f181(f932(x64471,a921)))+E(f862(f862(f32(x64471,f932(x64472,a921)),x64473),f862(f18(f932(x64472,a921),x64471),x64474)),f234(f932(x64472,a921)))
% 25.54/25.41 [6448]~E(x64483,f181(f932(x64481,a921)))+E(f862(f862(f33(x64481,f932(x64482,a921)),x64483),f862(f18(f932(x64482,a921),x64481),x64484)),f181(f932(x64482,a921)))
% 25.54/25.41 [6450]~P61(x64501)+E(f38(x64501,f862(f862(f74(x64501),x64502),x64503),f862(f862(f74(x64501),x64502),x64504)),f862(f862(f74(x64501),x64502),f38(x64501,x64503,x64504)))
% 25.54/25.41 [6623]E(f862(f303(x66231,x66232,f862(f18(x66232,x66231),x66233)),x66234),f234(f932(x66231,a921)))+~P1(f862(f862(f321(x66232),x66233),x66234))
% 25.54/25.41 [6644]~P1(f862(f862(f321(x66441),x66442),x66444))+P1(f862(f862(f321(x66441),x66442),f862(f862(f301(x66441),x66443),x66444)))
% 25.54/25.41 [6645]~P1(f862(f862(f321(x66451),x66452),x66454))+P1(f862(f862(f321(x66451),x66452),f862(f862(f301(x66451),x66453),x66454)))
% 25.54/25.41 [6646]~P1(f862(f862(f321(x66461),x66462),x66464))+P1(f862(f862(f321(x66461),x66462),f862(f862(f301(x66461),x66463),x66464)))
% 25.54/25.41 [6651]P1(f862(x66511,x66512))+~P1(f862(f153(x66513,x66511),f862(f862(f144(x66513),x66512),x66514)))
% 25.54/25.41 [6660]~E(x66603,f862(f862(f3(a924),f862(f182(f925(x66601)),x66602)),f71(a924)))+E(f107(x66601,f862(f862(f152(x66601,x66602),x66603),x66604)),f107(x66601,x66602))
% 25.54/25.41 [6680]~P109(x66801)+E(f862(f862(f94(f932(x66801,a921)),f862(f294(x66801),x66802)),f296(x66801,x66803,x66804)),f296(x66801,x66803,f862(f862(f225(x66801),x66802),x66804)))
% 25.54/25.41 [6681]~P109(x66811)+E(f862(f862(f94(f932(x66811,a921)),f862(f274(x66811),x66812)),f296(x66811,x66813,x66814)),f296(x66811,f862(f862(f226(x66811),x66812),x66813),x66814))
% 25.54/25.41 [6696]E(f862(f862(f94(f932(x66961,a921)),x66962),f862(f862(f301(x66961),x66963),x66964)),f862(f862(f94(f932(x66961,a921)),x66962),x66964))+P1(f862(f862(f321(x66961),x66963),x66962))
% 25.54/25.41 [6697]E(f862(f862(f94(f932(x66971,a921)),x66972),f862(f862(f301(x66971),x66973),x66974)),f862(f862(f94(f932(x66971,a921)),x66972),x66974))+P1(f862(f862(f321(x66971),x66973),x66972))
% 25.54/25.41 [6709]E(f163(x67091,x67092,f862(f862(f127(x67091),x67093),x67094)),f862(f862(f127(x67091),x67093),f163(x67091,x67092,x67094)))+P1(f862(f862(f321(x67091),x67092),f862(f165(x67091),x67093)))
% 25.54/25.41 [6714]~P80(x67141)+E(f862(f862(f74(x67141),f862(f862(f236(x67141),x67142),x67143)),f862(f862(f236(x67141),x67142),x67144)),f862(f862(f236(x67141),x67142),f862(f862(f73(a924),x67143),x67144)))
% 25.54/25.41 [6715]~P119(x67151)+E(f862(f862(f74(x67151),f862(f862(f236(x67151),x67152),x67153)),f862(f862(f236(x67151),x67152),x67154)),f862(f862(f236(x67151),x67152),f862(f862(f73(a924),x67153),x67154)))
% 25.54/25.41 [6752]~P102(x67521)+E(f862(f862(f94(x67521),f862(f862(f103(x67521),x67522),x67523)),f862(f862(f103(x67521),x67522),x67524)),f862(f862(f103(x67521),x67522),f862(f862(f94(x67521),x67523),x67524)))
% 25.54/25.41 [6753]~P102(x67531)+E(f862(f862(f103(x67531),f862(f862(f94(x67531),x67532),x67533)),f862(f862(f94(x67531),x67532),x67534)),f862(f862(f94(x67531),x67532),f862(f862(f103(x67531),x67533),x67534)))
% 25.54/25.41 [6754]~P119(x67541)+E(f862(f862(f73(x67541),f862(f862(f74(x67541),x67542),x67543)),f862(f862(f74(x67541),x67542),x67544)),f862(f862(f74(x67541),x67542),f862(f862(f73(x67541),x67543),x67544)))
% 25.54/25.41 [6755]~P109(x67551)+E(f862(f862(f226(x67551),f862(f862(f225(x67551),x67552),x67553)),f862(f862(f225(x67551),x67552),x67554)),f862(f862(f225(x67551),x67552),f862(f862(f226(x67551),x67553),x67554)))
% 25.54/25.41 [6756]~P109(x67561)+E(f862(f862(f225(x67561),f862(f862(f226(x67561),x67562),x67563)),f862(f862(f226(x67561),x67562),x67564)),f862(f862(f226(x67561),x67562),f862(f862(f225(x67561),x67563),x67564)))
% 25.54/25.41 [6787]~P61(x67871)+E(f38(x67871,f862(f862(f74(x67871),x67872),x67873),f862(f862(f74(x67871),x67874),x67873)),f862(f862(f74(x67871),f38(x67871,x67872,x67874)),x67873))
% 25.54/25.41 [6790]~E(f862(f182(f925(x67901)),x67903),f862(f182(f925(x67902)),x67904))+E(f862(f862(f147(f931(x67901,x67902),x67902),f248(x67901,x67902)),f862(f862(f174(x67901,x67902),x67903),x67904)),x67904)
% 25.54/25.41 [6791]~E(f862(f182(f925(x67911)),x67913),f862(f182(f925(x67912)),x67914))+E(f862(f862(f147(f931(x67911,x67912),x67911),f243(x67911,x67912)),f862(f862(f174(x67911,x67912),x67913),x67914)),x67913)
% 25.54/25.41 [6796]P1(f862(f153(x67961,x67962),x67963))+~P1(f862(f153(x67961,x67962),f862(f862(f144(x67961),x67964),x67963)))
% 25.54/25.41 [6797]P1(f862(f153(x67971,x67972),x67973))+~P1(f862(f153(x67971,x67972),f862(f862(f127(x67971),x67974),x67973)))
% 25.54/25.41 [6798]P1(f862(f153(x67981,x67982),x67983))+~P1(f862(f153(x67981,x67982),f862(f862(f127(x67981),x67983),x67984)))
% 25.54/25.41 [6803]~P62(x68031)+E(f38(x68031,f862(f862(f3(x68031),x68032),f38(x68031,x68033,x68034)),x68034),f38(x68031,f862(f862(f3(x68031),x68032),x68033),x68034))
% 25.54/25.41 [6804]~P61(x68041)+E(f38(x68041,f862(f862(f74(x68041),x68042),f38(x68041,x68043,x68044)),x68044),f38(x68041,f862(f862(f74(x68041),x68042),x68043),x68044))
% 25.54/25.41 [6805]~P61(x68051)+E(f38(x68051,f862(f862(f73(x68051),x68052),f38(x68051,x68053,x68054)),x68054),f38(x68051,f862(f862(f73(x68051),x68052),x68053),x68054))
% 25.54/25.41 [6806]~P61(x68061)+E(f38(x68061,f862(f862(f73(x68061),x68062),f38(x68061,x68063,x68064)),x68064),f38(x68061,f862(f862(f73(x68061),x68062),x68063),x68064))
% 25.54/25.41 [6885]~P109(x68851)+E(f862(f862(f94(f932(x68851,a921)),f296(x68851,x68852,x68853)),f862(f294(x68851),x68854)),f296(x68851,x68852,f862(f862(f225(x68851),x68853),x68854)))
% 25.54/25.41 [6886]~P109(x68861)+E(f862(f862(f94(f932(x68861,a921)),f296(x68861,x68862,x68863)),f862(f274(x68861),x68864)),f296(x68861,f862(f862(f226(x68861),x68862),x68864),x68863))
% 25.54/25.41 [6889]~E(f862(f182(f925(x68891)),x68893),f862(f182(f925(x68892)),x68894))+E(f862(f862(f174(x68891,x68892),f862(f161(x68891),x68893)),f862(f161(x68892),x68894)),f862(f161(f931(x68891,x68892)),f862(f862(f174(x68891,x68892),x68893),x68894)))
% 25.54/25.41 [6900]E(x69001,f862(f862(f3(a924),f862(f182(f925(x69002)),x69003)),f71(a924)))+E(f107(x69002,f862(f862(f152(x69002,x69003),x69001),x69004)),f862(f862(f152(x69002,f107(x69002,x69003)),x69001),x69004))
% 25.54/25.41 [6914]~P1(f862(f130(x69142),x69144))+P1(f862(f130(f931(x69141,x69142)),f862(f862(f174(x69141,x69142),x69143),x69144)))
% 25.54/25.41 [6915]~P1(f862(f130(x69151),x69153))+P1(f862(f130(f931(x69151,x69152)),f862(f862(f174(x69151,x69152),x69153),x69154)))
% 25.54/25.41 [7180]E(f862(f862(f29(a924),x71801),x71802),x71803)+~P1(f862(f41(x71801,x71802),f862(f862(f244(a924,a924),x71803),x71804)))
% 25.54/25.41 [7203]E(f38(a924,x72031,x72032),x72033)+~P1(f862(f41(x72031,x72032),f862(f862(f244(a924,a924),x72034),x72033)))
% 25.54/25.41 [7206]P1(f862(f130(x72061),x72062))+~P1(f862(f130(x72063),f862(f862(f147(x72061,x72063),x72064),x72062)))
% 25.54/25.41 [7290]E(f163(x72901,x72902,f862(f862(f127(x72901),x72903),x72904)),f862(f862(f127(x72901),f163(x72901,x72902,x72903)),x72904))+~P1(f862(f862(f321(x72901),x72902),f862(f165(x72901),x72903)))
% 25.54/25.41 [7356]E(f862(f96(a924),x73561),f2(a924))+E(f862(f862(f131(x73562),f862(f96(a924),x73561)),f862(f862(f144(x73562),x73563),x73564)),f862(f862(f131(x73562),f862(f862(f3(a924),f862(f96(a924),x73561)),f71(a924))),x73564))
% 25.54/25.41 [7383]~P62(x73831)+E(f38(x73831,f862(f862(f3(x73831),f38(x73831,x73832,x73833)),x73834),x73833),f38(x73831,f862(f862(f3(x73831),x73832),x73834),x73833))
% 25.54/25.41 [7384]~P61(x73841)+E(f38(x73841,f862(f862(f74(x73841),f38(x73841,x73842,x73843)),x73844),x73843),f38(x73841,f862(f862(f74(x73841),x73842),x73844),x73843))
% 25.54/25.41 [7385]~P61(x73851)+E(f38(x73851,f862(f862(f73(x73851),f38(x73851,x73852,x73853)),x73854),x73853),f38(x73851,f862(f862(f73(x73851),x73852),x73854),x73853))
% 25.54/25.41 [7386]~P61(x73861)+E(f38(x73861,f862(f862(f74(x73861),f38(x73861,x73862,x73863)),x73864),x73863),f38(x73861,f862(f862(f74(x73861),x73862),x73864),x73863))
% 25.54/25.41 [7387]~P61(x73871)+E(f38(x73871,f862(f862(f73(x73871),f38(x73871,x73872,x73873)),x73874),x73873),f38(x73871,f862(f862(f73(x73871),x73872),x73874),x73873))
% 25.54/25.41 [7585]~E(x75851,f862(f862(f144(x75852),x75853),x75854))+~P1(f862(f862(f227(a924),f862(f182(f925(x75852)),x75851)),f862(f182(f925(x75852)),x75854)))
% 25.54/25.41 [7790]P22(x77901,x77902,x77903,f862(f165(x77901),x77904))+~P1(f862(f130(x77902),f862(f862(f147(x77901,x77902),x77903),x77904)))
% 25.54/25.41 [7865]~P1(f862(f862(f227(f932(x78651,a921)),x78652),x78654))+P1(f862(f862(f227(f932(x78651,a921)),x78652),f862(f862(f301(x78651),x78653),x78654)))
% 25.54/25.41 [7900]~P62(x79001)+E(f38(x79001,f862(f862(f3(x79001),f38(x79001,x79002,x79003)),f38(x79001,x79004,x79003)),x79003),f38(x79001,f862(f862(f3(x79001),x79002),x79004),x79003))
% 25.54/25.41 [7901]~P61(x79011)+E(f38(x79011,f862(f862(f74(x79011),f38(x79011,x79012,x79013)),f38(x79011,x79014,x79013)),x79013),f38(x79011,f862(f862(f74(x79011),x79012),x79014),x79013))
% 25.54/25.41 [7902]~P61(x79021)+E(f38(x79021,f862(f862(f73(x79021),f38(x79021,x79022,x79023)),f38(x79021,x79024,x79023)),x79023),f38(x79021,f862(f862(f73(x79021),x79022),x79024),x79023))
% 25.54/25.41 [8005]~E(f862(x80054,f466(x80054,x80053,x80051,x80052)),f181(f932(x80052,a921)))+E(f862(f862(f33(x80051,f932(x80052,a921)),x80053),x80054),f181(f932(x80052,a921)))
% 25.54/25.41 [8006]~E(f862(x80064,f486(x80064,x80063,x80061,x80062)),f234(f932(x80062,a921)))+E(f862(f862(f32(x80061,f932(x80062,a921)),x80063),x80064),f234(f932(x80062,a921)))
% 25.54/25.41 [8007]~E(f862(x80074,f489(x80074,x80073,x80072,x80071)),f234(f932(x80072,a921)))+E(f862(f862(f32(x80071,f932(x80072,a921)),x80073),x80074),f234(f932(x80072,a921)))
% 25.54/25.41 [8008]~E(f862(x80084,f487(x80084,x80083,x80082,x80081)),f181(f932(x80082,a921)))+E(f862(f862(f33(x80081,f932(x80082,a921)),x80083),x80084),f181(f932(x80082,a921)))
% 25.54/25.41 [8406]P1(f862(x84061,x84062))+~P1(f862(f862(f321(x84063),x84062),f862(f862(f94(f932(x84063,a921)),x84064),f862(f254(x84063),x84061))))
% 25.54/25.41 [8443]~P1(f862(f862(f227(f932(x84431,a921)),x84433),x84434))+P1(f862(f862(f227(f932(x84431,a921)),f862(f862(f301(x84431),x84432),x84433)),f862(f862(f301(x84431),x84432),x84434)))
% 25.54/25.41 [8487]P1(f862(f862(f321(x84871),x84872),x84873))+~P1(f862(f862(f321(x84871),x84872),f862(f862(f94(f932(x84871,a921)),x84873),f862(f254(x84871),x84874))))
% 25.54/25.41 [8623]P1(f862(x86232,x86233))+E(f862(f862(f131(x86231),f862(f182(f925(x86231)),f170(x86231,x86232,f862(f862(f144(x86231),x86233),x86234)))),f862(f862(f144(x86231),x86233),x86234)),f862(f862(f144(x86231),x86233),x86234))
% 25.54/25.41 [8731]~P1(f862(f862(f228(a924),f862(x87314,x87312)),f862(x87314,x87313)))+P1(f862(f862(f321(f931(x87311,x87311)),f862(f862(f244(x87311,x87311),x87312),x87313)),f862(f862(f279(a924,x87311),a232),x87314)))
% 25.54/25.41 [8828]~P1(f862(x88282,f747(x88284,x88282,x88283,x88281)))+E(f170(x88281,x88282,f862(f862(f127(x88281),x88283),x88284)),f862(f862(f127(x88281),x88283),f170(x88281,x88282,x88284)))
% 25.54/25.41 [8906]P22(f925(x89061),f925(x89062),f862(f147(x89061,x89062),x89063),x89064)+~P22(x89061,x89062,x89063,f30(f932(x89061,a921),f862(f302(f925(x89061),f932(x89061,a921),f165(x89061)),x89064)))
% 25.54/25.41 [8981]~P1(f862(x89812,x89813))+E(f862(f862(f131(x89811),f862(f182(f925(x89811)),f170(x89811,x89812,f862(f862(f144(x89811),x89813),x89814)))),f862(f862(f144(x89811),x89813),x89814)),f862(f862(f131(x89811),f862(f182(f925(x89811)),f170(x89811,x89812,x89814))),x89814))
% 25.54/25.41 [9022]~E(x90222,x90223)+E(f862(f129(x90221,f862(f862(f10(a921,a921,x90221),a314),f862(a317,x90222))),f862(f862(f144(x90221),x90223),x90224)),f862(f129(x90221,f862(f862(f10(a921,a921,x90221),a314),f862(a317,x90222))),x90224))
% 25.54/25.41 [9033]E(f862(f862(f33(x90331,f932(x90332,a921)),x90333),x90334),f181(f932(x90332,a921)))+P1(f862(f862(f321(x90331),f466(x90334,x90333,x90331,x90332)),x90333))
% 25.54/25.41 [9034]E(f862(f862(f32(x90341,f932(x90342,a921)),x90343),x90344),f234(f932(x90342,a921)))+P1(f862(f862(f321(x90341),f486(x90344,x90343,x90341,x90342)),x90343))
% 25.54/25.41 [9035]E(f862(f862(f32(x90351,f932(x90352,a921)),x90353),x90354),f234(f932(x90352,a921)))+P1(f862(f862(f321(x90351),f489(x90354,x90353,x90352,x90351)),x90353))
% 25.54/25.41 [9036]E(f862(f862(f33(x90361,f932(x90362,a921)),x90363),x90364),f181(f932(x90362,a921)))+P1(f862(f862(f321(x90361),f487(x90364,x90363,x90362,x90361)),x90363))
% 25.54/25.41 [9075]P1(f862(f862(f228(a924),f862(x90751,x90752)),f862(x90751,x90753)))+~P1(f862(f862(f321(f931(x90754,x90754)),f862(f862(f244(x90754,x90754),x90752),x90753)),f862(f862(f279(a924,x90754),a232),x90751)))
% 25.54/25.41 [9101]E(f170(x91011,x91012,f862(f862(f127(x91011),x91013),x91014)),f862(f862(f127(x91011),x91013),f170(x91011,x91012,x91014)))+P1(f862(f862(f321(x91011),f747(x91014,x91012,x91013,x91011)),f862(f165(x91011),x91013)))
% 25.54/25.41 [9152]~P23(x91521,x91522,x91523,f234(f932(x91521,a921)),f234(f932(x91522,a921)))+E(f862(f302(x91521,x91522,x91523),f862(f72(f932(x91521,a921)),x91524)),f862(f72(f932(x91522,a921)),f862(f302(x91521,x91522,x91523),x91524)))
% 25.54/25.41 [9255]P1(f862(f862(f321(x92551),f525(x92552,x92553,x92554,x92551)),x92553))+~P1(f862(f862(f321(f932(x92551,a921)),x92554),f862(f862(f53(x92551),x92553),x92552)))
% 25.54/25.41 [9258]E(x92581,x92582)+~P1(f862(f862(f321(f931(x92583,x92583)),f862(f862(f244(x92583,x92583),x92581),x92582)),f862(f862(f176(f931(x92583,x92583),a921),f2(a924)),x92584)))
% 25.54/25.41 [9341]E(f862(f276(x93411,x93411,x93412),f862(f862(f301(x93411),f525(x93412,x93413,x93414,x93411)),f181(f932(x93411,a921)))),x93414)+~P1(f862(f862(f321(f932(x93411,a921)),x93414),f862(f862(f53(x93411),x93413),x93412)))
% 25.54/25.41 [9346]~P1(f862(f862(f321(f931(x93461,x93461)),f862(f862(f244(x93461,x93461),x93463),x93462)),f299(x93461,x93464)))+P1(f862(f862(f321(f931(x93461,x93461)),f862(f862(f244(x93461,x93461),x93462),x93463)),f299(x93461,f862(f277(x93461,x93461),x93464))))
% 25.54/25.41 [9359]~P61(x93591)+E(f862(f862(f73(x93591),f862(f862(f73(x93591),f862(f862(f74(x93591),x93592),f862(f862(f29(x93591),x93593),x93592))),f38(x93591,x93593,x93592))),x93594),f862(f862(f73(x93591),x93593),x93594))
% 25.54/25.41 [9370]~P1(f862(f862(f321(x93701),x93703),x93704))+P1(f862(f862(f321(f932(x93701,a921)),f862(f276(x93701,x93701,x93702),f862(f862(f301(x93701),x93703),f181(f932(x93701,a921))))),f862(f862(f53(x93701),x93704),x93702)))
% 25.54/25.41 [9382]P1(f862(f862(f321(f931(x93821,x93821)),f862(f862(f244(x93821,x93821),x93822),x93823)),f299(x93821,x93824)))+~P1(f862(f862(f321(f931(x93821,x93821)),f862(f862(f244(x93821,x93821),x93823),x93822)),f299(x93821,f862(f277(x93821,x93821),x93824))))
% 25.54/25.41 [9469]E(f862(f862(f152(x94691,f862(f161(x94691),x94692)),f862(f862(f3(a924),f862(f862(f3(a924),f862(f182(f925(x94691)),x94692)),x94693)),f71(a924))),x94694),f862(f161(x94691),f862(f862(f152(x94691,x94692),x94693),x94694)))+~P1(f862(f862(f228(a924),x94693),f862(f182(f925(x94691)),x94692)))
% 25.54/25.41 [9472]~P1(f862(x94722,f741(x94724,x94722,x94723,x94721)))+E(f862(f862(f131(x94721),f862(f182(f925(x94721)),f170(x94721,x94722,f862(f862(f127(x94721),x94723),x94724)))),f862(f862(f127(x94721),x94723),x94724)),f862(f862(f131(x94721),f862(f182(f925(x94721)),f170(x94721,x94722,x94724))),x94724))
% 25.54/25.41 [9516]~P22(x95162,x95161,x95163,f234(f932(x95162,a921)))+P1(f862(f862(f227(f932(x95161,a921)),f862(f302(x95162,x95161,x95163),f862(f72(f932(x95162,a921)),x95164))),f862(f72(f932(x95161,a921)),f862(f302(x95162,x95161,x95163),x95164))))
% 25.54/25.41 [9528]~P3(x95281)+E(f862(f135(x95281,x95282,f862(f9(x95282,x95281,x95281),f862(f862(f10(x95281,f932(x95281,x95281),x95282),f94(x95281)),x95283)),f234(x95281)),x95284),f862(f862(f32(x95282,x95281),f862(f165(x95282),x95284)),x95283))
% 25.54/25.41 [9529]~P3(x95291)+E(f862(f135(x95291,x95292,f862(f9(x95292,x95291,x95291),f862(f862(f10(x95291,f932(x95291,x95291),x95292),f103(x95291)),x95293)),f181(x95291)),x95294),f862(f862(f33(x95292,x95291),f862(f165(x95292),x95294)),x95293))
% 25.54/25.41 [9539]E(f862(f862(f131(x95391),f862(f182(f925(x95391)),f170(x95391,x95392,f862(f862(f127(x95391),x95393),x95394)))),f862(f862(f127(x95391),x95393),x95394)),f862(f862(f131(x95391),f862(f182(f925(x95391)),f170(x95391,x95392,x95394))),x95394))+P1(f862(f862(f321(x95391),f741(x95394,x95392,x95393,x95391)),f862(f165(x95391),x95393)))
% 25.54/25.41 [9612]~P1(f862(f862(f321(f931(f925(x96124),f925(x96124))),f862(f862(f244(f925(x96124),f925(x96124)),x96123),x96122)),f150(x96124,x96121)))+P1(f862(f862(f228(a924),f675(x96121,x96122,x96123,x96124)),f862(f182(f925(x96124)),x96123)))
% 25.54/25.41 [9613]~P61(x96131)+E(f862(f862(f73(x96131),f862(f862(f73(x96131),f862(f862(f74(x96131),f862(f862(f29(x96131),x96132),x96133)),x96133)),f38(x96131,x96132,x96133))),x96134),f862(f862(f73(x96131),x96132),x96134))
% 25.54/25.41 [9642]~P1(f862(f862(f321(f931(f925(x96421),f925(x96421))),f862(f862(f244(f925(x96421),f925(x96421)),x96422),x96423)),f862(f277(f925(x96421),f925(x96421)),f150(x96421,x96424))))+P1(f862(f862(f321(f931(f925(x96421),f925(x96421))),f862(f862(f244(f925(x96421),f925(x96421)),x96422),x96423)),f150(x96421,f862(f277(x96421,x96421),x96424))))
% 25.54/25.41 [9643]P1(f862(f862(f321(f931(f925(x96431),f925(x96431))),f862(f862(f244(f925(x96431),f925(x96431)),x96432),x96433)),f862(f277(f925(x96431),f925(x96431)),f150(x96431,x96434))))+~P1(f862(f862(f321(f931(f925(x96431),f925(x96431))),f862(f862(f244(f925(x96431),f925(x96431)),x96432),x96433)),f150(x96431,f862(f277(x96431,x96431),x96434))))
% 25.54/25.41 [9684]~P1(f862(f862(f321(x96841),x96843),f862(f256(x96841,x96842),x96844)))+P1(f862(f862(f321(f931(x96841,x96842)),f862(f862(f244(x96841,x96842),x96843),f565(x96844,x96842,x96843,x96841))),x96844))
% 25.54/25.41 [9685]~P1(f862(f862(f321(x96851),x96853),f862(f256(x96851,x96852),x96854)))+P1(f862(f862(f321(f931(x96851,x96852)),f862(f862(f244(x96851,x96852),x96853),f566(x96854,x96852,x96853,x96851))),x96854))
% 25.54/25.41 [9841]~P1(f862(f862(f321(f931(x98411,x98411)),f862(f862(f244(x98411,x98411),x98412),x98414)),f862(f862(f280(x98411,x98411,x98411),x98413),f299(x98411,x98413))))+P1(f862(f862(f321(f931(x98411,x98411)),f862(f862(f244(x98411,x98411),x98412),f637(x98413,x98414,x98412,x98411))),x98413))
% 25.54/25.41 [10001]P9(x100011,x100012,x100013,x100014)+P1(f862(f862(f321(f931(x100011,x100011)),f862(f862(f244(x100011,x100011),f835(x100012,x100014,x100013,x100011)),f834(x100012,x100014,x100013,x100011))),x100013))
% 25.54/25.41 [10009]~P1(f862(f862(f321(f931(x100092,x100091)),x100094),f862(f277(x100091,x100092),x100093)))+P1(f862(f862(f321(f931(x100091,x100092)),f862(f862(f244(x100091,x100092),f648(x100093,x100094,x100091,x100092)),f647(x100093,x100094,x100091,x100092))),x100093))
% 25.54/25.41 [10033]~P1(f862(f862(f321(f931(f925(x100331),f925(x100331))),f862(f862(f244(f925(x100331),f925(x100331)),x100334),x100333)),f150(x100331,x100332)))+P1(f862(f862(f321(f931(x100331,x100331)),f862(f862(f244(x100331,x100331),f691(x100332,x100333,x100334,x100331)),f692(x100332,x100333,x100334,x100331))),x100332))
% 25.54/25.41 [10126]~P1(f862(f862(f321(f931(f925(x101261),f925(x101261))),f862(f862(f244(f925(x101261),f925(x101261)),x101262),x101264)),f150(x101261,x101263)))+P1(f862(f862(f321(f931(x101261,x101261)),f862(f862(f244(x101261,x101261),f862(f862(f157(x101261),x101262),f675(x101263,x101264,x101262,x101261))),f676(x101263,x101264,x101262,x101261))),x101263))
% 25.54/25.41 [10146]~P1(f862(f54(x101462),x101464))+E(f862(f862(f862(f58(f932(x101461,a921),x101462,f103(f932(x101461,a921))),f862(f862(f9(x101462,f932(x101461,a921),f932(x101461,a921)),f862(f862(f10(x101461,f932(f932(x101461,a921),f932(x101461,a921)),x101462),f301(x101461)),x101463)),f181(f932(x101461,a921)))),f181(f932(x101461,a921))),x101464),f862(f302(x101462,x101461,x101463),x101464))
% 25.54/25.41 [10243]~P22(x102431,x102432,x102433,f234(f932(x102431,a921)))+P1(f862(f862(f227(f932(x102431,a921)),f862(f303(x102431,x102432,x102433),f862(f862(f301(x102432),x102434),f181(f932(x102432,a921))))),f862(f862(f301(x102431),f78(x102431,f862(f862(f9(x102431,x102432,a921),f862(f862(f10(x102432,f932(x102432,a921),x102431),a317),x102433)),x102434))),f181(f932(x102431,a921)))))
% 25.54/25.41 [5811]~E(f862(f862(f127(x58111),x58112),x58114),x58113)+E(f862(f862(f168(x58111),f862(f182(f925(x58111)),x58112)),x58113),x58112)
% 25.54/25.41 [5812]~E(f862(f862(f127(x58122),x58123),x58121),x58124)+E(x58121,f862(f862(f131(x58122),f862(f182(f925(x58122)),x58123)),x58124))
% 25.54/25.41 [5823]~E(x58234,f2(a924))+E(f862(f862(f157(x58231),f862(f862(f144(x58231),x58232),x58233)),x58234),x58232)
% 25.54/25.41 [6369]~P119(x63691)+E(f862(f862(f236(x63691),f862(f862(f236(x63691),x63692),x63693)),x63694),f862(f862(f236(x63691),x63692),f862(f862(f74(a924),x63693),x63694)))
% 25.54/25.41 [6370]~P80(x63701)+E(f862(f862(f236(x63701),f862(f862(f236(x63701),x63702),x63703)),x63704),f862(f862(f236(x63701),x63702),f862(f862(f74(a924),x63703),x63704)))
% 25.54/25.41 [6379]E(x63791,f2(a924))+E(f862(f862(f157(x63792),f862(f862(f144(x63792),x63793),x63794)),x63791),f862(f862(f157(x63792),x63794),f862(f862(f3(a924),x63791),f71(a924))))
% 25.54/25.41 [6405]~P119(x64051)+E(f862(f862(f74(x64051),f862(f862(f74(x64051),x64052),x64053)),x64054),f862(f862(f74(x64051),x64052),f862(f862(f74(x64051),x64053),x64054)))
% 25.54/25.41 [6406]~P121(x64061)+E(f862(f862(f281(x64061),f862(f862(f74(x64061),x64062),x64063)),x64064),f862(f862(f74(x64061),x64062),f862(f862(f281(x64061),x64063),x64064)))
% 25.54/25.41 [6407]~P119(x64071)+E(f862(f862(f73(x64071),f862(f862(f73(x64071),x64072),x64073)),x64074),f862(f862(f73(x64071),x64072),f862(f862(f73(x64071),x64073),x64074)))
% 25.54/25.41 [6408]~P93(x64081)+E(f862(f862(f103(x64081),f862(f862(f103(x64081),x64082),x64083)),x64084),f862(f862(f103(x64081),x64082),f862(f862(f103(x64081),x64083),x64084)))
% 25.54/25.41 [6409]~P103(x64091)+E(f862(f862(f103(x64091),f862(f862(f103(x64091),x64092),x64093)),x64094),f862(f862(f103(x64091),x64092),f862(f862(f103(x64091),x64093),x64094)))
% 25.54/25.41 [6410]~P103(x64101)+E(f862(f862(f103(x64101),f862(f862(f103(x64101),x64102),x64103)),x64104),f862(f862(f103(x64101),x64102),f862(f862(f103(x64101),x64103),x64104)))
% 25.54/25.41 [6411]~P93(x64111)+E(f862(f862(f94(x64111),f862(f862(f94(x64111),x64112),x64113)),x64114),f862(f862(f94(x64111),x64112),f862(f862(f94(x64111),x64113),x64114)))
% 25.54/25.41 [6412]~P104(x64121)+E(f862(f862(f94(x64121),f862(f862(f94(x64121),x64122),x64123)),x64124),f862(f862(f94(x64121),x64122),f862(f862(f94(x64121),x64123),x64124)))
% 25.54/25.41 [6413]~P104(x64131)+E(f862(f862(f94(x64131),f862(f862(f94(x64131),x64132),x64133)),x64134),f862(f862(f94(x64131),x64132),f862(f862(f94(x64131),x64133),x64134)))
% 25.54/25.41 [6414]~P69(x64141)+E(f862(f862(f74(x64141),f862(f862(f74(x64141),x64142),x64143)),x64144),f862(f862(f74(x64141),x64142),f862(f862(f74(x64141),x64143),x64144)))
% 25.54/25.41 [6415]~P119(x64151)+E(f862(f862(f74(x64151),f862(f862(f74(x64151),x64152),x64153)),x64154),f862(f862(f74(x64151),x64152),f862(f862(f74(x64151),x64153),x64154)))
% 25.54/25.41 [6417]~P70(x64171)+E(f862(f862(f73(x64171),f862(f862(f73(x64171),x64172),x64173)),x64174),f862(f862(f73(x64171),x64172),f862(f862(f73(x64171),x64173),x64174)))
% 25.54/25.41 [6418]~P119(x64181)+E(f862(f862(f73(x64181),f862(f862(f73(x64181),x64182),x64183)),x64184),f862(f862(f73(x64181),x64182),f862(f862(f73(x64181),x64183),x64184)))
% 25.54/25.41 [6419]~P109(x64191)+E(f862(f862(f225(x64191),f862(f862(f225(x64191),x64192),x64193)),x64194),f862(f862(f225(x64191),x64192),f862(f862(f225(x64191),x64193),x64194)))
% 25.54/25.41 [6420]~P109(x64201)+E(f862(f862(f225(x64201),f862(f862(f225(x64201),x64202),x64203)),x64204),f862(f862(f225(x64201),x64202),f862(f862(f225(x64201),x64203),x64204)))
% 25.54/25.41 [6421]~P109(x64211)+E(f862(f862(f226(x64211),f862(f862(f226(x64211),x64212),x64213)),x64214),f862(f862(f226(x64211),x64212),f862(f862(f226(x64211),x64213),x64214)))
% 25.54/25.41 [6422]~P109(x64221)+E(f862(f862(f226(x64221),f862(f862(f226(x64221),x64222),x64223)),x64224),f862(f862(f226(x64221),x64222),f862(f862(f226(x64221),x64223),x64224)))
% 25.54/25.41 [6431]~P61(x64311)+E(f38(x64311,f862(f862(f73(x64311),x64312),f862(f862(f74(x64311),x64313),x64314)),x64314),f38(x64311,x64312,x64314))
% 25.54/25.41 [6432]~P61(x64321)+E(f38(x64321,f862(f862(f73(x64321),x64322),f862(f862(f74(x64321),x64323),x64324)),x64323),f38(x64321,x64322,x64323))
% 25.54/25.41 [6570]E(f862(f862(f157(x65701),f862(f862(f168(x65701),x65702),x65703)),x65704),f862(f862(f157(x65701),x65703),x65704))+~P1(f862(f862(f228(a924),x65704),x65702))
% 25.54/25.41 [6748]~E(x67482,x67484)+P1(f862(f862(f165(x67481),f862(f862(f144(x67481),x67482),x67483)),x67484))
% 25.54/25.41 [6750]~P119(x67501)+E(f862(f862(f74(x67501),f862(f862(f74(x67501),x67502),x67503)),x67504),f862(f862(f74(x67501),f862(f862(f74(x67501),x67502),x67504)),x67503))
% 25.54/25.41 [6751]~P119(x67511)+E(f862(f862(f73(x67511),f862(f862(f73(x67511),x67512),x67513)),x67514),f862(f862(f73(x67511),f862(f862(f73(x67511),x67512),x67514)),x67513))
% 25.54/25.41 [6809]~P147(x68092)+E(f862(f862(f8(x68091,x68092),f862(f18(x68092,x68091),x68093)),x68094),f862(f862(f74(x68092),f862(f93(x68092),f862(f28(x68091),x68094))),x68093))
% 25.54/25.41 [6977]E(f862(f862(f94(f932(x69771,a921)),f862(f862(f301(x69771),x69772),x69773)),x69774),f862(f862(f94(f932(x69771,a921)),x69773),x69774))+P1(f862(f862(f321(x69771),x69772),x69774))
% 25.54/25.41 [6978]E(f862(f862(f94(f932(x69781,a921)),f862(f862(f301(x69781),x69782),x69783)),x69784),f862(f862(f94(f932(x69781,a921)),x69783),x69784))+P1(f862(f862(f321(x69781),x69782),x69784))
% 25.54/25.41 [7047]~P102(x70471)+E(f862(f862(f94(x70471),f862(f862(f103(x70471),x70472),x70473)),f862(f862(f103(x70471),x70474),x70473)),f862(f862(f103(x70471),f862(f862(f94(x70471),x70472),x70474)),x70473))
% 25.54/25.41 [7048]~P102(x70481)+E(f862(f862(f103(x70481),f862(f862(f94(x70481),x70482),x70483)),f862(f862(f94(x70481),x70484),x70483)),f862(f862(f94(x70481),f862(f862(f103(x70481),x70482),x70484)),x70483))
% 25.54/25.41 [7049]~P78(x70491)+E(f862(f862(f225(x70491),f862(f862(f3(x70491),x70492),x70493)),f862(f862(f3(x70491),x70494),x70493)),f862(f862(f3(x70491),f862(f862(f225(x70491),x70492),x70494)),x70493))
% 25.54/25.41 [7050]~P78(x70501)+E(f862(f862(f226(x70501),f862(f862(f3(x70501),x70502),x70503)),f862(f862(f3(x70501),x70504),x70503)),f862(f862(f3(x70501),f862(f862(f226(x70501),x70502),x70504)),x70503))
% 25.54/25.41 [7051]~P114(x70511)+E(f862(f862(f73(x70511),f862(f862(f74(x70511),x70512),x70513)),f862(f862(f74(x70511),x70514),x70513)),f862(f862(f74(x70511),f862(f862(f73(x70511),x70512),x70514)),x70513))
% 25.54/25.41 [7052]~P119(x70521)+E(f862(f862(f73(x70521),f862(f862(f74(x70521),x70522),x70523)),f862(f862(f74(x70521),x70524),x70523)),f862(f862(f74(x70521),f862(f862(f73(x70521),x70522),x70524)),x70523))
% 25.54/25.41 [7053]~P84(x70531)+E(f862(f862(f225(x70531),f862(f862(f73(x70531),x70532),x70533)),f862(f862(f73(x70531),x70534),x70533)),f862(f862(f73(x70531),f862(f862(f225(x70531),x70532),x70534)),x70533))
% 25.54/25.41 [7054]~P84(x70541)+E(f862(f862(f226(x70541),f862(f862(f73(x70541),x70542),x70543)),f862(f862(f73(x70541),x70544),x70543)),f862(f862(f73(x70541),f862(f862(f226(x70541),x70542),x70544)),x70543))
% 25.54/25.41 [7055]~P121(x70551)+E(f862(f862(f3(x70551),f862(f862(f281(x70551),x70552),x70553)),f862(f862(f281(x70551),x70554),x70553)),f862(f862(f281(x70551),f862(f862(f3(x70551),x70552),x70554)),x70553))
% 25.54/25.41 [7056]~P121(x70561)+E(f862(f862(f73(x70561),f862(f862(f281(x70561),x70562),x70563)),f862(f862(f281(x70561),x70564),x70563)),f862(f862(f281(x70561),f862(f862(f73(x70561),x70562),x70564)),x70563))
% 25.54/25.41 [7057]~P71(x70571)+E(f862(f862(f74(x70571),f862(f862(f236(x70571),x70572),x70573)),f862(f862(f236(x70571),x70574),x70573)),f862(f862(f236(x70571),f862(f862(f74(x70571),x70572),x70574)),x70573))
% 25.54/25.41 [7058]~P119(x70581)+E(f862(f862(f74(x70581),f862(f862(f236(x70581),x70582),x70583)),f862(f862(f236(x70581),x70584),x70583)),f862(f862(f236(x70581),f862(f862(f74(x70581),x70582),x70584)),x70583))
% 25.54/25.41 [7059]~P64(x70591)+E(f862(f862(f281(x70591),f862(f862(f236(x70591),x70592),x70593)),f862(f862(f236(x70591),x70594),x70593)),f862(f862(f236(x70591),f862(f862(f281(x70591),x70592),x70594)),x70593))
% 25.54/25.41 [7060]~P109(x70601)+E(f862(f862(f226(x70601),f862(f862(f225(x70601),x70602),x70603)),f862(f862(f225(x70601),x70604),x70603)),f862(f862(f225(x70601),f862(f862(f226(x70601),x70602),x70604)),x70603))
% 25.54/25.41 [7061]~P109(x70611)+E(f862(f862(f225(x70611),f862(f862(f226(x70611),x70612),x70613)),f862(f862(f226(x70611),x70614),x70613)),f862(f862(f226(x70611),f862(f862(f225(x70611),x70612),x70614)),x70613))
% 25.54/25.41 [7062]~P119(x70621)+E(f862(f862(f73(x70621),f862(f862(f74(x70621),x70622),x70623)),f862(f862(f74(x70621),x70624),x70623)),f862(f862(f74(x70621),f862(f862(f73(x70621),x70622),x70624)),x70623))
% 25.54/25.41 [7094]E(f862(f862(f152(x70941,x70942),x70943),x70944),x70942)+~P1(f862(f862(f227(a924),f862(f182(f925(x70941)),x70942)),x70943))
% 25.54/25.41 [7119]~P1(f862(x71193,x71194))+P1(f862(f862(f862(f103(f932(x71191,a921)),x71192),x71193),x71194))
% 25.54/25.41 [7120]~P1(f862(x71203,x71204))+P1(f862(f862(f862(f103(f932(x71201,a921)),x71202),x71203),x71204))
% 25.54/25.41 [7121]~P1(f862(x71212,x71214))+P1(f862(f862(f862(f103(f932(x71211,a921)),x71212),x71213),x71214))
% 25.54/25.41 [7122]~P1(f862(x71222,x71224))+P1(f862(f862(f862(f103(f932(x71221,a921)),x71222),x71223),x71224))
% 25.54/25.41 [7140]E(f862(f862(f157(x71401),f862(f862(f127(x71401),x71402),x71403)),x71404),f862(f862(f157(x71401),x71402),x71404))+~P1(f862(f862(f228(a924),x71404),f862(f182(f925(x71401)),x71402)))
% 25.54/25.41 [7150]E(f862(f862(f3(f932(x71501,a921)),f862(f862(f301(x71501),x71502),x71503)),x71504),f862(f862(f3(f932(x71501,a921)),x71503),x71504))+~P1(f862(f862(f321(x71501),x71502),x71504))
% 25.54/25.41 [7151]E(f862(f862(f3(f932(x71511,a921)),f862(f862(f301(x71511),x71512),x71513)),x71514),f862(f862(f3(f932(x71511,a921)),x71513),x71514))+~P1(f862(f862(f321(x71511),x71512),x71514))
% 25.54/25.41 [7193]~E(f132(a924,f862(f295(a924,x71931),x71932)),f862(f862(f144(a924),x71934),x71933))+E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x71931),f71(a924))),x71932)),x71933)
% 25.54/25.41 [7214]~P1(f862(f862(f165(x72141),x72143),x72144))+P1(f862(f862(f165(x72141),f862(f862(f144(x72141),x72142),x72143)),x72144))
% 25.54/25.41 [7264]E(x72641,f2(a924))+E(f862(f862(f144(x72642),x72643),f862(f862(f168(x72642),f862(f862(f3(a924),x72641),f71(a924))),x72644)),f862(f862(f168(x72642),x72641),f862(f862(f144(x72642),x72643),x72644)))
% 25.54/25.41 [7367]E(f862(f862(f157(x73671),x73672),f862(f862(f3(a924),x73673),f862(f182(f925(x73671)),x73674))),f862(f862(f157(x73671),f862(f862(f127(x73671),x73674),x73672)),x73673))+P1(f862(f862(f228(a924),x73673),f862(f182(f925(x73671)),x73674)))
% 25.54/25.41 [7395]E(f862(f862(f94(f932(x73951,a921)),x73952),f862(f862(f301(x73951),x73953),x73954)),f862(f862(f301(x73951),x73953),f862(f862(f94(f932(x73951,a921)),x73952),x73954)))+~P1(f862(f862(f321(x73951),x73953),x73952))
% 25.54/25.41 [7396]E(f862(f862(f94(f932(x73961,a921)),x73962),f862(f862(f301(x73961),x73963),x73964)),f862(f862(f301(x73961),x73963),f862(f862(f94(f932(x73961,a921)),x73962),x73964)))+~P1(f862(f862(f321(x73961),x73963),x73962))
% 25.54/25.41 [7435]E(f862(f862(f157(x74351),f862(f862(f152(x74351,x74352),x74353),x74354)),x74353),x74354)+~P1(f862(f862(f228(a924),x74353),f862(f182(f925(x74351)),x74352)))
% 25.54/25.41 [7458]E(x74581,f181(f932(x74582,a921)))+E(f862(f302(f931(x74583,x74582),x74583,f243(x74583,x74582)),f862(f862(f246(x74583,x74582),x74584),f862(f18(f932(x74582,a921),x74583),x74581))),x74584)
% 25.54/25.41 [7459]E(x74591,f181(f932(x74592,a921)))+E(f862(f302(f931(x74592,x74593),x74593,f248(x74592,x74593)),f862(f862(f246(x74592,x74593),x74591),f862(f18(f932(x74593,a921),x74592),x74594))),x74594)
% 25.54/25.41 [7535]E(f862(f862(f3(f932(x75351,a921)),f862(f862(f301(x75351),x75352),x75353)),x75354),f862(f862(f301(x75351),x75352),f862(f862(f3(f932(x75351,a921)),x75353),x75354)))+P1(f862(f862(f321(x75351),x75352),x75354))
% 25.54/25.41 [7571]~E(x75714,f181(f932(x75712,a921)))+E(f862(f302(f931(x75711,x75712),x75711,f243(x75711,x75712)),f862(f862(f246(x75711,x75712),x75713),f862(f18(f932(x75712,a921),x75711),x75714))),f181(f932(x75711,a921)))
% 25.54/25.41 [7572]~E(x75723,f181(f932(x75721,a921)))+E(f862(f302(f931(x75721,x75722),x75722,f248(x75721,x75722)),f862(f862(f246(x75721,x75722),x75723),f862(f18(f932(x75722,a921),x75721),x75724))),f181(f932(x75722,a921)))
% 25.54/25.41 [7623]~P1(f862(f862(f321(x76231),x76232),x76234))+P1(f862(f862(f321(x76231),x76232),f862(f862(f103(f932(x76231,a921)),x76233),x76234)))
% 25.54/25.41 [7624]~P1(f862(f862(f321(x76241),x76242),x76244))+P1(f862(f862(f321(x76241),x76242),f862(f862(f103(f932(x76241,a921)),x76243),x76244)))
% 25.54/25.41 [7625]~P1(f862(f862(f321(x76251),x76252),x76254))+P1(f862(f862(f321(x76251),x76252),f862(f862(f103(f932(x76251,a921)),x76253),x76254)))
% 25.54/25.41 [7626]~P1(f862(f862(f321(x76261),x76262),x76263))+P1(f862(f862(f321(x76261),x76262),f862(f862(f103(f932(x76261,a921)),x76263),x76264)))
% 25.54/25.41 [7627]~P1(f862(f862(f321(x76271),x76272),x76273))+P1(f862(f862(f321(x76271),x76272),f862(f862(f103(f932(x76271,a921)),x76273),x76274)))
% 25.54/25.41 [7628]~P1(f862(f862(f321(x76281),x76282),x76283))+P1(f862(f862(f321(x76281),x76282),f862(f862(f103(f932(x76281,a921)),x76283),x76284)))
% 25.54/25.41 [7645]E(f862(f862(f94(f932(x76451,a921)),f862(f862(f301(x76451),x76452),x76453)),x76454),f862(f862(f301(x76451),x76452),f862(f862(f94(f932(x76451,a921)),x76453),x76454)))+~P1(f862(f862(f321(x76451),x76452),x76454))
% 25.54/25.41 [7646]E(f862(f862(f94(f932(x76461,a921)),f862(f862(f301(x76461),x76462),x76463)),x76464),f862(f862(f301(x76461),x76462),f862(f862(f94(f932(x76461,a921)),x76463),x76464)))+~P1(f862(f862(f321(x76461),x76462),x76464))
% 25.54/25.41 [7920]P1(f862(x79201,x79202))+~P1(f862(f862(f862(f94(f932(x79203,a921)),x79204),x79201),x79202))
% 25.54/25.41 [7921]P1(f862(x79211,x79212))+~P1(f862(f862(f862(f94(f932(x79213,a921)),x79211),x79214),x79212))
% 25.54/25.41 [7922]P1(f862(x79221,x79222))+~P1(f862(f862(f862(f94(f932(x79223,a921)),x79224),x79221),x79222))
% 25.54/25.41 [7923]P1(f862(x79231,x79232))+~P1(f862(f862(f862(f94(f932(x79233,a921)),x79231),x79234),x79232))
% 25.54/25.41 [7924]E(f862(f862(f8(x79241,a924),x79242),f862(f862(f3(f932(x79241,a921)),x79243),f862(f862(f301(x79241),x79244),f181(f932(x79241,a921))))),f862(f862(f8(x79241,a924),x79242),x79243))+P1(f862(f862(f321(x79241),x79244),x79243))
% 25.54/25.41 [7929]~P72(x79291)+E(f862(f158(x79291),f862(f862(f147(a924,x79291),x79292),f132(a924,f862(f295(a924,x79293),x79294)))),f862(f862(f8(a924,x79291),x79292),f862(f165(a924),f132(a924,f862(f295(a924,x79293),x79294)))))
% 25.54/25.41 [7930]~P72(x79301)+E(f862(f862(f8(a924,x79301),x79302),f862(f165(a924),f132(a924,f862(f295(a924,x79303),x79304)))),f862(f158(x79301),f862(f862(f147(a924,x79301),x79302),f132(a924,f862(f295(a924,x79303),x79304)))))
% 25.54/25.41 [8044]~E(x80443,x80444)+P1(f862(f55(x80441,x80442,f862(f862(f301(x80441),x80443),f181(f932(x80441,a921)))),x80444))
% 25.54/25.41 [8142]P1(f862(f862(f321(x81421),x81422),f862(f165(x81421),x81423)))+~P1(f862(f862(f321(x81421),x81422),f862(f165(x81421),f862(f862(f168(x81421),x81424),x81423))))
% 25.54/25.41 [8143]P1(f862(f862(f321(x81431),x81432),f862(f165(x81431),x81433)))+~P1(f862(f862(f321(x81431),x81432),f862(f165(x81431),f862(f862(f131(x81431),x81434),x81433))))
% 25.54/25.41 [8213]P1(f862(f862(f321(x82131),x82132),x82133))+~P1(f862(f862(f321(x82131),x82132),f862(f862(f94(f932(x82131,a921)),x82134),x82133)))
% 25.54/25.41 [8214]P1(f862(f862(f321(x82141),x82142),x82143))+~P1(f862(f862(f321(x82141),x82142),f862(f862(f94(f932(x82141,a921)),x82144),x82143)))
% 25.54/25.41 [8215]P1(f862(f862(f321(x82151),x82152),x82153))+~P1(f862(f862(f321(x82151),x82152),f862(f862(f94(f932(x82151,a921)),x82154),x82153)))
% 25.54/25.41 [8216]P1(f862(f862(f321(x82161),x82162),x82163))+~P1(f862(f862(f321(x82161),x82162),f862(f862(f94(f932(x82161,a921)),x82163),x82164)))
% 25.54/25.41 [8217]P1(f862(f862(f321(x82171),x82172),x82173))+~P1(f862(f862(f321(x82171),x82172),f862(f862(f94(f932(x82171,a921)),x82173),x82174)))
% 25.54/25.41 [8218]P1(f862(f862(f321(x82181),x82182),x82183))+~P1(f862(f862(f321(x82181),x82182),f862(f862(f94(f932(x82181,a921)),x82183),x82184)))
% 25.54/25.41 [8219]P1(f862(f862(f321(x82191),x82192),x82193))+~P1(f862(f862(f321(x82191),x82192),f862(f862(f3(f932(x82191,a921)),x82193),x82194)))
% 25.54/25.41 [8220]P1(f862(f862(f321(x82201),x82202),x82203))+~P1(f862(f862(f321(x82201),x82202),f862(f862(f3(f932(x82201,a921)),x82203),x82204)))
% 25.54/25.41 [8221]P1(f862(f862(f321(x82211),x82212),x82213))+~P1(f862(f862(f321(x82211),x82212),f862(f862(f3(f932(x82211,a921)),x82213),x82214)))
% 25.54/25.41 [8236]E(f862(f862(f127(x82361),f862(f862(f168(x82361),x82362),x82363)),f862(f862(f144(x82361),x82364),f862(f862(f131(x82361),f862(a105,x82362)),x82363))),f862(f862(f152(x82361,x82363),x82362),x82364))+~P1(f862(f862(f228(a924),x82362),f862(f182(f925(x82361)),x82363)))
% 25.54/25.41 [8259]P1(f862(f862(f321(x82591),x82592),x82593))+~P1(f862(f862(f227(f932(x82591,a921)),f862(f862(f301(x82591),x82592),x82594)),x82593))
% 25.54/25.41 [8296]~P1(f862(f862(f321(x82961),x82962),x82963))+~P1(f862(f862(f321(x82961),x82962),f862(f862(f3(f932(x82961,a921)),x82964),x82963)))
% 25.54/25.41 [8297]~P1(f862(f862(f321(x82971),x82972),x82973))+~P1(f862(f862(f321(x82971),x82972),f862(f862(f3(f932(x82971,a921)),x82974),x82973)))
% 25.54/25.41 [8298]~P1(f862(f862(f321(x82981),x82982),x82983))+~P1(f862(f862(f321(x82981),x82982),f862(f862(f3(f932(x82981,a921)),x82984),x82983)))
% 25.54/25.41 [8331]~P1(f862(f862(f228(a924),x83314),f862(f182(f925(x83311)),x83313)))+P1(f862(f862(f321(x83311),x83312),f862(f165(x83311),f862(f862(f152(x83311,x83313),x83314),x83312))))
% 25.54/25.41 [8375]E(f862(f96(a924),x83751),f2(a924))+E(f862(f862(f144(x83752),x83753),f862(f862(f168(x83752),f862(f862(f3(a924),f862(f96(a924),x83751)),f71(a924))),x83754)),f862(f862(f168(x83752),f862(f96(a924),x83751)),f862(f862(f144(x83752),x83753),x83754)))
% 25.54/25.41 [8385]E(f862(f862(f157(x83851),f862(f862(f131(x83851),x83852),x83853)),x83854),f862(f862(f157(x83851),x83853),f862(f862(f73(a924),x83852),x83854)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x83852),x83854)),f862(f182(f925(x83851)),x83853)))
% 25.54/25.41 [8394]~P147(x83942)+E(f862(f862(f8(x83941,x83942),f862(f862(f10(a924,x83942,x83941),f93(x83942)),x83943)),x83944),f862(f93(x83942),f862(f862(f8(x83941,a924),x83943),x83944)))
% 25.54/25.41 [8395]~P142(x83952)+E(f862(f862(f8(x83951,x83952),f862(f862(f10(a1,x83952,x83951),f95(x83952)),x83953)),x83954),f862(f95(x83952),f862(f862(f8(x83951,a1),x83953),x83954)))
% 25.54/25.41 [8445]~P67(x84452)+E(f862(f862(f11(x84451,x84452),f862(f862(f10(x84452,x84452,x84451),f69(x84452)),x84453)),x84454),f862(f69(x84452),f862(f862(f11(x84451,x84452),x84453),x84454)))
% 25.54/25.41 [8446]~P59(x84462)+E(f862(f862(f8(x84461,x84462),f862(f862(f10(x84462,x84462,x84461),f72(x84462)),x84463)),x84464),f862(f72(x84462),f862(f862(f8(x84461,x84462),x84463),x84464)))
% 25.54/25.41 [8448]E(f862(f862(f8(x84481,a924),x84482),f862(f862(f3(f932(x84481,a921)),x84483),f862(f862(f301(x84481),x84484),f181(f932(x84481,a921))))),f862(f862(f3(a924),f862(f862(f8(x84481,a924),x84482),x84483)),f862(x84482,x84484)))+~P1(f862(f862(f321(x84481),x84484),x84483))
% 25.54/25.41 [8467]P1(f862(f862(f227(f932(x84671,a921)),x84672),x84673))+~P1(f862(f862(f227(f932(x84671,a921)),f862(f862(f301(x84671),x84674),x84672)),x84673))
% 25.54/25.41 [8590]~E(f862(f302(x85902,x85903,x85901),f234(f932(x85902,a921))),f234(f932(x85903,a921)))+E(f862(x85901,f862(f86(x85902,x85903,f234(f932(x85902,a921)),x85901),x85904)),x85904)
% 25.54/25.41 [8591]~E(f862(f302(x85912,x85913,x85911),f234(f932(x85912,a921))),f234(f932(x85913,a921)))+E(f862(x85911,f862(f86(x85912,x85913,f234(f932(x85912,a921)),x85911),x85914)),x85914)
% 25.54/25.41 [8676]P35(x86761,x86762)+~P35(x86761,f862(f862(f301(f931(x86761,x86761)),f862(f862(f244(x86761,x86761),x86763),x86764)),x86762))
% 25.54/25.41 [8677]P55(x86771,x86772)+~P55(x86771,f862(f862(f301(f931(x86771,x86771)),f862(f862(f244(x86771,x86771),x86773),x86774)),x86772))
% 25.54/25.41 [8682]~P109(x86821)+E(f862(f862(f141(x86821,x86821,f7(x86821)),x86822),f862(f862(f141(x86821,x86821,f7(x86821)),x86823),x86824)),f862(f862(f141(x86821,x86821,f7(x86821)),x86823),f862(f862(f141(x86821,x86821,f7(x86821)),x86822),x86824)))
% 25.54/25.41 [8697]E(x86971,x86972)+~P1(f862(f55(x86973,x86974,f862(f862(f301(x86973),x86971),f181(f932(x86973,a921)))),x86972))
% 25.54/25.41 [8707]E(f862(f862(f127(x87071),f862(f862(f168(x87071),x87072),x87073)),f862(f862(f168(x87071),x87074),f862(f862(f131(x87071),x87072),x87073))),f862(f862(f168(x87071),f862(f862(f73(a924),x87072),x87074)),x87073))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x87072),x87074)),f862(f182(f925(x87071)),x87073)))
% 25.54/25.41 [8746]P1(f862(f54(x87461),x87462))+~E(x87462,f862(f302(a924,x87461,x87463),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),x87464))))
% 25.54/25.41 [8747]P1(f862(f54(x87471),x87472))+~E(x87472,f862(f302(a924,x87471,x87473),f862(f254(a924),f862(f862(f9(a924,a924,a921),f228(a924)),x87474))))
% 25.54/25.41 [8768]~P89(x87681)+E(f862(f135(x87681,x87681,f73(x87681),f862(f862(f73(x87681),x87682),x87683)),x87684),f862(f862(f73(x87681),x87682),f862(f135(x87681,x87681,f73(x87681),x87683),x87684)))
% 25.54/25.41 [8804]P1(f862(f862(f227(f932(x88041,a921)),f862(f256(x88041,x88042),x88043)),f862(f256(x88041,x88042),x88044)))+~P1(f862(f862(f227(f932(f931(x88041,x88042),a921)),x88043),x88044))
% 25.54/25.41 [8816]~P1(f862(f862(f227(a924),x88162),x88164))+P1(f862(f862(f227(f932(x88161,a921)),f862(f165(x88161),f862(f862(f168(x88161),x88162),x88163))),f862(f165(x88161),f862(f862(f168(x88161),x88164),x88163))))
% 25.54/25.41 [8817]~P1(f862(f862(f227(a924),x88174),x88172))+P1(f862(f862(f227(f932(x88171,a921)),f862(f165(x88171),f862(f862(f131(x88171),x88172),x88173))),f862(f165(x88171),f862(f862(f131(x88171),x88174),x88173))))
% 25.54/25.41 [8874]~P1(f862(f54(x88741),f862(f862(f3(f932(x88741,a921)),x88742),x88744)))+P1(f862(f54(x88741),f862(f862(f3(f932(x88741,a921)),x88742),f862(f862(f301(x88741),x88743),x88744))))
% 25.54/25.41 [8916]P1(f862(f862(f321(f931(x89161,x89161)),x89162),f299(x89161,x89163)))+~P1(f862(f862(f321(f931(x89161,x89161)),x89162),f862(f862(f176(f931(x89161,x89161),a921),x89164),x89163)))
% 25.54/25.41 [8917]P1(f862(f862(f321(f931(x89171,x89171)),x89172),f299(x89171,x89173)))+~P1(f862(f862(f321(f931(x89171,x89171)),x89172),f862(f862(f176(f931(x89171,x89171),a921),x89174),x89173)))
% 25.54/25.41 [9003]~P1(f862(f54(x90031),f862(f862(f3(f932(x90031,a921)),x90032),f862(f862(f301(x90031),x90034),x90033))))+P1(f862(f54(x90031),f862(f862(f3(f932(x90031,a921)),x90032),x90033)))
% 25.54/25.41 [9080]P1(f862(f862(f321(f931(x90801,x90802)),f862(f862(f244(x90801,x90802),x90803),x90804)),f181(f932(f931(x90801,x90802),a921))))+~P1(f862(f862(f181(f932(x90801,f932(x90802,a921))),x90803),x90804))
% 25.54/25.41 [9216]~P93(x92161)+P1(f862(f862(f227(x92161),f862(f862(f103(x92161),x92162),f862(f862(f94(x92161),x92163),x92164))),f862(f862(f94(x92161),f862(f862(f103(x92161),x92162),x92163)),f862(f862(f103(x92161),x92162),x92164))))
% 25.54/25.41 [9217]~P109(x92171)+P1(f862(f862(f227(x92171),f862(f862(f226(x92171),x92172),f862(f862(f225(x92171),x92173),x92174))),f862(f862(f225(x92171),f862(f862(f226(x92171),x92172),x92173)),f862(f862(f226(x92171),x92172),x92174))))
% 25.54/25.41 [9234]~P1(f862(f862(f321(f931(x92341,x92342)),f862(f862(f244(x92341,x92342),x92343),x92344)),f181(f932(f931(x92341,x92342),a921))))+P1(f862(f862(f181(f932(x92341,f932(x92342,a921))),x92343),x92344))
% 25.54/25.41 [9366]E(x93661,x93662)+~P1(f862(f862(f321(f931(x93663,x93663)),f862(f862(f244(x93663,x93663),x93661),x93662)),f862(f165(f931(x93663,x93663)),f862(f862(f174(x93663,x93663),x93664),x93664))))
% 25.54/25.41 [9397]~P1(f862(f862(f321(f931(x93971,x93971)),f862(f862(f244(x93971,x93971),x93973),x93972)),f299(x93971,x93974)))+~P35(x93971,f862(f862(f301(f931(x93971,x93971)),f862(f862(f244(x93971,x93971),x93972),x93973)),x93974))
% 25.54/25.41 [9398]~P1(f862(f862(f321(f931(x93981,x93981)),f862(f862(f244(x93981,x93981),x93983),x93982)),f299(x93981,x93984)))+~P55(x93981,f862(f862(f301(f931(x93981,x93981)),f862(f862(f244(x93981,x93981),x93982),x93983)),x93984))
% 25.54/25.41 [9402]E(x94021,x94022)+E(f862(f129(x94023,f862(f862(f10(a921,a921,x94023),a314),f862(a317,x94021))),f862(f862(f144(x94023),x94022),x94024)),f862(f862(f144(x94023),x94022),f862(f129(x94023,f862(f862(f10(a921,a921,x94023),a314),f862(a317,x94021))),x94024)))
% 25.54/25.41 [9411]P1(f862(f862(f321(x94111),x94112),f862(f165(x94111),x94113)))+~P1(f862(f862(f321(f931(x94111,x94111)),f862(f862(f244(x94111,x94111),x94112),x94114)),f862(f165(f931(x94111,x94111)),f862(f862(f174(x94111,x94111),x94113),x94113))))
% 25.54/25.41 [9432]~P23(x94322,x94321,x94323,f234(f932(x94322,a921)),f234(f932(x94321,a921)))+E(f862(f302(x94321,x94322,f86(x94322,x94321,f234(f932(x94322,a921)),x94323)),x94324),f862(f303(x94322,x94321,x94323),x94324))
% 25.54/25.41 [9448]~P93(x94481)+P1(f862(f862(f227(x94481),f862(f862(f103(x94481),f862(f862(f94(x94481),x94482),x94483)),f862(f862(f94(x94481),x94482),x94484))),f862(f862(f94(x94481),x94482),f862(f862(f103(x94481),x94483),x94484))))
% 25.54/25.41 [9449]~P109(x94491)+P1(f862(f862(f227(x94491),f862(f862(f226(x94491),f862(f862(f225(x94491),x94492),x94493)),f862(f862(f225(x94491),x94492),x94494))),f862(f862(f225(x94491),x94492),f862(f862(f226(x94491),x94493),x94494))))
% 25.54/25.41 [9486]P1(f862(f862(f321(f931(x94861,x94861)),f862(f862(f244(x94861,x94861),x94862),x94863)),f862(f862(f280(x94861,x94861,x94861),x94864),f299(x94861,x94864))))+~P1(f862(f862(f321(f931(x94861,x94861)),f862(f862(f244(x94861,x94861),x94862),x94863)),x94864))
% 25.54/25.41 [9510]~P23(x95102,x95101,x95104,f234(f932(x95102,a921)),f234(f932(x95101,a921)))+E(f862(f254(x95101),f862(f862(f10(x95102,a921,x95101),x95103),f86(x95102,x95101,f234(f932(x95102,a921)),x95104))),f862(f302(x95102,x95101,x95104),f862(f254(x95102),x95103)))
% 25.54/25.41 [9524]~E(f862(f302(x95242,x95241,x95243),f234(f932(x95242,a921))),f234(f932(x95241,a921)))+P1(f862(f862(f227(f932(x95241,a921)),f862(f72(f932(x95241,a921)),f862(f302(x95242,x95241,x95243),x95244))),f862(f302(x95242,x95241,x95243),f862(f72(f932(x95242,a921)),x95244))))
% 25.54/25.41 [9854]P1(f862(f862(f321(f931(x98541,x98541)),f862(f862(f244(x98541,x98541),x98542),x98543)),f862(f277(x98541,x98541),f862(f862(f280(x98541,x98541,x98541),x98544),f299(x98541,x98544)))))+~P1(f862(f862(f321(f931(x98541,x98541)),f862(f862(f244(x98541,x98541),x98542),x98543)),f862(f862(f280(x98541,x98541,x98541),f862(f277(x98541,x98541),x98544)),f299(x98541,f862(f277(x98541,x98541),x98544)))))
% 25.54/25.41 [9855]~P1(f862(f862(f321(f931(x98551,x98551)),f862(f862(f244(x98551,x98551),x98552),x98553)),f862(f277(x98551,x98551),f862(f862(f280(x98551,x98551,x98551),x98554),f299(x98551,x98554)))))+P1(f862(f862(f321(f931(x98551,x98551)),f862(f862(f244(x98551,x98551),x98552),x98553)),f862(f862(f280(x98551,x98551,x98551),f862(f277(x98551,x98551),x98554)),f299(x98551,f862(f277(x98551,x98551),x98554)))))
% 25.54/25.41 [9876]~P1(f862(f862(f321(x98762),x98764),f862(f275(x98761,x98762),x98763)))+P1(f862(f862(f321(f931(x98761,x98762)),f862(f862(f244(x98761,x98762),f563(x98763,x98761,x98764,x98762)),x98764)),x98763))
% 25.54/25.41 [9877]~P1(f862(f862(f321(x98772),x98774),f862(f275(x98771,x98772),x98773)))+P1(f862(f862(f321(f931(x98771,x98772)),f862(f862(f244(x98771,x98772),f564(x98773,x98771,x98774,x98772)),x98774)),x98773))
% 25.54/25.41 [9903]~P1(f862(f862(f321(x99031),x99034),f862(f862(f103(f932(x99031,a921)),x99032),x99033)))+P1(f862(f862(f862(f103(f932(x99031,a921)),f862(f862(f9(x99031,f932(x99031,a921),a921),f321(x99031)),x99032)),f862(f862(f9(x99031,f932(x99031,a921),a921),f321(x99031)),x99033)),x99034))
% 25.54/25.41 [9904]~P1(f862(f862(f321(x99041),x99044),f862(f862(f94(f932(x99041,a921)),x99042),x99043)))+P1(f862(f862(f862(f94(f932(x99041,a921)),f862(f862(f9(x99041,f932(x99041,a921),a921),f321(x99041)),x99042)),f862(f862(f9(x99041,f932(x99041,a921),a921),f321(x99041)),x99043)),x99044))
% 25.54/25.41 [9985]~P1(f862(f862(f321(f931(x99851,x99851)),f862(f862(f244(x99851,x99851),x99854),x99853)),f862(f862(f280(x99851,x99851,x99851),x99852),f299(x99851,x99852))))+P1(f862(f862(f321(f931(x99851,x99851)),f862(f862(f244(x99851,x99851),f645(x99852,x99853,x99854,x99851)),x99853)),x99852))
% 25.54/25.41 [10021]P1(f862(f862(f321(x100211),x100212),f862(f862(f103(f932(x100211,a921)),x100213),x100214)))+~P1(f862(f862(f862(f103(f932(x100211,a921)),f862(f862(f9(x100211,f932(x100211,a921),a921),f321(x100211)),x100213)),f862(f862(f9(x100211,f932(x100211,a921),a921),f321(x100211)),x100214)),x100212))
% 25.54/25.41 [10022]P1(f862(f862(f321(x100221),x100222),f862(f862(f94(f932(x100221,a921)),x100223),x100224)))+~P1(f862(f862(f862(f94(f932(x100221,a921)),f862(f862(f9(x100221,f932(x100221,a921),a921),f321(x100221)),x100223)),f862(f862(f9(x100221,f932(x100221,a921),a921),f321(x100221)),x100224)),x100222))
% 25.54/25.41 [10295]P30(x102951,f862(f862(f9(x102951,f932(f931(x102951,x102951),a921),f932(x102951,a921)),f862(f862(f10(f932(x102951,f932(f932(f931(x102951,x102951),a921),a921)),f932(f932(f931(x102951,x102951),a921),f932(x102951,a921)),x102951),f9(x102951,f932(f931(x102951,x102951),a921),a921)),f862(f862(f10(f932(x102951,f931(x102951,x102951)),f932(x102951,f932(f932(f931(x102951,x102951),a921),a921)),x102951),f862(f10(f931(x102951,x102951),f932(f932(f931(x102951,x102951),a921),a921),x102951),f321(f931(x102951,x102951)))),f244(x102951,x102951)))),x102952),x102953,x102954)+~P1(f862(f862(f321(f931(f925(x102951),f925(x102951))),f862(f862(f244(f925(x102951),f925(x102951)),x102953),x102954)),f151(x102951,x102952)))
% 25.54/25.41 [10299]P56(x102991,f862(f862(f9(x102991,f932(f931(x102991,x102991),a921),f932(x102991,a921)),f862(f862(f10(f932(x102991,f932(f932(f931(x102991,x102991),a921),a921)),f932(f932(f931(x102991,x102991),a921),f932(x102991,a921)),x102991),f9(x102991,f932(f931(x102991,x102991),a921),a921)),f862(f862(f10(f932(x102991,f931(x102991,x102991)),f932(x102991,f932(f932(f931(x102991,x102991),a921),a921)),x102991),f862(f10(f931(x102991,x102991),f932(f932(f931(x102991,x102991),a921),a921),x102991),f321(f931(x102991,x102991)))),f244(x102991,x102991)))),x102992),x102993,x102994)+~P1(f862(f862(f321(f931(f932(x102991,a921),f932(x102991,a921))),f862(f862(f244(f932(x102991,a921),f932(x102991,a921)),x102993),x102994)),f310(x102991,x102992)))
% 25.54/25.41 [10334]E(x103341,x103342)+~E(f862(f862(f9(x103343,f932(f931(x103343,x103344),a921),f932(x103344,a921)),f862(f862(f10(f932(x103344,f932(f932(f931(x103343,x103344),a921),a921)),f932(f932(f931(x103343,x103344),a921),f932(x103344,a921)),x103343),f9(x103344,f932(f931(x103343,x103344),a921),a921)),f862(f862(f10(f932(x103344,f931(x103343,x103344)),f932(x103344,f932(f932(f931(x103343,x103344),a921),a921)),x103343),f862(f10(f931(x103343,x103344),f932(f932(f931(x103343,x103344),a921),a921),x103344),f321(f931(x103343,x103344)))),f244(x103343,x103344)))),x103341),f862(f862(f9(x103343,f932(f931(x103343,x103344),a921),f932(x103344,a921)),f862(f862(f10(f932(x103344,f932(f932(f931(x103343,x103344),a921),a921)),f932(f932(f931(x103343,x103344),a921),f932(x103344,a921)),x103343),f9(x103344,f932(f931(x103343,x103344),a921),a921)),f862(f862(f10(f932(x103344,f931(x103343,x103344)),f932(x103344,f932(f932(f931(x103343,x103344),a921),a921)),x103343),f862(f10(f931(x103343,x103344),f932(f932(f931(x103343,x103344),a921),a921),x103344),f321(f931(x103343,x103344)))),f244(x103343,x103344)))),x103342))
% 25.54/25.41 [10337]~P30(x103371,f862(f862(f9(x103371,f932(f931(x103371,x103371),a921),f932(x103371,a921)),f862(f862(f10(f932(x103371,f932(f932(f931(x103371,x103371),a921),a921)),f932(f932(f931(x103371,x103371),a921),f932(x103371,a921)),x103371),f9(x103371,f932(f931(x103371,x103371),a921),a921)),f862(f862(f10(f932(x103371,f931(x103371,x103371)),f932(x103371,f932(f932(f931(x103371,x103371),a921),a921)),x103371),f862(f10(f931(x103371,x103371),f932(f932(f931(x103371,x103371),a921),a921),x103371),f321(f931(x103371,x103371)))),f244(x103371,x103371)))),x103374),x103372,x103373)+P1(f862(f862(f321(f931(f925(x103371),f925(x103371))),f862(f862(f244(f925(x103371),f925(x103371)),x103372),x103373)),f151(x103371,x103374)))
% 25.54/25.41 [10338]~P56(x103381,f862(f862(f9(x103381,f932(f931(x103381,x103381),a921),f932(x103381,a921)),f862(f862(f10(f932(x103381,f932(f932(f931(x103381,x103381),a921),a921)),f932(f932(f931(x103381,x103381),a921),f932(x103381,a921)),x103381),f9(x103381,f932(f931(x103381,x103381),a921),a921)),f862(f862(f10(f932(x103381,f931(x103381,x103381)),f932(x103381,f932(f932(f931(x103381,x103381),a921),a921)),x103381),f862(f10(f931(x103381,x103381),f932(f932(f931(x103381,x103381),a921),a921),x103381),f321(f931(x103381,x103381)))),f244(x103381,x103381)))),x103384),x103382,x103383)+P1(f862(f862(f321(f931(f932(x103381,a921),f932(x103381,a921))),f862(f862(f244(f932(x103381,a921),f932(x103381,a921)),x103382),x103383)),f310(x103381,x103384)))
% 25.54/25.41 [7696]~P98(x76961)+E(f862(f862(f74(x76961),f862(f96(x76961),x76962)),f862(f862(f74(x76961),f862(f96(x76961),x76963)),x76964)),f862(f862(f74(x76961),f862(f96(x76961),f862(f862(f74(a1),x76962),x76963))),x76964))
% 25.54/25.41 [7697]~P98(x76971)+E(f862(f862(f73(x76971),f862(f96(x76971),x76972)),f862(f862(f3(x76971),f862(f96(x76971),x76973)),x76974)),f862(f862(f3(x76971),f862(f96(x76971),f862(f862(f73(a1),x76972),x76973))),x76974))
% 25.54/25.41 [7698]~P98(x76981)+E(f862(f862(f73(x76981),f862(f96(x76981),x76982)),f862(f862(f73(x76981),f862(f96(x76981),x76983)),x76984)),f862(f862(f73(x76981),f862(f96(x76981),f862(f862(f73(a1),x76982),x76983))),x76984))
% 25.54/25.41 [7739]~P147(x77391)+E(f862(f158(x77391),f862(f862(f147(x77392,x77391),f862(f18(x77391,x77392),x77393)),x77394)),f862(f862(f74(x77391),f862(f93(x77391),f862(f182(f925(x77392)),x77394))),x77393))
% 25.54/25.41 [7978]E(f862(f260(x79781,f862(f862(f144(f931(a92,x79781)),x79782),x79783)),x79784),f862(f248(a92,x79781),x79782))+~P1(f862(f862(f228(a92),x79784),f862(f243(a92,x79781),x79782)))
% 25.54/25.41 [8020]~P98(x80201)+E(f862(f862(f73(x80201),f862(f96(x80201),x80202)),f862(f862(f3(x80201),x80203),f862(f96(x80201),x80204))),f862(f862(f73(x80201),f862(f96(x80201),f862(f862(f73(a1),x80202),f862(f72(a1),x80204)))),x80203))
% 25.54/25.41 [8156]E(f862(f260(x81561,x81562),f862(f862(f3(a92),x81563),f862(f243(a92,x81561),x81564))),f862(f260(x81561,f862(f862(f144(f931(a92,x81561)),x81564),x81562)),x81563))+P1(f862(f862(f228(a92),x81563),f862(f243(a92,x81561),x81564)))
% 25.54/25.41 [8597]~P1(f862(f862(f321(x85971),x85972),f862(f165(x85971),f107(x85971,x85974))))+P1(f862(f862(f321(x85971),x85972),f862(f165(x85971),f107(x85971,f862(f862(f127(x85971),x85973),x85974)))))
% 25.54/25.41 [8598]~P1(f862(f862(f321(x85981),x85982),f862(f165(x85981),f107(x85981,x85983))))+P1(f862(f862(f321(x85981),x85982),f862(f165(x85981),f107(x85981,f862(f862(f127(x85981),x85983),x85984)))))
% 25.54/25.41 [8618]E(f862(f862(f103(f932(x86181,a921)),f862(f862(f94(f932(x86181,a921)),x86182),x86183)),x86184),f862(f862(f94(f932(x86181,a921)),x86182),f862(f862(f103(f932(x86181,a921)),x86183),x86184)))+~P1(f862(f862(f227(f932(x86181,a921)),x86184),x86182))
% 25.54/25.41 [8931]~E(f862(f862(f103(f932(x89311,a921)),f862(f862(f94(f932(x89311,a921)),x89313),x89314)),x89312),f862(f862(f94(f932(x89311,a921)),x89313),f862(f862(f103(f932(x89311,a921)),x89314),x89312)))+P1(f862(f862(f227(f932(x89311,a921)),x89312),x89313))
% 25.54/25.41 [9221]~P1(f862(f862(f227(f932(x92211,a921)),x92212),f862(f862(f103(f932(x92211,a921)),x92213),x92214)))+P1(f862(f862(f227(f932(x92211,a921)),f862(f862(f3(f932(x92211,a921)),x92212),x92213)),x92214))
% 25.54/25.41 [9338]~E(f862(f302(x93381,x93382,x93383),f234(f932(x93381,a921))),f234(f932(x93382,a921)))+E(f862(f302(x93381,x93382,x93383),f862(f302(x93382,x93381,f86(x93381,x93382,f234(f932(x93381,a921)),x93383)),x93384)),x93384)
% 25.54/25.41 [9343]P1(f862(f862(f227(f932(x93431,a921)),x93432),f862(f862(f103(f932(x93431,a921)),x93433),x93434)))+~P1(f862(f862(f227(f932(x93431,a921)),f862(f862(f3(f932(x93431,a921)),x93432),x93433)),x93434))
% 25.54/25.41 [9428]~P86(x94281)+E(f862(f69(x94281),f862(f862(f8(x94282,x94281),f862(f862(f10(x94281,x94281,x94282),f69(x94281)),x94283)),x94284)),f862(f862(f8(x94282,x94281),f862(f862(f10(x94281,x94281,x94282),f69(x94281)),x94283)),x94284))
% 25.54/25.41 [9603]~P86(x96031)+P1(f862(f862(f227(x96031),f2(x96031)),f862(f862(f8(x96032,x96031),f862(f862(f10(x96031,x96031,x96032),f69(x96031)),x96033)),x96034)))
% 25.54/25.41 [9607]~P59(x96071)+E(f862(f158(x96071),f862(f862(f147(x96072,x96071),f862(f66(x96071,x96071,x96072,f72(x96071)),x96073)),x96074)),f862(f72(x96071),f862(f158(x96071),f862(f862(f147(x96072,x96071),x96073),x96074))))
% 25.54/25.41 [9750]~P86(x97501)+P1(f862(f862(f227(x97501),f862(f69(x97501),f862(f862(f8(x97502,x97501),x97503),x97504))),f862(f862(f8(x97502,x97501),f862(f862(f10(x97501,x97501,x97502),f69(x97501)),x97503)),x97504)))
% 25.54/25.41 [9779]~E(f862(f862(f73(a924),x97791),x97794),f862(f862(f73(a924),x97793),x97792))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97791),x97792)),f862(f862(f244(a924,a924),x97793),x97794))),a101))
% 25.54/25.41 [9780]~P1(f862(f862(f228(a924),x97801),x97803))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97801),x97802)),f862(f862(f244(a924,a924),x97803),x97804))),a26))
% 25.54/25.41 [9781]~P1(f862(f862(f228(a924),x97811),x97813))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97811),x97812)),f862(f862(f244(a924,a924),x97813),x97814))),a64))
% 25.54/25.41 [9928]E(f862(f862(f73(a924),x99281),x99282),f862(f862(f73(a924),x99283),x99284))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x99281),x99284)),f862(f862(f244(a924,a924),x99283),x99282))),a101))
% 25.54/25.41 [9959]E(f862(f862(f157(x99591),f862(f862(f131(x99591),f862(f182(f925(x99591)),f170(x99591,x99592,x99593))),x99593)),x99594),f862(f862(f157(x99591),x99593),f862(f862(f73(a924),x99594),f862(f182(f925(x99591)),f170(x99591,x99592,x99593)))))+~P1(f862(f862(f228(a924),x99594),f862(f182(f925(x99591)),f862(f862(f131(x99591),f862(f182(f925(x99591)),f170(x99591,x99592,x99593))),x99593))))
% 25.54/25.41 [9976]~P1(f862(f862(f321(x99762),x99764),f862(f862(f32(x99761,f932(x99762,a921)),f234(f932(x99761,a921))),x99763)))+P1(f862(f862(f862(f32(x99761,f932(x99762,a921)),f234(f932(x99761,a921))),f862(f862(f10(f932(x99762,a921),f932(x99762,a921),x99761),f862(f9(x99762,f932(x99762,a921),a921),f321(x99762))),x99763)),x99764))
% 25.54/25.41 [9977]~P1(f862(f862(f321(x99772),x99774),f862(f862(f33(x99771,f932(x99772,a921)),f234(f932(x99771,a921))),x99773)))+P1(f862(f862(f862(f33(x99771,f932(x99772,a921)),f234(f932(x99771,a921))),f862(f862(f10(f932(x99772,a921),f932(x99772,a921),x99771),f862(f9(x99772,f932(x99772,a921),a921),f321(x99772))),x99773)),x99774))
% 25.54/25.41 [10047]~P1(f862(f42(x100471,x100472),f862(f862(f244(a1,a1),x100474),x100473)))+P1(f862(f42(f862(f72(a1),x100471),x100472),f862(f862(f244(a1,a1),f862(f862(f862(f89(a1),f862(f862(a317,x100473),f2(a1))),f862(f72(a1),x100474)),f862(f862(f3(a1),f862(f72(a1),x100474)),f71(a1)))),f862(f862(f862(f89(a1),f862(f862(a317,x100473),f2(a1))),f2(a1)),f862(f862(f3(a1),x100472),x100473)))))
% 25.54/25.41 [10059]P1(f862(f862(f321(x100591),x100592),f862(f862(f32(x100593,f932(x100591,a921)),f234(f932(x100593,a921))),x100594)))+~P1(f862(f862(f862(f32(x100593,f932(x100591,a921)),f234(f932(x100593,a921))),f862(f862(f10(f932(x100591,a921),f932(x100591,a921),x100593),f862(f9(x100591,f932(x100591,a921),a921),f321(x100591))),x100594)),x100592))
% 25.54/25.41 [10060]P1(f862(f862(f321(x100601),x100602),f862(f862(f33(x100603,f932(x100601,a921)),f234(f932(x100603,a921))),x100604)))+~P1(f862(f862(f862(f33(x100603,f932(x100601,a921)),f234(f932(x100603,a921))),f862(f862(f10(f932(x100601,a921),f932(x100601,a921),x100603),f862(f9(x100601,f932(x100601,a921),a921),f321(x100601))),x100604)),x100602))
% 25.54/25.41 [10072]E(f862(f862(f33(a924,f932(x100721,a921)),f234(f932(a924,a921))),x100722),f862(f862(f33(a924,f932(x100721,a921)),f234(f932(a924,a921))),x100723))+~E(f862(f862(f33(a924,f932(x100721,a921)),f862(f295(a924,f2(a924)),f518(x100722,x100724,x100723,x100721))),x100723),f862(f862(f33(a924,f932(x100721,a921)),f862(f295(a924,f2(a924)),f862(f862(f73(a924),f518(x100722,x100724,x100723,x100721)),x100724))),x100722))
% 25.54/25.41 [10415]~P1(f862(f862(f227(f932(f931(x104151,x104152),a921)),x104153),x104154))+P1(f862(f862(f227(f932(x104151,f932(x104152,a921))),f862(f862(f9(x104151,f932(f931(x104151,x104152),a921),f932(x104152,a921)),f862(f862(f10(f932(x104152,f932(f932(f931(x104151,x104152),a921),a921)),f932(f932(f931(x104151,x104152),a921),f932(x104152,a921)),x104151),f9(x104152,f932(f931(x104151,x104152),a921),a921)),f862(f862(f10(f932(x104152,f931(x104151,x104152)),f932(x104152,f932(f932(f931(x104151,x104152),a921),a921)),x104151),f862(f10(f931(x104151,x104152),f932(f932(f931(x104151,x104152),a921),a921),x104152),f321(f931(x104151,x104152)))),f244(x104151,x104152)))),x104153)),f862(f862(f9(x104151,f932(f931(x104151,x104152),a921),f932(x104152,a921)),f862(f862(f10(f932(x104152,f932(f932(f931(x104151,x104152),a921),a921)),f932(f932(f931(x104151,x104152),a921),f932(x104152,a921)),x104151),f9(x104152,f932(f931(x104151,x104152),a921),a921)),f862(f862(f10(f932(x104152,f931(x104151,x104152)),f932(x104152,f932(f932(f931(x104151,x104152),a921),a921)),x104151),f862(f10(f931(x104151,x104152),f932(f932(f931(x104151,x104152),a921),a921),x104152),f321(f931(x104151,x104152)))),f244(x104151,x104152)))),x104154)))
% 25.54/25.41 [10431]P1(f862(f862(f227(f932(f931(x104311,x104312),a921)),x104313),x104314))+~P1(f862(f862(f227(f932(x104311,f932(x104312,a921))),f862(f862(f9(x104311,f932(f931(x104311,x104312),a921),f932(x104312,a921)),f862(f862(f10(f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),f932(f932(f931(x104311,x104312),a921),f932(x104312,a921)),x104311),f9(x104312,f932(f931(x104311,x104312),a921),a921)),f862(f862(f10(f932(x104312,f931(x104311,x104312)),f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),x104311),f862(f10(f931(x104311,x104312),f932(f932(f931(x104311,x104312),a921),a921),x104312),f321(f931(x104311,x104312)))),f244(x104311,x104312)))),x104313)),f862(f862(f9(x104311,f932(f931(x104311,x104312),a921),f932(x104312,a921)),f862(f862(f10(f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),f932(f932(f931(x104311,x104312),a921),f932(x104312,a921)),x104311),f9(x104312,f932(f931(x104311,x104312),a921),a921)),f862(f862(f10(f932(x104312,f931(x104311,x104312)),f932(x104312,f932(f932(f931(x104311,x104312),a921),a921)),x104311),f862(f10(f931(x104311,x104312),f932(f932(f931(x104311,x104312),a921),a921),x104312),f321(f931(x104311,x104312)))),f244(x104311,x104312)))),x104314)))
% 25.54/25.41 [9475]~P1(f862(f862(f321(f931(x94751,x94751)),x94752),f299(x94751,x94754)))+P1(f862(f862(f321(f931(x94751,x94751)),x94752),f299(x94751,f862(f862(f103(f932(f931(x94751,x94751),a921)),x94753),x94754))))
% 25.54/25.41 [9476]~P1(f862(f862(f321(f931(x94761,x94761)),x94762),f299(x94761,x94763)))+P1(f862(f862(f321(f931(x94761,x94761)),x94762),f299(x94761,f862(f862(f103(f932(f931(x94761,x94761),a921)),x94763),x94764))))
% 25.54/25.41 [10160]~P1(f862(f862(f227(a924),f862(f862(f73(a924),x101601),x101604)),f862(f862(f73(a924),x101603),x101602)))+P1(f862(f862(f227(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101601),x101602)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101603),x101604)),f181(f932(f931(a924,a924),a921)))))))
% 25.54/25.41 [10161]~P1(f862(f862(f228(a924),f862(f862(f73(a924),x101611),x101614)),f862(f862(f73(a924),x101613),x101612)))+P1(f862(f862(f228(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101611),x101612)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x101613),x101614)),f181(f932(f931(a924,a924),a921)))))))
% 25.54/25.41 [10240]P1(f862(f862(f227(a924),f862(f862(f73(a924),x102401),x102402)),f862(f862(f73(a924),x102403),x102404)))+~P1(f862(f862(f227(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102401),x102404)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102403),x102402)),f181(f932(f931(a924,a924),a921)))))))
% 25.54/25.41 [10241]P1(f862(f862(f228(a924),f862(f862(f73(a924),x102411),x102412)),f862(f862(f73(a924),x102413),x102414)))+~P1(f862(f862(f228(a1),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102411),x102414)),f181(f932(f931(a924,a924),a921)))))),f862(a82,f862(f276(f931(a924,a924),f931(a924,a924),a101),f862(f862(f301(f931(a924,a924)),f862(f862(f244(a924,a924),x102413),x102412)),f181(f932(f931(a924,a924),a921)))))))
% 25.54/25.41 [10281]P1(f862(f862(f227(f932(x102811,a921)),f862(f862(f33(a924,f932(x102811,a921)),f234(f932(a924,a921))),x102812)),f862(f862(f33(a924,f932(x102811,a921)),f234(f932(a924,a921))),x102813)))+~P1(f862(f862(f227(f932(x102811,a921)),f862(f862(f33(a924,f932(x102811,a921)),f862(f295(a924,f2(a924)),f509(x102813,x102814,x102812,x102811))),x102812)),f862(f862(f33(a924,f932(x102811,a921)),f862(f295(a924,f2(a924)),f862(f862(f73(a924),f509(x102813,x102814,x102812,x102811)),x102814))),x102813)))
% 25.54/25.41 [10341]P1(f862(f862(f227(a92),x103414),f2(a92)))+E(f862(f862(f251(f931(a92,a92),f931(x103411,f932(a927,a315)),f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92))),f862(x103412,x103413)),f862(f862(f10(f932(f932(a92,f932(a921,f928(f926(x103411)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92))),f931(x103411,f932(a927,a315))),f862(f251(f931(a92,a92),f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92))),f269(x103411,x103412,f862(f862(f3(a92),x103414),f71(a92)),x103413))),f862(f862(f10(f932(f932(a92,f932(a921,f928(f926(x103411)))),f932(a92,f932(a921,f928(f926(x103411))))),f932(f932(a92,f932(a921,f928(f926(x103411)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92)))),f931(x103411,f932(a927,a315))),f862(f10(f932(a92,f932(a921,f928(f926(x103411)))),f932(f931(a92,a92),f931(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92))),f932(a92,f932(a921,f928(f926(x103411))))),f244(f932(a92,f932(a921,f928(f926(x103411)))),f931(a92,a92)))),f862(f862(f10(f932(a92,f932(a921,f928(f926(x103411)))),f932(f932(a92,f932(a921,f928(f926(x103411)))),f932(a92,f932(a921,f928(f926(x103411))))),f931(x103411,f932(a927,a315))),f37(x103411)),f862(f862(f10(x103411,f932(a92,f932(a921,f928(f926(x103411)))),f931(x103411,f932(a927,a315))),f35(x103411)),f243(x103411,f932(a927,a315))))))),f269(x103411,x103412,x103414,x103413))
% 25.54/25.41 [10405]~P1(f862(f862(f321(x104052),x104054),f862(f275(x104051,x104052),x104053)))+P1(f862(f242(x104051,x104052,f862(f862(f9(x104051,f932(f931(x104051,x104052),a921),f932(x104052,a921)),f862(f862(f10(f932(x104052,f932(f932(f931(x104051,x104052),a921),a921)),f932(f932(f931(x104051,x104052),a921),f932(x104052,a921)),x104051),f9(x104052,f932(f931(x104051,x104052),a921),a921)),f862(f862(f10(f932(x104052,f931(x104051,x104052)),f932(x104052,f932(f932(f931(x104051,x104052),a921),a921)),x104051),f862(f10(f931(x104051,x104052),f932(f932(f931(x104051,x104052),a921),a921),x104052),f321(f931(x104051,x104052)))),f244(x104051,x104052)))),x104053)),x104054))
% 25.54/25.41 [10406]~P1(f862(f862(f321(x104061),x104064),f862(f256(x104061,x104062),x104063)))+P1(f862(f241(x104061,x104062,f862(f862(f9(x104061,f932(f931(x104061,x104062),a921),f932(x104062,a921)),f862(f862(f10(f932(x104062,f932(f932(f931(x104061,x104062),a921),a921)),f932(f932(f931(x104061,x104062),a921),f932(x104062,a921)),x104061),f9(x104062,f932(f931(x104061,x104062),a921),a921)),f862(f862(f10(f932(x104062,f931(x104061,x104062)),f932(x104062,f932(f932(f931(x104061,x104062),a921),a921)),x104061),f862(f10(f931(x104061,x104062),f932(f932(f931(x104061,x104062),a921),a921),x104062),f321(f931(x104061,x104062)))),f244(x104061,x104062)))),x104063)),x104064))
% 25.54/25.41 [10418]P1(f862(f862(f321(x104181),x104182),f862(f275(x104183,x104181),x104184)))+~P1(f862(f242(x104183,x104181,f862(f862(f9(x104183,f932(f931(x104183,x104181),a921),f932(x104181,a921)),f862(f862(f10(f932(x104181,f932(f932(f931(x104183,x104181),a921),a921)),f932(f932(f931(x104183,x104181),a921),f932(x104181,a921)),x104183),f9(x104181,f932(f931(x104183,x104181),a921),a921)),f862(f862(f10(f932(x104181,f931(x104183,x104181)),f932(x104181,f932(f932(f931(x104183,x104181),a921),a921)),x104183),f862(f10(f931(x104183,x104181),f932(f932(f931(x104183,x104181),a921),a921),x104181),f321(f931(x104183,x104181)))),f244(x104183,x104181)))),x104184)),x104182))
% 25.54/25.41 [10419]P1(f862(f862(f321(x104191),x104192),f862(f256(x104191,x104193),x104194)))+~P1(f862(f241(x104191,x104193,f862(f862(f9(x104191,f932(f931(x104191,x104193),a921),f932(x104193,a921)),f862(f862(f10(f932(x104193,f932(f932(f931(x104191,x104193),a921),a921)),f932(f932(f931(x104191,x104193),a921),f932(x104193,a921)),x104191),f9(x104193,f932(f931(x104191,x104193),a921),a921)),f862(f862(f10(f932(x104193,f931(x104191,x104193)),f932(x104193,f932(f932(f931(x104191,x104193),a921),a921)),x104191),f862(f10(f931(x104191,x104193),f932(f932(f931(x104191,x104193),a921),a921),x104193),f321(f931(x104191,x104193)))),f244(x104191,x104193)))),x104194)),x104192))
% 25.54/25.41 [10083]P1(f862(f153(x100831,x100832),x100833))+~P1(f862(f153(x100831,f862(f862(f20(x100831,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100831),a318),x100834)),x100832)),x100833))
% 25.54/25.41 [10084]P1(f862(f153(x100841,x100842),x100843))+~P1(f862(f153(x100841,f862(f862(f20(x100841,a921,a921),f862(f862(f10(a921,f932(a921,a921),x100841),a318),x100842)),x100844)),x100843))
% 25.54/25.41 [10162]~P119(x101621)+E(f862(f862(f74(x101621),f862(f862(f73(x101621),f71(x101621)),f71(x101621))),f862(f862(f8(a924,x101621),f862(f862(f10(x101621,x101621,a924),f862(f73(x101621),x101622)),f862(f862(f9(a924,x101621,x101621),f862(f862(f10(x101621,f932(x101621,x101621),a924),f74(x101621)),f93(x101621))),x101623))),f862(f292(a924),x101624))),f862(f862(f74(x101621),f862(f93(x101621),x101624)),f862(f862(f73(x101621),x101622),f862(f862(f73(x101621),x101622),f862(f862(f74(x101621),f862(f93(x101621),f862(f862(f3(a924),x101624),f71(a924)))),x101623)))))
% 25.54/25.41 [10302]P1(f862(x103021,f555(x103022,x103023,x103024,x103021)))+P35(x103022,f862(f254(f931(x103022,x103022)),f862(f249(x103022,x103022,a921),f862(f862(f10(f932(x103022,a921),f932(x103022,a921),x103022),f862(f20(x103022,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103022),a318),x103021))),f862(f862(f9(x103022,f932(x103022,x103022),f932(x103022,a921)),f862(f862(f10(f932(x103022,a921),f932(f932(x103022,x103022),f932(x103022,a921)),x103022),f10(x103022,a921,x103022)),a317)),x103023)))))
% 25.54/25.41 [10316]~P1(f862(f862(f228(a924),f862(x103164,f862(x103163,f555(x103161,x103163,x103164,x103162)))),f862(x103164,f555(x103161,x103163,x103164,x103162))))+P35(x103161,f862(f254(f931(x103161,x103161)),f862(f249(x103161,x103161,a921),f862(f862(f10(f932(x103161,a921),f932(x103161,a921),x103161),f862(f20(x103161,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103161),a318),x103162))),f862(f862(f9(x103161,f932(x103161,x103161),f932(x103161,a921)),f862(f862(f10(f932(x103161,a921),f932(f932(x103161,x103161),f932(x103161,a921)),x103161),f10(x103161,a921,x103161)),a317)),x103163)))))
% 25.54/25.41 [10392]~P3(x103921)+E(f31(x103921,f862(f254(x103921),f862(f862(f10(f932(f932(x103922,x103921),a921),a921,x103921),f80(f932(x103922,x103921))),f862(f862(f10(f932(f932(x103922,x103921),a921),f932(f932(x103922,x103921),a921),x103921),f862(f20(f932(x103922,x103921),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103922,x103921)),a318),f862(f862(f9(f932(x103922,x103921),f932(f932(x103922,x103921),a921),a921),f321(f932(x103922,x103921))),x103923)))),f862(f862(f9(x103921,f932(f932(x103922,x103921),x103921),f932(f932(x103922,x103921),a921)),f862(f862(f10(f932(x103921,a921),f932(f932(f932(x103922,x103921),x103921),f932(f932(x103922,x103921),a921)),x103921),f10(x103921,a921,f932(x103922,x103921))),a317)),f862(f862(f9(f932(x103922,x103921),x103922,x103921),f7(f932(x103922,x103921))),x103924)))))),f862(f31(f932(x103922,x103921),x103923),x103924))
% 25.54/25.41 [10393]~P3(x103931)+E(f31(x103931,f862(f254(x103931),f862(f862(f10(f932(f932(x103932,x103931),a921),a921,x103931),f80(f932(x103932,x103931))),f862(f862(f10(f932(f932(x103932,x103931),a921),f932(f932(x103932,x103931),a921),x103931),f862(f20(f932(x103932,x103931),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103932,x103931)),a318),f862(f862(f9(f932(x103932,x103931),f932(f932(x103932,x103931),a921),a921),f321(f932(x103932,x103931))),x103933)))),f862(f862(f9(x103931,f932(f932(x103932,x103931),x103931),f932(f932(x103932,x103931),a921)),f862(f862(f10(f932(x103931,a921),f932(f932(f932(x103932,x103931),x103931),f932(f932(x103932,x103931),a921)),x103931),f10(x103931,a921,f932(x103932,x103931))),a317)),f862(f862(f9(f932(x103932,x103931),x103932,x103931),f7(f932(x103932,x103931))),x103934)))))),f862(f31(f932(x103932,x103931),x103933),x103934))
% 25.54/25.41 [10394]~P3(x103941)+E(f30(x103941,f862(f254(x103941),f862(f862(f10(f932(f932(x103942,x103941),a921),a921,x103941),f80(f932(x103942,x103941))),f862(f862(f10(f932(f932(x103942,x103941),a921),f932(f932(x103942,x103941),a921),x103941),f862(f20(f932(x103942,x103941),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103942,x103941)),a318),f862(f862(f9(f932(x103942,x103941),f932(f932(x103942,x103941),a921),a921),f321(f932(x103942,x103941))),x103943)))),f862(f862(f9(x103941,f932(f932(x103942,x103941),x103941),f932(f932(x103942,x103941),a921)),f862(f862(f10(f932(x103941,a921),f932(f932(f932(x103942,x103941),x103941),f932(f932(x103942,x103941),a921)),x103941),f10(x103941,a921,f932(x103942,x103941))),a317)),f862(f862(f9(f932(x103942,x103941),x103942,x103941),f7(f932(x103942,x103941))),x103944)))))),f862(f30(f932(x103942,x103941),x103943),x103944))
% 25.54/25.41 [10395]~P3(x103951)+E(f30(x103951,f862(f254(x103951),f862(f862(f10(f932(f932(x103952,x103951),a921),a921,x103951),f80(f932(x103952,x103951))),f862(f862(f10(f932(f932(x103952,x103951),a921),f932(f932(x103952,x103951),a921),x103951),f862(f20(f932(x103952,x103951),a921,a921),f862(f862(f10(a921,f932(a921,a921),f932(x103952,x103951)),a318),f862(f862(f9(f932(x103952,x103951),f932(f932(x103952,x103951),a921),a921),f321(f932(x103952,x103951))),x103953)))),f862(f862(f9(x103951,f932(f932(x103952,x103951),x103951),f932(f932(x103952,x103951),a921)),f862(f862(f10(f932(x103951,a921),f932(f932(f932(x103952,x103951),x103951),f932(f932(x103952,x103951),a921)),x103951),f10(x103951,a921,f932(x103952,x103951))),a317)),f862(f862(f9(f932(x103952,x103951),x103952,x103951),f7(f932(x103952,x103951))),x103954)))))),f862(f30(f932(x103952,x103951),x103953),x103954))
% 25.54/25.41 [10444]~P1(f862(f862(f321(f931(x104441,x104441)),f862(f862(f244(x104441,x104441),x104443),x104444)),f862(f862(f103(f932(f931(x104441,x104441),a921)),x104442),f299(x104441,f181(f932(f931(x104441,x104441),a921))))))+P1(f862(f862(f862(f862(f103(f932(x104441,f932(x104441,a921))),f862(f862(f9(x104441,f932(f931(x104441,x104441),a921),f932(x104441,a921)),f862(f862(f10(f932(x104441,f932(f932(f931(x104441,x104441),a921),a921)),f932(f932(f931(x104441,x104441),a921),f932(x104441,a921)),x104441),f9(x104441,f932(f931(x104441,x104441),a921),a921)),f862(f862(f10(f932(x104441,f931(x104441,x104441)),f932(x104441,f932(f932(f931(x104441,x104441),a921),a921)),x104441),f862(f10(f931(x104441,x104441),f932(f932(f931(x104441,x104441),a921),a921),x104441),f321(f931(x104441,x104441)))),f244(x104441,x104441)))),x104442)),a317),x104443),x104444))
% 25.54/25.41 [10454]P1(f862(f862(f321(f931(x104541,x104541)),f862(f862(f244(x104541,x104541),x104542),x104543)),f862(f862(f103(f932(f931(x104541,x104541),a921)),x104544),f299(x104541,f181(f932(f931(x104541,x104541),a921))))))+~P1(f862(f862(f862(f862(f103(f932(x104541,f932(x104541,a921))),f862(f862(f9(x104541,f932(f931(x104541,x104541),a921),f932(x104541,a921)),f862(f862(f10(f932(x104541,f932(f932(f931(x104541,x104541),a921),a921)),f932(f932(f931(x104541,x104541),a921),f932(x104541,a921)),x104541),f9(x104541,f932(f931(x104541,x104541),a921),a921)),f862(f862(f10(f932(x104541,f931(x104541,x104541)),f932(x104541,f932(f932(f931(x104541,x104541),a921),a921)),x104541),f862(f10(f931(x104541,x104541),f932(f932(f931(x104541,x104541),a921),a921),x104541),f321(f931(x104541,x104541)))),f244(x104541,x104541)))),x104544)),a317),x104542),x104543))
% 25.54/25.41 [10402]E(f862(f862(f144(f925(x104021)),f862(f862(f144(x104021),x104022),f862(f135(f925(x104021),f925(x104021),f127(x104021),f106(x104021)),f862(f862(f147(f925(x104021),f925(x104021)),f149(f925(x104021),x104021,f106(x104021),f862(f862(f10(f925(x104021),f932(f925(x104021),f925(x104021)),x104021),f18(f925(x104021),f925(x104021))),f862(f862(f9(x104021,f925(x104021),f925(x104021)),f144(x104021)),f106(x104021))))),x104023)))),f172(x104021,f862(f862(f144(f925(x104021)),x104024),f862(f135(f925(f925(x104021)),f925(f925(x104021)),f127(f925(x104021)),f106(f925(x104021))),f862(f862(f147(f925(x104021),f925(f925(x104021))),f149(f925(f925(x104021)),x104021,f106(f925(x104021)),f862(f18(f932(f925(x104021),f925(f925(x104021))),x104021),f862(f862(f9(f925(x104021),f925(f925(x104021)),f925(f925(x104021))),f144(f925(x104021))),f106(f925(x104021)))))),x104023))))),f172(x104021,f862(f862(f144(f925(x104021)),f862(f862(f144(x104021),x104022),x104024)),x104023)))+~P1(f862(f307(f925(f925(x104021)),f173(x104021)),f862(f862(f144(f925(x104021)),f862(f862(f144(x104021),x104022),x104024)),x104023)))
% 25.54/25.41 [10443]~P1(f862(f54(x104432),f862(f254(x104432),x104434)))+P1(f862(f54(x104431),f862(f254(x104431),f862(f862(f10(f932(x104432,a921),a921,x104431),f80(x104432)),f862(f862(f9(x104431,f932(x104432,a921),f932(x104432,a921)),f862(f862(f10(f932(x104432,f932(a921,a921)),f932(f932(x104432,a921),f932(x104432,a921)),x104431),f20(x104432,a921,a921)),f862(f862(f10(f932(x104432,a921),f932(x104432,f932(a921,a921)),x104431),f862(f10(a921,f932(a921,a921),x104432),a318)),f862(f862(f9(x104431,f932(x104432,x104431),f932(x104432,a921)),f862(f862(f10(f932(x104431,a921),f932(f932(x104432,x104431),f932(x104432,a921)),x104431),f10(x104431,a921,x104432)),a317)),x104433)))),x104434)))))
% 25.54/25.41 [8968]P22(x89681,x89682,x89683,x89684)+~P23(x89681,x89682,x89683,x89684,x89685)
% 25.54/25.41 [8969]P22(x89691,x89692,x89693,x89694)+~P23(x89691,x89692,x89693,x89694,x89695)
% 25.54/25.41 [5443]E(x54431,x54432)+~E(f162(x54433,x54431,x54434),f162(x54433,x54432,x54435))
% 25.54/25.41 [5444]E(x54441,x54442)+~E(f119(x54443,x54444,x54441),f119(x54443,x54445,x54442))
% 25.54/25.41 [5445]E(x54451,x54452)+~E(f119(x54453,x54451,x54454),f119(x54453,x54452,x54455))
% 25.54/25.41 [8289]~E(f862(x82893,x82894),x82895)+E(f68(x82891,x82892,x82893,x82894,x82895),x82893)
% 25.54/25.41 [8290]~E(f862(x82903,x82904),x82905)+E(f68(x82901,x82902,x82903,x82904,x82905),x82903)
% 25.54/25.41 [8826]~E(f68(x88264,x88265,x88261,x88262,x88263),x88261)+E(f862(x88261,x88262),x88263)
% 25.54/25.41 [9446]~P23(x94462,x94461,x94464,x94463,x94465)+P23(x94461,x94462,f70(x94462,x94461,x94463,x94464),x94465,x94463)
% 25.54/25.41 [9447]~P23(x94472,x94471,x94474,x94473,x94475)+P23(x94471,x94472,f86(x94472,x94471,x94473,x94474),x94475,x94473)
% 25.54/25.41 [6258]P1(f862(f242(x62581,x62582,x62583),x62584))+~P1(f862(f862(x62583,x62585),x62584))
% 25.54/25.41 [6259]P1(f862(f242(x62591,x62592,x62593),x62594))+~P1(f862(f862(x62593,x62595),x62594))
% 25.54/25.41 [6260]P1(f862(f241(x62601,x62602,x62603),x62604))+~P1(f862(f862(x62603,x62604),x62605))
% 25.54/25.41 [6261]P1(f862(f241(x62611,x62612,x62613),x62614))+~P1(f862(f862(x62613,x62614),x62615))
% 25.54/25.41 [6739]~E(x67395,f2(a92))+E(f862(f189(x67391,x67392,x67393,x67394),x67395),f117(x67392))
% 25.54/25.41 [6740]~E(x67405,f2(a92))+E(f862(f191(x67401,x67402,x67403,x67404),x67405),f108(x67402))
% 25.54/25.41 [6874]~E(x68743,f2(a92))+E(f862(f265(x68741,x68742,x68743,x68744),x68745),f862(f244(x68741,x68742),x68745))
% 25.54/25.41 [7934]~P18(x79344,x79341,x79342,x79345)+E(f862(f66(x79341,x79341,x79341,f862(x79342,x79343)),f862(x79342,x79343)),f862(x79342,x79343))
% 25.54/25.41 [8332]~P14(x83325,x83321,x83322)+E(f862(f66(x83321,x83321,x83321,f862(x83322,x83323)),f862(x83322,x83324)),f862(f66(x83321,x83321,x83321,f862(x83322,x83324)),f862(x83322,x83323)))
% 25.54/25.41 [8659]P1(f862(f862(f321(f931(x86591,x86591)),f862(f862(f244(x86591,x86591),x86592),x86593)),f313(x86591,x86594,x86595)))+~P1(f862(f862(f228(a924),f862(x86594,x86592)),f862(x86594,x86593)))
% 25.54/25.41 [8754]~P1(f862(f862(f321(x87544),x87543),f287(x87544,x87541,x87542,x87545)))+P1(f862(f862(x87541,x87542),x87543))
% 25.54/25.41 [8755]~P1(f862(f862(f321(x87554),x87553),f290(x87554,x87551,x87552,x87555)))+P1(f862(f862(x87551,x87552),x87553))
% 25.54/25.41 [8756]~P1(f862(f862(f321(x87564),x87562),f287(x87564,x87561,x87565,x87563)))+P1(f862(f862(x87561,x87562),x87563))
% 25.54/25.41 [8757]~P1(f862(f862(f321(x87574),x87572),f290(x87574,x87571,x87575,x87573)))+P1(f862(f862(x87571,x87572),x87573))
% 25.54/25.41 [8838]~P23(x88381,x88383,x88385,x88382,x88384)+E(f862(f28(x88381),x88382),f862(f28(x88383),x88384))
% 25.54/25.41 [8886]~P23(x88861,x88862,x88863,x88864,x88865)+E(f862(f302(x88861,x88862,x88863),x88864),x88865)
% 25.54/25.41 [8907]~P54(x89072,x89071,x89075,x89073,x89074)+E(f862(f302(x89071,x89072,x89073),x89074),f234(f932(x89072,a921)))
% 25.54/25.41 [9355]~P32(x93551,x93552,x93553,x93554,x93555)+P32(x93551,x93552,x93553,f862(f161(x93551),x93554),f862(f161(x93552),x93555))
% 25.54/25.41 [9357]~P32(x93571,x93572,x93573,f862(f161(x93571),x93574),x93575)+P32(x93571,x93572,x93573,x93574,f862(f161(x93572),x93575))
% 25.54/25.41 [9358]~P32(x93581,x93582,x93583,x93584,f862(f161(x93582),x93585))+P32(x93581,x93582,x93583,f862(f161(x93581),x93584),x93585)
% 25.54/25.41 [9364]P32(x93641,x93642,x93643,x93644,x93645)+~P32(x93641,x93642,x93643,f862(f161(x93641),x93644),f862(f161(x93642),x93645))
% 25.54/25.41 [9769]P1(f862(f862(f321(f931(f925(x97691),f925(x97691))),f862(f862(f244(f925(x97691),f925(x97691)),f862(f862(f144(x97691),x97692),x97693)),f862(f862(f144(x97691),x97692),x97694))),f150(x97691,x97695)))+~P1(f862(f862(f321(f931(f925(x97691),f925(x97691))),f862(f862(f244(f925(x97691),f925(x97691)),x97693),x97694)),f150(x97691,x97695)))
% 25.54/25.41 [9770]P1(f862(f862(f321(f931(f925(x97701),f925(x97701))),f862(f862(f244(f925(x97701),f925(x97701)),f862(f862(f127(x97701),x97702),x97703)),f862(f862(f127(x97701),x97702),x97704))),f140(x97701,x97705)))+~P1(f862(f862(f321(f931(f925(x97701),f925(x97701))),f862(f862(f244(f925(x97701),f925(x97701)),x97703),x97704)),f140(x97701,x97705)))
% 25.54/25.41 [9966]E(f862(f862(f144(x99661),f660(x99662,x99663,x99664,x99665,x99661)),f663(x99662,x99663,x99664,x99665,x99661)),x99665)+~P1(f862(f862(f321(f931(f925(x99661),f925(x99661))),f862(f862(f244(f925(x99661),f925(x99661)),x99665),f862(f862(f144(x99661),x99664),x99663))),f151(x99661,x99662)))
% 25.54/25.41 [9988]E(f862(f862(f144(x99881),f661(x99882,x99883,x99884,x99885,x99881)),f662(x99882,x99883,x99884,x99885,x99881)),x99883)+~P1(f862(f862(f321(f931(f925(x99881),f925(x99881))),f862(f862(f244(f925(x99881),f925(x99881)),f862(f862(f144(x99881),x99885),x99884)),x99883)),f151(x99881,x99882)))
% 25.54/25.41 [10136]~P1(f862(f862(f321(f931(f925(x101361),f925(x101361))),f862(f862(f244(f925(x101361),f925(x101361)),f862(f862(f144(x101361),x101365),x101362)),x101364)),f151(x101361,x101363)))+P1(f862(f862(f321(f931(f925(x101361),f925(x101361))),f862(f862(f244(f925(x101361),f925(x101361)),x101362),f662(x101363,x101364,x101362,x101365,x101361))),f151(x101361,x101363)))
% 25.54/25.41 [10206]~P1(f862(f862(f321(f931(f925(x102061),f925(x102061))),f862(f862(f244(f925(x102061),f925(x102061)),x102065),f862(f862(f144(x102061),x102064),x102063))),f151(x102061,x102062)))+P1(f862(f862(f321(f931(f925(x102061),f925(x102061))),f862(f862(f244(f925(x102061),f925(x102061)),f663(x102062,x102063,x102064,x102065,x102061)),x102063)),f151(x102061,x102062)))
% 25.54/25.41 [10396]P1(f862(f862(f321(f931(x103961,x103961)),f862(f862(f244(x103961,x103961),f862(x103962,f862(f862(f73(a924),x103963),x103964))),f862(x103962,x103963))),f299(x103961,x103965)))+~P1(f862(f862(f321(f931(x103961,x103961)),f862(f862(f244(x103961,x103961),f862(x103962,f862(a105,f624(x103964,x103963,x103965,x103962,x103961)))),f862(x103962,f624(x103964,x103963,x103965,x103962,x103961)))),f299(x103961,x103965)))
% 25.54/25.41 [5416]E(x54161,x54162)+~E(f862(f862(f144(x54163),x54164),x54161),f862(f862(f144(x54163),x54165),x54162))
% 25.54/25.41 [5417]E(x54171,x54172)+~E(f862(f862(f144(x54173),x54171),x54174),f862(f862(f144(x54173),x54172),x54175))
% 25.54/25.41 [5460]P1(f862(x54601,x54602))+~E(f862(f129(x54603,x54601),x54604),f862(f862(f144(x54603),x54602),x54605))
% 25.54/25.41 [5461]P1(f862(x54611,x54612))+~E(f862(f862(f144(x54613),x54612),x54614),f862(f129(x54613,x54611),x54615))
% 25.54/25.41 [5621]~E(f862(f862(f131(x56211),x56213),x56212),f862(f862(f144(x56211),x56214),x56215))+E(f862(f862(f157(x56211),x56212),x56213),x56214)
% 25.54/25.41 [5763]~P12(x57634,x57635,x57631)+E(f862(f862(x57631,x57632),f862(f862(x57631,x57632),x57633)),f862(f862(x57631,x57632),x57633))
% 25.54/25.41 [6317]~E(x63174,f2(a92))+E(f862(f862(f110(x63171,x63172,x63173),x63174),x63175),f862(f862(f244(f925(x63172),x63171),f106(x63172)),x63175))
% 25.54/25.41 [6389]~P109(x63892)+~E(f862(f862(f141(x63891,x63892,x63893),x63894),x63895),f106(x63891))
% 25.54/25.41 [6777]E(x67771,x67772)+~E(f862(f862(f127(x67773),x67774),f862(f862(f144(x67773),x67771),f106(x67773))),f862(f862(f127(x67773),x67775),f862(f862(f144(x67773),x67772),f106(x67773))))
% 25.54/25.41 [6778]E(x67781,x67782)+~E(f862(f862(f127(x67783),x67781),f862(f862(f144(x67783),x67784),f106(x67783))),f862(f862(f127(x67783),x67782),f862(f862(f144(x67783),x67785),f106(x67783))))
% 25.54/25.41 [7092]E(f862(f862(f301(x70921),f862(x70922,x70923)),f862(f302(x70924,x70921,x70922),x70925)),f862(f302(x70924,x70921,x70922),x70925))+~P1(f862(f862(f321(x70924),x70923),x70925))
% 25.54/25.41 [7098]~P1(f862(x70984,f862(x70983,x70985)))+P1(f862(f862(f303(x70981,x70982,x70983),x70984),x70985))
% 25.54/25.41 [7099]~P1(f862(f862(x70993,x70995),x70994))+P1(f862(f862(f235(x70991,x70992,x70993),x70994),x70995))
% 25.54/25.41 [7100]~P1(f862(f862(x71003,x71005),x71004))+P1(f862(f862(f235(x71001,x71002,x71003),x71004),x71005))
% 25.54/25.41 [7101]~P1(f862(f862(x71013,x71015),x71014))+P1(f862(f862(f235(x71011,x71012,x71013),x71014),x71015))
% 25.54/25.41 [7197]~E(f862(f302(x71971,x71972,x71973),x71974),x71975)+E(f862(f302(f932(x71971,a921),f932(x71972,a921),f302(x71971,x71972,x71973)),f862(f300(x71971),x71974)),f862(f300(x71972),x71975))
% 25.54/25.41 [7224]E(f862(f263(x72241,x72242,x72243,x72244),x72245),f862(x72244,x72245))+~P1(f862(f862(f321(x72241),x72245),x72243))
% 25.54/25.41 [7543]P22(x75431,x75432,x75433,x75434)+~P22(x75431,x75432,x75433,f862(f862(f301(x75431),x75435),x75434))
% 25.54/25.41 [7649]~P1(f862(f862(f321(x76494),x76493),x76495))+P1(f862(f862(f321(x76491),f862(x76492,x76493)),f862(f302(x76494,x76491,x76492),x76495)))
% 25.54/25.41 [7670]~P109(x76702)+E(f143(x76701,x76702,x76703,f862(f129(x76701,x76704),x76705)),f862(f129(x76701,x76704),f143(x76701,x76702,x76703,x76705)))
% 25.54/25.41 [7702]P1(f862(x77021,f862(x77022,x77023)))+~P1(f862(f862(f303(x77024,x77025,x77022),x77021),x77023))
% 25.54/25.41 [7703]P1(f862(f862(x77031,x77032),x77033))+~P1(f862(f862(f235(x77034,x77035,x77031),x77033),x77032))
% 25.54/25.41 [7704]P1(f862(f862(x77041,x77042),x77043))+~P1(f862(f862(f235(x77044,x77045,x77041),x77043),x77042))
% 25.54/25.41 [7705]P1(f862(f862(x77051,x77052),x77053))+~P1(f862(f862(f235(x77054,x77055,x77051),x77053),x77052))
% 25.54/25.41 [7769]~P1(f862(f862(f321(x77693),f862(x77694,x77692)),x77695))+P1(f862(f862(f321(x77691),x77692),f862(f303(x77691,x77693,x77694),x77695)))
% 25.54/25.41 [7770]~P1(f862(f862(f321(x77703),f862(x77704,x77702)),x77705))+P1(f862(f862(f321(x77701),x77702),f862(f303(x77701,x77703,x77704),x77705)))
% 25.54/25.41 [8169]~P1(f862(f862(f321(x81695),x81693),f862(f303(x81695,x81691,x81692),x81694)))+P1(f862(f862(f321(x81691),f862(x81692,x81693)),x81694))
% 25.54/25.41 [8170]~P1(f862(f862(f321(x81705),x81703),f862(f303(x81705,x81701,x81702),x81704)))+P1(f862(f862(f321(x81701),f862(x81702,x81703)),x81704))
% 25.54/25.41 [8472]~P14(x84722,x84721,x84723)+E(f862(f135(x84721,x84722,f862(f9(x84722,x84721,x84721),x84723),x84724),f145(x84722,x84725)),f862(f862(f57(x84722,x84721,x84723),x84724),f862(f165(x84722),x84725)))
% 25.54/25.41 [8494]E(f862(x84941,f812(x84942,x84941,x84943,x84944)),x84944)+~P1(f862(f862(f321(x84945),x84944),f862(f302(x84943,x84945,x84941),x84942)))
% 25.54/25.41 [8801]~E(x88012,f862(f862(f144(x88011),x88014),x88015))+P1(f862(f862(f321(f931(f925(x88011),f925(x88011))),f862(f862(f244(f925(x88011),f925(x88011)),f106(x88011)),x88012)),f140(x88011,x88013)))
% 25.54/25.41 [8847]E(f862(x88471,f862(f86(x88472,x88473,x88474,x88471),x88475)),x88475)+~P1(f862(f862(f321(x88473),x88475),f862(f302(x88472,x88473,x88471),x88474)))
% 25.54/25.41 [8850]P22(x88501,x88502,f86(x88502,x88501,x88503,x88504),x88505)+~P1(f862(f862(f227(f932(x88501,a921)),x88505),f862(f302(x88502,x88501,x88504),x88503)))
% 25.54/25.41 [8855]~P32(x88551,x88553,x88555,x88552,x88554)+E(f862(f182(f925(x88551)),x88552),f862(f182(f925(x88553)),x88554))
% 25.54/25.41 [8856]~P32(x88561,x88563,x88565,x88562,x88564)+E(f862(f182(f925(x88561)),x88562),f862(f182(f925(x88563)),x88564))
% 25.54/25.41 [8857]~P32(x88571,x88573,x88575,x88572,x88574)+E(f862(f182(f925(x88571)),x88572),f862(f182(f925(x88573)),x88574))
% 25.54/25.41 [8868]P1(f862(f862(f227(f932(x88681,a921)),f862(f862(f32(x88682,f932(x88681,a921)),x88683),x88684)),f862(x88684,x88685)))+~P1(f862(f862(f321(x88682),x88685),x88683))
% 25.54/25.41 [8923]~P54(x89231,x89232,x89233,x89235,x89234)+E(f862(f302(x89231,x89232,x89233),f234(f932(x89231,a921))),x89234)
% 25.54/25.41 [9150]E(f862(f129(x91501,x91502),f748(x91503,x91504,x91505,x91502,x91501)),x91503)+~E(f862(f129(x91501,x91502),x91505),f862(f862(f144(x91501),x91504),x91503))
% 25.54/25.41 [9151]E(f862(f129(x91511,x91512),f752(x91513,x91512,x91514,x91515,x91511)),x91514)+~E(f862(f862(f144(x91511),x91515),x91514),f862(f129(x91511,x91512),x91513))
% 25.54/25.41 [9242]E(f862(f182(f925(x92421)),x92422),x92423)+~P1(f862(f862(f321(f931(f925(x92421),f925(x92421))),f862(f862(f244(f925(x92421),f925(x92421)),x92424),x92422)),f862(f136(x92421,x92425),x92423)))
% 25.54/25.41 [9243]E(f862(f182(f925(x92431)),x92432),x92433)+~P1(f862(f862(f321(f931(f925(x92431),f925(x92431))),f862(f862(f244(f925(x92431),f925(x92431)),x92432),x92434)),f862(f136(x92431,x92435),x92433)))
% 25.54/25.41 [9313]P1(f862(f862(f321(x93131),f812(x93132,x93133,x93131,x93134)),x93132))+~P1(f862(f862(f321(x93135),x93134),f862(f302(x93131,x93135,x93133),x93132)))
% 25.54/25.41 [9473]E(f862(f302(x94731,x94732,x94733),f822(x94734,x94733,x94731,x94735,x94732)),x94735)+~P1(f862(f862(f227(f932(x94732,a921)),x94735),f862(f302(x94731,x94732,x94733),x94734)))
% 25.54/25.41 [9787]P1(f862(f862(f321(f931(f925(x97871),f925(x97871))),f862(f862(f244(f925(x97871),f925(x97871)),f862(f862(f144(x97871),x97872),x97873)),f862(f862(f144(x97871),x97872),x97874))),f299(f925(x97871),f150(x97871,x97875))))+~P1(f862(f862(f321(f931(f925(x97871),f925(x97871))),f862(f862(f244(f925(x97871),f925(x97871)),x97873),x97874)),f299(f925(x97871),f150(x97871,x97875))))
% 25.54/25.41 [9818]~E(f862(x98183,f700(x98185,x98184,x98183,x98182,x98181)),f862(x98185,f700(x98185,x98184,x98183,x98182,x98181)))+E(f862(f862(f147(x98181,x98182),x98183),x98184),f862(f862(f147(x98181,x98182),x98185),x98184))
% 25.54/25.41 [9893]~E(f862(f129(x98931,x98935),x98934),f862(f862(f144(x98931),x98933),x98932))+E(f862(f862(f127(x98931),f749(x98932,x98933,x98934,x98935,x98931)),f862(f862(f144(x98931),x98933),f748(x98932,x98933,x98934,x98935,x98931))),x98934)
% 25.54/25.41 [9894]~E(f862(f862(f144(x98941),x98945),x98944),f862(f129(x98941,x98943),x98942))+E(f862(f862(f127(x98941),f753(x98942,x98943,x98944,x98945,x98941)),f862(f862(f144(x98941),x98945),f752(x98942,x98943,x98944,x98945,x98941))),x98942)
% 25.54/25.41 [9898]E(f862(f862(f147(x98981,x98982),x98983),x98984),f862(f862(f147(x98981,x98982),x98985),x98984))+P1(f862(f862(f321(x98981),f700(x98983,x98984,x98985,x98982,x98981)),f862(f165(x98981),x98984)))
% 25.54/25.41 [9929]~P1(f862(f862(f321(x99295),x99294),f862(f276(x99291,x99295,x99293),x99292)))+P1(f862(f862(f321(x99291),f521(x99292,x99293,x99291,x99294,x99295)),x99292))
% 25.54/25.41 [9930]~P1(f862(f862(f321(x99305),x99304),f862(f276(x99301,x99305,x99303),x99302)))+P1(f862(f862(f321(x99301),f526(x99302,x99303,x99301,x99304,x99305)),x99302))
% 25.54/25.41 [9960]~P1(f862(f862(f227(f932(x99605,a921)),x99604),f862(f302(x99601,x99605,x99603),x99602)))+P1(f862(f862(f227(f932(x99601,a921)),f822(x99602,x99603,x99601,x99604,x99605)),x99602))
% 25.54/25.41 [10397]E(x103971,f2(a92))+E(f216(f931(f925(x103972),x103973),f931(x103972,x103973),f862(f862(f244(f925(x103972),x103973),f106(x103972)),x103974),f862(f249(x103972,x103973,f931(f925(x103972),x103973)),f862(f862(f9(x103972,f932(x103973,f931(f925(x103972),x103973)),f932(x103973,f931(f925(x103972),x103973))),f862(f862(f10(f932(f931(f925(x103972),x103973),f931(f925(x103972),x103973)),f932(f932(x103973,f931(f925(x103972),x103973)),f932(x103973,f931(f925(x103972),x103973))),x103972),f10(f931(f925(x103972),x103973),f931(f925(x103972),x103973),x103973)),f862(f862(f10(f932(f925(x103972),f932(x103973,f931(f925(x103972),x103973))),f932(f931(f925(x103972),x103973),f931(f925(x103972),x103973)),x103972),f249(f925(x103972),x103973,f931(f925(x103972),x103973))),f862(f862(f10(f932(f925(x103972),f925(x103972)),f932(f925(x103972),f932(x103973,f931(f925(x103972),x103973))),x103972),f862(f10(f925(x103972),f932(x103973,f931(f925(x103972),x103973)),f925(x103972)),f244(f925(x103972),x103973))),f144(x103972))))),f862(f110(x103973,x103972,x103975),f862(f862(f3(a92),x103971),f71(a92))))),f862(x103975,x103974)),f862(f862(f110(x103973,x103972,x103975),x103971),x103974))
% 25.54/25.41 [6199]E(x61991,x61992)+~E(f862(f248(x61993,x61994),f862(f862(f244(x61993,x61994),x61995),x61991)),x61992)
% 25.54/25.41 [6200]E(x62001,x62002)+~E(f862(f243(x62003,x62004),f862(f862(f244(x62003,x62004),x62001),x62005)),x62002)
% 25.54/25.41 [6462]~E(x64623,f862(f862(f127(x64621),x64624),f862(f862(f144(x64621),x64622),x64625)))+P1(f862(f862(f321(x64621),x64622),f862(f165(x64621),x64623)))
% 25.54/25.41 [6861]E(f862(f302(x68611,x68612,f862(f18(x68612,x68611),x68613)),x68614),f862(f862(f301(x68612),x68613),f181(f932(x68612,a921))))+~P1(f862(f862(f321(x68611),x68615),x68614))
% 25.54/25.41 [6930]E(f862(f862(f103(f932(x69301,a921)),f862(f165(x69301),x69302)),f862(f165(x69301),x69303)),f862(f165(x69301),x69304))+~E(f159(x69301,x69305,x69304),f862(f862(f244(f925(x69301),f925(x69301)),x69302),x69303))
% 25.54/25.41 [7032]~P109(x70322)+E(f862(f182(f925(x70321)),f862(f862(f141(x70321,x70322,x70323),x70324),x70325)),f862(a105,f862(f182(f925(x70321)),x70325)))
% 25.54/25.41 [7046]~P109(x70462)+E(f862(f165(x70461),f862(f862(f141(x70461,x70462,x70463),x70464),x70465)),f862(f862(f301(x70461),x70464),f862(f165(x70461),x70465)))
% 25.54/25.41 [7319]~P119(x73191)+E(f862(f862(f74(x73191),f862(f862(f74(x73191),x73192),x73193)),f862(f862(f74(x73191),x73194),x73195)),f862(f862(f74(x73191),f862(f862(f74(x73191),x73192),x73194)),f862(f862(f74(x73191),x73193),x73195)))
% 25.54/25.41 [7320]~P119(x73201)+E(f862(f862(f73(x73201),f862(f862(f73(x73201),x73202),x73203)),f862(f862(f73(x73201),x73204),x73205)),f862(f862(f73(x73201),f862(f862(f73(x73201),x73202),x73204)),f862(f862(f73(x73201),x73203),x73205)))
% 25.54/25.41 [7321]~P64(x73211)+E(f862(f862(f281(x73211),f862(f862(f74(x73211),x73212),x73213)),f862(f862(f74(x73211),x73214),x73215)),f862(f862(f74(x73211),f862(f862(f281(x73211),x73212),x73214)),f862(f862(f281(x73211),x73213),x73215)))
% 25.54/25.41 [7335]~P109(x73351)+E(f298(x73351,f862(f862(f226(x73351),x73352),x73353),f862(f862(f225(x73351),x73354),x73355)),f862(f862(f94(f932(x73351,a921)),f298(x73351,x73352,x73354)),f298(x73351,x73353,x73355)))
% 25.54/25.41 [7336]~P109(x73361)+E(f297(x73361,f862(f862(f226(x73361),x73362),x73363),f862(f862(f225(x73361),x73364),x73365)),f862(f862(f94(f932(x73361,a921)),f297(x73361,x73362,x73364)),f297(x73361,x73363,x73365)))
% 25.54/25.41 [7337]~P109(x73371)+E(f296(x73371,f862(f862(f226(x73371),x73372),x73373),f862(f862(f225(x73371),x73374),x73375)),f862(f862(f94(f932(x73371,a921)),f296(x73371,x73372,x73374)),f296(x73371,x73373,x73375)))
% 25.54/25.41 [7338]~P109(x73381)+E(f862(f862(f94(f932(x73381,a921)),f862(f295(x73381,x73382),x73383)),f862(f295(x73381,x73384),x73385)),f862(f295(x73381,f862(f862(f226(x73381),x73382),x73384)),f862(f862(f225(x73381),x73383),x73385)))
% 25.54/25.41 [7461]~P1(f862(x74611,f464(x74613,x74612,x74611)))+P1(f862(x74611,f862(f862(f244(x74612,x74613),x74614),x74615)))
% 25.54/25.41 [7574]~E(x75742,f862(x75744,x75745))+P1(f862(f862(f321(x75741),x75742),f862(f302(x75743,x75741,x75744),f234(f932(x75743,a921)))))
% 25.54/25.41 [7647]~P14(x76473,x76472,x76474)+P14(x76471,x76472,f862(f862(f10(x76473,f932(x76472,x76472),x76471),x76474),x76475))
% 25.54/25.41 [7648]~P12(x76483,x76482,x76484)+P12(x76481,x76482,f862(f862(f10(x76483,f932(x76482,x76482),x76481),x76484),x76485))
% 25.54/25.41 [7787]~P22(x77871,x77872,x77873,x77874)+P22(x77871,x77872,x77873,f862(f862(f3(f932(x77871,a921)),x77874),x77875))
% 25.54/25.41 [7942]~P1(f862(f862(x79423,x79424),x79425))+P1(f862(f862(f249(x79421,x79422,a921),x79423),f862(f862(f244(x79421,x79422),x79424),x79425)))
% 25.54/25.41 [7943]~P1(f862(f862(x79433,x79434),x79435))+P1(f862(f862(f249(x79431,x79432,a921),x79433),f862(f862(f244(x79431,x79432),x79434),x79435)))
% 25.54/25.41 [8057]~P1(f862(x80572,x80574))+~E(f862(f862(f131(x80571),f862(f182(f925(x80571)),f170(x80571,x80572,x80573))),x80573),f862(f862(f144(x80571),x80574),x80575))
% 25.54/25.41 [8077]P22(x80771,x80772,x80773,x80774)+~P22(x80771,x80772,x80773,f862(f862(f103(f932(x80771,a921)),x80775),x80774))
% 25.54/25.41 [8078]P22(x80781,x80782,x80783,x80784)+~P22(x80781,x80782,x80783,f862(f862(f103(f932(x80781,a921)),x80784),x80785))
% 25.54/25.41 [8126]~P109(x81262)+E(f862(f862(f141(x81261,x81262,x81263),x81264),f143(x81261,x81262,x81263,x81265)),f143(x81261,x81262,x81263,f862(f862(f144(x81261),x81264),x81265)))
% 25.54/25.41 [8449]~P12(x84492,x84491,x84493)+E(f862(f135(x84491,x84492,f862(f9(x84492,x84491,x84491),x84493),x84494),x84495),f862(f862(f57(x84492,x84491,x84493),x84494),f862(f165(x84492),x84495)))
% 25.54/25.41 [8477]~E(f862(f862(f131(x84771),f862(f182(f925(x84771)),f170(x84771,x84772,x84773))),x84773),f862(f862(f144(x84771),x84774),x84775))+E(f862(f862(f127(x84771),f170(x84771,x84772,x84773)),f862(f862(f144(x84771),x84774),x84775)),x84773)
% 25.54/25.41 [8504]P1(f862(f862(x85041,x85042),x85043))+~P1(f862(f862(f249(x85044,x85045,a921),x85041),f862(f862(f244(x85044,x85045),x85042),x85043)))
% 25.54/25.41 [8986]P1(f862(f862(f227(f932(x89861,a921)),f862(f302(x89862,x89861,x89863),x89864)),f862(f302(x89862,x89861,x89863),x89865)))+~P1(f862(f862(f227(f932(x89862,a921)),x89864),x89865))
% 25.54/25.41 [8987]P1(f862(f862(f227(f932(x89871,a921)),f862(f303(x89871,x89872,x89873),x89874)),f862(f303(x89871,x89872,x89873),x89875)))+~P1(f862(f862(f227(f932(x89872,a921)),x89874),x89875))
% 25.54/25.41 [9068]E(x90681,f2(a92))+E(f862(f862(f251(x90682,x90683,x90682,f931(x90683,x90682)),f862(x90684,x90685)),f265(x90683,x90682,f862(f862(f3(a92),x90681),f71(a92)),x90684)),f862(f265(x90683,x90682,x90681,x90684),x90685))
% 25.54/25.41 [9175]P1(f862(f862(f247(x91751,x91752,a921,x91753),x91754),x91755))+~P1(f862(x91753,f862(f862(f244(x91751,x91752),x91754),x91755)))
% 25.54/25.41 [9451]~P1(f862(f862(f247(x94512,x94513,a921,x94511),x94514),x94515))+P1(f862(x94511,f862(f862(f244(x94512,x94513),x94514),x94515)))
% 25.54/25.41 [9452]~P1(f862(f862(f247(x94522,x94523,a921,x94521),x94524),x94525))+P1(f862(x94521,f862(f862(f244(x94522,x94523),x94524),x94525)))
% 25.54/25.41 [9637]~P1(f862(f862(f321(x96372),x96375),f862(f302(x96371,x96372,x96374),x96373)))+P1(f862(f862(f321(x96371),f862(f86(x96371,x96372,x96373,x96374),x96375)),x96373))
% 25.54/25.41 [9729]~P1(f862(f54(x97293),f862(f302(x97292,x97293,x97295),f234(f932(x97292,a921)))))+P1(f862(f54(x97291),f862(f302(x97292,x97291,f862(f862(f10(x97293,x97291,x97292),x97294),x97295)),f234(f932(x97292,a921)))))
% 25.54/25.41 [9754]P1(f862(f862(f227(f932(f932(x97541,a921),a921)),f862(f302(f932(x97542,a921),f932(x97541,a921),f302(x97542,x97541,x97543)),f862(f300(x97542),x97544))),f862(f300(x97541),x97545)))+~P1(f862(f862(f227(f932(x97541,a921)),f862(f302(x97542,x97541,x97543),x97544)),x97545))
% 25.54/25.41 [9826]E(x98261,x98262)+~P1(f862(f59(x98263,x98264,x98265,x98261,f181(f932(x98263,a921))),x98262))
% 25.54/25.41 [9842]E(f862(f862(f244(x98421,x98422),f576(x98423,x98424,x98425,x98422,x98421)),f577(x98423,x98424,x98425,x98422,x98421)),x98425)+~P1(f862(f862(f321(f931(x98421,x98422)),x98425),f862(f862(f246(x98421,x98422),x98424),x98423)))
% 25.54/25.41 [9935]P1(f862(f862(f321(x99351),f576(x99352,x99353,x99354,x99355,x99351)),x99353))+~P1(f862(f862(f321(f931(x99351,x99355)),x99354),f862(f862(f246(x99351,x99355),x99353),x99352)))
% 25.54/25.41 [10094]P1(f862(f862(f321(x100941),f577(x100942,x100943,x100944,x100941,x100945)),f862(x100942,f576(x100942,x100943,x100944,x100941,x100945))))+~P1(f862(f862(f321(f931(x100945,x100941)),x100944),f862(f862(f246(x100945,x100941),x100943),x100942)))
% 25.54/25.41 [10115]P1(f862(f862(f321(f931(x101151,x101151)),f862(f862(f244(x101151,x101151),x101152),f642(x101153,x101154,x101155,x101152,x101151))),x101153))+~P1(f862(f862(f321(f931(x101151,x101151)),f862(f862(f244(x101151,x101151),x101152),x101155)),f862(f862(f176(f931(x101151,x101151),a921),f862(a105,x101154)),x101153)))
% 25.54/25.41 [10116]P1(f862(f862(f321(f931(x101161,x101161)),f862(f862(f244(x101161,x101161),x101162),f643(x101163,x101164,x101165,x101162,x101161))),x101163))+~P1(f862(f862(f321(f931(x101161,x101161)),f862(f862(f244(x101161,x101161),x101162),x101165)),f862(f862(f176(f931(x101161,x101161),a921),f862(a105,x101164)),x101163)))
% 25.54/25.41 [10133]~P1(f862(f862(f321(f931(f925(x101331),f925(x101331))),f862(f862(f244(f925(x101331),f925(x101331)),f862(f862(f144(x101331),x101332),x101335)),x101334)),f151(x101331,x101333)))+P1(f862(f862(f321(f931(x101331,x101331)),f862(f862(f244(x101331,x101331),x101332),f661(x101333,x101334,x101335,x101332,x101331))),x101333))
% 25.54/25.41 [6541]P1(f862(x65412,x65414))+E(f170(x65411,x65412,f862(f862(f127(x65411),x65413),f862(f862(f144(x65411),x65414),x65415))),f170(x65411,x65412,x65413))
% 25.54/25.41 [6590]~P93(x65902)+E(f862(f862(f862(f103(f932(x65901,x65902)),x65903),x65904),x65905),f862(f862(f103(x65902),f862(x65903,x65905)),f862(x65904,x65905)))
% 25.54/25.41 [6591]~P93(x65912)+E(f862(f862(f862(f103(f932(x65911,x65912)),x65913),x65914),x65915),f862(f862(f103(x65912),f862(x65913,x65915)),f862(x65914,x65915)))
% 25.54/25.41 [6592]~P93(x65922)+E(f862(f862(f862(f94(f932(x65921,x65922)),x65923),x65924),x65925),f862(f862(f94(x65922),f862(x65923,x65925)),f862(x65924,x65925)))
% 25.54/25.41 [6593]~P93(x65932)+E(f862(f862(f862(f94(f932(x65931,x65932)),x65933),x65934),x65935),f862(f862(f94(x65932),f862(x65933,x65935)),f862(x65934,x65935)))
% 25.54/25.41 [6594]~P58(x65942)+E(f862(f862(f862(f3(f932(x65941,x65942)),x65943),x65944),x65945),f862(f862(f3(x65942),f862(x65943,x65945)),f862(x65944,x65945)))
% 25.54/25.41 [6595]~P58(x65952)+E(f862(f862(f862(f3(f932(x65951,x65952)),x65953),x65954),x65955),f862(f862(f3(x65952),f862(x65953,x65955)),f862(x65954,x65955)))
% 25.54/25.41 [6614]E(x66141,x66142)+E(f862(f862(f157(x66143),f862(f862(f152(x66143,x66144),x66141),x66145)),x66142),f862(f862(f157(x66143),x66144),x66142))
% 25.54/25.41 [6879]~E(x68794,f181(f932(x68793,a921)))+E(f862(f862(f103(f932(x68791,a921)),x68792),f862(f862(f33(x68793,f932(x68791,a921)),x68794),x68795)),x68792)
% 25.54/25.41 [6880]~E(x68804,f181(f932(x68803,a921)))+E(f862(f862(f94(f932(x68801,a921)),x68802),f862(f862(f32(x68803,f932(x68801,a921)),x68804),x68805)),x68802)
% 25.54/25.41 [6881]~E(x68814,f181(f932(x68813,a921)))+E(f862(f862(f3(f932(x68811,a921)),x68812),f862(f862(f33(x68813,f932(x68811,a921)),x68814),x68815)),x68812)
% 25.54/25.41 [6896]~E(x68964,f181(f932(x68963,a921)))+E(f862(f862(f301(x68961),x68962),f862(f862(f33(x68963,f932(x68961,a921)),x68964),x68965)),f862(f862(f301(x68961),x68962),f181(f932(x68961,a921))))
% 25.54/25.41 [7318]~P119(x73181)+E(f862(f862(f74(x73181),f862(f862(f74(x73181),x73182),x73183)),f862(f862(f74(x73181),x73184),x73185)),f862(f862(f74(x73181),x73182),f862(f862(f74(x73181),x73183),f862(f862(f74(x73181),x73184),x73185))))
% 25.54/25.41 [7694]E(f862(f862(f157(x76941),f862(f862(f147(x76942,x76941),x76943),x76944)),x76945),f862(x76943,f862(f862(f157(x76942),x76944),x76945)))+~P1(f862(f862(f228(a924),x76945),f862(f182(f925(x76942)),x76944)))
% 25.54/25.41 [7758]E(f862(f862(f103(f932(x77581,a921)),f862(x77582,x77583)),f862(f862(f33(x77584,f932(x77581,a921)),x77585),x77582)),f862(f862(f33(x77584,f932(x77581,a921)),x77585),x77582))+~P1(f862(f862(f321(x77584),x77583),x77585))
% 25.54/25.41 [7759]E(f862(f862(f94(f932(x77591,a921)),f862(x77592,x77593)),f862(f862(f32(x77594,f932(x77591,a921)),x77595),x77592)),f862(f862(f32(x77594,f932(x77591,a921)),x77595),x77592))+~P1(f862(f862(f321(x77594),x77593),x77595))
% 25.54/25.41 [8371]~E(x83713,f181(f932(x83711,a921)))+E(f862(f862(f33(x83711,f932(x83712,a921)),x83713),f862(f862(f10(f932(x83712,a921),f932(x83712,a921),x83711),f862(f301(x83712),x83714)),x83715)),f181(f932(x83712,a921)))
% 25.54/25.41 [8376]~P1(f862(f862(f321(x83764),x83763),x83765))+P1(f862(f862(f227(f932(x83761,a921)),f862(x83762,x83763)),f862(f862(f33(x83764,f932(x83761,a921)),x83765),x83762)))
% 25.54/25.41 [8503]~E(f862(x85034,x85032),x85035)+P1(f862(f862(f321(x85031),x85032),f862(f303(x85031,x85033,x85034),f862(f862(f301(x85033),x85035),f181(f932(x85033,a921))))))
% 25.54/25.41 [8550]~P52(x85501,x85502,f862(f277(x85502,x85501),x85503))+E(f862(f862(f94(f932(x85501,a921)),f862(f276(x85502,x85501,x85503),x85504)),f862(f276(x85502,x85501,x85503),x85505)),f862(f276(x85502,x85501,x85503),f862(f862(f94(f932(x85502,a921)),x85504),x85505)))
% 25.54/25.41 [8627]E(x86271,f2(a92))+E(f862(f111(x86272,x86273,f862(x86274,f862(f862(f3(a92),x86271),f71(a92)))),f862(f862(f9(x86272,a92,f926(x86273)),x86275),x86271)),f862(f191(x86272,x86273,x86274,x86275),x86271))
% 25.54/25.41 [8665]E(x86651,f181(f932(x86652,a921)))+E(f862(f862(f33(x86652,f932(x86653,a921)),x86651),f862(f862(f10(f932(x86653,a921),f932(x86653,a921),x86652),f862(f301(x86653),x86654)),x86655)),f862(f862(f301(x86653),x86654),f862(f862(f33(x86652,f932(x86653,a921)),x86651),x86655)))
% 25.54/25.41 [8666]E(x86661,f181(f932(x86662,a921)))+E(f862(f862(f33(x86662,f932(x86663,a921)),x86661),f862(f862(f10(f932(x86663,a921),f932(x86663,a921),x86662),f862(f301(x86663),x86664)),x86665)),f862(f862(f301(x86663),x86664),f862(f862(f33(x86662,f932(x86663,a921)),x86661),x86665)))
% 25.54/25.41 [8718]~P22(x87182,x87181,x87183,f234(f932(x87182,a921)))+E(f862(f862(f94(f932(x87181,a921)),f862(f302(x87182,x87181,x87183),x87184)),f862(f302(x87182,x87181,x87183),x87185)),f862(f302(x87182,x87181,x87183),f862(f862(f94(f932(x87182,a921)),x87184),x87185)))
% 25.54/25.41 [8719]~P22(x87192,x87191,x87193,f234(f932(x87192,a921)))+E(f862(f862(f3(f932(x87191,a921)),f862(f302(x87192,x87191,x87193),x87194)),f862(f302(x87192,x87191,x87193),x87195)),f862(f302(x87192,x87191,x87193),f862(f862(f3(f932(x87192,a921)),x87194),x87195)))
% 25.54/25.41 [8788]~P1(f862(f862(f60(x87881,x87882,x87885),x87883),x87884))+P1(f862(f862(f321(f931(x87881,x87882)),f862(f862(f244(x87881,x87882),x87883),x87884)),x87885))
% 25.54/25.41 [8819]P1(f862(f862(f321(x88191),x88192),f862(f275(x88193,x88191),x88194)))+~P1(f862(f862(f321(f931(x88193,x88191)),f862(f862(f244(x88193,x88191),x88195),x88192)),x88194))
% 25.54/25.41 [8820]P1(f862(f862(f321(x88201),x88202),f862(f275(x88203,x88201),x88204)))+~P1(f862(f862(f321(f931(x88203,x88201)),f862(f862(f244(x88203,x88201),x88205),x88202)),x88204))
% 25.54/25.41 [8821]P1(f862(f862(f321(x88211),x88212),f862(f256(x88211,x88213),x88214)))+~P1(f862(f862(f321(f931(x88211,x88213)),f862(f862(f244(x88211,x88213),x88212),x88215)),x88214))
% 25.54/25.41 [8822]P1(f862(f862(f321(x88221),x88222),f862(f256(x88221,x88223),x88224)))+~P1(f862(f862(f321(f931(x88221,x88223)),f862(f862(f244(x88221,x88223),x88222),x88225)),x88224))
% 25.54/25.41 [8970]P1(f862(f862(f60(x89701,x89702,x89703),x89704),x89705))+~P1(f862(f862(f321(f931(x89701,x89702)),f862(f862(f244(x89701,x89702),x89704),x89705)),x89703))
% 25.54/25.41 [9009]E(f862(x90091,x90092),x90093)+~P1(f862(f862(f321(x90094),x90092),f862(f303(x90094,x90095,x90091),f862(f862(f301(x90095),x90093),f181(f932(x90095,a921))))))
% 25.54/25.41 [9238]P1(f862(f862(f321(f931(x92381,x92382)),f862(f862(f244(x92381,x92382),x92383),x92384)),f862(f277(x92382,x92381),x92385)))+~P1(f862(f862(f321(f931(x92382,x92381)),f862(f862(f244(x92382,x92381),x92384),x92383)),x92385))
% 25.54/25.41 [9239]P1(f862(f862(f321(f931(x92391,x92392)),f862(f862(f244(x92391,x92392),x92393),x92394)),f862(f277(x92392,x92391),x92395)))+~P1(f862(f862(f321(f931(x92392,x92391)),f862(f862(f244(x92392,x92391),x92394),x92393)),x92395))
% 25.54/25.41 [9257]~P1(f862(f862(x92571,x92575),x92574))+P1(f862(f862(x92571,f862(f248(x92572,x92573),f862(f862(f244(x92572,x92573),x92574),x92575))),f862(f243(x92572,x92573),f862(f862(f244(x92572,x92573),x92574),x92575))))
% 25.54/25.41 [9286]~P1(f862(f862(f321(f931(x92862,x92861)),f862(f862(f244(x92862,x92861),x92864),x92863)),f862(f277(x92861,x92862),x92865)))+P1(f862(f862(f321(f931(x92861,x92862)),f862(f862(f244(x92861,x92862),x92863),x92864)),x92865))
% 25.54/25.41 [9287]~P1(f862(f862(f321(f931(x92872,x92871)),f862(f862(f244(x92872,x92871),x92874),x92873)),f862(f277(x92871,x92872),x92875)))+P1(f862(f862(f321(f931(x92871,x92872)),f862(f862(f244(x92871,x92872),x92873),x92874)),x92875))
% 25.54/25.41 [9320]~P1(f862(f862(f321(f931(x93203,x93201)),f862(f862(f244(x93203,x93201),x93205),x93202)),x93204))+P1(f862(f862(f321(x93201),x93202),f862(f276(x93203,x93201,x93204),f862(f862(f301(x93203),x93205),f181(f932(x93203,a921))))))
% 25.54/25.41 [9368]P1(f862(f862(f321(f931(x93681,x93682)),f862(f862(f244(x93681,x93682),x93683),x93684)),x93685))+~P1(f862(f862(f321(x93682),x93684),f862(f276(x93681,x93682,x93685),f862(f862(f301(x93681),x93683),f181(f932(x93681,a921))))))
% 25.54/25.41 [9459]~P72(x94591)+E(f862(f862(f8(a924,x94591),x94592),f296(a924,f862(f862(f73(a924),x94593),x94594),f862(f862(f73(a924),x94595),x94594))),f862(f862(f8(a924,x94591),f862(f862(f10(a924,x94591,a924),x94592),f862(f862(f9(a924,a924,a924),f73(a924)),x94594))),f296(a924,x94593,x94595)))
% 25.54/25.41 [9478]~P72(x94781)+E(f862(f862(f8(a924,x94781),x94782),f862(f295(a924,f862(f862(f73(a924),x94783),x94784)),f862(f862(f73(a924),x94785),x94784))),f862(f862(f8(a924,x94781),f862(f862(f10(a924,x94781,a924),x94782),f862(f862(f9(a924,a924,a924),f73(a924)),x94784))),f862(f295(a924,x94783),x94785)))
% 25.54/25.41 [9534]~P22(x95341,x95342,x95343,f234(f932(x95341,a921)))+E(f862(f862(f147(x95341,x95342),x95343),f862(f129(x95341,f862(f862(f10(a921,a921,x95341),a314),f862(a317,x95344))),x95345)),f862(f129(x95342,f862(f862(f10(a921,a921,x95342),a314),f862(a317,f862(x95343,x95344)))),f862(f862(f147(x95341,x95342),x95343),x95345)))
% 25.54/25.41 [9553]~P22(x95531,x95532,x95533,f862(f862(f301(x95531),x95534),f862(f165(x95531),x95535)))+E(f862(f862(f147(x95531,x95532),x95533),f862(f129(x95531,f862(f862(f10(a921,a921,x95531),a314),f862(a317,x95534))),x95535)),f862(f129(x95532,f862(f862(f10(a921,a921,x95532),a314),f862(a317,f862(x95533,x95534)))),f862(f862(f147(x95531,x95532),x95533),x95535)))
% 25.54/25.41 [9717]P1(f862(f862(f321(f931(f925(x97171),f925(x97171))),f862(f862(f244(f925(x97171),f925(x97171)),f862(f862(f144(x97171),x97172),x97173)),f862(f862(f144(x97171),x97174),x97173))),f150(x97171,x97175)))+~P1(f862(f862(f321(f931(x97171,x97171)),f862(f862(f244(x97171,x97171),x97172),x97174)),x97175))
% 25.54/25.41 [9837]E(f862(f862(f301(x98371),f832(x98372,x98373,x98374,x98375,x98371)),f838(x98372,x98373,x98374,x98375,x98371)),f862(f862(f301(x98371),x98374),x98373))+~P1(f862(f55(x98371,x98375,f862(f862(f301(x98371),x98374),x98373)),x98372))
% 25.54/25.41 [9838]E(f862(f862(f301(x98381),f853(x98382,x98383,x98384,x98385,x98381)),f870(x98382,x98383,x98384,x98385,x98381)),f862(f862(f301(x98381),x98384),x98383))+~P1(f862(f55(x98381,x98385,f862(f862(f301(x98381),x98384),x98383)),x98382))
% 25.54/25.41 [9920]P1(f862(f862(f321(x99201),f491(x99202,x99203,x99204,x99205,x99201)),x99204))+P1(f862(f862(f862(f32(x99201,f932(x99205,a921)),x99204),x99203),x99202))
% 25.54/25.41 [9925]P1(f862(f862(f321(x99251),f483(x99252,x99253,x99251,x99254,x99255)),x99253))+P1(f862(f862(f321(x99255),x99254),f862(f862(f32(x99251,f932(x99255,a921)),x99253),x99252)))
% 25.54/25.41 [9933]P1(f862(f862(f321(x99331),f482(x99332,x99333,x99331,x99334,x99335)),x99333))+P1(f862(f862(f227(f932(x99335,a921)),x99334),f862(f862(f32(x99331,f932(x99335,a921)),x99333),x99332)))
% 25.54/25.41 [9934]P1(f862(f862(f321(x99341),f839(x99342,x99343,x99344,x99345,x99341)),x99345))+P1(f862(f862(f227(f932(x99344,a921)),x99343),f862(f862(f32(x99341,f932(x99344,a921)),x99345),x99342)))
% 25.54/25.41 [9936]P1(f862(f862(x99361,f488(x99362,x99361,x99363,x99364,x99365)),x99362))+~P1(f862(f862(f862(f33(x99365,f932(x99364,a921)),x99363),x99361),x99362))
% 25.54/25.41 [9940]P1(f862(f862(f321(x99401),f488(x99402,x99403,x99404,x99405,x99401)),x99404))+~P1(f862(f862(f862(f33(x99401,f932(x99405,a921)),x99404),x99403),x99402))
% 25.54/25.41 [9941]P50(x99414,f862(f862(f32(x99411,f932(x99414,a921)),x99415),x99413),f862(f862(f32(x99411,f932(f931(x99414,x99414),a921)),x99415),x99412))+P1(f862(f862(f321(x99411),f781(x99412,x99413,x99414,x99415,x99411)),x99415))
% 25.54/25.41 [9942]P50(x99424,f862(f862(f33(x99421,f932(x99424,a921)),x99425),x99423),f862(f862(f33(x99421,f932(f931(x99424,x99424),a921)),x99425),x99422))+P1(f862(f862(f321(x99421),f831(x99422,x99423,x99424,x99425,x99421)),x99425))
% 25.54/25.41 [9952]P1(f862(f862(f321(x99521),f484(x99522,x99523,x99521,x99524,x99525)),x99523))+~P1(f862(f862(f321(x99525),x99524),f862(f862(f33(x99521,f932(x99525,a921)),x99523),x99522)))
% 25.54/25.41 [9958]P1(f862(f862(f321(x99581),x99582),f862(x99583,f484(x99583,x99584,x99585,x99582,x99581))))+~P1(f862(f862(f321(x99581),x99582),f862(f862(f33(x99585,f932(x99581,a921)),x99584),x99583)))
% 25.54/25.41 [10041]~P1(f862(f862(x100414,f491(x100415,x100414,x100413,x100412,x100411)),x100415))+P1(f862(f862(f862(f32(x100411,f932(x100412,a921)),x100413),x100414),x100415))
% 25.54/25.41 [10044]~P1(f862(f862(f321(x100441),x100442),f862(x100445,f483(x100445,x100444,x100443,x100442,x100441))))+P1(f862(f862(f321(x100441),x100442),f862(f862(f32(x100443,f932(x100441,a921)),x100444),x100445)))
% 25.54/25.41 [10048]~P50(x100481,f862(x100484,f781(x100485,x100484,x100481,x100483,x100482)),f862(x100485,f781(x100485,x100484,x100481,x100483,x100482)))+P50(x100481,f862(f862(f32(x100482,f932(x100481,a921)),x100483),x100484),f862(f862(f32(x100482,f932(f931(x100481,x100481),a921)),x100483),x100485))
% 25.54/25.41 [10049]~P50(x100491,f862(x100494,f831(x100495,x100494,x100491,x100493,x100492)),f862(x100495,f831(x100495,x100494,x100491,x100493,x100492)))+P50(x100491,f862(f862(f33(x100492,f932(x100491,a921)),x100493),x100494),f862(f862(f33(x100492,f932(f931(x100491,x100491),a921)),x100493),x100495))
% 25.54/25.41 [10050]~P1(f862(f862(f227(f932(x100501,a921)),x100502),f862(x100505,f482(x100505,x100504,x100503,x100502,x100501))))+P1(f862(f862(f227(f932(x100501,a921)),x100502),f862(f862(f32(x100503,f932(x100501,a921)),x100504),x100505)))
% 25.54/25.41 [10051]~P1(f862(f862(f227(f932(x100511,a921)),x100512),f862(x100515,f839(x100515,x100512,x100511,x100514,x100513))))+P1(f862(f862(f227(f932(x100511,a921)),x100512),f862(f862(f32(x100513,f932(x100511,a921)),x100514),x100515)))
% 25.54/25.41 [10119]~P1(f862(f862(f321(x101191),f832(x101195,x101194,x101193,x101192,x101191)),f838(x101195,x101194,x101193,x101192,x101191)))+~P1(f862(f55(x101191,x101192,f862(f862(f301(x101191),x101193),x101194)),x101195))
% 25.54/25.41 [10120]~P1(f862(f862(f321(x101201),f853(x101205,x101204,x101203,x101202,x101201)),f870(x101205,x101204,x101203,x101202,x101201)))+~P1(f862(f55(x101201,x101202,f862(f862(f301(x101201),x101203),x101204)),x101205))
% 25.54/25.41 [10121]~P1(f862(f862(f321(f931(x101211,x101211)),f862(f862(f244(x101211,x101211),x101212),x101215)),f862(f862(f176(f931(x101211,x101211),a921),f862(a105,x101214)),x101213)))+P1(f862(f862(f321(f931(x101211,x101211)),f862(f862(f244(x101211,x101211),x101212),f644(x101213,x101214,x101215,x101212,x101211))),f862(f862(f176(f931(x101211,x101211),a921),x101214),x101213)))
% 25.54/25.41 [10127]P1(f862(f59(x101271,x101271,x101272,f832(x101273,x101274,x101275,x101272,x101271),f838(x101273,x101274,x101275,x101272,x101271)),x101273))+~P1(f862(f55(x101271,x101272,f862(f862(f301(x101271),x101275),x101274)),x101273))
% 25.54/25.41 [10128]P1(f862(f59(x101281,x101281,x101282,f853(x101283,x101284,x101285,x101282,x101281),f870(x101283,x101284,x101285,x101282,x101281)),x101283))+~P1(f862(f55(x101281,x101282,f862(f862(f301(x101281),x101285),x101284)),x101283))
% 25.54/25.41 [10138]~P109(x101381)+P11(x101381,f862(f862(f147(x101382,x101381),x101383),f862(f129(x101382,f862(f862(f9(x101382,x101381,a921),f862(f862(f10(x101381,f932(x101381,a921),x101382),a317),x101383)),f862(x101384,x101385))),x101385)))
% 25.54/25.41 [10178]~P1(f862(f862(f321(x101782),x101785),f862(f276(x101781,x101782,x101784),x101783)))+P1(f862(f862(f321(f931(x101781,x101782)),f862(f862(f244(x101781,x101782),f521(x101783,x101784,x101781,x101785,x101782)),x101785)),x101784))
% 25.54/25.41 [10179]~P1(f862(f862(f321(x101792),x101795),f862(f276(x101791,x101792,x101794),x101793)))+P1(f862(f862(f321(f931(x101791,x101792)),f862(f862(f244(x101791,x101792),f526(x101793,x101794,x101791,x101795,x101792)),x101795)),x101794))
% 25.54/25.41 [10199]~P1(f862(f862(f321(f931(x101991,x101991)),f862(f862(f244(x101991,x101991),x101995),x101994)),f862(f862(f176(f931(x101991,x101991),a921),f862(a105,x101993)),x101992)))+P1(f862(f862(f321(f931(x101991,x101991)),f862(f862(f244(x101991,x101991),f644(x101992,x101993,x101994,x101995,x101991)),x101994)),x101992))
% 25.54/25.41 [10202]~P1(f862(f862(f321(f931(x102021,x102021)),f862(f862(f244(x102021,x102021),x102025),x102024)),f862(f862(f176(f931(x102021,x102021),a921),f862(a105,x102023)),x102022)))+P1(f862(f862(f321(f931(x102021,x102021)),f862(f862(f244(x102021,x102021),f642(x102022,x102023,x102024,x102025,x102021)),x102024)),f862(f862(f176(f931(x102021,x102021),a921),x102023),x102022)))
% 25.54/25.41 [10203]~P1(f862(f862(f321(f931(x102031,x102031)),f862(f862(f244(x102031,x102031),x102035),x102034)),f862(f862(f176(f931(x102031,x102031),a921),f862(a105,x102033)),x102032)))+P1(f862(f862(f321(f931(x102031,x102031)),f862(f862(f244(x102031,x102031),f643(x102032,x102033,x102034,x102035,x102031)),x102034)),f862(f862(f176(f931(x102031,x102031),a921),x102033),x102032)))
% 25.54/25.41 [10204]~P1(f862(f862(f321(f931(f925(x102041),f925(x102041))),f862(f862(f244(f925(x102041),f925(x102041)),x102045),f862(f862(f144(x102041),x102044),x102043))),f151(x102041,x102042)))+P1(f862(f862(f321(f931(x102041,x102041)),f862(f862(f244(x102041,x102041),f660(x102042,x102043,x102044,x102045,x102041)),x102044)),x102042))
% 25.54/25.41 [7779]~E(x77793,f181(f932(x77792,a921)))+E(f862(f862(f103(f932(x77791,a921)),f862(f862(f33(x77792,f932(x77791,a921)),x77793),x77794)),x77795),x77795)
% 25.54/25.41 [7780]~E(x77803,f181(f932(x77802,a921)))+E(f862(f862(f94(f932(x77801,a921)),f862(f862(f32(x77802,f932(x77801,a921)),x77803),x77804)),x77805),x77805)
% 25.54/25.41 [7833]~P119(x78331)+E(f862(f862(f74(x78331),f862(f862(f74(x78331),x78332),x78333)),f862(f862(f74(x78331),x78334),x78335)),f862(f862(f74(x78331),x78334),f862(f862(f74(x78331),f862(f862(f74(x78331),x78332),x78333)),x78335)))
% 25.54/25.41 [8210]~E(x82103,f181(f932(x82102,a921)))+E(f862(f862(f3(f932(x82101,a921)),f862(f862(f32(x82102,f932(x82101,a921)),x82103),x82104)),x82105),f862(f862(f3(f932(x82101,a921)),f234(f932(x82101,a921))),x82105))
% 25.54/25.41 [8344]E(f862(f862(f152(x83441,f862(f862(f127(x83441),x83442),x83443)),x83444),x83445),f862(f862(f127(x83441),f862(f862(f152(x83441,x83442),x83444),x83445)),x83443))+~P1(f862(f862(f228(a924),x83444),f862(f182(f925(x83441)),x83442)))
% 25.54/25.41 [8345]E(f862(f862(f152(x83451,f862(f862(f127(x83451),x83452),x83453)),x83454),x83455),f862(f862(f127(x83451),f862(f862(f152(x83451,x83452),x83454),x83455)),x83453))+~P1(f862(f862(f228(a924),x83454),f862(f182(f925(x83451)),x83452)))
% 25.54/25.41 [8617]E(f862(f862(f157(x86171),f862(f862(f147(a924,x86171),x86172),f132(a924,f862(f295(a924,x86173),x86174)))),x86175),f862(x86172,f862(f862(f73(a924),x86173),x86175)))+~P1(f862(f862(f228(a924),x86175),f862(f862(f3(a924),x86174),x86173)))
% 25.54/25.41 [8631]E(x86311,f2(a92))+E(f115(x86312,x86313,f862(x86314,f862(f862(f3(a92),x86311),f71(a92))),f862(f862(f9(x86312,a92,f926(f928(x86313))),x86315),x86311)),f862(f189(x86312,x86313,x86314,x86315),x86311))
% 25.54/25.41 [8656]~E(x86563,f181(f932(x86561,a921)))+E(f862(f862(f32(x86561,f932(x86562,a921)),x86563),f862(f862(f10(f932(x86562,a921),f932(x86562,a921),x86561),f862(f94(f932(x86562,a921)),x86564)),x86565)),f234(f932(x86562,a921)))
% 25.54/25.41 [8657]~E(x86573,f181(f932(x86571,a921)))+E(f862(f862(f32(x86571,f932(x86572,a921)),x86573),f862(f862(f10(f932(x86572,a921),f932(x86572,a921),x86571),f862(f3(f932(x86572,a921)),x86574)),x86575)),f234(f932(x86572,a921)))
% 25.54/25.41 [8658]~E(x86583,f181(f932(x86581,a921)))+E(f862(f862(f33(x86581,f932(x86582,a921)),x86583),f862(f862(f10(f932(x86582,a921),f932(x86582,a921),x86581),f862(f103(f932(x86582,a921)),x86584)),x86585)),f181(f932(x86582,a921)))
% 25.54/25.41 [8660]~P146(x86602)+E(f862(f862(f8(x86601,x86602),f862(f862(f10(x86602,x86602,x86601),f862(f74(x86602),x86603)),x86604)),x86605),f862(f862(f74(x86602),x86603),f862(f862(f8(x86601,x86602),x86604),x86605)))
% 25.54/25.41 [8951]E(x89511,f181(f932(x89512,a921)))+E(f862(f862(f33(x89512,f932(x89513,a921)),x89511),f862(f862(f10(f932(x89513,a921),f932(x89513,a921),x89512),f862(f103(f932(x89513,a921)),x89514)),x89515)),f862(f862(f103(f932(x89513,a921)),x89514),f862(f862(f33(x89512,f932(x89513,a921)),x89511),x89515)))
% 25.54/25.41 [8952]E(x89521,f181(f932(x89522,a921)))+E(f862(f862(f32(x89522,f932(x89523,a921)),x89521),f862(f862(f10(f932(x89523,a921),f932(x89523,a921),x89522),f862(f94(f932(x89523,a921)),x89524)),x89525)),f862(f862(f94(f932(x89523,a921)),x89524),f862(f862(f32(x89522,f932(x89523,a921)),x89521),x89525)))
% 25.54/25.41 [8953]E(x89531,f181(f932(x89532,a921)))+E(f862(f862(f32(x89532,f932(x89533,a921)),x89531),f862(f862(f10(f932(x89533,a921),f932(x89533,a921),x89532),f862(f3(f932(x89533,a921)),x89534)),x89535)),f862(f862(f3(f932(x89533,a921)),x89534),f862(f862(f33(x89532,f932(x89533,a921)),x89531),x89535)))
% 25.54/25.41 [8954]E(x89541,f181(f932(x89542,a921)))+E(f862(f862(f32(x89542,f932(x89543,a921)),x89541),f862(f862(f10(f932(x89543,a921),f932(x89543,a921),x89542),f862(f94(f932(x89543,a921)),x89544)),x89545)),f862(f862(f94(f932(x89543,a921)),x89544),f862(f862(f32(x89542,f932(x89543,a921)),x89541),x89545)))
% 25.54/25.41 [8955]E(x89551,f181(f932(x89552,a921)))+E(f862(f862(f32(x89552,f932(x89553,a921)),x89551),f862(f862(f10(f932(x89553,a921),f932(x89553,a921),x89552),f862(f3(f932(x89553,a921)),x89554)),x89555)),f862(f862(f3(f932(x89553,a921)),x89554),f862(f862(f33(x89552,f932(x89553,a921)),x89551),x89555)))
% 25.54/25.41 [8956]E(x89561,f181(f932(x89562,a921)))+E(f862(f862(f33(x89562,f932(x89563,a921)),x89561),f862(f862(f10(f932(x89563,a921),f932(x89563,a921),x89562),f862(f103(f932(x89563,a921)),x89564)),x89565)),f862(f862(f103(f932(x89563,a921)),x89564),f862(f862(f33(x89562,f932(x89563,a921)),x89561),x89565)))
% 25.54/25.41 [9156]~P1(f862(f862(f228(a924),f862(x91564,x91562)),f862(x91564,x91563)))+P1(f862(f862(f321(f931(x91561,x91561)),f862(f862(f244(x91561,x91561),x91562),x91563)),f146(x91561,f862(f862(f144(f932(x91561,a924)),x91564),x91565))))
% 25.54/25.41 [9157]~P1(f862(f862(f228(a924),f862(x91574,x91572)),f862(x91574,x91573)))+P1(f862(f862(f321(f931(x91571,x91571)),f862(f862(f244(x91571,x91571),x91572),x91573)),f146(x91571,f862(f862(f144(f932(x91571,a924)),x91574),x91575))))
% 25.54/25.41 [9424]~P22(x94242,x94241,x94243,f862(f862(f103(f932(x94242,a921)),x94244),x94245))+E(f862(f862(f94(f932(x94241,a921)),f862(f302(x94242,x94241,x94243),f862(f862(f3(f932(x94242,a921)),x94244),x94245))),f862(f302(x94242,x94241,x94243),f862(f862(f3(f932(x94242,a921)),x94245),x94244))),f181(f932(x94241,a921)))
% 25.54/25.41 [9683]~P22(x96833,x96831,x96835,f234(f932(x96833,a921)))+E(f862(f66(x96831,x96832,x96833,f862(f66(x96833,x96832,x96831,x96834),f86(x96833,x96831,f234(f932(x96833,a921)),x96835))),x96835),x96834)
% 25.54/25.41 [9713]~P1(f862(f862(f227(f932(x97133,a921)),f862(f276(x97131,x97133,x97134),x97132)),x97135))+P1(f862(f862(f227(f932(x97131,a921)),x97132),f862(f72(f932(x97131,a921)),f862(f276(x97133,x97131,f862(f277(x97131,x97133),x97134)),f862(f72(f932(x97133,a921)),x97135)))))
% 25.54/25.41 [9738]~P22(x97381,x97382,x97383,f862(f862(f301(x97381),x97384),x97385))+~P1(f862(f862(f321(x97382),f862(x97383,x97384)),f862(f302(x97381,x97382,x97383),f862(f862(f3(f932(x97381,a921)),x97385),f862(f862(f301(x97381),x97384),f181(f932(x97381,a921)))))))
% 25.54/25.41 [9791]P1(f862(f862(f227(f932(x97911,a921)),f862(f276(x97912,x97911,x97913),x97914)),x97915))+~P1(f862(f862(f227(f932(x97912,a921)),x97914),f862(f72(f932(x97912,a921)),f862(f276(x97911,x97912,f862(f277(x97912,x97911),x97913)),f862(f72(f932(x97911,a921)),x97915)))))
% 25.54/25.41 [9864]~P86(x98641)+P1(f862(f862(f227(x98641),f862(f69(x98641),f862(f862(f3(x98641),f862(f862(f73(x98641),x98642),x98643)),f862(f862(f73(x98641),x98644),x98645)))),f862(f862(f73(x98641),f862(f69(x98641),f862(f862(f3(x98641),x98642),x98644))),f862(f69(x98641),f862(f862(f3(x98641),x98643),x98645)))))
% 25.54/25.41 [9973]P1(f862(f862(f321(x99731),f485(x99732,x99733,x99734,x99731,x99735)),x99734))+P1(f862(f862(f227(f932(x99735,a921)),f862(f862(f33(x99731,f932(x99735,a921)),x99734),x99733)),x99732))
% 25.54/25.41 [10156]~P1(f862(f862(f227(f932(x101561,a921)),f862(x101564,f485(x101565,x101564,x101563,x101562,x101561))),x101565))+P1(f862(f862(f227(f932(x101561,a921)),f862(f862(f33(x101562,f932(x101561,a921)),x101563),x101564)),x101565))
% 25.54/25.41 [8767]E(f862(f862(f127(x87671),x87672),f862(f862(f152(x87671,x87673),f862(f862(f3(a924),x87674),f862(f182(f925(x87671)),x87672))),x87675)),f862(f862(f152(x87671,f862(f862(f127(x87671),x87672),x87673)),x87674),x87675))+P1(f862(f862(f228(a924),x87674),f862(f182(f925(x87671)),x87672)))
% 25.54/25.41 [8795]~P140(x87951)+E(f862(f862(f73(x87951),f862(f862(f74(x87951),x87952),x87953)),f862(f862(f73(x87951),f862(f862(f74(x87951),x87954),x87953)),x87955)),f862(f862(f73(x87951),f862(f862(f74(x87951),f862(f862(f73(x87951),x87952),x87954)),x87953)),x87955))
% 25.54/25.41 [9377]~P146(x93771)+E(f862(f158(x93771),f862(f862(f147(x93772,x93771),f862(f862(f10(x93771,x93771,x93772),f862(f74(x93771),x93773)),x93774)),x93775)),f862(f862(f74(x93771),x93773),f862(f158(x93771),f862(f862(f147(x93772,x93771),x93774),x93775))))
% 25.54/25.41 [9552]E(f862(f182(f925(x95521)),f862(f862(f168(x95521),f862(f862(f225(a924),f862(f182(f925(x95521)),x95522)),f862(f182(f925(x95523)),x95524))),x95522)),f862(f182(f925(x95523)),f862(f862(f168(x95523),f862(f862(f225(a924),f862(f182(f925(x95521)),x95522)),f862(f182(f925(x95523)),x95524))),x95524)))+P1(f862(x95525,f862(f862(f174(x95521,x95523),x95522),x95524)))
% 25.54/25.41 [9801]~P146(x98012)+E(f862(f862(f8(x98011,x98012),f862(f862(f9(x98011,x98012,x98012),f862(f862(f10(x98012,f932(x98012,x98012),x98011),f74(x98012)),x98013)),x98014)),x98015),f862(f862(f74(x98012),f862(f862(f8(x98011,x98012),x98013),x98015)),x98014))
% 25.54/25.41 [9802]~P65(x98022)+E(f862(f862(f8(x98021,x98022),f862(f862(f9(x98021,x98022,x98022),f862(f862(f10(x98022,f932(x98022,x98022),x98021),f281(x98022)),x98023)),x98024)),x98025),f862(f862(f281(x98022),f862(f862(f8(x98021,x98022),x98023),x98025)),x98024))
% 25.54/25.41 [9809]~P59(x98092)+E(f862(f862(f8(x98091,x98092),f862(f862(f20(x98091,x98092,x98092),f862(f862(f10(x98092,f932(x98092,x98092),x98091),f3(x98092)),x98093)),x98094)),x98095),f862(f862(f3(x98092),f862(f862(f8(x98091,x98092),x98093),x98095)),f862(f862(f8(x98091,x98092),x98094),x98095)))
% 25.54/25.41 [9810]~P72(x98102)+E(f862(f862(f8(x98101,x98102),f862(f862(f20(x98101,x98102,x98102),f862(f862(f10(x98102,f932(x98102,x98102),x98101),f73(x98102)),x98103)),x98104)),x98105),f862(f862(f73(x98102),f862(f862(f8(x98101,x98102),x98103),x98105)),f862(f862(f8(x98101,x98102),x98104),x98105)))
% 25.54/25.41 [9811]~P71(x98112)+E(f862(f862(f11(x98111,x98112),f862(f862(f20(x98111,x98112,x98112),f862(f862(f10(x98112,f932(x98112,x98112),x98111),f74(x98112)),x98113)),x98114)),x98115),f862(f862(f74(x98112),f862(f862(f11(x98111,x98112),x98113),x98115)),f862(f862(f11(x98111,x98112),x98114),x98115)))
% 25.54/25.41 [9849]~E(x98493,f181(f932(x98491,a921)))+E(f862(f862(f32(x98491,f932(x98492,a921)),x98493),f862(f862(f9(x98491,f932(x98492,a921),f932(x98492,a921)),f862(f862(f10(f932(x98492,a921),f932(f932(x98492,a921),f932(x98492,a921)),x98491),f94(f932(x98492,a921))),x98494)),x98495)),f234(f932(x98492,a921)))
% 25.54/25.41 [9850]~E(x98503,f181(f932(x98501,a921)))+E(f862(f862(f32(x98501,f932(x98502,a921)),x98503),f862(f862(f9(x98501,f932(x98502,a921),f932(x98502,a921)),f862(f862(f10(f932(x98502,a921),f932(f932(x98502,a921),f932(x98502,a921)),x98501),f3(f932(x98502,a921))),x98504)),x98505)),f234(f932(x98502,a921)))
% 25.54/25.41 [9851]~E(x98513,f181(f932(x98511,a921)))+E(f862(f862(f33(x98511,f932(x98512,a921)),x98513),f862(f862(f9(x98511,f932(x98512,a921),f932(x98512,a921)),f862(f862(f10(f932(x98512,a921),f932(f932(x98512,a921),f932(x98512,a921)),x98511),f103(f932(x98512,a921))),x98514)),x98515)),f181(f932(x98512,a921)))
% 25.54/25.41 [9869]E(x98691,f181(f932(x98692,a921)))+E(f862(f862(f33(x98692,f932(x98693,a921)),x98691),f862(f862(f9(x98692,f932(x98693,a921),f932(x98693,a921)),f862(f862(f10(f932(x98693,a921),f932(f932(x98693,a921),f932(x98693,a921)),x98692),f103(f932(x98693,a921))),x98694)),x98695)),f862(f862(f103(f932(x98693,a921)),f862(f862(f33(x98692,f932(x98693,a921)),x98691),x98694)),x98695))
% 25.54/25.41 [9870]E(x98701,f181(f932(x98702,a921)))+E(f862(f862(f32(x98702,f932(x98703,a921)),x98701),f862(f862(f9(x98702,f932(x98703,a921),f932(x98703,a921)),f862(f862(f10(f932(x98703,a921),f932(f932(x98703,a921),f932(x98703,a921)),x98702),f94(f932(x98703,a921))),x98704)),x98705)),f862(f862(f94(f932(x98703,a921)),f862(f862(f32(x98702,f932(x98703,a921)),x98701),x98704)),x98705))
% 25.54/25.41 [9871]E(x98711,f181(f932(x98712,a921)))+E(f862(f862(f32(x98712,f932(x98713,a921)),x98711),f862(f862(f9(x98712,f932(x98713,a921),f932(x98713,a921)),f862(f862(f10(f932(x98713,a921),f932(f932(x98713,a921),f932(x98713,a921)),x98712),f3(f932(x98713,a921))),x98714)),x98715)),f862(f862(f3(f932(x98713,a921)),f862(f862(f32(x98712,f932(x98713,a921)),x98711),x98714)),x98715))
% 25.54/25.41 [9872]E(x98721,f181(f932(x98722,a921)))+E(f862(f862(f32(x98722,f932(x98723,a921)),x98721),f862(f862(f9(x98722,f932(x98723,a921),f932(x98723,a921)),f862(f862(f10(f932(x98723,a921),f932(f932(x98723,a921),f932(x98723,a921)),x98722),f94(f932(x98723,a921))),x98724)),x98725)),f862(f862(f94(f932(x98723,a921)),f862(f862(f32(x98722,f932(x98723,a921)),x98721),x98724)),x98725))
% 25.54/25.41 [9873]E(x98731,f181(f932(x98732,a921)))+E(f862(f862(f32(x98732,f932(x98733,a921)),x98731),f862(f862(f9(x98732,f932(x98733,a921),f932(x98733,a921)),f862(f862(f10(f932(x98733,a921),f932(f932(x98733,a921),f932(x98733,a921)),x98732),f3(f932(x98733,a921))),x98734)),x98735)),f862(f862(f3(f932(x98733,a921)),f862(f862(f32(x98732,f932(x98733,a921)),x98731),x98734)),x98735))
% 25.54/25.41 [9874]E(x98741,f181(f932(x98742,a921)))+E(f862(f862(f33(x98742,f932(x98743,a921)),x98741),f862(f862(f9(x98742,f932(x98743,a921),f932(x98743,a921)),f862(f862(f10(f932(x98743,a921),f932(f932(x98743,a921),f932(x98743,a921)),x98742),f103(f932(x98743,a921))),x98744)),x98745)),f862(f862(f103(f932(x98743,a921)),f862(f862(f33(x98742,f932(x98743,a921)),x98741),x98744)),x98745))
% 25.54/25.41 [9429]~P1(f862(f862(f227(a924),x94291),x94294))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),x94291),x94292)),x94293)),f862(f862(f73(a924),f862(f862(f74(a924),x94294),x94292)),x94295)),f862(f862(f3(a924),x94293),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x94294),x94291)),x94292)),x94295)))
% 25.54/25.41 [10024]~P146(x100241)+E(f862(f158(x100241),f862(f862(f147(x100242,x100241),f862(f862(f9(x100242,x100241,x100241),f862(f862(f10(x100241,f932(x100241,x100241),x100242),f74(x100241)),x100243)),x100244)),x100245)),f862(f862(f74(x100241),f862(f158(x100241),f862(f862(f147(x100242,x100241),x100243),x100245))),x100244))
% 25.54/25.41 [10030]~P59(x100301)+E(f862(f158(x100301),f862(f862(f147(x100302,x100301),f862(f862(f20(x100302,x100301,x100301),f862(f862(f10(x100301,f932(x100301,x100301),x100302),f3(x100301)),x100303)),x100304)),x100305)),f862(f862(f3(x100301),f862(f158(x100301),f862(f862(f147(x100302,x100301),x100303),x100305))),f862(f158(x100301),f862(f862(f147(x100302,x100301),x100304),x100305))))
% 25.54/25.41 [10031]~P72(x100311)+E(f862(f158(x100311),f862(f862(f147(x100312,x100311),f862(f862(f20(x100312,x100311,x100311),f862(f862(f10(x100311,f932(x100311,x100311),x100312),f73(x100311)),x100313)),x100314)),x100315)),f862(f862(f73(x100311),f862(f158(x100311),f862(f862(f147(x100312,x100311),x100313),x100315))),f862(f158(x100311),f862(f862(f147(x100312,x100311),x100314),x100315))))
% 25.54/25.41 [10169]P1(f862(x101691,f862(f862(f174(x101692,x101693),x101694),x101695)))+~P1(f862(x101691,f862(f862(f174(x101692,x101693),f862(f862(f168(x101692),f862(f862(f225(a924),f862(f182(f925(x101692)),x101694)),f862(f182(f925(x101693)),x101695))),x101694)),f862(f862(f168(x101693),f862(f862(f225(a924),f862(f182(f925(x101692)),x101694)),f862(f182(f925(x101693)),x101695))),x101695))))
% 25.54/25.41 [10430]~P1(f862(f862(f321(f931(x104302,x104301)),f862(f862(f244(x104302,x104301),x104304),x104305)),f862(f277(x104301,x104302),x104303)))+P1(f862(f862(f235(x104301,x104302,f862(f862(f9(x104301,f932(f931(x104301,x104302),a921),f932(x104302,a921)),f862(f862(f10(f932(x104302,f932(f932(f931(x104301,x104302),a921),a921)),f932(f932(f931(x104301,x104302),a921),f932(x104302,a921)),x104301),f9(x104302,f932(f931(x104301,x104302),a921),a921)),f862(f862(f10(f932(x104302,f931(x104301,x104302)),f932(x104302,f932(f932(f931(x104301,x104302),a921),a921)),x104301),f862(f10(f931(x104301,x104302),f932(f932(f931(x104301,x104302),a921),a921),x104302),f321(f931(x104301,x104302)))),f244(x104301,x104302)))),x104303)),x104304),x104305))
% 25.54/25.41 [10440]P1(f862(f862(f321(f931(x104401,x104402)),f862(f862(f244(x104401,x104402),x104403),x104404)),f862(f277(x104402,x104401),x104405)))+~P1(f862(f862(f235(x104402,x104401,f862(f862(f9(x104402,f932(f931(x104402,x104401),a921),f932(x104401,a921)),f862(f862(f10(f932(x104401,f932(f932(f931(x104402,x104401),a921),a921)),f932(f932(f931(x104402,x104401),a921),f932(x104401,a921)),x104402),f9(x104401,f932(f931(x104402,x104401),a921),a921)),f862(f862(f10(f932(x104401,f931(x104402,x104401)),f932(x104401,f932(f932(f931(x104402,x104401),a921),a921)),x104402),f862(f10(f931(x104402,x104401),f932(f932(f931(x104402,x104401),a921),a921),x104401),f321(f931(x104402,x104401)))),f244(x104402,x104401)))),x104405)),x104403),x104404))
% 25.54/25.41 [9682]~P1(f862(f862(f227(a924),x96824),x96821))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),x96821),x96822)),x96823)),f862(f862(f73(a924),f862(f862(f74(a924),x96824),x96822)),x96825)),f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x96821),x96824)),x96822)),x96823)),x96825))
% 25.54/25.41 [7469]E(x74691,x74692)+~E(f213(x74693,x74694,x74695,x74691),f213(x74693,x74694,x74696,x74692))
% 25.54/25.41 [7470]E(x74701,x74702)+~E(f213(x74703,x74704,x74701,x74705),f213(x74703,x74704,x74702,x74706))
% 25.54/25.41 [8600]~P17(x86005,x86001,x86002,x86006)+E(f862(f66(x86001,x86001,x86001,f862(x86002,x86003)),f862(x86002,x86004)),f862(f66(x86001,x86001,x86001,f862(x86002,x86004)),f862(x86002,x86003)))
% 25.54/25.41 [8839]~P54(x88394,x88395,x88392,x88391,x88396)+E(f862(x88391,f862(x88392,x88393)),x88393)
% 25.54/25.41 [9007]P22(x90071,x90072,x90073,x90074)+~P22(x90071,x90075,f862(f66(x90072,x90075,x90071,x90076),x90073),x90074)
% 25.54/25.41 [9081]~E(x90816,x90814)+E(f862(f68(x90811,x90812,x90813,x90814,x90815),x90816),x90815)
% 25.54/25.41 [9082]~E(x90826,x90824)+E(f862(f68(x90821,x90822,x90823,x90824,x90825),x90826),x90825)
% 25.54/25.41 [9086]E(x90861,x90862)+E(f862(f68(x90863,x90864,x90865,x90862,x90866),x90861),f862(x90865,x90861))
% 25.54/25.41 [9087]E(x90871,x90872)+E(f862(f68(x90873,x90874,x90875,x90872,x90876),x90871),f862(x90875,x90871))
% 25.54/25.41 [9088]E(x90881,x90882)+E(f862(f68(x90883,x90884,x90885,x90882,x90886),x90881),f862(x90885,x90881))
% 25.54/25.41 [9100]~P22(x91004,x91002,f862(f66(x91001,x91002,x91004,x91003),x91005),x91006)+P22(x91001,x91002,x91003,f862(f302(x91004,x91001,x91005),x91006))
% 25.54/25.41 [9542]~P54(x95426,x95425,x95424,x95421,x95423)+E(f862(x95421,f884(x95422,x95423,x95421,x95424,x95425)),x95422)
% 25.54/25.41 [9812]P1(f862(f54(x98121),x98122))+~P1(f862(f59(x98121,x98123,x98124,x98125,x98122),x98126))
% 25.54/25.41 [9821]~P1(f862(f862(f321(x98214),x98213),f291(x98214,x98215,x98211,x98212,x98216)))+P1(f862(f862(x98211,x98212),x98213))
% 25.54/25.41 [9822]~P1(f862(f862(f321(x98224),x98223),f288(x98224,x98221,x98225,x98222,x98226)))+P1(f862(f862(x98221,x98222),x98223))
% 25.54/25.41 [9823]~P1(f862(f862(f321(x98234),x98232),f291(x98234,x98231,x98235,x98236,x98233)))+P1(f862(f862(x98231,x98232),x98233))
% 25.54/25.41 [9824]~P1(f862(f862(f321(x98244),x98242),f288(x98244,x98245,x98241,x98246,x98243)))+P1(f862(f862(x98241,x98242),x98243))
% 25.54/25.41 [10317]P10(x103171,x103172,x103173,x103174,x103175,x103176)+~E(f862(f862(x103176,f855(x103173,x103176,x103175,x103172,x103174,x103171)),f856(x103173,x103176,x103175,x103172,x103174,x103171)),f862(f862(x103176,f854(x103173,x103176,x103175,x103172,x103174,x103171)),f857(x103173,x103176,x103175,x103172,x103174,x103171)))
% 25.54/25.41 [5953]E(x59531,x59532)+~E(f862(f862(f244(x59533,x59534),x59535),x59531),f862(f862(f244(x59533,x59534),x59536),x59532))
% 25.54/25.41 [5954]E(x59541,x59542)+~E(f862(f862(f244(x59543,x59544),x59545),x59541),f862(f862(f244(x59543,x59544),x59546),x59542))
% 25.54/25.41 [5955]E(x59551,x59552)+~E(f862(f862(f244(x59553,x59554),x59551),x59555),f862(f862(f244(x59553,x59554),x59552),x59556))
% 25.54/25.41 [5956]E(x59561,x59562)+~E(f862(f862(f244(x59563,x59564),x59561),x59565),f862(f862(f244(x59563,x59564),x59562),x59566))
% 25.54/25.41 [6101]~P14(x61015,x61016,x61011)+E(f862(f862(x61011,x61012),f862(f862(x61011,x61013),x61014)),f862(f862(x61011,x61013),f862(f862(x61011,x61012),x61014)))
% 25.54/25.41 [7537]~P30(x75374,x75371,f862(f862(f144(x75374),x75372),x75375),f862(f862(f144(x75374),x75373),x75376))+P1(f862(f862(x75371,x75372),x75373))
% 25.54/25.41 [7896]P30(x78961,x78962,x78963,x78964)+~P30(x78961,x78962,f862(f862(f144(x78961),x78965),x78963),f862(f862(f144(x78961),x78966),x78964))
% 25.54/25.41 [8944]~P54(x89445,x89441,x89442,x89446,x89444)+P1(f862(f862(f321(x89441),f862(x89442,x89443)),x89444))
% 25.54/25.41 [9148]~E(x91483,f862(f862(f144(x91481),x91485),x91486))+P1(f862(f862(f321(f931(f925(x91481),f925(x91481))),f862(f862(f244(f925(x91481),f925(x91481)),x91482),f862(f862(f127(x91481),x91482),x91483))),f140(x91481,x91484)))
% 25.54/25.41 [9383]~P32(x93831,x93832,x93833,x93835,x93836)+P32(x93831,x93832,x93833,f862(f862(f168(x93831),x93834),x93835),f862(f862(f168(x93832),x93834),x93836))
% 25.54/25.41 [9384]~P32(x93841,x93842,x93843,x93845,x93846)+P32(x93841,x93842,x93843,f862(f862(f131(x93841),x93844),x93845),f862(f862(f131(x93842),x93844),x93846))
% 25.54/25.41 [9647]E(f862(f302(x96471,x96472,f68(x96471,x96472,x96473,x96474,x96475)),x96476),f862(f302(x96471,x96472,x96473),x96476))+P1(f862(f862(f321(x96471),x96474),x96476))
% 25.54/25.41 [9650]E(f862(f862(f147(x96501,x96502),f68(x96501,x96502,x96503,x96504,x96505)),x96506),f862(f862(f147(x96501,x96502),x96503),x96506))+P1(f862(f862(f321(x96501),x96504),f862(f165(x96501),x96506)))
% 25.54/25.41 [9884]~P21(x98844,x98842,x98845,x98843,x98846,x98841)+E(f862(x98841,f181(f932(x98842,a921))),x98843)
% 25.54/25.41 [9974]~P54(x99746,x99741,x99745,x99744,x99743)+P1(f862(f862(f321(x99741),f884(x99742,x99743,x99744,x99745,x99741)),x99743))
% 25.54/25.41 [10122]~E(f862(x101224,f862(f243(x101221,x101223),x101225)),f862(x101226,f862(f243(x101221,x101223),x101225)))+E(f862(f250(x101221,x101222,x101223,x101223,x101224,f25(x101223)),x101225),f862(f250(x101221,x101222,x101223,x101223,x101226,f25(x101223)),x101225))
% 25.54/25.41 [10123]~E(f862(x101234,f862(f248(x101231,x101232),x101235)),f862(x101236,f862(f248(x101231,x101232),x101235)))+E(f862(f250(x101231,x101231,x101232,x101233,f25(x101231),x101234),x101235),f862(f250(x101231,x101231,x101232,x101233,f25(x101231),x101236),x101235))
% 25.54/25.41 [10165]~E(f862(f250(x101652,x101656,x101653,x101653,x101651,f25(x101653)),x101654),f862(f250(x101652,x101656,x101653,x101653,x101655,f25(x101653)),x101654))+E(f862(x101651,f862(f243(x101652,x101653),x101654)),f862(x101655,f862(f243(x101652,x101653),x101654)))
% 25.54/25.41 [10166]~E(f862(f250(x101662,x101662,x101663,x101666,f25(x101662),x101661),x101664),f862(f250(x101662,x101662,x101663,x101666,f25(x101662),x101665),x101664))+E(f862(x101661,f862(f248(x101662,x101663),x101664)),f862(x101665,f862(f248(x101662,x101663),x101664)))
% 25.54/25.41 [9047]P1(f862(f862(f321(x90471),x90472),x90473))+~P1(f862(f862(f321(f931(x90471,x90474)),f862(f862(f244(x90471,x90474),x90472),x90475)),f862(f862(f246(x90471,x90474),x90473),x90476)))
% 25.54/25.41 [9048]P1(f862(f862(f321(x90481),x90482),x90483))+~P1(f862(f862(f321(f931(x90481,x90484)),f862(f862(f244(x90481,x90484),x90482),x90485)),f862(f862(f246(x90481,x90484),x90483),x90486)))
% 25.54/25.41 [9049]P1(f862(f862(f321(x90491),x90492),x90493))+~P1(f862(f862(f321(f931(x90491,x90494)),f862(f862(f244(x90491,x90494),x90492),x90495)),f862(f862(f246(x90491,x90494),x90493),x90496)))
% 25.54/25.41 [9063]P1(f862(f862(f321(x90631),x90632),f862(x90633,x90634)))+~P1(f862(f862(f321(f931(x90635,x90631)),f862(f862(f244(x90635,x90631),x90634),x90632)),f862(f862(f246(x90635,x90631),x90636),x90633)))
% 25.54/25.41 [9064]P1(f862(f862(f321(x90641),x90642),f862(x90643,x90644)))+~P1(f862(f862(f321(f931(x90645,x90641)),f862(f862(f244(x90645,x90641),x90644),x90642)),f862(f862(f246(x90645,x90641),x90646),x90643)))
% 25.54/25.41 [9065]P1(f862(f862(f321(x90651),x90652),f862(x90653,x90654)))+~P1(f862(f862(f321(f931(x90655,x90651)),f862(f862(f244(x90655,x90651),x90654),x90652)),f862(f862(f246(x90655,x90651),x90656),x90653)))
% 25.54/25.41 [9501]P1(f862(f862(f321(f931(x95011,x95011)),f862(f862(f244(x95011,x95011),f862(x95012,x95013)),f862(x95012,x95014))),x95015))+~P1(f862(f862(f321(f931(x95016,x95016)),f862(f862(f244(x95016,x95016),x95013),x95014)),f862(f862(f279(x95011,x95016),x95015),x95012)))
% 25.54/25.41 [9521]~P1(f862(f862(f321(f931(x95214,x95214)),f862(f862(f244(x95214,x95214),f862(x95216,x95212)),f862(x95216,x95213))),x95215))+P1(f862(f862(f321(f931(x95211,x95211)),f862(f862(f244(x95211,x95211),x95212),x95213)),f862(f862(f279(x95214,x95211),x95215),x95216)))
% 25.54/25.41 [10168]E(f862(f862(f244(x101681,x101682),f652(x101683,x101684,x101685,x101686,x101682,x101681)),f653(x101683,x101684,x101685,x101686,x101682,x101681)),x101686)+~P1(f862(f862(f321(f931(x101681,x101682)),x101686),f862(f862(f280(x101681,x101685,x101682),x101684),x101683)))
% 25.54/25.41 [10388]~P1(f862(f862(f321(f931(x103881,x103886)),x103885),f862(f862(f280(x103881,x103882,x103886),x103884),x103883)))+P1(f862(f862(f321(f931(x103881,x103882)),f862(f862(f244(x103881,x103882),f652(x103883,x103884,x103882,x103885,x103886,x103881)),f654(x103883,x103884,x103882,x103885,x103886,x103881))),x103884))
% 25.54/25.41 [10389]~P1(f862(f862(f321(f931(x103896,x103892)),x103895),f862(f862(f280(x103896,x103891,x103892),x103894),x103893)))+P1(f862(f862(f321(f931(x103891,x103892)),f862(f862(f244(x103891,x103892),f654(x103893,x103894,x103891,x103895,x103892,x103896)),f653(x103893,x103894,x103891,x103895,x103892,x103896))),x103893))
% 25.54/25.41 [10390]P10(x103901,x103902,x103903,x103904,x103905,x103906)+P1(f862(f862(f321(f931(x103902,x103902)),f862(f862(f244(x103902,x103902),f857(x103903,x103906,x103905,x103902,x103904,x103901)),f856(x103903,x103906,x103905,x103902,x103904,x103901))),x103905))
% 25.54/25.41 [10391]P10(x103911,x103912,x103913,x103914,x103915,x103916)+P1(f862(f862(f321(f931(x103911,x103911)),f862(f862(f244(x103911,x103911),f854(x103913,x103916,x103915,x103912,x103914,x103911)),f855(x103913,x103916,x103915,x103912,x103914,x103911))),x103914))
% 25.54/25.41 [7966]~P3(x79662)+E(f862(f862(f32(x79661,x79662),x79663),f862(f862(f9(x79661,x79664,x79662),x79665),x79666)),f862(f862(f862(f32(x79661,f932(x79664,x79662)),x79663),x79665),x79666))
% 25.54/25.41 [7967]~P3(x79672)+E(f862(f862(f33(x79671,x79672),x79673),f862(f862(f9(x79671,x79674,x79672),x79675),x79676)),f862(f862(f862(f33(x79671,f932(x79674,x79672)),x79673),x79675),x79676))
% 25.54/25.41 [8748]E(f862(f862(f32(x87481,f932(x87482,a921)),x87483),f862(f862(f10(f932(x87482,a921),f932(x87482,a921),x87481),f862(f301(x87482),x87484)),x87485)),f862(f862(f301(x87482),x87484),f862(f862(f32(x87481,f932(x87482,a921)),x87483),x87485)))+~P1(f862(f862(f321(x87481),x87486),x87483))
% 25.54/25.41 [8749]E(f862(f862(f33(x87491,f932(x87492,a921)),x87493),f862(f862(f10(f932(x87492,a921),f932(x87492,a921),x87491),f862(f301(x87492),x87494)),x87495)),f862(f862(f301(x87492),x87494),f862(f862(f33(x87491,f932(x87492,a921)),x87493),x87495)))+~P1(f862(f862(f321(x87491),x87496),x87493))
% 25.54/25.41 [9201]~P3(x92012)+E(f862(f862(f32(x92011,x92012),x92013),f862(f862(f10(f932(x92014,x92012),x92012,x92011),f862(f32(x92014,x92012),x92015)),f862(f9(x92014,x92011,x92012),x92016))),f862(f862(f32(x92014,x92012),x92015),f862(f862(f10(f932(x92011,x92012),x92012,x92014),f862(f32(x92011,x92012),x92013)),x92016)))
% 25.54/25.41 [9202]~P3(x92022)+E(f862(f862(f33(x92021,x92022),x92023),f862(f862(f10(f932(x92024,x92022),x92022,x92021),f862(f33(x92024,x92022),x92025)),f862(f9(x92024,x92021,x92022),x92026))),f862(f862(f33(x92024,x92022),x92025),f862(f862(f10(f932(x92021,x92022),x92022,x92024),f862(f33(x92021,x92022),x92023)),x92026)))
% 25.54/25.41 [9407]P1(f862(f862(f321(x94071),x94072),f862(f165(x94071),x94073)))+~P1(f862(f862(f321(f931(x94074,x94071)),f862(f862(f244(x94074,x94071),x94075),x94072)),f862(f165(f931(x94074,x94071)),f862(f862(f174(x94074,x94071),x94076),x94073))))
% 25.54/25.41 [9408]P1(f862(f862(f321(x94081),x94082),f862(f165(x94081),x94083)))+~P1(f862(f862(f321(f931(x94081,x94084)),f862(f862(f244(x94081,x94084),x94082),x94085)),f862(f165(f931(x94081,x94084)),f862(f862(f174(x94081,x94084),x94083),x94086))))
% 25.54/25.41 [9409]P1(f862(f862(f321(x94091),x94092),f862(f165(x94091),x94093)))+~P1(f862(f862(f321(f931(x94094,x94091)),f862(f862(f244(x94094,x94091),x94095),x94092)),f862(f165(f931(x94094,x94091)),f862(f862(f174(x94094,x94091),x94096),x94093))))
% 25.54/25.41 [9410]P1(f862(f862(f321(x94101),x94102),f862(f165(x94101),x94103)))+~P1(f862(f862(f321(f931(x94101,x94104)),f862(f862(f244(x94101,x94104),x94102),x94105)),f862(f165(f931(x94101,x94104)),f862(f862(f174(x94101,x94104),x94103),x94106))))
% 25.54/25.41 [9517]P1(f862(f862(f227(f932(x95171,a921)),f862(f276(x95172,x95171,x95173),x95174)),x95175))+~P1(f862(f862(f227(f932(f931(x95172,x95171),a921)),x95173),f862(f862(f246(x95172,x95171),x95176),f862(f18(f932(x95171,a921),x95172),x95175))))
% 25.54/25.41 [9522]~P23(x95224,x95222,x95225,f234(f932(x95224,a921)),f234(f932(x95222,a921)))+E(f862(f862(f32(x95221,f932(x95222,a921)),x95223),f862(f862(f10(f932(x95224,a921),f932(x95222,a921),x95221),f302(x95224,x95222,x95225)),x95226)),f862(f302(x95224,x95222,x95225),f862(f862(f32(x95221,f932(x95224,a921)),x95223),x95226)))
% 25.54/25.41 [9716]P1(f862(f862(f321(f931(f925(x97161),f925(x97161))),f862(f862(f244(f925(x97161),f925(x97161)),f862(f862(f144(x97161),x97162),x97163)),f862(f862(f144(x97161),x97164),x97165))),f140(x97161,x97166)))+~P1(f862(f862(f321(f931(x97161,x97161)),f862(f862(f244(x97161,x97161),x97162),x97164)),x97166))
% 25.54/25.41 [10164]E(f862(f862(f244(x101641,x101642),f599(x101643,x101644,x101645,x101642,x101641,x101646)),f600(x101643,x101644,x101645,x101642,x101641,x101646)),x101646)+P1(f862(f862(f321(x101645),x101644),f862(f862(f249(x101641,x101642,f932(x101645,a921)),x101643),x101646)))
% 25.54/25.41 [10170]E(f862(f862(f244(x101701,x101702),f601(x101703,x101704,x101702,x101701,x101705,x101706)),f604(x101703,x101704,x101702,x101701,x101705,x101706)),x101703)+~P1(f862(f862(f321(x101706),x101705),f862(f862(f249(x101701,x101702,f932(x101706,a921)),x101704),x101703)))
% 25.54/25.41 [10332]P1(f862(f862(f321(x103321),x103322),f862(f862(x103323,f601(x103324,x103323,x103325,x103326,x103322,x103321)),f604(x103324,x103323,x103325,x103326,x103322,x103321))))+~P1(f862(f862(f321(x103321),x103322),f862(f862(f249(x103326,x103325,f932(x103321,a921)),x103323),x103324)))
% 25.54/25.41 [10361]~P1(f862(f862(f321(x103611),x103612),f862(f862(x103615,f599(x103615,x103612,x103611,x103614,x103613,x103616)),f600(x103615,x103612,x103611,x103614,x103613,x103616))))+P1(f862(f862(f321(x103611),x103612),f862(f862(f249(x103613,x103614,f932(x103611,a921)),x103615),x103616)))
% 25.54/25.41 [8648]E(x86481,x86482)+E(f862(f862(f152(x86483,f862(f862(f152(x86483,x86484),x86481),x86485)),x86482),x86486),f862(f862(f152(x86483,f862(f862(f152(x86483,x86484),x86482),x86486)),x86481),x86485))
% 25.54/25.41 [9776]~P1(f862(f862(f321(x97763),x97766),x97765))+E(f862(f862(f301(x97761),x97762),f862(f302(x97763,x97761,x97764),f862(f862(f3(f932(x97763,a921)),x97765),f862(f862(f301(x97763),x97766),f181(f932(x97763,a921)))))),f862(f302(x97763,x97761,f68(x97763,x97761,x97764,x97766,x97762)),x97765))
% 25.54/25.41 [9279]~P1(f862(f862(x92794,x92795),x92796))+P1(f862(f862(f862(f862(f103(f932(x92791,f932(x92792,a921))),x92793),x92794),x92795),x92796))
% 25.54/25.41 [9280]~P1(f862(f862(x92804,x92805),x92806))+P1(f862(f862(f862(f862(f103(f932(x92801,f932(x92802,a921))),x92803),x92804),x92805),x92806))
% 25.54/25.41 [9281]~P1(f862(f862(x92813,x92815),x92816))+P1(f862(f862(f862(f862(f103(f932(x92811,f932(x92812,a921))),x92813),x92814),x92815),x92816))
% 25.54/25.41 [9282]~P1(f862(f862(x92823,x92825),x92826))+P1(f862(f862(f862(f862(f103(f932(x92821,f932(x92822,a921))),x92823),x92824),x92825),x92826))
% 25.54/25.41 [9572]P1(f862(f862(x95721,x95722),x95723))+~P1(f862(f862(f862(f862(f94(f932(x95724,f932(x95725,a921))),x95726),x95721),x95722),x95723))
% 25.54/25.41 [9573]P1(f862(f862(x95731,x95732),x95733))+~P1(f862(f862(f862(f862(f94(f932(x95734,f932(x95735,a921))),x95731),x95736),x95732),x95733))
% 25.54/25.41 [9574]P1(f862(f862(x95741,x95742),x95743))+~P1(f862(f862(f862(f862(f94(f932(x95744,f932(x95745,a921))),x95746),x95741),x95742),x95743))
% 25.54/25.41 [9575]P1(f862(f862(x95751,x95752),x95753))+~P1(f862(f862(f862(f862(f94(f932(x95754,f932(x95755,a921))),x95751),x95756),x95752),x95753))
% 25.54/25.41 [10012]~P72(x100122)+E(f862(f862(f8(x100121,x100122),f862(f862(f9(x100121,f932(x100123,a921),x100122),f862(f862(f10(f932(x100123,x100122),f932(f932(x100123,a921),x100122),x100121),f8(x100123,x100122)),x100124)),x100125)),x100126),f862(f862(f8(f931(x100121,x100123),x100122),f862(f249(x100121,x100123,x100122),x100124)),f862(f862(f246(x100121,x100123),x100126),f862(f18(f932(x100123,a921),x100121),x100125))))
% 25.54/25.41 [10013]~P71(x100132)+E(f862(f862(f11(x100131,x100132),f862(f862(f9(x100131,f932(x100133,a921),x100132),f862(f862(f10(f932(x100133,x100132),f932(f932(x100133,a921),x100132),x100131),f11(x100133,x100132)),x100134)),x100135)),x100136),f862(f862(f11(f931(x100131,x100133),x100132),f862(f249(x100131,x100133,x100132),x100134)),f862(f862(f246(x100131,x100133),x100136),f862(f18(f932(x100133,a921),x100131),x100135))))
% 25.54/25.41 [10147]~P72(x101472)+E(f862(f862(f8(x101471,x101472),f862(f862(f9(x101471,f932(x101473,a921),x101472),f862(f862(f10(f932(x101473,x101472),f932(f932(x101473,a921),x101472),x101471),f8(x101473,x101472)),f862(f9(x101473,x101471,x101472),x101474))),x101475)),x101476),f862(f862(f8(x101473,x101472),f862(f862(f9(x101473,f932(x101471,a921),x101472),f862(f862(f10(f932(x101471,x101472),f932(f932(x101471,a921),x101472),x101473),f8(x101471,x101472)),x101474)),x101476)),x101475))
% 25.54/25.41 [10452]~P1(f862(f862(f321(f931(x104521,x104522)),f862(f862(f244(x104521,x104522),x104525),x104526)),f862(f862(f103(f932(f931(x104521,x104522),a921)),x104523),x104524)))+P1(f862(f862(f862(f862(f103(f932(x104521,f932(x104522,a921))),f862(f862(f9(x104521,f932(f931(x104521,x104522),a921),f932(x104522,a921)),f862(f862(f10(f932(x104522,f932(f932(f931(x104521,x104522),a921),a921)),f932(f932(f931(x104521,x104522),a921),f932(x104522,a921)),x104521),f9(x104522,f932(f931(x104521,x104522),a921),a921)),f862(f862(f10(f932(x104522,f931(x104521,x104522)),f932(x104522,f932(f932(f931(x104521,x104522),a921),a921)),x104521),f862(f10(f931(x104521,x104522),f932(f932(f931(x104521,x104522),a921),a921),x104522),f321(f931(x104521,x104522)))),f244(x104521,x104522)))),x104523)),f862(f862(f9(x104521,f932(f931(x104521,x104522),a921),f932(x104522,a921)),f862(f862(f10(f932(x104522,f932(f932(f931(x104521,x104522),a921),a921)),f932(f932(f931(x104521,x104522),a921),f932(x104522,a921)),x104521),f9(x104522,f932(f931(x104521,x104522),a921),a921)),f862(f862(f10(f932(x104522,f931(x104521,x104522)),f932(x104522,f932(f932(f931(x104521,x104522),a921),a921)),x104521),f862(f10(f931(x104521,x104522),f932(f932(f931(x104521,x104522),a921),a921),x104522),f321(f931(x104521,x104522)))),f244(x104521,x104522)))),x104524)),x104525),x104526))
% 25.54/25.41 [10453]~P1(f862(f862(f321(f931(x104531,x104532)),f862(f862(f244(x104531,x104532),x104535),x104536)),f862(f862(f94(f932(f931(x104531,x104532),a921)),x104533),x104534)))+P1(f862(f862(f862(f862(f94(f932(x104531,f932(x104532,a921))),f862(f862(f9(x104531,f932(f931(x104531,x104532),a921),f932(x104532,a921)),f862(f862(f10(f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),f932(f932(f931(x104531,x104532),a921),f932(x104532,a921)),x104531),f9(x104532,f932(f931(x104531,x104532),a921),a921)),f862(f862(f10(f932(x104532,f931(x104531,x104532)),f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),x104531),f862(f10(f931(x104531,x104532),f932(f932(f931(x104531,x104532),a921),a921),x104532),f321(f931(x104531,x104532)))),f244(x104531,x104532)))),x104533)),f862(f862(f9(x104531,f932(f931(x104531,x104532),a921),f932(x104532,a921)),f862(f862(f10(f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),f932(f932(f931(x104531,x104532),a921),f932(x104532,a921)),x104531),f9(x104532,f932(f931(x104531,x104532),a921),a921)),f862(f862(f10(f932(x104532,f931(x104531,x104532)),f932(x104532,f932(f932(f931(x104531,x104532),a921),a921)),x104531),f862(f10(f931(x104531,x104532),f932(f932(f931(x104531,x104532),a921),a921),x104532),f321(f931(x104531,x104532)))),f244(x104531,x104532)))),x104534)),x104535),x104536))
% 25.54/25.41 [10462]P1(f862(f862(f321(f931(x104621,x104622)),f862(f862(f244(x104621,x104622),x104623),x104624)),f862(f862(f103(f932(f931(x104621,x104622),a921)),x104625),x104626)))+~P1(f862(f862(f862(f862(f103(f932(x104621,f932(x104622,a921))),f862(f862(f9(x104621,f932(f931(x104621,x104622),a921),f932(x104622,a921)),f862(f862(f10(f932(x104622,f932(f932(f931(x104621,x104622),a921),a921)),f932(f932(f931(x104621,x104622),a921),f932(x104622,a921)),x104621),f9(x104622,f932(f931(x104621,x104622),a921),a921)),f862(f862(f10(f932(x104622,f931(x104621,x104622)),f932(x104622,f932(f932(f931(x104621,x104622),a921),a921)),x104621),f862(f10(f931(x104621,x104622),f932(f932(f931(x104621,x104622),a921),a921),x104622),f321(f931(x104621,x104622)))),f244(x104621,x104622)))),x104625)),f862(f862(f9(x104621,f932(f931(x104621,x104622),a921),f932(x104622,a921)),f862(f862(f10(f932(x104622,f932(f932(f931(x104621,x104622),a921),a921)),f932(f932(f931(x104621,x104622),a921),f932(x104622,a921)),x104621),f9(x104622,f932(f931(x104621,x104622),a921),a921)),f862(f862(f10(f932(x104622,f931(x104621,x104622)),f932(x104622,f932(f932(f931(x104621,x104622),a921),a921)),x104621),f862(f10(f931(x104621,x104622),f932(f932(f931(x104621,x104622),a921),a921),x104622),f321(f931(x104621,x104622)))),f244(x104621,x104622)))),x104626)),x104623),x104624))
% 25.54/25.41 [10463]P1(f862(f862(f321(f931(x104631,x104632)),f862(f862(f244(x104631,x104632),x104633),x104634)),f862(f862(f94(f932(f931(x104631,x104632),a921)),x104635),x104636)))+~P1(f862(f862(f862(f862(f94(f932(x104631,f932(x104632,a921))),f862(f862(f9(x104631,f932(f931(x104631,x104632),a921),f932(x104632,a921)),f862(f862(f10(f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),f932(f932(f931(x104631,x104632),a921),f932(x104632,a921)),x104631),f9(x104632,f932(f931(x104631,x104632),a921),a921)),f862(f862(f10(f932(x104632,f931(x104631,x104632)),f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),x104631),f862(f10(f931(x104631,x104632),f932(f932(f931(x104631,x104632),a921),a921),x104632),f321(f931(x104631,x104632)))),f244(x104631,x104632)))),x104635)),f862(f862(f9(x104631,f932(f931(x104631,x104632),a921),f932(x104632,a921)),f862(f862(f10(f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),f932(f932(f931(x104631,x104632),a921),f932(x104632,a921)),x104631),f9(x104632,f932(f931(x104631,x104632),a921),a921)),f862(f862(f10(f932(x104632,f931(x104631,x104632)),f932(x104632,f932(f932(f931(x104631,x104632),a921),a921)),x104631),f862(f10(f931(x104631,x104632),f932(f932(f931(x104631,x104632),a921),a921),x104632),f321(f931(x104631,x104632)))),f244(x104631,x104632)))),x104636)),x104633),x104634))
% 25.54/25.41 [10446]~P1(f862(f862(f321(f931(x104462,x104463)),f862(f862(f244(x104462,x104463),x104465),x104466)),f862(f862(f32(x104461,f932(f931(x104462,x104463),a921)),f234(f932(x104461,a921))),x104464)))+P1(f862(f862(f862(f862(f32(x104461,f932(x104462,f932(x104463,a921))),f234(f932(x104461,a921))),f862(f862(f10(f932(f931(x104462,x104463),a921),f932(x104462,f932(x104463,a921)),x104461),f862(f9(x104462,f932(f931(x104462,x104463),a921),f932(x104463,a921)),f862(f862(f10(f932(x104463,f932(f932(f931(x104462,x104463),a921),a921)),f932(f932(f931(x104462,x104463),a921),f932(x104463,a921)),x104462),f9(x104463,f932(f931(x104462,x104463),a921),a921)),f862(f862(f10(f932(x104463,f931(x104462,x104463)),f932(x104463,f932(f932(f931(x104462,x104463),a921),a921)),x104462),f862(f10(f931(x104462,x104463),f932(f932(f931(x104462,x104463),a921),a921),x104463),f321(f931(x104462,x104463)))),f244(x104462,x104463))))),x104464)),x104465),x104466))
% 25.54/25.41 [10447]~P1(f862(f862(f321(f931(x104472,x104473)),f862(f862(f244(x104472,x104473),x104475),x104476)),f862(f862(f33(x104471,f932(f931(x104472,x104473),a921)),f234(f932(x104471,a921))),x104474)))+P1(f862(f862(f862(f862(f33(x104471,f932(x104472,f932(x104473,a921))),f234(f932(x104471,a921))),f862(f862(f10(f932(f931(x104472,x104473),a921),f932(x104472,f932(x104473,a921)),x104471),f862(f9(x104472,f932(f931(x104472,x104473),a921),f932(x104473,a921)),f862(f862(f10(f932(x104473,f932(f932(f931(x104472,x104473),a921),a921)),f932(f932(f931(x104472,x104473),a921),f932(x104473,a921)),x104472),f9(x104473,f932(f931(x104472,x104473),a921),a921)),f862(f862(f10(f932(x104473,f931(x104472,x104473)),f932(x104473,f932(f932(f931(x104472,x104473),a921),a921)),x104472),f862(f10(f931(x104472,x104473),f932(f932(f931(x104472,x104473),a921),a921),x104473),f321(f931(x104472,x104473)))),f244(x104472,x104473))))),x104474)),x104475),x104476))
% 25.54/25.41 [10456]P1(f862(f862(f321(f931(x104561,x104562)),f862(f862(f244(x104561,x104562),x104563),x104564)),f862(f862(f32(x104565,f932(f931(x104561,x104562),a921)),f234(f932(x104565,a921))),x104566)))+~P1(f862(f862(f862(f862(f32(x104565,f932(x104561,f932(x104562,a921))),f234(f932(x104565,a921))),f862(f862(f10(f932(f931(x104561,x104562),a921),f932(x104561,f932(x104562,a921)),x104565),f862(f9(x104561,f932(f931(x104561,x104562),a921),f932(x104562,a921)),f862(f862(f10(f932(x104562,f932(f932(f931(x104561,x104562),a921),a921)),f932(f932(f931(x104561,x104562),a921),f932(x104562,a921)),x104561),f9(x104562,f932(f931(x104561,x104562),a921),a921)),f862(f862(f10(f932(x104562,f931(x104561,x104562)),f932(x104562,f932(f932(f931(x104561,x104562),a921),a921)),x104561),f862(f10(f931(x104561,x104562),f932(f932(f931(x104561,x104562),a921),a921),x104562),f321(f931(x104561,x104562)))),f244(x104561,x104562))))),x104566)),x104563),x104564))
% 25.54/25.41 [10457]P1(f862(f862(f321(f931(x104571,x104572)),f862(f862(f244(x104571,x104572),x104573),x104574)),f862(f862(f33(x104575,f932(f931(x104571,x104572),a921)),f234(f932(x104575,a921))),x104576)))+~P1(f862(f862(f862(f862(f33(x104575,f932(x104571,f932(x104572,a921))),f234(f932(x104575,a921))),f862(f862(f10(f932(f931(x104571,x104572),a921),f932(x104571,f932(x104572,a921)),x104575),f862(f9(x104571,f932(f931(x104571,x104572),a921),f932(x104572,a921)),f862(f862(f10(f932(x104572,f932(f932(f931(x104571,x104572),a921),a921)),f932(f932(f931(x104571,x104572),a921),f932(x104572,a921)),x104571),f9(x104572,f932(f931(x104571,x104572),a921),a921)),f862(f862(f10(f932(x104572,f931(x104571,x104572)),f932(x104572,f932(f932(f931(x104571,x104572),a921),a921)),x104571),f862(f10(f931(x104571,x104572),f932(f932(f931(x104571,x104572),a921),a921),x104572),f321(f931(x104571,x104572)))),f244(x104571,x104572))))),x104576)),x104573),x104574))
% 25.54/25.41 [7643]E(f862(x76431,f862(x76432,x76433)),f862(x76434,x76433))+~E(f862(f66(x76435,x76436,x76437,x76431),x76432),x76434)
% 25.54/25.41 [9792]E(x97921,x97922)+E(f68(x97923,x97924,f68(x97923,x97924,x97925,x97921,x97926),x97922,x97927),f68(x97923,x97924,f68(x97923,x97924,x97925,x97922,x97927),x97921,x97926))
% 25.54/25.41 [9883]~P20(x98833,x98834,x98831,x98835,x98836,x98837)+E(f862(f862(x98831,x98832),x98832),x98832)
% 25.54/25.41 [6201]~E(f862(f862(f147(x62011,x62015),x62016),x62012),f862(f862(f147(x62013,x62015),x62017),x62014))+E(f862(f182(f925(x62011)),x62012),f862(f182(f925(x62013)),x62014))
% 25.54/25.41 [8679]E(f862(x86791,f862(x86792,x86793)),f862(x86794,x86793))+~E(f862(f66(x86795,x86796,x86797,x86791),x86792),f862(f66(x86796,x86796,x86797,f25(x86796)),x86794))
% 25.54/25.41 [9038]~P32(x90384,x90385,x90381,f862(f862(f144(x90384),x90382),x90386),f862(f862(f144(x90385),x90383),x90387))+P1(f862(f862(x90381,x90382),x90383))
% 25.54/25.41 [9416]P32(x94161,x94162,x94163,x94164,x94165)+~P32(x94161,x94162,x94163,f862(f862(f144(x94161),x94166),x94164),f862(f862(f144(x94162),x94167),x94165))
% 25.54/25.41 [10045]P1(f862(f862(x100451,x100452),f552(x100453,x100452,x100454,x100451)))+~P1(f862(f862(f245(x100455,x100456,x100457,x100451,x100454),x100452),x100453))
% 25.54/25.41 [10069]P1(f862(f862(x100691,f552(x100692,x100693,x100691,x100694)),x100692))+~P1(f862(f862(f245(x100695,x100696,x100697,x100694,x100691),x100693),x100692))
% 25.54/25.41 [9155]~P18(x91556,x91551,x91553,x91557)+E(f862(f66(x91551,x91551,x91552,f862(x91553,x91554)),f862(f66(x91551,x91551,x91552,f862(x91553,x91554)),x91555)),f862(f66(x91551,x91551,x91552,f862(x91553,x91554)),x91555))
% 25.54/25.41 [9525]~P32(x95253,x95252,x95254,f862(f862(f147(x95251,x95253),x95255),x95256),x95257)+P32(x95251,x95252,f862(f862(f10(x95253,f932(x95252,a921),x95251),x95254),x95255),x95256,x95257)
% 25.54/25.41 [9549]P32(x95491,x95492,x95493,f862(f862(f147(x95494,x95491),x95495),x95496),x95497)+~P32(x95494,x95492,f862(f862(f10(x95491,f932(x95492,a921),x95494),x95493),x95495),x95496,x95497)
% 25.54/25.41 [9154]~P1(f862(f862(f321(x91541),x91542),f862(f862(x91545,x91546),x91547)))+P1(f862(f862(f321(x91541),x91542),f862(f862(f249(x91543,x91544,f932(x91541,a921)),x91545),f862(f862(f244(x91543,x91544),x91546),x91547))))
% 25.54/25.41 [9441]P1(f862(f862(f862(x94411,x94412),x94413),x94414))+~P1(f862(f862(f862(f249(x94415,x94416,f932(x94417,a921)),x94411),f862(f862(f244(x94415,x94416),x94412),x94413)),x94414))
% 25.54/25.41 [9590]P1(f862(f862(f321(x95901),f862(f862(x95902,x95903),x95904)),f862(f302(f931(x95905,x95906),x95901,f862(f249(x95905,x95906,x95901),x95902)),x95907)))+~P1(f862(f862(f321(f931(x95905,x95906)),f862(f862(f244(x95905,x95906),x95903),x95904)),x95907))
% 25.54/25.41 [9931]P1(f862(f862(f321(f931(f925(x99311),f925(x99311))),f862(f862(f244(f925(x99311),f925(x99311)),f862(f862(f127(x99311),x99312),f862(f862(f144(x99311),x99313),x99314))),f862(f862(f127(x99311),x99312),f862(f862(f144(x99311),x99315),x99316)))),f140(x99311,x99317)))+~P1(f862(f862(f321(f931(x99311,x99311)),f862(f862(f244(x99311,x99311),x99313),x99315)),x99317))
% 25.54/25.41 [9996]~P32(x99961,x99963,x99964,x99966,f862(f862(f147(x99962,x99963),x99965),x99967))+P32(x99961,x99962,f862(f862(f9(x99961,f932(x99962,x99963),f932(x99962,a921)),f862(f862(f10(f932(x99963,a921),f932(f932(x99962,x99963),f932(x99962,a921)),x99961),f10(x99963,a921,x99962)),x99964)),x99965),x99966,x99967)
% 25.54/25.41 [10073]P32(x100731,x100732,x100733,x100734,f862(f862(f147(x100735,x100732),x100736),x100737))+~P32(x100731,x100735,f862(f862(f9(x100731,f932(x100735,x100732),f932(x100735,a921)),f862(f862(f10(f932(x100732,a921),f932(f932(x100735,x100732),f932(x100735,a921)),x100731),f10(x100732,a921,x100735)),x100733)),x100736),x100734,x100737)
% 25.54/25.41 [10375]P1(f862(f862(f321(x103751),f492(x103752,x103753,x103754,x103755,x103756,x103757,x103751)),x103755))+P1(f862(f862(f862(f862(f32(x103751,f932(x103757,f932(x103756,a921))),x103755),x103754),x103753),x103752))
% 25.54/25.41 [10376]P1(f862(f862(f321(x103761),f790(x103762,x103763,x103764,x103765,x103766,x103767,x103761)),x103767))+P1(f862(f862(f862(f862(f32(x103761,f932(x103763,f932(x103762,a921))),x103767),x103766),x103765),x103764))
% 25.54/25.41 [10377]P1(f862(f862(f321(x103771),f494(x103772,x103773,x103774,x103775,x103776,x103777,x103771)),x103775))+~P1(f862(f862(f862(f862(f33(x103771,f932(x103777,f932(x103776,a921))),x103775),x103774),x103773),x103772))
% 25.54/25.41 [10378]P1(f862(f862(f321(x103781),f791(x103782,x103783,x103784,x103785,x103786,x103787,x103781)),x103785))+~P1(f862(f862(f862(f862(f33(x103781,f932(x103787,f932(x103786,a921))),x103785),x103784),x103783),x103782))
% 25.54/25.41 [10411]P1(f862(f862(f862(x104111,f494(x104112,x104113,x104111,x104114,x104115,x104116,x104117)),x104113),x104112))+~P1(f862(f862(f862(f862(f33(x104117,f932(x104116,f932(x104115,a921))),x104114),x104111),x104113),x104112))
% 25.54/25.41 [10412]P1(f862(f862(f862(x104121,f791(x104122,x104123,x104121,x104124,x104125,x104126,x104127)),x104123),x104122))+~P1(f862(f862(f862(f862(f33(x104127,f932(x104126,f932(x104125,a921))),x104124),x104121),x104123),x104122))
% 25.54/25.41 [10427]~P1(f862(f862(f862(x104275,f492(x104277,x104276,x104275,x104274,x104273,x104272,x104271)),x104276),x104277))+P1(f862(f862(f862(f862(f32(x104271,f932(x104272,f932(x104273,a921))),x104274),x104275),x104276),x104277))
% 25.54/25.41 [10428]~P1(f862(f862(f862(x104285,f790(x104283,x104282,x104287,x104286,x104285,x104284,x104281)),x104286),x104287))+P1(f862(f862(f862(f862(f32(x104281,f932(x104282,f932(x104283,a921))),x104284),x104285),x104286),x104287))
% 25.54/25.41 [10445]~P1(f862(f862(f321(f931(x104451,x104453)),f862(f862(f244(x104451,x104453),x104456),x104457)),f862(f862(f280(x104451,x104452,x104453),x104454),x104455)))+P1(f862(f862(f245(x104451,x104452,x104453,f862(f862(f9(x104451,f932(f931(x104451,x104452),a921),f932(x104452,a921)),f862(f862(f10(f932(x104452,f932(f932(f931(x104451,x104452),a921),a921)),f932(f932(f931(x104451,x104452),a921),f932(x104452,a921)),x104451),f9(x104452,f932(f931(x104451,x104452),a921),a921)),f862(f862(f10(f932(x104452,f931(x104451,x104452)),f932(x104452,f932(f932(f931(x104451,x104452),a921),a921)),x104451),f862(f10(f931(x104451,x104452),f932(f932(f931(x104451,x104452),a921),a921),x104452),f321(f931(x104451,x104452)))),f244(x104451,x104452)))),x104454),f862(f862(f9(x104452,f932(f931(x104452,x104453),a921),f932(x104453,a921)),f862(f862(f10(f932(x104453,f932(f932(f931(x104452,x104453),a921),a921)),f932(f932(f931(x104452,x104453),a921),f932(x104453,a921)),x104452),f9(x104453,f932(f931(x104452,x104453),a921),a921)),f862(f862(f10(f932(x104453,f931(x104452,x104453)),f932(x104453,f932(f932(f931(x104452,x104453),a921),a921)),x104452),f862(f10(f931(x104452,x104453),f932(f932(f931(x104452,x104453),a921),a921),x104453),f321(f931(x104452,x104453)))),f244(x104452,x104453)))),x104455)),x104456),x104457))
% 25.54/25.41 [10455]P1(f862(f862(f321(f931(x104551,x104552)),f862(f862(f244(x104551,x104552),x104553),x104554)),f862(f862(f280(x104551,x104555,x104552),x104556),x104557)))+~P1(f862(f862(f245(x104551,x104555,x104552,f862(f862(f9(x104551,f932(f931(x104551,x104555),a921),f932(x104555,a921)),f862(f862(f10(f932(x104555,f932(f932(f931(x104551,x104555),a921),a921)),f932(f932(f931(x104551,x104555),a921),f932(x104555,a921)),x104551),f9(x104555,f932(f931(x104551,x104555),a921),a921)),f862(f862(f10(f932(x104555,f931(x104551,x104555)),f932(x104555,f932(f932(f931(x104551,x104555),a921),a921)),x104551),f862(f10(f931(x104551,x104555),f932(f932(f931(x104551,x104555),a921),a921),x104555),f321(f931(x104551,x104555)))),f244(x104551,x104555)))),x104556),f862(f862(f9(x104555,f932(f931(x104555,x104552),a921),f932(x104552,a921)),f862(f862(f10(f932(x104552,f932(f932(f931(x104555,x104552),a921),a921)),f932(f932(f931(x104555,x104552),a921),f932(x104552,a921)),x104555),f9(x104552,f932(f931(x104555,x104552),a921),a921)),f862(f862(f10(f932(x104552,f931(x104555,x104552)),f932(x104552,f932(f932(f931(x104555,x104552),a921),a921)),x104555),f862(f10(f931(x104555,x104552),f932(f932(f931(x104555,x104552),a921),a921),x104552),f321(f931(x104555,x104552)))),f244(x104555,x104552)))),x104557)),x104553),x104554))
% 25.54/25.41 [10387]~P146(x103872)+E(f862(f862(f8(x103871,x103872),f862(f862(f9(x103871,f932(x103873,a921),x103872),f862(f862(f10(f932(x103873,x103872),f932(f932(x103873,a921),x103872),x103871),f8(x103873,x103872)),f862(f862(f9(x103871,f932(x103873,x103872),f932(x103873,x103872)),f862(f862(f10(f932(x103872,x103872),f932(f932(x103873,x103872),f932(x103873,x103872)),x103871),f10(x103872,x103872,x103873)),f862(f862(f10(x103872,f932(x103872,x103872),x103871),f74(x103872)),x103874))),x103875))),x103876)),x103877),f862(f862(f74(x103872),f862(f862(f8(x103871,x103872),x103874),x103877)),f862(f862(f8(x103873,x103872),x103875),x103876)))
% 25.54/25.41 [9474]~P17(x94747,x94741,x94743,x94748)+E(f862(f66(x94741,x94741,x94742,f862(x94743,x94744)),f862(f66(x94741,x94741,x94742,f862(x94743,x94745)),x94746)),f862(f66(x94741,x94741,x94742,f862(x94743,x94745)),f862(f66(x94741,x94741,x94742,f862(x94743,x94744)),x94746)))
% 25.54/25.41 [10450]E(f862(f862(f244(x104501,x104502),f862(x104503,f583(x104504,x104505,x104503,x104506,x104507,x104508,x104502,x104501))),f862(x104505,f584(x104504,x104505,x104503,x104506,x104507,x104508,x104502,x104501))),x104508)+~P1(f862(f862(f321(f931(x104501,x104502)),x104508),f862(f302(f931(x104507,x104506),f931(x104501,x104502),f250(x104507,x104501,x104506,x104502,x104503,x104505)),x104504)))
% 25.54/25.41 [10468]~P1(f862(f862(f321(f931(x104688,x104687)),x104686),f862(f302(f931(x104681,x104682),f931(x104688,x104687),f250(x104681,x104688,x104682,x104687,x104685,x104684)),x104683)))+P1(f862(f862(f321(f931(x104681,x104682)),f862(f862(f244(x104681,x104682),f583(x104683,x104684,x104685,x104682,x104681,x104686,x104687,x104688)),f584(x104683,x104684,x104685,x104682,x104681,x104686,x104687,x104688))),x104683))
% 25.54/25.41 [9921]P1(f862(f862(f321(f931(f931(x99211,x99212),f931(x99211,x99212))),f862(f862(f244(f931(x99211,x99212),f931(x99211,x99212)),f862(f862(f244(x99211,x99212),x99213),x99214)),f862(f862(f244(x99211,x99212),x99215),x99216))),f311(x99211,x99212,x99217,x99218)))+~P1(f862(f862(f321(f931(x99211,x99211)),f862(f862(f244(x99211,x99211),x99213),x99215)),x99217))
% 25.54/25.41 [10439]E(f862(f135(x104391,x104392,f862(f9(x104392,x104391,x104391),x104393),f862(x104394,x104395)),x104396),f862(x104394,f862(f135(x104397,x104392,f862(f9(x104392,x104397,x104397),x104398),x104395),x104396)))+P1(f862(f862(f321(x104392),f739(x104395,x104398,x104394,x104393,x104397,x104391,x104396,x104392)),f862(f165(x104392),x104396)))
% 25.54/25.41 [10458]~E(f862(f66(x104581,x104581,x104587,f862(x104583,f739(x104585,x104588,x104584,x104583,x104587,x104581,x104586,x104582))),x104584),f862(f66(x104587,x104581,x104587,x104584),f862(x104588,f739(x104585,x104588,x104584,x104583,x104587,x104581,x104586,x104582))))+E(f862(f135(x104581,x104582,f862(f9(x104582,x104581,x104581),x104583),f862(x104584,x104585)),x104586),f862(x104584,f862(f135(x104587,x104582,f862(f9(x104582,x104587,x104587),x104588),x104585),x104586)))
% 25.54/25.41 [8683]E(f862(x86831,f862(x86832,x86833)),f862(x86834,f862(x86835,x86833)))+~E(f862(f66(x86836,x86837,x86838,x86831),x86832),f862(f66(x86839,x86837,x86838,x86834),x86835))
% 25.54/25.41 [8684]E(f862(x86841,f862(x86842,x86843)),f862(x86844,f862(x86845,x86843)))+~E(f862(f66(x86846,x86847,x86848,x86841),x86842),f862(f66(x86849,x86847,x86848,x86844),x86845))
% 25.54/25.41 [10296]P1(f862(f862(f321(f931(x102961,x102962)),f862(f862(f244(x102961,x102962),f862(x102963,x102964)),f862(x102965,x102966))),f862(f302(f931(x102967,x102968),f931(x102961,x102962),f250(x102967,x102961,x102968,x102962,x102963,x102965)),x102969)))+~P1(f862(f862(f321(f931(x102967,x102968)),f862(f862(f244(x102967,x102968),x102964),x102966)),x102969))
% 25.54/25.41 [8982]~E(f862(x89824,f862(x89825,x89826)),f862(x89829,f862(x898210,x898211)))+E(f862(f862(f66(x89821,x89822,x89823,x89824),x89825),x89826),f862(f862(f66(x89827,x89822,x89828,x89829),x898210),x898211))
% 25.54/25.41 [9559]~P17(x95598,x95599,x955910,x955911)+E(f862(f66(x95591,x95592,x95593,x95594),f862(f66(x95595,x95591,x95593,x95596),x95597)),f862(f66(x95595,x95592,x95593,f862(f66(x95591,x95592,x95595,x95594),x95596)),x95597))
% 25.54/25.41 [4753]~P109(x47531)+~P104(x47531)+E(f94(x47531),f225(x47531))
% 25.54/25.41 [4754]~P109(x47541)+~P103(x47541)+E(f103(x47541),f226(x47541))
% 25.54/25.41 [5003]~P112(x50031)+~P98(x50031)+E(f862(f69(x50031),f862(f96(x50031),a90)),f71(x50031))
% 25.54/25.41 [5298]E(x52981,f2(a1))+E(f75(a1,x52981),f862(f72(a1),f71(a1)))+P1(f862(f862(f228(a1),f2(a1)),x52981))
% 25.54/25.41 [5504]E(x55041,f2(a1))+E(f75(a1,x55041),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x55041))
% 25.54/25.41 [6831]~P38(x68311)+~P1(f862(f54(a1),x68311))+P1(f862(f54(a924),f862(f302(a1,a924,a97),x68311)))
% 25.54/25.41 [7194]E(f40(f71(a1),f862(f96(a1),x71941)),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x71941)))+~P1(f862(f862(f228(a1),f71(a1)),f862(f96(a1),x71941)))
% 25.54/25.41 [7541]~P38(x75411)+P1(f862(f54(a1),x75411))+~P1(f862(f54(a924),f862(f302(a1,a924,a97),x75411)))
% 25.54/25.41 [8387]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),f71(a1)),f862(f96(a1),x83871))),f43(f71(a1),f862(f96(a1),x83871)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x83871)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f71(a1)),f862(f96(a1),x83871))))
% 25.54/25.41 [10188]E(f862(f36(f862(f96(a1),x101881)),f40(f71(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),x101881)))),f40(f71(a1),f862(f96(a1),x101881)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x101881)))+P1(f862(f862(f228(a1),f71(a1)),f862(f96(a1),x101881)))
% 25.54/25.41 [10194]E(f862(f36(f862(f96(a1),x101941)),f43(f71(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),x101941)))),f43(f71(a1),f862(f96(a1),x101941)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x101941)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f71(a1)),f862(f96(a1),x101941))))
% 25.54/25.41 [9882]E(x98821,f181(f932(f931(a924,a924),a921)))+~P1(f862(f54(f931(a924,a924)),x98821))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f181(f932(f931(a924,a924),a921))),x98821)),a27))
% 25.54/25.41 [10046]E(x100461,f2(a924))+E(x100461,f862(a105,f2(a924)))+~P1(f862(f862(f228(a924),x100461),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [10325]E(x103251,f2(a92))+E(f862(f862(f73(a1),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a24,f862(f862(f29(a92),x103251),f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))),f71(a1)),f862(a24,x103251))+E(f38(a92,x103251,f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(a92))
% 25.54/25.41 [10174]E(x101741,f2(a92))+~E(f38(a92,x101741,f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(a92))+E(f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(a24,f862(f862(f29(a92),x101741),f862(f96(a92),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f862(a24,x101741))
% 25.54/25.41 [4836]~P55(x48361,x48362)+P41(x48361,x48362)+~P42(a921)
% 25.54/25.41 [4763]~P147(x47631)+P26(x47631,x47632)+~E(x47632,f2(x47631))
% 25.54/25.41 [4764]~P109(x47641)+P11(x47641,x47642)+~E(x47642,f106(x47641))
% 25.54/25.41 [4774]~P112(x47741)+~E(x47742,f2(x47741))+E(f75(x47741,x47742),f2(x47741))
% 25.54/25.41 [4775]~P88(x47751)+~E(x47752,f2(x47751))+E(f75(x47751,x47752),f2(x47751))
% 25.54/25.41 [4783]~P147(x47832)+~P26(x47832,x47831)+E(x47831,f2(x47832))
% 25.54/25.41 [4829]~P112(x48292)+~E(f75(x48292,x48291),f2(x48292))+E(x48291,f2(x48292))
% 25.54/25.41 [4843]~P2(x48432)+~P63(x48431)+P2(f932(x48431,x48432))
% 25.54/25.41 [4844]~P60(x48442)+~P60(x48441)+P60(f932(x48441,x48442))
% 25.54/25.41 [4845]~P60(x48452)+~P60(x48451)+P60(f930(x48451,x48452))
% 25.54/25.41 [4846]~P60(x48462)+~P60(x48461)+P60(f931(x48461,x48462))
% 25.54/25.41 [4847]~P4(x48472)+~P4(x48471)+P4(f187(x48471,x48472))
% 25.54/25.41 [4848]~P63(x48482)+~P63(x48481)+P63(f932(x48481,x48482))
% 25.54/25.41 [4849]~P63(x48492)+~P63(x48491)+P63(f930(x48491,x48492))
% 25.54/25.41 [4850]~P63(x48502)+~P63(x48501)+P63(f931(x48501,x48502))
% 25.54/25.41 [4851]~P106(x48512)+~P106(x48511)+P106(f931(x48511,x48512))
% 25.54/25.41 [4975]~P109(x49751)+~P11(x49751,x49752)+P11(x49751,f145(x49751,x49752))
% 25.54/25.41 [5225]~P4(x52252)+~P4(x52251)+P4(f38(a1,x52251,x52252))
% 25.54/25.41 [4784]~P76(x47841)+~E(x47842,f2(x47841))+E(f862(f72(x47841),x47842),x47842)
% 25.54/25.41 [4785]~P76(x47851)+~E(x47852,f2(x47851))+E(f862(f72(x47851),x47852),x47852)
% 25.54/25.41 [4800]~P97(x48001)+~E(x48002,f2(a1))+E(f862(f95(x48001),x48002),f2(x48001))
% 25.54/25.41 [4801]~P142(x48011)+~E(x48012,f2(a1))+E(f862(f95(x48011),x48012),f2(x48011))
% 25.54/25.41 [4802]~P97(x48021)+~E(x48022,f2(a1))+E(f862(f95(x48021),x48022),f2(x48021))
% 25.54/25.41 [4826]~P68(x48261)+~E(f2(x48261),x48262)+E(f862(f72(x48261),x48262),f2(x48261))
% 25.54/25.41 [4827]~P68(x48271)+~E(x48272,f2(x48271))+E(f862(f72(x48271),x48272),f2(x48271))
% 25.54/25.41 [4828]~P86(x48281)+~E(x48282,f2(x48281))+E(f862(f69(x48281),x48282),f2(x48281))
% 25.54/25.41 [4852]~P76(x48522)+E(x48521,f2(x48522))+~E(f862(f72(x48522),x48521),x48521)
% 25.54/25.41 [4853]~P76(x48532)+E(x48531,f2(x48532))+~E(f862(f72(x48532),x48531),x48531)
% 25.54/25.41 [4855]E(x48551,f862(a97,x48552))+~E(x48551,f2(a924))+~E(x48552,f862(f93(a1),x48551))
% 25.54/25.41 [4856]E(f862(a97,x48561),x48562)+~E(x48562,f2(a924))+~E(x48561,f862(f93(a1),x48562))
% 25.54/25.41 [4859]~P97(x48592)+E(x48591,f2(a1))+~E(f862(f95(x48592),x48591),f2(x48592))
% 25.54/25.41 [4860]~P97(x48602)+E(x48601,f2(a1))+~E(f862(f95(x48602),x48601),f2(x48602))
% 25.54/25.41 [4864]~P68(x48642)+E(x48641,f2(x48642))+~E(f862(f72(x48642),x48641),f2(x48642))
% 25.54/25.41 [4865]~P86(x48652)+E(x48651,f2(x48652))+~E(f862(f69(x48652),x48651),f2(x48652))
% 25.54/25.41 [4866]~P68(x48661)+E(f2(x48661),x48662)+~E(f862(f72(x48661),x48662),f2(x48661))
% 25.54/25.41 [5050]~P109(x50501)+~P11(x50501,x50502)+P11(x50501,f862(f164(x50501),x50502))
% 25.54/25.41 [5077]~P1(x50772)+~P1(x50771)+P1(f862(f862(a318,x50771),x50772))
% 25.54/25.41 [5115]~E(f71(a924),f2(a924))+E(f862(f28(x51151),x51152),f2(a924))+~P1(f862(f54(x51151),x51152))
% 25.54/25.41 [5151]~P116(x51511)+~P146(x51511)+E(f862(f862(f236(x51511),f2(x51511)),f862(a105,x51512)),f2(x51511))
% 25.54/25.41 [5192]~P109(x51921)+P11(x51921,f132(x51921,x51922))+~P1(f862(f54(x51921),x51922))
% 25.54/25.41 [5193]~P109(x51931)+P11(x51931,f731(x51932,x51931))+~P1(f862(f54(x51931),x51932))
% 25.54/25.41 [5217]~P109(x52171)+E(f862(f165(x52171),f132(x52171,x52172)),x52172)+~P1(f862(f54(x52171),x52172))
% 25.54/25.41 [5218]~P109(x52181)+E(f862(f165(x52181),f731(x52182,x52181)),x52182)+~P1(f862(f54(x52181),x52182))
% 25.54/25.41 [5247]P1(x52471)+P1(x52472)+~P1(f862(f862(a319,x52472),x52471))
% 25.54/25.41 [5260]E(x52601,f181(f932(x52602,a921)))+~E(f862(f28(x52602),x52601),f2(a924))+~P1(f862(f54(x52602),x52601))
% 25.54/25.41 [5265]P1(x52651)+~P1(x52652)+~P1(f862(f862(a322,x52652),x52651))
% 25.54/25.41 [5316]~P75(x53161)+E(f862(f69(x53161),x53162),x53162)+P1(f862(f862(f228(x53161),x53162),f2(x53161)))
% 25.54/25.41 [5376]~P63(x53762)+~P1(f862(f49(x53762),x53761))+P1(f862(x53761,f732(x53761,x53762)))
% 25.54/25.41 [5377]~P63(x53772)+~P1(f862(f49(x53772),x53771))+P1(f862(x53771,f740(x53771,x53772)))
% 25.54/25.41 [5420]E(x54201,f106(x54202))+P1(f862(f130(x54202),f107(x54202,x54201)))+~P1(f862(f130(x54202),x54201))
% 25.54/25.41 [5425]~P109(x54251)+~P1(f862(f54(x54251),x54252))+P1(f862(f130(x54251),f132(x54251,x54252)))
% 25.54/25.41 [5426]~P109(x54261)+~P1(f862(f54(x54261),x54262))+P1(f862(f130(x54261),f731(x54262,x54261)))
% 25.54/25.41 [5431]~P142(x54311)+E(f862(f93(x54311),f862(a97,x54312)),f862(f95(x54311),x54312))+P1(f862(f862(f228(a1),x54312),f2(a1)))
% 25.54/25.41 [5453]P5(x54532,x54531)+E(f862(x54531,f524(x54531)),f862(x54531,f527(x54531)))+P1(f862(f862(x54531,f524(x54531)),f527(x54531)))
% 25.54/25.41 [5466]E(f862(f93(a1),f428(x54661,x54662)),x54661)+P1(f862(x54662,f862(a97,x54661)))+~P1(f862(x54662,f2(a924)))
% 25.54/25.41 [5478]~P63(x54781)+~P1(f862(x54782,f746(x54782,x54781)))+P1(f862(f50(x54781),x54782))
% 25.54/25.41 [5479]~P63(x54791)+~P1(f862(x54792,f756(x54792,x54791)))+P1(f862(f50(x54791),x54792))
% 25.54/25.41 [5514]~P112(x55141)+~E(f75(x55141,x55142),f862(f72(x55141),f71(x55141)))+P1(f862(f862(f228(x55141),x55142),f2(x55141)))
% 25.54/25.41 [5590]~E(x55902,f2(a1))+E(f208(x55901,x55902),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x55902),f2(a1)))
% 25.54/25.41 [5591]~E(x55911,f2(a1))+E(f208(x55911,x55912),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x55912),f2(a1)))
% 25.54/25.41 [5644]E(f862(f93(a1),f428(x56441,x56442)),x56441)+P1(f862(x56442,f862(a97,x56441)))+P1(f862(f862(f228(a1),x56441),f2(a1)))
% 25.54/25.41 [5711]~P112(x57111)+E(f75(x57111,x57112),f862(f72(x57111),f71(x57111)))+~P1(f862(f862(f228(x57111),x57112),f2(x57111)))
% 25.54/25.41 [5712]~P112(x57121)+E(f75(x57121,x57122),f862(f72(x57121),f71(x57121)))+~P1(f862(f862(f228(x57121),x57122),f2(x57121)))
% 25.54/25.41 [5713]~P86(x57131)+E(f862(f69(x57131),x57132),f862(f72(x57131),x57132))+~P1(f862(f862(f227(x57131),x57132),f2(x57131)))
% 25.54/25.41 [5714]~P86(x57141)+E(f862(f69(x57141),x57142),f862(f72(x57141),x57142))+~P1(f862(f862(f228(x57141),x57142),f2(x57141)))
% 25.54/25.41 [5715]~P75(x57151)+E(f862(f69(x57151),x57152),f862(f72(x57151),x57152))+~P1(f862(f862(f228(x57151),x57152),f2(x57151)))
% 25.54/25.41 [5817]~P1(f862(x58171,f428(x58172,x58171)))+P1(f862(x58171,f862(a97,x58172)))+~P1(f862(x58171,f2(a924)))
% 25.54/25.41 [5824]E(x58241,f2(a924))+E(f862(a105,f329(x58242,x58241)),x58241)+~P1(f862(f862(f228(a924),x58241),f862(a105,x58242)))
% 25.54/25.41 [5828]P5(x58281,x58282)+~E(f862(x58282,f524(x58282)),f862(x58282,f527(x58282)))+~P1(f862(f862(x58282,f524(x58282)),f527(x58282)))
% 25.54/25.41 [5846]~P109(x58461)+P11(x58461,x58462)+P1(f862(f862(f227(a924),f715(x58462,x58461)),f716(x58462,x58461)))
% 25.54/25.41 [5847]~P109(x58471)+P11(x58471,x58472)+P1(f862(f862(f227(a924),f722(x58472,x58471)),f727(x58472,x58471)))
% 25.54/25.41 [5933]~P86(x59331)+~E(x59332,f2(x59331))+P1(f862(f862(f227(x59331),f862(f69(x59331),x59332)),f2(x59331)))
% 25.54/25.41 [6030]~P1(f862(x60301,f428(x60302,x60301)))+P1(f862(x60301,f862(a97,x60302)))+P1(f862(f862(f228(a1),x60302),f2(a1)))
% 25.54/25.41 [6055]~P1(f862(x60551,f862(a97,x60552)))+P1(f862(x60551,f2(a924)))+~P1(f862(f862(f228(a1),x60552),f2(a1)))
% 25.54/25.41 [6399]~P112(x63991)+~P1(f862(f862(f228(x63991),x63992),f2(x63991)))+P1(f862(f862(f228(x63991),f75(x63991,x63992)),f2(x63991)))
% 25.54/25.41 [6514]~P112(x65141)+P1(f862(f862(f227(x65141),f862(f95(x65141),x65142)),f2(x65141)))+~P1(f862(f862(f227(a1),x65142),f2(a1)))
% 25.54/25.41 [6515]~P112(x65151)+P1(f862(f862(f228(x65151),f862(f95(x65151),x65152)),f2(x65151)))+~P1(f862(f862(f228(a1),x65152),f2(a1)))
% 25.54/25.41 [6524]~P86(x65242)+E(x65241,f2(x65242))+~P1(f862(f862(f227(x65242),f862(f69(x65242),x65241)),f2(x65242)))
% 25.54/25.41 [6603]~P142(x66031)+~P1(f862(f862(f321(x66031),x66032),f102(x66031)))+P1(f862(f862(f321(x66031),f862(f72(x66031),x66032)),f102(x66031)))
% 25.54/25.41 [6635]~P112(x66351)+~P1(f862(f862(f228(x66351),f75(x66351,x66352)),f2(x66351)))+P1(f862(f862(f228(x66351),x66352),f2(x66351)))
% 25.54/25.41 [6807]~P112(x68072)+~P1(f862(f862(f227(x68072),f862(f95(x68072),x68071)),f2(x68072)))+P1(f862(f862(f227(a1),x68071),f2(a1)))
% 25.54/25.41 [6808]~P112(x68082)+~P1(f862(f862(f228(x68082),f862(f95(x68082),x68081)),f2(x68082)))+P1(f862(f862(f228(a1),x68081),f2(a1)))
% 25.54/25.41 [7312]~P76(x73121)+~P1(f862(f862(f227(x73121),x73122),f2(x73121)))+P1(f862(f862(f227(x73121),f862(f862(f73(x73121),x73122),x73122)),f2(x73121)))
% 25.54/25.41 [7313]~P112(x73131)+~P1(f862(f862(f228(x73131),x73132),f2(x73131)))+P1(f862(f862(f228(x73131),f862(f862(f73(x73131),x73132),x73132)),f2(x73131)))
% 25.54/25.41 [7314]~P76(x73141)+~P1(f862(f862(f228(x73141),x73142),f2(x73141)))+P1(f862(f862(f228(x73141),f862(f862(f73(x73141),x73142),x73142)),f2(x73141)))
% 25.54/25.41 [7890]~P76(x78901)+~P1(f862(f862(f227(x78901),f862(f862(f73(x78901),x78902),x78902)),f2(x78901)))+P1(f862(f862(f227(x78901),x78902),f2(x78901)))
% 25.54/25.41 [7891]~P112(x78911)+~P1(f862(f862(f228(x78911),f862(f862(f73(x78911),x78912),x78912)),f2(x78911)))+P1(f862(f862(f228(x78911),x78912),f2(x78911)))
% 25.54/25.41 [7892]~P76(x78921)+~P1(f862(f862(f228(x78921),f862(f862(f73(x78921),x78922),x78922)),f2(x78921)))+P1(f862(f862(f228(x78921),x78922),f2(x78921)))
% 25.54/25.41 [4900]~E(x49002,f71(a924))+~E(x49001,f71(a924))+E(f862(f862(f74(a924),x49001),x49002),f71(a924))
% 25.54/25.41 [4901]~E(x49012,f71(a924))+~E(x49011,f71(a924))+E(f862(f862(f74(a924),x49011),x49012),f71(a924))
% 25.54/25.41 [4902]~E(x49022,f71(a1))+~E(x49021,f71(a1))+E(f862(f862(f74(a1),x49021),x49022),f71(a1))
% 25.54/25.41 [4903]~E(x49032,f2(a924))+~E(x49031,f2(a924))+E(f862(f862(f73(a924),x49031),x49032),f2(a924))
% 25.54/25.41 [4959]~P121(x49592)+E(x49591,f2(x49592))+E(f862(f862(f281(x49592),x49591),x49591),f71(x49592))
% 25.54/25.41 [4960]~P61(x49602)+E(x49601,f2(x49602))+E(f862(f862(f29(x49602),x49601),x49601),f71(x49602))
% 25.54/25.41 [4961]~P122(x49612)+E(x49611,f2(x49612))+E(f862(f862(f281(x49612),x49611),x49611),f71(x49612))
% 25.54/25.41 [4978]~P76(x49781)+~E(x49782,f2(x49781))+E(f862(f862(f73(x49781),x49782),x49782),f2(x49781))
% 25.54/25.41 [4981]~P141(x49811)+~E(x49812,f71(x49811))+E(f862(f862(f74(x49811),x49812),x49812),f71(x49811))
% 25.54/25.41 [4982]~P76(x49821)+~E(x49822,f2(x49821))+E(f862(f862(f73(x49821),x49822),x49822),f2(x49821))
% 25.54/25.41 [4983]~P122(x49831)+~E(x49832,f2(x49831))+E(f862(f862(f281(x49831),x49832),x49832),f2(x49831))
% 25.54/25.41 [5028]~E(x50282,f2(a924))+~E(x50281,f2(a924))+E(f862(f72(a1),f862(f93(a1),x50281)),f862(f93(a1),x50282))
% 25.54/25.41 [5047]E(x50471,f71(a924))+E(x50472,f2(a924))+~E(f862(f862(f74(a924),x50472),x50471),x50472)
% 25.54/25.41 [5059]E(x50591,f2(a924))+E(x50592,f2(a924))+~E(f862(f862(f74(a924),x50592),x50591),f2(a924))
% 25.54/25.41 [5084]~E(x50842,f2(a924))+~E(x50841,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50841),x50842),f862(a105,f2(a924)))
% 25.54/25.41 [5085]~E(x50851,f2(a924))+~E(x50852,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50851),x50852),f862(a105,f2(a924)))
% 25.54/25.41 [5086]~E(x50862,f2(a924))+~E(x50861,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50861),x50862),f862(a105,f2(a924)))
% 25.54/25.41 [5087]~E(x50871,f2(a924))+~E(x50872,f862(a105,f2(a924)))+E(f862(f862(f73(a924),x50871),x50872),f862(a105,f2(a924)))
% 25.54/25.41 [5094]E(x50941,f71(a1))+E(x50942,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50941),x50942),f71(a1))
% 25.54/25.41 [5095]E(x50951,f71(a1))+E(x50952,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50952),x50951),f71(a1))
% 25.54/25.41 [5096]E(x50961,f71(a1))+E(x50961,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50962),x50961),f71(a1))
% 25.54/25.41 [5097]E(x50971,f71(a1))+E(x50971,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50971),x50972),f71(a1))
% 25.54/25.41 [5098]E(x50981,f71(a1))+E(x50981,f862(f96(a1),a90))+~E(f862(f862(f74(a1),x50981),x50982),f71(a1))
% 25.54/25.41 [5122]~P76(x51222)+E(x51221,f2(x51222))+~E(f862(f862(f73(x51222),x51221),x51221),f2(x51222))
% 25.54/25.41 [5123]~P76(x51232)+E(x51231,f2(x51232))+~E(f862(f862(f73(x51232),x51231),x51231),f2(x51232))
% 25.54/25.41 [5129]~E(x51291,f862(f96(a1),a90))+~E(x51292,f862(f96(a1),a90))+E(f862(f862(f74(a1),x51291),x51292),f71(a1))
% 25.54/25.41 [5139]E(x51391,f2(a924))+E(x51392,f2(a924))+~E(f862(f862(f73(a924),x51392),x51391),f862(a105,f2(a924)))
% 25.54/25.41 [5140]E(x51401,f2(a924))+E(x51402,f2(a924))+~E(f862(f862(f73(a924),x51402),x51401),f862(a105,f2(a924)))
% 25.54/25.41 [5150]~P64(x51501)+~P98(x51501)+E(f862(f862(f281(x51501),x51502),f862(f96(x51501),a76)),f2(x51501))
% 25.54/25.41 [5157]~P141(x51571)+~E(x51572,f862(f72(x51571),f71(x51571)))+E(f862(f862(f74(x51571),x51572),x51572),f71(x51571))
% 25.54/25.41 [5162]~P4(x51622)+~P4(x51621)+P4(f862(f862(f74(a1),x51621),x51622))
% 25.54/25.41 [5163]~P4(x51632)+~P4(x51631)+P4(f862(f862(f73(a1),x51631),x51632))
% 25.54/25.41 [5164]~P4(x51642)+~P4(x51641)+P4(f862(f862(f29(a1),x51641),x51642))
% 25.54/25.41 [5165]~E(x51652,f2(a1))+E(x51651,f2(a1))+E(f39(x51651,x51652),f862(f862(f244(a1,a1),f2(a1)),x51651))
% 25.54/25.41 [5166]~E(x51662,f2(a1))+E(x51661,f2(a1))+E(f39(x51661,x51662),f862(f862(f244(a1,a1),f2(a1)),x51661))
% 25.54/25.41 [5190]~E(x51902,f862(a105,f2(a924)))+~E(x51901,f862(a105,f2(a924)))+E(f862(f862(f74(a924),x51901),x51902),f862(a105,f2(a924)))
% 25.54/25.41 [5206]E(x52061,f2(a924))+E(x52061,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52062),x52061),f862(a105,f2(a924)))
% 25.54/25.41 [5207]E(x52071,f2(a924))+E(x52071,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52071),x52072),f862(a105,f2(a924)))
% 25.54/25.41 [5208]E(x52081,f2(a924))+E(x52082,f862(a105,f2(a924)))+~E(f862(f862(f236(a924),x52082),x52081),f862(a105,f2(a924)))
% 25.54/25.41 [5209]E(x52091,f2(a924))+E(x52091,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52092),x52091),f862(a105,f2(a924)))
% 25.54/25.41 [5210]E(x52101,f2(a924))+E(x52101,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52101),x52102),f862(a105,f2(a924)))
% 25.54/25.41 [5219]~P64(x52191)+~P98(x52191)+E(f862(f862(f281(x52191),x52192),f862(f96(x52191),a90)),f862(f72(x52191),x52192))
% 25.54/25.41 [5239]E(x52391,f862(a97,x52392))+~E(x52391,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52392))
% 25.54/25.41 [5240]E(f862(a97,x52401),x52402)+~E(x52402,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52401))
% 25.54/25.41 [5255]E(x52551,f862(a105,f2(a924)))+E(x52552,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52551),x52552),f862(a105,f2(a924)))
% 25.54/25.41 [5256]E(x52561,f862(a105,f2(a924)))+E(x52562,f862(a105,f2(a924)))+~E(f862(f862(f73(a924),x52561),x52562),f862(a105,f2(a924)))
% 25.54/25.41 [5267]~E(x52671,f862(a97,x52672))+E(x52671,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52672))
% 25.54/25.41 [5268]~E(f862(a97,x52682),x52681)+E(x52681,f2(a924))+P1(f862(f862(f227(a1),f2(a1)),x52682))
% 25.54/25.41 [5291]~P93(x52911)+E(f862(f56(x52911,f94(x52911)),x52912),f12(x52911,x52912))+~P1(f862(f54(x52911),x52912))
% 25.54/25.41 [5292]~P93(x52921)+E(f862(f56(x52921,f103(x52921)),x52922),f15(x52921,x52922))+~P1(f862(f54(x52921),x52922))
% 25.54/25.41 [5293]~P109(x52931)+E(f862(f56(x52931,f225(x52931)),x52932),f16(x52931,x52932))+~P1(f862(f54(x52931),x52932))
% 25.54/25.41 [5294]~P109(x52941)+E(f862(f56(x52941,f226(x52941)),x52942),f17(x52941,x52942))+~P1(f862(f54(x52941),x52942))
% 25.54/25.41 [5371]E(x53711,x53712)+~E(f862(f862(f3(a924),x53712),x53711),f2(a924))+~E(f862(f862(f3(a924),x53711),x53712),f2(a924))
% 25.54/25.41 [5390]P4(x53901)+~P38(x53902)+~P1(f862(f862(f321(a1),x53901),x53902))
% 25.54/25.41 [5421]~P112(x54211)+~E(f75(x54211,x54212),f71(x54211))+P1(f862(f862(f228(x54211),f2(x54211)),x54212))
% 25.54/25.41 [5432]~P98(x54321)+E(f862(f93(x54321),f862(f96(a924),x54322)),f862(f96(x54321),x54322))+P1(f862(a186,f862(f96(a1),x54322)))
% 25.54/25.41 [5438]~P41(x54381,x54382)+P42(a921)+P1(f862(f54(f931(x54381,x54381)),x54382))
% 25.54/25.41 [5506]~P109(x55061)+E(f862(f56(x55061,f225(x55061)),x55062),f13(x55061,f225(x55061),x55062))+~P1(f862(f54(x55061),x55062))
% 25.54/25.41 [5507]~P109(x55071)+E(f862(f56(x55071,f226(x55071)),x55072),f14(x55071,f226(x55071),x55072))+~P1(f862(f54(x55071),x55072))
% 25.54/25.41 [5520]E(x55201,x55202)+P1(f862(f862(f228(a924),x55202),x55201))+P1(f862(f862(f228(a924),x55201),x55202))
% 25.54/25.41 [5521]E(x55211,x55212)+P1(f862(f862(f228(a924),x55212),x55211))+P1(f862(f862(f228(a924),x55211),x55212))
% 25.54/25.41 [5522]E(x55221,x55222)+P1(f862(f862(f228(a1),x55222),x55221))+P1(f862(f862(f228(a1),x55221),x55222))
% 25.54/25.41 [5577]~P98(x55771)+E(f862(f93(x55771),f862(f96(a924),x55772)),f2(x55771))+~P1(f862(a186,f862(f96(a1),x55772)))
% 25.54/25.41 [5580]~E(x55802,f862(a97,x55801))+E(x55801,f862(f93(a1),x55802))+~P1(f862(f862(f227(a1),f2(a1)),x55801))
% 25.54/25.41 [5581]~E(f862(a97,x55811),x55812)+E(x55811,f862(f93(a1),x55812))+~P1(f862(f862(f227(a1),f2(a1)),x55811))
% 25.54/25.41 [5582]~E(x55821,f862(a97,x55822))+E(f862(f93(a1),x55821),x55822)+~P1(f862(f862(f227(a1),f2(a1)),x55822))
% 25.54/25.41 [5592]E(x55921,f862(a97,x55922))+~E(x55922,f862(f93(a1),x55921))+~P1(f862(f862(f227(a1),f2(a1)),x55922))
% 25.54/25.41 [5593]E(f862(a97,x55931),x55932)+~E(x55931,f862(f93(a1),x55932))+~P1(f862(f862(f227(a1),f2(a1)),x55931))
% 25.54/25.41 [5624]~P119(x56242)+E(x56241,f2(x56242))+~P1(f862(f862(f278(x56242),f2(x56242)),x56241))
% 25.54/25.41 [5635]~P86(x56352)+E(x56351,f2(x56352))+P1(f862(f862(f228(x56352),f2(x56352)),f862(f69(x56352),x56351)))
% 25.54/25.41 [5698]~P112(x56981)+E(f75(x56981,x56982),f71(x56981))+~P1(f862(f862(f228(x56981),f2(x56981)),x56982))
% 25.54/25.41 [5699]~P112(x56991)+E(f75(x56991,x56992),f71(x56991))+~P1(f862(f862(f228(x56991),f2(x56991)),x56992))
% 25.54/25.41 [5705]~P98(x57051)+E(f862(f93(x57051),f862(f96(a924),x57052)),f2(x57051))+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x57052)))
% 25.54/25.41 [5716]~P86(x57161)+E(f862(f69(x57161),x57162),x57162)+~P1(f862(f862(f227(x57161),f2(x57161)),x57162))
% 25.54/25.41 [5717]~P86(x57171)+E(f862(f69(x57171),x57172),x57172)+~P1(f862(f862(f228(x57171),f2(x57171)),x57172))
% 25.54/25.41 [5726]E(x57261,f2(a924))+~E(f132(a924,f862(f295(a924,x57262),x57261)),f106(a924))+P1(f862(f862(f227(a924),x57261),x57262))
% 25.54/25.41 [5737]~P72(x57371)+E(f862(f862(f8(x57371,x57371),f7(x57371)),f862(f165(x57371),x57372)),f862(f158(x57371),x57372))+~P1(f862(f130(x57371),x57372))
% 25.54/25.41 [5740]~P142(x57401)+E(f862(f93(x57401),f862(a97,x57402)),f862(f95(x57401),x57402))+~P1(f862(f862(f227(a1),f2(a1)),x57402))
% 25.54/25.41 [5742]~E(x57421,x57422)+P1(f862(f862(f228(a924),x57421),f862(a105,x57422)))+P1(f862(f862(f228(a924),x57421),x57422))
% 25.54/25.41 [5766]E(x57661,x57662)+P1(f862(f862(f228(a924),x57661),x57662))+~P1(f862(f862(f227(a924),x57661),x57662))
% 25.54/25.41 [5767]E(x57671,x57672)+P1(f862(f862(f228(a924),x57671),x57672))+~P1(f862(f862(f227(a924),x57671),x57672))
% 25.54/25.41 [5768]E(x57681,x57682)+P1(f862(f862(f228(a924),x57681),x57682))+~P1(f862(f862(f227(a924),x57681),x57682))
% 25.54/25.41 [5769]E(x57691,x57692)+P1(f862(f862(f228(a1),x57691),x57692))+~P1(f862(f862(f227(a1),x57691),x57692))
% 25.54/25.41 [5773]E(x57731,f71(a1))+~E(f862(f862(f74(a1),x57732),x57731),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x57732))
% 25.54/25.41 [5774]E(x57741,f71(a1))+~E(f862(f862(f74(a1),x57741),x57742),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x57741))
% 25.54/25.41 [5813]~P38(x58132)+P1(f862(f862(f227(a1),f2(a1)),x58131))+~P1(f862(f862(f321(a1),x58131),x58132))
% 25.54/25.41 [5814]~P38(x58142)+P1(f862(f862(f227(a1),f2(a1)),x58141))+~P1(f862(f862(f321(a1),x58141),x58142))
% 25.54/25.41 [5832]~P55(x58321,x58322)+P35(x58321,x58322)+~P1(f862(f54(f931(x58321,x58321)),x58322))
% 25.54/25.41 [5833]~P55(x58331,x58332)+P35(x58331,x58332)+~P1(f862(f54(f931(x58331,x58331)),x58332))
% 25.54/25.41 [5834]~P35(x58341,x58342)+P55(x58341,x58342)+~P1(f862(f54(f931(x58341,x58341)),x58342))
% 25.54/25.41 [5835]~P55(x58351,x58352)+P41(x58351,x58352)+~P1(f862(f54(f931(x58351,x58351)),x58352))
% 25.54/25.41 [5877]E(x58771,f181(f932(x58772,a921)))+~P1(f862(f54(x58772),x58771))+P1(f862(f862(f228(a924),f2(a924)),f862(f28(x58772),x58771)))
% 25.54/25.41 [5904]~P1(f862(x59041,x59042))+P1(f862(x59041,f2(a924)))+P1(f862(f862(f228(a924),f360(x59042,x59041)),x59042))
% 25.54/25.41 [5927]E(x59271,f2(a924))+~E(f862(f158(a924),x59272),f2(a924))+~P1(f862(f862(f321(a924),x59271),f862(f165(a924),x59272)))
% 25.54/25.41 [5963]~E(x59631,x59632)+P1(f862(f862(f228(a924),x59631),f862(a105,x59632)))+~P1(f862(f862(f227(a924),x59632),x59631))
% 25.54/25.41 [5995]E(x59951,x59952)+~P1(f862(f862(f227(a924),x59952),x59951))+~P1(f862(f862(f227(a924),x59951),x59952))
% 25.54/25.41 [5996]E(x59961,x59962)+~P1(f862(f862(f227(a1),x59962),x59961))+~P1(f862(f862(f227(a1),x59961),x59962))
% 25.54/25.41 [5997]E(x59971,x59972)+~P1(f862(f862(f278(a924),x59972),x59971))+~P1(f862(f862(f278(a924),x59971),x59972))
% 25.54/25.41 [5998]E(x59981,x59982)+~P1(f862(f862(f278(a924),x59982),x59981))+~P1(f862(f862(f278(a924),x59981),x59982))
% 25.54/25.41 [5999]E(x59991,x59992)+~P1(f862(f862(f278(a924),x59992),x59991))+~P1(f862(f862(f278(a924),x59991),x59992))
% 25.54/25.41 [6000]E(x60001,x60002)+~P1(f862(f862(f278(a924),x60002),x60001))+~P1(f862(f862(f278(a924),x60001),x60002))
% 25.54/25.41 [6001]E(x60011,x60012)+~P1(f862(f862(f278(a924),x60012),x60011))+~P1(f862(f862(f278(a924),x60011),x60012))
% 25.54/25.41 [6002]E(x60021,x60022)+~P1(f862(f862(f278(a924),x60022),x60021))+~P1(f862(f862(f278(a924),x60021),x60022))
% 25.54/25.41 [6003]E(x60031,x60032)+~P1(f862(f862(f278(a924),x60032),x60031))+~P1(f862(f862(f278(a924),x60031),x60032))
% 25.54/25.41 [6004]E(x60041,x60042)+~P1(f862(f862(f278(a924),x60042),x60041))+~P1(f862(f862(f278(a924),x60041),x60042))
% 25.54/25.41 [6005]E(x60051,x60052)+~P1(f862(f862(f278(a924),x60052),x60051))+~P1(f862(f862(f278(a924),x60051),x60052))
% 25.54/25.41 [6007]E(f862(f28(x60071),x60072),f2(a924))+~P1(f862(f54(x60071),x60072))+P1(f862(f862(f321(x60071),f362(x60072,x60071)),x60072))
% 25.54/25.41 [6016]E(f43(x60161,x60162),f39(x60161,x60162))+P1(f862(f862(f227(a1),f2(a1)),x60161))+~P1(f862(f862(f228(a1),f2(a1)),x60162))
% 25.54/25.41 [6042]~P1(f862(x60421,f426(x60421)))+P1(f862(x60421,f862(a97,x60422)))+~P1(f862(f862(f227(a1),f2(a1)),x60422))
% 25.54/25.41 [6045]P1(f862(f862(f227(a924),x60451),f866(x60452)))+~P1(f862(f54(a924),x60452))+~P1(f862(f862(f321(a924),x60451),x60452))
% 25.54/25.41 [6046]P1(f862(f862(f228(a924),x60461),f913(x60462)))+~P1(f862(f54(a924),x60462))+~P1(f862(f862(f321(a924),x60461),x60462))
% 25.54/25.41 [6074]E(x60741,x60742)+~P1(f862(f862(f228(a924),x60741),f862(a105,x60742)))+P1(f862(f862(f228(a924),x60741),x60742))
% 25.54/25.41 [6075]E(x60751,x60752)+~P1(f862(f862(f228(a924),x60751),f862(a105,x60752)))+P1(f862(f862(f228(a924),x60751),x60752))
% 25.54/25.41 [6076]E(x60761,x60762)+~P1(f862(f862(f228(a924),x60761),f862(a105,x60762)))+P1(f862(f862(f228(a924),x60761),x60762))
% 25.54/25.41 [6077]E(x60771,x60772)+~P1(f862(f862(f228(a924),x60771),f862(a105,x60772)))+P1(f862(f862(f228(a924),x60771),x60772))
% 25.54/25.41 [6112]E(x61121,f862(a105,x61122))+~P1(f862(f862(f227(a924),x61121),f862(a105,x61122)))+P1(f862(f862(f227(a924),x61121),x61122))
% 25.54/25.41 [6113]E(x61131,f862(a105,x61132))+~P1(f862(f862(f227(a924),x61131),f862(a105,x61132)))+P1(f862(f862(f227(a924),x61131),x61132))
% 25.54/25.41 [6129]P1(f862(x61291,f423(x61291)))+~P1(f862(x61291,f862(a97,x61292)))+~P1(f862(f862(f227(a1),f2(a1)),x61292))
% 25.54/25.41 [6145]~P1(f862(x61451,x61452))+~P1(f862(f862(f227(a1),f2(a1)),x61452))+P1(f862(x61451,f862(f93(a1),f406(x61451))))
% 25.54/25.41 [6156]~P86(x61562)+~E(x61561,f2(x61562))+~P1(f862(f862(f228(x61562),f2(x61562)),f862(f69(x61562),x61561)))
% 25.54/25.41 [6180]~P55(x61801,x61802)+P35(x61801,f862(f277(x61801,x61801),x61802))+~P1(f862(f54(f931(x61801,x61801)),x61802))
% 25.54/25.41 [6188]~P98(x61881)+E(f862(f93(x61881),f862(f96(a924),x61882)),f862(f96(x61881),x61882))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x61882)))
% 25.54/25.41 [6191]E(f862(a105,x61911),x61912)+~P1(f862(f862(f228(a924),x61911),x61912))+P1(f862(f862(f228(a924),f862(a105,x61911)),x61912))
% 25.54/25.41 [6206]E(f862(f862(f29(a1),x62061),x62062),f2(a1))+~P1(f862(f862(f227(a1),x62061),f2(a1)))+~P1(f862(f862(f228(a1),x62062),x62061))
% 25.54/25.41 [6207]E(f862(f862(f29(a1),x62071),x62072),f2(a1))+~P1(f862(f862(f227(a1),x62071),f2(a1)))+~P1(f862(f862(f228(a1),x62072),x62071))
% 25.54/25.41 [6218]E(f38(a1,x62181,x62182),x62181)+~P1(f862(f862(f227(a1),x62181),f2(a1)))+~P1(f862(f862(f228(a1),x62182),x62181))
% 25.54/25.41 [6232]E(f40(x62321,x62322),f39(x62321,x62322))+~P1(f862(f862(f227(a1),f2(a1)),x62321))+~P1(f862(f862(f227(a1),f2(a1)),x62322))
% 25.54/25.41 [6240]E(f862(f862(f29(a924),x62401),x62402),f2(a924))+~P1(f862(f862(f228(a924),f2(a924)),x62402))+~P1(f862(f862(f228(a924),x62401),x62402))
% 25.54/25.41 [6241]E(f862(f862(f29(a1),x62411),x62412),f2(a1))+~P1(f862(f862(f227(a1),f2(a1)),x62411))+~P1(f862(f862(f228(a1),x62411),x62412))
% 25.54/25.41 [6242]E(f862(f862(f29(a1),x62421),x62422),f2(a1))+~P1(f862(f862(f227(a1),f2(a1)),x62421))+~P1(f862(f862(f228(a1),x62421),x62422))
% 25.54/25.41 [6251]E(f38(a924,f862(f96(a924),x62511),f862(f96(a924),x62512)),f862(f96(a924),x62511))+P1(f862(a186,f862(f96(a1),x62511)))+~P1(f862(a186,f862(f96(a1),x62512)))
% 25.54/25.41 [6253]E(f38(a1,x62531,x62532),x62531)+~P1(f862(f862(f227(a1),f2(a1)),x62531))+~P1(f862(f862(f228(a1),x62531),x62532))
% 25.54/25.41 [6254]E(x62541,x62542)+~P1(f862(f862(f228(a924),x62541),f862(a105,x62542)))+~P1(f862(f862(f227(a924),x62542),x62541))
% 25.54/25.41 [6264]E(f862(f93(a1),x62641),f862(f96(a1),x62642))+~E(x62641,f862(a97,f862(f96(a1),x62642)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x62642)))
% 25.54/25.41 [6268]~P76(x62681)+~P1(f862(f862(f227(x62681),x62682),f2(x62681)))+P1(f862(f862(f227(x62681),x62682),f862(f72(x62681),x62682)))
% 25.54/25.41 [6269]~P112(x62691)+~P1(f862(f862(f228(x62691),x62692),f2(x62691)))+P1(f862(f862(f228(x62691),x62692),f862(f72(x62691),x62692)))
% 25.54/25.41 [6278]~P3(x62781)+E(f862(f862(f57(x62781,x62781,f94(x62781)),f234(x62781)),x62782),f31(x62781,x62782))+~P1(f862(f54(x62781),x62782))
% 25.54/25.41 [6279]~P3(x62791)+E(f862(f862(f57(x62791,x62791,f103(x62791)),f181(x62791)),x62792),f30(x62791,x62792))+~P1(f862(f54(x62791),x62792))
% 25.54/25.41 [6296]~P112(x62961)+~P1(f862(f862(f227(a1),f2(a1)),x62962))+P1(f862(f862(f227(x62961),f2(x62961)),f862(f95(x62961),x62962)))
% 25.54/25.41 [6297]~P127(x62971)+~P1(f862(f862(f228(a924),f2(a924)),x62972))+P1(f862(f862(f228(x62971),f2(x62971)),f862(f93(x62971),x62972)))
% 25.54/25.41 [6298]~P112(x62981)+~P1(f862(f862(f228(a1),f2(a1)),x62982))+P1(f862(f862(f228(x62981),f2(x62981)),f862(f95(x62981),x62982)))
% 25.54/25.41 [6301]~P4(x63012)+~P4(x63011)+E(f862(f302(a924,a1,f93(a1)),f296(a924,f862(a97,x63011),f862(a97,x63012))),f296(a1,x63011,x63012))
% 25.54/25.41 [6307]P1(f862(x63071,x63072))+~P1(f862(f862(f227(a1),f2(a1)),x63072))+~P1(f862(x63071,f862(f93(a1),f410(x63071))))
% 25.54/25.41 [6337]E(f862(f862(f73(a924),f862(f96(a924),x63371)),f862(f96(a924),x63372)),f862(f96(a924),x63371))+P1(f862(f862(f228(a1),x63371),a76))+~P1(f862(f862(f228(a1),x63372),a76))
% 25.54/25.41 [6341]~P112(x63411)+P1(f862(f862(f228(x63411),f2(x63411)),f75(x63411,x63412)))+~P1(f862(f862(f228(x63411),f2(x63411)),x63412))
% 25.54/25.41 [6353]~P78(x63531)+~P1(f862(f862(f227(x63531),x63532),f2(x63531)))+P1(f862(f862(f227(x63531),f2(x63531)),f862(f72(x63531),x63532)))
% 25.54/25.41 [6354]~P78(x63541)+~P1(f862(f862(f228(x63541),x63542),f2(x63541)))+P1(f862(f862(f228(x63541),f2(x63541)),f862(f72(x63541),x63542)))
% 25.54/25.41 [6357]E(x63571,f234(f932(x63572,a921)))+~E(f862(f28(x63572),x63571),f862(f28(x63572),f234(f932(x63572,a921))))+~P1(f862(f54(x63572),f234(f932(x63572,a921))))
% 25.54/25.41 [6384]~P1(f862(f862(f228(a924),f2(a924)),x63842))+~P1(f862(f862(f278(a924),x63841),x63842))+P1(f862(f862(f227(a924),x63841),x63842))
% 25.54/25.41 [6391]~P76(x63911)+P1(f862(f862(f227(x63911),x63912),f2(x63911)))+~P1(f862(f862(f227(x63911),x63912),f862(f72(x63911),x63912)))
% 25.54/25.41 [6392]~P112(x63921)+P1(f862(f862(f228(x63921),x63922),f2(x63921)))+~P1(f862(f862(f228(x63921),x63922),f862(f72(x63921),x63922)))
% 25.54/25.41 [6398]E(f40(x63981,x63982),f862(f862(f244(a1,a1),f2(a1)),x63981))+~P1(f862(f862(f228(a1),f2(a1)),x63982))+~P1(f862(f862(f228(a1),x63981),x63982))
% 25.54/25.41 [6401]~P98(x64011)+P1(f862(f862(f321(x64011),f862(f96(x64011),x64012)),f179(x64011)))+~P1(f862(f862(f227(a1),a76),x64012))
% 25.54/25.41 [6430]E(x64301,f2(a924))+~P1(f862(f862(f228(a924),x64301),f862(a105,x64302)))+P1(f862(f862(f228(a924),f329(x64302,x64301)),x64302))
% 25.54/25.41 [6452]~P112(x64521)+~P1(f862(f862(f228(x64521),f2(x64521)),f75(x64521,x64522)))+P1(f862(f862(f228(x64521),f2(x64521)),x64522))
% 25.54/25.41 [6454]~E(f862(f96(a924),x64542),f862(f96(a924),x64541))+P1(f862(f862(f227(a1),f862(f96(a1),x64541)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x64542)))
% 25.54/25.41 [6483]E(f862(f243(a1,a1),f43(x64831,x64832)),f862(f862(f29(a1),x64831),x64832))+~P1(f862(f862(f228(a1),x64831),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x64832))
% 25.54/25.41 [6522]E(f862(f248(a1,a1),f43(x65221,x65222)),f38(a1,x65221,x65222))+~P1(f862(f862(f228(a1),x65221),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x65222))
% 25.54/25.41 [6525]~P112(x65252)+~P1(f862(f862(f227(x65252),f2(x65252)),f862(f95(x65252),x65251)))+P1(f862(f862(f227(a1),f2(a1)),x65251))
% 25.54/25.41 [6526]~P127(x65262)+~P1(f862(f862(f228(x65262),f2(x65262)),f862(f93(x65262),x65261)))+P1(f862(f862(f228(a924),f2(a924)),x65261))
% 25.54/25.41 [6527]~P112(x65272)+~P1(f862(f862(f228(x65272),f2(x65272)),f862(f95(x65272),x65271)))+P1(f862(f862(f228(a1),f2(a1)),x65271))
% 25.54/25.41 [6531]E(f862(f243(a1,a1),f40(x65311,x65312)),f862(f862(f29(a1),x65311),x65312))+~P1(f862(f862(f227(a1),f2(a1)),x65312))+~P1(f862(f862(f228(a1),f2(a1)),x65311))
% 25.54/25.41 [6545]E(f862(f248(a1,a1),f40(x65451,x65452)),f38(a1,x65451,x65452))+~P1(f862(f862(f227(a1),f2(a1)),x65452))+~P1(f862(f862(f228(a1),f2(a1)),x65451))
% 25.54/25.41 [6561]~P78(x65611)+P1(f862(f862(f227(x65611),x65612),f2(x65611)))+~P1(f862(f862(f227(x65611),f2(x65611)),f862(f72(x65611),x65612)))
% 25.54/25.41 [6562]~P78(x65621)+P1(f862(f862(f228(x65621),x65622),f2(x65621)))+~P1(f862(f862(f228(x65621),f2(x65621)),f862(f72(x65621),x65622)))
% 25.54/25.41 [6589]P1(f862(f42(x65891,x65892),f43(x65891,x65892)))+~P1(f862(f862(f228(a1),x65891),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x65892))
% 25.54/25.41 [6615]P1(f862(f42(x66151,x66152),f40(x66151,x66152)))+~P1(f862(f862(f227(a1),f2(a1)),x66151))+~P1(f862(f862(f228(a1),f2(a1)),x66152))
% 25.54/25.41 [6658]~P78(x66581)+P1(f862(f862(f227(x66581),f862(f72(x66581),x66582)),f2(x66581)))+~P1(f862(f862(f227(x66581),f2(x66581)),x66582))
% 25.54/25.41 [6659]~P78(x66591)+P1(f862(f862(f228(x66591),f862(f72(x66591),x66592)),f2(x66591)))+~P1(f862(f862(f228(x66591),f2(x66591)),x66592))
% 25.54/25.41 [6677]E(f862(f862(f3(a924),f862(a97,x66771)),f862(a97,x66772)),f862(a97,f187(x66771,x66772)))+~P1(f862(f862(f227(a1),f2(a1)),x66772))+~P1(f862(f862(f227(a1),f2(a1)),x66771))
% 25.54/25.41 [6695]P1(f862(f862(f227(a1),f2(a1)),f187(x66951,x66952)))+~P1(f862(f862(f227(a1),f2(a1)),x66952))+~P1(f862(f862(f227(a1),f2(a1)),x66951))
% 25.54/25.41 [6733]~P1(f862(x67331,x67332))+P1(f862(x67331,f2(a924)))+P1(f862(x67331,f862(f862(f73(a924),f360(x67332,x67331)),f71(a924))))
% 25.54/25.41 [6814]E(f862(f96(a924),x68141),f862(f96(a924),x68142))+~P1(f862(f862(f227(a1),f862(f96(a1),x68142)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x68141)))
% 25.54/25.41 [6824]~E(x68241,f2(a924))+~E(f681(x68242,x68241),f2(a924))+E(f862(f135(a924,a924,f73(a924),x68241),x68242),f2(a924))
% 25.54/25.41 [6849]~P1(f862(f54(x68491),f883(x68492,x68491)))+~P1(f862(f54(f932(x68491,a921)),x68492))+P1(f862(f54(x68491),f30(f932(x68491,a921),x68492)))
% 25.54/25.41 [6855]E(x68551,x68552)+P1(f862(f862(f228(a1),x68551),x68552))+~P1(f862(f862(f228(a1),x68551),f862(f862(f73(a1),x68552),f71(a1))))
% 25.54/25.41 [6856]P1(f862(f862(f227(a924),f862(a97,x68561)),f862(a97,x68562)))+~P1(f862(f862(f227(a1),f2(a1)),x68562))+~P1(f862(f862(f227(a1),x68561),x68562))
% 25.54/25.41 [6857]P1(f862(f862(f227(a924),f862(a97,x68571)),f862(a97,x68572)))+~P1(f862(f862(f228(a1),f2(a1)),x68571))+~P1(f862(f862(f227(a1),x68571),x68572))
% 25.54/25.41 [6858]P1(f862(f862(f228(a924),f862(a97,x68581)),f862(a97,x68582)))+~P1(f862(f862(f228(a1),f2(a1)),x68582))+~P1(f862(f862(f228(a1),x68581),x68582))
% 25.54/25.41 [6859]P1(f862(f862(f228(a924),f862(a97,x68591)),f862(a97,x68592)))+~P1(f862(f862(f227(a1),f2(a1)),x68591))+~P1(f862(f862(f228(a1),x68591),x68592))
% 25.54/25.41 [6860]P1(f862(f862(f228(a924),f862(a97,x68601)),f862(a97,x68602)))+~P1(f862(f862(f228(a1),f2(a1)),x68602))+~P1(f862(f862(f228(a1),x68601),x68602))
% 25.54/25.41 [6870]E(f38(a924,f862(a97,x68701),f862(a97,x68702)),f862(a97,f38(a1,x68701,x68702)))+~P1(f862(f862(f227(a1),f2(a1)),x68702))+~P1(f862(f862(f227(a1),f2(a1)),x68701))
% 25.54/25.41 [6871]E(f38(a924,f862(a97,x68711),f862(a97,x68712)),f862(a97,f38(a1,x68711,x68712)))+~P1(f862(f862(f227(a1),f2(a1)),x68712))+~P1(f862(f862(f227(a1),f2(a1)),x68711))
% 25.54/25.41 [6894]~P78(x68941)+~P1(f862(f862(f227(x68941),f862(f72(x68941),x68942)),f2(x68941)))+P1(f862(f862(f227(x68941),f2(x68941)),x68942))
% 25.54/25.41 [6895]~P78(x68951)+~P1(f862(f862(f228(x68951),f862(f72(x68951),x68952)),f2(x68951)))+P1(f862(f862(f228(x68951),f2(x68951)),x68952))
% 25.54/25.41 [6909]~P1(f862(f862(f228(a1),a76),x69092))+~P1(f862(f862(f228(a1),x69091),x69092))+P1(f862(f862(f228(a924),f862(f96(a924),x69091)),f862(f96(a924),x69092)))
% 25.54/25.41 [7001]~P1(f862(f862(f227(a1),f2(a1)),x70011))+P1(f862(f862(f228(a924),f862(a97,x70011)),x70012))+~P1(f862(f862(f228(a1),x70011),f862(f93(a1),x70012)))
% 25.54/25.41 [7006]P1(f862(x70061,x70062))+~P1(f862(x70061,f862(a22,f815(x70061,x70062))))+~P1(f862(f862(f321(a924),x70062),f234(f932(a924,a921))))
% 25.54/25.41 [7017]E(x70171,f2(a1))+E(f38(a1,x70172,x70171),f2(a1))+E(f862(f862(f3(a1),f862(f72(a1),f862(f862(f29(a1),x70172),x70171))),f71(a1)),f862(f862(f29(a1),x70172),f862(f72(a1),x70171)))
% 25.54/25.41 [7031]~P1(f862(f862(f227(a1),f2(a1)),x70311))+~P1(f862(f862(f228(a924),f862(a97,x70311)),x70312))+P1(f862(f862(f228(a1),x70311),f862(f93(a1),x70312)))
% 25.54/25.41 [7067]~P1(f862(f862(f227(a924),f862(a97,x70671)),f862(a97,x70672)))+~P1(f862(f862(f227(a1),f2(a1)),x70672))+P1(f862(f862(f227(a1),x70671),x70672))
% 25.54/25.41 [7068]~P1(f862(f862(f227(a924),f862(a97,x70681)),f862(a97,x70682)))+~P1(f862(f862(f228(a1),f2(a1)),x70681))+P1(f862(f862(f227(a1),x70681),x70682))
% 25.54/25.41 [7069]~P1(f862(f862(f228(a924),f862(a97,x70691)),f862(a97,x70692)))+~P1(f862(f862(f227(a1),f2(a1)),x70691))+P1(f862(f862(f228(a1),x70691),x70692))
% 25.54/25.41 [7070]~P1(f862(f862(f228(a924),f862(a97,x70701)),f862(a97,x70702)))+~P1(f862(f862(f228(a1),f2(a1)),x70702))+P1(f862(f862(f228(a1),x70701),x70702))
% 25.54/25.41 [7097]P1(f862(f862(f227(a1),x70971),x70972))+~P1(f862(f862(f227(a924),f862(f96(a924),x70971)),f862(f96(a924),x70972)))+P1(f862(f862(f227(a1),x70971),a76))
% 25.54/25.41 [7123]P1(f862(f862(f227(a1),f2(a1)),f38(a1,x71231,x71232)))+~P1(f862(f862(f227(a1),f2(a1)),x71232))+~P1(f862(f862(f227(a1),f2(a1)),x71231))
% 25.54/25.41 [7219]P1(f862(f862(f228(a1),a76),x72191))+~P1(f862(f862(f228(a1),x72192),x72191))+~P1(f862(f862(f228(a924),f862(f96(a924),x72192)),f862(f96(a924),x72191)))
% 25.54/25.41 [7274]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x72741),x72742)),f38(a1,x72741,x72742)),f43(x72741,x72742))+~P1(f862(f862(f228(a1),x72741),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x72742))
% 25.54/25.41 [7294]E(f862(f862(f244(a1,a1),f862(f862(f29(a1),x72941),x72942)),f38(a1,x72941,x72942)),f40(x72941,x72942))+~P1(f862(f862(f227(a1),f2(a1)),x72942))+~P1(f862(f862(f227(a1),f2(a1)),x72941))
% 25.54/25.41 [7348]~P100(x73482)+E(x73481,f106(x73482))+E(f862(f135(x73482,x73482,f74(x73482),f862(f134(x73482),x73481)),f862(f164(x73482),x73481)),f862(f56(x73482,f74(x73482)),f862(f165(x73482),x73481)))
% 25.54/25.41 [7466]~E(x74661,f2(a924))+E(f862(f135(a924,a924,f73(a924),x74661),x74662),f2(a924))+P1(f862(f862(f321(a924),f681(x74662,x74661)),f862(f165(a924),x74662)))
% 25.54/25.41 [7520]~P1(f862(f862(f227(a1),x75201),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x75201),x75202)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75202))
% 25.54/25.41 [7521]~P1(f862(f862(f228(a1),x75212),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x75211),x75212)),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x75211))
% 25.54/25.41 [7522]~P1(f862(f862(f228(a1),x75222),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75221),x75222)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75221))
% 25.54/25.41 [7523]~P1(f862(f862(f228(a1),x75231),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75231),x75232)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75232))
% 25.54/25.41 [7524]~P1(f862(f862(f228(a1),x75241),f2(a1)))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75241),x75242)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x75242))
% 25.54/25.41 [7531]P1(f862(f862(f321(f932(x75311,a921)),f883(x75312,x75311)),x75312))+~P1(f862(f54(f932(x75311,a921)),x75312))+P1(f862(f54(x75311),f30(f932(x75311,a921),x75312)))
% 25.54/25.41 [7622]P22(x76221,x76221,x76222,f234(f932(x76221,a921)))+~E(f862(f302(x76221,x76221,x76222),f234(f932(x76221,a921))),f234(f932(x76221,a921)))+~P1(f862(f54(x76221),f234(f932(x76221,a921))))
% 25.54/25.41 [7743]~P22(x77431,x77431,x77432,f234(f932(x77431,a921)))+E(f862(f302(x77431,x77431,x77432),f234(f932(x77431,a921))),f234(f932(x77431,a921)))+~P1(f862(f54(x77431),f234(f932(x77431,a921))))
% 25.54/25.41 [7767]E(f40(f862(f96(a1),x77671),f862(f96(a1),x77672)),f862(f862(f244(a1,a1),f2(a1)),f862(f96(a1),x77671)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x77672)))+~P1(f862(f862(f228(a1),f862(f96(a1),x77671)),f862(f96(a1),x77672)))
% 25.54/25.41 [7884]E(f862(f862(f29(a1),x78841),x78842),f862(f96(a1),a90))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x78841),x78842)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x78841))
% 25.54/25.41 [7940]~P1(f862(f862(f228(a1),x79402),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f29(a1),x79401),x79402)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x79401))
% 25.54/25.41 [7945]E(f862(f862(f73(a1),x79451),x79452),f38(a1,x79451,x79452))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),x79451),x79452)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x79451))
% 25.54/25.41 [7948]P1(f862(f862(f228(a1),x79481),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f29(a1),x79481),x79482)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x79482))
% 25.54/25.41 [8653]~P109(x86531)+P11(x86531,x86532)+~P1(f862(f862(f227(x86531),f862(f862(f157(x86531),x86532),f715(x86532,x86531))),f862(f862(f157(x86531),x86532),f716(x86532,x86531))))
% 25.54/25.41 [8654]~P109(x86541)+P11(x86541,x86542)+~P1(f862(f862(f227(x86541),f862(f862(f157(x86541),x86542),f722(x86542,x86541))),f862(f862(f157(x86541),x86542),f727(x86542,x86541))))
% 25.54/25.41 [5870]E(x58701,f2(a1))+~E(f38(a1,x58702,x58701),f2(a1))+E(f862(f862(f29(a1),x58702),f862(f72(a1),x58701)),f862(f72(a1),f862(f862(f29(a1),x58702),x58701)))
% 25.54/25.41 [5888]~P38(x58882)+~P38(x58881)+P38(f862(f862(f103(f932(a1,a921)),x58881),x58882))
% 25.54/25.41 [5889]~P38(x58892)+~P38(x58891)+P38(f862(f862(f94(f932(a1,a921)),x58891),x58892))
% 25.54/25.41 [5907]~P64(x59071)+~P98(x59071)+E(f862(f72(x59071),f862(f862(f281(x59071),f71(x59071)),x59072)),f862(f862(f281(x59071),f862(f96(x59071),a90)),x59072))
% 25.54/25.41 [6034]E(x60341,f2(a1))+~E(f38(a1,x60342,x60341),f2(a1))+E(f862(f862(f29(a1),f862(f72(a1),x60342)),x60341),f862(f72(a1),f862(f862(f29(a1),x60342),x60341)))
% 25.54/25.41 [6174]~P109(x61741)+P11(x61741,x61742)+P1(f862(f862(f228(a924),f716(x61742,x61741)),f862(f182(f925(x61741)),x61742)))
% 25.54/25.41 [6175]~P109(x61751)+P11(x61751,x61752)+P1(f862(f862(f228(a924),f727(x61752,x61751)),f862(f182(f925(x61751)),x61752)))
% 25.54/25.41 [6331]~P98(x63311)+~E(f862(f96(x63311),x63312),f2(x63311))+P26(x63311,f862(f96(x63311),f862(f862(f73(a1),x63312),f862(f72(a1),a76))))
% 25.54/25.41 [6332]~P98(x63321)+~E(f862(f96(x63321),x63322),f2(x63321))+P26(x63321,f862(f96(x63321),f862(f862(f73(a1),a76),f862(f72(a1),x63322))))
% 25.54/25.41 [6334]E(f862(a44,f40(f862(f72(a1),x63341),f862(f72(a1),x63342))),f39(x63341,x63342))+P1(f862(f862(f227(a1),f2(a1)),x63341))+P1(f862(f862(f228(a1),f2(a1)),x63342))
% 25.54/25.41 [6460]~E(x64602,f2(a924))+~E(x64601,f2(a924))+P1(f862(f862(f227(a1),f862(f93(a1),x64601)),f862(f72(a1),f862(f93(a1),x64602))))
% 25.54/25.41 [6489]E(f862(f862(f73(a924),f862(f96(a924),x64891)),f862(f96(a924),x64892)),f862(f96(a924),f862(f862(f73(a1),x64891),x64892)))+P1(f862(f862(f228(a1),x64891),a76))+P1(f862(f862(f228(a1),x64892),a76))
% 25.54/25.41 [6624]~P76(x66241)+~P1(f862(f862(f227(x66241),f2(x66241)),x66242))+P1(f862(f862(f227(x66241),f862(f72(x66241),x66242)),x66242))
% 25.54/25.41 [6625]~P76(x66251)+~P1(f862(f862(f228(x66251),f2(x66251)),x66252))+P1(f862(f862(f228(x66251),f862(f72(x66251),x66252)),x66252))
% 25.54/25.41 [6800]E(f862(f862(f3(a924),f862(a97,x68001)),f862(a97,x68002)),f862(a97,f862(f862(f3(a1),x68001),x68002)))+~P1(f862(f862(f227(a1),f2(a1)),x68002))+~P1(f862(f862(f227(a1),x68002),x68001))
% 25.54/25.41 [6832]E(f862(a97,f38(a1,f862(f96(a1),x68321),f862(f96(a1),x68322))),f38(a924,f862(f96(a924),x68321),f862(f96(a924),x68322)))+P1(f862(a186,f862(f96(a1),x68321)))+P1(f862(a186,f862(f96(a1),x68322)))
% 25.54/25.41 [6850]~P76(x68501)+P1(f862(f862(f227(x68501),f2(x68501)),x68502))+~P1(f862(f862(f227(x68501),f862(f72(x68501),x68502)),x68502))
% 25.54/25.41 [6851]~P76(x68511)+P1(f862(f862(f228(x68511),f2(x68511)),x68512))+~P1(f862(f862(f228(x68511),f862(f72(x68511),x68512)),x68512))
% 25.54/25.41 [6863]~P76(x68631)+~P1(f862(f862(f227(x68631),f2(x68631)),x68632))+P1(f862(f862(f227(x68631),f2(x68631)),f862(f862(f73(x68631),x68632),x68632)))
% 25.54/25.41 [6865]~P76(x68651)+~P1(f862(f862(f228(x68651),f2(x68651)),x68652))+P1(f862(f862(f228(x68651),f2(x68651)),f862(f862(f73(x68651),x68652),x68652)))
% 25.54/25.41 [6875]E(f862(f862(f73(a924),f862(a97,x68751)),f862(a97,x68752)),f862(a97,f862(f862(f73(a1),x68751),x68752)))+~P1(f862(f862(f227(a1),f2(a1)),x68752))+~P1(f862(f862(f227(a1),f2(a1)),x68751))
% 25.54/25.41 [6876]E(f862(f862(f74(a924),f862(a97,x68761)),f862(a97,x68762)),f862(a97,f862(f862(f74(a1),x68761),x68762)))+~P1(f862(f862(f227(a1),f2(a1)),x68762))+~P1(f862(f862(f227(a1),f2(a1)),x68761))
% 25.54/25.41 [6877]E(f862(f862(f73(a924),f862(a97,x68771)),f862(a97,x68772)),f862(a97,f862(f862(f73(a1),x68771),x68772)))+~P1(f862(f862(f227(a1),f2(a1)),x68772))+~P1(f862(f862(f227(a1),f2(a1)),x68771))
% 25.54/25.41 [6878]E(f862(f862(f29(a924),f862(a97,x68781)),f862(a97,x68782)),f862(a97,f862(f862(f29(a1),x68781),x68782)))+~P1(f862(f862(f227(a1),f2(a1)),x68782))+~P1(f862(f862(f227(a1),f2(a1)),x68781))
% 25.54/25.41 [6888]E(x68881,f2(a924))+P1(f862(f862(f228(a924),f2(a924)),x68882))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f236(a924),x68882),x68881)))
% 25.54/25.41 [6919]~P98(x69191)+E(f862(f96(x69191),x69192),f2(x69191))+~P26(x69191,f862(f96(x69191),f862(f862(f73(a1),a76),f862(f72(a1),x69192))))
% 25.54/25.41 [6920]~P98(x69201)+E(f862(f96(x69201),x69202),f2(x69201))+~P26(x69201,f862(f96(x69201),f862(f862(f73(a1),x69202),f862(f72(a1),a76))))
% 25.54/25.41 [6979]~P1(f862(f54(x69791),x69792))+~P1(f862(f54(x69791),f234(f932(x69791,a921))))+P1(f862(f54(x69791),f862(f72(f932(x69791,a921)),x69792)))
% 25.54/25.41 [7002]~P1(f862(f862(f228(a1),f2(a1)),x70022))+~P1(f862(f862(f227(a1),x70022),x70021))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x70021),x70022)))
% 25.54/25.41 [7003]~P1(f862(f862(f227(a1),x70031),f2(a1)))+~P1(f862(f862(f228(a1),x70032),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70031),x70032)))
% 25.54/25.41 [7041]~P1(f862(f862(f227(a1),f2(a1)),x70412))+~P1(f862(f862(f227(a1),f2(a1)),x70411))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f74(a1),x70411),x70412)))
% 25.54/25.41 [7042]~P1(f862(f862(f227(a1),f2(a1)),x70422))+~P1(f862(f862(f227(a1),f2(a1)),x70421))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x70421),x70422)))
% 25.54/25.41 [7043]~P1(f862(f862(f227(a1),f2(a1)),x70432))+~P1(f862(f862(f227(a1),f2(a1)),x70431))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70431),x70432)))
% 25.54/25.41 [7044]~P1(f862(f862(f227(a1),f2(a1)),x70441))+~P1(f862(f862(f228(a1),f2(a1)),x70442))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x70441),x70442)))
% 25.54/25.41 [7045]~P1(f862(f862(f228(a924),f2(a924)),x70452))+~P1(f862(f862(f228(a924),f2(a924)),x70451))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f74(a924),x70451),x70452)))
% 25.54/25.41 [7110]E(x71101,f2(a1))+E(f38(a1,x71102,x71101),f2(a1))+E(f862(f862(f3(a1),f862(f72(a1),f862(f862(f29(a1),x71102),x71101))),f71(a1)),f862(f862(f29(a1),f862(f72(a1),x71102)),x71101))
% 25.54/25.41 [7165]P1(f862(f862(f228(a924),f2(a924)),x71651))+P1(f862(f862(f228(a924),f2(a924)),x71652))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f73(a924),x71652),x71651)))
% 25.54/25.41 [7169]~P76(x71691)+P1(f862(f862(f227(x71691),f2(x71691)),x71692))+~P1(f862(f862(f227(x71691),f2(x71691)),f862(f862(f73(x71691),x71692),x71692)))
% 25.54/25.41 [7170]~P76(x71701)+P1(f862(f862(f228(x71701),f2(x71701)),x71702))+~P1(f862(f862(f228(x71701),f2(x71701)),f862(f862(f73(x71701),x71702),x71702)))
% 25.54/25.41 [7220]~P1(f862(f54(x72201),x72202))+P1(f862(f54(x72201),f234(f932(x72201,a921))))+~P1(f862(f54(x72201),f862(f72(f932(x72201,a921)),x72202)))
% 25.54/25.41 [7286]P1(f862(f862(f227(a1),x72861),f2(a1)))+~P1(f862(f862(f228(a1),x72862),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x72861),x72862)))
% 25.54/25.41 [7292]~P1(f862(f862(f228(a1),f2(a1)),x72921))+P1(f862(f862(f227(a1),x72921),x72922))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x72922),x72921)))
% 25.54/25.41 [7293]~P1(f862(f862(f227(a1),f2(a1)),x72932))+P1(f862(f862(f227(a1),x72931),x72932))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x72932),x72931)))
% 25.54/25.41 [7323]P1(f862(f862(f227(a1),f2(a1)),x73231))+~P1(f862(f862(f228(a1),f2(a1)),x73232))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f29(a1),x73231),x73232)))
% 25.54/25.41 [7324]P1(f862(f862(f228(a1),f2(a1)),x73241))+~P1(f862(f862(f227(a1),f2(a1)),x73242))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x73242),x73241)))
% 25.54/25.41 [7427]E(f209(x74271,x74272),x74271)+~E(x74272,f2(a924))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x74271),x74272)))
% 25.54/25.41 [7641]E(f171(x76411,x76412),f106(a1))+P1(f862(f862(f227(a1),x76411),x76412))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x76411),x76412)))
% 25.54/25.41 [7661]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x76611),x76612)),f43(x76611,x76612))+~P1(f862(f862(f228(a1),f2(a1)),x76612))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x76611),x76612)))
% 25.54/25.41 [7692]E(x76921,f2(a924))+E(f209(x76921,f38(a924,x76922,x76921)),f209(x76922,x76921))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x76922),x76921)))
% 25.54/25.41 [7746]E(f121(x77461,x77462),f108(a1))+~P1(f862(f862(f228(a1),x77461),x77462))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x77461),x77462)))
% 25.54/25.41 [7775]~P1(f862(f54(x77752),f234(f932(x77752,a921))))+~P1(f862(f54(x77751),f234(f932(x77751,a921))))+P1(f862(f54(f930(x77751,x77752)),f234(f932(f930(x77751,x77752),a921))))
% 25.54/25.41 [7776]~P1(f862(f54(x77762),f234(f932(x77762,a921))))+~P1(f862(f54(x77761),f234(f932(x77761,a921))))+P1(f862(f54(f931(x77761,x77762)),f234(f932(f931(x77761,x77762),a921))))
% 25.54/25.41 [7848]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78481))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78482))+P1(f862(f862(f228(a924),x78481),f862(f862(f74(a924),x78482),x78481)))
% 25.54/25.41 [7849]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78491))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x78492))+P1(f862(f862(f228(a924),x78491),f862(f862(f74(a924),x78491),x78492)))
% 25.54/25.41 [7883]E(f862(f28(x78831),f234(f932(x78831,a921))),f862(a105,f2(a924)))+P1(f862(f54(x78832),f234(f932(x78832,a921))))+~P1(f862(f54(f932(x78832,x78831)),f234(f932(f932(x78832,x78831),a921))))
% 25.54/25.41 [7933]E(f40(x79331,x79332),f862(f862(f244(a1,a1),f2(a1)),x79331))+~P1(f862(f862(f228(a1),x79331),x79332))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x79331),x79332)))
% 25.54/25.41 [7937]E(f208(f862(f72(a1),x79371),f862(f72(a1),x79372)),f208(x79371,x79372))+~P1(f862(f862(f228(a1),x79372),f2(a1)))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x79371),x79372)))
% 25.54/25.41 [7958]E(f40(x79581,x79582),f862(f862(f244(a1,a1),f2(a1)),x79581))+~P1(f862(f862(f227(a1),x79582),f2(a1)))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x79581),x79582)))
% 25.54/25.41 [8009]~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x80091))+~P1(f862(f862(f227(a924),f862(a105,f2(a924))),x80092))+P1(f862(f862(f227(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x80091),x80092)))
% 25.54/25.41 [8010]~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x80102))+~P1(f862(f862(f228(a924),f862(a105,f2(a924))),x80101))+P1(f862(f862(f228(a924),f862(a105,f2(a924))),f862(f862(f74(a924),x80101),x80102)))
% 25.54/25.41 [8174]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x81741),x81742)),f43(x81741,x81742))+~P1(f862(f862(f227(a1),x81742),f2(a1)))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x81741),x81742)))
% 25.54/25.41 [8198]E(f109(a1,f862(f122(a1),x81981),f121(x81982,f862(f862(f73(a1),x81981),f71(a1)))),f121(x81982,x81981))+P1(f862(f862(f228(a1),x81982),x81981))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x81982),x81981)))
% 25.54/25.41 [8211]E(f862(f862(f144(a1),x82111),f171(f862(f862(f73(a1),x82111),f71(a1)),x82112)),f171(x82111,x82112))+~P1(f862(f862(f227(a1),x82111),x82112))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x82111),x82112)))
% 25.54/25.41 [8496]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),x84961),x84962)),f43(x84961,x84962))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x84961),x84962)))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x84961),x84962)))
% 25.54/25.41 [8700]E(x87001,f106(x87002))+~P1(f862(f130(x87002),x87001))+E(f170(x87002,f862(f862(f10(a921,a921,x87002),a314),f862(f862(f9(x87002,x87002,a921),a317),f137(x87002,x87001))),x87001),f107(x87002,x87001))
% 25.54/25.41 [8773]E(f862(f862(f244(a1,a1),f862(f96(a1),a90)),f862(f862(f73(a1),f862(f96(a1),x87731)),f862(f96(a1),x87732))),f43(f862(f96(a1),x87731),f862(f96(a1),x87732)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x87732)))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f96(a1),x87731)),f862(f96(a1),x87732))))
% 25.54/25.41 [8797]~P38(x87972)+~P38(x87971)+E(f862(f302(a924,a1,f93(a1)),f862(f862(f103(f932(a924,a921)),f862(f302(a1,a924,a97),x87971)),f862(f302(a1,a924,a97),x87972))),f862(f862(f103(f932(a1,a921)),x87971),x87972))
% 25.54/25.41 [8798]~P38(x87982)+~P38(x87981)+E(f862(f302(a924,a1,f93(a1)),f862(f862(f94(f932(a924,a921)),f862(f302(a1,a924,a97),x87981)),f862(f302(a1,a924,a97),x87982))),f862(f862(f94(f932(a1,a921)),x87981),x87982))
% 25.54/25.41 [9468]~P98(x94681)+~E(f862(f96(x94681),x94682),f71(x94681))+P26(x94681,f862(f96(x94681),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x94682))))
% 25.54/25.41 [9714]~P98(x97141)+E(f862(f96(x97141),x97142),f71(x97141))+~P26(x97141,f862(f96(x97141),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f72(a1),x97142))))
% 25.54/25.41 [10465]E(x104651,f2(a1))+E(x104652,f2(a1))+E(f862(f250(a1,a1,a1,a1,f25(a1),f862(f74(a1),f75(a1,x104652))),f862(f862(f862(f89(f931(a1,a1)),f862(f862(a317,f75(a1,x104651)),f75(a1,x104652))),f46(x104651,x104652)),f862(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f9(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f9(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f72(a1))),f2(a1))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f862(f3(a1),f862(f69(a1),x104652))))),f46(x104651,x104652)))),f39(x104651,x104652))
% 25.54/25.41 [10466]E(x104661,f2(a1))+E(x104662,f2(a1))+E(f862(f250(a1,a1,a1,a1,f25(a1),f862(f74(a1),f75(a1,x104662))),f862(f862(f862(f89(f931(a1,a1)),f862(f862(a319,f862(f862(a318,f862(f862(f228(a1),f2(a1)),x104662)),f862(f862(f227(a1),f2(a1)),x104661))),f862(f862(a318,f862(f862(f228(a1),x104662),f2(a1))),f862(f862(f228(a1),x104661),f2(a1))))),f46(x104661,x104662)),f862(f862(f249(a1,a1,f931(a1,a1)),f862(f862(f20(a1,f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f932(f931(a1,a1),f931(a1,a1))),f932(f932(a1,f931(a1,a1)),f932(a1,f931(a1,a1))),a1),f20(a1,f931(a1,a1),f931(a1,a1))),f862(f862(f10(f931(a1,a1),f932(a1,f932(f931(a1,a1),f931(a1,a1))),a1),f862(f9(a1,f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),f862(f862(f10(a921,f932(f931(a1,a1),f932(f931(a1,a1),f931(a1,a1))),a1),f89(f931(a1,a1))),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f9(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f72(a1))),f2(a1))))),f862(f862(f9(a1,f932(a1,a1),f932(a1,f931(a1,a1))),f862(f862(f10(f932(a1,f931(a1,a1)),f932(f932(a1,a1),f932(a1,f931(a1,a1))),a1),f10(a1,f931(a1,a1),a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f862(f9(a1,a1,a1),f862(f862(f10(a1,f932(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f862(f3(a1),f862(f69(a1),x104662))))),f46(x104661,x104662)))),f39(x104661,x104662))
% 25.54/25.41 [5896]~P112(x58961)+~P98(x58961)+E(f862(f69(x58961),f862(f862(f236(x58961),f862(f96(x58961),a90)),x58962)),f71(x58961))
% 25.54/25.41 [6402]~P142(x64021)+~P1(f862(f862(f228(a1),x64022),f2(a1)))+E(f862(f72(x64021),f862(f93(x64021),f862(a97,f862(f72(a1),x64022)))),f862(f95(x64021),x64022))
% 25.54/25.41 [6608]P1(f862(f862(f227(a92),x66081),f71(a92)))+E(f862(f862(f73(a92),f71(a92)),f264(x66081,f862(f862(f29(a92),x66082),x66081))),f264(x66081,x66082))+P1(f862(f862(f228(a92),x66082),x66081))
% 25.54/25.41 [7210]~P97(x72101)+~P1(f862(f862(f321(x72101),x72102),f102(x72101)))+~E(f862(f862(f73(x72101),f862(f862(f73(x72101),f71(x72101)),x72102)),x72102),f2(x72101))
% 25.54/25.41 [7325]~P1(f862(f862(f227(a1),x73252),f2(a1)))+~P1(f862(f862(f228(a1),x73251),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f40(f862(f72(a1),x73251),f862(f72(a1),x73252)))),f862(f862(f29(a1),x73251),x73252))
% 25.54/25.41 [7342]~P1(f862(f862(f227(a1),x73422),f2(a1)))+~P1(f862(f862(f228(a1),x73421),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f40(f862(f72(a1),x73421),f862(f72(a1),x73422)))),f38(a1,x73421,x73422))
% 25.54/25.41 [7350]~P1(f862(f862(f228(a1),x73502),f2(a1)))+E(f862(f243(a1,a1),f862(a44,f43(f862(f72(a1),x73501),f862(f72(a1),x73502)))),f862(f862(f29(a1),x73501),x73502))+~P1(f862(f862(f228(a1),f2(a1)),x73501))
% 25.54/25.41 [7368]~P1(f862(f862(f228(a1),x73682),f2(a1)))+E(f862(f248(a1,a1),f862(a44,f43(f862(f72(a1),x73681),f862(f72(a1),x73682)))),f38(a1,x73681,x73682))+~P1(f862(f862(f228(a1),f2(a1)),x73681))
% 25.54/25.41 [7421]E(f862(f862(f29(a1),f862(f862(f236(a1),x74211),x74212)),x74211),f862(f862(f236(a1),x74211),f862(f862(f3(a924),x74212),f862(a105,f2(a924)))))+~P1(f862(f862(f228(a924),f2(a924)),x74212))+~P1(f862(f862(f228(a1),f2(a1)),x74211))
% 25.54/25.41 [7527]~P1(f862(f862(f228(a924),f2(a924)),x75271))+~P1(f862(f862(f228(a924),f2(a924)),x75272))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x75271),x75272)),x75271))
% 25.54/25.41 [7528]~P1(f862(f862(f228(a924),f2(a924)),x75281))+~P1(f862(f862(f228(a924),f71(a924)),x75282))+P1(f862(f862(f228(a924),f862(f862(f29(a924),x75281),x75282)),x75281))
% 25.54/25.41 [7529]~P1(f862(f862(f228(a1),f2(a1)),x75291))+~P1(f862(f862(f228(a1),f71(a1)),x75292))+P1(f862(f862(f228(a1),f862(f862(f29(a1),x75291),x75292)),x75291))
% 25.54/25.41 [7667]E(x76671,f2(a924))+~E(x76672,f2(a1))+~P1(f862(f862(f228(a1),f2(a1)),f862(f862(f236(a1),f862(f69(a1),x76672)),x76671)))
% 25.54/25.41 [8089]~E(x80892,f106(f925(x80891)))+E(f862(f182(f925(f925(x80891))),f172(x80891,x80892)),f2(a924))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x80891),a924),f182(f925(x80891))),x80892)))
% 25.54/25.41 [8348]P1(f862(x83481,x83482))+~P1(f862(x83481,f862(a100,f569(x83481,x83482))))+~P1(f862(f862(f321(f932(f931(a924,a924),a921)),x83482),a91))
% 25.54/25.41 [8364]E(x83641,f106(f925(x83642)))+E(f862(f182(f925(x83642)),f862(f862(f157(f925(x83642)),x83641),f2(a924))),f862(f182(f925(f925(x83642))),f172(x83642,x83641)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x83642),a924),f182(f925(x83642))),x83641)))
% 25.54/25.41 [8505]~P36(x85051,x85052)+~P37(x85051,x85052)+P36(x85051,f862(f862(f3(f932(f931(x85051,x85051),a921)),x85052),f299(x85051,f181(f932(f931(x85051,x85051),a921)))))
% 25.54/25.41 [9085]~P1(f862(f54(x90851),f862(f254(x90851),x90852)))+~P1(f862(f54(x90851),f234(f932(x90851,a921))))+P1(f862(f54(x90851),f862(f254(x90851),f862(f862(f10(a921,a921,x90851),a314),x90852))))
% 25.54/25.41 [9149]E(f862(f862(f244(a924,a924),f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x91491),x91492)),x91492))),f38(a924,f862(f862(f3(a924),x91491),x91492),x91492)),f78(f931(a924,a924),f41(x91491,x91492)))+~P1(f862(f862(f228(a924),f2(a924)),x91492))+~P1(f862(f862(f227(a924),x91492),x91491))
% 25.54/25.41 [9433]~P1(f862(f54(x94331),f862(f254(x94331),x94332)))+P1(f862(f54(x94331),f234(f932(x94331,a921))))+~P1(f862(f54(x94331),f862(f254(x94331),f862(f862(f10(a921,a921,x94331),a314),x94332))))
% 25.54/25.41 [10158]P24(x101581,x101582)+~P35(x101581,f862(f243(f932(f931(x101581,x101581),a921),f932(f931(x101581,x101581),a921)),x101582))+~P1(f862(f862(f227(f932(f931(x101581,x101581),a921)),f862(f862(f280(x101581,x101581,x101581),f862(f243(f932(f931(x101581,x101581),a921),f932(f931(x101581,x101581),a921)),x101582)),f862(f248(f932(f931(x101581,x101581),a921),f932(f931(x101581,x101581),a921)),x101582))),f862(f243(f932(f931(x101581,x101581),a921),f932(f931(x101581,x101581),a921)),x101582)))
% 25.54/25.41 [10192]E(f862(f36(f862(f96(a1),x101921)),f40(f862(f96(a1),x101922),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),x101921)))),f40(f862(f96(a1),x101922),f862(f96(a1),x101921)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x101921)))+P1(f862(f862(f228(a1),f862(f96(a1),x101922)),f862(f96(a1),x101921)))
% 25.54/25.41 [10198]E(f862(f36(f862(f96(a1),x101981)),f43(f862(f96(a1),x101982),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f96(a1),x101981)))),f43(f862(f96(a1),x101982),f862(f96(a1),x101981)))+~P1(f862(f862(f228(a1),f2(a1)),f862(f96(a1),x101981)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f96(a1),x101982)),f862(f96(a1),x101981))))
% 25.54/25.41 [7451]~P1(f862(f862(f228(a924),f2(a924)),x74512))+P1(f862(f862(f228(a924),x74511),x74512))+E(f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x74511),x74512)),x74512)),f862(f862(f29(a924),x74511),x74512))
% 25.54/25.41 [7452]~P1(f862(f862(f228(a924),f2(a924)),x74522))+P1(f862(f862(f228(a924),x74521),x74522))+E(f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x74521),x74522)),x74522)),f862(f862(f29(a924),x74521),x74522))
% 25.54/25.41 [7595]~P1(f862(f862(f228(a924),f2(a924)),x75952))+~P1(f862(f862(f227(a924),x75952),x75951))+E(f862(a105,f862(f862(f29(a924),f862(f862(f3(a924),x75951),x75952)),x75952)),f862(f862(f29(a924),x75951),x75952))
% 25.54/25.41 [8569]~P98(x85691)+~P97(x85691)+~P26(x85691,f862(f96(x85691),f862(f862(f3(a1),f862(f862(f73(a1),x85692),x85692)),a90)))
% 25.54/25.41 [9340]E(x93401,f2(a924))+E(f862(f862(f249(a924,a924,f931(a924,a924)),f862(f862(f10(a924,f932(a924,f931(a924,a924)),a924),f244(a924,a924)),a105)),f78(f931(a924,a924),f41(f862(f862(f3(a924),x93402),x93401),x93401))),f78(f931(a924,a924),f41(x93402,x93401)))+P1(f862(f862(f228(a924),x93402),x93401))
% 25.54/25.41 [9520]~P36(x95201,x95202)+~P49(x95201,x95202)+P1(f862(f862(f227(f932(f931(x95201,x95201),a921)),f862(f862(f280(x95201,x95201,x95201),f862(f277(x95201,x95201),x95202)),x95202)),x95202))
% 25.54/25.41 [9778]P1(f862(x97782,f649(x97782,x97781)))+P1(f862(x97781,f649(x97782,x97781)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97781)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97782)))
% 25.54/25.41 [9782]~P1(f862(x97822,f649(x97822,x97821)))+~P1(f862(x97821,f649(x97822,x97821)))+E(f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97821)),f862(f254(a1),f862(f862(f20(a1,a921,a921),f862(f862(f10(a921,f932(a921,a921),a1),a318),f862(f227(a1),f2(a1)))),x97822)))
% 25.54/25.41 [10326]~P1(f862(f862(f278(a924),x103262),x103261))+P1(f862(f862(f278(a924),x103261),x103262))+P1(f862(f862(f321(a924),x103261),f285(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103262)))
% 25.54/25.41 [10327]~P1(f862(f862(f278(a924),x103272),x103271))+P1(f862(f862(f278(a924),x103271),x103272))+P1(f862(f862(f321(a924),x103272),f289(a924,f862(f862(f20(a924,f932(a924,a921),f932(a924,a921)),f862(f862(f10(f932(a924,f932(a921,a921)),f932(f932(a924,a921),f932(a924,a921)),a924),f20(a924,a921,a921)),f862(f862(f10(f932(a924,a921),f932(a924,f932(a921,a921)),a924),f862(f10(a921,f932(a921,a921),a924),a318)),f278(a924)))),f862(f862(f10(f932(a924,a921),f932(a924,a921),a924),f862(f10(a921,a921,a924),a314)),f862(f9(a924,a924,a921),f278(a924)))),x103271)))
% 25.54/25.41 [7805]~P65(x78051)+~P98(x78051)+E(f862(f862(f281(x78051),x78052),f862(f96(x78051),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x78052)
% 25.54/25.41 [7806]~P65(x78061)+~P98(x78061)+E(f862(f862(f281(x78061),x78062),f862(f96(x78061),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))),x78062)
% 25.54/25.41 [9467]~P98(x94671)+~E(f862(f96(x94671),x94672),f71(x94671))+P26(x94671,f862(f96(x94671),f862(f862(f73(a1),x94672),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9654]~P141(x96541)+~E(x96542,f71(x96541))+E(f862(f862(f236(x96541),x96542),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96541))
% 25.54/25.41 [9655]~P141(x96551)+~E(x96552,f2(x96551))+E(f862(f862(f236(x96551),x96552),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(x96551))
% 25.54/25.41 [9670]~P141(x96701)+~E(x96702,f862(f72(x96701),f71(x96701)))+E(f862(f862(f236(x96701),x96702),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x96701))
% 25.54/25.41 [9691]~P80(x96911)+~P99(x96911)+E(f862(f862(f236(x96911),f862(f96(x96911),x96912)),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f74(x96911),f862(f96(x96911),x96912)),f862(f96(x96911),x96912)))
% 25.54/25.41 [9715]~P98(x97151)+E(f862(f96(x97151),x97152),f71(x97151))+~P26(x97151,f862(f96(x97151),f862(f862(f73(a1),x97152),f862(f72(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.41 [9833]~P141(x98332)+E(x98331,f2(x98332))+~E(f862(f862(f236(x98332),x98331),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f2(x98332))
% 25.54/25.41 [10102]~P112(x101022)+E(x101021,f2(x101022))+P1(f862(f862(f228(x101022),f2(x101022)),f862(f862(f236(x101022),x101021),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10157]~P112(x101572)+~E(x101571,f2(x101572))+~P1(f862(f862(f228(x101572),f2(x101572)),f862(f862(f236(x101572),x101571),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.41 [10183]P1(f862(f862(f227(a1),x101831),f2(a1)))+P1(f862(f862(f228(a1),x101832),x101831))+E(f862(f36(x101831),f40(x101832,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101831))),f40(x101832,x101831))
% 25.54/25.41 [10184]~P1(f862(f862(f228(a1),f2(a1)),x101841))+P1(f862(f862(f228(a1),x101842),x101841))+E(f862(f36(x101841),f40(x101842,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101841))),f40(x101842,x101841))
% 25.54/25.41 [10185]P1(f862(f862(f227(a1),x101851),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x101852),x101851)))+E(f862(f36(x101851),f43(x101852,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101851))),f43(x101852,x101851))
% 25.54/25.41 [10186]~P1(f862(f862(f228(a1),f2(a1)),x101861))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x101862),x101861)))+E(f862(f36(x101861),f43(x101862,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101861))),f43(x101862,x101861))
% 25.54/25.41 [10187]~P147(x101871)+~P1(f862(f862(f227(a1),f2(a1)),x101872))+E(f862(f93(x101871),f862(a97,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101872))),f862(f862(f73(x101871),f862(f93(x101871),f862(a97,x101872))),f862(f93(x101871),f862(a97,x101872))))
% 25.54/25.41 [5226]~P148(x52261,x52263,x52262)+~E(x52263,f2(a1))+P1(f862(x52261,x52262))
% 25.54/25.41 [5350]~P109(x53501)+~P11(x53501,x53503)+P11(x53501,f163(x53501,x53502,x53503))
% 25.54/25.41 [5351]~P109(x53511)+~P11(x53511,x53513)+P11(x53511,f170(x53511,x53512,x53513))
% 25.54/25.41 [4910]~P68(x49102)+~E(x49103,f862(f72(x49102),x49101))+E(x49101,f862(f72(x49102),x49103))
% 25.54/25.41 [4911]~P68(x49112)+~E(x49113,f862(f72(x49112),x49111))+E(x49111,f862(f72(x49112),x49113))
% 25.54/25.41 [4912]~P68(x49121)+~E(f862(f72(x49121),x49123),x49122)+E(f862(f72(x49121),x49122),x49123)
% 25.54/25.41 [4913]~P68(x49131)+~E(f862(f72(x49131),x49133),x49132)+E(f862(f72(x49131),x49132),x49133)
% 25.54/25.41 [4993]~P109(x49933)+E(x49931,x49932)+~E(f862(f293(x49933),x49931),f862(f293(x49933),x49932))
% 25.54/25.41 [4994]~P109(x49943)+E(x49941,x49942)+~E(f862(f294(x49943),x49941),f862(f294(x49943),x49942))
% 25.54/25.41 [4995]~P109(x49953)+E(x49951,x49952)+~E(f862(f274(x49953),x49951),f862(f274(x49953),x49952))
% 25.54/25.41 [4996]~P109(x49963)+E(x49961,x49962)+~E(f862(f292(x49963),x49961),f862(f292(x49963),x49962))
% 25.54/25.41 [4997]~P96(x49973)+E(x49971,x49972)+~E(f862(f72(x49973),x49971),f862(f72(x49973),x49972))
% 25.54/25.41 [4998]~P68(x49983)+E(x49981,x49982)+~E(f862(f72(x49983),x49981),f862(f72(x49983),x49982))
% 25.54/25.41 [4999]~P105(x49993)+E(x49991,x49992)+~E(f862(f93(x49993),x49991),f862(f93(x49993),x49992))
% 25.54/25.41 [5000]~P97(x50003)+E(x50001,x50002)+~E(f862(f95(x50003),x50001),f862(f95(x50003),x50002))
% 25.54/25.41 [5101]~P63(x51011)+~P1(f862(x51012,x51013))+P1(f862(f49(x51011),x51012))
% 25.54/25.41 [5102]~P63(x51021)+~P1(f862(x51022,x51023))+P1(f862(f49(x51021),x51022))
% 25.54/25.41 [5141]~P63(x51413)+P1(f862(x51411,x51412))+~P1(f862(f50(x51413),x51411))
% 25.54/25.41 [5142]~P63(x51423)+P1(f862(x51421,x51422))+~P1(f862(f50(x51423),x51421))
% 25.54/25.41 [5246]~P149(x52461,x52462,x52463)+~E(x52462,f2(a1))+P1(f862(x52461,f2(a1)))
% 25.54/25.41 [5286]~E(x52861,f2(a924))+E(f327(x52861,x52862,x52863),f181(f932(x52863,a921)))+~E(f862(f28(x52863),x52862),f862(a105,x52861))
% 25.54/25.41 [5437]~E(x54372,f2(a924))+E(f862(f243(a924,a924),x54371),f2(a924))+~P1(f862(f41(x54373,x54372),x54371))
% 25.54/25.41 [5475]P1(f862(x54751,x54752))+~E(x54753,f862(f93(a1),x54752))+~P1(f862(x54751,f862(a97,x54753)))
% 25.54/25.41 [5960]~E(x59603,f2(a924))+~P1(f862(x59601,x59602))+P1(f862(x59601,f38(a924,x59602,x59603)))
% 25.54/25.41 [6202]~P106(x62022)+~P106(x62021)+E(f124(x62021,x62022,f125(x62021,x62023),f125(x62022,x62023)),f125(f931(x62021,x62022),x62023))
% 25.54/25.41 [6383]~E(x63833,f2(a924))+P1(f862(x63831,x63832))+~P1(f862(x63831,f38(a924,x63832,x63833)))
% 25.54/25.41 [7066]E(x70661,f2(a924))+~P1(f862(x70662,f429(x70661,x70663,x70662)))+P1(f862(x70662,f38(a924,x70663,x70661)))
% 25.54/25.41 [7175]~P3(x71751)+~P1(f862(f862(f227(x71751),x71752),f368(x71753,x71752,x71751)))+P1(f862(f862(f227(x71751),x71752),f31(x71751,x71753)))
% 25.54/25.41 [7176]~P3(x71761)+~P1(f862(f862(f227(x71761),x71762),f498(x71762,x71763,x71761)))+P1(f862(f862(f227(x71761),x71762),f31(x71761,x71763)))
% 25.54/25.41 [7178]~P1(f862(x71781,x71782))+~P1(f862(x71781,f429(x71783,x71782,x71781)))+P1(f862(x71781,f38(a924,x71782,x71783)))
% 25.54/25.41 [7280]E(x72801,f106(x72802))+E(f862(f862(f144(x72802),f696(x72803,x72801,x72802)),f699(x72803,x72801,x72802)),x72801)+~P1(f862(f862(f321(f925(x72802)),x72801),f154(x72802,x72803)))
% 25.54/25.41 [7311]~P142(x73111)+~P1(f862(f862(f321(x73111),x73112),f102(x73111)))+P1(f862(f862(f321(x73111),f862(f862(f236(x73111),x73112),x73113)),f102(x73111)))
% 25.54/25.41 [7640]P35(x76401,x76402)+~P1(f862(f862(f321(x76401),x76403),f610(x76402,x76401)))+P1(f862(f862(f321(x76401),f620(x76402,x76401,x76403)),f610(x76402,x76401)))
% 25.54/25.41 [7910]E(x79101,f106(x79102))+~P1(f862(f862(f321(f925(x79102)),x79101),f154(x79102,x79103)))+P1(f862(f862(f321(f925(x79102)),f699(x79103,x79101,x79102)),f154(x79102,x79103)))
% 25.54/25.41 [7962]E(x79621,f2(a924))+E(f862(f862(f73(a924),f862(f862(f74(a924),x79621),f430(x79621,x79622,x79623))),f429(x79621,x79622,x79623)),x79622)+P1(f862(x79623,f38(a924,x79622,x79621)))
% 25.54/25.41 [8004]~P1(f862(x80043,x80042))+E(f862(f862(f73(a924),f862(f862(f74(a924),x80041),f430(x80041,x80042,x80043))),f429(x80041,x80042,x80043)),x80042)+P1(f862(x80043,f38(a924,x80042,x80041)))
% 25.54/25.41 [8146]P1(f862(f862(f228(a1),x81461),f416(x81462,x81463,x81461)))+P1(f862(f862(x81463,f862(f862(f29(a1),x81462),x81461)),f38(a1,x81462,x81461)))+~P1(f862(f862(f228(a1),x81461),f2(a1)))
% 25.54/25.41 [8420]P1(f862(f862(x84202,f862(f862(f29(a1),x84201),x84203)),f38(a1,x84201,x84203)))+~P1(f862(f862(f228(a1),x84203),f2(a1)))+P1(f862(f862(f227(a1),f416(x84201,x84202,x84203)),f2(a1)))
% 25.54/25.41 [8604]E(f862(f862(f73(a1),f862(f862(f74(a1),x86041),f412(x86042,x86043,x86041))),f416(x86042,x86043,x86041)),x86042)+P1(f862(f862(x86043,f862(f862(f29(a1),x86042),x86041)),f38(a1,x86042,x86041)))+~P1(f862(f862(f228(a1),x86041),f2(a1)))
% 25.54/25.41 [8845]~P1(f862(f862(x88451,f412(x88452,x88451,x88453)),f416(x88452,x88451,x88453)))+P1(f862(f862(x88451,f862(f862(f29(a1),x88452),x88453)),f38(a1,x88452,x88453)))+~P1(f862(f862(f228(a1),x88453),f2(a1)))
% 25.54/25.41 [9098]~P109(x90981)+~P11(x90981,x90983)+P11(x90981,f142(x90981,x90981,f7(x90981),x90982,x90983))
% 25.54/25.41 [9600]~P128(x96002)+E(x96001,f2(x96002))+~P1(f862(f862(f227(x96002),f862(f862(f73(x96002),f862(f862(f74(x96002),x96003),x96003)),f862(f862(f74(x96002),x96001),x96001))),f2(x96002)))
% 25.54/25.41 [9601]~P128(x96012)+E(x96011,f2(x96012))+~P1(f862(f862(f227(x96012),f862(f862(f73(x96012),f862(f862(f74(x96012),x96011),x96011)),f862(f862(f74(x96012),x96013),x96013))),f2(x96012)))
% 25.54/25.41 [10400]~P112(x104001)+~P1(f862(f862(f228(x104001),x104002),f2(x104001)))+P1(f862(f862(f228(x104001),f862(f862(f236(x104001),x104002),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x104003)))),f2(x104001)))
% 25.54/25.41 [10409]~P112(x104092)+E(x104091,f2(x104092))+~P1(f862(f862(f227(x104092),f862(f862(f73(x104092),f862(f862(f236(x104092),x104093),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104092),x104091),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104092)))
% 25.54/25.41 [10410]~P112(x104102)+E(x104101,f2(x104102))+~P1(f862(f862(f227(x104102),f862(f862(f73(x104102),f862(f862(f236(x104102),x104101),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x104102),x104103),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x104102)))
% 25.54/25.41 [4948]~E(x49482,x49483)+~P59(x49481)+E(f862(f862(f3(x49481),x49482),x49483),f2(x49481))
% 25.54/25.41 [4949]~E(x49492,x49493)+~P68(x49491)+E(f862(f862(f3(x49491),x49492),x49493),f2(x49491))
% 25.54/25.41 [4962]~P144(x49621)+~E(x49623,f2(x49621))+E(f862(f862(f73(x49621),x49622),x49623),x49622)
% 25.54/25.41 [4979]~P143(x49791)+~E(x49793,f2(x49791))+E(f862(f862(f74(x49791),x49792),x49793),f2(x49791))
% 25.54/25.41 [4980]~P143(x49801)+~E(x49802,f2(x49801))+E(f862(f862(f74(x49801),x49802),x49803),f2(x49801))
% 25.54/25.41 [5001]~E(x50013,f106(x50011))+~E(x50012,f106(x50011))+E(f862(f862(f127(x50011),x50012),x50013),f106(x50011))
% 25.54/25.41 [5002]~E(x50023,f106(x50021))+~E(x50022,f106(x50021))+E(f862(f862(f127(x50021),x50022),x50023),f106(x50021))
% 25.54/25.41 [5092]~P144(x50922)+E(x50921,f2(x50922))+~E(f862(f862(f73(x50922),x50923),x50921),x50923)
% 25.54/25.41 [5093]~P68(x50931)+~E(x50932,f862(f72(x50931),x50933))+E(f862(f862(f73(x50931),x50932),x50933),f2(x50931))
% 25.54/25.41 [5100]E(x51001,f106(x51002))+E(x51003,f2(a924))+~E(f862(f862(f168(x51002),x51003),x51001),f106(x51002))
% 25.54/25.41 [5110]~P59(x51103)+E(x51101,x51102)+~E(f862(f862(f3(x51103),x51101),x51102),f2(x51103))
% 25.54/25.41 [5111]~P68(x51113)+E(x51111,x51112)+~E(f862(f862(f3(x51113),x51111),x51112),f2(x51113))
% 25.54/25.41 [5124]~P141(x51242)+E(x51241,f2(x51242))+~E(f862(f862(f236(x51242),x51241),x51243),f2(x51242))
% 25.54/25.41 [5125]~P95(x51252)+E(x51251,f181(x51252))+~E(f862(f862(f103(x51252),x51253),x51251),f181(x51252))
% 25.54/25.41 [5126]~P95(x51262)+E(x51261,f181(x51262))+~E(f862(f862(f103(x51262),x51261),x51263),f181(x51262))
% 25.54/25.41 [5127]~P94(x51272)+E(x51271,f234(x51272))+~E(f862(f862(f94(x51272),x51273),x51271),f234(x51272))
% 25.54/25.41 [5128]~P94(x51282)+E(x51281,f234(x51282))+~E(f862(f862(f94(x51282),x51281),x51283),f234(x51282))
% 25.54/25.41 [5199]~P68(x51992)+E(x51991,f862(f72(x51992),x51993))+~E(f862(f862(f73(x51992),x51991),x51993),f2(x51992))
% 25.54/25.41 [5200]~P68(x52001)+E(f862(f72(x52001),x52002),x52003)+~E(f862(f862(f73(x52001),x52002),x52003),f2(x52001))
% 25.54/25.41 [5201]~E(x52012,x52013)+~P2(x52011)+P1(f862(f862(f84(x52011),x52012),x52013))
% 25.54/25.41 [5202]~E(x52022,x52023)+~P110(x52021)+P1(f862(f862(f227(x52021),x52022),x52023))
% 25.54/25.41 [5203]~E(x52032,x52033)+~P91(x52031)+P1(f862(f862(f227(x52031),x52032),x52033))
% 25.54/25.41 [5204]~E(x52042,x52043)+~P110(x52041)+P1(f862(f862(f227(x52041),x52042),x52043))
% 25.54/25.41 [5205]~E(x52052,x52053)+~P110(x52051)+P1(f862(f862(f227(x52051),x52052),x52053))
% 25.54/25.41 [5303]~P113(x53031)+~E(x53032,f862(f72(x53031),x53033))+E(f862(f862(f74(x53031),x53032),x53032),f862(f862(f74(x53031),x53033),x53033))
% 25.54/25.41 [5311]~P109(x53111)+~P11(x53111,x53113)+P11(x53111,f862(f862(f168(x53111),x53112),x53113))
% 25.54/25.41 [5312]~P109(x53121)+~P11(x53121,x53123)+P11(x53121,f862(f862(f131(x53121),x53122),x53123))
% 25.54/25.41 [5347]E(x53471,x53472)+E(x53473,f2(a924))+~E(f862(f862(f74(a924),x53473),x53471),f862(f862(f74(a924),x53473),x53472))
% 25.54/25.41 [5348]E(x53481,x53482)+E(x53483,f2(a924))+~E(f862(f862(f74(a924),x53483),x53481),f862(f862(f74(a924),x53483),x53482))
% 25.54/25.41 [5349]E(x53491,x53492)+E(x53493,f2(a924))+~E(f862(f862(f74(a924),x53491),x53493),f862(f862(f74(a924),x53492),x53493))
% 25.54/25.41 [5429]~E(x54292,x54293)+~P110(x54291)+E(f296(x54291,x54292,x54293),f862(f862(f301(x54291),x54292),f181(f932(x54291,a921))))
% 25.54/25.41 [5462]E(x54621,x54622)+~P2(x54623)+~P1(f862(f862(f84(x54623),x54621),x54622))
% 25.54/25.41 [5468]~E(x54681,x54682)+~P109(x54683)+~P1(f862(f862(f228(x54683),x54681),x54682))
% 25.54/25.41 [5469]~E(x54691,x54692)+~P109(x54693)+~P1(f862(f862(f228(x54693),x54691),x54692))
% 25.54/25.41 [5470]~E(x54701,x54702)+~P110(x54703)+~P1(f862(f862(f228(x54703),x54701),x54702))
% 25.54/25.41 [5471]~E(x54711,x54712)+~P110(x54713)+~P1(f862(f862(f228(x54713),x54711),x54712))
% 25.54/25.41 [5472]~E(x54721,x54722)+~P110(x54723)+~P1(f862(f862(f228(x54723),x54721),x54722))
% 25.54/25.41 [5473]~E(x54731,x54732)+~P109(x54733)+~P1(f862(f862(f228(x54733),x54731),x54732))
% 25.54/25.41 [5474]~E(x54741,x54742)+~P110(x54743)+~P1(f862(f862(f228(x54743),x54741),x54742))
% 25.54/25.41 [5485]~P110(x54851)+E(f862(f295(x54851,x54852),x54853),f181(f932(x54851,a921)))+P1(f862(f862(f228(x54851),x54852),x54853))
% 25.54/25.41 [5486]~P110(x54861)+E(f862(f295(x54861,x54862),x54863),f181(f932(x54861,a921)))+P1(f862(f862(f228(x54861),x54862),x54863))
% 25.54/25.41 [5534]~P110(x55341)+E(f297(x55341,x55342,x55343),f181(f932(x55341,a921)))+P1(f862(f862(f228(x55341),x55342),x55343))
% 25.54/25.41 [5535]~P110(x55351)+E(f296(x55351,x55352,x55353),f181(f932(x55351,a921)))+P1(f862(f862(f227(x55351),x55352),x55353))
% 25.54/25.41 [5536]~P110(x55361)+E(f181(f932(x55361,a921)),f297(x55361,x55362,x55363))+P1(f862(f862(f228(x55361),x55362),x55363))
% 25.54/25.41 [5537]~P110(x55371)+E(f181(f932(x55371,a921)),f296(x55371,x55372,x55373))+P1(f862(f862(f227(x55371),x55372),x55373))
% 25.54/25.41 [5546]~P103(x55461)+~E(f862(f862(f103(x55461),x55462),x55463),x55463)+P1(f862(f862(f227(x55461),x55462),x55463))
% 25.54/25.41 [5547]~P104(x55471)+~E(f862(f862(f94(x55471),x55472),x55473),x55472)+P1(f862(f862(f227(x55471),x55472),x55473))
% 25.54/25.41 [5548]~P109(x55481)+~E(f862(f862(f225(x55481),x55482),x55483),x55482)+P1(f862(f862(f227(x55481),x55482),x55483))
% 25.54/25.41 [5549]~P109(x55491)+~E(f862(f862(f226(x55491),x55492),x55493),x55493)+P1(f862(f862(f227(x55491),x55492),x55493))
% 25.54/25.41 [5567]~P109(x55671)+P11(x55671,x55672)+~P11(x55671,f862(f862(f144(x55671),x55673),x55672))
% 25.54/25.41 [5568]~P109(x55681)+P11(x55681,x55682)+~P11(x55681,f862(f862(f144(x55681),x55683),x55682))
% 25.54/25.41 [5569]~P109(x55691)+P11(x55691,x55692)+~P11(x55691,f862(f862(f127(x55691),x55693),x55692))
% 25.54/25.41 [5570]~P109(x55701)+P11(x55701,x55702)+~P11(x55701,f862(f862(f127(x55701),x55702),x55703))
% 25.54/25.41 [5575]~P61(x55751)+~E(f38(x55751,x55753,x55752),f2(x55751))+P1(f862(f862(f278(x55751),x55752),x55753))
% 25.54/25.41 [5636]~P109(x56361)+P1(f862(f862(f227(x56361),x56363),x56362))+P1(f862(f862(f227(x56361),x56362),x56363))
% 25.54/25.41 [5637]~P109(x56371)+P1(f862(f862(f227(x56371),x56373),x56372))+P1(f862(f862(f227(x56371),x56372),x56373))
% 25.54/25.41 [5638]~P109(x56381)+P1(f862(f862(f228(x56381),x56383),x56382))+P1(f862(f862(f227(x56381),x56382),x56383))
% 25.54/25.41 [5639]~P109(x56391)+P1(f862(f862(f228(x56391),x56393),x56392))+P1(f862(f862(f227(x56391),x56392),x56393))
% 25.54/25.41 [5640]~P109(x56401)+P1(f862(f862(f228(x56401),x56403),x56402))+P1(f862(f862(f227(x56401),x56402),x56403))
% 25.54/25.41 [5641]~P109(x56411)+P1(f862(f862(f228(x56411),x56413),x56412))+P1(f862(f862(f227(x56411),x56412),x56413))
% 25.54/25.41 [5642]~P109(x56421)+P1(f862(f862(f228(x56421),x56423),x56422))+P1(f862(f862(f227(x56421),x56422),x56423))
% 25.54/25.41 [5679]~P103(x56791)+E(f862(f862(f103(x56791),x56792),x56793),x56792)+~P1(f862(f862(f227(x56791),x56793),x56792))
% 25.54/25.41 [5680]~P103(x56801)+E(f862(f862(f103(x56801),x56802),x56803),x56803)+~P1(f862(f862(f227(x56801),x56802),x56803))
% 25.54/25.41 [5681]~P103(x56811)+E(f862(f862(f103(x56811),x56812),x56813),x56813)+~P1(f862(f862(f227(x56811),x56812),x56813))
% 25.54/25.41 [5682]~P104(x56821)+E(f862(f862(f94(x56821),x56822),x56823),x56823)+~P1(f862(f862(f227(x56821),x56823),x56822))
% 25.54/25.41 [5683]~P104(x56831)+E(f862(f862(f94(x56831),x56832),x56833),x56832)+~P1(f862(f862(f227(x56831),x56832),x56833))
% 25.54/25.41 [5684]~P104(x56841)+E(f862(f862(f94(x56841),x56842),x56843),x56842)+~P1(f862(f862(f227(x56841),x56842),x56843))
% 25.54/25.41 [5685]~P109(x56851)+E(f862(f862(f225(x56851),x56852),x56853),x56853)+~P1(f862(f862(f227(x56851),x56853),x56852))
% 25.54/25.41 [5686]~P109(x56861)+E(f862(f862(f225(x56861),x56862),x56863),x56862)+~P1(f862(f862(f227(x56861),x56862),x56863))
% 25.54/25.41 [5687]~P109(x56871)+E(f862(f862(f225(x56871),x56872),x56873),x56872)+~P1(f862(f862(f227(x56871),x56872),x56873))
% 25.54/25.41 [5688]~P109(x56881)+E(f862(f862(f226(x56881),x56882),x56883),x56882)+~P1(f862(f862(f227(x56881),x56883),x56882))
% 25.54/25.41 [5689]~P109(x56891)+E(f862(f862(f226(x56891),x56892),x56893),x56893)+~P1(f862(f862(f227(x56891),x56892),x56893))
% 25.54/25.41 [5690]~P109(x56901)+E(f862(f862(f226(x56901),x56902),x56903),x56903)+~P1(f862(f862(f227(x56901),x56902),x56903))
% 25.54/25.41 [5697]~P121(x56972)+E(x56971,f2(x56972))+E(f862(f862(f281(x56972),f862(f72(x56972),x56973)),f862(f72(x56972),x56971)),f862(f862(f281(x56972),x56973),x56971))
% 25.54/25.41 [5703]~P61(x57031)+E(f38(x57031,x57032,x57033),f2(x57031))+~P1(f862(f862(f278(x57031),x57033),x57032))
% 25.54/25.41 [5704]~P61(x57041)+E(f38(x57041,x57042,x57043),f2(x57041))+~P1(f862(f862(f278(x57041),x57043),x57042))
% 25.54/25.41 [5752]~P110(x57521)+E(f862(f295(x57521,x57522),x57523),f181(f932(x57521,a921)))+~P1(f862(f862(f227(x57521),x57523),x57522))
% 25.54/25.41 [5785]~P110(x57851)+E(f298(x57851,x57852,x57853),f181(f932(x57851,a921)))+~P1(f862(f862(f227(x57851),x57853),x57852))
% 25.54/25.41 [5786]~P110(x57861)+E(f297(x57861,x57862,x57863),f181(f932(x57861,a921)))+~P1(f862(f862(f227(x57861),x57863),x57862))
% 25.54/25.41 [5787]~P110(x57871)+E(f296(x57871,x57872,x57873),f181(f932(x57871,a921)))+~P1(f862(f862(f228(x57871),x57873),x57872))
% 25.54/25.41 [5839]~E(f862(f862(f3(a924),x58391),x58393),x58392)+E(x58391,f862(f862(f73(a924),x58392),x58393))+~P1(f862(f862(f227(a924),x58393),x58391))
% 25.54/25.41 [5840]~E(x58401,f862(f862(f73(a924),x58403),x58402))+E(f862(f862(f3(a924),x58401),x58402),x58403)+~P1(f862(f862(f227(a924),x58402),x58401))
% 25.54/25.41 [5885]~P1(f862(x58851,x58853))+P1(f862(x58851,f331(x58851,x58852)))+~P1(f862(f862(f227(a924),x58853),x58852))
% 25.54/25.41 [5886]~P1(f862(x58861,x58863))+P1(f862(x58861,f343(x58861,x58862)))+~P1(f862(f862(f228(a924),x58863),x58862))
% 25.54/25.41 [5893]~P110(x58931)+~E(f862(f295(x58931,x58932),x58933),f181(f932(x58931,a921)))+~P1(f862(f862(f228(x58931),x58932),x58933))
% 25.54/25.41 [5894]~P110(x58941)+~E(f862(f295(x58941,x58942),x58943),f181(f932(x58941,a921)))+~P1(f862(f862(f228(x58941),x58942),x58943))
% 25.54/25.41 [5898]~P91(x58981)+~P1(f862(f862(f228(x58981),x58982),x58983))+P1(f862(f862(f227(x58981),x58982),x58983))
% 25.54/25.41 [5899]~P91(x58991)+~P1(f862(f862(f228(x58991),x58992),x58993))+P1(f862(f862(f227(x58991),x58992),x58993))
% 25.54/25.41 [5900]~P110(x59001)+~P1(f862(f862(f228(x59001),x59002),x59003))+P1(f862(f862(f227(x59001),x59002),x59003))
% 25.54/25.41 [5901]~P110(x59011)+~P1(f862(f862(f228(x59011),x59012),x59013))+P1(f862(f862(f227(x59011),x59012),x59013))
% 25.54/25.41 [6019]~P110(x60191)+~E(f297(x60191,x60192,x60193),f181(f932(x60191,a921)))+~P1(f862(f862(f228(x60191),x60192),x60193))
% 25.54/25.41 [6020]~P110(x60201)+~E(f296(x60201,x60202,x60203),f181(f932(x60201,a921)))+~P1(f862(f862(f227(x60201),x60202),x60203))
% 25.54/25.41 [6021]~P110(x60211)+~E(f181(f932(x60211,a921)),f297(x60211,x60212,x60213))+~P1(f862(f862(f228(x60211),x60212),x60213))
% 25.54/25.41 [6022]~P110(x60221)+~E(f181(f932(x60221,a921)),f296(x60221,x60222,x60223))+~P1(f862(f862(f227(x60221),x60222),x60223))
% 25.54/25.41 [6032]P1(f862(x60321,x60322))+~P1(f862(x60321,f344(x60321,x60323)))+~P1(f862(f862(f227(a924),x60322),x60323))
% 25.54/25.41 [6033]P1(f862(x60331,x60332))+~P1(f862(x60331,f347(x60331,x60333)))+~P1(f862(f862(f228(a924),x60332),x60333))
% 25.54/25.41 [6041]~E(x60411,f862(a105,x60413))+P1(f862(f862(f228(a924),x60411),f862(a105,x60412)))+~P1(f862(f862(f228(a924),x60413),x60412))
% 25.54/25.41 [6060]E(x60601,x60602)+~E(f862(f862(f74(a924),x60603),x60601),f862(f862(f74(a924),x60603),x60602))+~P1(f862(f862(f228(a924),f2(a924)),x60603))
% 25.54/25.41 [6120]E(f862(x61201,f335(x61201,x61202,x61203)),f71(a924))+~E(f862(f862(f8(x61203,a924),x61201),x61202),f71(a924))+~P1(f862(f54(x61203),x61202))
% 25.54/25.41 [6137]~P3(x61371)+P1(f862(f862(f227(x61371),x61372),f30(x61371,x61373)))+~P1(f862(f862(f321(x61371),x61372),x61373))
% 25.54/25.41 [6160]~P91(x61601)+~P1(f862(f862(f228(x61601),x61603),x61602))+~P1(f862(f862(f227(x61601),x61602),x61603))
% 25.54/25.41 [6161]~P91(x61611)+~P1(f862(f862(f228(x61611),x61613),x61612))+~P1(f862(f862(f228(x61611),x61612),x61613))
% 25.54/25.41 [6162]~P91(x61621)+~P1(f862(f862(f228(x61621),x61623),x61622))+~P1(f862(f862(f228(x61621),x61622),x61623))
% 25.54/25.41 [6163]~P91(x61631)+~P1(f862(f862(f228(x61631),x61633),x61632))+~P1(f862(f862(f228(x61631),x61632),x61633))
% 25.54/25.41 [6164]~P91(x61641)+~P1(f862(f862(f228(x61641),x61643),x61642))+~P1(f862(f862(f228(x61641),x61642),x61643))
% 25.54/25.41 [6165]~P109(x61651)+~P1(f862(f862(f228(x61651),x61653),x61652))+~P1(f862(f862(f227(x61651),x61652),x61653))
% 25.54/25.41 [6166]~P109(x61661)+~P1(f862(f862(f228(x61661),x61663),x61662))+~P1(f862(f862(f227(x61661),x61662),x61663))
% 25.54/25.41 [6167]~P109(x61671)+~P1(f862(f862(f228(x61671),x61673),x61672))+~P1(f862(f862(f227(x61671),x61672),x61673))
% 25.54/25.41 [6168]~P109(x61681)+~P1(f862(f862(f228(x61681),x61683),x61682))+~P1(f862(f862(f228(x61681),x61682),x61683))
% 25.54/25.41 [6169]~P110(x61691)+~P1(f862(f862(f228(x61691),x61693),x61692))+~P1(f862(f862(f228(x61691),x61692),x61693))
% 25.54/25.41 [6194]~E(f862(x61942,f336(x61942,x61943,x61941)),f2(a924))+E(f862(f862(f8(x61941,a924),x61942),x61943),f2(a924))+~P1(f862(f54(x61941),x61943))
% 25.54/25.41 [6195]~E(f862(x61952,f914(x61952,x61953,x61951)),f71(a924))+E(f862(f862(f11(x61951,a924),x61952),x61953),f71(a924))+~P1(f862(f54(x61951),x61953))
% 25.54/25.41 [6211]~P108(x62111)+~P1(f862(f862(f228(x62111),x62113),x62112))+P1(f862(f862(f321(x62111),x62112),f862(f293(x62111),x62113)))
% 25.54/25.41 [6212]~P108(x62121)+~P1(f862(f862(f227(x62121),x62123),x62122))+P1(f862(f862(f321(x62121),x62122),f862(f274(x62121),x62123)))
% 25.54/25.41 [6213]~P108(x62131)+~P1(f862(f862(f227(x62131),x62132),x62133))+P1(f862(f862(f321(x62131),x62132),f862(f294(x62131),x62133)))
% 25.54/25.41 [6214]~P108(x62141)+~P1(f862(f862(f228(x62141),x62142),x62143))+P1(f862(f862(f321(x62141),x62142),f862(f292(x62141),x62143)))
% 25.54/25.41 [6227]E(f862(x62271,f333(x62271,x62272,x62273)),f862(a105,f2(a924)))+~E(f862(f862(f8(x62273,a924),x62271),x62272),f862(a105,f2(a924)))+~P1(f862(f54(x62273),x62272))
% 25.54/25.41 [6308]~P3(x63081)+~P1(f862(f862(f321(x63081),x63083),x63082))+P1(f862(f862(f227(x63081),f31(x63081,x63082)),x63083))
% 25.54/25.41 [6328]~P1(f862(f862(f227(a924),x63281),x63283))+P1(f862(f862(f227(a924),x63281),x63282))+~P1(f862(f862(f227(a924),x63283),x63282))
% 25.54/25.41 [6329]~P1(f862(f862(f227(a1),x63291),x63293))+P1(f862(f862(f227(a1),x63291),x63292))+~P1(f862(f862(f227(a1),x63293),x63292))
% 25.54/25.41 [6349]~P108(x63491)+~P1(f862(f862(f321(x63491),x63493),f862(f274(x63491),x63492)))+P1(f862(f862(f227(x63491),x63492),x63493))
% 25.54/25.41 [6350]~P108(x63501)+~P1(f862(f862(f321(x63501),x63502),f862(f294(x63501),x63503)))+P1(f862(f862(f227(x63501),x63502),x63503))
% 25.54/25.41 [6351]~P108(x63511)+~P1(f862(f862(f321(x63511),x63513),f862(f293(x63511),x63512)))+P1(f862(f862(f228(x63511),x63512),x63513))
% 25.54/25.41 [6352]~P108(x63521)+~P1(f862(f862(f321(x63521),x63522),f862(f292(x63521),x63523)))+P1(f862(f862(f228(x63521),x63522),x63523))
% 25.54/25.41 [6427]~P1(f862(x64271,x64272))+P1(f862(x64271,f792(x64271)))+~P1(f862(f862(f321(x64273),x64272),f234(f932(x64273,a921))))
% 25.54/25.41 [6571]~P66(x65711)+P1(f862(f862(f228(x65711),f2(x65711)),f363(x65713,x65712,x65711)))+P1(f862(f862(f227(x65711),x65712),x65713))
% 25.54/25.41 [6572]~P67(x65721)+P1(f862(f862(f228(x65721),f2(x65721)),f436(x65723,x65722,x65721)))+P1(f862(f862(f227(x65721),x65722),x65723))
% 25.54/25.41 [6640]~P78(x66401)+~P1(f862(f862(f227(x66401),x66403),f862(f72(x66401),x66402)))+P1(f862(f862(f227(x66401),x66402),f862(f72(x66401),x66403)))
% 25.54/25.41 [6641]~P78(x66411)+~P1(f862(f862(f227(x66411),x66413),f862(f72(x66411),x66412)))+P1(f862(f862(f227(x66411),x66412),f862(f72(x66411),x66413)))
% 25.54/25.41 [6642]~P78(x66421)+~P1(f862(f862(f228(x66421),x66423),f862(f72(x66421),x66422)))+P1(f862(f862(f228(x66421),x66422),f862(f72(x66421),x66423)))
% 25.54/25.41 [6643]~P78(x66431)+~P1(f862(f862(f228(x66431),x66433),f862(f72(x66431),x66432)))+P1(f862(f862(f228(x66431),x66432),f862(f72(x66431),x66433)))
% 25.54/25.41 [6655]~P1(f862(f862(f228(a924),x66551),x66553))+~P1(f862(f862(f228(a924),x66553),x66552))+P1(f862(f862(f228(a924),f862(a105,x66551)),x66552))
% 25.54/25.41 [6683]~P127(x66831)+P1(f862(f862(f227(x66831),f862(f93(x66831),x66832)),f862(f93(x66831),x66833)))+~P1(f862(f862(f227(a924),x66832),x66833))
% 25.54/25.41 [6684]~P112(x66841)+P1(f862(f862(f227(x66841),f862(f95(x66841),x66842)),f862(f95(x66841),x66843)))+~P1(f862(f862(f227(a1),x66842),x66843))
% 25.54/25.41 [6685]~P127(x66851)+P1(f862(f862(f228(x66851),f862(f93(x66851),x66852)),f862(f93(x66851),x66853)))+~P1(f862(f862(f228(a924),x66852),x66853))
% 25.54/25.41 [6686]~P112(x66861)+P1(f862(f862(f228(x66861),f862(f95(x66861),x66862)),f862(f95(x66861),x66863)))+~P1(f862(f862(f228(a1),x66862),x66863))
% 25.54/25.41 [6687]~P127(x66871)+P1(f862(f862(f228(x66871),f862(f93(x66871),x66872)),f862(f93(x66871),x66873)))+~P1(f862(f862(f228(a924),x66872),x66873))
% 25.54/25.41 [6693]~P109(x66931)+E(f862(f862(f103(f932(x66931,a921)),f862(f292(x66931),x66932)),f862(f295(x66931,x66932),x66933)),f862(f292(x66931),x66933))+~P1(f862(f862(f227(x66931),x66932),x66933))
% 25.54/25.41 [6723]~P78(x67231)+~P1(f862(f862(f227(x67231),x67233),x67232))+P1(f862(f862(f227(x67231),f862(f72(x67231),x67232)),f862(f72(x67231),x67233)))
% 25.54/25.41 [6724]~P78(x67241)+~P1(f862(f862(f227(x67241),x67243),x67242))+P1(f862(f862(f227(x67241),f862(f72(x67241),x67242)),f862(f72(x67241),x67243)))
% 25.54/25.41 [6725]~P96(x67251)+~P1(f862(f862(f227(x67251),x67253),x67252))+P1(f862(f862(f227(x67251),f862(f72(x67251),x67252)),f862(f72(x67251),x67253)))
% 25.54/25.41 [6726]~P96(x67261)+~P1(f862(f862(f227(x67261),x67263),x67262))+P1(f862(f862(f227(x67261),f862(f72(x67261),x67262)),f862(f72(x67261),x67263)))
% 25.54/25.41 [6727]~P78(x67271)+~P1(f862(f862(f228(x67271),x67273),x67272))+P1(f862(f862(f228(x67271),f862(f72(x67271),x67272)),f862(f72(x67271),x67273)))
% 25.54/25.41 [6760]~P109(x67601)+E(f862(f862(f103(f932(x67601,a921)),f862(f294(x67601),x67602)),f298(x67601,x67602,x67603)),f862(f292(x67601),x67603))+~P1(f862(f862(f228(x67601),x67602),x67603))
% 25.54/25.41 [6761]~P109(x67611)+E(f862(f862(f103(f932(x67611,a921)),f862(f294(x67611),x67612)),f297(x67611,x67612,x67613)),f862(f294(x67611),x67613))+~P1(f862(f862(f227(x67611),x67612),x67613))
% 25.54/25.41 [6762]~P109(x67621)+E(f862(f862(f103(f932(x67621,a921)),f862(f292(x67621),x67622)),f296(x67621,x67622,x67623)),f862(f294(x67621),x67623))+~P1(f862(f862(f227(x67621),x67622),x67623))
% 25.54/25.41 [6795]~P109(x67951)+E(f862(f862(f103(f932(x67951,a921)),f862(f295(x67951,x67952),x67953)),f862(f274(x67951),x67953)),f862(f274(x67951),x67952))+~P1(f862(f862(f227(x67951),x67952),x67953))
% 25.54/25.41 [6948]~P109(x69481)+E(f862(f862(f103(f932(x69481,a921)),f298(x69481,x69482,x69483)),f862(f274(x69481),x69483)),f862(f293(x69481),x69482))+~P1(f862(f862(f228(x69481),x69482),x69483))
% 25.54/25.41 [6949]~P109(x69491)+E(f862(f862(f103(f932(x69491,a921)),f297(x69491,x69492,x69493)),f862(f293(x69491),x69493)),f862(f293(x69491),x69492))+~P1(f862(f862(f227(x69491),x69492),x69493))
% 25.54/25.41 [6950]~P109(x69501)+E(f862(f862(f103(f932(x69501,a921)),f296(x69501,x69502,x69503)),f862(f293(x69501),x69503)),f862(f274(x69501),x69502))+~P1(f862(f862(f227(x69501),x69502),x69503))
% 25.54/25.41 [6970]P1(f862(x69701,x69702))+~P1(f862(f862(f227(a924),x69702),x69703))+P1(f862(f862(f321(a924),f344(x69701,x69703)),f296(a924,f2(a924),x69703)))
% 25.54/25.41 [7004]E(x70041,x70042)+~E(f862(f862(f157(x70043),x70041),f658(x70043,x70042,x70041)),f862(f862(f157(x70043),x70042),f658(x70043,x70042,x70041)))+~E(f862(f182(f925(x70043)),x70041),f862(f182(f925(x70043)),x70042))
% 25.54/25.41 [7009]~E(x70093,f862(f862(f29(a924),x70091),x70092))+~P1(f862(f862(f228(a924),f2(a924)),x70092))+P1(f862(f862(f228(a924),x70091),f862(f862(f74(a924),x70092),f862(a105,x70093))))
% 25.54/25.41 [7025]~P1(f862(x70251,x70253))+~P1(f862(f862(f227(a924),x70253),x70252))+P1(f862(f862(f321(a924),f331(x70251,x70252)),f296(a924,f2(a924),x70252)))
% 25.54/25.41 [7064]~P1(f862(x70641,x70643))+P1(f862(x70641,f345(x70641,x70642)))+~P1(f862(f862(f321(a924),x70643),f296(a924,f2(a924),x70642)))
% 25.54/25.41 [7083]~P127(x70833)+~P1(f862(f862(f227(x70833),f862(f93(x70833),x70831)),f862(f93(x70833),x70832)))+P1(f862(f862(f227(a924),x70831),x70832))
% 25.54/25.41 [7084]~P112(x70843)+~P1(f862(f862(f227(x70843),f862(f95(x70843),x70841)),f862(f95(x70843),x70842)))+P1(f862(f862(f227(a1),x70841),x70842))
% 25.54/25.41 [7085]~P127(x70853)+~P1(f862(f862(f228(x70853),f862(f93(x70853),x70851)),f862(f93(x70853),x70852)))+P1(f862(f862(f228(a924),x70851),x70852))
% 25.54/25.41 [7086]~P127(x70863)+~P1(f862(f862(f228(x70863),f862(f93(x70863),x70861)),f862(f93(x70863),x70862)))+P1(f862(f862(f228(a924),x70861),x70862))
% 25.54/25.41 [7087]~P112(x70873)+~P1(f862(f862(f228(x70873),f862(f95(x70873),x70871)),f862(f95(x70873),x70872)))+P1(f862(f862(f228(a1),x70871),x70872))
% 25.54/25.41 [7103]~P127(x71031)+~P1(f862(f862(f228(x71031),f71(x71031)),x71032))+P1(f862(f862(f228(x71031),f71(x71031)),f862(f862(f236(x71031),x71032),f862(a105,x71033))))
% 25.54/25.41 [7106]~P78(x71061)+~P1(f862(f862(f227(x71061),f862(f72(x71061),x71063)),f862(f72(x71061),x71062)))+P1(f862(f862(f227(x71061),x71062),x71063))
% 25.54/25.41 [7107]~P96(x71071)+~P1(f862(f862(f227(x71071),f862(f72(x71071),x71073)),f862(f72(x71071),x71072)))+P1(f862(f862(f227(x71071),x71072),x71073))
% 25.54/25.41 [7108]~P78(x71081)+~P1(f862(f862(f228(x71081),f862(f72(x71081),x71083)),f862(f72(x71081),x71082)))+P1(f862(f862(f228(x71081),x71082),x71083))
% 25.54/25.41 [7132]P1(f862(x71321,x71322))+~P1(f862(x71321,f346(x71321,x71323)))+~P1(f862(f862(f321(a924),x71322),f296(a924,f2(a924),x71323)))
% 25.54/25.41 [7152]~P66(x71521)+P1(f862(f862(f228(x71521),f363(x71523,x71522,x71521)),f71(x71521)))+P1(f862(f862(f227(x71521),x71522),x71523))
% 25.54/25.41 [7172]~E(f38(a924,x71723,x71722),f38(a924,x71721,x71722))+E(f862(f862(f73(a924),x71721),f862(f862(f74(a924),x71722),f438(x71721,x71722,x71723))),x71723)+~P1(f862(f862(f227(a924),x71721),x71723))
% 25.54/25.41 [7227]E(f862(f862(f8(x72271,a924),x72272),x72273),f2(a924))+~P1(f862(f54(x72271),x72273))+P1(f862(f862(f321(x72271),f336(x72272,x72273,x72271)),x72273))
% 25.54/25.41 [7228]E(f862(f862(f11(x72281,a924),x72282),x72283),f71(a924))+~P1(f862(f54(x72281),x72283))+P1(f862(f862(f321(x72281),f914(x72282,x72283,x72281)),x72283))
% 25.54/25.41 [7250]~P109(x72501)+~P1(f862(f862(f227(x72501),x72503),x72502))+P1(f862(f862(f227(f932(x72501,a921)),f862(f293(x72501),x72502)),f862(f293(x72501),x72503)))
% 25.54/25.41 [7251]~P110(x72511)+~P1(f862(f862(f227(x72511),x72512),x72513))+P1(f862(f862(f227(f932(x72511,a921)),f862(f294(x72511),x72512)),f862(f294(x72511),x72513)))
% 25.54/25.41 [7252]~P110(x72521)+~P1(f862(f862(f227(x72521),x72523),x72522))+P1(f862(f862(f227(f932(x72521,a921)),f862(f274(x72521),x72522)),f862(f274(x72521),x72523)))
% 25.54/25.41 [7253]~P109(x72531)+~P1(f862(f862(f227(x72531),x72532),x72533))+P1(f862(f862(f227(f932(x72531,a921)),f862(f292(x72531),x72532)),f862(f292(x72531),x72533)))
% 25.54/25.41 [7254]~P109(x72541)+~P1(f862(f862(f228(x72541),x72542),x72543))+P1(f862(f862(f228(f932(x72541,a921)),f862(f292(x72541),x72542)),f862(f292(x72541),x72543)))
% 25.54/25.41 [7265]~P3(x72651)+P1(f862(f862(f227(x72651),x72652),f31(x72651,x72653)))+P1(f862(f862(f321(x72651),f368(x72653,x72652,x72651)),x72653))
% 25.54/25.41 [7266]~P3(x72661)+P1(f862(f862(f227(x72661),x72662),f31(x72661,x72663)))+P1(f862(f862(f321(x72661),f498(x72662,x72663,x72661)),x72663))
% 25.54/25.41 [7272]~P78(x72721)+P1(f862(f862(f227(x72721),f862(f862(f3(x72721),x72722),x72723)),f2(x72721)))+~P1(f862(f862(f227(x72721),x72722),x72723))
% 25.54/25.41 [7273]~P78(x72731)+P1(f862(f862(f228(x72731),f862(f862(f3(x72731),x72732),x72733)),f2(x72731)))+~P1(f862(f862(f228(x72731),x72732),x72733))
% 25.54/25.41 [7315]P1(f862(x73151,x73152))+P1(f862(f862(f227(a924),f346(x73151,x73153)),x73153))+~P1(f862(f862(f321(a924),x73152),f296(a924,f2(a924),x73153)))
% 25.54/25.41 [7357]~E(f862(f862(f8(x73571,a924),x73572),x73573),f71(a924))+~P1(f862(f54(x73571),x73573))+P1(f862(f862(f321(x73571),f335(x73572,x73573,x73571)),x73573))
% 25.54/25.41 [7358]~P1(f862(x73581,x73583))+P1(f862(f862(f227(a924),f345(x73581,x73582)),x73582))+~P1(f862(f862(f321(a924),x73583),f296(a924,f2(a924),x73582)))
% 25.54/25.41 [7397]~P3(x73971)+P1(f862(f862(f321(x73971),f375(x73973,x73972,x73971)),x73972))+P1(f862(f862(f227(x73971),f30(x73971,x73972)),x73973))
% 25.54/25.41 [7398]~P3(x73981)+P1(f862(f862(f321(x73981),f502(x73983,x73982,x73981)),x73982))+P1(f862(f862(f227(x73981),f30(x73981,x73982)),x73983))
% 25.54/25.41 [7432]~E(f862(f862(f8(x74321,a924),x74322),x74323),f862(a105,f2(a924)))+~P1(f862(f54(x74321),x74323))+P1(f862(f862(f321(x74321),f333(x74322,x74323,x74321)),x74323))
% 25.54/25.41 [7444]E(x74441,f2(a924))+P1(f862(x74442,f38(a924,x74443,x74441)))+P1(f862(f862(f228(a924),f429(x74441,x74443,x74442)),x74441))
% 25.54/25.41 [7558]~P1(f862(x75581,x75582))+P1(f862(x75581,f38(a924,x75582,x75583)))+P1(f862(f862(f228(a924),f429(x75583,x75582,x75581)),x75583))
% 25.54/25.41 [7671]E(x76711,f106(x76712))+~P1(f862(f862(f321(f925(x76712)),x76711),f154(x76712,x76713)))+P1(f862(f862(f321(x76712),f696(x76713,x76711,x76712)),x76713))
% 25.54/25.41 [7695]~P109(x76951)+E(f862(f862(f103(f932(x76951,a921)),f862(f862(f301(x76951),x76952),f181(f932(x76951,a921)))),f298(x76951,x76952,x76953)),f862(f295(x76951,x76952),x76953))+~P1(f862(f862(f228(x76951),x76952),x76953))
% 25.54/25.41 [7716]~P109(x77161)+E(f862(f862(f103(f932(x77161,a921)),f862(f862(f301(x77161),x77162),f181(f932(x77161,a921)))),f297(x77161,x77162,x77163)),f296(x77161,x77162,x77163))+~P1(f862(f862(f227(x77161),x77162),x77163))
% 25.54/25.41 [7828]~P109(x78281)+P1(f862(f862(f227(x78281),x78282),x78283))+~P1(f862(f862(f227(f932(x78281,a921)),f862(f293(x78281),x78283)),f862(f293(x78281),x78282)))
% 25.54/25.41 [7829]~P110(x78291)+P1(f862(f862(f227(x78291),x78292),x78293))+~P1(f862(f862(f227(f932(x78291,a921)),f862(f274(x78291),x78293)),f862(f274(x78291),x78292)))
% 25.54/25.41 [7830]~P109(x78301)+P1(f862(f862(f227(x78301),x78302),x78303))+~P1(f862(f862(f227(f932(x78301,a921)),f862(f292(x78301),x78302)),f862(f292(x78301),x78303)))
% 25.54/25.41 [7831]~P110(x78311)+P1(f862(f862(f227(x78311),x78312),x78313))+~P1(f862(f862(f227(f932(x78311,a921)),f862(f294(x78311),x78312)),f862(f294(x78311),x78313)))
% 25.54/25.41 [7832]~P109(x78321)+P1(f862(f862(f228(x78321),x78322),x78323))+~P1(f862(f862(f228(f932(x78321,a921)),f862(f292(x78321),x78322)),f862(f292(x78321),x78323)))
% 25.54/25.41 [7855]~P78(x78551)+~P1(f862(f862(f227(x78551),f862(f862(f3(x78551),x78552),x78553)),f2(x78551)))+P1(f862(f862(f227(x78551),x78552),x78553))
% 25.54/25.41 [7856]~P78(x78561)+~P1(f862(f862(f228(x78561),f862(f862(f3(x78561),x78562),x78563)),f2(x78561)))+P1(f862(f862(f228(x78561),x78562),x78563))
% 25.54/25.41 [8011]E(x80111,f2(a924))+~E(f862(f135(a924,a924,f73(a924),x80112),x80113),f2(a924))+~P1(f862(f862(f321(a924),x80111),f862(f165(a924),x80113)))
% 25.54/25.41 [8015]~P3(x80151)+~P1(f862(f862(f227(x80151),f375(x80153,x80152,x80151)),x80153))+P1(f862(f862(f227(x80151),f30(x80151,x80152)),x80153))
% 25.54/25.41 [8016]~P3(x80161)+~P1(f862(f862(f227(x80161),f502(x80163,x80162,x80161)),x80163))+P1(f862(f862(f227(x80161),f30(x80161,x80162)),x80163))
% 25.54/25.41 [8173]P1(f862(f862(f227(a1),f2(a1)),f417(x81731,x81732,x81733)))+P1(f862(f862(x81732,f862(f862(f29(a1),x81731),x81733)),f38(a1,x81731,x81733)))+~P1(f862(f862(f228(a1),f2(a1)),x81733))
% 25.54/25.41 [8262]E(x82621,x82622)+~E(f862(f182(f925(x82623)),x82621),f862(f182(f925(x82623)),x82622))+~P1(f862(f862(f249(x82623,x82623,a921),a317),f670(x82623,x82621,x82622)))
% 25.54/25.41 [8335]~P35(x83352,x83353)+E(x83351,f181(f932(x83352,a921)))+~P1(f862(f862(f227(f932(x83352,a921)),x83351),f862(f276(x83352,x83352,x83353),x83351)))
% 25.54/25.41 [8366]~P67(x83661)+~P1(f862(f862(f227(x83661),x83662),f862(f862(f73(x83661),x83663),f436(x83663,x83662,x83661))))+P1(f862(f862(f227(x83661),x83662),x83663))
% 25.54/25.41 [8402]P50(x84021,x84022,x84023)+P1(f862(f862(f321(x84021),f579(x84023,x84022,x84021)),x84022))+P1(f862(f862(f321(f931(x84021,x84021)),f580(x84023,x84022,x84021)),x84023))
% 25.54/25.41 [8423]P1(f862(f862(x84232,f862(f862(f29(a1),x84231),x84233)),f38(a1,x84231,x84233)))+~P1(f862(f862(f228(a1),f2(a1)),x84233))+P1(f862(f862(f228(a1),f417(x84231,x84232,x84233)),x84233))
% 25.54/25.41 [8447]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x84471)),f862(f295(a924,x84472),x84473)),f181(f932(a924,a921)))+P1(f862(f862(f228(a924),x84471),x84473))+P1(f862(f862(f228(a924),x84472),x84473))
% 25.54/25.41 [8558]E(f862(f302(a924,a924,f862(f862(f9(a924,a924,a924),f3(a924)),x85581)),f862(f295(a924,x85582),x85583)),f862(f862(f301(a924),f2(a924)),f181(f932(a924,a921))))+P1(f862(f862(f228(a924),x85581),x85583))+~P1(f862(f862(f228(a924),x85582),x85583))
% 25.54/25.41 [8572]~P109(x85721)+E(f142(x85721,x85721,f7(x85721),x85722,x85723),x85723)+~P1(f862(f862(f321(x85721),x85722),f862(f165(x85721),x85723)))
% 25.54/25.41 [8585]P22(x85851,x85851,x85852,x85853)+~P1(f862(f54(x85851),x85853))+~P1(f862(f862(f227(f932(x85851,a921)),x85853),f862(f302(x85851,x85851,x85852),x85853)))
% 25.54/25.41 [8612]E(f862(f862(f73(a1),f862(f862(f74(a1),x86121),f418(x86122,x86123,x86121))),f417(x86122,x86123,x86121)),x86122)+P1(f862(f862(x86123,f862(f862(f29(a1),x86122),x86121)),f38(a1,x86122,x86121)))+~P1(f862(f862(f228(a1),f2(a1)),x86121))
% 25.54/25.41 [8852]~P1(f862(f862(x88521,f418(x88522,x88521,x88523)),f417(x88522,x88521,x88523)))+P1(f862(f862(x88521,f862(f862(f29(a1),x88522),x88523)),f38(a1,x88522,x88523)))+~P1(f862(f862(f228(a1),f2(a1)),x88523))
% 25.54/25.41 [8935]P23(x89351,x89352,x89353,f234(f932(x89351,a921)),f234(f932(x89352,a921)))+~P22(x89351,x89352,x89353,f234(f932(x89351,a921)))+~E(f862(f302(x89351,x89352,x89353),f234(f932(x89351,a921))),f234(f932(x89352,a921)))
% 25.54/25.41 [8936]P23(x89361,x89362,x89363,f234(f932(x89361,a921)),f234(f932(x89362,a921)))+~P22(x89361,x89362,x89363,f234(f932(x89361,a921)))+~E(f862(f302(x89361,x89362,x89363),f234(f932(x89361,a921))),f234(f932(x89362,a921)))
% 25.54/25.41 [9746]~P1(f862(f54(x97461),x97462))+~P1(f862(f862(f321(x97461),x97463),x97462))+P1(f862(f862(f228(a924),f862(f28(x97461),f862(f862(f3(f932(x97461,a921)),x97462),f862(f862(f301(x97461),x97463),f181(f932(x97461,a921)))))),f862(f28(x97461),x97462)))
% 25.54/25.41 [10100]P1(f862(x101001,x101002))+~P1(f862(x101001,f862(f87(x101003),f773(x101001,x101002,x101003))))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101003,f932(a920,a921))),f930(a920,x101003)),a921)),x101002),f862(f254(f932(f922(f930(a919,f932(x101003,f932(a920,a921))),f930(a920,x101003)),a921)),f88(x101003))))
% 25.54/25.41 [10340]P50(x103401,x103402,x103403)+~P1(f862(f862(f249(x103401,x103401,a921),f862(f862(f9(x103401,f932(x103401,a921),f932(x103401,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103401,a921),f932(x103401,a921)),x103401),f10(a921,a921,x103401)),f862(f862(f10(a921,f932(a921,a921),x103401),a318),f862(f862(f9(x103401,f932(x103401,a921),a921),f321(x103401)),x103402)))),f862(f862(f9(x103401,f932(x103401,a921),a921),f321(x103401)),x103402))),f580(x103403,x103402,x103401)))+P1(f862(f862(f321(x103401),f579(x103403,x103402,x103401)),x103402))
% 25.54/25.41 [5659]~P121(x56592)+E(x56591,f2(x56592))+E(f862(f862(f281(x56592),x56593),f862(f72(x56592),x56591)),f862(f72(x56592),f862(f862(f281(x56592),x56593),x56591)))
% 25.54/25.41 [5801]~E(x58013,f181(f932(x58011,a921)))+~E(x58012,f181(f932(x58011,a921)))+E(f862(f862(f103(f932(x58011,a921)),x58012),x58013),f181(f932(x58011,a921)))
% 25.54/25.41 [5858]~E(x58583,f2(a924))+~P1(f862(x58581,f2(a924)))+P1(f862(x58581,f862(f862(f29(a924),x58582),x58583)))
% 25.54/25.41 [5859]~E(x58593,f2(a924))+~P1(f862(x58591,f2(a924)))+P1(f862(x58591,f862(f862(f29(a924),x58592),x58593)))
% 25.54/25.41 [6011]~P67(x60112)+E(x60111,f2(x60112))+E(f862(f862(f281(x60112),f862(f69(x60112),x60113)),f862(f69(x60112),x60111)),f862(f69(x60112),f862(f862(f281(x60112),x60113),x60111)))
% 25.54/25.41 [6130]~P61(x61301)+E(f862(f862(f74(x61301),x61302),f862(f862(f29(x61301),x61303),x61302)),x61303)+~P1(f862(f862(f278(x61301),x61302),x61303))
% 25.54/25.41 [6183]~P1(f862(f54(x61831),x61833))+E(f862(f28(x61831),f862(f862(f301(x61831),x61832),x61833)),f862(a105,f862(f28(x61831),x61833)))+P1(f862(f862(f321(x61831),x61832),x61833))
% 25.54/25.41 [6184]~P1(f862(f54(x61841),x61843))+E(f862(f28(x61841),f862(f862(f301(x61841),x61842),x61843)),f862(a105,f862(f28(x61841),x61843)))+P1(f862(f862(f321(x61841),x61842),x61843))
% 25.54/25.41 [6257]~E(x62572,f2(a924))+P1(f862(x62571,f2(a924)))+~P1(f862(x62571,f862(f862(f29(a924),x62573),x62572)))
% 25.54/25.41 [6274]~P1(f862(f54(x62741),x62743))+E(f862(f28(x62741),f862(f862(f301(x62741),x62742),x62743)),f862(f28(x62741),x62743))+~P1(f862(f862(f321(x62741),x62742),x62743))
% 25.54/25.41 [6310]~P1(f862(f54(x63101),x63103))+E(f862(f28(x63101),f862(f862(f301(x63101),x63102),x63103)),f862(f862(f73(a924),f71(a924)),f862(f28(x63101),x63103)))+P1(f862(f862(f321(x63101),x63102),x63103))
% 25.54/25.41 [6428]E(f862(f862(f73(a924),x64281),f339(x64281,x64282,x64283)),x64282)+~P1(f862(x64283,f2(a924)))+P1(f862(x64283,f862(f862(f3(a924),x64282),x64281)))
% 25.54/25.41 [6429]E(f862(f862(f73(a924),x64291),f340(x64291,x64292,x64293)),x64292)+~P1(f862(x64293,f2(a924)))+P1(f862(x64293,f862(f862(f3(a924),x64292),x64291)))
% 25.54/25.41 [6475]~P3(x64751)+~P1(f862(f54(x64751),x64753))+E(f862(f862(f57(x64751,x64751,f103(x64751)),x64752),x64753),f862(f862(f103(x64751),x64752),f30(x64751,x64753)))
% 25.54/25.41 [6476]~P3(x64761)+~P1(f862(f54(x64761),x64763))+E(f862(f862(f57(x64761,x64761,f94(x64761)),x64762),x64763),f862(f862(f94(x64761),x64762),f31(x64761,x64763)))
% 25.54/25.41 [6482]~P98(x64821)+~E(f862(f96(x64821),x64822),f862(f96(x64821),x64823))+P26(x64821,f862(f96(x64821),f862(f862(f73(a1),x64822),f862(f72(a1),x64823))))
% 25.54/25.41 [6491]~P142(x64911)+E(f862(f862(f3(x64911),f862(f93(x64911),x64912)),f862(f93(x64911),x64913)),f862(f93(x64911),f862(f862(f3(a924),x64912),x64913)))+~P1(f862(f862(f227(a924),x64913),x64912))
% 25.54/25.41 [6582]E(f862(f862(f73(a924),x65821),f339(x65821,x65822,x65823)),x65822)+P1(f862(f862(f228(a924),x65822),x65821))+P1(f862(x65823,f862(f862(f3(a924),x65822),x65821)))
% 25.54/25.41 [6583]E(f862(f862(f73(a924),x65831),f340(x65831,x65832,x65833)),x65832)+P1(f862(f862(f228(a924),x65832),x65831))+P1(f862(x65833,f862(f862(f3(a924),x65832),x65831)))
% 25.54/25.41 [6600]~P112(x66001)+E(f862(f862(f74(x66001),f862(f69(x66001),x66002)),x66003),f862(f69(x66001),f862(f862(f74(x66001),x66002),x66003)))+~P1(f862(f862(f227(x66001),f2(x66001)),x66003))
% 25.54/25.41 [6601]~P66(x66011)+E(f862(f862(f281(x66011),f862(f69(x66011),x66012)),x66013),f862(f69(x66011),f862(f862(f281(x66011),x66012),x66013)))+~P1(f862(f862(f228(x66011),f2(x66011)),x66013))
% 25.54/25.41 [6609]~P93(x66091)+~P1(f862(f54(x66091),x66093))+E(f862(f862(f57(x66091,x66091,f94(x66091)),x66092),x66093),f12(x66091,f862(f862(f301(x66091),x66092),x66093)))
% 25.54/25.41 [6610]~P93(x66101)+~P1(f862(f54(x66101),x66103))+E(f862(f862(f57(x66101,x66101,f103(x66101)),x66102),x66103),f15(x66101,f862(f862(f301(x66101),x66102),x66103)))
% 25.54/25.41 [6611]~P109(x66111)+~P1(f862(f54(x66111),x66113))+E(f862(f862(f57(x66111,x66111,f225(x66111)),x66112),x66113),f16(x66111,f862(f862(f301(x66111),x66112),x66113)))
% 25.54/25.41 [6612]~P109(x66121)+~P1(f862(f54(x66121),x66123))+E(f862(f862(f57(x66121,x66121,f226(x66121)),x66122),x66123),f17(x66121,f862(f862(f301(x66121),x66122),x66123)))
% 25.54/25.41 [6657]E(x66571,f106(x66572))+~E(f172(x66572,x66573),f106(f925(x66572)))+~P1(f862(f862(f321(f925(x66572)),x66571),f862(f165(f925(x66572)),x66573)))
% 25.54/25.41 [6701]~P1(f862(f130(x67011),x67013))+P1(f862(f862(f321(x67011),x67012),f862(f165(x67011),x67013)))+P1(f862(f130(x67011),f862(f862(f144(x67011),x67012),x67013)))
% 25.54/25.41 [6712]~P100(x67121)+~P1(f862(f54(x67121),x67123))+E(f862(f56(x67121,f74(x67121)),f862(f862(f301(x67121),x67122),x67123)),f862(f862(f57(x67121,x67121,f74(x67121)),x67122),x67123))
% 25.54/25.41 [6735]~P109(x67351)+~P1(f862(f54(x67351),x67353))+E(f13(x67351,f225(x67351),f862(f862(f301(x67351),x67352),x67353)),f862(f862(f57(x67351,x67351,f225(x67351)),x67352),x67353))
% 25.54/25.41 [6736]~P109(x67361)+~P1(f862(f54(x67361),x67363))+E(f14(x67361,f226(x67361),f862(f862(f301(x67361),x67362),x67363)),f862(f862(f57(x67361,x67361,f226(x67361)),x67362),x67363))
% 25.54/25.41 [6737]P1(f862(x67371,f2(a924)))+~P1(f862(f862(f228(a924),x67372),x67373))+~P1(f862(x67371,f862(f862(f3(a924),x67372),x67373)))
% 25.54/25.41 [6738]P1(f862(x67381,f2(a924)))+~P1(f862(f862(f228(a924),x67382),x67383))+~P1(f862(x67381,f862(f862(f3(a924),x67382),x67383)))
% 25.54/25.41 [6757]~P86(x67571)+P1(f862(f862(f227(x67571),x67572),x67573))+~P1(f862(f862(f227(x67571),f862(f69(x67571),x67572)),x67573))
% 25.54/25.41 [6758]~P86(x67581)+P1(f862(f862(f227(x67581),x67582),x67583))+~P1(f862(f862(f227(x67581),f862(f69(x67581),x67582)),x67583))
% 25.54/25.41 [6759]~P112(x67591)+P1(f862(f862(f228(x67591),x67592),x67593))+~P1(f862(f862(f228(x67591),f862(f69(x67591),x67592)),x67593))
% 25.54/25.41 [6776]E(x67761,f106(x67762))+E(f862(f134(x67762),f862(f862(f131(x67762),x67763),x67761)),f862(f862(f157(x67762),x67761),x67763))+~P1(f862(f862(f228(a924),x67763),f862(f182(f925(x67762)),x67761)))
% 25.54/25.41 [6826]~P1(f862(x68261,x68263))+P1(f862(x68261,f349(x68261,x68262)))+~P1(f862(f862(f321(a924),x68263),f862(f295(a924,f2(a924)),x68262)))
% 25.54/25.41 [6847]P1(f862(x68471,x68472))+~P1(f862(f862(f228(a924),x68472),x68473))+P1(f862(f862(f321(a924),f347(x68471,x68473)),f862(f295(a924,f2(a924)),x68473)))
% 25.54/25.41 [6862]~P127(x68621)+~P1(f862(f862(f227(x68621),f71(x68621)),x68622))+P1(f862(f862(f227(x68621),f71(x68621)),f862(f862(f236(x68621),x68622),x68623)))
% 25.54/25.41 [6864]~P127(x68641)+~P1(f862(f862(f227(x68641),f2(x68641)),x68642))+P1(f862(f862(f227(x68641),f2(x68641)),f862(f862(f236(x68641),x68642),x68643)))
% 25.54/25.41 [6866]~P127(x68661)+~P1(f862(f862(f228(x68661),f2(x68661)),x68662))+P1(f862(f862(f228(x68661),f2(x68661)),f862(f862(f236(x68661),x68662),x68663)))
% 25.54/25.41 [6890]~P1(f862(x68901,x68903))+~P1(f862(f862(f228(a924),x68903),x68902))+P1(f862(f862(f321(a924),f343(x68901,x68902)),f862(f295(a924,f2(a924)),x68902)))
% 25.54/25.41 [6897]P1(f862(f54(x68971),x68972))+~P1(f862(f54(x68971),x68973))+~P1(f862(f862(f227(f932(x68971,a921)),x68972),x68973))
% 25.54/25.41 [6898]P1(f862(f54(x68981),x68982))+~P1(f862(f54(x68981),x68983))+~P1(f862(f862(f227(f932(x68981,a921)),x68982),x68983))
% 25.54/25.41 [6905]P1(f862(x69051,x69052))+~P1(f862(x69051,f350(x69051,x69053)))+~P1(f862(f862(f321(a924),x69052),f862(f295(a924,f2(a924)),x69053)))
% 25.54/25.41 [6916]E(x69161,f2(a924))+P1(f862(x69162,f420(x69161,x69163,x69162)))+~P1(f862(x69162,f862(f862(f29(a924),x69163),x69161)))
% 25.54/25.41 [6923]~P128(x69232)+E(x69231,f2(x69232))+~E(f862(f862(f73(x69232),f862(f862(f74(x69232),x69233),x69233)),f862(f862(f74(x69232),x69231),x69231)),f2(x69232))
% 25.54/25.41 [6924]~P128(x69242)+E(x69241,f2(x69242))+~E(f862(f862(f73(x69242),f862(f862(f74(x69242),x69241),x69241)),f862(f862(f74(x69242),x69243),x69243)),f2(x69242))
% 25.54/25.41 [6971]E(x69711,f2(a924))+~P1(f862(x69712,f421(x69711,x69713,x69712)))+P1(f862(x69712,f862(f862(f29(a924),x69713),x69711)))
% 25.54/25.41 [6976]~P109(x69761)+~P11(x69761,x69763)+P11(x69761,f862(f862(f141(x69761,x69761,f7(x69761)),x69762),x69763))
% 25.54/25.41 [7018]P1(f862(x70181,f420(x70182,x70183,x70181)))+P1(f862(x70181,f2(a924)))+~P1(f862(x70181,f862(f862(f29(a924),x70183),x70182)))
% 25.54/25.41 [7024]~P98(x70241)+E(f862(f96(x70241),x70242),f862(f96(x70241),x70243))+~P26(x70241,f862(f96(x70241),f862(f862(f73(a1),x70242),f862(f72(a1),x70243))))
% 25.54/25.41 [7090]E(x70901,f2(a1))+E(x70902,f2(a1))+~P1(f862(f42(x70902,x70902),f862(f862(f244(a1,a1),x70903),x70901)))
% 25.54/25.41 [7091]E(x70911,f71(a1))+E(x70912,f2(a1))+~P1(f862(f42(x70912,x70912),f862(f862(f244(a1,a1),x70911),x70913)))
% 25.54/25.41 [7105]P1(f862(x71051,x71052))+P1(f862(f862(f228(a924),f350(x71051,x71053)),x71053))+~P1(f862(f862(f321(a924),x71052),f862(f295(a924,f2(a924)),x71053)))
% 25.54/25.41 [7128]~P1(f862(x71281,f339(x71283,x71282,x71281)))+~P1(f862(x71281,f2(a924)))+P1(f862(x71281,f862(f862(f3(a924),x71282),x71283)))
% 25.54/25.41 [7129]~P1(f862(x71291,f340(x71293,x71292,x71291)))+~P1(f862(x71291,f2(a924)))+P1(f862(x71291,f862(f862(f3(a924),x71292),x71293)))
% 25.54/25.41 [7130]~P1(f862(x71301,f421(x71303,x71302,x71301)))+~P1(f862(x71301,f2(a924)))+P1(f862(x71301,f862(f862(f29(a924),x71302),x71303)))
% 25.54/25.41 [7148]~P1(f862(x71481,x71483))+P1(f862(f862(f228(a924),f349(x71481,x71482)),x71482))+~P1(f862(f862(f321(a924),x71483),f862(f295(a924,f2(a924)),x71482)))
% 25.54/25.41 [7149]E(f862(f862(f3(a924),f862(f862(f3(a924),x71491),x71492)),f862(f862(f3(a924),x71493),x71492)),f862(f862(f3(a924),x71491),x71493))+~P1(f862(f862(f227(a924),x71492),x71491))+~P1(f862(f862(f227(a924),x71492),x71493))
% 25.54/25.41 [7185]~P78(x71851)+~P1(f862(f862(f227(x71851),f862(f72(x71851),x71853)),x71852))+P1(f862(f862(f227(x71851),f862(f72(x71851),x71852)),x71853))
% 25.54/25.41 [7186]~P78(x71861)+~P1(f862(f862(f227(x71861),f862(f72(x71861),x71863)),x71862))+P1(f862(f862(f227(x71861),f862(f72(x71861),x71862)),x71863))
% 25.54/25.41 [7187]~P86(x71871)+~P1(f862(f862(f227(x71871),f862(f69(x71871),x71872)),x71873))+P1(f862(f862(f227(x71871),f862(f72(x71871),x71872)),x71873))
% 25.54/25.41 [7188]~P86(x71881)+~P1(f862(f862(f227(x71881),f862(f69(x71881),x71882)),x71883))+P1(f862(f862(f227(x71881),f862(f72(x71881),x71882)),x71883))
% 25.54/25.41 [7189]~P78(x71891)+~P1(f862(f862(f228(x71891),f862(f72(x71891),x71893)),x71892))+P1(f862(f862(f228(x71891),f862(f72(x71891),x71892)),x71893))
% 25.54/25.41 [7190]~P78(x71901)+~P1(f862(f862(f228(x71901),f862(f72(x71901),x71903)),x71902))+P1(f862(f862(f228(x71901),f862(f72(x71901),x71902)),x71903))
% 25.54/25.41 [7191]~P112(x71911)+~P1(f862(f862(f228(x71911),f862(f69(x71911),x71912)),x71913))+P1(f862(f862(f228(x71911),f862(f72(x71911),x71912)),x71913))
% 25.54/25.41 [7222]~P1(f862(x72223,f339(x72222,x72221,x72223)))+P1(f862(f862(f228(a924),x72221),x72222))+P1(f862(x72223,f862(f862(f3(a924),x72221),x72222)))
% 25.54/25.41 [7223]~P1(f862(x72233,f340(x72232,x72231,x72233)))+P1(f862(f862(f228(a924),x72231),x72232))+P1(f862(x72233,f862(f862(f3(a924),x72231),x72232)))
% 25.54/25.41 [7276]~E(f711(x72763,x72762,x72761),f703(x72763,x72762,x72761))+E(f862(f862(f94(f932(x72761,a921)),x72762),f30(f932(x72761,a921),x72763)),f181(f932(x72761,a921)))+P1(f862(f862(f321(f932(x72761,a921)),x72762),x72763))
% 25.54/25.41 [7284]~P1(f862(f54(x72841),x72843))+P1(f862(f54(x72841),f31(f932(x72841,a921),x72842)))+~P1(f862(f862(f321(f932(x72841,a921)),x72843),x72842))
% 25.54/25.41 [7344]~P109(x73441)+E(f862(f862(f103(f932(x73441,a921)),f862(f295(x73441,x73442),x73443)),f862(f862(f301(x73441),x73443),f181(f932(x73441,a921)))),f296(x73441,x73442,x73443))+~P1(f862(f862(f227(x73441),x73442),x73443))
% 25.54/25.41 [7347]E(x73471,f2(a924))+P1(f862(f862(f228(a924),f422(x73471,x73473,x73472)),x73471))+P1(f862(x73472,f862(f862(f29(a924),x73473),x73471)))
% 25.54/25.41 [7376]P1(f862(f862(f228(a924),f862(f182(f925(x73761)),x73762)),f789(x73763,x73761)))+~P1(f862(f54(f925(x73761)),x73763))+~P1(f862(f862(f321(f925(x73761)),x73762),x73763))
% 25.54/25.41 [7381]E(x73811,x73812)+~P1(f862(f862(f227(f932(x73813,a921)),x73811),x73812))+P1(f862(f862(f228(f932(x73813,a921)),x73811),x73812))
% 25.54/25.41 [7382]E(x73821,x73822)+~P1(f862(f862(f227(f932(x73823,a921)),x73821),x73822))+P1(f862(f862(f228(f932(x73823,a921)),x73821),x73822))
% 25.54/25.41 [7394]E(x73941,x73942)+~E(f862(f182(f925(x73943)),x73941),f862(f182(f925(x73943)),x73942))+P1(f862(f862(f228(a924),f658(x73943,x73941,x73942)),f862(f182(f925(x73943)),x73942)))
% 25.54/25.41 [7445]P6(x74451,x74452,x74453)+~E(f862(f256(x74451,x74451),x74453),x74452)+~E(f862(f862(f280(x74451,x74451,x74451),f862(f277(x74451,x74451),x74453)),x74453),x74453)
% 25.54/25.41 [7526]~P1(f862(x75261,f2(a924)))+P1(f862(f862(f228(a924),f422(x75263,x75262,x75261)),x75263))+P1(f862(x75261,f862(f862(f29(a924),x75262),x75263)))
% 25.54/25.41 [7536]~P109(x75361)+E(f862(f862(f103(f932(x75361,a921)),f298(x75361,x75362,x75363)),f862(f862(f301(x75361),x75363),f181(f932(x75361,a921)))),f297(x75361,x75362,x75363))+~P1(f862(f862(f228(x75361),x75362),x75363))
% 25.54/25.41 [7629]~P1(f862(f54(x76291),x76293))+P1(f862(f862(f227(a924),f862(f28(x76291),x76292)),f862(f28(x76291),x76293)))+~P1(f862(f862(f227(f932(x76291,a921)),x76292),x76293))
% 25.54/25.41 [7630]~P1(f862(f54(x76301),x76303))+P1(f862(f862(f228(a924),f862(f28(x76301),x76302)),f862(f28(x76301),x76303)))+~P1(f862(f862(f228(f932(x76301,a921)),x76302),x76303))
% 25.54/25.41 [7762]E(x77621,x77622)+~P1(f862(f862(f227(f932(x77623,a921)),x77622),x77621))+~P1(f862(f862(f227(f932(x77623,a921)),x77621),x77622))
% 25.54/25.41 [7763]E(x77631,x77632)+~P1(f862(f862(f227(f932(x77633,a921)),x77632),x77631))+~P1(f862(f862(f227(f932(x77633,a921)),x77631),x77632))
% 25.54/25.41 [7766]~P109(x77661)+P11(x77661,x77662)+~P11(x77661,f862(f862(f141(x77661,x77661,f7(x77661)),x77663),x77662))
% 25.54/25.41 [7837]~P1(f862(f862(f228(a924),x78373),x78372))+~P1(f862(f862(f228(a924),x78373),x78371))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x78371),x78372)),f862(f862(f3(a924),x78371),x78373)))
% 25.54/25.41 [7838]~P1(f862(f862(f227(a924),x78382),x78381))+~P1(f862(f862(f228(a924),x78381),x78383))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x78381),x78382)),f862(f862(f3(a924),x78383),x78382)))
% 25.54/25.41 [7853]~P1(f862(f862(f228(a1),x78532),f2(a1)))+~P1(f862(f862(f227(a1),x78533),x78531))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x78531),x78532)),f862(f862(f29(a1),x78533),x78532)))
% 25.54/25.41 [7869]~P1(f862(f862(f228(a924),f2(a924)),x78691))+~P1(f862(f862(f227(a924),x78692),x78693))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x78691),x78692)),f862(f862(f74(a924),x78691),x78693)))
% 25.54/25.41 [7870]~P1(f862(f862(f228(a924),f2(a924)),x78703))+~P1(f862(f862(f227(a924),x78703),x78702))+P1(f862(f862(f227(a924),f862(f862(f29(a924),x78701),x78702)),f862(f862(f29(a924),x78701),x78703)))
% 25.54/25.41 [7871]~P1(f862(f862(f228(a1),f2(a1)),x78712))+~P1(f862(f862(f227(a1),x78711),x78713))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x78711),x78712)),f862(f862(f29(a1),x78713),x78712)))
% 25.54/25.41 [7872]~P1(f862(f862(f228(a924),f2(a924)),x78721))+~P1(f862(f862(f228(a924),x78722),x78723))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78721),x78722)),f862(f862(f74(a924),x78721),x78723)))
% 25.54/25.41 [7873]~P1(f862(f862(f228(a924),f2(a924)),x78731))+~P1(f862(f862(f228(a924),x78732),x78733))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78731),x78732)),f862(f862(f74(a924),x78731),x78733)))
% 25.54/25.41 [7874]~P1(f862(f862(f228(a924),f2(a924)),x78742))+~P1(f862(f862(f228(a924),x78741),x78743))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78741),x78742)),f862(f862(f74(a924),x78743),x78742)))
% 25.54/25.41 [7875]~P1(f862(f862(f228(a924),f2(a924)),x78752))+~P1(f862(f862(f228(a924),x78751),x78753))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78751),x78752)),f862(f862(f74(a924),x78753),x78752)))
% 25.54/25.41 [7876]~P1(f862(f862(f228(a924),f2(a924)),x78761))+~P1(f862(f862(f228(a924),x78762),x78763))+P1(f862(f862(f228(a924),f862(f862(f74(a924),x78761),x78762)),f862(f862(f74(a924),x78761),x78763)))
% 25.54/25.41 [7877]~P1(f862(f862(f228(a1),f2(a1)),x78771))+~P1(f862(f862(f228(a1),x78772),x78773))+P1(f862(f862(f228(a1),f862(f862(f74(a1),x78771),x78772)),f862(f862(f74(a1),x78771),x78773)))
% 25.54/25.41 [7878]~P1(f862(f862(f228(a924),f2(a924)),x78781))+~P1(f862(f862(f278(a924),x78782),x78783))+P1(f862(f862(f278(a924),f862(f862(f74(a924),x78781),x78782)),f862(f862(f74(a924),x78781),x78783)))
% 25.54/25.41 [7925]E(x79251,f2(a924))+E(f862(f862(f73(a924),f862(f862(f74(a924),x79251),f421(x79251,x79252,x79253))),f422(x79251,x79252,x79253)),x79252)+P1(f862(x79253,f862(f862(f29(a924),x79252),x79251)))
% 25.54/25.41 [7984]E(f862(f862(f73(a924),f862(f862(f74(a924),x79841),f421(x79841,x79842,x79843))),f422(x79841,x79842,x79843)),x79842)+~P1(f862(x79843,f2(a924)))+P1(f862(x79843,f862(f862(f29(a924),x79842),x79841)))
% 25.54/25.41 [8002]~P1(f862(f54(x80021),x80023))+P1(f862(f862(f321(x80021),f338(x80022,x80023,x80021)),x80023))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x80021,a924),x80022),x80023)))
% 25.54/25.41 [8003]~P1(f862(f54(x80031),x80033))+P1(f862(f862(f321(x80031),f369(x80032,x80033,x80031)),x80033))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x80031,a924),x80032),x80033)))
% 25.54/25.41 [8105]E(x81051,f2(a924))+P1(f862(f862(f278(a924),x81052),x81053))+~P1(f862(f862(f278(a924),f862(f862(f74(a924),x81051),x81052)),f862(f862(f74(a924),x81051),x81053)))
% 25.54/25.41 [8300]E(x83001,f181(f932(x83002,a921)))+E(x83001,f862(f862(f301(x83002),x83003),f181(f932(x83002,a921))))+~P1(f862(f862(f227(f932(x83002,a921)),x83001),f862(f862(f301(x83002),x83003),f181(f932(x83002,a921)))))
% 25.54/25.41 [8324]~P109(x83241)+~P11(x83241,x83243)+P11(x83241,f862(f862(f131(x83241),f862(f182(f925(x83241)),f170(x83241,x83242,x83243))),x83243))
% 25.54/25.41 [8336]~P1(f862(f862(f228(a924),f71(a924)),x83363))+P1(f862(f862(f227(a924),x83361),x83362))+~P1(f862(f862(f278(a924),f862(f862(f236(a924),x83363),x83361)),f862(f862(f236(a924),x83363),x83362)))
% 25.54/25.41 [8337]~P1(f862(f862(f228(a924),f2(a924)),x83373))+P1(f862(f862(f227(a924),x83371),x83372))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x83373),x83371)),f862(f862(f74(a924),x83373),x83372)))
% 25.54/25.41 [8338]~P1(f862(f862(f228(a924),f2(a924)),x83383))+P1(f862(f862(f227(a924),x83381),x83382))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x83383),x83381)),f862(f862(f74(a924),x83383),x83382)))
% 25.54/25.41 [8339]~P1(f862(f862(f228(a924),f2(a924)),x83393))+P1(f862(f862(f227(a924),x83391),x83392))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x83391),x83393)),f862(f862(f74(a924),x83392),x83393)))
% 25.54/25.41 [8340]~P1(f862(f862(f228(a924),f2(a924)),x83403))+P1(f862(f862(f228(a924),x83401),x83402))+~P1(f862(f862(f228(a924),f862(f862(f74(a924),x83403),x83401)),f862(f862(f74(a924),x83403),x83402)))
% 25.54/25.41 [8341]~P1(f862(f862(f228(a924),f2(a924)),x83413))+P1(f862(f862(f228(a924),x83411),x83412))+~P1(f862(f862(f228(a924),f862(f862(f236(a924),x83413),x83411)),f862(f862(f236(a924),x83413),x83412)))
% 25.54/25.41 [8342]~P1(f862(f862(f228(a924),f2(a924)),x83423))+P1(f862(f862(f278(a924),x83421),x83422))+~P1(f862(f862(f278(a924),f862(f862(f74(a924),x83423),x83421)),f862(f862(f74(a924),x83423),x83422)))
% 25.54/25.41 [8343]~P1(f862(f862(f228(a924),f2(a924)),x83433))+P1(f862(f862(f278(a924),x83431),x83432))+~P1(f862(f862(f278(a924),f862(f862(f74(a924),x83433),x83431)),f862(f862(f74(a924),x83433),x83432)))
% 25.54/25.41 [8383]~E(f862(f862(f94(f932(x83831,a921)),f703(x83833,x83832,x83831)),f711(x83833,x83832,x83831)),f181(f932(x83831,a921)))+E(f862(f862(f94(f932(x83831,a921)),x83832),f30(f932(x83831,a921),x83833)),f181(f932(x83831,a921)))+P1(f862(f862(f321(f932(x83831,a921)),x83832),x83833))
% 25.54/25.41 [8396]E(x83961,f106(x83962))+~E(f862(f135(f925(x83962),f925(x83962),f127(x83962),f106(x83962)),x83963),f106(x83962))+~P1(f862(f862(f321(f925(x83962)),x83961),f862(f165(f925(x83962)),x83963)))
% 25.54/25.41 [8397]E(x83971,f106(x83972))+~E(f862(f135(f925(x83972),f925(x83972),f127(x83972),f106(x83972)),x83973),f106(x83972))+~P1(f862(f862(f321(f925(x83972)),x83971),f862(f165(f925(x83972)),x83973)))
% 25.54/25.41 [8452]E(x84521,f181(f932(f932(x84522,a921),a921)))+P1(f862(f862(f321(f932(x84522,a921)),f472(x84523,x84521,x84522)),x84521))+P1(f862(f862(f227(f932(x84522,a921)),f31(f932(x84522,a921),x84521)),x84523))
% 25.54/25.41 [8458]~P71(x84581)+~P72(x84581)+E(f862(f862(f8(a1,x84581),f862(f862(f10(a924,x84581,a1),x84582),a97)),f862(f302(a924,a1,f93(a1)),x84583)),f862(f862(f8(a924,x84581),x84582),x84583))
% 25.54/25.41 [8459]~P71(x84591)+~P72(x84591)+E(f862(f862(f11(a1,x84591),f862(f862(f10(a924,x84591,a1),x84592),a97)),f862(f302(a924,a1,f93(a1)),x84593)),f862(f862(f11(a924,x84591),x84592),x84593))
% 25.54/25.41 [8501]~P1(f862(f54(x85011),x85013))+~P1(f862(f862(f228(a924),f2(a924)),f862(x85012,f338(x85012,x85013,x85011))))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x85011,a924),x85012),x85013)))
% 25.54/25.41 [8502]~P1(f862(f54(x85021),x85023))+~P1(f862(f862(f228(a924),f2(a924)),f862(x85022,f369(x85022,x85023,x85021))))+P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x85021,a924),x85022),x85023)))
% 25.54/25.41 [8538]~P65(x85382)+E(x85381,f71(x85382))+E(f862(f862(f281(x85382),f862(f862(f3(x85382),f862(f862(f236(x85382),x85381),x85383)),f71(x85382))),f862(f862(f3(x85382),x85381),f71(x85382))),f862(f862(f8(a924,x85382),f862(f236(x85382),x85381)),f862(f295(a924,f2(a924)),x85383)))
% 25.54/25.41 [8596]E(x85961,f2(a924))+~P1(f862(x85963,f862(f862(f29(a924),x85962),x85961)))+P1(f862(f862(f228(a924),x85962),f862(f862(f74(a924),x85961),f862(a105,f420(x85961,x85962,x85963)))))
% 25.54/25.41 [8616]P1(f862(x86161,f2(a924)))+~P1(f862(x86161,f862(f862(f29(a924),x86162),x86163)))+P1(f862(f862(f228(a924),x86162),f862(f862(f74(a924),x86163),f862(a105,f420(x86163,x86162,x86161)))))
% 25.54/25.41 [8655]E(x86551,f2(a924))+~P1(f862(x86553,f862(f862(f29(a924),x86552),x86551)))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x86551),f420(x86551,x86552,x86553))),x86552))
% 25.54/25.41 [8686]P1(f862(x86861,f2(a924)))+~P1(f862(x86861,f862(f862(f29(a924),x86863),x86862)))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x86862),f420(x86862,x86863,x86861))),x86863))
% 25.54/25.41 [8694]~P109(x86941)+E(f862(f862(f141(x86941,x86941,f7(x86941)),x86942),x86943),f142(x86941,x86941,f7(x86941),x86942,x86943))+P1(f862(f862(f321(x86941),x86942),f862(f165(x86941),x86943)))
% 25.54/25.41 [8730]~E(f862(x87303,f595(x87302,x87303,x87301)),f862(x87303,f597(x87302,x87303,x87301)))+~P57(x87301,f862(x87303,f596(x87302,x87303,x87301)))+P57(x87301,f862(f862(f33(x87302,f932(x87301,f932(x87301,a921))),f234(f932(x87302,a921))),x87303))
% 25.54/25.41 [8739]E(x87391,f181(f932(f932(x87392,a921),a921)))+~P1(f862(f862(f227(f932(x87392,a921)),f472(x87393,x87391,x87392)),x87393))+P1(f862(f862(f227(f932(x87392,a921)),f31(f932(x87392,a921),x87391)),x87393))
% 25.54/25.41 [8800]~P67(x88001)+~P1(f862(f862(f228(x88001),x88002),x88003))+P1(f862(f862(f228(x88001),x88002),f862(f862(f281(x88001),f862(f862(f73(x88001),x88002),x88003)),f862(f862(f73(x88001),f71(x88001)),f71(x88001)))))
% 25.54/25.41 [8858]~P1(f862(f862(x88581,f499(x88581,x88583,x88582)),f500(x88581,x88583,x88582)))+P1(f862(f862(x88581,x88582),x88583))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x88582),x88583)))
% 25.54/25.41 [8859]~P1(f862(f862(x88591,f501(x88591,x88593,x88592)),f503(x88591,x88593,x88592)))+P1(f862(f862(x88591,x88592),x88593))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x88592),x88593)))
% 25.54/25.41 [8860]~P1(f862(f862(x88601,f504(x88601,x88603,x88602)),f507(x88601,x88603,x88602)))+P1(f862(f862(x88601,x88602),x88603))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x88602),x88603)))
% 25.54/25.41 [8861]~P1(f862(f862(x88611,f508(x88611,x88613,x88612)),f510(x88611,x88613,x88612)))+P1(f862(f862(x88611,x88612),x88613))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x88612),x88613)))
% 25.54/25.41 [8862]~P1(f862(f862(x88621,f683(x88621,x88623,x88622)),f685(x88621,x88623,x88622)))+P1(f862(f862(x88621,x88622),x88623))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x88622),x88623)))
% 25.54/25.41 [8863]~P1(f862(f862(x88631,f779(x88631,x88633,x88632)),f780(x88631,x88633,x88632)))+P1(f862(f862(x88631,x88632),x88633))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x88632),x88633)))
% 25.54/25.41 [9139]P1(f862(f862(x91391,x91392),x91393))+P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),f508(x91391,x91393,x91392)),f510(x91391,x91393,x91392))))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x91392),x91393)))
% 25.54/25.41 [9140]P1(f862(f862(x91401,x91402),x91403))+P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),f499(x91401,x91403,x91402)),f500(x91401,x91403,x91402))))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x91402),x91403)))
% 25.54/25.41 [9141]P1(f862(f862(x91411,x91412),x91413))+P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),f501(x91411,x91413,x91412)),f503(x91411,x91413,x91412))))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x91412),x91413)))
% 25.54/25.41 [9142]P1(f862(f862(x91421,x91422),x91423))+P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),f504(x91421,x91423,x91422)),f507(x91421,x91423,x91422))))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x91422),x91423)))
% 25.54/25.41 [9143]P1(f862(f862(x91431,x91432),x91433))+P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),f683(x91431,x91433,x91432)),f685(x91431,x91433,x91432))))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x91432),x91433)))
% 25.54/25.41 [9144]P1(f862(f862(x91441,x91442),x91443))+P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),f779(x91441,x91443,x91442)),f780(x91441,x91443,x91442))))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x91442),x91443)))
% 25.54/25.41 [9480]~P1(f862(f54(x94801),x94803))+P1(f862(f862(f321(f931(f932(x94801,a921),f932(x94801,a921))),f862(f862(f244(f932(x94801,a921),f932(x94801,a921)),x94802),x94803)),f306(x94801)))+~P1(f862(f862(f228(f932(x94801,a921)),x94802),x94803))
% 25.54/25.41 [9554]~P57(x95541,f862(x95543,f596(x95542,x95543,x95541)))+P57(x95541,f862(f862(f33(x95542,f932(x95541,f932(x95541,a921))),f234(f932(x95542,a921))),x95543))+~E(f862(f862(f94(f932(x95541,a921)),f241(x95541,x95541,f862(x95543,f595(x95542,x95543,x95541)))),f242(x95541,x95541,f862(x95543,f597(x95542,x95543,x95541)))),f181(f932(x95541,a921)))
% 25.54/25.41 [9759]P50(x97591,x97592,x97593)+P1(f862(f862(f321(f931(x97591,x97591)),f580(x97593,x97592,x97591)),x97593))+~P1(f862(f862(f321(f931(x97591,x97591)),f862(f862(f244(x97591,x97591),f579(x97593,x97592,x97591)),f579(x97593,x97592,x97591))),x97593))
% 25.54/25.41 [10343]P50(x103431,x103432,x103433)+~P1(f862(f862(f249(x103431,x103431,a921),f862(f862(f9(x103431,f932(x103431,a921),f932(x103431,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103431,a921),f932(x103431,a921)),x103431),f10(a921,a921,x103431)),f862(f862(f10(a921,f932(a921,a921),x103431),a318),f862(f862(f9(x103431,f932(x103431,a921),a921),f321(x103431)),x103432)))),f862(f862(f9(x103431,f932(x103431,a921),a921),f321(x103431)),x103432))),f580(x103433,x103432,x103431)))+~P1(f862(f862(f321(f931(x103431,x103431)),f862(f862(f244(x103431,x103431),f579(x103433,x103432,x103431)),f579(x103433,x103432,x103431))),x103433))
% 25.54/25.41 [5841]~P61(x58412)+E(x58411,f2(x58412))+E(f862(f862(f29(x58412),f862(f862(f74(x58412),x58413),x58411)),x58411),x58413)
% 25.54/25.41 [5842]~P61(x58422)+E(x58421,f2(x58422))+E(f862(f862(f29(x58422),f862(f862(f74(x58422),x58421),x58423)),x58421),x58423)
% 25.54/25.41 [6492]~P61(x64921)+E(f862(f862(f74(x64921),f862(f862(f29(x64921),x64922),x64923)),x64923),x64922)+~P1(f862(f862(f278(x64921),x64923),x64922))
% 25.54/25.41 [6656]~P72(x66561)+~E(f862(x66562,f2(a924)),f2(x66561))+E(f862(f862(f8(a924,x66561),x66562),f862(f295(a924,f862(a105,f2(a924))),x66563)),f862(f862(f8(a924,x66561),x66562),f862(f295(a924,f2(a924)),x66563)))
% 25.54/25.41 [6788]~P61(x67882)+E(x67881,f2(x67882))+E(f862(f862(f29(x67882),f862(f862(f73(x67882),x67883),x67881)),x67881),f862(f862(f73(x67882),f862(f862(f29(x67882),x67883),x67881)),f71(x67882)))
% 25.54/25.41 [6789]~P61(x67892)+E(x67891,f2(x67892))+E(f862(f862(f29(x67892),f862(f862(f73(x67892),x67891),x67893)),x67891),f862(f862(f73(x67892),f862(f862(f29(x67892),x67893),x67891)),f71(x67892)))
% 25.54/25.41 [7007]~P1(f862(x70073,f2(a1)))+P1(f862(f862(f227(a924),x70071),x70072))+P1(f862(x70073,f862(f93(a1),f862(f862(f3(a924),x70072),x70071))))
% 25.54/25.41 [7111]P1(f862(f862(f228(a924),x71112),x71111))+P1(f862(f862(f227(a924),x71111),x71112))+P1(f862(x71113,f862(f93(a1),f862(f862(f3(a924),x71112),x71111))))
% 25.54/25.41 [7184]E(f862(f862(f73(a924),f862(f96(a924),x71841)),f862(f862(f73(a924),f862(f96(a924),x71842)),x71843)),f862(f862(f73(a924),f862(f96(a924),x71841)),x71843))+P1(f862(a186,f862(f96(a1),x71841)))+~P1(f862(a186,f862(f96(a1),x71842)))
% 25.54/25.41 [7262]~E(x72622,f862(f862(f29(a924),x72623),x72621))+~P1(f862(f862(f228(a924),f2(a924)),x72621))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x72621),x72622)),x72623))
% 25.54/25.41 [7378]~P1(f862(f54(x73781),x73783))+~P1(f862(f54(x73781),x73782))+P1(f862(f54(x73781),f862(f862(f103(f932(x73781,a921)),x73782),x73783)))
% 25.54/25.41 [7379]~P1(f862(f54(x73791),x73793))+~P1(f862(f54(x73791),x73792))+P1(f862(f54(x73791),f862(f862(f103(f932(x73791,a921)),x73792),x73793)))
% 25.54/25.41 [7380]~P1(f862(f54(x73801),x73803))+~P1(f862(f54(x73801),x73802))+P1(f862(f54(x73801),f862(f862(f3(f932(x73801,a921)),x73802),x73803)))
% 25.54/25.41 [7429]~P36(x74291,x74293)+~P36(x74291,x74292)+P36(x74291,f862(f862(f94(f932(f931(x74291,x74291),a921)),x74292),x74293))
% 25.54/25.41 [7430]~P49(x74301,x74303)+~P49(x74301,x74302)+P49(x74301,f862(f862(f103(f932(f931(x74301,x74301),a921)),x74302),x74303))
% 25.54/25.41 [7431]~P49(x74311,x74313)+~P49(x74311,x74312)+P49(x74311,f862(f862(f94(f932(f931(x74311,x74311),a921)),x74312),x74313))
% 25.54/25.41 [7677]~P109(x76771)+~P1(f862(f54(x76771),x76772))+E(f132(x76771,f862(f862(f3(f932(x76771,a921)),x76772),f862(f862(f301(x76771),x76773),f181(f932(x76771,a921))))),f163(x76771,x76773,f132(x76771,x76772)))
% 25.54/25.41 [7741]P1(f862(x77411,f2(a1)))+~P1(f862(f862(f228(a924),x77412),x77413))+~P1(f862(x77411,f862(f93(a1),f862(f862(f3(a924),x77412),x77413))))
% 25.54/25.41 [7760]~P1(f862(f54(x77601),x77602))+E(f862(f28(x77601),f862(f862(f3(f932(x77601,a921)),x77602),f862(f862(f301(x77601),x77603),f181(f932(x77601,a921))))),f862(f28(x77601),x77602))+P1(f862(f862(f321(x77601),x77603),x77602))
% 25.54/25.41 [7893]~P127(x78931)+~P1(f862(f862(f228(x78931),f71(x78931)),x78932))+P1(f862(f862(f228(x78931),f71(x78931)),f862(f862(f74(x78931),x78932),f862(f862(f236(x78931),x78932),x78933))))
% 25.54/25.41 [7935]~P1(f862(f54(x79351),x79353))+E(f862(f862(f3(a924),f862(f28(x79351),x79352)),f862(f28(x79351),x79353)),f862(f28(x79351),f862(f862(f3(f932(x79351,a921)),x79352),x79353)))+~P1(f862(f862(f227(f932(x79351,a921)),x79353),x79352))
% 25.54/25.41 [7992]~P1(f862(f862(f227(a924),x79922),x79923))+~P1(f862(f862(f227(a924),x79921),f862(f862(f3(a924),x79923),x79922)))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x79921),x79922)),x79923))
% 25.54/25.41 [8047]P1(f862(f54(x80471),x80472))+~P1(f862(f54(x80471),x80473))+~P1(f862(f54(x80471),f862(f862(f3(f932(x80471,a921)),x80472),x80473)))
% 25.54/25.41 [8052]~P1(f862(f54(x80521),x80522))+E(f862(f28(x80521),f862(f862(f3(f932(x80521,a921)),x80522),f862(f862(f301(x80521),x80523),f181(f932(x80521,a921))))),f862(f862(f3(a924),f862(f28(x80521),x80522)),f71(a924)))+~P1(f862(f862(f321(x80521),x80523),x80522))
% 25.54/25.41 [8053]~P1(f862(f54(x80531),x80532))+E(f862(f28(x80531),f862(f862(f3(f932(x80531,a921)),x80532),f862(f862(f301(x80531),x80533),f181(f932(x80531,a921))))),f862(f862(f3(a924),f862(f28(x80531),x80532)),f71(a924)))+~P1(f862(f862(f321(x80531),x80533),x80532))
% 25.54/25.41 [8130]P57(x81301,x81302)+~P57(x81301,x81303)+~P1(f862(f862(f227(f932(x81301,f932(x81301,a921))),x81302),x81303))
% 25.54/25.41 [8172]~P1(f862(f862(f227(a924),x81723),x81722))+P1(f862(f862(f227(a924),x81721),f862(f862(f3(a924),x81722),x81723)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),x81721),x81723)),x81722))
% 25.54/25.41 [8190]P35(x81901,x81902)+~P35(x81901,x81903)+~P1(f862(f862(f227(f932(f931(x81901,x81901),a921)),x81902),x81903))
% 25.54/25.42 [8191]P55(x81911,x81912)+~P55(x81911,x81913)+~P1(f862(f862(f227(f932(f931(x81911,x81911),a921)),x81912),x81913))
% 25.54/25.42 [8192]P37(x81921,x81922)+~P37(x81921,x81923)+~P1(f862(f862(f227(f932(f931(x81921,x81921),a921)),x81922),x81923))
% 25.54/25.42 [8430]~P127(x84301)+~P1(f862(f862(f228(x84301),f71(x84301)),x84302))+P1(f862(f862(f228(x84301),f862(f862(f236(x84301),x84302),x84303)),f862(f862(f74(x84301),x84302),f862(f862(f236(x84301),x84302),x84303))))
% 25.54/25.42 [8520]~P1(f862(x85201,f2(a1)))+~P1(f862(x85201,f862(f862(f3(a1),f862(f93(a1),x85202)),f862(f93(a1),x85203))))+P1(f862(x85201,f862(f93(a1),f862(f862(f3(a924),x85202),x85203))))
% 25.54/25.42 [8535]~P1(f862(f862(f227(a924),x85353),x85352))+P1(f862(x85351,f862(f862(f3(a1),f862(f93(a1),x85352)),f862(f93(a1),x85353))))+~P1(f862(x85351,f862(f93(a1),f862(f862(f3(a924),x85352),x85353))))
% 25.54/25.42 [8555]P1(f862(f862(f228(a924),x85551),x85552))+~P1(f862(x85553,f862(f862(f3(a1),f862(f93(a1),x85551)),f862(f93(a1),x85552))))+P1(f862(x85553,f862(f93(a1),f862(f862(f3(a924),x85551),x85552))))
% 25.54/25.42 [8609]~P128(x86092)+E(x86091,f2(x86092))+P1(f862(f862(f228(x86092),f2(x86092)),f862(f862(f73(x86092),f862(f862(f74(x86092),x86093),x86093)),f862(f862(f74(x86092),x86091),x86091))))
% 25.54/25.42 [8610]~P128(x86102)+E(x86101,f2(x86102))+P1(f862(f862(f228(x86102),f2(x86102)),f862(f862(f73(x86102),f862(f862(f74(x86102),x86101),x86101)),f862(f862(f74(x86102),x86103),x86103))))
% 25.54/25.42 [8712]~P1(f862(f862(f228(a924),f2(a924)),x87121))+~P1(f862(f862(f228(a1),x87122),x87123))+P1(f862(f862(f228(a1),f862(f862(f74(a1),f862(f93(a1),x87121)),x87122)),f862(f862(f74(a1),f862(f93(a1),x87121)),x87123)))
% 25.54/25.42 [8769]E(f862(f862(f94(f932(x87691,a921)),x87692),f30(f932(x87691,a921),x87693)),f181(f932(x87691,a921)))+P1(f862(f862(f321(f932(x87691,a921)),x87692),x87693))+P1(f862(f862(f321(f932(x87691,a921)),f703(x87693,x87692,x87691)),f862(f862(f301(f932(x87691,a921)),x87692),x87693)))
% 25.54/25.42 [8770]E(f862(f862(f94(f932(x87701,a921)),x87702),f30(f932(x87701,a921),x87703)),f181(f932(x87701,a921)))+P1(f862(f862(f321(f932(x87701,a921)),x87702),x87703))+P1(f862(f862(f321(f932(x87701,a921)),f711(x87703,x87702,x87701)),f862(f862(f301(f932(x87701,a921)),x87702),x87703)))
% 25.54/25.42 [8799]E(x87991,x87992)+~E(f862(f182(f925(x87993)),x87991),f862(f182(f925(x87993)),x87992))+P1(f862(f862(f321(f931(x87993,x87993)),f670(x87993,x87991,x87992)),f862(f165(f931(x87993,x87993)),f862(f862(f174(x87993,x87993),x87992),x87991))))
% 25.54/25.42 [9052]E(f299(x90521,x90522),f299(x90521,x90523))+~P1(f862(f862(f227(f932(f931(x90521,x90521),a921)),x90523),f299(x90521,x90522)))+~P1(f862(f862(f227(f932(f931(x90521,x90521),a921)),x90522),x90523))
% 25.54/25.42 [9119]~P50(x91191,f234(f932(x91191,a921)),x91193)+P1(f862(f862(f227(f932(f931(f925(x91191),f925(x91191)),a921)),f150(x91191,x91192)),f151(x91191,x91193)))+~P1(f862(f862(f227(f932(f931(x91191,x91191),a921)),x91192),x91193))
% 25.54/25.42 [9315]P35(x93151,x93152)+~P1(f862(f862(f321(x93151),x93153),f610(x93152,x93151)))+P1(f862(f862(f321(f931(x93151,x93151)),f862(f862(f244(x93151,x93151),f620(x93152,x93151,x93153)),x93153)),x93152))
% 25.54/25.42 [9351]~P1(f862(f54(x93511),x93512))+P1(f862(f54(f932(x93511,a921)),f862(f862(f53(x93511),x93512),x93513)))+~P1(f862(f862(f227(f932(f931(x93511,x93511),a921)),x93513),f862(f862(f246(x93511,x93511),x93512),f862(f18(f932(x93511,a921),x93511),x93512))))
% 25.54/25.42 [9387]P50(x93871,x93872,x93873)+P1(f862(f862(f321(x93871),f582(x93873,x93872,x93871)),x93872))+~P1(f862(f862(f227(f932(f931(x93871,x93871),a921)),x93873),f862(f862(f246(x93871,x93871),x93872),f862(f18(f932(x93871,a921),x93871),x93872))))
% 25.54/25.42 [9388]P50(x93881,x93882,x93883)+P1(f862(f862(f321(x93881),f585(x93882,x93883,x93881)),x93882))+~P1(f862(f862(f227(f932(f931(x93881,x93881),a921)),x93883),f862(f862(f246(x93881,x93881),x93882),f862(f18(f932(x93881,a921),x93881),x93882))))
% 25.54/25.42 [9423]~P67(x94231)+~P1(f862(f862(f228(x94231),x94232),x94233))+P1(f862(f862(f228(x94231),f862(f862(f281(x94231),f862(f862(f73(x94231),x94232),x94233)),f862(f862(f73(x94231),f71(x94231)),f71(x94231)))),x94233))
% 25.54/25.42 [9453]~P66(x94531)+P1(f862(f862(f227(x94531),x94532),x94533))+~P1(f862(f862(f227(x94531),f862(f862(f74(x94531),f363(x94533,x94532,x94531)),x94532)),x94533))
% 25.54/25.42 [9591]E(f862(f182(f925(f925(x95911))),f862(f129(f925(x95911),f862(f862(f10(a924,a921,f925(x95911)),f862(f228(a924),x95912)),f182(f925(x95911)))),f172(x95911,x95913))),f862(f182(f925(x95911)),f862(f862(f157(f925(x95911)),x95913),x95912)))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x95911),a924),f182(f925(x95911))),x95913)))+~P1(f862(f862(f228(a924),x95912),f862(f182(f925(f925(x95911))),x95913)))
% 25.54/25.42 [9707]~P35(x97071,x97072)+P24(x97071,f862(f862(f244(f932(f931(x97071,x97071),a921),f932(f931(x97071,x97071),a921)),x97072),x97073))+~P1(f862(f862(f227(f932(f931(x97071,x97071),a921)),f862(f862(f280(x97071,x97071,x97071),x97072),x97073)),x97072))
% 25.54/25.42 [9712]E(f862(f862(f147(f925(x97121),x97121),f862(f862(f9(f925(x97121),a924,x97121),f157(x97121)),x97122)),f862(f129(f925(x97121),f862(f862(f10(a924,a921,f925(x97121)),f862(f228(a924),x97122)),f182(f925(x97121)))),f172(x97121,x97123))),f862(f862(f157(f925(x97121)),x97123),x97122))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x97121),a924),f182(f925(x97121))),x97123)))+~P1(f862(f862(f228(a924),x97122),f862(f182(f925(f925(x97121))),x97123)))
% 25.54/25.42 [9847]P50(x98471,x98472,x98473)+~P1(f862(f862(f321(f931(x98471,x98471)),f862(f862(f244(x98471,x98471),f582(x98473,x98472,x98471)),f582(x98473,x98472,x98471))),x98473))+~P1(f862(f862(f227(f932(f931(x98471,x98471),a921)),x98473),f862(f862(f246(x98471,x98471),x98472),f862(f18(f932(x98471,a921),x98471),x98472))))
% 25.54/25.42 [9848]P50(x98481,x98482,x98483)+~P1(f862(f862(f321(f931(x98481,x98481)),f862(f862(f244(x98481,x98481),f585(x98482,x98483,x98481)),f585(x98482,x98483,x98481))),x98483))+~P1(f862(f862(f227(f932(f931(x98481,x98481),a921)),x98483),f862(f862(f246(x98481,x98481),x98482),f862(f18(f932(x98481,a921),x98481),x98482))))
% 25.54/25.42 [10019]~P142(x100191)+~P124(x100191)+E(f862(f862(f281(x100191),f862(f95(x100191),f862(f862(f66(f931(a1,a1),a1,x100192,f243(a1,a1)),f205(x100192)),x100193))),f862(f95(x100191),f862(f862(f66(f931(a1,a1),a1,x100192,f248(a1,a1)),f205(x100192)),x100193))),f215(x100192,x100191,x100193))
% 25.54/25.42 [10215]~E(x102153,f2(a924))+~E(f862(f182(f925(x102151)),f862(f862(f157(f925(x102151)),x102152),f718(x102153,x102151,x102152))),x102153)+E(f862(f862(f147(a924,f925(x102151)),f862(f862(f9(a924,f925(a924),f925(x102151)),f862(f862(f10(f932(a924,x102151),f932(f925(a924),f925(x102151)),a924),f147(a924,x102151)),f862(f9(a924,a924,x102151),f862(f862(f10(f925(x102151),f932(a924,x102151),a924),f157(x102151)),f862(f157(f925(x102151)),x102152))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102151))),x102152))))),f132(a924,f862(f295(a924,f2(a924)),x102153))),f172(x102151,x102152))
% 25.54/25.42 [10216]E(x102161,f106(f925(x102162)))+~E(f862(f182(f925(x102162)),f862(f862(f157(f925(x102162)),x102161),f718(x102163,x102162,x102161))),x102163)+E(f862(f862(f147(a924,f925(x102162)),f862(f862(f9(a924,f925(a924),f925(x102162)),f862(f862(f10(f932(a924,x102162),f932(f925(a924),f925(x102162)),a924),f147(a924,x102162)),f862(f9(a924,a924,x102162),f862(f862(f10(f925(x102162),f932(a924,x102162),a924),f157(x102162)),f862(f157(f925(x102162)),x102161))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102162))),x102161))))),f132(a924,f862(f295(a924,f2(a924)),x102163))),f172(x102162,x102161))
% 25.54/25.42 [10217]~E(x102173,f2(a924))+E(f862(f862(f147(a924,f925(x102171)),f862(f862(f9(a924,f925(a924),f925(x102171)),f862(f862(f10(f932(a924,x102171),f932(f925(a924),f925(x102171)),a924),f147(a924,x102171)),f862(f9(a924,a924,x102171),f862(f862(f10(f925(x102171),f932(a924,x102171),a924),f157(x102171)),f862(f157(f925(x102171)),x102172))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102171))),x102172))))),f132(a924,f862(f295(a924,f2(a924)),x102173))),f172(x102171,x102172))+P1(f862(f862(f228(a924),f718(x102173,x102171,x102172)),f862(f182(f925(f925(x102171))),x102172)))
% 25.54/25.42 [10218]E(x102181,f106(f925(x102182)))+E(f862(f862(f147(a924,f925(x102182)),f862(f862(f9(a924,f925(a924),f925(x102182)),f862(f862(f10(f932(a924,x102182),f932(f925(a924),f925(x102182)),a924),f147(a924,x102182)),f862(f9(a924,a924,x102182),f862(f862(f10(f925(x102182),f932(a924,x102182),a924),f157(x102182)),f862(f157(f925(x102182)),x102181))))),f132(a924,f862(f295(a924,f2(a924)),f862(f182(f925(f925(x102182))),x102181))))),f132(a924,f862(f295(a924,f2(a924)),x102183))),f172(x102182,x102181))+P1(f862(f862(f228(a924),f718(x102183,x102182,x102181)),f862(f182(f925(f925(x102182))),x102181)))
% 25.54/25.42 [7932]E(f862(f862(f73(a924),f862(f96(a924),x79321)),f862(f862(f73(a924),f862(f96(a924),x79322)),x79323)),f862(f862(f73(a924),f862(f96(a924),f862(f862(f73(a1),x79321),x79322))),x79323))+P1(f862(a186,f862(f96(a1),x79321)))+P1(f862(a186,f862(f96(a1),x79322)))
% 25.54/25.42 [8703]~P1(f862(f54(x87031),x87032))+~P1(f862(f862(f321(x87031),x87033),x87032))+E(f862(a105,f862(f28(x87031),f862(f862(f3(f932(x87031,a921)),x87032),f862(f862(f301(x87031),x87033),f181(f932(x87031,a921)))))),f862(f28(x87031),x87032))
% 25.54/25.42 [8720]~P1(f862(f54(x87201),x87202))+~P1(f862(f862(f321(x87201),x87203),x87202))+E(f862(f862(f73(a924),f71(a924)),f862(f28(x87201),f862(f862(f3(f932(x87201,a921)),x87202),f862(f862(f301(x87201),x87203),f181(f932(x87201,a921)))))),f862(f28(x87201),x87202))
% 25.54/25.42 [8808]~P109(x88081)+~P1(f862(f54(x88081),x88083))+E(f862(f862(f141(x88081,x88081,f7(x88081)),x88082),f132(x88081,f862(f862(f3(f932(x88081,a921)),x88083),f862(f862(f301(x88081),x88082),f181(f932(x88081,a921)))))),f132(x88081,f862(f862(f301(x88081),x88082),x88083)))
% 25.54/25.42 [8974]~P1(f862(f54(x89741),x89743))+~P1(f862(f54(x89741),x89742))+E(f862(f862(f73(a924),f862(f28(x89741),f862(f862(f103(f932(x89741,a921)),x89742),x89743))),f862(f28(x89741),f862(f862(f94(f932(x89741,a921)),x89742),x89743))),f862(f862(f73(a924),f862(f28(x89741),x89742)),f862(f28(x89741),x89743)))
% 25.54/25.42 [8975]~P1(f862(f54(x89751),x89753))+~P1(f862(f54(x89751),x89752))+E(f862(f862(f73(a924),f862(f28(x89751),f862(f862(f103(f932(x89751,a921)),x89752),x89753))),f862(f28(x89751),f862(f862(f94(f932(x89751,a921)),x89752),x89753))),f862(f862(f73(a924),f862(f28(x89751),x89752)),f862(f28(x89751),x89753)))
% 25.54/25.42 [10163]~P22(x101631,f932(f932(x101631,a921),a921),f862(f862(f9(x101631,f932(f931(x101631,x101631),a921),f932(f932(x101631,a921),a921)),f862(f862(f10(f932(x101631,a921),f932(f932(f931(x101631,x101631),a921),f932(f932(x101631,a921),a921)),x101631),f53(x101631)),f862(f862(f9(x101631,f932(x101631,a921),f932(x101631,a921)),f301(x101631)),f181(f932(x101631,a921))))),x101633),x101632)+~P1(f862(f54(x101631),x101632))+E(f862(f28(f932(x101631,a921)),f862(f862(f53(x101631),x101632),x101633)),f862(f28(x101631),x101632))
% 25.54/25.42 [8205]~P98(x82051)+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x82053)))+E(f862(f862(f236(x82051),x82052),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x82053),x82053)),a90))),f71(x82051))
% 25.54/25.42 [8301]~P98(x83011)+P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x83013)))+E(f862(f862(f236(x83011),f862(f96(x83011),x83012)),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x83013),x83013)),a90))),f71(x83011))
% 25.54/25.42 [9692]~P98(x96921)+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x96923)))+E(f862(f862(f236(x96921),x96922),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x96923),x96923)),a90))),f862(f862(f79(x96921,x96921),f862(f862(f236(x96921),x96922),f862(f96(a924),x96923))),f862(f862(f20(x96921,x96921,x96921),f862(f862(f10(x96921,f932(x96921,x96921),x96921),f74(x96921)),f862(f74(x96921),x96922))),f7(x96921))))
% 25.54/25.42 [9758]~P98(x97581)+~P1(f862(f862(f227(a1),f2(a1)),f862(f96(a1),x97583)))+E(f862(f862(f236(x97581),f862(f96(x97581),x97582)),f862(f96(a924),f862(f862(f3(a1),f862(f862(f73(a1),x97583),x97583)),a90))),f862(f862(f79(x97581,x97581),f862(f862(f236(x97581),f862(f96(x97581),x97582)),f862(f96(a924),x97583))),f862(f862(f20(x97581,x97581,x97581),f862(f862(f10(x97581,f932(x97581,x97581),x97581),f74(x97581)),f862(f74(x97581),f862(f96(x97581),x97582)))),f7(x97581))))
% 25.54/25.42 [10081]~P1(f862(f130(x100811),x100813))+~P1(f862(f862(f321(x100811),x100812),f862(f165(x100811),x100813)))+E(f862(f862(f131(x100811),f862(f182(f925(x100811)),f170(x100811,f862(f862(f10(a921,a921,x100811),a314),f862(f862(f9(x100811,x100811,a921),a317),x100812)),f862(f161(x100811),x100813)))),f862(f161(x100811),x100813)),f862(f862(f144(x100811),x100812),f862(f161(x100811),f170(x100811,f862(f862(f10(a921,a921,x100811),a314),f862(f862(f9(x100811,x100811,a921),a317),x100812)),x100813))))
% 25.54/25.42 [10144]P1(f862(f862(f227(f932(f931(x101441,x101441),a921)),f299(x101441,x101442)),x101443))+~P1(f862(f862(f227(f932(f931(x101441,x101441),a921)),f299(x101441,f181(f932(f931(x101441,x101441),a921)))),x101443))+~P1(f862(f862(f227(f932(f931(x101441,x101441),a921)),f862(f862(f280(x101441,x101441,x101441),f862(f862(f94(f932(f931(x101441,x101441),a921)),f299(x101441,x101442)),x101443)),x101442)),x101443))
% 25.54/25.42 [9998]~P1(f862(f54(x99981),f862(f254(x99981),x99983)))+~P1(f862(f54(x99981),f862(f254(x99981),x99982)))+P1(f862(f54(x99981),f862(f254(x99981),f862(f862(f20(x99981,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99981),a319),x99982)),x99983))))
% 25.54/25.42 [10278]P1(f862(f862(f227(f932(f931(x102781,x102781),a921)),f862(f862(f280(x102781,x102781,x102781),x102782),f299(x102781,x102782))),x102783))+~P1(f862(f862(f227(f932(f931(x102781,x102781),a921)),x102782),x102783))+~P1(f862(f862(f227(f932(f931(x102781,x102781),a921)),f862(f862(f280(x102781,x102781,x102781),f862(f862(f94(f932(f931(x102781,x102781),a921)),f862(f862(f280(x102781,x102781,x102781),x102782),f299(x102781,x102782))),x102783)),x102782)),x102783))
% 25.54/25.42 [10231]~P112(x102312)+E(x102311,f2(x102312))+~E(f862(f862(f73(x102312),f862(f862(f236(x102312),x102313),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102312),x102311),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102312))
% 25.54/25.42 [10232]~P112(x102322)+E(x102321,f2(x102322))+~E(f862(f862(f73(x102322),f862(f862(f236(x102322),x102321),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102322),x102323),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x102322))
% 25.54/25.42 [10238]~P1(f862(f130(x102381),x102383))+~P1(f862(f862(f321(x102381),x102382),f862(f165(x102381),x102383)))+E(f862(f161(x102381),f862(f164(x102381),f862(f862(f131(x102381),f862(f182(f925(x102381)),f170(x102381,f862(f862(f10(a921,a921,x102381),a314),f862(f862(f9(x102381,x102381,a921),a317),x102382)),x102383))),x102383))),f170(x102381,f862(f862(f10(a921,a921,x102381),a314),f862(f862(f9(x102381,x102381,a921),a317),x102382)),f862(f161(x102381),x102383)))
% 25.54/25.42 [10323]~P112(x103232)+E(x103231,f2(x103232))+P1(f862(f862(f228(x103232),f2(x103232)),f862(f862(f73(x103232),f862(f862(f236(x103232),x103233),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103232),x103231),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))))
% 25.54/25.42 [10324]~P112(x103242)+E(x103241,f2(x103242))+P1(f862(f862(f228(x103242),f2(x103242)),f862(f862(f73(x103242),f862(f862(f236(x103242),x103241),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103242),x103243),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))))
% 25.54/25.42 [10385]~P112(x103851)+P1(f862(f862(f227(x103851),f2(x103851)),x103852))+~P1(f862(f862(f227(x103851),f2(x103851)),f862(f862(f236(x103851),x103852),f862(a105,f862(f862(f74(a924),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x103853)))))
% 25.54/25.42 [5134]~E(x51342,f83(x51343,x51341))+P1(f862(x51341,x51342))+~P1(f862(x51341,x51344))
% 25.54/25.42 [5383]E(f61(x53833,x53832,x53834),x53832)+E(x53831,f744(x53832,x53833,x53834))+~P1(f862(x53834,x53831))
% 25.54/25.42 [6713]E(f61(x67131,x67132,x67133),f78(x67131,x67133))+~E(f782(x67132,x67131,x67133,x67134),x67134)+~P1(f862(x67133,x67134))
% 25.54/25.42 [6917]~P35(x69172,x69174)+~P35(x69171,x69173)+P35(f931(x69171,x69172),f311(x69171,x69172,x69173,x69174))
% 25.54/25.42 [6918]~P36(x69182,x69184)+~P36(x69181,x69183)+P36(f931(x69181,x69182),f311(x69181,x69182,x69183,x69184))
% 25.54/25.42 [5322]~P5(x53224,x53221)+~E(f862(x53221,x53222),f862(x53221,x53223))+P1(f862(f862(x53221,x53222),x53223))
% 25.54/25.42 [5483]~P5(x54834,x54831)+E(f862(x54831,x54832),f862(x54831,x54833))+~P1(f862(f862(x54831,x54832),x54833))
% 25.54/25.42 [5484]~P13(x54844,x54841)+E(f862(x54841,x54842),f862(x54841,x54843))+~P1(f862(f862(x54841,x54842),x54843))
% 25.54/25.42 [5578]~P16(x55783,x55784,x55781)+E(f862(x55781,x55782),f862(f56(x55783,x55784),x55782))+~P1(f862(f54(x55783),x55782))
% 25.54/25.42 [5579]~P7(x55793,x55794,x55791)+E(f862(x55791,x55792),f862(f56(x55793,x55794),x55792))+~P1(f862(f54(x55793),x55792))
% 25.54/25.42 [5706]~P5(x57064,x57061)+~P1(f862(f862(x57061,x57063),x57062))+P1(f862(f862(x57061,x57062),x57063))
% 25.54/25.42 [5707]~P48(x57074,x57071)+~P1(f862(f862(x57071,x57073),x57072))+P1(f862(f862(x57071,x57072),x57073))
% 25.54/25.42 [5708]~P13(x57084,x57081)+~P1(f862(f862(x57081,x57083),x57082))+P1(f862(f862(x57081,x57082),x57083))
% 25.54/25.42 [5709]~P13(x57093,x57091)+P1(f862(f862(x57091,x57092),x57092))+~P1(f862(f862(x57091,x57094),x57092))
% 25.54/25.42 [5710]~P13(x57103,x57101)+P1(f862(f862(x57101,x57102),x57102))+~P1(f862(f862(x57101,x57102),x57104))
% 25.54/25.42 [5782]E(x57821,x57822)+~E(f862(f243(x57823,x57824),x57821),f862(f243(x57823,x57824),x57822))+~E(f862(f248(x57823,x57824),x57821),f862(f248(x57823,x57824),x57822))
% 25.54/25.42 [5783]E(x57831,x57832)+~E(f862(f243(x57833,x57834),x57831),f862(f243(x57833,x57834),x57832))+~E(f862(f248(x57833,x57834),x57831),f862(f248(x57833,x57834),x57832))
% 25.54/25.42 [5810]E(x58101,x58102)+~P1(f862(f41(x58103,x58104),x58102))+~P1(f862(f41(x58103,x58104),x58101))
% 25.54/25.42 [6010]~P72(x60102)+E(f224(x60101,x60102,x60103,x60104),f2(x60102))+P1(f862(f54(x60101),x60104))
% 25.54/25.42 [6058]~P5(x60583,x60582)+~P1(f862(x60581,x60584))+P1(f862(x60581,f824(x60581,x60582,x60583)))
% 25.54/25.42 [6153]~P1(f862(f307(x61531,x61532),x61534))+P1(f862(f307(x61531,x61532),x61533))+~P1(f862(f862(x61532,x61533),x61534))
% 25.54/25.42 [6154]~P1(f862(f307(x61541,x61542),x61544))+P1(f862(f307(x61541,x61542),x61543))+~P1(f862(f862(x61542,x61543),x61544))
% 25.54/25.42 [6155]~P1(f862(f307(x61551,x61552),x61554))+P1(f862(f307(x61551,x61552),x61553))+~P1(f862(f862(x61552,x61553),x61554))
% 25.54/25.42 [6953]~P27(x69531,x69533,x69534)+P1(f862(x69531,x69532))+~P1(f862(f862(f321(a1),x69532),f296(a1,x69533,x69534)))
% 25.54/25.42 [7145]~P5(x71451,x71453)+~P1(f862(x71452,x71454))+P1(f862(f862(f321(x71451),f824(x71452,x71453,x71451)),f262(x71451,x71453)))
% 25.54/25.42 [8042]E(x80421,f2(a924))+~P1(f862(x80422,x80423))+P1(f862(x80422,f777(x80422,x80423,x80421,x80424)))
% 25.54/25.42 [8125]~P109(x81252)+~P1(f862(f130(x81251),x81254))+P1(f862(f130(x81251),f143(x81251,x81252,x81253,x81254)))
% 25.54/25.42 [8171]E(f61(x81711,x81712,x81713),f78(x81711,x81713))+~P1(f862(x81713,x81714))+P1(f862(x81713,f782(x81712,x81711,x81713,x81714)))
% 25.54/25.42 [8355]~P1(f862(f54(x83552),x83554))+~P1(f862(f54(x83551),x83553))+P1(f862(f54(f930(x83551,x83552)),f305(x83551,x83552,x83553,x83554)))
% 25.54/25.42 [8356]~P1(f862(f54(x83562),x83564))+~P1(f862(f54(x83561),x83563))+P1(f862(f54(f930(x83561,x83562)),f305(x83561,x83562,x83563,x83564)))
% 25.54/25.42 [8357]~P1(f862(f130(x83572),x83574))+~P1(f862(f130(x83571),x83573))+P1(f862(f130(f931(x83571,x83572)),f52(x83571,x83572,x83573,x83574)))
% 25.54/25.42 [8360]P1(f862(f862(f321(f925(x83601)),f862(f862(f127(x83601),x83602),x83603)),f154(x83601,x83604)))+~P1(f862(f862(f321(f925(x83601)),x83603),f154(x83601,x83604)))+~P1(f862(f862(f321(f925(x83601)),x83602),f154(x83601,x83604)))
% 25.54/25.42 [8640]E(x86401,f2(a924))+P1(f862(x86402,x86403))+~P1(f862(x86402,f778(x86402,x86403,x86401,x86404)))
% 25.54/25.42 [8678]~P109(x86783)+~P1(f862(f130(x86781),f143(x86781,x86783,x86784,x86782)))+P1(f862(f130(x86781),x86782))
% 25.54/25.42 [8963]~P1(f862(f862(f321(f931(x89631,x89631)),f862(f862(f244(x89631,x89631),x89632),x89634)),f299(x89631,x89633)))+P1(f862(f862(f321(x89631),x89632),f308(x89631,x89633)))+~P1(f862(f862(f321(x89631),x89634),f308(x89631,x89633)))
% 25.54/25.42 [8964]~P1(f862(f862(f321(f931(x89641,x89641)),f862(f862(f244(x89641,x89641),x89642),x89644)),f299(x89641,x89643)))+P1(f862(f862(f321(x89641),x89642),f308(x89641,x89643)))+~P1(f862(f862(f321(x89641),x89644),f308(x89641,x89643)))
% 25.54/25.42 [5304]~P72(x53042)+E(f862(f862(f8(x53041,x53042),x53043),x53044),f2(x53042))+P1(f862(f54(x53041),x53044))
% 25.54/25.42 [5305]~P72(x53052)+E(f862(f862(f8(x53051,x53052),x53053),x53054),f2(x53052))+P1(f862(f54(x53051),x53054))
% 25.54/25.42 [5306]~P72(x53062)+E(f862(f862(f8(x53061,x53062),x53063),x53064),f2(x53062))+P1(f862(f54(x53061),x53064))
% 25.54/25.42 [5307]~P71(x53072)+E(f862(f862(f11(x53071,x53072),x53073),x53074),f71(x53072))+P1(f862(f54(x53071),x53074))
% 25.54/25.42 [5308]~P71(x53082)+E(f862(f862(f11(x53081,x53082),x53083),x53084),f71(x53082))+P1(f862(f54(x53081),x53084))
% 25.54/25.42 [5309]~P71(x53092)+E(f862(f862(f11(x53091,x53092),x53093),x53094),f71(x53092))+P1(f862(f54(x53091),x53094))
% 25.54/25.42 [5446]~P73(x54463)+E(x54461,x54462)+~E(f862(f862(f73(x54463),x54464),x54461),f862(f862(f73(x54463),x54464),x54462))
% 25.54/25.42 [5447]~P73(x54473)+E(x54471,x54472)+~E(f862(f862(f73(x54473),x54474),x54471),f862(f862(f73(x54473),x54474),x54472))
% 25.54/25.42 [5448]~P74(x54483)+E(x54481,x54482)+~E(f862(f862(f73(x54483),x54484),x54481),f862(f862(f73(x54483),x54484),x54482))
% 25.54/25.42 [5449]~P73(x54493)+E(x54491,x54492)+~E(f862(f862(f73(x54493),x54491),x54494),f862(f862(f73(x54493),x54492),x54494))
% 25.54/25.42 [5450]~P73(x54503)+E(x54501,x54502)+~E(f862(f862(f73(x54503),x54501),x54504),f862(f862(f73(x54503),x54502),x54504))
% 25.54/25.42 [5545]~P120(x55451)+~E(x55453,f862(f862(f74(x55451),x55452),x55454))+P1(f862(f862(f278(x55451),x55452),x55453))
% 25.54/25.42 [5573]~P3(x55733)+E(x55731,f181(f932(x55732,a921)))+E(f862(f862(f32(x55732,x55733),x55731),f862(f18(x55733,x55732),x55734)),x55734)
% 25.54/25.42 [5574]~P3(x55743)+E(x55741,f181(f932(x55742,a921)))+E(f862(f862(f33(x55742,x55743),x55741),f862(f18(x55743,x55742),x55744)),x55744)
% 25.54/25.42 [5727]~E(x57274,f181(f932(x57271,a921)))+~E(x57274,f862(f862(f301(x57271),x57272),x57273))+P1(f862(f862(f321(x57271),x57272),x57273))
% 25.54/25.42 [5796]~P110(x57963)+E(x57961,x57962)+~E(f296(x57963,x57964,x57961),f862(f862(f301(x57963),x57962),f181(f932(x57963,a921))))
% 25.54/25.42 [5797]~P110(x57973)+E(x57971,x57972)+~E(f296(x57973,x57971,x57972),f862(f862(f301(x57973),x57974),f181(f932(x57973,a921))))
% 25.54/25.42 [5857]~P33(x58573,x58571,x58574)+P33(x58573,x58571,f862(f862(f144(x58573),x58572),x58574))+P1(f862(x58571,x58572))
% 25.54/25.42 [5959]~P29(x59591,x59592,x59594)+~P1(f862(x59592,x59593))+P29(x59591,x59592,f862(f862(f144(x59591),x59593),x59594))
% 25.54/25.42 [6110]P1(f862(x61101,x61102))+~P1(f862(f240(x61103,x61101),x61104))+~P1(f862(f862(f321(x61103),x61102),x61104))
% 25.54/25.42 [6119]~P29(x61191,x61192,x61194)+~P29(x61191,x61192,x61193)+P29(x61191,x61192,f862(f862(f127(x61191),x61193),x61194))
% 25.54/25.42 [6134]P31(x61341,x61342,x61343)+~P31(x61341,x61342,f862(f862(f144(x61341),x61344),x61343))+P1(f862(x61342,x61344))
% 25.54/25.42 [6135]P33(x61351,x61352,x61353)+~P33(x61351,x61352,f862(f862(f144(x61351),x61354),x61353))+P1(f862(x61352,x61354))
% 25.54/25.42 [6208]P31(x62081,x62082,x62083)+P31(x62081,x62082,x62084)+~P31(x62081,x62082,f862(f862(f127(x62081),x62084),x62083))
% 25.54/25.42 [6228]~P72(x62281)+E(f862(f862(f8(a924,x62281),x62282),f862(f295(a924,x62283),f862(a105,x62284))),f2(x62281))+~P1(f862(f862(f228(a924),x62284),x62283))
% 25.54/25.42 [6233]~P62(x62331)+~E(f38(x62331,x62332,x62333),f38(x62331,x62334,x62333))+E(f38(x62331,f862(f72(x62331),x62332),x62333),f38(x62331,f862(f72(x62331),x62334),x62333))
% 25.54/25.42 [6299]P1(f862(x62991,x62992))+~E(f862(f129(x62993,x62991),x62994),x62994)+~P1(f862(f862(f321(x62993),x62992),f862(f165(x62993),x62994)))
% 25.54/25.42 [6318]~E(f862(f862(f73(a924),x63183),x63182),f862(f862(f73(a924),x63181),x63184))+~P1(f862(f862(f228(a924),x63183),x63184))+P1(f862(f862(f228(a924),x63181),x63182))
% 25.54/25.42 [6322]P31(x63221,x63222,x63223)+~P1(f862(x63222,x63224))+~P1(f862(f862(f321(x63221),x63224),f862(f165(x63221),x63223)))
% 25.54/25.42 [6323]P31(x63231,x63232,x63233)+~P1(f862(x63232,x63234))+~P1(f862(f862(f321(x63231),x63234),f862(f165(x63231),x63233)))
% 25.54/25.42 [6324]P31(x63241,x63242,x63243)+~P1(f862(x63242,x63244))+~P1(f862(f862(f321(x63241),x63244),f862(f165(x63241),x63243)))
% 25.54/25.42 [6327]~P61(x63271)+E(f38(x63271,f38(x63271,x63272,x63273),x63274),f38(x63271,x63272,x63274))+~P1(f862(f862(f278(x63271),x63274),x63273))
% 25.54/25.42 [6362]~P29(x63623,x63621,x63624)+P1(f862(x63621,x63622))+~P1(f862(f862(f321(x63623),x63622),f862(f165(x63623),x63624)))
% 25.54/25.42 [6363]~P29(x63633,x63631,x63634)+P1(f862(x63631,x63632))+~P1(f862(f862(f321(x63633),x63632),f862(f165(x63633),x63634)))
% 25.54/25.42 [6364]~P29(x63643,x63641,x63644)+P1(f862(x63641,x63642))+~P1(f862(f862(f321(x63643),x63642),f862(f165(x63643),x63644)))
% 25.54/25.42 [6366]~E(f862(f129(x63661,x63662),x63663),f106(x63661))+~P1(f862(x63662,x63664))+~P1(f862(f862(f321(x63661),x63664),f862(f165(x63661),x63663)))
% 25.54/25.42 [6367]~E(f170(x63673,x63671,x63674),x63674)+P1(f862(x63671,x63672))+~P1(f862(f862(f321(x63673),x63672),f862(f165(x63673),x63674)))
% 25.54/25.42 [6395]~E(x63954,f181(f932(x63952,a921)))+~E(x63953,f181(f932(x63951,a921)))+E(f305(x63951,x63952,x63953,x63954),f181(f932(f930(x63951,x63952),a921)))
% 25.54/25.42 [6543]P1(f862(x65431,x65432))+~P1(f862(f153(x65433,x65431),x65434))+~P1(f862(f862(f321(x65433),x65432),f862(f165(x65433),x65434)))
% 25.54/25.42 [6586]~P1(f862(x65861,x65864))+P1(f862(x65861,f348(x65861,x65862,x65863)))+~P1(f862(f862(f321(x65863),x65864),x65862))
% 25.54/25.42 [6682]~P28(x66821,x66823,x66824)+P1(f862(x66821,x66822))+~P1(f862(f862(f321(a924),x66822),f862(f295(a924,x66823),x66824)))
% 25.54/25.42 [6816]~P72(x68161)+E(f862(f862(f8(a924,x68161),x68162),f296(a924,x68163,f862(a105,x68164))),f2(x68161))+~P1(f862(f862(f228(a924),f862(a105,x68164)),x68163))
% 25.54/25.42 [6956]~P109(x69561)+E(f862(f862(f3(f932(x69561,a921)),f862(f295(x69561,x69562),x69563)),f862(f295(x69561,x69562),x69564)),f862(f295(x69561,x69564),x69563))+~P1(f862(f862(f227(x69561),x69562),x69564))
% 25.54/25.42 [7028]~E(x70283,x70284)+E(x70281,f2(a924))+P1(f862(f862(f321(x70282),x70283),f862(f165(x70282),f162(x70282,x70281,x70284))))
% 25.54/25.42 [7309]~P1(f862(f862(f321(f925(x73091)),x73094),f154(x73091,x73093)))+P1(f862(f862(f321(x73091),x73092),x73093))+~P1(f862(f862(f321(x73091),x73092),f862(f165(x73091),x73094)))
% 25.54/25.42 [7316]~P35(x73161,x73162)+P1(f862(f862(f321(x73161),f611(x73162,x73161,x73163)),x73163))+~P1(f862(f862(f321(x73161),x73164),x73163))
% 25.54/25.42 [7349]~P22(x73492,x73491,x73493,x73494)+E(f862(f28(x73491),f862(f302(x73492,x73491,x73493),x73494)),f862(f28(x73492),x73494))+~P1(f862(f54(x73492),x73494))
% 25.54/25.42 [7372]~P72(x73721)+E(f862(f862(f862(f58(x73721,x73722,f73(x73721)),x73723),f2(x73721)),x73724),f862(f862(f8(x73722,x73721),x73723),x73724))+~P1(f862(f54(x73722),x73724))
% 25.54/25.42 [7373]~P72(x73731)+E(f862(f862(f862(f58(x73731,x73732,f73(x73731)),x73733),f2(x73731)),x73734),f862(f862(f8(x73732,x73731),x73733),x73734))+~P1(f862(f54(x73732),x73734))
% 25.54/25.42 [7374]~P71(x73741)+E(f862(f862(f862(f58(x73741,x73742,f74(x73741)),x73743),f71(x73741)),x73744),f862(f862(f11(x73742,x73741),x73743),x73744))+~P1(f862(f54(x73742),x73744))
% 25.54/25.42 [7375]~P71(x73751)+E(f862(f862(f862(f58(x73751,x73752,f74(x73751)),x73753),f71(x73751)),x73754),f862(f862(f11(x73752,x73751),x73753),x73754))+~P1(f862(f54(x73752),x73754))
% 25.54/25.42 [7390]~P1(f862(x73902,x73904))+~P1(f862(f862(f321(x73901),x73904),x73903))+P1(f862(f862(f321(x73901),f348(x73902,x73903,x73901)),x73903))
% 25.54/25.42 [7403]P22(x74031,x74032,x74033,x74034)+~E(f862(f28(x74032),f862(f302(x74031,x74032,x74033),x74034)),f862(f28(x74031),x74034))+~P1(f862(f54(x74031),x74034))
% 25.54/25.42 [7404]P22(x74041,x74042,x74043,x74044)+~E(f862(f28(x74042),f862(f302(x74041,x74042,x74043),x74044)),f862(f28(x74041),x74044))+~P1(f862(f54(x74041),x74044))
% 25.54/25.42 [7601]~P72(x76011)+E(f862(f862(f73(x76011),f862(x76012,x76013)),f862(f862(f8(a924,x76011),x76012),f297(a924,x76013,x76014))),f862(f862(f8(a924,x76011),x76012),f296(a924,x76013,x76014)))+~P1(f862(f862(f227(a924),x76013),x76014))
% 25.54/25.42 [7610]~P72(x76101)+~P22(x76102,x76101,x76103,x76104)+E(f862(f862(f8(x76101,x76101),f25(x76101)),f862(f302(x76102,x76101,x76103),x76104)),f862(f862(f8(x76102,x76101),x76103),x76104))
% 25.54/25.42 [7611]~P71(x76111)+~P22(x76112,x76111,x76113,x76114)+E(f862(f862(f11(x76111,x76111),f25(x76111)),f862(f302(x76112,x76111,x76113),x76114)),f862(f862(f11(x76112,x76111),x76113),x76114))
% 25.54/25.42 [7658]E(f862(f28(f930(x76581,x76582)),f305(x76581,x76582,x76583,x76584)),f862(f862(f73(a924),f862(f28(x76581),x76583)),f862(f28(x76582),x76584)))+~P1(f862(f54(x76582),x76584))+~P1(f862(f54(x76581),x76583))
% 25.54/25.42 [7659]E(f862(f28(f930(x76591,x76592)),f305(x76591,x76592,x76593,x76594)),f862(f862(f73(a924),f862(f28(x76591),x76593)),f862(f28(x76592),x76594)))+~P1(f862(f54(x76592),x76594))+~P1(f862(f54(x76591),x76593))
% 25.54/25.42 [7742]E(x77421,x77422)+P1(f862(f862(f321(x77423),x77421),f862(f165(x77423),f163(x77423,x77422,x77424))))+~P1(f862(f862(f321(x77423),x77421),f862(f165(x77423),x77424)))
% 25.54/25.42 [7971]~P72(x79711)+E(f862(f862(f73(x79711),f862(f862(f8(a924,x79711),x79712),f862(f295(a924,x79713),x79714))),f862(x79712,x79714)),f862(f862(f8(a924,x79711),x79712),f862(f295(a924,x79713),f862(a105,x79714))))+P1(f862(f862(f228(a924),x79714),x79713))
% 25.54/25.42 [8022]~P22(x80221,x80222,x80223,f234(f932(x80221,a921)))+~P1(f862(f54(x80222),x80224))+P1(f862(f54(x80221),f862(f303(x80221,x80222,x80223),x80224)))
% 25.54/25.42 [8140]P1(f862(f862(f321(f925(x81401)),f862(f862(f144(x81401),x81402),x81403)),f154(x81401,x81404)))+~P1(f862(f862(f321(f925(x81401)),x81403),f154(x81401,x81404)))+~P1(f862(f862(f321(x81401),x81402),x81404))
% 25.54/25.42 [8189]E(x81891,x81892)+~P1(f862(f862(f321(x81893),x81891),f862(f165(x81893),f163(x81893,x81892,x81894))))+P1(f862(f862(f321(x81893),x81891),f862(f165(x81893),x81894)))
% 25.54/25.42 [8229]~E(f862(f302(x82293,x82291,x82294),f234(f932(x82293,a921))),f234(f932(x82291,a921)))+P1(f862(f54(x82291),x82292))+~P1(f862(f54(x82293),f862(f303(x82293,x82291,x82294),x82292)))
% 25.54/25.42 [8293]~P1(f862(x82931,x82934))+P1(f862(x82931,f364(x82932,x82933,x82934,x82931)))+~P1(f862(f862(f321(x82933),x82934),x82932))
% 25.54/25.42 [8326]~P22(x83261,x83263,x83264,x83262)+P1(f862(f54(x83261),x83262))+~P1(f862(f54(x83263),f862(f302(x83261,x83263,x83264),x83262)))
% 25.54/25.42 [8349]~E(x83492,x83493)+P1(f862(f862(f321(f931(x83491,x83491)),f862(f862(f244(x83491,x83491),x83492),x83493)),f255(x83491,x83494)))+~P1(f862(f862(f321(x83491),x83492),x83494))
% 25.54/25.42 [8350]~E(x83502,x83503)+P1(f862(f862(f321(f931(x83501,x83501)),f862(f862(f244(x83501,x83501),x83502),x83503)),f255(x83501,x83504)))+~P1(f862(f862(f321(x83501),x83502),x83504))
% 25.54/25.42 [8384]~P72(x83841)+E(f862(f862(f73(x83841),f862(f862(f8(a924,x83841),x83842),f296(a924,x83843,x83844))),f862(x83842,f862(a105,x83844))),f862(f862(f8(a924,x83841),x83842),f296(a924,x83843,f862(a105,x83844))))+P1(f862(f862(f228(a924),f862(a105,x83844)),x83843))
% 25.54/25.42 [8442]~E(x84422,x84424)+P1(f862(f862(f321(f931(x84421,x84421)),f862(f862(f244(x84421,x84421),x84422),x84424)),f299(x84421,x84423)))+P1(f862(f862(f321(x84421),x84422),f862(f256(x84421,x84421),x84423)))
% 25.54/25.42 [8444]P1(f862(x84441,x84442))+~P1(f862(x84441,f862(f862(f157(x84443),x84444),f667(x84441,x84444,x84443))))+~P1(f862(f862(f321(x84443),x84442),f862(f165(x84443),x84444)))
% 25.54/25.42 [8584]~P1(f862(f862(f321(x85841),x85842),f308(x85841,x85844)))+P1(f862(f862(f321(f925(x85841)),f862(f862(f144(x85841),x85842),x85843)),f308(f925(x85841),f150(x85841,x85844))))+~P1(f862(f862(f321(f925(x85841)),x85843),f308(f925(x85841),f150(x85841,x85844))))
% 25.54/25.42 [8599]~P22(x85992,x85993,x85994,f560(x85994,x85993,x85992,x85991))+P22(x85992,x85993,x85994,f31(f932(x85992,a921),x85991))+E(x85991,f181(f932(f932(x85992,a921),a921)))
% 25.54/25.42 [8753]P1(f862(x87531,x87532))+~P1(f862(x87531,f341(x87532,x87531,x87533,x87534)))+~P1(f862(f862(f321(x87534),x87532),x87533))
% 25.54/25.42 [8872]E(x88721,x88722)+~P1(f862(f862(f321(f931(x88723,x88723)),f862(f862(f244(x88723,x88723),x88721),x88722)),f299(x88723,x88724)))+P1(f862(f862(f321(x88723),x88721),f862(f256(x88723,x88723),x88724)))
% 25.54/25.42 [9025]P1(f862(x90251,x90252))+P1(f862(f862(f321(x90253),f341(x90252,x90251,x90254,x90253)),x90254))+~P1(f862(f862(f321(x90253),x90252),x90254))
% 25.54/25.42 [9037]~P1(f862(x90374,x90373))+~P1(f862(f862(f321(x90371),x90373),x90372))+P1(f862(f862(f321(x90371),f364(x90372,x90371,x90373,x90374)),x90372))
% 25.54/25.42 [9153]E(x91531,f2(a924))+P1(f862(x91532,x91533))+P1(f862(f862(f321(x91534),f778(x91532,x91533,x91531,x91534)),f862(f165(x91534),f162(x91534,x91531,x91533))))
% 25.54/25.42 [9165]E(x91651,f2(a924))+~P1(f862(x91653,x91654))+P1(f862(f862(f321(x91652),f777(x91653,x91654,x91651,x91652)),f862(f165(x91652),f162(x91652,x91651,x91654))))
% 25.54/25.42 [9167]~P23(x91671,x91672,x91673,f234(f932(x91671,a921)),f234(f932(x91672,a921)))+~P1(f862(f54(x91672),x91674))+P1(f862(f54(x91671),f862(f303(x91671,x91672,x91673),x91674)))
% 25.54/25.42 [9170]P22(x91702,x91703,x91704,f31(f932(x91702,a921),x91701))+E(x91701,f181(f932(f932(x91702,a921),a921)))+P1(f862(f862(f321(f932(x91702,a921)),f560(x91704,x91703,x91702,x91701)),x91701))
% 25.54/25.42 [9285]~P23(x92853,x92851,x92854,f234(f932(x92853,a921)),f234(f932(x92851,a921)))+P1(f862(f54(x92851),x92852))+~P1(f862(f54(x92853),f862(f303(x92853,x92851,x92854),x92852)))
% 25.54/25.42 [9303]P1(f862(f54(x93031),x93032))+~P1(f862(f54(x93034),f862(f302(x93031,x93034,x93033),x93032)))+P1(f862(f862(f321(x93031),f581(x93033,x93034,x93032,x93031)),x93032))
% 25.54/25.42 [9399]~P3(x93992)+E(f862(f862(f57(x93991,x93992,f862(f862(f10(x93992,f932(x93992,x93992),x93991),f94(x93992)),x93993)),f234(x93992)),x93994),f862(f862(f32(x93991,x93992),x93994),x93993))+~P1(f862(f54(x93991),x93994))
% 25.54/25.42 [9400]~P3(x94002)+E(f862(f862(f57(x94001,x94002,f862(f862(f10(x94002,f932(x94002,x94002),x94001),f103(x94002)),x94003)),f181(x94002)),x94004),f862(f862(f33(x94001,x94002),x94004),x94003))+~P1(f862(f54(x94001),x94004))
% 25.54/25.42 [9442]~P1(f862(f862(f278(a924),x94422),x94424))+~P1(f862(f862(f278(a924),x94423),x94421))+P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x94421,x94422)),f287(a924,f278(a924),x94423,x94424)))
% 25.54/25.42 [9483]P1(f862(x94831,x94832))+~P1(f862(x94831,f862(f862(f157(x94833),x94834),f704(x94832,x94831,x94834,x94833))))+~P1(f862(f862(f321(x94833),x94832),f862(f165(x94833),x94834)))
% 25.54/25.42 [9503]E(x95031,x95032)+~P1(f862(f862(f321(f931(x95033,x95033)),f862(f862(f244(x95033,x95033),x95031),x95032)),f299(x95033,x95034)))+P1(f862(f862(f321(f931(x95033,x95033)),f862(f862(f244(x95033,x95033),x95031),x95032)),f862(f862(f280(x95033,x95033,x95033),x95034),f299(x95033,x95034))))
% 25.54/25.42 [9504]E(x95041,x95042)+~P1(f862(f862(f321(f931(x95043,x95043)),f862(f862(f244(x95043,x95043),x95041),x95042)),f299(x95043,x95044)))+P1(f862(f862(f321(f931(x95043,x95043)),f862(f862(f244(x95043,x95043),x95041),x95042)),f862(f862(f280(x95043,x95043,x95043),x95044),f299(x95043,x95044))))
% 25.54/25.42 [9555]~E(f862(f182(f925(x95551)),x95552),f862(f182(f925(x95551)),x95553))+~P1(f862(f862(f321(f931(f925(x95551),f925(x95551))),f862(f862(f244(f925(x95551),f925(x95551)),x95552),x95553)),f140(x95551,x95554)))+P1(f862(f862(f321(f931(f925(x95551),f925(x95551))),f862(f862(f244(f925(x95551),f925(x95551)),x95552),x95553)),f138(x95551,x95554)))
% 25.54/25.42 [9579]E(x95791,x95792)+P1(f862(f862(f321(f931(x95793,x95793)),f862(f862(f244(x95793,x95793),x95791),x95792)),f299(x95793,x95794)))+~P1(f862(f862(f321(f931(x95793,x95793)),f862(f862(f244(x95793,x95793),x95791),x95792)),f862(f862(f280(x95793,x95793,x95793),x95794),f299(x95793,x95794))))
% 25.54/25.42 [9679]P1(f862(f862(f278(a924),x96791),x96792))+~P1(f862(f862(f278(a924),x96793),x96791))+~P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x96793,x96791)),f287(a924,f278(a924),x96794,x96792)))
% 25.54/25.42 [9680]P1(f862(f862(f278(a924),x96801),x96802))+~P1(f862(f862(f278(a924),x96802),x96803))+~P1(f862(f862(f227(f932(a924,a921)),f287(a924,f278(a924),x96802,x96803)),f287(a924,f278(a924),x96801,x96804)))
% 25.54/25.42 [9795]P29(x97951,f862(f862(f20(x97951,a921,a921),f862(f862(f10(a921,f932(a921,a921),x97951),a319),f862(f862(f10(a921,a921,x97951),a314),x97952))),f862(a317,x97953)),x97954)+~P1(f862(x97952,x97953))+~P33(x97951,x97952,f862(f862(f144(x97951),x97953),x97954))
% 25.54/25.42 [9961]~P29(x99611,f862(f862(f20(x99611,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99611),a319),f862(f862(f10(a921,a921,x99611),a314),x99612))),f862(a317,x99613)),x99614)+~P1(f862(x99612,x99613))+P33(x99611,x99612,f862(f862(f144(x99611),x99613),x99614))
% 25.54/25.42 [9965]~P33(x99651,x99652,x99654)+~P29(x99651,f862(f862(f20(x99651,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99651),a319),f862(f862(f10(a921,a921,x99651),a314),x99652))),f862(a317,x99653)),x99654)+P33(x99651,x99652,f862(f862(f144(x99651),x99653),x99654))
% 25.54/25.42 [9999]~P59(x99991)+E(f862(f862(f8(a924,x99991),f862(f862(f20(a924,x99991,x99991),f862(f862(f10(x99991,f932(x99991,x99991),a924),f3(x99991)),x99992)),f862(f862(f10(a924,x99991,a924),x99992),f862(f862(f9(a924,a924,a924),f73(a924)),f71(a924))))),f296(a924,x99993,x99994)),f2(x99991))+P1(f862(f862(f227(a924),x99993),x99994))
% 25.54/25.42 [10230]~P35(x102302,x102304)+~P22(x102302,x102301,x102303,f234(f932(x102302,a921)))+P35(x102301,f862(f302(f931(x102302,x102302),f931(x102301,x102301),f250(x102302,x102301,x102302,x102301,x102303,x102303)),x102304))
% 25.54/25.42 [10420]~E(f862(f182(f925(x104201)),x104203),f862(f182(f925(x104201)),x104202))+P1(f862(f862(f321(f931(f925(x104201),f925(x104201))),f862(f862(f244(f925(x104201),f925(x104201)),x104202),x104203)),f151(x104201,x104204)))+~P1(f862(f862(f249(x104201,x104201,a921),f862(f862(f9(x104201,f932(f931(x104201,x104201),a921),f932(x104201,a921)),f862(f862(f10(f932(x104201,f932(f932(f931(x104201,x104201),a921),a921)),f932(f932(f931(x104201,x104201),a921),f932(x104201,a921)),x104201),f9(x104201,f932(f931(x104201,x104201),a921),a921)),f862(f862(f10(f932(x104201,f931(x104201,x104201)),f932(x104201,f932(f932(f931(x104201,x104201),a921),a921)),x104201),f862(f10(f931(x104201,x104201),f932(f932(f931(x104201,x104201),a921),a921),x104201),f321(f931(x104201,x104201)))),f244(x104201,x104201)))),x104204)),f671(x104204,x104203,x104202,x104201)))
% 25.54/25.42 [6280]~P61(x62801)+~E(x62802,f2(x62801))+E(f862(f862(f29(x62801),f862(f862(f74(x62801),x62802),x62803)),f862(f862(f74(x62801),x62802),x62804)),f2(x62801))
% 25.54/25.42 [6321]E(x63211,f106(x63212))+E(x63213,f862(f862(f3(a924),f862(f182(f925(x63212)),x63211)),f71(a924)))+E(f137(x63212,f862(f862(f152(x63212,x63211),x63213),x63214)),f137(x63212,x63211))
% 25.54/25.42 [6355]E(x63551,x63552)+P1(f862(x63553,x63552))+~P1(f862(f862(f862(f301(x63554),x63551),x63553),x63552))
% 25.54/25.42 [6371]~P72(x63711)+~P1(f862(f130(x63712),x63714))+E(f862(f158(x63711),f862(f862(f147(x63712,x63711),x63713),x63714)),f862(f862(f8(x63712,x63711),x63713),f862(f165(x63712),x63714)))
% 25.54/25.42 [6388]~P71(x63882)+~P1(f862(f54(x63881),x63884))+E(f862(f862(f11(x63881,x63882),f862(f18(x63882,x63881),x63883)),x63884),f862(f862(f236(x63882),x63883),f862(f28(x63881),x63884)))
% 25.54/25.42 [6441]~P64(x64412)+E(x64411,f2(x64412))+E(f862(f862(f281(x64412),f862(f862(f74(x64412),x64413),x64411)),f862(f862(f74(x64412),x64414),x64411)),f862(f862(f281(x64412),x64413),x64414))
% 25.54/25.42 [6442]~P64(x64422)+E(x64421,f2(x64422))+E(f862(f862(f281(x64422),f862(f862(f74(x64422),x64421),x64423)),f862(f862(f74(x64422),x64421),x64424)),f862(f862(f281(x64422),x64423),x64424))
% 25.54/25.42 [6443]~P61(x64432)+E(x64431,f2(x64432))+E(f862(f862(f29(x64432),f862(f862(f74(x64432),x64433),x64431)),f862(f862(f74(x64432),x64434),x64431)),f862(f862(f29(x64432),x64433),x64434))
% 25.54/25.42 [6444]~P61(x64442)+E(x64441,f2(x64442))+E(f862(f862(f29(x64442),f862(f862(f74(x64442),x64441),x64443)),f862(f862(f74(x64442),x64441),x64444)),f862(f862(f29(x64442),x64443),x64444))
% 25.54/25.42 [6445]~P61(x64452)+E(x64451,f2(x64452))+E(f862(f862(f29(x64452),f862(f862(f74(x64452),x64451),x64453)),f862(f862(f74(x64452),x64451),x64454)),f862(f862(f29(x64452),x64453),x64454))
% 25.54/25.42 [6510]P1(f862(x65101,x65102))+~E(x65103,f862(f862(f73(a924),x65104),x65102))+~P1(f862(x65101,f862(f862(f3(a924),x65103),x65104)))
% 25.54/25.42 [6511]P1(f862(x65111,x65112))+~E(x65113,f862(f862(f73(a924),x65114),x65112))+~P1(f862(x65111,f862(f862(f3(a924),x65113),x65114)))
% 25.54/25.42 [6599]~P1(f862(x65992,x65993))+~P1(f862(f153(x65991,x65992),x65994))+P1(f862(f153(x65991,x65992),f862(f862(f144(x65991),x65993),x65994)))
% 25.54/25.42 [6639]E(x66391,f106(x66392))+~E(x66393,f862(f862(f3(a924),f862(f182(f925(x66392)),x66391)),f71(a924)))+E(f137(x66392,f862(f862(f152(x66392,x66391),x66393),x66394)),x66394)
% 25.54/25.42 [6662]~P103(x66621)+~P1(f862(f862(f227(x66621),x66622),x66624))+P1(f862(f862(f227(x66621),x66622),f862(f862(f103(x66621),x66623),x66624)))
% 25.54/25.42 [6663]~P103(x66631)+~P1(f862(f862(f227(x66631),x66632),x66633))+P1(f862(f862(f227(x66631),x66632),f862(f862(f103(x66631),x66633),x66634)))
% 25.54/25.42 [6664]~P109(x66641)+~P1(f862(f862(f227(x66641),x66642),x66644))+P1(f862(f862(f227(x66641),x66642),f862(f862(f226(x66641),x66643),x66644)))
% 25.54/25.42 [6665]~P109(x66651)+~P1(f862(f862(f227(x66651),x66652),x66654))+P1(f862(f862(f227(x66651),x66652),f862(f862(f226(x66651),x66653),x66654)))
% 25.54/25.42 [6666]~P109(x66661)+~P1(f862(f862(f227(x66661),x66662),x66663))+P1(f862(f862(f227(x66661),x66662),f862(f862(f226(x66661),x66663),x66664)))
% 25.54/25.42 [6667]~P109(x66671)+~P1(f862(f862(f227(x66671),x66672),x66673))+P1(f862(f862(f227(x66671),x66672),f862(f862(f226(x66671),x66673),x66674)))
% 25.54/25.42 [6668]~P103(x66681)+~P1(f862(f862(f228(x66681),x66682),x66684))+P1(f862(f862(f228(x66681),x66682),f862(f862(f103(x66681),x66683),x66684)))
% 25.54/25.42 [6669]~P103(x66691)+~P1(f862(f862(f228(x66691),x66692),x66693))+P1(f862(f862(f228(x66691),x66692),f862(f862(f103(x66691),x66693),x66694)))
% 25.54/25.42 [6670]~P109(x66701)+~P1(f862(f862(f228(x66701),x66702),x66704))+P1(f862(f862(f228(x66701),x66702),f862(f862(f226(x66701),x66703),x66704)))
% 25.54/25.42 [6671]~P109(x66711)+~P1(f862(f862(f228(x66711),x66712),x66714))+P1(f862(f862(f228(x66711),x66712),f862(f862(f226(x66711),x66713),x66714)))
% 25.54/25.42 [6672]~P109(x66721)+~P1(f862(f862(f228(x66721),x66722),x66723))+P1(f862(f862(f228(x66721),x66722),f862(f862(f226(x66721),x66723),x66724)))
% 25.54/25.42 [6673]~P109(x66731)+~P1(f862(f862(f228(x66731),x66732),x66733))+P1(f862(f862(f228(x66731),x66732),f862(f862(f226(x66731),x66733),x66734)))
% 25.54/25.42 [6674]~P119(x66741)+~P1(f862(f862(f278(x66741),x66742),x66744))+P1(f862(f862(f278(x66741),x66742),f862(f862(f74(x66741),x66743),x66744)))
% 25.54/25.42 [6675]~P119(x66751)+~P1(f862(f862(f278(x66751),x66752),x66753))+P1(f862(f862(f278(x66751),x66752),f862(f862(f74(x66751),x66753),x66754)))
% 25.54/25.42 [6763]~E(f862(f862(f157(x67631),x67632),x67633),x67634)+E(f862(f862(f152(x67631,x67632),x67633),x67634),x67632)+~P1(f862(f862(f228(a924),x67633),f862(f182(f925(x67631)),x67632)))
% 25.54/25.42 [6801]P1(f862(x68011,x68012))+~P1(f862(x68013,x68012))+~P1(f862(f862(f227(f932(x68014,a921)),x68013),x68011))
% 25.54/25.42 [6802]P1(f862(x68021,x68022))+~P1(f862(x68023,x68022))+~P1(f862(f862(f227(f932(x68024,a921)),x68023),x68021))
% 25.54/25.42 [6833]~E(f862(f862(f152(x68331,x68332),x68333),x68334),x68332)+E(f862(f862(f157(x68331),x68332),x68333),x68334)+~P1(f862(f862(f228(a924),x68333),f862(f182(f925(x68331)),x68332)))
% 25.54/25.42 [6848]~P1(f862(f153(x68481,x68482),x68484))+~P1(f862(f153(x68481,x68482),x68483))+P1(f862(f153(x68481,x68482),f862(f862(f127(x68481),x68483),x68484)))
% 25.54/25.42 [6952]E(x69521,f181(f932(x69522,a921)))+E(x69523,f181(f932(x69524,a921)))+~E(f862(f862(f246(x69524,x69522),x69523),f862(f18(f932(x69522,a921),x69524),x69521)),f181(f932(f931(x69524,x69522),a921)))
% 25.54/25.42 [6972]E(x69721,x69722)+P1(f862(f862(f321(x69723),x69721),x69724))+~P1(f862(f862(f321(x69723),x69721),f862(f862(f301(x69723),x69722),x69724)))
% 25.54/25.42 [6973]E(x69731,x69732)+P1(f862(f862(f321(x69733),x69731),x69734))+~P1(f862(f862(f321(x69733),x69731),f862(f862(f301(x69733),x69732),x69734)))
% 25.54/25.42 [6989]~P109(x69891)+P1(f862(f862(f227(x69891),x69892),x69893))+~P1(f862(f862(f227(x69891),x69892),f862(f862(f225(x69891),x69894),x69893)))
% 25.54/25.42 [6990]~P109(x69901)+P1(f862(f862(f227(x69901),x69902),x69903))+~P1(f862(f862(f227(x69901),x69902),f862(f862(f225(x69901),x69904),x69903)))
% 25.54/25.42 [6991]~P109(x69911)+P1(f862(f862(f227(x69911),x69912),x69913))+~P1(f862(f862(f227(x69911),x69912),f862(f862(f225(x69911),x69913),x69914)))
% 25.54/25.42 [6992]~P109(x69921)+P1(f862(f862(f227(x69921),x69922),x69923))+~P1(f862(f862(f227(x69921),x69922),f862(f862(f225(x69921),x69923),x69924)))
% 25.54/25.42 [6993]~P104(x69931)+P1(f862(f862(f227(x69931),x69932),x69933))+~P1(f862(f862(f227(x69931),x69932),f862(f862(f94(x69931),x69934),x69933)))
% 25.54/25.42 [6994]~P104(x69941)+P1(f862(f862(f227(x69941),x69942),x69943))+~P1(f862(f862(f227(x69941),x69942),f862(f862(f94(x69941),x69944),x69943)))
% 25.54/25.42 [6995]~P104(x69951)+P1(f862(f862(f227(x69951),x69952),x69953))+~P1(f862(f862(f227(x69951),x69952),f862(f862(f94(x69951),x69953),x69954)))
% 25.54/25.42 [6996]~P104(x69961)+P1(f862(f862(f227(x69961),x69962),x69963))+~P1(f862(f862(f227(x69961),x69962),f862(f862(f94(x69961),x69963),x69964)))
% 25.54/25.42 [6997]~P109(x69971)+P1(f862(f862(f228(x69971),x69972),x69973))+~P1(f862(f862(f228(x69971),x69972),f862(f862(f225(x69971),x69974),x69973)))
% 25.54/25.42 [6998]~P109(x69981)+P1(f862(f862(f228(x69981),x69982),x69983))+~P1(f862(f862(f228(x69981),x69982),f862(f862(f225(x69981),x69983),x69984)))
% 25.54/25.42 [7019]~E(f862(f862(f157(x70191),x70193),x70194),x70192)+P1(f862(f862(f321(x70191),x70192),f862(f165(x70191),x70193)))+~P1(f862(f862(f228(a924),x70194),f862(f182(f925(x70191)),x70193)))
% 25.54/25.42 [7029]~P109(x70291)+~P11(x70291,f862(f862(f144(x70291),x70292),f862(f862(f144(x70291),x70293),x70294)))+P1(f862(f862(f227(x70291),x70292),x70293))
% 25.54/25.42 [7082]~P109(x70821)+P11(x70821,f862(f862(f144(x70821),x70822),x70823))+~P11(x70821,f862(f862(f144(x70821),x70824),f862(f862(f144(x70821),x70822),x70823)))
% 25.54/25.42 [7173]~P29(x71732,x71731,x71733)+P1(f862(x71731,f862(f862(f157(x71732),x71733),x71734)))+~P1(f862(f862(f228(a924),x71734),f862(f182(f925(x71732)),x71733)))
% 25.54/25.42 [7192]E(x71921,f2(a1))+E(f862(f862(f29(a1),x71922),x71921),x71923)+~P1(f862(f42(x71922,x71921),f862(f862(f244(a1,a1),x71923),x71924)))
% 25.54/25.42 [7213]E(f38(a1,x72132,x72131),x72133)+E(x72131,f2(a1))+~P1(f862(f42(x72132,x72131),f862(f862(f244(a1,a1),x72134),x72133)))
% 25.54/25.42 [7330]P1(f862(f862(f321(x73301),x73302),x73303))+~P1(f862(f862(f321(x73301),x73302),x73304))+~P1(f862(f862(f227(f932(x73301,a921)),x73304),x73303))
% 25.54/25.42 [7331]P1(f862(f862(f321(x73311),x73312),x73313))+~P1(f862(f862(f321(x73311),x73312),x73314))+~P1(f862(f862(f227(f932(x73311,a921)),x73314),x73313))
% 25.54/25.42 [7332]P1(f862(f862(f321(x73321),x73322),x73323))+~P1(f862(f862(f321(x73321),x73322),x73324))+~P1(f862(f862(f227(f932(x73321,a921)),x73324),x73323))
% 25.54/25.42 [7333]P1(f862(f862(f321(x73331),x73332),x73333))+~P1(f862(f862(f321(x73331),x73332),x73334))+~P1(f862(f862(f228(f932(x73331,a921)),x73334),x73333))
% 25.54/25.42 [7334]P1(f862(f862(f321(x73341),x73342),x73343))+~P1(f862(f862(f321(x73341),x73342),x73344))+~P1(f862(f862(f227(f932(x73341,a921)),x73344),x73343))
% 25.54/25.42 [7345]~P113(x73451)+~E(x73453,f2(x73451))+P1(f862(f862(f278(x73451),f862(f862(f74(x73451),x73452),x73453)),f862(f862(f74(x73451),x73454),x73453)))
% 25.54/25.42 [7346]~P113(x73461)+~E(x73462,f2(x73461))+P1(f862(f862(f278(x73461),f862(f862(f74(x73461),x73462),x73463)),f862(f862(f74(x73461),x73462),x73464)))
% 25.54/25.42 [7449]P31(x74491,x74492,x74493)+~P1(f862(x74492,f862(f862(f157(x74491),x74493),x74494)))+~P1(f862(f862(f228(a924),x74494),f862(f182(f925(x74491)),x74493)))
% 25.54/25.42 [7566]~P108(x75662)+~P1(f862(f862(f228(f932(x75661,x75662)),x75663),x75664))+P1(f862(f862(f227(f932(x75661,x75662)),x75663),x75664))
% 25.54/25.42 [7691]~P1(f862(f862(f321(x76911),x76912),x76914))+P1(f862(f862(f321(x76911),x76912),f30(f932(x76911,a921),x76913)))+~P1(f862(f862(f321(f932(x76911,a921)),x76914),x76913))
% 25.54/25.42 [7693]~P119(x76931)+~P1(f862(f862(f227(a924),x76933),x76934))+P1(f862(f862(f278(x76931),f862(f862(f236(x76931),x76932),x76933)),f862(f862(f236(x76931),x76932),x76934)))
% 25.54/25.42 [7719]~P84(x77191)+~P1(f862(f862(f227(x77191),x77193),x77194))+P1(f862(f862(f227(x77191),f862(f862(f73(x77191),x77192),x77193)),f862(f862(f73(x77191),x77192),x77194)))
% 25.54/25.42 [7720]~P85(x77201)+~P1(f862(f862(f227(x77201),x77203),x77204))+P1(f862(f862(f227(x77201),f862(f862(f73(x77201),x77202),x77203)),f862(f862(f73(x77201),x77202),x77204)))
% 25.54/25.42 [7721]~P84(x77211)+~P1(f862(f862(f227(x77211),x77212),x77214))+P1(f862(f862(f227(x77211),f862(f862(f73(x77211),x77212),x77213)),f862(f862(f73(x77211),x77214),x77213)))
% 25.54/25.42 [7722]~P85(x77221)+~P1(f862(f862(f227(x77221),x77222),x77224))+P1(f862(f862(f227(x77221),f862(f862(f73(x77221),x77222),x77223)),f862(f862(f73(x77221),x77224),x77223)))
% 25.54/25.42 [7723]~P83(x77231)+~P1(f862(f862(f228(x77231),x77233),x77234))+P1(f862(f862(f228(x77231),f862(f862(f73(x77231),x77232),x77233)),f862(f862(f73(x77231),x77232),x77234)))
% 25.54/25.42 [7724]~P84(x77241)+~P1(f862(f862(f228(x77241),x77243),x77244))+P1(f862(f862(f228(x77241),f862(f862(f73(x77241),x77242),x77243)),f862(f862(f73(x77241),x77242),x77244)))
% 25.54/25.42 [7725]~P83(x77251)+~P1(f862(f862(f228(x77251),x77252),x77254))+P1(f862(f862(f228(x77251),f862(f862(f73(x77251),x77252),x77253)),f862(f862(f73(x77251),x77254),x77253)))
% 25.54/25.42 [7726]~P84(x77261)+~P1(f862(f862(f228(x77261),x77262),x77264))+P1(f862(f862(f228(x77261),f862(f862(f73(x77261),x77262),x77263)),f862(f862(f73(x77261),x77264),x77263)))
% 25.54/25.42 [7727]~P113(x77271)+~P1(f862(f862(f278(x77271),x77273),x77274))+P1(f862(f862(f278(x77271),f862(f862(f74(x77271),x77272),x77273)),f862(f862(f74(x77271),x77272),x77274)))
% 25.54/25.42 [7728]~P113(x77281)+~P1(f862(f862(f278(x77281),x77282),x77284))+P1(f862(f862(f278(x77281),f862(f862(f74(x77281),x77282),x77283)),f862(f862(f74(x77281),x77284),x77283)))
% 25.54/25.42 [7729]~P119(x77291)+~P1(f862(f862(f278(x77291),x77292),x77294))+P1(f862(f862(f278(x77291),f862(f862(f236(x77291),x77292),x77293)),f862(f862(f236(x77291),x77294),x77293)))
% 25.54/25.42 [7736]~P125(x77361)+~P99(x77361)+E(f862(f862(f3(x77361),f862(f862(f74(x77361),x77362),f862(f96(x77361),x77363))),f862(f862(f74(x77361),x77364),f862(f96(x77361),x77363))),f862(f862(f74(x77361),f862(f862(f3(x77361),x77362),x77364)),f862(f96(x77361),x77363)))
% 25.54/25.42 [7737]~P140(x77371)+~P99(x77371)+E(f862(f862(f73(x77371),f862(f862(f74(x77371),x77372),f862(f96(x77371),x77373))),f862(f862(f74(x77371),x77374),f862(f96(x77371),x77373))),f862(f862(f74(x77371),f862(f862(f73(x77371),x77372),x77374)),f862(f96(x77371),x77373)))
% 25.54/25.42 [7774]~P72(x77741)+E(f862(f862(f73(x77741),f862(x77742,x77743)),f862(f862(f8(a924,x77741),x77742),f296(a924,f862(a105,x77743),x77744))),f862(f862(f8(a924,x77741),x77742),f296(a924,x77743,x77744)))+~P1(f862(f862(f227(a924),x77743),x77744))
% 25.54/25.42 [7786]~P22(x77862,x77861,x77863,f862(f165(x77862),x77864))+~P1(f862(f130(x77862),x77864))+P1(f862(f130(x77861),f862(f862(f147(x77862,x77861),x77863),x77864)))
% 25.54/25.42 [7835]~P1(f862(f862(f227(a924),x78352),x78354))+~P1(f862(f862(f227(a924),x78351),x78353))+P1(f862(f862(f227(a924),f862(f862(f74(a924),x78351),x78352)),f862(f862(f74(a924),x78353),x78354)))
% 25.54/25.42 [7836]~P1(f862(f862(f227(a924),x78362),x78364))+~P1(f862(f862(f227(a924),x78361),x78363))+P1(f862(f862(f227(a924),f862(f862(f73(a924),x78361),x78362)),f862(f862(f73(a924),x78363),x78364)))
% 25.54/25.42 [7839]~P1(f862(f862(f228(a924),x78392),x78394))+~P1(f862(f862(f228(a924),x78391),x78393))+P1(f862(f862(f228(a924),f862(f862(f73(a924),x78391),x78392)),f862(f862(f73(a924),x78393),x78394)))
% 25.54/25.42 [7840]~P1(f862(f862(f227(a1),x78402),x78404))+~P1(f862(f862(f228(a1),x78401),x78403))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x78401),x78402)),f862(f862(f73(a1),x78403),x78404)))
% 25.54/25.42 [7887]P1(f862(f862(f321(x78871),x78872),x78873))+~P1(f862(f862(f321(x78871),x78872),f31(f932(x78871,a921),x78874)))+~P1(f862(f862(f321(f932(x78871,a921)),x78873),x78874))
% 25.54/25.42 [7888]P1(f862(f862(f321(x78881),x78882),x78883))+~P1(f862(f862(f321(x78881),x78882),f31(f932(x78881,a921),x78884)))+~P1(f862(f862(f321(f932(x78881,a921)),x78883),x78884))
% 25.54/25.42 [7904]~P1(f862(x79041,f665(x79041,x79043,x79042)))+P1(f862(x79041,f862(f862(f157(x79042),x79043),x79044)))+~P1(f862(f862(f228(a924),x79044),f862(f182(f925(x79042)),x79043)))
% 25.54/25.42 [7909]P1(f862(x79091,x79092))+~P1(f862(f862(f321(x79094),x79092),f862(f165(x79094),x79093)))+P1(f862(f862(f228(a924),f667(x79091,x79093,x79094)),f862(f182(f925(x79094)),x79093)))
% 25.54/25.42 [7956]~P108(x79561)+~P1(f862(f862(f228(f932(x79562,x79561)),x79564),x79563))+~P1(f862(f862(f227(f932(x79562,x79561)),x79563),x79564))
% 25.54/25.42 [8000]~P1(f862(x80004,x80002))+~P1(f862(f862(f321(x80001),x80002),x80003))+P1(f862(f862(f321(x80001),x80002),f862(f862(f94(f932(x80001,a921)),x80003),f862(f254(x80001),x80004))))
% 25.54/25.42 [8013]P1(f862(f862(f321(x80131),x80132),x80133))+~P1(f862(f862(f227(f932(x80131,a921)),x80133),x80134))+P1(f862(f862(f227(f932(x80131,a921)),x80133),f862(f862(f301(x80131),x80132),x80134)))
% 25.54/25.42 [8014]P1(f862(f862(f321(x80141),x80142),x80143))+~P1(f862(f862(f227(f932(x80141,a921)),x80143),x80144))+P1(f862(f862(f227(f932(x80141,a921)),x80143),f862(f862(f301(x80141),x80142),x80144)))
% 25.54/25.42 [8147]~P1(f862(f862(f321(x81471),x81473),x81474))+~P1(f862(f862(f228(f932(x81471,a921)),x81472),x81474))+P1(f862(f862(f228(f932(x81471,a921)),x81472),f862(f862(f301(x81471),x81473),x81474)))
% 25.54/25.42 [8149]E(f862(f862(f94(f932(x81491,a921)),x81492),x81493),f181(f932(x81491,a921)))+~E(f862(f862(f94(f932(x81491,a921)),f30(f932(x81491,a921),x81494)),x81493),f181(f932(x81491,a921)))+~P1(f862(f862(f321(f932(x81491,a921)),x81492),x81494))
% 25.54/25.42 [8224]P1(f862(f862(f321(x82241),x82242),x82243))+~P1(f862(f862(f227(f932(x82241,a921)),x82243),f862(f862(f301(x82241),x82242),x82244)))+P1(f862(f862(f227(f932(x82241,a921)),x82243),x82244))
% 25.54/25.42 [8225]P1(f862(f862(f321(x82251),x82252),x82253))+~P1(f862(f862(f227(f932(x82251,a921)),x82253),f862(f862(f301(x82251),x82252),x82254)))+P1(f862(f862(f227(f932(x82251,a921)),x82253),x82254))
% 25.54/25.42 [8242]P1(f862(f862(f321(x82422),f665(x82421,x82423,x82422)),f862(f165(x82422),x82423)))+P1(f862(x82421,f862(f862(f157(x82422),x82423),x82424)))+~P1(f862(f862(f228(a924),x82424),f862(f182(f925(x82422)),x82423)))
% 25.54/25.42 [8250]~P1(f862(f862(f227(f932(x82501,a921)),x82502),x82504))+P1(f862(f862(f227(f932(x82501,a921)),x82502),x82503))+~P1(f862(f862(f227(f932(x82501,a921)),x82504),x82503))
% 25.54/25.42 [8251]~P1(f862(f862(f228(f932(x82511,a921)),x82512),x82514))+~P1(f862(f862(f227(f932(x82511,a921)),x82514),x82513))+P1(f862(f862(f228(f932(x82511,a921)),x82512),x82513))
% 25.54/25.42 [8252]~P1(f862(f862(f227(f932(x82521,a921)),x82522),x82524))+~P1(f862(f862(f228(f932(x82521,a921)),x82524),x82523))+P1(f862(f862(f228(f932(x82521,a921)),x82522),x82523))
% 25.54/25.42 [8253]~P1(f862(f862(f228(f932(x82531,a921)),x82532),x82534))+P1(f862(f862(f228(f932(x82531,a921)),x82532),x82533))+~P1(f862(f862(f228(f932(x82531,a921)),x82534),x82533))
% 25.54/25.42 [8299]~P1(f862(f862(f321(x82991),x82994),x82993))+~P1(f862(f862(f228(f932(x82991,a921)),x82992),f862(f862(f301(x82991),x82994),x82993)))+P1(f862(f862(f228(f932(x82991,a921)),x82992),x82993))
% 25.54/25.42 [8309]~P84(x83091)+P1(f862(f862(f227(x83091),x83092),x83093))+~P1(f862(f862(f227(x83091),f862(f862(f73(x83091),x83094),x83092)),f862(f862(f73(x83091),x83094),x83093)))
% 25.54/25.42 [8310]~P84(x83101)+P1(f862(f862(f227(x83101),x83102),x83103))+~P1(f862(f862(f227(x83101),f862(f862(f73(x83101),x83104),x83102)),f862(f862(f73(x83101),x83104),x83103)))
% 25.54/25.42 [8311]~P84(x83111)+P1(f862(f862(f227(x83111),x83112),x83113))+~P1(f862(f862(f227(x83111),f862(f862(f73(x83111),x83112),x83114)),f862(f862(f73(x83111),x83113),x83114)))
% 25.54/25.42 [8312]~P84(x83121)+P1(f862(f862(f227(x83121),x83122),x83123))+~P1(f862(f862(f227(x83121),f862(f862(f73(x83121),x83122),x83124)),f862(f862(f73(x83121),x83123),x83124)))
% 25.54/25.42 [8313]~P84(x83131)+P1(f862(f862(f228(x83131),x83132),x83133))+~P1(f862(f862(f228(x83131),f862(f862(f73(x83131),x83134),x83132)),f862(f862(f73(x83131),x83134),x83133)))
% 25.54/25.42 [8314]~P84(x83141)+P1(f862(f862(f228(x83141),x83142),x83143))+~P1(f862(f862(f228(x83141),f862(f862(f73(x83141),x83144),x83142)),f862(f862(f73(x83141),x83144),x83143)))
% 25.54/25.42 [8315]~P84(x83151)+P1(f862(f862(f228(x83151),x83152),x83153))+~P1(f862(f862(f228(x83151),f862(f862(f73(x83151),x83152),x83154)),f862(f862(f73(x83151),x83153),x83154)))
% 25.54/25.42 [8316]~P84(x83161)+P1(f862(f862(f228(x83161),x83162),x83163))+~P1(f862(f862(f228(x83161),f862(f862(f73(x83161),x83162),x83164)),f862(f862(f73(x83161),x83163),x83164)))
% 25.54/25.42 [8367]P1(f862(x83671,x83672))+~E(f862(f862(f131(x83673),f862(f182(f925(x83673)),f170(x83673,x83671,x83674))),x83674),f106(x83673))+~P1(f862(f862(f321(x83673),x83672),f862(f165(x83673),x83674)))
% 25.54/25.42 [8486]P1(f862(x84861,x84862))+~P1(f862(f862(f321(x84863),x84862),f862(f165(x84863),x84864)))+P1(f862(f862(f228(a924),f862(f182(f925(x84863)),f862(f129(x84863,x84861),x84864))),f862(f182(f925(x84863)),x84864)))
% 25.54/25.42 [8980]~P1(f862(x89801,f759(x89801,x89803,x89802,x89804)))+P1(f862(x89801,f862(f862(f157(x89802),x89803),x89804)))+~P1(f862(f862(f228(a924),x89804),f862(f182(f925(x89802)),x89803)))
% 25.54/25.42 [9004]~P22(x90044,x90043,x90041,f234(f932(x90044,a921)))+E(f862(x90041,f539(x90042,x90041,x90043,x90044)),x90042)+~P1(f862(f862(f321(x90043),x90042),f862(f302(x90044,x90043,x90041),f234(f932(x90044,a921)))))
% 25.54/25.42 [9074]E(f170(x90741,x90742,x90743),f862(f862(f168(x90741),x90744),x90743))+P1(f862(f862(f228(a924),f729(x90742,x90743,x90741,x90744)),x90744))+P1(f862(f862(f228(a924),x90744),f862(f182(f925(x90741)),x90743)))
% 25.54/25.42 [9077]E(f170(x90771,x90772,x90773),f862(f862(f168(x90771),x90774),x90773))+P1(f862(f862(f228(a924),f729(x90772,x90773,x90771,x90774)),x90774))+P1(f862(x90772,f862(f862(f157(x90771),x90773),x90774)))
% 25.54/25.42 [9112]P1(f862(x91121,x91122))+~P1(f862(f862(f321(x91124),x91122),f862(f165(x91124),x91123)))+P1(f862(f862(f228(a924),f704(x91122,x91121,x91123,x91124)),f862(f182(f925(x91124)),x91123)))
% 25.54/25.42 [9114]E(f170(x91141,x91142,x91143),f862(f862(f168(x91141),x91144),x91143))+P1(f862(f862(f228(a924),x91144),f862(f182(f925(x91141)),x91143)))+P1(f862(f862(f228(a924),f729(x91142,x91143,x91141,x91144)),f862(f182(f925(x91141)),x91143)))
% 25.54/25.42 [9121]E(f170(x91211,x91212,x91213),f862(f862(f168(x91211),x91214),x91213))+P1(f862(x91212,f862(f862(f157(x91211),x91213),x91214)))+P1(f862(f862(f228(a924),f729(x91212,x91213,x91211,x91214)),f862(f182(f925(x91211)),x91213)))
% 25.54/25.42 [9146]~P127(x91464)+P1(f862(f862(f321(x91461),f445(x91462,x91463,x91461,x91464)),x91463))+P1(f862(f862(f228(x91464),f2(x91464)),f862(f862(f11(x91461,x91464),x91462),x91463)))
% 25.54/25.42 [9147]~P127(x91474)+P1(f862(f862(f321(x91471),f446(x91472,x91473,x91471,x91474)),x91473))+P1(f862(f862(f227(x91474),f2(x91474)),f862(f862(f11(x91471,x91474),x91472),x91473)))
% 25.54/25.42 [9172]~P1(f862(f54(x91721),x91724))+P1(f862(f862(f321(x91721),f571(x91722,x91723,x91724,x91721)),x91724))+P1(f862(f54(f931(x91721,x91723)),f862(f862(f246(x91721,x91723),x91724),x91722)))
% 25.54/25.42 [9204]P1(f862(f862(f321(x92042),f759(x92041,x92043,x92042,x92044)),f862(f165(x92042),x92043)))+P1(f862(x92041,f862(f862(f157(x92042),x92043),x92044)))+~P1(f862(f862(f228(a924),x92044),f862(f182(f925(x92042)),x92043)))
% 25.54/25.42 [9335]P1(f862(f862(f227(a924),x93354),f862(f182(f925(x93352)),f170(x93352,x93353,x93351))))+P1(f862(f862(f228(a924),f730(x93351,x93352,x93353,x93354)),x93354))+~P1(f862(f862(f227(a924),x93354),f862(f182(f925(x93352)),x93351)))
% 25.54/25.42 [9487]E(f170(x94871,x94872,x94873),f862(f862(f168(x94871),x94874),x94873))+~P1(f862(x94872,f862(f862(f157(x94871),x94873),f729(x94872,x94873,x94871,x94874))))+P1(f862(f862(f228(a924),x94874),f862(f182(f925(x94871)),x94873)))
% 25.54/25.42 [9494]E(f170(x94941,x94942,x94943),f862(f862(f168(x94941),x94944),x94943))+~P1(f862(x94942,f862(f862(f157(x94941),x94943),f729(x94942,x94943,x94941,x94944))))+P1(f862(x94942,f862(f862(f157(x94941),x94943),x94944)))
% 25.54/25.42 [9498]~P1(f862(f54(x94981),x94983))+~P1(f862(f54(x94982),f862(x94984,f571(x94984,x94982,x94983,x94981))))+P1(f862(f54(f931(x94981,x94982)),f862(f862(f246(x94981,x94982),x94983),x94984)))
% 25.54/25.42 [9506]~P127(x95061)+~P1(f862(f862(f227(x95061),f2(x95061)),f862(x95063,f446(x95063,x95064,x95062,x95061))))+P1(f862(f862(f227(x95061),f2(x95061)),f862(f862(f11(x95062,x95061),x95063),x95064)))
% 25.54/25.42 [9507]~P127(x95071)+~P1(f862(f862(f228(x95071),f2(x95071)),f862(x95073,f445(x95073,x95074,x95072,x95071))))+P1(f862(f862(f228(x95071),f2(x95071)),f862(f862(f11(x95072,x95071),x95073),x95074)))
% 25.54/25.42 [9515]~E(f862(f182(f925(x95154)),x95152),f862(f182(f925(x95154)),x95153))+P1(f862(f862(f321(f931(f925(x95154),f925(x95154))),f862(f862(f244(f925(x95154),f925(x95154)),x95153),x95152)),f151(x95154,x95151)))+P1(f862(f862(f228(a924),f659(x95151,x95152,x95153,x95154)),f862(f182(f925(x95154)),x95153)))
% 25.54/25.42 [9569]~P1(f862(x95693,f862(f862(f157(x95692),x95694),f730(x95694,x95692,x95693,x95691))))+P1(f862(f862(f227(a924),x95691),f862(f182(f925(x95692)),f170(x95692,x95693,x95694))))+~P1(f862(f862(f227(a924),x95691),f862(f182(f925(x95692)),x95694)))
% 25.54/25.42 [9651]E(f862(f862(f168(x96511),f666(x96512,x96513,x96514,x96511)),x96513),f862(f862(f168(x96511),f666(x96512,x96513,x96514,x96511)),x96514))+~P1(f862(f862(f321(f931(f925(x96511),f925(x96511))),f862(f862(f244(f925(x96511),f925(x96511)),x96514),x96513)),f140(x96511,x96512)))+P1(f862(f862(f228(a924),f862(f182(f925(x96511)),x96514)),f862(f182(f925(x96511)),x96513)))
% 25.54/25.42 [9709]~P1(f862(f862(f228(a924),f2(a924)),x97093))+~P1(f862(f862(f228(a924),x97094),x97091))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x97091),f38(a924,x97092,x97093))),x97094)),f862(f862(f74(a924),x97091),x97093)))
% 25.54/25.42 [9900]~P108(x99002)+~P1(f862(f862(f227(x99002),f862(x99003,f435(x99004,x99003,x99001,x99002))),f862(x99004,f435(x99004,x99003,x99001,x99002))))+P1(f862(f862(f227(f932(x99001,x99002)),x99003),x99004))
% 25.54/25.42 [9901]~P108(x99012)+~P1(f862(f862(f227(x99012),f862(x99013,f568(x99011,x99014,x99013,x99012))),f862(x99014,f568(x99011,x99014,x99013,x99012))))+P1(f862(f862(f227(f932(x99011,x99012)),x99013),x99014))
% 25.54/25.42 [10005]~P59(x100051)+E(f862(f862(f8(a924,x100051),f862(f862(f20(a924,x100051,x100051),f862(f862(f10(x100051,f932(x100051,x100051),a924),f3(x100051)),x100052)),f862(f862(f10(a924,x100051,a924),x100052),f862(f862(f9(a924,a924,a924),f73(a924)),f71(a924))))),f296(a924,x100053,x100054)),f862(f862(f3(x100051),f862(x100052,x100053)),f862(x100052,f862(f862(f73(a924),x100054),f71(a924)))))+~P1(f862(f862(f227(a924),x100053),x100054))
% 25.54/25.42 [10080]~P35(x100803,f862(f862(f280(x100803,x100803,x100803),x100802),f299(x100803,x100802)))+~P1(f862(f862(f321(f931(x100803,x100803)),f862(f862(f244(x100803,x100803),f862(x100801,f862(a105,f841(x100802,x100801,x100803)))),f862(x100801,f841(x100802,x100801,x100803)))),f299(x100803,x100802)))+E(f862(x100801,f862(f862(f73(a924),f840(x100802,x100801,x100803)),x100804)),f862(x100801,f840(x100802,x100801,x100803)))
% 25.54/25.42 [6935]~P61(x69351)+E(f862(f862(f29(x69351),f862(f862(f74(x69351),x69352),x69353)),x69354),f862(f862(f74(x69351),x69352),f862(f862(f29(x69351),x69353),x69354)))+~P1(f862(f862(f278(x69351),x69354),x69353))
% 25.54/25.42 [7023]E(f862(f862(f127(x70231),x70232),x70233),x70234)+~E(x70233,f862(f862(f131(x70231),f862(f182(f925(x70231)),x70232)),x70234))+~E(f862(f862(f168(x70231),f862(f182(f925(x70231)),x70232)),x70234),x70232)
% 25.54/25.42 [7079]~P65(x70792)+E(x70791,f2(x70792))+E(f862(f862(f281(x70792),f862(f862(f236(x70792),x70793),x70794)),f862(f862(f236(x70792),x70791),x70794)),f862(f862(f236(x70792),f862(f862(f281(x70792),x70793),x70791)),x70794))
% 25.54/25.42 [7221]~P61(x72211)+E(f862(f862(f29(x72211),f862(f862(f74(x72211),x72212),x72213)),x72214),f862(f862(f74(x72211),f862(f862(f29(x72211),x72212),x72214)),x72213))+~P1(f862(f862(f278(x72211),x72214),x72212))
% 25.54/25.42 [7229]~P104(x72291)+~P1(f862(f862(f227(x72291),x72293),x72294))+P1(f862(f862(f227(x72291),f862(f862(f94(x72291),x72292),x72293)),x72294))
% 25.54/25.42 [7230]~P104(x72301)+~P1(f862(f862(f227(x72301),x72302),x72304))+P1(f862(f862(f227(x72301),f862(f862(f94(x72301),x72302),x72303)),x72304))
% 25.54/25.42 [7231]~P109(x72311)+~P1(f862(f862(f227(x72311),x72313),x72314))+P1(f862(f862(f227(x72311),f862(f862(f225(x72311),x72312),x72313)),x72314))
% 25.54/25.42 [7232]~P109(x72321)+~P1(f862(f862(f227(x72321),x72323),x72324))+P1(f862(f862(f227(x72321),f862(f862(f225(x72321),x72322),x72323)),x72324))
% 25.54/25.42 [7233]~P109(x72331)+~P1(f862(f862(f227(x72331),x72332),x72334))+P1(f862(f862(f227(x72331),f862(f862(f225(x72331),x72332),x72333)),x72334))
% 25.54/25.42 [7234]~P109(x72341)+~P1(f862(f862(f227(x72341),x72342),x72344))+P1(f862(f862(f227(x72341),f862(f862(f225(x72341),x72342),x72343)),x72344))
% 25.54/25.42 [7235]~P104(x72351)+~P1(f862(f862(f228(x72351),x72353),x72354))+P1(f862(f862(f228(x72351),f862(f862(f94(x72351),x72352),x72353)),x72354))
% 25.54/25.42 [7236]~P104(x72361)+~P1(f862(f862(f228(x72361),x72362),x72364))+P1(f862(f862(f228(x72361),f862(f862(f94(x72361),x72362),x72363)),x72364))
% 25.54/25.42 [7237]~P109(x72371)+~P1(f862(f862(f228(x72371),x72373),x72374))+P1(f862(f862(f228(x72371),f862(f862(f225(x72371),x72372),x72373)),x72374))
% 25.54/25.42 [7238]~P109(x72381)+~P1(f862(f862(f228(x72381),x72383),x72384))+P1(f862(f862(f228(x72381),f862(f862(f225(x72381),x72382),x72383)),x72384))
% 25.54/25.42 [7239]~P109(x72391)+~P1(f862(f862(f228(x72391),x72392),x72394))+P1(f862(f862(f228(x72391),f862(f862(f225(x72391),x72392),x72393)),x72394))
% 25.54/25.42 [7240]~P109(x72401)+~P1(f862(f862(f228(x72401),x72402),x72404))+P1(f862(f862(f228(x72401),f862(f862(f225(x72401),x72402),x72403)),x72404))
% 25.54/25.42 [7263]~P1(f862(x72633,x72634))+~P1(f862(x72632,x72634))+P1(f862(f862(f862(f94(f932(x72631,a921)),x72632),x72633),x72634))
% 25.54/25.42 [7530]~P61(x75301)+E(f862(f862(f29(x75301),f862(f862(f236(x75301),x75302),x75303)),f862(f862(f236(x75301),x75304),x75303)),f862(f862(f236(x75301),f862(f862(f29(x75301),x75302),x75304)),x75303))+~P1(f862(f862(f278(x75301),x75304),x75302))
% 25.54/25.42 [7764]~P72(x77641)+E(f862(f862(f73(x77641),f862(x77642,x77643)),f862(f862(f8(a924,x77641),x77642),f862(f295(a924,f862(a105,x77643)),x77644))),f862(f862(f8(a924,x77641),x77642),f862(f295(a924,x77643),x77644)))+~P1(f862(f862(f228(a924),x77643),x77644))
% 25.54/25.42 [7782]E(x77821,x77822)+P1(f862(f862(f165(x77823),x77824),x77822))+~P1(f862(f862(f165(x77823),f862(f862(f144(x77823),x77821),x77824)),x77822))
% 25.54/25.42 [7793]~P109(x77931)+P1(f862(f862(f227(x77931),x77932),x77933))+~P1(f862(f862(f227(x77931),f862(f862(f226(x77931),x77934),x77932)),x77933))
% 25.54/25.42 [7794]~P109(x77941)+P1(f862(f862(f227(x77941),x77942),x77943))+~P1(f862(f862(f227(x77941),f862(f862(f226(x77941),x77944),x77942)),x77943))
% 25.54/25.42 [7795]~P109(x77951)+P1(f862(f862(f227(x77951),x77952),x77953))+~P1(f862(f862(f227(x77951),f862(f862(f226(x77951),x77952),x77954)),x77953))
% 25.54/25.42 [7796]~P109(x77961)+P1(f862(f862(f227(x77961),x77962),x77963))+~P1(f862(f862(f227(x77961),f862(f862(f226(x77961),x77962),x77964)),x77963))
% 25.54/25.42 [7797]~P103(x77971)+P1(f862(f862(f227(x77971),x77972),x77973))+~P1(f862(f862(f227(x77971),f862(f862(f103(x77971),x77974),x77972)),x77973))
% 25.54/25.42 [7798]~P103(x77981)+P1(f862(f862(f227(x77981),x77982),x77983))+~P1(f862(f862(f227(x77981),f862(f862(f103(x77981),x77984),x77982)),x77983))
% 25.54/25.42 [7799]~P103(x77991)+P1(f862(f862(f227(x77991),x77992),x77993))+~P1(f862(f862(f227(x77991),f862(f862(f103(x77991),x77992),x77994)),x77993))
% 25.54/25.42 [7800]~P103(x78001)+P1(f862(f862(f227(x78001),x78002),x78003))+~P1(f862(f862(f227(x78001),f862(f862(f103(x78001),x78002),x78004)),x78003))
% 25.54/25.42 [7801]~P109(x78011)+P1(f862(f862(f228(x78011),x78012),x78013))+~P1(f862(f862(f228(x78011),f862(f862(f226(x78011),x78014),x78012)),x78013))
% 25.54/25.42 [7802]~P109(x78021)+P1(f862(f862(f228(x78021),x78022),x78023))+~P1(f862(f862(f228(x78021),f862(f862(f226(x78021),x78022),x78024)),x78023))
% 25.54/25.42 [7803]~P119(x78031)+P1(f862(f862(f278(x78031),x78032),x78033))+~P1(f862(f862(f278(x78031),f862(f862(f74(x78031),x78034),x78032)),x78033))
% 25.54/25.42 [7804]~P119(x78041)+P1(f862(f862(f278(x78041),x78042),x78043))+~P1(f862(f862(f278(x78041),f862(f862(f74(x78041),x78042),x78044)),x78043))
% 25.54/25.42 [7879]~P1(f862(f862(f321(x78791),x78792),x78794))+P1(f862(f862(f321(x78791),x78792),x78793))+P1(f862(f862(f321(x78791),x78792),f862(f862(f3(f932(x78791,a921)),x78794),x78793)))
% 25.54/25.42 [7880]~P1(f862(f862(f321(x78801),x78802),x78804))+P1(f862(f862(f321(x78801),x78802),x78803))+P1(f862(f862(f321(x78801),x78802),f862(f862(f3(f932(x78801,a921)),x78804),x78803)))
% 25.54/25.42 [7963]P1(f862(x79631,x79632))+P1(f862(x79633,x79632))+~P1(f862(f862(f862(f103(f932(x79634,a921)),x79633),x79631),x79632))
% 25.54/25.42 [7973]~P1(f862(f862(f321(x79731),x79732),x79734))+~P1(f862(f862(f321(x79731),x79732),x79733))+P1(f862(f862(f321(x79731),x79732),f862(f862(f94(f932(x79731,a921)),x79733),x79734)))
% 25.54/25.42 [7974]~P1(f862(f862(f321(x79741),x79742),x79744))+~P1(f862(f862(f321(x79741),x79742),x79743))+P1(f862(f862(f321(x79741),x79742),f862(f862(f94(f932(x79741,a921)),x79743),x79744)))
% 25.54/25.42 [8023]~P103(x80231)+~P1(f862(f54(x80231),x80234))+E(f862(f862(f57(x80231,x80231,f103(x80231)),x80232),f862(f862(f301(x80231),x80233),x80234)),f862(f862(f103(x80231),x80233),f862(f862(f57(x80231,x80231,f103(x80231)),x80232),x80234)))
% 25.54/25.42 [8024]~P104(x80241)+~P1(f862(f54(x80241),x80244))+E(f862(f862(f57(x80241,x80241,f94(x80241)),x80242),f862(f862(f301(x80241),x80243),x80244)),f862(f862(f94(x80241),x80243),f862(f862(f57(x80241,x80241,f94(x80241)),x80242),x80244)))
% 25.54/25.42 [8025]~P109(x80251)+~P1(f862(f54(x80251),x80254))+E(f862(f862(f57(x80251,x80251,f225(x80251)),x80252),f862(f862(f301(x80251),x80253),x80254)),f862(f862(f225(x80251),x80253),f862(f862(f57(x80251,x80251,f225(x80251)),x80252),x80254)))
% 25.54/25.42 [8026]~P109(x80261)+~P1(f862(f54(x80261),x80264))+E(f862(f862(f57(x80261,x80261,f226(x80261)),x80262),f862(f862(f301(x80261),x80263),x80264)),f862(f862(f226(x80261),x80263),f862(f862(f57(x80261,x80261,f226(x80261)),x80262),x80264)))
% 25.54/25.42 [8028]~P125(x80281)+~P99(x80281)+E(f862(f862(f3(x80281),f862(f862(f74(x80281),f862(f96(x80281),x80282)),x80283)),f862(f862(f74(x80281),f862(f96(x80281),x80282)),x80284)),f862(f862(f74(x80281),f862(f96(x80281),x80282)),f862(f862(f3(x80281),x80283),x80284)))
% 25.54/25.42 [8029]~P140(x80291)+~P99(x80291)+E(f862(f862(f73(x80291),f862(f862(f74(x80291),f862(f96(x80291),x80292)),x80293)),f862(f862(f74(x80291),f862(f96(x80291),x80292)),x80294)),f862(f862(f74(x80291),f862(f96(x80291),x80292)),f862(f862(f73(x80291),x80293),x80294)))
% 25.54/25.42 [8145]E(x81451,x81452)+P1(f862(f862(f321(x81453),x81451),f862(f165(x81453),x81454)))+~P1(f862(f862(f321(x81453),x81451),f862(f165(x81453),f862(f862(f144(x81453),x81452),x81454))))
% 25.54/25.42 [8321]P52(x83211,x83212,x83213)+~P52(x83211,x83212,x83214)+~P1(f862(f862(f227(f932(f931(x83211,x83212),a921)),x83213),x83214))
% 25.54/25.42 [8368]P1(f862(f862(f321(x83681),x83682),x83683))+P1(f862(f862(f321(x83681),x83682),x83684))+~P1(f862(f862(f321(x83681),x83682),f862(f862(f103(f932(x83681,a921)),x83684),x83683)))
% 25.54/25.42 [8369]P1(f862(f862(f321(x83691),x83692),x83693))+P1(f862(f862(f321(x83691),x83692),x83694))+~P1(f862(f862(f321(x83691),x83692),f862(f862(f103(f932(x83691,a921)),x83694),x83693)))
% 25.54/25.42 [8378]~P50(x83781,x83784,x83783)+~P1(f862(f862(f321(x83781),x83782),x83784))+P1(f862(f862(f321(f931(x83781,x83781)),f862(f862(f244(x83781,x83781),x83782),x83782)),x83783))
% 25.54/25.42 [8379]~P50(x83791,x83794,x83793)+~P1(f862(f862(f321(x83791),x83792),x83794))+P1(f862(f862(f321(f931(x83791,x83791)),f862(f862(f244(x83791,x83791),x83792),x83792)),x83793))
% 25.54/25.42 [8380]~P50(x83801,x83804,x83803)+~P1(f862(f862(f321(x83801),x83802),x83804))+P1(f862(f862(f321(f931(x83801,x83801)),f862(f862(f244(x83801,x83801),x83802),x83802)),x83803))
% 25.54/25.42 [8392]~P1(f862(f54(x83922),x83924))+~P1(f862(f54(x83921),x83923))+P1(f862(f54(f931(x83921,x83922)),f862(f862(f246(x83921,x83922),x83923),f862(f18(f932(x83922,a921),x83921),x83924))))
% 25.54/25.42 [8393]~P1(f862(f862(f321(x83931),x83932),x83934))+~P1(f862(f862(f227(f932(x83931,a921)),x83933),x83934))+P1(f862(f862(f227(f932(x83931,a921)),f862(f862(f301(x83931),x83932),x83933)),x83934))
% 25.54/25.42 [8400]~P71(x84002)+~P147(x84002)+E(f862(f862(f11(x84001,x84002),f862(f862(f10(a924,x84002,x84001),f93(x84002)),x84003)),x84004),f862(f93(x84002),f862(f862(f11(x84001,a924),x84003),x84004)))
% 25.54/25.42 [8401]~P71(x84012)+~P142(x84012)+E(f862(f862(f11(x84011,x84012),f862(f862(f10(a1,x84012,x84011),f95(x84012)),x84013)),x84014),f862(f95(x84012),f862(f862(f11(x84011,a1),x84013),x84014)))
% 25.54/25.42 [8425]E(f862(f862(f3(f932(x84251,a921)),x84252),f862(f862(f3(f932(x84251,a921)),x84253),x84254)),x84254)+~P1(f862(f862(f227(f932(x84251,a921)),x84252),x84253))+~P1(f862(f862(f227(f932(x84251,a921)),x84254),x84252))
% 25.54/25.42 [8521]~P1(f862(f54(x85211),x85214))+E(f862(f862(f3(a924),f862(f862(f8(x85211,a924),x85212),x85213)),f862(f862(f8(x85211,a924),x85212),x85214)),f862(f862(f8(x85211,a924),x85212),f862(f862(f3(f932(x85211,a921)),x85213),x85214)))+~P1(f862(f862(f227(f932(x85211,a921)),x85214),x85213))
% 25.54/25.42 [8675]~P6(x86751,x86754,x86753)+~P1(f862(f862(f321(x86751),x86752),x86754))+P1(f862(f862(f321(x86751),x86752),f862(f276(x86751,x86751,x86753),f862(f862(f301(x86751),x86752),f181(f932(x86751,a921))))))
% 25.54/25.42 [8737]~P1(f862(f862(f227(f932(x87371,a921)),x87372),x87373))+~P1(f862(f862(f227(f932(x87371,a921)),x87372),x87374))+P1(f862(f862(f227(f932(x87371,a921)),x87372),f862(f862(f94(f932(x87371,a921)),x87373),x87374)))
% 25.54/25.42 [8840]E(x88401,f181(f932(x88402,a921)))+P1(f862(f54(x88403),x88404))+~P1(f862(f54(f931(x88403,x88402)),f862(f862(f246(x88403,x88402),x88404),f862(f18(f932(x88402,a921),x88403),x88401))))
% 25.54/25.42 [8841]E(x88411,f181(f932(x88412,a921)))+P1(f862(f54(x88413),x88414))+~P1(f862(f54(f931(x88412,x88413)),f862(f862(f246(x88412,x88413),x88411),f862(f18(f932(x88413,a921),x88412),x88414))))
% 25.54/25.42 [8914]P1(f862(f862(f321(x89141),x89142),f308(x89141,x89143)))+~P1(f862(f862(f321(x89141),x89144),f308(x89141,x89143)))+~P1(f862(f862(f321(f931(x89141,x89141)),f862(f862(f244(x89141,x89141),x89142),x89144)),x89143))
% 25.54/25.42 [8915]P1(f862(f862(f321(x89151),x89152),f308(x89151,x89153)))+~P1(f862(f862(f321(x89151),x89154),f308(x89151,x89153)))+~P1(f862(f862(f321(f931(x89151,x89151)),f862(f862(f244(x89151,x89151),x89152),x89154)),x89153))
% 25.54/25.42 [8972]~P35(x89721,x89724)+P1(f862(f862(f321(f931(x89721,x89721)),f862(f862(f244(x89721,x89721),x89723),x89722)),f299(x89721,x89724)))+P35(x89721,f862(f862(f301(f931(x89721,x89721)),f862(f862(f244(x89721,x89721),x89722),x89723)),x89724))
% 25.54/25.42 [8973]~P55(x89731,x89734)+P1(f862(f862(f321(f931(x89731,x89731)),f862(f862(f244(x89731,x89731),x89733),x89732)),f299(x89731,x89734)))+P55(x89731,f862(f862(f301(f931(x89731,x89731)),f862(f862(f244(x89731,x89731),x89732),x89733)),x89734))
% 25.54/25.42 [9057]~E(x90572,x90573)+~P1(f862(f862(f321(x90571),x90572),f862(f165(x90571),x90574)))+P1(f862(f862(f321(f931(x90571,x90571)),f862(f862(f244(x90571,x90571),x90572),x90573)),f862(f165(f931(x90571,x90571)),f862(f862(f174(x90571,x90571),x90574),x90574))))
% 25.54/25.42 [9145]~E(x91453,x91454)+P1(f862(f862(f249(x91451,x91451,a921),a317),x91452))+~P1(f862(f862(f321(f931(x91451,x91451)),x91452),f862(f165(f931(x91451,x91451)),f862(f862(f174(x91451,x91451),x91453),x91454))))
% 25.54/25.42 [9189]P1(f862(f862(f321(f931(f925(x91891),f925(x91891))),f862(f862(f244(f925(x91891),f925(x91891)),x91892),x91893)),f140(x91891,x91894)))+~E(f862(f862(f168(x91891),f862(f182(f925(x91891)),x91892)),x91893),x91892)+~P1(f862(f862(f228(a924),f862(f182(f925(x91891)),x91892)),f862(f182(f925(x91891)),x91893)))
% 25.54/25.42 [9191]~P49(x91911,x91914)+~P1(f862(f862(f321(f931(x91911,x91911)),f862(f862(f244(x91911,x91911),x91913),x91912)),x91914))+P1(f862(f862(f321(f931(x91911,x91911)),f862(f862(f244(x91911,x91911),x91912),x91913)),x91914))
% 25.54/25.42 [9192]~P49(x91921,x91924)+~P1(f862(f862(f321(f931(x91921,x91921)),f862(f862(f244(x91921,x91921),x91923),x91922)),x91924))+P1(f862(f862(f321(f931(x91921,x91921)),f862(f862(f244(x91921,x91921),x91922),x91923)),x91924))
% 25.54/25.42 [9283]~P1(f862(f54(x92831),x92834))+P1(f862(f862(f321(x92831),f878(x92832,x92833,x92834,x92831)),x92834))+P1(f862(f54(x92833),f862(f862(f33(x92831,f932(x92833,a921)),x92834),x92832)))
% 25.54/25.42 [9284]~P1(f862(f54(x92841),x92844))+P1(f862(f862(f321(x92841),f594(x92842,x92843,x92844,x92841)),x92844))+P1(f862(f54(x92843),f862(f862(f33(x92841,f932(x92843,a921)),x92844),x92842)))
% 25.54/25.42 [9371]P1(f862(f862(f321(f931(x93711,x93711)),x93712),f862(f862(f280(x93711,x93711,x93711),x93713),f299(x93711,x93713))))+~P1(f862(f862(f228(a924),f2(a924)),x93714))+~P1(f862(f862(f321(f931(x93711,x93711)),x93712),f862(f862(f176(f931(x93711,x93711),a921),x93714),x93713)))
% 25.54/25.42 [9378]~P35(x93781,x93782)+~P1(f862(f862(f321(f931(x93781,x93781)),f862(f862(f244(x93781,x93781),x93784),x93783)),x93782))+~P1(f862(f862(f321(f931(x93781,x93781)),f862(f862(f244(x93781,x93781),x93783),x93784)),x93782))
% 25.54/25.42 [9379]~P35(x93791,x93792)+~P1(f862(f862(f321(f931(x93791,x93791)),f862(f862(f244(x93791,x93791),x93794),x93793)),x93792))+~P1(f862(f862(f321(f931(x93791,x93791)),f862(f862(f244(x93791,x93791),x93793),x93794)),x93792))
% 25.54/25.42 [9505]~P1(f862(f54(x95051),x95054))+E(f862(f862(f8(x95051,a924),f862(f862(f10(f932(x95052,a921),a924,x95051),f28(x95052)),x95053)),x95054),f862(f28(f931(x95051,x95052)),f862(f862(f246(x95051,x95052),x95054),x95053)))+P1(f862(f862(f321(x95051),f572(x95053,x95052,x95054,x95051)),x95054))
% 25.54/25.42 [9509]~P1(f862(f130(x95091),x95092))+P1(f862(f130(x95091),f862(f862(f152(x95091,x95092),x95093),x95094)))+P1(f862(f862(f321(x95091),x95094),f862(f862(f3(f932(x95091,a921)),f862(f165(x95091),x95092)),f862(f862(f301(x95091),f862(f862(f157(x95091),x95092),x95093)),f181(f932(x95091,a921))))))
% 25.54/25.42 [9526]~P1(f862(f54(x95262),x95263))+~P1(f862(f54(x95261),f862(x95264,f878(x95264,x95261,x95263,x95262))))+P1(f862(f54(x95261),f862(f862(f33(x95262,f932(x95261,a921)),x95263),x95264)))
% 25.54/25.42 [9527]~P1(f862(f54(x95272),x95273))+~P1(f862(f54(x95271),f862(x95274,f594(x95274,x95271,x95273,x95272))))+P1(f862(f54(x95271),f862(f862(f33(x95272,f932(x95271,a921)),x95273),x95274)))
% 25.54/25.42 [9608]~P1(f862(f862(f321(f931(x96081,x96081)),x96082),f862(f862(f280(x96081,x96081,x96081),x96084),f299(x96081,x96084))))+P1(f862(f862(f321(f931(x96081,x96081)),x96082),f862(f862(f280(x96081,x96081,x96081),x96083),f299(x96081,x96083))))+~P1(f862(f862(f227(f932(f931(x96081,x96081),a921)),x96084),x96083))
% 25.54/25.42 [9618]E(f862(f862(f168(x96181),f666(x96184,x96183,x96182,x96181)),x96183),f862(f862(f168(x96181),f666(x96184,x96183,x96182,x96181)),x96182))+~P1(f862(f862(f321(f931(f925(x96181),f925(x96181))),f862(f862(f244(f925(x96181),f925(x96181)),x96182),x96183)),f140(x96181,x96184)))+E(f862(f862(f168(x96181),f862(f182(f925(x96181)),x96182)),x96183),x96182)
% 25.54/25.42 [9634]~P1(f862(f54(x96341),x96344))+E(f862(f862(f8(x96341,a924),f862(f862(f10(f932(x96342,a921),a924,x96341),f28(x96342)),x96343)),x96344),f862(f28(f931(x96341,x96342)),f862(f862(f246(x96341,x96342),x96344),x96343)))+~P1(f862(f54(x96342),f862(x96343,f572(x96343,x96342,x96344,x96341))))
% 25.54/25.42 [9638]~E(f862(f182(f925(x96381)),x96383),f862(f182(f925(x96381)),x96382))+P1(f862(f862(f321(f931(f925(x96381),f925(x96381))),f862(f862(f244(f925(x96381),f925(x96381)),x96382),x96383)),f151(x96381,x96384)))+P1(f862(f862(f321(f931(x96381,x96381)),f671(x96384,x96383,x96382,x96381)),f862(f165(f931(x96381,x96381)),f862(f862(f174(x96381,x96381),x96382),x96383))))
% 25.54/25.42 [9720]~P1(f862(f862(f321(f931(f925(x97201),f925(x97201))),f862(f862(f244(f925(x97201),f925(x97201)),x97202),x97203)),f140(x97201,x97204)))+E(f862(f862(f168(x97201),f862(f182(f925(x97201)),x97202)),x97203),x97202)+P1(f862(f862(f228(a924),f666(x97204,x97203,x97202,x97201)),f862(f862(f225(a924),f862(f182(f925(x97201)),x97202)),f862(f182(f925(x97201)),x97203))))
% 25.54/25.42 [9744]~P1(f862(f862(f321(f931(f925(x97441),f925(x97441))),f862(f862(f244(f925(x97441),f925(x97441)),x97442),x97443)),f140(x97441,x97444)))+P1(f862(f862(f228(a924),f862(f182(f925(x97441)),x97442)),f862(f182(f925(x97441)),x97443)))+P1(f862(f862(f228(a924),f666(x97444,x97443,x97442,x97441)),f862(f862(f225(a924),f862(f182(f925(x97441)),x97442)),f862(f182(f925(x97441)),x97443))))
% 25.54/25.42 [10150]~P1(f862(f862(f321(f931(f925(x101501),f925(x101501))),f862(f862(f244(f925(x101501),f925(x101501)),x101502),x101503)),f140(x101501,x101504)))+E(f862(f862(f168(x101501),f862(f182(f925(x101501)),x101502)),x101503),x101502)+P1(f862(f862(f321(f931(x101501,x101501)),f862(f862(f244(x101501,x101501),f862(f862(f157(x101501),x101502),f666(x101504,x101503,x101502,x101501))),f862(f862(f157(x101501),x101503),f666(x101504,x101503,x101502,x101501)))),x101504))
% 25.54/25.42 [10151]~P1(f862(f862(f321(f931(f925(x101511),f925(x101511))),f862(f862(f244(f925(x101511),f925(x101511)),x101512),x101513)),f140(x101511,x101514)))+P1(f862(f862(f228(a924),f862(f182(f925(x101511)),x101512)),f862(f182(f925(x101511)),x101513)))+P1(f862(f862(f321(f931(x101511,x101511)),f862(f862(f244(x101511,x101511),f862(f862(f157(x101511),x101512),f666(x101514,x101513,x101512,x101511))),f862(f862(f157(x101511),x101513),f666(x101514,x101513,x101512,x101511)))),x101514))
% 25.54/25.42 [10208]~E(f862(f182(f925(x102081)),x102082),f862(f182(f925(x102081)),x102083))+P1(f862(f862(f321(f931(f925(x102081),f925(x102081))),f862(f862(f244(f925(x102081),f925(x102081)),x102082),x102083)),f151(x102081,x102084)))+~P1(f862(f862(f321(f931(x102081,x102081)),f862(f862(f244(x102081,x102081),f862(f862(f157(x102081),x102082),f659(x102084,x102083,x102082,x102081))),f862(f862(f157(x102081),x102083),f659(x102084,x102083,x102082,x102081)))),x102084))
% 25.54/25.42 [10354]~P72(x103541)+~P1(f862(f54(x103542),x103544))+E(f862(f158(x103541),f862(f862(f147(x103542,x103541),x103543),f83(f925(x103542),f862(f862(f20(f925(x103542),a921,a921),f862(f862(f10(a921,f932(a921,a921),f925(x103542)),a318),f862(f862(f9(f925(x103542),f932(x103542,a921),a921),f862(f862(f10(f932(x103542,a921),f932(f932(x103542,a921),a921),f925(x103542)),a317),f165(x103542))),x103544))),f130(x103542))))),f224(x103542,x103541,x103543,x103544))
% 25.54/25.42 [7612]~P64(x76122)+E(x76121,f2(x76122))+E(f862(f862(f281(x76122),f862(f862(f73(x76122),x76123),f862(f862(f74(x76122),x76124),x76121))),x76121),f862(f862(f73(x76122),x76124),f862(f862(f281(x76122),x76123),x76121)))
% 25.54/25.42 [7613]~P61(x76132)+E(x76131,f2(x76132))+E(f862(f862(f29(x76132),f862(f862(f73(x76132),x76133),f862(f862(f74(x76132),x76134),x76131))),x76131),f862(f862(f73(x76132),x76134),f862(f862(f29(x76132),x76133),x76131)))
% 25.54/25.42 [7614]~P61(x76142)+E(x76141,f2(x76142))+E(f862(f862(f29(x76142),f862(f862(f73(x76142),x76143),f862(f862(f74(x76142),x76141),x76144))),x76141),f862(f862(f73(x76142),x76144),f862(f862(f29(x76142),x76143),x76141)))
% 25.54/25.42 [7843]~P65(x78432)+E(x78431,f2(x78432))+E(f862(f862(f281(x78432),f862(f862(f3(x78432),x78433),f862(f862(f74(x78432),x78431),x78434))),x78431),f862(f862(f3(x78432),f862(f862(f281(x78432),x78433),x78431)),x78434))
% 25.54/25.42 [7844]~P64(x78442)+E(x78441,f2(x78442))+E(f862(f862(f281(x78442),f862(f862(f73(x78442),x78443),f862(f862(f74(x78442),x78444),x78441))),x78441),f862(f862(f73(x78442),f862(f862(f281(x78442),x78443),x78441)),x78444))
% 25.54/25.42 [7845]~P65(x78452)+E(x78451,f2(x78452))+E(f862(f862(f281(x78452),f862(f862(f73(x78452),x78453),f862(f862(f74(x78452),x78451),x78454))),x78451),f862(f862(f73(x78452),f862(f862(f281(x78452),x78453),x78451)),x78454))
% 25.54/25.42 [8553]~P1(f862(f153(x85531,x85533),x85534))+~P1(f862(f153(x85531,x85532),x85534))+P1(f862(f153(x85531,f862(f862(f94(f932(x85531,a921)),x85532),x85533)),x85534))
% 25.54/25.42 [8930]~E(f862(f862(f280(x89301,x89301,x89301),x89302),x89304),f181(f932(f931(x89301,x89301),a921)))+~E(f862(f862(f280(x89301,x89301,x89301),x89302),x89303),f181(f932(f931(x89301,x89301),a921)))+E(f862(f862(f280(x89301,x89301,x89301),x89302),f862(f862(f103(f932(f931(x89301,x89301),a921)),x89303),x89304)),f181(f932(f931(x89301,x89301),a921)))
% 25.54/25.42 [9058]~P1(f862(f862(f227(f932(x90581,a921)),x90583),x90584))+~P1(f862(f862(f227(f932(x90581,a921)),x90582),x90584))+P1(f862(f862(f227(f932(x90581,a921)),f862(f862(f103(f932(x90581,a921)),x90582),x90583)),x90584))
% 25.54/25.42 [9434]~P1(f862(f54(x94341),x94344))+~P1(f862(f54(x94341),x94343))+E(f862(f862(f3(a924),f862(f862(f73(a924),f862(f862(f8(x94341,a924),x94342),x94343)),f862(f862(f8(x94341,a924),x94342),x94344))),f862(f862(f8(x94341,a924),x94342),f862(f862(f94(f932(x94341,a921)),x94343),x94344))),f862(f862(f8(x94341,a924),x94342),f862(f862(f103(f932(x94341,a921)),x94343),x94344)))
% 25.54/25.42 [9523]~P1(f862(f862(f321(x95231),x95233),x95232))+~P1(f862(f862(f227(f932(x95231,a921)),x95232),f862(f862(f301(x95231),x95233),x95234)))+P1(f862(f862(f227(f932(x95231,a921)),f862(f862(f3(f932(x95231,a921)),x95232),f862(f862(f301(x95231),x95233),f181(f932(x95231,a921))))),x95234))
% 25.54/25.42 [9695]~P1(f862(f862(f321(x96951),x96953),x96952))+P1(f862(f862(f227(f932(x96951,a921)),x96952),f862(f862(f301(x96951),x96953),x96954)))+~P1(f862(f862(f227(f932(x96951,a921)),f862(f862(f3(f932(x96951,a921)),x96952),f862(f862(f301(x96951),x96953),f181(f932(x96951,a921))))),x96954))
% 25.54/25.42 [9696]~P1(f862(f862(f321(x96961),x96963),x96962))+P1(f862(f862(f227(f932(x96961,a921)),x96962),f862(f862(f301(x96961),x96963),x96964)))+~P1(f862(f862(f227(f932(x96961,a921)),f862(f862(f3(f932(x96961,a921)),x96962),f862(f862(f301(x96961),x96963),f181(f932(x96961,a921))))),x96964))
% 25.54/25.42 [9719]~P1(f862(f862(f227(f932(x97191,a921)),x97192),x97194))+P1(f862(f862(f227(f932(x97191,a921)),x97192),f862(f862(f301(x97191),x97193),x97194)))+~P1(f862(f862(f227(f932(x97191,a921)),f862(f862(f3(f932(x97191,a921)),x97192),f862(f862(f301(x97191),x97193),f181(f932(x97191,a921))))),x97194))
% 25.54/25.42 [9784]~P1(f862(f862(f227(a924),x97841),x97843))+~P1(f862(f862(f228(a924),x97842),x97844))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97841),x97842)),f862(f862(f244(a924,a924),x97843),x97844))),a26))
% 25.54/25.42 [9785]~P1(f862(f862(f227(a924),x97852),x97854))+~P1(f862(f862(f227(a924),x97851),x97853))+P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),f862(f862(f244(a924,a924),x97851),x97852)),f862(f862(f244(a924,a924),x97853),x97854))),a64))
% 25.54/25.42 [10078]~P1(f862(f862(f321(f925(x100781)),x100784),f154(x100781,x100783)))+~P1(f862(f862(f321(f925(x100781)),x100784),f154(x100781,x100782)))+P1(f862(f153(x100781,f862(f862(f94(f932(x100781,a921)),f862(f862(f9(x100781,f932(x100781,a921),a921),f321(x100781)),x100782)),f862(f862(f9(x100781,f932(x100781,a921),a921),f321(x100781)),x100783))),x100784))
% 25.54/25.42 [10173]~P22(x101731,f932(f932(x101731,a921),a921),f862(f862(f9(x101731,f932(f931(x101731,x101731),a921),f932(f932(x101731,a921),a921)),f862(f862(f10(f932(x101731,a921),f932(f932(f931(x101731,x101731),a921),f932(f932(x101731,a921),a921)),x101731),f53(x101731)),f862(f862(f9(x101731,f932(x101731,a921),f932(x101731,a921)),f301(x101731)),f181(f932(x101731,a921))))),x101733),x101732)+~P1(f862(f862(f321(x101731),x101734),x101732))+E(f862(f862(f3(f932(f932(x101731,a921),a921)),f862(f862(f53(x101731),x101732),x101733)),f862(f862(f53(x101731),f862(f862(f301(x101731),x101734),f181(f932(x101731,a921)))),x101733)),f862(f862(f53(x101731),f862(f862(f3(f932(x101731,a921)),x101732),f862(f862(f301(x101731),x101734),f181(f932(x101731,a921))))),x101733))
% 25.54/25.42 [10308]~P50(x103081,x103082,x103084)+~P1(f862(f862(f321(f931(x103081,x103081)),x103083),x103084))+P1(f862(f862(f249(x103081,x103081,a921),f862(f862(f9(x103081,f932(x103081,a921),f932(x103081,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x103081,a921),f932(x103081,a921)),x103081),f10(a921,a921,x103081)),f862(f862(f10(a921,f932(a921,a921),x103081),a318),f862(f862(f9(x103081,f932(x103081,a921),a921),f321(x103081)),x103082)))),f862(f862(f9(x103081,f932(x103081,a921),a921),f321(x103081)),x103082))),x103083))
% 25.54/25.42 [10320]P1(f862(f54(x103201),x103202))+~P1(f862(f54(x103203),f862(f302(x103201,x103203,x103204),x103202)))+~P1(f862(f54(x103201),f862(f254(x103201),f862(f862(f20(x103201,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103201),a318),f862(f862(f9(x103201,f932(x103201,a921),a921),f321(x103201)),x103202))),f862(f862(f9(x103201,x103203,a921),f862(f862(f10(x103203,f932(x103203,a921),x103201),a317),x103204)),f862(x103204,f581(x103204,x103203,x103202,x103201)))))))
% 25.54/25.42 [8305]~P65(x83052)+E(x83051,f2(x83052))+E(f862(f862(f281(x83052),f862(f862(f3(x83052),f862(f862(f74(x83052),x83051),x83053)),x83054)),x83051),f862(f862(f3(x83052),x83053),f862(f862(f281(x83052),x83054),x83051)))
% 25.54/25.42 [8306]~P65(x83062)+E(x83061,f2(x83062))+E(f862(f862(f281(x83062),f862(f862(f73(x83062),f862(f862(f74(x83062),x83061),x83063)),x83064)),x83061),f862(f862(f73(x83062),x83063),f862(f862(f281(x83062),x83064),x83061)))
% 25.54/25.42 [9218]~E(f862(f862(f280(x92181,x92181,x92181),x92183),x92184),f181(f932(f931(x92181,x92181),a921)))+~E(f862(f862(f280(x92181,x92181,x92181),x92182),x92184),f181(f932(f931(x92181,x92181),a921)))+E(f862(f862(f280(x92181,x92181,x92181),f862(f862(f103(f932(f931(x92181,x92181),a921)),x92182),x92183)),x92184),f181(f932(f931(x92181,x92181),a921)))
% 25.54/25.42 [9994]~P1(f862(f153(x99941,x99943),x99944))+~P1(f862(f153(x99941,x99942),x99944))+P1(f862(f153(x99941,f862(f862(f20(x99941,a921,a921),f862(f862(f10(a921,f932(a921,a921),x99941),a318),x99942)),x99943)),x99944))
% 25.54/25.42 [10244]P1(f862(x102441,f511(x102442,x102443,x102441,x102444)))+~P1(f862(f54(x102444),f862(f254(x102444),x102441)))+P1(f862(f54(x102443),f862(f254(x102443),f862(f862(f10(f932(x102444,a921),a921,x102443),f80(x102444)),f862(f862(f10(f932(x102444,a921),f932(x102444,a921),x102443),f862(f20(x102444,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102444),a318),x102441))),x102442)))))
% 25.54/25.42 [10262]~P1(f862(f54(x102622),f862(f254(x102622),x102623)))+~P1(f862(f54(x102621),f862(f254(x102621),f862(f862(f9(x102621,x102622,a921),x102624),f511(x102624,x102621,x102623,x102622)))))+P1(f862(f54(x102621),f862(f254(x102621),f862(f862(f10(f932(x102622,a921),a921,x102621),f80(x102622)),f862(f862(f10(f932(x102622,a921),f932(x102622,a921),x102621),f862(f20(x102622,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102622),a318),x102623))),x102624)))))
% 25.54/25.42 [10333]~P1(f862(f54(x103331),x103334))+P1(f862(f862(f321(x103331),f800(x103332,x103333,x103334,x103331)),x103334))+P1(f862(f54(x103333),f862(f254(x103333),f862(f862(f10(f932(x103331,a921),a921,x103333),f80(x103331)),f862(f862(f10(f932(x103331,a921),f932(x103331,a921),x103333),f862(f20(x103331,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103331),a318),f862(f862(f9(x103331,f932(x103331,a921),a921),f321(x103331)),x103334)))),x103332)))))
% 25.54/25.42 [10339]~P1(f862(f54(x103392),x103393))+~P1(f862(f54(x103391),f862(f254(x103391),f862(f862(f9(x103391,x103392,a921),x103394),f800(x103394,x103391,x103393,x103392)))))+P1(f862(f54(x103391),f862(f254(x103391),f862(f862(f10(f932(x103392,a921),a921,x103391),f80(x103392)),f862(f862(f10(f932(x103392,a921),f932(x103392,a921),x103391),f862(f20(x103392,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103392),a318),f862(f862(f9(x103392,f932(x103392,a921),a921),f321(x103392)),x103393)))),x103394)))))
% 25.54/25.42 [5214]~E(x52142,x52144)+E(f162(x52141,x52142,x52143),f162(x52141,x52144,x52145))+~E(x52142,f2(a924))
% 25.54/25.42 [5465]E(x54651,x54652)+~E(f162(x54654,x54653,x54651),f162(x54654,x54655,x54652))+E(x54653,f2(a924))
% 25.54/25.42 [6742]E(x67421,x67422)+~E(f862(x67423,x67421),f862(x67423,x67422))+~P22(x67424,x67425,x67423,f234(f932(x67424,a921)))
% 25.54/25.42 [6743]E(x67431,x67432)+~E(f862(x67433,x67431),f862(x67433,x67432))+~P22(x67434,x67435,x67433,f234(f932(x67434,a921)))
% 25.54/25.42 [7644]E(x76441,x76442)+~P22(x76443,x76444,x76445,f234(f932(x76443,a921)))+~E(f862(f302(x76443,x76444,x76445),x76441),f862(f302(x76443,x76444,x76445),x76442))
% 25.54/25.42 [7897]P22(x78972,x78973,f535(x78974,x78973,x78972,x78971),x78971)+~E(f862(f302(x78973,x78972,x78975),x78974),x78971)+E(x78971,f181(f932(x78972,a921)))
% 25.54/25.42 [8436]~P1(f862(f862(x84363,x84362),x84365))+~P1(f862(f862(x84363,x84364),x84362))+P1(f862(f862(f321(x84361),x84362),f287(x84361,x84363,x84364,x84365)))
% 25.54/25.42 [8437]~P1(f862(f862(x84373,x84372),x84375))+~P1(f862(f862(x84373,x84374),x84372))+P1(f862(f862(f321(x84371),x84372),f290(x84371,x84373,x84374,x84375)))
% 25.54/25.42 [8745]~P22(x87451,x87452,x87453,x87454)+P23(x87451,x87452,x87453,x87454,x87455)+~E(f862(f302(x87451,x87452,x87453),x87454),x87455)
% 25.54/25.42 [8879]~P23(x88791,x88793,x88794,x88792,x88795)+~P1(f862(f54(x88793),x88795))+P1(f862(f54(x88791),x88792))
% 25.54/25.42 [8880]~P23(x88803,x88801,x88804,x88805,x88802)+~P1(f862(f54(x88803),x88805))+P1(f862(f54(x88801),x88802))
% 25.54/25.42 [9013]~P22(x90131,x90133,x90135,f234(f932(x90131,a921)))+~P22(x90133,x90132,x90134,f234(f932(x90133,a921)))+P22(x90131,x90132,f862(f66(x90133,x90132,x90131,x90134),x90135),f234(f932(x90131,a921)))
% 25.54/25.42 [9585]P1(f862(f862(f321(f931(x95851,x95851)),f862(f862(f244(x95851,x95851),x95852),x95853)),f299(x95851,x95854)))+~P1(f862(f862(f321(f931(x95851,x95851)),f862(f862(f244(x95851,x95851),x95852),x95855)),f299(x95851,x95854)))+~P1(f862(f862(f321(f931(x95851,x95851)),f862(f862(f244(x95851,x95851),x95855),x95853)),f299(x95851,x95854)))
% 25.54/25.42 [9625]~P109(x96252)+~P1(f862(f130(x96251),x96255))+P1(f862(f130(x96251),f142(x96251,x96252,x96253,x96254,x96255)))
% 25.54/25.42 [9755]~P23(x97553,x97552,x97554,f234(f932(x97553,a921)),f234(f932(x97552,a921)))+~P23(x97551,x97553,x97555,f234(f932(x97551,a921)),f234(f932(x97553,a921)))+P23(x97551,x97552,f862(f66(x97553,x97552,x97551,x97554),x97555),f234(f932(x97551,a921)),f234(f932(x97552,a921)))
% 25.54/25.42 [5539]~E(x55392,f106(x55391))+E(f862(f862(f127(x55391),x55392),x55393),f862(f862(f144(x55391),x55394),x55395))+~E(x55393,f862(f862(f144(x55391),x55394),x55395))
% 25.54/25.42 [5540]~E(x55402,f106(x55401))+E(f862(f862(f127(x55401),x55402),x55403),f862(f862(f144(x55401),x55404),x55405))+~E(f862(f862(f144(x55401),x55404),x55405),x55403)
% 25.54/25.42 [6699]~E(f862(f182(f925(x66991)),x66995),f862(f182(f925(x66992)),x66994))+E(f862(f862(f147(f931(x66991,x66992),x66992),f248(x66991,x66992)),x66993),x66994)+~E(f862(f862(f174(x66991,x66992),x66995),x66994),x66993)
% 25.54/25.42 [6700]~E(f862(f182(f925(x67001)),x67004),f862(f182(f925(x67002)),x67005))+E(f862(f862(f147(f931(x67001,x67002),x67001),f243(x67001,x67002)),x67003),x67004)+~E(f862(f862(f174(x67001,x67002),x67004),x67005),x67003)
% 25.54/25.42 [7174]~P109(x71741)+~P11(x71741,f862(f862(f147(x71742,x71741),x71743),x71745))+P11(x71741,f862(f862(f147(x71742,x71741),x71743),f862(f129(x71742,x71744),x71745)))
% 25.54/25.42 [7317]~P109(x73171)+P11(x73171,f862(f862(f147(x73172,x73171),x73173),f163(x73172,x73174,x73175)))+~P11(x73171,f862(f862(f147(x73172,x73171),x73173),x73175))
% 25.54/25.42 [7340]~P52(x73403,x73402,x73405)+~P52(x73401,x73403,x73404)+P52(x73401,x73402,f862(f862(f280(x73401,x73403,x73402),x73404),x73405))
% 25.54/25.42 [7436]E(x74361,x74362)+~P22(x74363,x74364,x74365,f234(f932(x74363,a921)))+~E(f862(f862(f147(x74363,x74364),x74365),x74361),f862(f862(f147(x74363,x74364),x74365),x74362))
% 25.54/25.42 [7437]E(x74371,x74372)+~P22(x74373,x74374,x74375,f234(f932(x74373,a921)))+~E(f862(f862(f147(x74373,x74374),x74375),x74371),f862(f862(f147(x74373,x74374),x74375),x74372))
% 25.54/25.42 [7599]~P1(f862(f862(f227(a924),x75991),f862(x75993,x75995)))+P1(f862(f862(f227(a924),x75991),f148(x75992,x75993,x75994)))+~P1(f862(f862(f321(x75992),x75995),f862(f165(x75992),x75994)))
% 25.54/25.42 [7600]~P1(f862(f862(f228(a924),x76001),f862(x76003,x76005)))+P1(f862(f862(f228(a924),x76001),f148(x76002,x76003,x76004)))+~P1(f862(f862(f321(x76002),x76005),f862(f165(x76002),x76004)))
% 25.54/25.42 [7957]~E(x79573,f2(a924))+P1(f862(x79571,x79572))+~P1(f862(f862(f321(x79574),x79572),f862(f165(x79574),f162(x79574,x79573,x79575))))
% 25.54/25.42 [7972]~E(x79721,f2(a924))+~P1(f862(x79722,x79723))+~P1(f862(f862(f321(x79724),x79723),f862(f165(x79724),f162(x79724,x79721,x79725))))
% 25.54/25.42 [7993]P1(f862(x79931,x79932))+~P1(f862(x79931,x79933))+~P1(f862(f862(f321(x79934),x79932),f862(f165(x79934),f162(x79934,x79935,x79933))))
% 25.54/25.42 [7994]P1(f862(x79941,x79942))+~P1(f862(x79941,x79943))+~P1(f862(f862(f321(x79944),x79943),f862(f165(x79944),f162(x79944,x79945,x79942))))
% 25.54/25.42 [7999]~P110(x79991)+P1(f862(f862(f227(f932(x79991,a921)),f296(x79991,x79992,x79993)),f296(x79991,x79994,x79995)))+P1(f862(f862(f227(x79991),x79992),x79993))
% 25.54/25.42 [8021]~P3(x80211)+P1(f862(f862(f227(x80211),f862(f862(f32(x80212,x80211),x80213),x80214)),f862(x80214,x80215)))+~P1(f862(f862(f321(x80212),x80215),x80213))
% 25.54/25.42 [8090]~P22(x80901,x80902,x80904,x80903)+E(f862(f70(x80901,x80902,x80903,x80904),f862(x80904,x80905)),x80905)+~P1(f862(f862(f321(x80901),x80905),x80903))
% 25.54/25.42 [8091]~P22(x80911,x80912,x80914,x80913)+E(f862(f86(x80911,x80912,x80913,x80914),f862(x80914,x80915)),x80915)+~P1(f862(f862(f321(x80911),x80915),x80913))
% 25.54/25.42 [8294]~P1(f862(x82941,x82945))+P1(f862(x82941,f628(x82941,x82942,x82943,x82944)))+~P1(f862(f862(f321(x82944),x82945),x82943))
% 25.54/25.42 [8295]~P1(f862(x82951,x82955))+P1(f862(x82951,f628(x82951,x82952,x82953,x82954)))+~P1(f862(f862(f321(x82954),x82955),x82952))
% 25.54/25.42 [8390]P1(f862(f54(x83901),x83902))+~P1(f862(f54(x83903),x83904))+~P1(f862(f862(f227(f932(x83901,a921)),x83902),f862(f302(x83903,x83901,x83905),x83904)))
% 25.54/25.42 [8399]~P22(x83994,x83991,x83992,f234(f932(x83994,a921)))+~P1(f862(f862(f321(x83994),x83993),x83995))+P1(f862(f862(f321(x83991),f862(x83992,x83993)),f862(f302(x83994,x83991,x83992),x83995)))
% 25.54/25.42 [8556]E(x85561,x85562)+~P22(x85563,x85564,x85565,f862(f862(f103(f932(x85563,a921)),f862(f165(x85563),x85561)),f862(f165(x85563),x85562)))+~E(f862(f862(f147(x85563,x85564),x85565),x85561),f862(f862(f147(x85563,x85564),x85565),x85562))
% 25.54/25.42 [8557]E(x85571,x85572)+~P22(x85573,x85574,x85575,f862(f862(f103(f932(x85573,a921)),f862(f165(x85573),x85571)),f862(f165(x85573),x85572)))+~E(f862(f862(f147(x85573,x85574),x85575),x85571),f862(f862(f147(x85573,x85574),x85575),x85572))
% 25.54/25.42 [8611]~P110(x86111)+~P1(f862(f862(f228(f932(x86111,a921)),f296(x86111,x86114,x86115)),f296(x86111,x86112,x86113)))+P1(f862(f862(f227(x86111),x86112),x86113))
% 25.54/25.42 [8674]~P22(x86741,x86744,x86745,f234(f932(x86741,a921)))+~P1(f862(f862(f321(x86744),f862(x86745,x86742)),f862(f302(x86741,x86744,x86745),x86743)))+P1(f862(f862(f321(x86741),x86742),x86743))
% 25.54/25.42 [8751]P1(f862(x87511,x87512))+~P1(f862(x87511,f591(x87511,x87513,x87514,x87515)))+~P1(f862(f862(f321(x87515),x87512),x87514))
% 25.54/25.42 [8752]P1(f862(x87521,x87522))+~P1(f862(x87521,f591(x87521,x87523,x87524,x87525)))+~P1(f862(f862(f321(x87525),x87522),x87523))
% 25.54/25.42 [9055]~P22(x90552,x90553,x90551,x90554)+E(f862(x90551,f862(f70(x90552,x90553,x90554,x90551),x90555)),x90555)+~P1(f862(f862(f321(x90553),x90555),f862(f302(x90552,x90553,x90551),x90554)))
% 25.54/25.42 [9158]E(x91581,f106(x91582))+E(f862(f862(f144(x91582),x91583),f686(x91584,x91583,x91585,x91581,x91582)),x91581)+~E(f862(f862(f127(x91582),x91581),x91585),f862(f862(f144(x91582),x91583),x91584))
% 25.54/25.42 [9159]E(x91591,f106(x91592))+E(f862(f862(f144(x91592),x91593),f687(x91594,x91591,x91595,x91593,x91592)),x91591)+~E(f862(f862(f127(x91592),x91591),x91594),f862(f862(f144(x91592),x91593),x91595))
% 25.54/25.42 [9177]E(f862(f862(f144(x91772),x91773),f686(x91774,x91773,x91771,x91775,x91772)),x91775)+~E(f862(f862(f127(x91772),x91775),x91771),f862(f862(f144(x91772),x91773),x91774))+E(x91771,f862(f862(f144(x91772),x91773),x91774))
% 25.54/25.42 [9178]E(f862(f862(f144(x91781),x91782),f687(x91784,x91785,x91783,x91782,x91781)),x91785)+~E(f862(f862(f127(x91781),x91785),x91784),f862(f862(f144(x91781),x91782),x91783))+E(f862(f862(f144(x91781),x91782),x91783),x91784)
% 25.54/25.42 [9254]~E(f862(f302(x92543,x92542,x92544),f234(f932(x92543,a921))),f234(f932(x92542,a921)))+~E(f862(f302(x92541,x92543,x92545),f234(f932(x92541,a921))),f234(f932(x92543,a921)))+E(f862(f302(x92541,x92542,f862(f66(x92543,x92542,x92541,x92544),x92545)),f234(f932(x92541,a921))),f234(f932(x92542,a921)))
% 25.54/25.42 [9631]E(x96311,f106(x96312))+~E(f862(f862(f127(x96312),x96311),x96313),f862(f862(f144(x96312),x96315),x96314))+E(f862(f862(f127(x96312),f687(x96313,x96311,x96314,x96315,x96312)),x96313),x96314)
% 25.54/25.42 [9632]E(x96321,f106(x96322))+~E(f862(f862(f127(x96322),x96321),x96325),f862(f862(f144(x96322),x96324),x96323))+E(f862(f862(f127(x96322),f686(x96323,x96324,x96325,x96321,x96322)),x96325),x96323)
% 25.54/25.42 [9639]E(f862(f862(f127(x96392),f686(x96394,x96393,x96391,x96395,x96392)),x96391),x96394)+~E(f862(f862(f127(x96392),x96395),x96391),f862(f862(f144(x96392),x96393),x96394))+E(x96391,f862(f862(f144(x96392),x96393),x96394))
% 25.54/25.42 [9640]~E(f862(f862(f127(x96401),x96405),x96404),f862(f862(f144(x96401),x96402),x96403))+E(f862(f862(f127(x96401),f687(x96404,x96405,x96403,x96402,x96401)),x96404),x96403)+E(f862(f862(f144(x96401),x96402),x96403),x96404)
% 25.54/25.42 [9641]E(f862(f862(f127(x96411),x96415),f689(x96413,x96412,x96414,x96415,x96411)),x96412)+E(f862(f862(f127(x96411),x96412),f688(x96413,x96412,x96414,x96415,x96411)),x96415)+~E(f862(f862(f127(x96411),x96415),x96414),f862(f862(f127(x96411),x96412),x96413))
% 25.54/25.42 [9677]~P109(x96771)+P11(x96771,f862(f862(f147(x96772,x96771),x96773),f142(x96772,x96771,x96773,x96774,x96775)))+~P11(x96771,f862(f862(f147(x96772,x96771),x96773),x96775))
% 25.54/25.42 [9693]~P56(x96935,x96931,x96934,x96933)+P1(f862(f862(x96931,x96932),f551(x96933,x96934,x96931,x96935,x96932)))+~P1(f862(f862(f321(x96935),x96932),x96934))
% 25.54/25.42 [9694]~P56(x96945,x96941,x96944,x96943)+P1(f862(f862(x96941,x96942),f805(x96943,x96944,x96941,x96945,x96942)))+~P1(f862(f862(f321(x96945),x96942),x96944))
% 25.54/25.42 [9796]~P1(f862(f862(f321(f931(x97961,x97961)),f862(f862(f244(x97961,x97961),x97965),x97963)),f299(x97961,x97964)))+P1(f862(f862(f321(f931(x97961,x97961)),f862(f862(f244(x97961,x97961),x97962),x97963)),f862(f862(f280(x97961,x97961,x97961),x97964),f299(x97961,x97964))))+~P1(f862(f862(f321(f931(x97961,x97961)),f862(f862(f244(x97961,x97961),x97962),x97965)),f862(f862(f280(x97961,x97961,x97961),x97964),f299(x97961,x97964))))
% 25.54/25.42 [9797]~P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97972),x97975)),f299(x97971,x97974)))+P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97972),x97973)),f862(f862(f280(x97971,x97971,x97971),x97974),f299(x97971,x97974))))+~P1(f862(f862(f321(f931(x97971,x97971)),f862(f862(f244(x97971,x97971),x97975),x97973)),f862(f862(f280(x97971,x97971,x97971),x97974),f299(x97971,x97974))))
% 25.54/25.42 [9799]P1(f862(f862(f321(f931(f925(x97991),f925(x97991))),f862(f862(f244(f925(x97991),f925(x97991)),x97992),x97993)),f151(x97991,f299(x97991,x97994))))+~P1(f862(f862(f321(f931(f925(x97991),f925(x97991))),f862(f862(f244(f925(x97991),f925(x97991)),x97992),x97995)),f151(x97991,f299(x97991,x97994))))+~P1(f862(f862(f321(f931(f925(x97991),f925(x97991))),f862(f862(f244(f925(x97991),f925(x97991)),x97995),x97993)),f151(x97991,f299(x97991,x97994))))
% 25.54/25.42 [9803]E(f862(f862(f127(x98031),x98032),f688(x98033,x98032,x98034,x98035,x98031)),x98035)+E(f862(f862(f127(x98031),f689(x98033,x98032,x98034,x98035,x98031)),x98033),x98034)+~E(f862(f862(f127(x98031),x98032),x98033),f862(f862(f127(x98031),x98035),x98034))
% 25.54/25.42 [9804]E(f862(f862(f127(x98041),x98042),f689(x98043,x98044,x98045,x98042,x98041)),x98044)+E(f862(f862(f127(x98041),f688(x98043,x98044,x98045,x98042,x98041)),x98045),x98043)+~E(f862(f862(f127(x98041),x98042),x98045),f862(f862(f127(x98041),x98044),x98043))
% 25.54/25.42 [9858]P1(f862(f862(f321(f931(x98581,x98581)),f862(f862(f244(x98581,x98581),x98582),x98583)),f862(f862(f280(x98581,x98581,x98581),x98584),f299(x98581,x98584))))+~P1(f862(f862(f321(f931(x98581,x98581)),f862(f862(f244(x98581,x98581),x98582),x98585)),f862(f862(f280(x98581,x98581,x98581),x98584),f299(x98581,x98584))))+~P1(f862(f862(f321(f931(x98581,x98581)),f862(f862(f244(x98581,x98581),x98585),x98583)),f862(f862(f280(x98581,x98581,x98581),x98584),f299(x98581,x98584))))
% 25.54/25.42 [9885]P32(x98851,x98852,x98853,x98854,x98855)+~E(f862(f182(f925(x98851)),x98854),f862(f182(f925(x98852)),x98855))+~P1(f862(f862(f249(x98851,x98852,a921),x98853),f705(x98855,x98854,x98853,x98852,x98851)))
% 25.54/25.42 [9886]P32(x98861,x98862,x98863,x98864,x98865)+~E(f862(f182(f925(x98861)),x98864),f862(f182(f925(x98862)),x98865))+~P1(f862(f862(f249(x98861,x98862,a921),x98863),f706(x98863,x98865,x98864,x98862,x98861)))
% 25.54/25.42 [9891]E(f862(f862(f127(x98911),f688(x98912,x98913,x98914,x98915,x98911)),x98914),x98912)+~E(f862(f862(f127(x98911),x98913),x98912),f862(f862(f127(x98911),x98915),x98914))+E(f862(f862(f127(x98911),f689(x98912,x98913,x98914,x98915,x98911)),x98912),x98914)
% 25.54/25.42 [9907]~P109(x99072)+E(f862(f862(f141(x99071,x99072,x99073),x99074),x99075),f862(f862(f144(x99071),x99074),x99075))+P1(f862(f862(f321(x99071),f750(x99074,x99073,x99075,x99071,x99072)),f862(f165(x99071),x99075)))
% 25.54/25.42 [9911]~P56(x99111,x99114,x99113,x99112)+~P1(f862(f862(f321(x99111),x99115),x99113))+P1(f862(f862(f321(x99111),f551(x99112,x99113,x99114,x99111,x99115)),x99112))
% 25.54/25.42 [9912]~P56(x99121,x99124,x99123,x99122)+~P1(f862(f862(f321(x99121),x99125),x99123))+P1(f862(f862(f321(x99121),f805(x99122,x99123,x99124,x99121,x99125)),x99122))
% 25.54/25.42 [10028]~P1(f862(f862(f321(f931(f932(x100281,a921),f932(x100281,a921))),f862(f862(f244(f932(x100281,a921),f932(x100281,a921)),x100284),x100283)),f310(x100281,x100282)))+~P1(f862(f862(f321(x100281),x100285),x100284))+P1(f862(f862(f321(x100281),f616(x100282,x100283,x100284,x100281,x100285)),x100283))
% 25.54/25.42 [10038]~P109(x100382)+E(f862(f862(f141(x100381,x100382,x100383),x100384),x100385),f862(f862(f144(x100381),x100384),x100385))+~P1(f862(f862(f227(x100382),f862(x100383,x100384)),f862(x100383,f750(x100384,x100383,x100385,x100381,x100382))))
% 25.54/25.42 [10087]~P22(x100873,x100874,x100875,f234(f932(x100873,a921)))+P1(f862(x100871,x100872))+~P1(f862(x100871,f862(f86(x100873,x100874,f234(f932(x100873,a921)),x100875),f818(x100872,x100871,x100875,x100874,x100873))))
% 25.54/25.42 [10225]P32(x102251,x102252,x102253,x102254,x102255)+~E(f862(f182(f925(x102251)),x102254),f862(f182(f925(x102252)),x102255))+~P1(f862(f862(x102253,f862(f862(f157(x102251),x102254),f707(x102255,x102254,x102253,x102252,x102251))),f862(f862(f157(x102252),x102255),f707(x102255,x102254,x102253,x102252,x102251))))
% 25.54/25.42 [10226]P32(x102261,x102262,x102263,x102264,x102265)+~E(f862(f182(f925(x102261)),x102264),f862(f182(f925(x102262)),x102265))+~P1(f862(f862(x102263,f862(f862(f157(x102261),x102264),f742(x102263,x102265,x102262,x102264,x102261))),f862(f862(f157(x102262),x102265),f742(x102263,x102265,x102262,x102264,x102261))))
% 25.54/25.42 [6772]~P15(x67722,x67725,x67721)+~P1(f862(f54(x67722),x67724))+E(f862(x67721,f862(f862(f301(x67722),x67723),x67724)),f862(f862(f57(x67722,x67722,x67725),x67723),x67724))
% 25.54/25.42 [6773]~E(x67733,x67734)+~E(x67732,x67735)+E(f862(f862(f301(x67731),x67732),f862(f862(f301(x67731),x67733),f181(f932(x67731,a921)))),f862(f862(f301(x67731),x67734),f862(f862(f301(x67731),x67735),f181(f932(x67731,a921)))))
% 25.54/25.42 [6783]P1(f862(x67832,x67835))+E(f170(x67831,x67832,f862(f862(f127(x67831),x67833),x67834)),f170(x67831,x67832,x67833))+~P1(f862(f862(f321(x67831),x67835),f862(f165(x67831),x67833)))
% 25.54/25.42 [6817]E(f862(x68171,x68172),f181(f932(x68173,a921)))+~E(f862(f862(f33(x68174,f932(x68173,a921)),x68175),x68171),f181(f932(x68173,a921)))+~P1(f862(f862(f321(x68174),x68172),x68175))
% 25.54/25.42 [6818]E(f862(x68181,x68182),f234(f932(x68183,a921)))+~E(f862(f862(f32(x68184,f932(x68183,a921)),x68185),x68181),f234(f932(x68183,a921)))+~P1(f862(f862(f321(x68184),x68182),x68185))
% 25.54/25.42 [6819]E(f862(x68191,x68192),f181(f932(x68193,a921)))+~E(f862(f862(f33(x68194,f932(x68193,a921)),x68195),x68191),f181(f932(x68193,a921)))+~P1(f862(f862(f321(x68194),x68192),x68195))
% 25.54/25.42 [6820]E(f862(x68201,x68202),f234(f932(x68203,a921)))+~E(f862(f862(f32(x68204,f932(x68203,a921)),x68205),x68201),f234(f932(x68203,a921)))+~P1(f862(f862(f321(x68204),x68202),x68205))
% 25.54/25.42 [7015]~E(x70154,f862(f862(f127(x70151),x70155),f862(f862(f144(x70151),x70152),x70153)))+P1(f862(f862(f321(x70151),x70152),f862(f165(x70151),x70153)))+P1(f862(f862(f321(x70151),x70152),f862(f165(x70151),x70154)))
% 25.54/25.42 [7016]~E(x70164,f862(f862(f127(x70161),x70163),f862(f862(f144(x70161),x70162),x70165)))+P1(f862(f862(f321(x70161),x70162),f862(f165(x70161),x70163)))+P1(f862(f862(f321(x70161),x70162),f862(f165(x70161),x70164)))
% 25.54/25.42 [7326]~E(x73262,x73264)+~P144(x73261)+E(f862(f862(f73(x73261),f862(f862(f74(x73261),x73262),x73263)),f862(f862(f74(x73261),x73264),x73265)),f862(f862(f73(x73261),f862(f862(f74(x73261),x73262),x73265)),f862(f862(f74(x73261),x73264),x73263)))
% 25.54/25.42 [7327]~E(x73272,x73274)+~P144(x73271)+E(f862(f862(f73(x73271),f862(f862(f74(x73271),x73272),x73273)),f862(f862(f74(x73271),x73274),x73275)),f862(f862(f73(x73271),f862(f862(f74(x73271),x73272),x73275)),f862(f862(f74(x73271),x73274),x73273)))
% 25.54/25.42 [7389]~P3(x73891)+~P1(f862(f862(f321(x73894),x73893),x73895))+P1(f862(f862(f227(x73891),f862(x73892,x73893)),f862(f862(f33(x73894,x73891),x73895),x73892)))
% 25.54/25.42 [7441]~P108(x74411)+P1(f862(f862(f227(x74411),f862(x74412,x74413)),f862(x74414,x74413)))+~P1(f862(f862(f227(f932(x74415,x74411)),x74412),x74414))
% 25.54/25.42 [7442]~P108(x74421)+P1(f862(f862(f227(x74421),f862(x74422,x74423)),f862(x74424,x74423)))+~P1(f862(f862(f227(f932(x74425,x74421)),x74422),x74424))
% 25.54/25.42 [7443]~P108(x74431)+P1(f862(f862(f227(x74431),f862(x74432,x74433)),f862(x74434,x74433)))+~P1(f862(f862(f227(f932(x74435,x74431)),x74432),x74434))
% 25.54/25.42 [7567]E(x75671,x75672)+E(x75673,x75671)+~E(f862(f862(f301(x75674),x75671),f862(f862(f301(x75674),x75675),f181(f932(x75674,a921)))),f862(f862(f301(x75674),x75672),f862(f862(f301(x75674),x75673),f181(f932(x75674,a921)))))
% 25.54/25.42 [7568]E(x75681,x75682)+E(x75683,x75681)+~E(f862(f862(f301(x75684),x75683),f862(f862(f301(x75684),x75682),f181(f932(x75684,a921)))),f862(f862(f301(x75684),x75685),f862(f862(f301(x75684),x75681),f181(f932(x75684,a921)))))
% 25.54/25.42 [7569]E(x75691,x75692)+E(x75691,x75693)+~E(f862(f862(f301(x75694),x75693),f862(f862(f301(x75694),x75692),f181(f932(x75694,a921)))),f862(f862(f301(x75694),x75695),f862(f862(f301(x75694),x75691),f181(f932(x75694,a921)))))
% 25.54/25.42 [7570]E(x75701,x75702)+E(x75701,x75703)+~E(f862(f862(f301(x75704),x75701),f862(f862(f301(x75704),x75705),f181(f932(x75704,a921)))),f862(f862(f301(x75704),x75702),f862(f862(f301(x75704),x75703),f181(f932(x75704,a921)))))
% 25.54/25.42 [8101]P22(x81011,x81012,x81013,x81014)+~P22(x81011,x81012,x81013,x81015)+~P1(f862(f862(f227(f932(x81011,a921)),x81014),x81015))
% 25.54/25.42 [8131]~E(f862(x81313,x81315),x81314)+~P22(x81311,x81312,x81313,f234(f932(x81311,a921)))+E(f862(f86(x81311,x81312,f234(f932(x81311,a921)),x81313),x81314),x81315)
% 25.54/25.42 [8280]E(x82801,x82802)+~E(f862(f302(x82803,x82804,x82805),x82801),f862(f302(x82803,x82804,x82805),x82802))+~P22(x82803,x82804,x82805,f862(f862(f103(f932(x82803,a921)),x82801),x82802))
% 25.54/25.42 [8359]P1(f862(x83592,x83594))+E(f862(f862(f131(x83591),f862(f182(f925(x83591)),f170(x83591,x83592,x83593))),x83593),f862(f862(f144(x83591),x83594),x83595))+~E(f862(f862(f127(x83591),f170(x83591,x83592,x83593)),f862(f862(f144(x83591),x83594),x83595)),x83593)
% 25.54/25.42 [8388]~P22(x83881,x83882,x83883,x83885)+~P22(x83881,x83882,x83883,x83884)+P22(x83881,x83882,x83883,f862(f862(f94(f932(x83881,a921)),x83884),x83885))
% 25.54/25.42 [8495]~P72(x84951)+E(f862(f862(f73(x84951),f862(x84952,x84953)),f862(f158(x84951),f862(f862(f147(x84954,x84951),x84952),f163(x84954,x84953,x84955)))),f862(f158(x84951),f862(f862(f147(x84954,x84951),x84952),x84955)))+~P1(f862(f862(f321(x84954),x84953),f862(f165(x84954),x84955)))
% 25.54/25.42 [8583]~P109(x85831)+~P11(x85831,f862(f862(f147(x85832,x85831),x85833),x85835))+P11(x85831,f862(f862(f147(x85832,x85831),x85833),f862(f862(f141(x85832,x85831,x85833),x85834),x85835)))
% 25.54/25.42 [8670]~P3(x86701)+P1(f862(f862(f227(x86701),f862(f862(f32(x86702,x86701),x86703),x86704)),f862(f862(f32(x86702,x86701),x86705),x86704)))+~P1(f862(f862(f227(f932(x86702,a921)),x86705),x86703))
% 25.54/25.42 [8671]~P3(x86711)+P1(f862(f862(f227(x86711),f862(f862(f33(x86712,x86711),x86713),x86714)),f862(f862(f33(x86712,x86711),x86715),x86714)))+~P1(f862(f862(f227(f932(x86712,a921)),x86713),x86715))
% 25.54/25.42 [8705]~P109(x87053)+P1(f862(f130(x87051),x87052))+~P1(f862(f130(x87051),f862(f862(f141(x87051,x87053,x87054),x87055),x87052)))
% 25.54/25.42 [8851]~P109(x88511)+~P1(f862(f862(f321(x88512),x88513),f862(f165(x88512),x88514)))+~P1(f862(f130(x88512),f862(f862(f141(x88512,x88511,x88515),x88513),x88514)))
% 25.54/25.42 [8942]~P109(x89421)+P11(x89421,f862(f862(f147(x89422,x89421),x89423),x89424))+~P11(x89421,f862(f862(f147(x89422,x89421),x89423),f862(f862(f141(x89422,x89421,x89423),x89425),x89424)))
% 25.54/25.42 [8988]~P22(x89882,x89881,x89884,x89883)+E(f862(f302(x89881,x89882,f86(x89882,x89881,x89883,x89884)),f862(f302(x89882,x89881,x89884),x89885)),x89885)+~P1(f862(f862(f227(f932(x89882,a921)),x89885),x89883))
% 25.54/25.42 [9043]~P109(x90432)+E(f862(f862(f141(x90431,x90432,x90433),x90434),x90435),f142(x90431,x90432,x90433,x90434,x90435))+P1(f862(f862(f321(x90432),f862(x90433,x90434)),f862(f302(x90431,x90432,x90433),f862(f165(x90431),x90435))))
% 25.54/25.42 [9124]~P109(x91242)+E(f142(x91241,x91242,x91243,x91244,x91245),x91245)+~P1(f862(f862(f321(x91242),f862(x91243,x91244)),f862(f302(x91241,x91242,x91243),f862(f165(x91241),x91245))))
% 25.54/25.42 [9138]~P22(x91382,x91381,x91383,x91385)+P1(f862(f862(f228(f932(x91381,a921)),f862(f302(x91382,x91381,x91383),x91384)),f862(f302(x91382,x91381,x91383),x91385)))+~P1(f862(f862(f228(f932(x91382,a921)),x91384),x91385))
% 25.54/25.42 [9169]~P22(x91692,x91691,x91693,f234(f932(x91692,a921)))+P1(f862(f862(f227(f932(x91691,a921)),f862(f302(x91692,x91691,x91693),x91694)),f862(f302(x91692,x91691,x91693),x91695)))+~P1(f862(f862(f227(f932(x91692,a921)),x91694),x91695))
% 25.54/25.42 [9296]~P22(x92961,x92962,x92963,f234(f932(x92961,a921)))+~P1(f862(f862(f227(f932(x92962,a921)),x92964),f862(f302(x92961,x92962,x92963),x92965)))+P1(f862(f862(f227(f932(x92961,a921)),f862(f303(x92961,x92962,x92963),x92964)),x92965))
% 25.54/25.42 [9319]~E(f862(f302(x93193,x93191,x93194),f234(f932(x93193,a921))),f234(f932(x93191,a921)))+P1(f862(f862(f227(f932(x93191,a921)),x93192),f862(f302(x93193,x93191,x93194),x93195)))+~P1(f862(f862(f227(f932(x93193,a921)),f862(f303(x93193,x93191,x93194),x93192)),x93195))
% 25.54/25.42 [9427]~P22(x94271,x94274,x94275,f234(f932(x94271,a921)))+~P1(f862(f862(f227(f932(x94274,a921)),f862(f302(x94271,x94274,x94275),x94272)),f862(f302(x94271,x94274,x94275),x94273)))+P1(f862(f862(f227(f932(x94271,a921)),x94272),x94273))
% 25.54/25.42 [9551]~P81(x95511)+~E(f862(x95513,f726(x95513,x95514,x95515,x95512,x95511)),f2(x95511))+E(f862(f158(x95511),f862(f862(f147(x95512,x95511),x95513),f862(f129(x95512,x95514),x95515))),f862(f158(x95511),f862(f862(f147(x95512,x95511),x95513),x95515)))
% 25.54/25.42 [9580]~P23(x95801,x95802,x95803,f234(f932(x95801,a921)),f234(f932(x95802,a921)))+~P1(f862(f862(f227(f932(x95802,a921)),x95804),f862(f302(x95801,x95802,x95803),x95805)))+P1(f862(f862(f227(f932(x95801,a921)),f862(f303(x95801,x95802,x95803),x95804)),x95805))
% 25.54/25.42 [9609]~P23(x96093,x96091,x96094,f234(f932(x96093,a921)),f234(f932(x96091,a921)))+P1(f862(f862(f227(f932(x96091,a921)),x96092),f862(f302(x96093,x96091,x96094),x96095)))+~P1(f862(f862(f227(f932(x96093,a921)),f862(f303(x96093,x96091,x96094),x96092)),x96095))
% 25.54/25.42 [9737]~P14(x97371,x97372,x97373)+~P1(f862(f54(x97371),x97375))+P1(f862(f59(x97371,x97372,x97373,x97374,x97375),f862(f862(f57(x97371,x97372,x97373),x97374),x97375)))
% 25.54/25.42 [9816]~P23(x98162,x98161,x98164,f234(f932(x98162,a921)),f234(f932(x98161,a921)))+~P23(x98161,x98163,x98165,f234(f932(x98161,a921)),f234(f932(x98163,a921)))+E(f862(f66(x98161,x98162,x98163,f86(x98162,x98161,f234(f932(x98162,a921)),x98164)),f86(x98161,x98163,f234(f932(x98161,a921)),x98165)),f86(x98162,x98163,f234(f932(x98162,a921)),f862(f66(x98161,x98163,x98162,x98165),x98164)))
% 25.54/25.42 [9817]P1(f862(x98171,f694(x98172,x98171,x98173,x98174,x98175)))+~P1(f862(f862(f227(f932(x98175,a921)),x98174),x98173))+P1(f862(f862(f227(f932(x98175,a921)),f862(f862(f94(f932(x98175,a921)),x98174),f862(f254(x98175),x98171))),f862(f862(f94(f932(x98175,a921)),x98173),f862(f254(x98175),x98172))))
% 25.54/25.42 [9831]~P81(x98311)+~P1(f862(x98314,f726(x98313,x98314,x98315,x98312,x98311)))+E(f862(f158(x98311),f862(f862(f147(x98312,x98311),x98313),f862(f129(x98312,x98314),x98315))),f862(f158(x98311),f862(f862(f147(x98312,x98311),x98313),x98315)))
% 25.54/25.42 [9909]~P3(x99095)+P1(f862(f862(f321(x99091),f478(x99092,x99093,x99091,x99094,x99095)),x99093))+P1(f862(f862(f227(x99095),x99094),f862(f862(f32(x99091,x99095),x99093),x99092)))
% 25.54/25.42 [9913]~P81(x99131)+E(f862(f158(x99131),f862(f862(f147(x99132,x99131),x99133),f862(f129(x99132,x99134),x99135))),f862(f158(x99131),f862(f862(f147(x99132,x99131),x99133),x99135)))+P1(f862(f862(f321(x99132),f726(x99133,x99134,x99135,x99132,x99131)),f862(f165(x99132),x99135)))
% 25.54/25.42 [9923]~P1(f862(x99235,f694(x99235,x99233,x99234,x99232,x99231)))+~P1(f862(f862(f227(f932(x99231,a921)),x99232),x99234))+P1(f862(f862(f227(f932(x99231,a921)),f862(f862(f94(f932(x99231,a921)),x99232),f862(f254(x99231),x99233))),f862(f862(f94(f932(x99231,a921)),x99234),f862(f254(x99231),x99235))))
% 25.54/25.42 [9939]~P22(x99395,x99393,x99394,f234(f932(x99395,a921)))+P1(f862(x99391,x99392))+P1(f862(f862(f321(x99393),f818(x99392,x99391,x99394,x99393,x99395)),f862(f302(x99395,x99393,x99394),f234(f932(x99395,a921)))))
% 25.54/25.42 [9962]P32(x99621,x99622,x99623,x99624,x99625)+~E(f862(f182(f925(x99622)),x99625),f862(f182(f925(x99621)),x99624))+P1(f862(f862(f228(a924),f707(x99625,x99624,x99623,x99622,x99621)),f862(f182(f925(x99621)),x99624)))
% 25.54/25.42 [9963]P32(x99631,x99632,x99633,x99634,x99635)+~E(f862(f182(f925(x99632)),x99635),f862(f182(f925(x99631)),x99634))+P1(f862(f862(f228(a924),f742(x99633,x99635,x99632,x99634,x99631)),f862(f182(f925(x99631)),x99634)))
% 25.54/25.42 [9995]P1(f862(f862(f321(x99951),f694(x99952,x99953,x99954,x99955,x99951)),x99955))+~P1(f862(f862(f227(f932(x99951,a921)),x99955),x99954))+P1(f862(f862(f227(f932(x99951,a921)),f862(f862(f94(f932(x99951,a921)),x99955),f862(f254(x99951),x99953))),f862(f862(f94(f932(x99951,a921)),x99954),f862(f254(x99951),x99952))))
% 25.54/25.42 [10039]~P3(x100391)+~P1(f862(f862(f227(x100391),x100392),f862(x100395,f478(x100395,x100394,x100393,x100392,x100391))))+P1(f862(f862(f227(x100391),x100392),f862(f862(f32(x100393,x100391),x100394),x100395)))
% 25.54/25.42 [10076]~P71(x100761)+~P1(f862(f54(x100762),x100765))+E(f862(f862(f862(f58(x100761,x100762,f74(x100761)),f862(f862(f20(x100762,x100761,x100761),f862(f862(f10(x100761,f932(x100761,x100761),x100762),f74(x100761)),x100763)),x100764)),f71(x100761)),x100765),f862(f862(f74(x100761),f862(f862(f862(f58(x100761,x100762,f74(x100761)),x100763),f71(x100761)),x100765)),f862(f862(f862(f58(x100761,x100762,f74(x100761)),x100764),f71(x100761)),x100765)))
% 25.54/25.42 [10134]~P1(f862(f862(f321(f931(f932(x101341,a921),f932(x101341,a921))),f862(f862(f244(f932(x101341,a921),f932(x101341,a921)),x101345),x101344)),f310(x101341,x101343)))+~P1(f862(f862(f321(x101341),x101342),x101345))+P1(f862(f862(f321(f931(x101341,x101341)),f862(f862(f244(x101341,x101341),x101342),f616(x101343,x101344,x101345,x101341,x101342))),x101343))
% 25.54/25.42 [10259]~P1(f862(f862(f321(f931(f925(x102591),f925(x102591))),f862(f862(f244(f925(x102591),f925(x102591)),f862(f862(f127(x102591),x102595),x102592)),f862(f862(f127(x102591),x102595),x102593))),f140(x102591,x102594)))+P1(f862(f862(f321(f931(f925(x102591),f925(x102591))),f862(f862(f244(f925(x102591),f925(x102591)),x102592),x102593)),f140(x102591,x102594)))+P1(f862(f862(f321(f931(x102591,x102591)),f862(f862(f244(x102591,x102591),f695(x102594,x102593,x102592,x102595,x102591)),f695(x102594,x102593,x102592,x102595,x102591))),x102594))
% 25.54/25.42 [7446]~E(x74463,x74465)+E(f862(f862(f157(x74461),f862(f862(f152(x74461,x74462),x74463),x74464)),x74465),x74464)+~P1(f862(f862(f228(a924),x74463),f862(f182(f925(x74461)),x74462)))
% 25.54/25.42 [7564]~E(f862(f862(f127(x75641),x75642),x75644),f862(f862(f127(x75641),x75643),x75645))+E(f862(f862(f168(x75641),f862(f182(f925(x75641)),x75642)),x75643),x75642)+P1(f862(f862(f227(a924),f862(f182(f925(x75641)),x75643)),f862(f182(f925(x75641)),x75642)))
% 25.54/25.42 [7565]E(x75651,x75652)+E(f862(f862(f157(x75653),f862(f862(f152(x75653,x75654),x75651),x75655)),x75652),f862(f862(f157(x75653),x75654),x75652))+~P1(f862(f862(f228(a924),x75651),f862(f182(f925(x75653)),x75654)))
% 25.54/25.42 [8061]~E(f862(f862(f127(x80611),x80612),x80614),f862(f862(f127(x80611),x80613),x80615))+E(f862(f862(f168(x80611),f862(f182(f925(x80611)),x80612)),x80613),x80612)+~P1(f862(f862(f227(a924),f862(f182(f925(x80611)),x80612)),f862(f182(f925(x80611)),x80613)))
% 25.54/25.42 [8085]~P1(f862(f54(x80851),f862(x80854,x80855)))+~P1(f862(f862(f321(x80852),x80855),x80853))+P1(f862(f54(x80851),f862(f862(f32(x80852,f932(x80851,a921)),x80853),x80854)))
% 25.54/25.42 [8264]~P50(x82641,x82643,x82645)+~P50(x82641,x82642,x82644)+P50(x82641,f862(f862(f103(f932(x82641,a921)),x82642),x82643),f862(f862(f103(f932(f931(x82641,x82641),a921)),x82644),x82645))
% 25.54/25.42 [8265]~P50(x82651,x82653,x82655)+~P50(x82651,x82652,x82654)+P50(x82651,f862(f862(f94(f932(x82651,a921)),x82652),x82653),f862(f862(f94(f932(f931(x82651,x82651),a921)),x82654),x82655))
% 25.54/25.42 [8624]E(f862(f862(f244(x86241,x86242),f862(f862(f157(x86241),x86243),x86244)),f862(f862(f157(x86242),x86245),x86244)),f862(f862(f157(f931(x86241,x86242)),f862(f862(f174(x86241,x86242),x86243),x86245)),x86244))+~P1(f862(f862(f228(a924),x86244),f862(f182(f925(x86241)),x86243)))+~P1(f862(f862(f228(a924),x86244),f862(f182(f925(x86242)),x86245)))
% 25.54/25.42 [8780]~P50(x87801,x87803,x87804)+P1(f862(f862(f321(x87801),x87802),x87803))+~P1(f862(f862(f321(f931(x87801,x87801)),f862(f862(f244(x87801,x87801),x87805),x87802)),x87804))
% 25.54/25.42 [8781]~P50(x87811,x87813,x87814)+P1(f862(f862(f321(x87811),x87812),x87813))+~P1(f862(f862(f321(f931(x87811,x87811)),f862(f862(f244(x87811,x87811),x87812),x87815)),x87814))
% 25.54/25.42 [8782]~P6(x87821,x87823,x87824)+P1(f862(f862(f321(x87821),x87822),x87823))+~P1(f862(f862(f321(f931(x87821,x87821)),f862(f862(f244(x87821,x87821),x87825),x87822)),x87824))
% 25.54/25.42 [8783]~P6(x87831,x87833,x87834)+P1(f862(f862(f321(x87831),x87832),x87833))+~P1(f862(f862(f321(f931(x87831,x87831)),f862(f862(f244(x87831,x87831),x87832),x87835)),x87834))
% 25.54/25.42 [9066]~P6(x90661,x90665,x90662)+E(f862(f276(x90661,x90661,x90662),f862(f862(f301(x90661),x90663),f181(f932(x90661,a921)))),f862(f276(x90661,x90661,x90662),f862(f862(f301(x90661),x90664),f181(f932(x90661,a921)))))+~P1(f862(f862(f321(f931(x90661,x90661)),f862(f862(f244(x90661,x90661),x90663),x90664)),x90662))
% 25.54/25.42 [9067]~P6(x90671,x90675,x90672)+E(f862(f276(x90671,x90671,x90672),f862(f862(f301(x90671),x90673),f181(f932(x90671,a921)))),f862(f276(x90671,x90671,x90672),f862(f862(f301(x90671),x90674),f181(f932(x90671,a921)))))+~P1(f862(f862(f321(f931(x90671,x90671)),f862(f862(f244(x90671,x90671),x90673),x90674)),x90672))
% 25.54/25.42 [9251]P1(f862(x92511,x92512))+~P1(f862(f862(f321(x92513),x92512),x92515))+P1(f862(f862(f321(x92513),f591(x92511,x92514,x92515,x92513)),f862(f862(f103(f932(x92513,a921)),x92515),x92514)))
% 25.54/25.42 [9252]P1(f862(x92521,x92522))+~P1(f862(f862(f321(x92523),x92522),x92524))+P1(f862(f862(f321(x92523),f591(x92521,x92524,x92525,x92523)),f862(f862(f103(f932(x92523,a921)),x92525),x92524)))
% 25.54/25.42 [9260]~P1(f862(x92602,x92605))+~P1(f862(f862(f321(x92601),x92605),x92604))+P1(f862(f862(f321(x92601),f628(x92602,x92603,x92604,x92601)),f862(f862(f103(f932(x92601,a921)),x92604),x92603)))
% 25.54/25.42 [9261]~P1(f862(x92612,x92615))+~P1(f862(f862(f321(x92611),x92615),x92613))+P1(f862(f862(f321(x92611),f628(x92612,x92613,x92614,x92611)),f862(f862(f103(f932(x92611,a921)),x92614),x92613)))
% 25.54/25.42 [9276]~P1(f862(f862(f227(f932(x92761,a921)),x92763),x92765))+~P1(f862(f862(f227(f932(x92761,a921)),x92762),x92764))+P1(f862(f862(f227(f932(x92761,a921)),f862(f862(f103(f932(x92761,a921)),x92762),x92763)),f862(f862(f103(f932(x92761,a921)),x92764),x92765)))
% 25.54/25.42 [9277]~P1(f862(f862(f227(f932(x92771,a921)),x92773),x92775))+~P1(f862(f862(f227(f932(x92771,a921)),x92772),x92774))+P1(f862(f862(f227(f932(x92771,a921)),f862(f862(f94(f932(x92771,a921)),x92772),x92773)),f862(f862(f94(f932(x92771,a921)),x92774),x92775)))
% 25.54/25.42 [9278]~P1(f862(f862(f227(f932(x92781,a921)),x92785),x92783))+~P1(f862(f862(f227(f932(x92781,a921)),x92782),x92784))+P1(f862(f862(f227(f932(x92781,a921)),f862(f862(f3(f932(x92781,a921)),x92782),x92783)),f862(f862(f3(f932(x92781,a921)),x92784),x92785)))
% 25.54/25.42 [9374]P1(f862(f862(f321(f931(x93741,x93741)),f862(f862(f244(x93741,x93741),x93742),x93743)),f313(x93741,x93744,x93745)))+~P1(f862(f862(f227(a924),f862(x93744,x93742)),f862(x93744,x93743)))+~P1(f862(f862(f321(f931(x93741,x93741)),f862(f862(f244(x93741,x93741),x93742),x93743)),x93745))
% 25.54/25.42 [9561]P1(f862(f862(f321(f931(x95611,x95611)),f862(f862(f244(x95611,x95611),x95612),x95613)),f299(x95611,x95614)))+~P1(f862(f862(f321(f931(x95611,x95611)),f862(f862(f244(x95611,x95611),x95612),x95615)),f299(x95611,x95614)))+~P1(f862(f862(f321(f931(x95611,x95611)),f862(f862(f244(x95611,x95611),x95615),x95613)),x95614))
% 25.54/25.42 [9562]P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95622),x95623)),f299(x95621,x95624)))+~P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95625),x95623)),f299(x95621,x95624)))+~P1(f862(f862(f321(f931(x95621,x95621)),f862(f862(f244(x95621,x95621),x95622),x95625)),x95624))
% 25.54/25.42 [9664]E(x96641,x96642)+E(f862(a105,f633(x96643,x96644,x96641,x96642,x96645)),x96644)+~P1(f862(f862(f321(f931(x96645,x96645)),f862(f862(f244(x96645,x96645),x96642),x96641)),f862(f862(f176(f931(x96645,x96645),a921),x96644),x96643)))
% 25.54/25.42 [9665]E(x96651,x96652)+E(f862(a105,f636(x96653,x96654,x96651,x96652,x96655)),x96654)+~P1(f862(f862(f321(f931(x96655,x96655)),f862(f862(f244(x96655,x96655),x96652),x96651)),f862(f862(f176(f931(x96655,x96655),a921),x96654),x96653)))
% 25.54/25.42 [9666]E(x96661,f2(a924))+E(f862(a105,f633(x96662,x96661,x96663,x96664,x96665)),x96661)+~P1(f862(f862(f321(f931(x96665,x96665)),f862(f862(f244(x96665,x96665),x96664),x96663)),f862(f862(f176(f931(x96665,x96665),a921),x96661),x96662)))
% 25.54/25.42 [9667]E(x96671,f2(a924))+E(f862(a105,f636(x96672,x96671,x96673,x96674,x96675)),x96671)+~P1(f862(f862(f321(f931(x96675,x96675)),f862(f862(f244(x96675,x96675),x96674),x96673)),f862(f862(f176(f931(x96675,x96675),a921),x96671),x96672)))
% 25.54/25.42 [9690]P1(f862(f862(f321(f931(x96901,x96901)),f862(f862(f244(x96901,x96901),x96902),x96903)),f862(f862(f280(x96901,x96901,x96901),x96904),f299(x96901,x96904))))+~P1(f862(f862(f321(f931(x96901,x96901)),f862(f862(f244(x96901,x96901),x96902),x96905)),x96904))+~P1(f862(f862(f321(f931(x96901,x96901)),f862(f862(f244(x96901,x96901),x96905),x96903)),x96904))
% 25.54/25.42 [9697]~P1(f862(f862(f321(f931(x96971,x96971)),f862(f862(f244(x96971,x96971),x96972),x96975)),f299(x96971,x96974)))+P1(f862(f862(f321(f931(x96971,x96971)),f862(f862(f244(x96971,x96971),x96972),x96973)),f862(f862(f280(x96971,x96971,x96971),x96974),f299(x96971,x96974))))+~P1(f862(f862(f321(f931(x96971,x96971)),f862(f862(f244(x96971,x96971),x96975),x96973)),x96974))
% 25.54/25.42 [9698]~P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96985),x96983)),f299(x96981,x96984)))+P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96982),x96983)),f862(f862(f280(x96981,x96981,x96981),x96984),f299(x96981,x96984))))+~P1(f862(f862(f321(f931(x96981,x96981)),f862(f862(f244(x96981,x96981),x96982),x96985)),x96984))
% 25.54/25.42 [9731]~P6(x97311,x97315,x97312)+~P1(f862(f862(f321(f931(x97311,x97311)),f862(f862(f244(x97311,x97311),x97313),x97314)),x97312))+P1(f862(f862(f227(f932(x97311,a921)),f862(f276(x97311,x97311,x97312),f862(f862(f301(x97311),x97313),f181(f932(x97311,a921))))),f862(f276(x97311,x97311,x97312),f862(f862(f301(x97311),x97314),f181(f932(x97311,a921))))))
% 25.54/25.42 [9789]P1(f862(f862(f321(f931(x97891,x97891)),f862(f862(f244(x97891,x97891),x97892),x97893)),f862(f862(f280(x97891,x97891,x97891),x97894),f299(x97891,x97894))))+~P1(f862(f862(f321(f931(x97891,x97891)),f862(f862(f244(x97891,x97891),x97892),x97895)),f862(f862(f280(x97891,x97891,x97891),x97894),f299(x97891,x97894))))+~P1(f862(f862(f321(f931(x97891,x97891)),f862(f862(f244(x97891,x97891),x97895),x97893)),x97894))
% 25.54/25.42 [9790]P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97902),x97903)),f862(f862(f280(x97901,x97901,x97901),x97904),f299(x97901,x97904))))+~P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97905),x97903)),f862(f862(f280(x97901,x97901,x97901),x97904),f299(x97901,x97904))))+~P1(f862(f862(f321(f931(x97901,x97901)),f862(f862(f244(x97901,x97901),x97902),x97905)),x97904))
% 25.54/25.42 [9840]~P1(f862(f59(x98401,x98401,x98404,x98402,x98403),x98405))+P1(f862(f862(f321(x98401),x98402),x98403))+P1(f862(f55(x98401,x98404,f862(f862(f301(x98401),x98402),x98403)),x98405))
% 25.54/25.42 [9878]~E(f862(f302(x98783,x98782,x98785),x98784),x98781)+E(x98781,f181(f932(x98782,a921)))+P1(f862(f862(f227(f932(x98783,a921)),f862(f302(x98782,x98783,f535(x98784,x98783,x98782,x98781)),x98781)),x98784))
% 25.54/25.42 [9926]~P3(x99265)+P1(f862(f862(f321(x99261),f481(x99262,x99263,x99264,x99261,x99265)),x99264))+P1(f862(f862(f227(x99265),f862(f862(f33(x99261,x99265),x99264),x99263)),x99262))
% 25.54/25.42 [9982]P32(x99821,x99822,x99823,x99824,x99825)+~E(f862(f182(f925(x99821)),x99824),f862(f182(f925(x99822)),x99825))+P1(f862(f862(f321(f931(x99821,x99822)),f705(x99825,x99824,x99823,x99822,x99821)),f862(f165(f931(x99821,x99822)),f862(f862(f174(x99821,x99822),x99824),x99825))))
% 25.54/25.42 [9983]P32(x99831,x99832,x99833,x99834,x99835)+~E(f862(f182(f925(x99831)),x99834),f862(f182(f925(x99832)),x99835))+P1(f862(f862(f321(f931(x99831,x99832)),f706(x99833,x99835,x99834,x99832,x99831)),f862(f165(f931(x99831,x99832)),f862(f862(f174(x99831,x99832),x99834),x99835))))
% 25.54/25.42 [10113]E(x101131,x101132)+P1(f862(f862(f321(f931(x101133,x101133)),f862(f862(f244(x101133,x101133),x101131),f634(x101134,x101135,x101132,x101131,x101133))),x101134))+~P1(f862(f862(f321(f931(x101133,x101133)),f862(f862(f244(x101133,x101133),x101131),x101132)),f862(f862(f176(f931(x101133,x101133),a921),x101135),x101134)))
% 25.54/25.42 [10114]E(x101141,f2(a924))+P1(f862(f862(f321(f931(x101142,x101142)),f862(f862(f244(x101142,x101142),x101143),f634(x101144,x101141,x101145,x101143,x101142))),x101144))+~P1(f862(f862(f321(f931(x101142,x101142)),f862(f862(f244(x101142,x101142),x101143),x101145)),f862(f862(f176(f931(x101142,x101142),a921),x101141),x101144)))
% 25.54/25.42 [10153]~P3(x101531)+~P1(f862(f862(f227(x101531),f862(x101534,f481(x101535,x101534,x101533,x101532,x101531))),x101535))+P1(f862(f862(f227(x101531),f862(f862(f33(x101532,x101531),x101533),x101534)),x101535))
% 25.54/25.42 [10195]E(x101951,x101952)+P1(f862(f862(f321(f931(x101953,x101953)),f862(f862(f244(x101953,x101953),f635(x101954,x101955,x101951,x101952,x101953)),x101951)),x101954))+~P1(f862(f862(f321(f931(x101953,x101953)),f862(f862(f244(x101953,x101953),x101952),x101951)),f862(f862(f176(f931(x101953,x101953),a921),x101955),x101954)))
% 25.54/25.42 [10196]E(x101961,f2(a924))+P1(f862(f862(f321(f931(x101962,x101962)),f862(f862(f244(x101962,x101962),f635(x101963,x101961,x101964,x101965,x101962)),x101964)),x101963))+~P1(f862(f862(f321(f931(x101962,x101962)),f862(f862(f244(x101962,x101962),x101965),x101964)),f862(f862(f176(f931(x101962,x101962),a921),x101961),x101963)))
% 25.54/25.42 [10200]E(x102001,x102002)+P1(f862(f862(f321(f931(x102003,x102003)),f862(f862(f244(x102003,x102003),x102001),f635(x102004,x102005,x102002,x102001,x102003))),f862(f862(f176(f931(x102003,x102003),a921),f636(x102004,x102005,x102002,x102001,x102003)),x102004)))+~P1(f862(f862(f321(f931(x102003,x102003)),f862(f862(f244(x102003,x102003),x102001),x102002)),f862(f862(f176(f931(x102003,x102003),a921),x102005),x102004)))
% 25.54/25.42 [10201]E(x102011,f2(a924))+P1(f862(f862(f321(f931(x102012,x102012)),f862(f862(f244(x102012,x102012),x102013),f635(x102014,x102011,x102015,x102013,x102012))),f862(f862(f176(f931(x102012,x102012),a921),f636(x102014,x102011,x102015,x102013,x102012)),x102014)))+~P1(f862(f862(f321(f931(x102012,x102012)),f862(f862(f244(x102012,x102012),x102013),x102015)),f862(f862(f176(f931(x102012,x102012),a921),x102011),x102014)))
% 25.54/25.42 [10250]E(x102501,x102502)+P1(f862(f862(f321(f931(x102503,x102503)),f862(f862(f244(x102503,x102503),f634(x102504,x102505,x102501,x102502,x102503)),x102501)),f862(f862(f176(f931(x102503,x102503),a921),f633(x102504,x102505,x102501,x102502,x102503)),x102504)))+~P1(f862(f862(f321(f931(x102503,x102503)),f862(f862(f244(x102503,x102503),x102502),x102501)),f862(f862(f176(f931(x102503,x102503),a921),x102505),x102504)))
% 25.54/25.42 [10251]E(x102511,f2(a924))+P1(f862(f862(f321(f931(x102512,x102512)),f862(f862(f244(x102512,x102512),f634(x102513,x102511,x102514,x102515,x102512)),x102514)),f862(f862(f176(f931(x102512,x102512),a921),f633(x102513,x102511,x102514,x102515,x102512)),x102513)))+~P1(f862(f862(f321(f931(x102512,x102512)),f862(f862(f244(x102512,x102512),x102515),x102514)),f862(f862(f176(f931(x102512,x102512),a921),x102511),x102513)))
% 25.54/25.42 [10286]~P72(x102862)+~P1(f862(f54(x102861),x102865))+E(f862(f862(f8(x102861,x102862),f862(f862(f9(x102861,x102862,x102862),f862(f862(f20(x102861,x102862,f932(x102862,x102862)),f862(f862(f10(a921,f932(x102862,f932(x102862,x102862)),x102861),f89(x102862)),f862(f862(f9(x102861,f932(x102861,a921),a921),f321(x102861)),x102863))),x102864)),f2(x102862))),x102865),f862(f862(f8(x102861,x102862),x102864),f862(f862(f94(f932(x102861,a921)),x102865),x102863)))
% 25.54/25.42 [8848]~P72(x88481)+~P1(f862(f54(x88484),x88485))+E(f862(f862(f73(x88481),f862(x88482,x88483)),f862(f862(f8(x88484,x88481),x88482),f862(f862(f3(f932(x88484,a921)),x88485),f862(f862(f301(x88484),x88483),f181(f932(x88484,a921)))))),f862(f862(f8(x88484,x88481),x88482),f862(f862(f301(x88484),x88483),x88485)))
% 25.54/25.42 [8849]~P71(x88491)+~P1(f862(f54(x88494),x88495))+E(f862(f862(f74(x88491),f862(x88492,x88493)),f862(f862(f11(x88494,x88491),x88492),f862(f862(f3(f932(x88494,a921)),x88495),f862(f862(f301(x88494),x88493),f181(f932(x88494,a921)))))),f862(f862(f11(x88494,x88491),x88492),f862(f862(f301(x88494),x88493),x88495)))
% 25.54/25.42 [9184]~P109(x91842)+~P11(x91842,f862(f161(x91842),f862(f862(f147(x91841,x91842),x91844),x91845)))+E(f862(f129(x91841,f862(f862(f10(x91842,a921,x91841),f862(f228(x91842),x91843)),x91844)),x91845),f170(x91841,f862(f862(f10(x91842,a921,x91841),f862(f228(x91842),x91843)),x91844),x91845))
% 25.54/25.42 [9208]~P72(x92081)+E(f862(f862(f73(x92081),f862(f862(f8(a924,x92081),x92082),f296(a924,x92083,x92084))),f862(f862(f8(a924,x92081),x92082),f296(a924,f862(f862(f73(a924),x92084),f71(a924)),f862(f862(f73(a924),x92084),x92085)))),f862(f862(f8(a924,x92081),x92082),f296(a924,x92083,f862(f862(f73(a924),x92084),x92085))))+~P1(f862(f862(f227(a924),x92083),f862(f862(f73(a924),x92084),f71(a924))))
% 25.54/25.42 [9209]~P1(f862(f862(f321(x92091),x92094),x92095))+~P1(f862(f862(f227(f932(x92091,a921)),f862(f165(x92091),x92092)),x92095))+P1(f862(f862(f227(f932(x92091,a921)),f862(f165(x92091),f862(f862(f152(x92091,x92092),x92093),x92094))),x92095))
% 25.54/25.42 [9435]~P3(x94352)+~P1(f862(f54(x94351),x94355))+E(f862(f862(f57(x94351,x94352,f862(f862(f10(x94352,f932(x94352,x94352),x94351),f103(x94352)),x94353)),x94354),x94355),f862(f862(f103(x94352),x94354),f862(f862(f33(x94351,x94352),x94355),x94353)))
% 25.54/25.42 [9436]~P3(x94362)+~P1(f862(f54(x94361),x94365))+E(f862(f862(f57(x94361,x94362,f862(f862(f10(x94362,f932(x94362,x94362),x94361),f94(x94362)),x94363)),x94364),x94365),f862(f862(f94(x94362),x94364),f862(f862(f32(x94361,x94362),x94365),x94363)))
% 25.54/25.42 [9485]E(f862(x94851,x94852),f862(x94851,x94853))+P1(f862(f862(f228(a924),f862(x94851,x94852)),f862(x94851,x94853)))+~P1(f862(f862(f321(f931(x94854,x94854)),f862(f862(f244(x94854,x94854),x94852),x94853)),f146(x94854,f862(f862(f144(f932(x94854,a924)),x94851),x94855))))
% 25.54/25.42 [9518]~E(f862(x95184,x95182),f862(x95184,x95183))+~P1(f862(f862(f321(f931(x95181,x95181)),f862(f862(f244(x95181,x95181),x95182),x95183)),f146(x95181,x95185)))+P1(f862(f862(f321(f931(x95181,x95181)),f862(f862(f244(x95181,x95181),x95182),x95183)),f146(x95181,f862(f862(f144(f932(x95181,a924)),x95184),x95185))))
% 25.54/25.42 [9538]~P22(x95381,x95382,x95383,x95385)+P22(x95381,x95382,x95383,f862(f862(f301(x95381),x95384),x95385))+P1(f862(f862(f321(x95382),f862(x95383,x95384)),f862(f302(x95381,x95382,x95383),f862(f862(f3(f932(x95381,a921)),x95385),f862(f862(f301(x95381),x95384),f181(f932(x95381,a921)))))))
% 25.54/25.42 [9541]P1(f862(x95412,x95415))+~P1(f862(f862(f321(x95411),x95415),f862(f165(x95411),x95413)))+E(f862(f862(f131(x95411),f862(f182(f925(x95411)),f170(x95411,x95412,f862(f862(f127(x95411),x95413),x95414)))),f862(f862(f127(x95411),x95413),x95414)),f862(f862(f127(x95411),f862(f862(f131(x95411),f862(f182(f925(x95411)),f170(x95411,x95412,x95413))),x95413)),x95414))
% 25.54/25.42 [9547]~P1(f862(f862(f321(f931(x95471,x95471)),f862(f862(f244(x95471,x95471),x95472),x95473)),f146(x95471,x95475)))+~P1(f862(f862(f227(a924),f862(x95474,x95472)),f862(x95474,x95473)))+P1(f862(f862(f321(f931(x95471,x95471)),f862(f862(f244(x95471,x95471),x95472),x95473)),f146(x95471,f862(f862(f144(f932(x95471,a924)),x95474),x95475))))
% 25.54/25.42 [9616]P1(f862(f862(f321(f931(x96164,x96164)),f862(f862(f244(x96164,x96164),x96162),x96163)),f146(x96164,x96165)))+P1(f862(f862(f228(a924),f862(x96161,x96162)),f862(x96161,x96163)))+~P1(f862(f862(f321(f931(x96164,x96164)),f862(f862(f244(x96164,x96164),x96162),x96163)),f146(x96164,f862(f862(f144(f932(x96164,a924)),x96161),x96165))))
% 25.54/25.42 [9761]~P1(f862(f862(f321(f931(f925(x97611),f925(x97611))),f862(f862(f244(f925(x97611),f925(x97611)),x97612),x97614)),f151(x97611,x97615)))+~P1(f862(f862(f228(a924),x97613),f862(f182(f925(x97611)),x97612)))+P1(f862(f862(f321(f931(x97611,x97611)),f862(f862(f244(x97611,x97611),f862(f862(f157(x97611),x97612),x97613)),f862(f862(f157(x97611),x97614),x97613))),x97615))
% 25.54/25.42 [10006]E(x100061,f2(a1))+~P1(f862(f42(x100063,x100061),f862(f862(f244(a1,a1),x100064),x100065)))+P1(f862(f42(f862(f862(f74(a1),x100062),x100063),x100061),f862(f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f74(a1),x100062),x100064)),f862(f862(f29(a1),f862(f862(f74(a1),x100062),x100065)),x100061))),f38(a1,f862(f862(f74(a1),x100062),x100065),x100061))))
% 25.54/25.42 [10007]~P1(f862(f862(f228(a924),f2(a924)),x100073))+~P1(f862(f41(x100072,x100073),f862(f862(f244(a924,a924),x100074),x100075)))+P1(f862(f41(f862(f862(f74(a924),x100071),x100072),x100073),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f74(a924),x100071),x100074)),f862(f862(f29(a924),f862(f862(f74(a924),x100071),x100075)),x100073))),f38(a924,f862(f862(f74(a924),x100071),x100075),x100073))))
% 25.54/25.42 [10309]~P72(x103092)+~P1(f862(f54(x103091),x103094))+E(f862(f862(f8(x103091,x103092),x103093),f862(f254(x103091),f862(f862(f20(x103091,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103091),a318),f862(f862(f9(x103091,f932(x103091,a921),a921),f321(x103091)),x103094))),f862(f862(f9(x103091,f932(x103091,a921),a921),f321(x103091)),x103095)))),f862(f862(f8(x103091,x103092),f862(f862(f9(x103091,x103092,x103092),f862(f862(f20(x103091,x103092,f932(x103092,x103092)),f862(f862(f10(a921,f932(x103092,f932(x103092,x103092)),x103091),f89(x103092)),f862(f862(f9(x103091,f932(x103091,a921),a921),f321(x103091)),x103095))),x103093)),f2(x103092))),x103094))
% 25.54/25.42 [8474]~E(f862(f862(f127(x84741),x84742),x84745),f862(f862(f127(x84741),x84743),x84744))+E(f862(f862(f127(x84741),f862(f862(f131(x84741),f862(f182(f925(x84741)),x84742)),x84743)),x84744),x84745)+P1(f862(f862(f227(a924),f862(f182(f925(x84741)),x84743)),f862(f182(f925(x84741)),x84742)))
% 25.54/25.42 [8673]~E(f862(f862(f127(x86732),x86733),x86731),f862(f862(f127(x86732),x86734),x86735))+E(x86731,f862(f862(f127(x86732),f862(f862(f131(x86732),f862(f182(f925(x86732)),x86733)),x86734)),x86735))+~P1(f862(f862(f227(a924),f862(f182(f925(x86732)),x86733)),f862(f182(f925(x86732)),x86734)))
% 25.54/25.42 [8763]~E(f862(f862(f73(a924),f862(f862(f74(a924),x87633),x87634)),x87631),f862(f862(f73(a924),f862(f862(f74(a924),x87632),x87634)),x87635))+~P1(f862(f862(f227(a924),x87633),x87632))+E(x87631,f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x87632),x87633)),x87634)),x87635))
% 25.54/25.42 [8764]~E(f862(f862(f73(a924),f862(f862(f74(a924),x87641),x87643)),x87644),f862(f862(f73(a924),f862(f862(f74(a924),x87642),x87643)),x87645))+~P1(f862(f862(f227(a924),x87642),x87641))+E(f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x87641),x87642)),x87643)),x87644),x87645)
% 25.54/25.42 [8933]E(f862(f862(f73(a924),f862(f862(f74(a924),x89331),x89332)),x89333),f862(f862(f73(a924),f862(f862(f74(a924),x89334),x89332)),x89335))+~P1(f862(f862(f227(a924),x89334),x89331))+~E(x89335,f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x89331),x89334)),x89332)),x89333))
% 25.54/25.42 [8934]E(f862(f862(f73(a924),f862(f862(f74(a924),x89341),x89342)),x89343),f862(f862(f73(a924),f862(f862(f74(a924),x89344),x89342)),x89345))+~P1(f862(f862(f227(a924),x89344),x89341))+~E(f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x89341),x89344)),x89342)),x89343),x89345)
% 25.54/25.42 [9813]~P72(x98132)+~P1(f862(f54(x98131),x98135))+E(f862(f862(f8(x98131,x98132),f862(f862(f20(x98131,x98132,x98132),f862(f862(f10(x98132,f932(x98132,x98132),x98131),f73(x98132)),x98133)),x98134)),x98135),f862(f862(f73(x98132),f862(f862(f8(x98131,x98132),x98133),x98135)),f862(f862(f8(x98131,x98132),x98134),x98135)))
% 25.54/25.42 [9814]~P71(x98142)+~P1(f862(f54(x98141),x98145))+E(f862(f862(f11(x98141,x98142),f862(f862(f20(x98141,x98142,x98142),f862(f862(f10(x98142,f932(x98142,x98142),x98141),f74(x98142)),x98143)),x98144)),x98145),f862(f862(f74(x98142),f862(f862(f11(x98141,x98142),x98143),x98145)),f862(f862(f11(x98141,x98142),x98144),x98145)))
% 25.54/25.42 [9815]~P64(x98152)+~P1(f862(f54(x98151),x98155))+E(f862(f862(f11(x98151,x98152),f862(f862(f20(x98151,x98152,x98152),f862(f862(f10(x98152,f932(x98152,x98152),x98151),f281(x98152)),x98153)),x98154)),x98155),f862(f862(f281(x98152),f862(f862(f11(x98151,x98152),x98153),x98155)),f862(f862(f11(x98151,x98152),x98154),x98155)))
% 25.54/25.42 [9945]~E(f638(x99455,x99454,x99453,x99452,x99451),f639(x99455,x99454,x99453,x99452,x99451))+P1(f862(f862(f321(f931(x99451,x99451)),f862(f862(f244(x99451,x99451),x99452),x99453)),f299(x99451,x99454)))+~P1(f862(f862(f321(f931(x99451,x99451)),f862(f862(f244(x99451,x99451),x99452),x99453)),f299(x99451,f862(f862(f103(f932(f931(x99451,x99451),a921)),x99454),x99455))))
% 25.54/25.42 [9946]~E(f640(x99465,x99464,x99463,x99462,x99461),f641(x99465,x99464,x99463,x99462,x99461))+P1(f862(f862(f321(f931(x99461,x99461)),f862(f862(f244(x99461,x99461),x99462),x99463)),f299(x99461,x99464)))+~P1(f862(f862(f321(f931(x99461,x99461)),f862(f862(f244(x99461,x99461),x99462),x99463)),f299(x99461,f862(f862(f103(f932(f931(x99461,x99461),a921)),x99464),x99465))))
% 25.54/25.42 [10143]P1(f862(f862(f321(f931(x101431,x101431)),f862(f862(f244(x101431,x101431),x101432),f639(x101435,x101434,x101433,x101432,x101431))),f299(x101431,x101434)))+P1(f862(f862(f321(f931(x101431,x101431)),f862(f862(f244(x101431,x101431),x101432),x101433)),f299(x101431,x101434)))+~P1(f862(f862(f321(f931(x101431,x101431)),f862(f862(f244(x101431,x101431),x101432),x101433)),f299(x101431,f862(f862(f103(f932(f931(x101431,x101431),a921)),x101434),x101435))))
% 25.54/25.42 [10222]P1(f862(f862(f321(f931(x102221,x102221)),f862(f862(f244(x102221,x102221),f641(x102225,x102224,x102223,x102222,x102221)),x102223)),f299(x102221,x102224)))+P1(f862(f862(f321(f931(x102221,x102221)),f862(f862(f244(x102221,x102221),x102222),x102223)),f299(x102221,x102224)))+~P1(f862(f862(f321(f931(x102221,x102221)),f862(f862(f244(x102221,x102221),x102222),x102223)),f299(x102221,f862(f862(f103(f932(f931(x102221,x102221),a921)),x102224),x102225))))
% 25.54/25.42 [10257]P1(f862(f862(f321(f931(x102571,x102571)),f862(f862(f244(x102571,x102571),x102572),x102573)),f299(x102571,x102574)))+P1(f862(f862(f321(f931(x102571,x102571)),f862(f862(f244(x102571,x102571),f639(x102575,x102574,x102573,x102572,x102571)),f638(x102575,x102574,x102573,x102572,x102571))),x102575))+~P1(f862(f862(f321(f931(x102571,x102571)),f862(f862(f244(x102571,x102571),x102572),x102573)),f299(x102571,f862(f862(f103(f932(f931(x102571,x102571),a921)),x102574),x102575))))
% 25.54/25.42 [10258]P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),x102582),x102583)),f299(x102581,x102584)))+P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),f640(x102585,x102584,x102583,x102582,x102581)),f641(x102585,x102584,x102583,x102582,x102581))),x102585))+~P1(f862(f862(f321(f931(x102581,x102581)),f862(f862(f244(x102581,x102581),x102582),x102583)),f299(x102581,f862(f862(f103(f932(f931(x102581,x102581),a921)),x102584),x102585))))
% 25.54/25.42 [10407]~P1(f862(f862(f321(f931(f925(x104071),f925(x104071))),f862(f862(f244(f925(x104071),f925(x104071)),x104074),x104075)),f151(x104071,x104072)))+~P1(f862(f862(f321(f931(x104071,x104071)),x104073),f862(f165(f931(x104071,x104071)),f862(f862(f174(x104071,x104071),x104074),x104075))))+P1(f862(f862(f249(x104071,x104071,a921),f862(f862(f9(x104071,f932(f931(x104071,x104071),a921),f932(x104071,a921)),f862(f862(f10(f932(x104071,f932(f932(f931(x104071,x104071),a921),a921)),f932(f932(f931(x104071,x104071),a921),f932(x104071,a921)),x104071),f9(x104071,f932(f931(x104071,x104071),a921),a921)),f862(f862(f10(f932(x104071,f931(x104071,x104071)),f932(x104071,f932(f932(f931(x104071,x104071),a921),a921)),x104071),f862(f10(f931(x104071,x104071),f932(f932(f931(x104071,x104071),a921),a921),x104071),f321(f931(x104071,x104071)))),f244(x104071,x104071)))),x104072)),x104073))
% 25.54/25.42 [9844]~P1(f862(f862(f227(a924),x98443),x98442))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98443),x98444)),x98441)),f862(f862(f73(a924),f862(f862(f74(a924),x98442),x98444)),x98445)))+P1(f862(f862(f227(a924),x98441),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98442),x98443)),x98444)),x98445)))
% 25.54/25.42 [9845]~P1(f862(f862(f227(a924),x98453),x98452))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98453),x98454)),x98451)),f862(f862(f73(a924),f862(f862(f74(a924),x98452),x98454)),x98455)))+P1(f862(f862(f228(a924),x98451),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98452),x98453)),x98454)),x98455)))
% 25.54/25.42 [9862]~P1(f862(f862(f227(a924),x98621),x98624))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98621),x98622)),x98623)),f862(f862(f73(a924),f862(f862(f74(a924),x98624),x98622)),x98625)))+~P1(f862(f862(f227(a924),x98623),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98624),x98621)),x98622)),x98625)))
% 25.54/25.42 [9863]~P1(f862(f862(f227(a924),x98631),x98634))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x98631),x98632)),x98633)),f862(f862(f73(a924),f862(f862(f74(a924),x98634),x98632)),x98635)))+~P1(f862(f862(f228(a924),x98633),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x98634),x98631)),x98632)),x98635)))
% 25.54/25.42 [9980]~P1(f862(f862(f227(a924),x99802),x99801))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x99801),x99803)),x99804)),f862(f862(f73(a924),f862(f862(f74(a924),x99802),x99803)),x99805)))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x99801),x99802)),x99803)),x99804)),x99805))
% 25.54/25.42 [9981]~P1(f862(f862(f227(a924),x99812),x99811))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x99811),x99813)),x99814)),f862(f862(f73(a924),f862(f862(f74(a924),x99812),x99813)),x99815)))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x99811),x99812)),x99813)),x99814)),x99815))
% 25.54/25.42 [10025]~P1(f862(f862(f227(a924),x100254),x100251))+P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),x100251),x100252)),x100253)),f862(f862(f73(a924),f862(f862(f74(a924),x100254),x100252)),x100255)))+~P1(f862(f862(f227(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x100251),x100254)),x100252)),x100253)),x100255))
% 25.54/25.42 [10026]~P1(f862(f862(f227(a924),x100264),x100261))+P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),x100261),x100262)),x100263)),f862(f862(f73(a924),f862(f862(f74(a924),x100264),x100262)),x100265)))+~P1(f862(f862(f228(a924),f862(f862(f73(a924),f862(f862(f74(a924),f862(f862(f3(a924),x100261),x100264)),x100262)),x100263)),x100265))
% 25.54/25.42 [10245]~P9(x102451,x102452,x102455,x102453)+~P1(f862(f862(f321(f931(x102451,x102451)),x102454),x102455))+P1(f862(f862(f249(x102451,x102451,a921),f862(f862(f9(x102451,f932(x102451,x102452),f932(x102451,a921)),f862(f862(f10(f932(x102452,a921),f932(f932(x102451,x102452),f932(x102451,a921)),x102451),f10(x102452,a921,x102451)),f862(f862(f10(x102452,f932(x102452,a921),x102451),a317),x102453))),x102453)),x102454))
% 25.54/25.42 [8636]~P17(x86366,x86361,x86362,x86364)+E(f862(f66(x86361,x86361,x86361,f862(x86362,x86363)),f862(x86364,x86365)),f862(f66(x86361,x86361,x86361,f862(x86364,x86365)),f862(x86362,x86363)))+~P1(f862(f54(x86366),x86365))
% 25.54/25.42 [9078]~P22(x90781,x90783,x90785,x90786)+~P22(x90783,x90782,x90784,f862(f302(x90781,x90783,x90785),x90786))+P22(x90781,x90782,f862(f66(x90783,x90782,x90781,x90784),x90785),x90786)
% 25.54/25.42 [9079]~P22(x90791,x90793,x90795,x90796)+~P22(x90793,x90792,x90794,f862(f302(x90791,x90793,x90795),x90796))+P22(x90791,x90792,f862(f66(x90793,x90792,x90791,x90794),x90795),x90796)
% 25.54/25.42 [9256]~P22(x92564,x92561,x92565,x92566)+~P22(x92564,x92562,f862(f66(x92561,x92562,x92564,x92563),x92565),x92566)+P22(x92561,x92562,x92563,f862(f302(x92564,x92561,x92565),x92566))
% 25.54/25.42 [9648]~P1(f862(f862(x96483,x96482),x96486))+~P1(f862(f862(x96484,x96485),x96482))+P1(f862(f862(f321(x96481),x96482),f291(x96481,x96483,x96484,x96485,x96486)))
% 25.54/25.42 [9649]~P1(f862(f862(x96494,x96492),x96496))+~P1(f862(f862(x96493,x96495),x96492))+P1(f862(f862(f321(x96491),x96492),f288(x96491,x96493,x96494,x96495,x96496)))
% 25.54/25.42 [9762]E(x97621,x97622)+E(x97623,x97624)+~P1(f862(f862(f321(f931(f925(x97625),f925(x97625))),f862(f862(f244(f925(x97625),f925(x97625)),f862(f862(f144(x97625),x97623),x97621)),f862(f862(f144(x97625),x97624),x97622))),f150(x97625,x97626)))
% 25.54/25.42 [9771]~E(x97712,x97714)+P1(f862(f862(f321(f931(f925(x97711),f925(x97711))),f862(f862(f244(f925(x97711),f925(x97711)),f862(f862(f144(x97711),x97712),x97713)),f862(f862(f144(x97711),x97714),x97715))),f138(x97711,x97716)))+~P1(f862(f862(f321(f931(f925(x97711),f925(x97711))),f862(f862(f244(f925(x97711),f925(x97711)),x97713),x97715)),f138(x97711,x97716)))
% 25.54/25.42 [9772]~E(x97722,x97724)+P1(f862(f862(f321(f931(f925(x97721),f925(x97721))),f862(f862(f244(f925(x97721),f925(x97721)),f862(f862(f144(x97721),x97722),x97723)),f862(f862(f144(x97721),x97724),x97725))),f140(x97721,x97726)))+~P1(f862(f862(f321(f931(f925(x97721),f925(x97721))),f862(f862(f244(f925(x97721),f925(x97721)),x97723),x97725)),f140(x97721,x97726)))
% 25.54/25.42 [9773]~E(x97732,x97734)+P1(f862(f862(f321(f931(f925(x97731),f925(x97731))),f862(f862(f244(f925(x97731),f925(x97731)),f862(f862(f144(x97731),x97732),x97733)),f862(f862(f144(x97731),x97734),x97735))),f150(x97731,x97736)))+~P1(f862(f862(f321(f931(f925(x97731),f925(x97731))),f862(f862(f244(f925(x97731),f925(x97731)),x97733),x97735)),f150(x97731,x97736)))
% 25.54/25.42 [9774]~E(x97742,x97744)+P1(f862(f862(f321(f931(f925(x97741),f925(x97741))),f862(f862(f244(f925(x97741),f925(x97741)),f862(f862(f127(x97741),x97742),x97743)),f862(f862(f127(x97741),x97744),x97745))),f150(x97741,x97746)))+~P1(f862(f862(f321(f931(f925(x97741),f925(x97741))),f862(f862(f244(f925(x97741),f925(x97741)),x97743),x97745)),f150(x97741,x97746)))
% 25.54/25.42 [9775]~E(x97753,x97755)+P1(f862(f862(f321(f931(f925(x97751),f925(x97751))),f862(f862(f244(f925(x97751),f925(x97751)),f862(f862(f127(x97751),x97752),x97753)),f862(f862(f127(x97751),x97754),x97755))),f150(x97751,x97756)))+~P1(f862(f862(f321(f931(f925(x97751),f925(x97751))),f862(f862(f244(f925(x97751),f925(x97751)),x97752),x97754)),f150(x97751,x97756)))
% 25.54/25.42 [9832]E(x98321,x98322)+P1(f862(f862(f321(f931(f925(x98323),f925(x98323))),f862(f862(f244(f925(x98323),f925(x98323)),x98321),x98322)),f150(x98323,x98324)))+~P1(f862(f862(f321(f931(f925(x98323),f925(x98323))),f862(f862(f244(f925(x98323),f925(x98323)),f862(f862(f144(x98323),x98325),x98321)),f862(f862(f144(x98323),x98326),x98322))),f150(x98323,x98324)))
% 25.54/25.42 [9984]~E(x99843,x99845)+P1(f862(f862(f321(f931(f925(x99841),f925(x99841))),f862(f862(f244(f925(x99841),f925(x99841)),f862(f862(f127(x99841),x99842),f862(f862(f144(x99841),x99843),f106(x99841)))),f862(f862(f127(x99841),x99844),f862(f862(f144(x99841),x99845),f106(x99841))))),f150(x99841,x99846)))+~P1(f862(f862(f321(f931(f925(x99841),f925(x99841))),f862(f862(f244(f925(x99841),f925(x99841)),x99842),x99844)),f150(x99841,x99846)))
% 25.54/25.42 [10029]E(x100291,x100292)+E(x100293,x100294)+~P1(f862(f862(f321(f931(f925(x100295),f925(x100295))),f862(f862(f244(f925(x100295),f925(x100295)),f862(f862(f127(x100295),x100293),f862(f862(f144(x100295),x100291),f106(x100295)))),f862(f862(f127(x100295),x100294),f862(f862(f144(x100295),x100292),f106(x100295))))),f150(x100295,x100296)))
% 25.54/25.42 [10055]E(x100551,x100552)+~P1(f862(f862(f321(f931(f925(x100553),f925(x100553))),f862(f862(f244(f925(x100553),f925(x100553)),f862(f862(f127(x100553),x100551),f862(f862(f144(x100553),x100555),f106(x100553)))),f862(f862(f127(x100553),x100552),f862(f862(f144(x100553),x100556),f106(x100553))))),f150(x100553,x100554)))+P1(f862(f862(f321(f931(f925(x100553),f925(x100553))),f862(f862(f244(f925(x100553),f925(x100553)),x100551),x100552)),f150(x100553,x100554)))
% 25.54/25.42 [10095]~P1(f862(f862(f321(f931(f932(x100951,a921),f932(x100951,a921))),f862(f862(f244(f932(x100951,a921),f932(x100951,a921)),x100952),x100954)),f310(x100951,x100956)))+~P1(f862(f862(f321(f931(f932(x100951,a921),f932(x100951,a921))),f862(f862(f244(f932(x100951,a921),f932(x100951,a921)),x100953),x100955)),f310(x100951,x100956)))+P1(f862(f862(f321(f931(f932(x100951,a921),f932(x100951,a921))),f862(f862(f244(f932(x100951,a921),f932(x100951,a921)),f862(f862(f103(f932(x100951,a921)),x100952),x100953)),f862(f862(f103(f932(x100951,a921)),x100954),x100955))),f310(x100951,x100956)))
% 25.54/25.42 [5849]~E(f862(f862(f127(x58491),x58496),x58493),x58495)+E(f862(f862(f127(x58491),x58492),x58493),f862(f862(f144(x58491),x58494),x58495))+~E(x58492,f862(f862(f144(x58491),x58494),x58496))
% 25.54/25.42 [5850]~E(f862(f862(f127(x58501),x58506),x58503),x58505)+E(f862(f862(f127(x58501),x58502),x58503),f862(f862(f127(x58501),x58504),x58505))+~E(x58502,f862(f862(f127(x58501),x58504),x58506))
% 25.54/25.42 [5851]E(f862(f862(f127(x58511),x58512),x58513),f862(f862(f144(x58511),x58514),x58515))+~E(f862(f862(f144(x58511),x58514),x58516),x58512)+~E(x58515,f862(f862(f127(x58511),x58516),x58513))
% 25.54/25.42 [5852]E(f862(f862(f127(x58521),x58522),x58523),f862(f862(f144(x58521),x58524),x58525))+~E(f862(f862(f144(x58521),x58524),x58526),x58522)+~E(x58525,f862(f862(f127(x58521),x58526),x58523))
% 25.54/25.42 [5853]~E(f862(f862(f127(x58531),x58532),x58536),x58534)+E(f862(f862(f127(x58531),x58532),x58533),f862(f862(f127(x58531),x58534),x58535))+~E(x58533,f862(f862(f127(x58531),x58536),x58535))
% 25.54/25.42 [5854]~E(f862(f862(f127(x58541),x58542),x58546),x58544)+E(f862(f862(f127(x58541),x58542),x58543),f862(f862(f127(x58541),x58544),x58545))+~E(x58543,f862(f862(f127(x58541),x58546),x58545))
% 25.54/25.42 [7005]E(f862(x70051,x70052),f862(x70053,x70052))+~E(f862(f862(f147(x70054,x70055),x70051),x70056),f862(f862(f147(x70054,x70055),x70053),x70056))+~P1(f862(f862(f321(x70054),x70052),f862(f165(x70054),x70056)))
% 25.54/25.42 [7391]~P17(x73914,x73915,x73916,x73911)+E(f862(f862(x73911,x73912),x73913),f862(f862(f57(x73914,x73915,x73916),x73913),x73912))+~P1(f862(f54(x73914),x73912))
% 25.54/25.42 [7462]~E(x74622,f862(x74624,x74626))+~P1(f862(f862(f321(x74623),x74626),x74625))+P1(f862(f862(f321(x74621),x74622),f862(f302(x74623,x74621,x74624),x74625)))
% 25.54/25.42 [7463]~E(x74632,f862(x74634,x74636))+~P1(f862(f862(f321(x74633),x74636),x74635))+P1(f862(f862(f321(x74631),x74632),f862(f302(x74633,x74631,x74634),x74635)))
% 25.54/25.42 [7464]~E(x74642,f862(x74644,x74646))+~P1(f862(f862(f321(x74643),x74646),x74645))+P1(f862(f862(f321(x74641),x74642),f862(f302(x74643,x74641,x74644),x74645)))
% 25.54/25.42 [7465]~E(f862(x74654,x74652),x74656)+~P1(f862(f862(f321(x74653),x74656),x74655))+P1(f862(f862(f321(x74651),x74652),f862(f303(x74651,x74653,x74654),x74655)))
% 25.54/25.42 [7917]~P30(x79171,x79172,x79174,x79176)+P30(x79171,x79172,f862(f862(f144(x79171),x79173),x79174),f862(f862(f144(x79171),x79175),x79176))+~P1(f862(f862(x79172,x79173),x79175))
% 25.54/25.42 [7918]~P30(x79181,x79182,x79184,x79186)+P30(x79181,x79182,f862(f862(f144(x79181),x79183),x79184),f862(f862(f144(x79181),x79185),x79186))+~P1(f862(f862(x79182,x79183),x79185))
% 25.54/25.42 [8943]~P54(x89434,x89435,x89431,x89432,x89436)+E(f862(x89431,f862(x89432,x89433)),x89433)+~P1(f862(f862(f321(x89435),x89433),x89436))
% 25.54/25.42 [9445]~P23(x94452,x94451,x94455,x94454,x94453)+E(f862(f86(x94451,x94452,x94453,f86(x94452,x94451,x94454,x94455)),x94456),f862(x94455,x94456))+~P1(f862(f862(f321(x94452),x94456),x94454))
% 25.54/25.42 [9456]~P22(x94561,x94562,x94563,x94566)+P22(x94561,x94562,f68(x94561,x94562,x94563,x94564,x94565),x94566)+P1(f862(f862(f321(x94562),x94565),f862(f302(x94561,x94562,x94563),x94566)))
% 25.54/25.42 [9578]~P54(x95786,x95785,x95781,x95784,x95783)+E(f862(x95781,f915(x95782,x95783,x95784,x95781,x95785)),x95782)+~P1(f862(f862(f321(x95785),x95782),x95783))
% 25.54/25.42 [9764]E(x97641,x97642)+E(f862(f182(f925(x97643)),x97644),f862(f182(f925(x97643)),x97645))+~P1(f862(f862(f321(f931(f925(x97643),f925(x97643))),f862(f862(f244(f925(x97643),f925(x97643)),f862(f862(f144(x97643),x97641),x97644)),f862(f862(f144(x97643),x97642),x97645))),f138(x97643,x97646)))
% 25.54/25.42 [9827]~P14(x98271,x98272,x98273)+E(f862(f862(f57(x98271,x98272,x98273),x98274),x98275),x98276)+~P1(f862(f59(x98271,x98272,x98273,x98274,x98275),x98276))
% 25.54/25.42 [9835]E(f862(f182(f925(x98351)),x98352),f862(f182(f925(x98351)),x98353))+P1(f862(f862(f321(f931(f925(x98351),f925(x98351))),f862(f862(f244(f925(x98351),f925(x98351)),x98352),x98353)),f138(x98351,x98354)))+~P1(f862(f862(f321(f931(f925(x98351),f925(x98351))),f862(f862(f244(f925(x98351),f925(x98351)),f862(f862(f144(x98351),x98355),x98352)),f862(f862(f144(x98351),x98356),x98353))),f138(x98351,x98354)))
% 25.54/25.42 [9856]~P1(f862(f862(f321(f931(x98561,x98561)),f862(f862(f244(x98561,x98561),x98562),x98564)),f299(x98561,x98566)))+P1(f862(f862(f321(f931(f925(x98561),f925(x98561))),f862(f862(f244(f925(x98561),f925(x98561)),f862(f862(f144(x98561),x98562),x98563)),f862(f862(f144(x98561),x98564),x98565))),f299(f925(x98561),f150(x98561,x98566))))+~P1(f862(f862(f321(f931(f925(x98561),f925(x98561))),f862(f862(f244(f925(x98561),f925(x98561)),x98563),x98565)),f299(f925(x98561),f150(x98561,x98566))))
% 25.54/25.42 [10035]~P1(f862(x100352,x100356))+~E(f862(f129(x100351,x100352),x100353),f862(f862(f144(x100351),x100354),x100355))+~P1(f862(f862(f321(x100351),x100356),f862(f165(x100351),f749(x100355,x100354,x100353,x100352,x100351))))
% 25.54/25.42 [10036]~P1(f862(x100364,x100366))+~E(f862(f862(f144(x100361),x100362),x100363),f862(f129(x100361,x100364),x100365))+~P1(f862(f862(f321(x100361),x100366),f862(f165(x100361),f753(x100365,x100364,x100363,x100362,x100361))))
% 25.54/25.42 [10344]~P72(x103442)+E(f862(f862(f8(x103441,x103442),f862(f862(f10(f932(x103443,a921),x103442,x103441),f862(f8(x103443,x103442),x103444)),f862(f862(f10(f932(x103443,a921),f932(x103443,a921),x103441),f254(x103443)),f862(f862(f10(f932(x103443,a921),f932(x103443,a921),x103441),f862(f20(x103443,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103443),a318),f862(f862(f9(x103443,f932(x103443,a921),a921),f321(x103443)),x103445)))),f862(f9(x103443,x103441,a921),f862(f862(f10(x103441,f932(x103441,a921),x103443),a317),x103446)))))),f862(f302(x103443,x103441,x103446),x103445)),f862(f862(f8(x103443,x103442),x103444),x103445))+~P1(f862(f54(x103443),x103445))
% 25.54/25.42 [7063]~P109(x70633)+P1(f862(x70632,x70635))+E(f862(f129(x70631,x70632),f862(f862(f141(x70631,x70633,x70634),x70635),x70636)),f862(f129(x70631,x70632),x70636))
% 25.54/25.42 [7065]P1(f862(x70651,x70652))+~E(f159(x70653,x70651,x70654),f862(f862(f244(f925(x70653),f925(x70653)),x70655),x70656))+~P1(f862(f862(f321(x70653),x70652),f862(f165(x70653),x70655)))
% 25.54/25.42 [7109]~P1(f862(x71092,x71096))+~E(f159(x71091,x71092,x71093),f862(f862(f244(f925(x71091),f925(x71091)),x71094),x71095))+~P1(f862(f862(f321(x71091),x71096),f862(f165(x71091),x71095)))
% 25.54/25.42 [7781]~P12(x77811,x77812,x77813)+~P1(f862(f54(x77811),x77816))+E(f862(f862(f57(x77811,x77812,x77813),x77814),f862(f862(f301(x77811),x77815),x77816)),f862(f862(f57(x77811,x77812,x77813),f862(f862(x77813,x77815),x77814)),x77816))
% 25.54/25.42 [7834]~P109(x78342)+~P1(f862(f862(f227(x78342),f862(x78343,x78344)),f862(x78343,x78345)))+E(f862(f862(f141(x78341,x78342,x78343),x78344),f862(f862(f144(x78341),x78345),x78346)),f862(f862(f144(x78341),x78344),f862(f862(f144(x78341),x78345),x78346)))
% 25.54/25.42 [7946]E(x79461,x79462)+~E(f862(f862(f246(x79463,x79464),x79461),f862(f18(f932(x79464,a921),x79463),x79465)),f862(f862(f246(x79463,x79464),x79462),f862(f18(f932(x79464,a921),x79463),x79465)))+~P1(f862(f862(f321(x79464),x79466),x79465))
% 25.54/25.42 [8012]~P12(x80121,x80122,x80123)+~P1(f862(f54(x80121),x80126))+E(f862(f862(f57(x80121,x80122,x80123),x80124),f862(f862(f301(x80121),x80125),x80126)),f862(f862(x80123,x80125),f862(f862(f57(x80121,x80122,x80123),x80124),x80126)))
% 25.54/25.42 [8132]~P14(x81321,x81322,x81323)+~P1(f862(f54(x81321),x81326))+E(f862(f862(f57(x81321,x81322,x81323),f862(f862(x81323,x81324),x81325)),x81326),f862(f862(x81323,x81324),f862(f862(f57(x81321,x81322,x81323),x81325),x81326)))
% 25.54/25.42 [8203]~P18(x82032,x82035,x82036,x82031)+~P1(f862(f54(x82032),x82034))+E(f862(x82031,f862(f862(f301(x82032),x82033),x82034)),f862(f66(x82035,x82035,x82035,f862(x82031,x82034)),f862(x82036,x82033)))
% 25.54/25.42 [8235]~P109(x82352)+P1(f862(f862(f227(x82352),f862(x82353,x82354)),f862(x82353,x82355)))+E(f862(f862(f141(x82351,x82352,x82353),x82354),f862(f862(f144(x82351),x82355),x82356)),f862(f862(f144(x82351),x82355),f862(f862(f141(x82351,x82352,x82353),x82354),x82356)))
% 25.54/25.42 [8381]~E(f862(f182(f925(x83811)),x83815),f862(f182(f925(x83812)),x83816))+~E(f862(f182(f925(x83811)),x83813),f862(f182(f925(x83812)),x83814))+E(f862(f862(f127(f931(x83811,x83812)),f862(f862(f174(x83811,x83812),x83813),x83814)),f862(f862(f174(x83811,x83812),x83815),x83816)),f862(f862(f174(x83811,x83812),f862(f862(f127(x83811),x83813),x83815)),f862(f862(f127(x83812),x83814),x83816)))
% 25.54/25.42 [8492]~E(x84922,f862(f302(x84923,x84921,x84924),x84926))+P1(f862(f862(f227(f932(x84921,a921)),x84922),f862(f302(x84923,x84921,x84924),x84925)))+~P1(f862(f862(f227(f932(x84923,a921)),x84926),x84925))
% 25.54/25.42 [8594]~P109(x85945)+E(f862(x85941,x85942),f862(x85941,x85943))+E(f862(f862(f141(x85944,x85945,x85941),x85942),f862(f862(f141(x85944,x85945,x85941),x85943),x85946)),f862(f862(f141(x85944,x85945,x85941),x85943),f862(f862(f141(x85944,x85945,x85941),x85942),x85946)))
% 25.54/25.42 [8771]~P1(f862(f862(f321(x87712),x87714),f862(x87716,x87713)))+~P1(f862(f862(f321(x87711),x87713),x87715))+P1(f862(f862(f321(f931(x87711,x87712)),f862(f862(f244(x87711,x87712),x87713),x87714)),f862(f862(f246(x87711,x87712),x87715),x87716)))
% 25.54/25.42 [8772]~P1(f862(f862(f321(x87722),x87724),f862(x87726,x87723)))+~P1(f862(f862(f321(x87721),x87723),x87725))+P1(f862(f862(f321(f931(x87721,x87722)),f862(f862(f244(x87721,x87722),x87723),x87724)),f862(f862(f246(x87721,x87722),x87725),x87726)))
% 25.54/25.42 [9249]~P72(x92492)+~P22(x92494,x92491,x92495,x92496)+E(f862(f862(f8(x92491,x92492),x92493),f862(f302(x92494,x92491,x92495),x92496)),f862(f862(f8(x92494,x92492),f862(f66(x92491,x92492,x92494,x92493),x92495)),x92496))
% 25.54/25.42 [9250]~P71(x92502)+~P22(x92504,x92501,x92505,x92506)+E(f862(f862(f11(x92501,x92502),x92503),f862(f302(x92504,x92501,x92505),x92506)),f862(f862(f11(x92504,x92502),f862(f66(x92501,x92502,x92504,x92503),x92505)),x92506))
% 25.54/25.42 [9297]~P32(x92972,x92975,x92971,x92973,x92976)+P1(f862(f862(x92971,f862(f862(f157(x92972),x92973),x92974)),f862(f862(f157(x92975),x92976),x92974)))+~P1(f862(f862(f228(a924),x92974),f862(f182(f925(x92972)),x92973)))
% 25.54/25.42 [9298]~P32(x92982,x92985,x92981,x92983,x92986)+P1(f862(f862(x92981,f862(f862(f157(x92982),x92983),x92984)),f862(f862(f157(x92985),x92986),x92984)))+~P1(f862(f862(f228(a924),x92984),f862(f182(f925(x92985)),x92986)))
% 25.54/25.42 [9299]~P32(x92992,x92995,x92991,x92993,x92996)+P1(f862(f862(x92991,f862(f862(f157(x92992),x92993),x92994)),f862(f862(f157(x92995),x92996),x92994)))+~P1(f862(f862(f228(a924),x92994),f862(f182(f925(x92992)),x92993)))
% 25.54/25.42 [9310]~E(f862(f302(x93101,x93102,x93103),x93104),x93106)+E(f862(f302(x93101,x93102,x93103),f862(f302(x93102,x93101,f86(x93101,x93102,x93104,x93103)),x93105)),x93105)+~P1(f862(f862(f227(f932(x93102,a921)),x93105),x93106))
% 25.54/25.42 [9513]~P17(x95133,x95131,x95136,x95132)+~P1(f862(f54(x95133),x95134))+E(f862(f66(x95131,x95131,x95131,f862(x95132,f862(f862(f3(f932(x95133,a921)),x95134),f862(f862(f301(x95133),x95135),f181(f932(x95133,a921)))))),f862(x95136,x95135)),f862(x95132,f862(f862(f301(x95133),x95135),x95134)))
% 25.54/25.42 [10125]~E(f862(f302(x101252,x101254,x101256),f234(f932(x101252,a921))),f234(f932(x101254,a921)))+~E(f862(f302(x101251,x101253,x101255),f234(f932(x101251,a921))),f234(f932(x101253,a921)))+E(f862(f302(f931(x101251,x101252),f931(x101253,x101254),f250(x101251,x101253,x101252,x101254,x101255,x101256)),f234(f932(f931(x101251,x101252),a921))),f234(f932(f931(x101253,x101254),a921)))
% 25.54/25.42 [10171]~P22(x101713,x101714,x101715,f862(x101716,f586(x101716,x101715,x101714,x101713,x101712,x101711)))+P22(x101713,x101714,x101715,f862(f862(f32(x101712,f932(x101713,a921)),x101711),x101716))+E(x101711,f181(f932(x101712,a921)))
% 25.54/25.42 [10229]P22(x102296,x102295,x102294,f862(f862(f32(x102292,f932(x102296,a921)),x102291),x102293))+E(x102291,f181(f932(x102292,a921)))+P1(f862(f862(f321(x102292),f586(x102293,x102294,x102295,x102296,x102292,x102291)),x102291))
% 25.54/25.42 [10235]P1(f862(f862(f321(x102351),f613(x102352,x102353,x102354,x102355,x102356,x102351)),x102356))+P1(f862(f862(f227(f932(f931(x102351,x102354),a921)),f862(f862(f246(x102351,x102354),x102356),x102353)),f862(f862(f246(x102351,x102354),x102355),x102352)))+~P1(f862(f862(f227(f932(x102351,a921)),x102356),x102355))
% 25.54/25.42 [10362]~P1(f862(f862(f227(f932(x103622,a921)),f862(x103624,f613(x103626,x103624,x103622,x103625,x103623,x103621))),f862(x103626,f613(x103626,x103624,x103622,x103625,x103623,x103621))))+~P1(f862(f862(f227(f932(x103621,a921)),x103623),x103625))+P1(f862(f862(f227(f932(f931(x103621,x103622),a921)),f862(f862(f246(x103621,x103622),x103623),x103624)),f862(f862(f246(x103621,x103622),x103625),x103626)))
% 25.54/25.42 [7968]~P1(f862(x79681,x79685))+~P1(f862(x79686,x79684))+P1(f862(x79681,f862(f248(x79682,x79683),f862(f862(f244(x79682,x79683),x79684),x79685))))
% 25.54/25.42 [7969]~P1(f862(x79691,x79694))+~P1(f862(x79696,x79695))+P1(f862(x79691,f862(f243(x79692,x79693),f862(f862(f244(x79692,x79693),x79694),x79695))))
% 25.54/25.42 [8017]~P1(f862(f862(x80174,x80176),x80175))+~P1(f862(f862(f321(x80171),x80176),x80173))+P1(f862(f862(f862(f33(x80171,f932(x80172,a921)),x80173),x80174),x80175))
% 25.54/25.42 [8018]~P1(f862(f862(x80184,x80186),x80185))+~P1(f862(f862(f321(x80181),x80186),x80183))+P1(f862(f862(f862(f33(x80181,f932(x80182,a921)),x80183),x80184),x80185))
% 25.54/25.42 [8329]~P1(f862(f862(f321(x83291),x83292),f862(x83295,x83296)))+~P1(f862(f862(f321(x83293),x83296),x83294))+P1(f862(f862(f321(x83291),x83292),f862(f862(f33(x83293,f932(x83291,a921)),x83294),x83295)))
% 25.54/25.42 [8330]~P1(f862(f862(f321(x83301),x83302),f862(x83305,x83306)))+~P1(f862(f862(f321(x83303),x83306),x83304))+P1(f862(f862(f321(x83301),x83302),f862(f862(f33(x83303,f932(x83301,a921)),x83304),x83305)))
% 25.54/25.42 [8373]P1(f862(f862(x83731,x83732),x83733))+~P1(f862(f862(x83734,x83732),x83733))+~P1(f862(f862(f227(f932(x83735,f932(x83736,a921))),x83734),x83731))
% 25.54/25.42 [8374]P1(f862(f862(x83741,x83742),x83743))+~P1(f862(f862(x83744,x83742),x83743))+~P1(f862(f862(f227(f932(x83745,f932(x83746,a921))),x83744),x83741))
% 25.54/25.42 [8513]P1(f862(f862(x85131,x85132),x85133))+~P1(f862(f862(f321(x85134),x85132),x85135))+~P1(f862(f862(f862(f32(x85134,f932(x85136,a921)),x85135),x85131),x85133))
% 25.54/25.42 [8514]P1(f862(f862(x85141,x85142),x85143))+~P1(f862(f862(f321(x85144),x85142),x85145))+~P1(f862(f862(f862(f32(x85144,f932(x85146,a921)),x85145),x85141),x85143))
% 25.54/25.42 [8515]P1(f862(f862(x85151,x85152),x85153))+~P1(f862(f862(f321(x85154),x85152),x85155))+~P1(f862(f862(f862(f32(x85154,f932(x85156,a921)),x85155),x85151),x85153))
% 25.54/25.42 [8650]P1(f862(f862(f321(x86501),x86502),f862(x86503,x86504)))+~P1(f862(f862(f321(x86505),x86504),x86506))+~P1(f862(f862(f321(x86501),x86502),f862(f862(f32(x86505,f932(x86501,a921)),x86506),x86503)))
% 25.54/25.42 [8651]P1(f862(f862(f321(x86511),x86512),f862(x86513,x86514)))+~P1(f862(f862(f321(x86515),x86514),x86516))+~P1(f862(f862(f321(x86511),x86512),f862(f862(f32(x86515,f932(x86511,a921)),x86516),x86513)))
% 25.54/25.42 [8652]P1(f862(f862(f321(x86521),x86522),f862(x86523,x86524)))+~P1(f862(f862(f321(x86525),x86524),x86526))+~P1(f862(f862(f321(x86521),x86522),f862(f862(f32(x86525,f932(x86521,a921)),x86526),x86523)))
% 25.54/25.42 [8922]~P9(x89224,x89225,x89226,x89221)+E(f862(x89221,x89222),f862(x89221,x89223))+~P1(f862(f862(f321(f931(x89224,x89224)),f862(f862(f244(x89224,x89224),x89222),x89223)),x89226))
% 25.54/25.42 [8957]P1(f862(f862(f227(f932(x89571,a921)),x89572),f862(x89573,x89574)))+~P1(f862(f862(f321(x89575),x89574),x89576))+~P1(f862(f862(f227(f932(x89571,a921)),x89572),f862(f862(f32(x89575,f932(x89571,a921)),x89576),x89573)))
% 25.54/25.42 [8990]~P52(x89903,x89904,f862(f277(x89904,x89903),x89905))+E(x89901,f181(f932(x89902,a921)))+E(f862(f862(f32(x89902,f932(x89903,a921)),x89901),f862(f862(f10(f932(x89904,a921),f932(x89903,a921),x89902),f276(x89904,x89903,x89905)),x89906)),f862(f276(x89904,x89903,x89905),f862(f862(f32(x89902,f932(x89904,a921)),x89901),x89906)))
% 25.54/25.42 [9069]P1(f862(f862(f321(x90691),x90692),f862(f276(x90693,x90691,x90694),x90695)))+~P1(f862(f862(f321(x90693),x90696),x90695))+~P1(f862(f862(f321(f931(x90693,x90691)),f862(f862(f244(x90693,x90691),x90696),x90692)),x90694))
% 25.54/25.42 [9070]P1(f862(f862(f321(x90701),x90702),f862(f276(x90703,x90701,x90704),x90705)))+~P1(f862(f862(f321(x90703),x90706),x90705))+~P1(f862(f862(f321(f931(x90703,x90701)),f862(f862(f244(x90703,x90701),x90706),x90702)),x90704))
% 25.54/25.42 [9376]P1(f862(f862(f227(f932(x93761,a921)),f862(f276(x93762,x93761,x93763),x93764)),f862(f276(x93762,x93761,x93765),x93766)))+~P1(f862(f862(f227(f932(x93762,a921)),x93764),x93766))+~P1(f862(f862(f227(f932(f931(x93762,x93761),a921)),x93763),x93765))
% 25.54/25.42 [9563]~P1(f862(f862(f321(x95632),x95636),x95634))+~P1(f862(f862(f227(f932(x95631,a921)),x95633),x95635))+P1(f862(f862(f227(f932(f931(x95631,x95632),a921)),f862(f862(f246(x95631,x95632),x95633),f862(f18(f932(x95632,a921),x95631),x95634))),f862(f862(f246(x95631,x95632),x95635),f862(f18(f932(x95632,a921),x95631),x95634))))
% 25.54/25.42 [9576]~P32(x95761,x95762,x95763,x95765,x95766)+P1(f862(f862(f249(x95761,x95762,a921),x95763),x95764))+~P1(f862(f862(f321(f931(x95761,x95762)),x95764),f862(f165(f931(x95761,x95762)),f862(f862(f174(x95761,x95762),x95765),x95766))))
% 25.54/25.42 [9718]~E(x97183,x97185)+P1(f862(f862(f321(f931(f925(x97181),f925(x97181))),f862(f862(f244(f925(x97181),f925(x97181)),f862(f862(f144(x97181),x97182),x97183)),f862(f862(f144(x97181),x97184),x97185))),f150(x97181,x97186)))+~P1(f862(f862(f321(f931(x97181,x97181)),f862(f862(f244(x97181,x97181),x97182),x97184)),x97186))
% 25.54/25.42 [9724]~E(f862(f182(f925(x97241)),x97243),f862(f182(f925(x97241)),x97245))+P1(f862(f862(f321(f931(f925(x97241),f925(x97241))),f862(f862(f244(f925(x97241),f925(x97241)),f862(f862(f144(x97241),x97242),x97243)),f862(f862(f144(x97241),x97244),x97245))),f138(x97241,x97246)))+~P1(f862(f862(f321(f931(x97241,x97241)),f862(f862(f244(x97241,x97241),x97242),x97244)),x97246))
% 25.54/25.42 [9756]P1(f862(f862(f321(f931(x97561,x97561)),f862(f862(f244(x97561,x97561),x97562),x97563)),f862(f862(f176(f931(x97561,x97561),a921),f862(a105,x97564)),x97565)))+~P1(f862(f862(f321(f931(x97561,x97561)),f862(f862(f244(x97561,x97561),x97566),x97563)),x97565))+~P1(f862(f862(f321(f931(x97561,x97561)),f862(f862(f244(x97561,x97561),x97562),x97566)),f862(f862(f176(f931(x97561,x97561),a921),x97564),x97565)))
% 25.54/25.42 [9757]P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97572),x97573)),f862(f862(f176(f931(x97571,x97571),a921),f862(a105,x97574)),x97575)))+~P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97572),x97576)),x97575))+~P1(f862(f862(f321(f931(x97571,x97571)),f862(f862(f244(x97571,x97571),x97576),x97573)),f862(f862(f176(f931(x97571,x97571),a921),x97574),x97575)))
% 25.54/25.42 [9760]~P1(f862(f862(f321(x97604),x97605),x97606))+P1(f862(f862(f227(f932(x97601,a921)),x97602),x97603))+~P1(f862(f862(f227(f932(f931(x97601,x97604),a921)),f862(f862(f246(x97601,x97604),x97602),f862(f18(f932(x97604,a921),x97601),x97606))),f862(f862(f246(x97601,x97604),x97603),f862(f18(f932(x97604,a921),x97601),x97606))))
% 25.54/25.42 [9805]E(x98051,x98052)+~P1(f862(f862(f321(f931(f925(x98053),f925(x98053))),f862(f862(f244(f925(x98053),f925(x98053)),f862(f862(f144(x98053),x98051),x98055)),f862(f862(f144(x98053),x98052),x98056))),f138(x98053,x98054)))+P1(f862(f862(f321(f931(x98053,x98053)),f862(f862(f244(x98053,x98053),x98051),x98052)),x98054))
% 25.54/25.42 [9806]E(x98061,x98062)+~P1(f862(f862(f321(f931(f925(x98063),f925(x98063))),f862(f862(f244(f925(x98063),f925(x98063)),f862(f862(f144(x98063),x98061),x98065)),f862(f862(f144(x98063),x98062),x98066))),f140(x98063,x98064)))+P1(f862(f862(f321(f931(x98063,x98063)),f862(f862(f244(x98063,x98063),x98061),x98062)),x98064))
% 25.54/25.42 [9807]E(x98071,x98072)+~P1(f862(f862(f321(f931(f925(x98073),f925(x98073))),f862(f862(f244(f925(x98073),f925(x98073)),f862(f862(f144(x98073),x98071),x98075)),f862(f862(f144(x98073),x98072),x98076))),f150(x98073,x98074)))+P1(f862(f862(f321(f931(x98073,x98073)),f862(f862(f244(x98073,x98073),x98071),x98072)),x98074))
% 25.54/25.42 [9843]P1(f862(f862(f321(f931(f925(x98431),f925(x98431))),f862(f862(f244(f925(x98431),f925(x98431)),f862(f862(f144(x98431),x98432),x98433)),f862(f862(f144(x98431),x98434),x98435))),f151(x98431,x98436)))+~P1(f862(f862(f321(f931(f925(x98431),f925(x98431))),f862(f862(f244(f925(x98431),f925(x98431)),x98433),x98435)),f151(x98431,x98436)))+~P1(f862(f862(f321(f931(x98431,x98431)),f862(f862(f244(x98431,x98431),x98432),x98434)),x98436))
% 25.54/25.42 [9860]P1(f862(x98601,x98602))+~P1(f862(x98601,f887(x98601,x98603,x98604,x98605,x98606)))+~P1(f862(f862(f321(x98606),x98602),f862(f862(f33(x98605,f932(x98606,a921)),x98604),x98603)))
% 25.54/25.42 [9865]~P1(f862(f862(f321(f931(f925(x98651),f925(x98651))),f862(f862(f244(f925(x98651),f925(x98651)),f862(f862(f144(x98651),x98652),x98655)),f862(f862(f144(x98651),x98653),x98656))),f138(x98651,x98654)))+P1(f862(f862(f321(f931(f925(x98651),f925(x98651))),f862(f862(f244(f925(x98651),f925(x98651)),x98655),x98656)),f138(x98651,x98654)))+P1(f862(f862(f321(f931(x98651,x98651)),f862(f862(f244(x98651,x98651),x98652),x98653)),x98654))
% 25.54/25.42 [9866]~P1(f862(f862(f321(f931(f925(x98661),f925(x98661))),f862(f862(f244(f925(x98661),f925(x98661)),f862(f862(f144(x98661),x98662),x98665)),f862(f862(f144(x98661),x98663),x98666))),f140(x98661,x98664)))+P1(f862(f862(f321(f931(f925(x98661),f925(x98661))),f862(f862(f244(f925(x98661),f925(x98661)),x98665),x98666)),f140(x98661,x98664)))+P1(f862(f862(f321(f931(x98661,x98661)),f862(f862(f244(x98661,x98661),x98662),x98663)),x98664))
% 25.54/25.42 [9867]~P1(f862(f862(f321(f931(f925(x98671),f925(x98671))),f862(f862(f244(f925(x98671),f925(x98671)),f862(f862(f144(x98671),x98672),x98675)),f862(f862(f144(x98671),x98673),x98676))),f150(x98671,x98674)))+P1(f862(f862(f321(f931(f925(x98671),f925(x98671))),f862(f862(f244(f925(x98671),f925(x98671)),x98675),x98676)),f150(x98671,x98674)))+P1(f862(f862(f321(f931(x98671,x98671)),f862(f862(f244(x98671,x98671),x98672),x98673)),x98674))
% 25.54/25.42 [9956]P1(f862(x99561,x99562))+P1(f862(f862(f321(x99563),f888(x99561,x99564,x99565,x99563,x99566)),x99565))+~P1(f862(f862(f321(x99566),x99562),f862(f862(f33(x99563,f932(x99566,a921)),x99565),x99564)))
% 25.54/25.42 [9967]~E(x99672,x99674)+P1(f862(f862(f321(f931(f925(x99671),f925(x99671))),f862(f862(f244(f925(x99671),f925(x99671)),f862(f862(f127(x99671),x99672),f862(f862(f144(x99671),x99673),f106(x99671)))),f862(f862(f127(x99671),x99674),f862(f862(f144(x99671),x99675),f106(x99671))))),f150(x99671,x99676)))+~P1(f862(f862(f321(f931(x99671,x99671)),f862(f862(f244(x99671,x99671),x99673),x99675)),x99676))
% 25.54/25.42 [10043]E(x100431,x100432)+~P1(f862(f862(f321(f931(f925(x100433),f925(x100433))),f862(f862(f244(f925(x100433),f925(x100433)),f862(f862(f127(x100433),x100435),f862(f862(f144(x100433),x100431),f106(x100433)))),f862(f862(f127(x100433),x100436),f862(f862(f144(x100433),x100432),f106(x100433))))),f150(x100433,x100434)))+P1(f862(f862(f321(f931(x100433,x100433)),f862(f862(f244(x100433,x100433),x100431),x100432)),x100434))
% 25.54/25.42 [10074]~P1(f862(f862(f321(f931(f925(x100741),f925(x100741))),f862(f862(f244(f925(x100741),f925(x100741)),f862(f862(f127(x100741),x100745),f862(f862(f144(x100741),x100742),f106(x100741)))),f862(f862(f127(x100741),x100746),f862(f862(f144(x100741),x100743),f106(x100741))))),f150(x100741,x100744)))+P1(f862(f862(f321(f931(f925(x100741),f925(x100741))),f862(f862(f244(f925(x100741),f925(x100741)),x100745),x100746)),f150(x100741,x100744)))+P1(f862(f862(f321(f931(x100741,x100741)),f862(f862(f244(x100741,x100741),x100742),x100743)),x100744))
% 25.54/25.42 [10096]P1(f862(x100961,x100962))+P1(f862(f862(f321(x100963),f887(x100961,x100964,x100965,x100966,x100963)),f862(x100964,f888(x100961,x100964,x100965,x100966,x100963))))+~P1(f862(f862(f321(x100963),x100962),f862(f862(f33(x100966,f932(x100963,a921)),x100965),x100964)))
% 25.54/25.42 [10239]P1(f862(f862(f321(x102391),f842(x102392,x102393,x102394,x102395,x102396,x102391)),x102395))+~P1(f862(f862(f227(f932(x102391,a921)),x102396),x102395))+P1(f862(f862(f227(f932(x102394,a921)),f862(f862(f32(x102391,f932(x102394,a921)),x102395),x102393)),f862(f862(f32(x102391,f932(x102394,a921)),x102395),x102392)))
% 25.54/25.42 [10363]~P1(f862(f862(f227(f932(x103631,a921)),f862(x103634,f842(x103635,x103634,x103631,x103633,x103636,x103632))),f862(x103635,f842(x103635,x103634,x103631,x103633,x103636,x103632))))+~P1(f862(f862(f227(f932(x103632,a921)),x103636),x103633))+P1(f862(f862(f227(f932(x103631,a921)),f862(f862(f32(x103632,f932(x103631,a921)),x103633),x103634)),f862(f862(f32(x103632,f932(x103631,a921)),x103633),x103635)))
% 25.54/25.42 [9090]~P14(x90903,x90904,x90901)+~P1(f862(f54(x90903),x90906))+E(f862(f862(x90901,x90902),f862(f862(f57(x90903,x90904,x90901),x90905),f862(f862(f3(f932(x90903,a921)),x90906),f862(f862(f301(x90903),x90902),f181(f932(x90903,a921)))))),f862(f862(f57(x90903,x90904,x90901),x90905),f862(f862(f301(x90903),x90902),x90906)))
% 25.54/25.42 [9385]~P1(f862(f862(f321(x93855),x93853),x93856))+P1(f862(f862(f227(f932(x93851,a921)),f862(x93852,x93853)),x93854))+~P1(f862(f862(f227(f932(x93851,a921)),f862(f862(f33(x93855,f932(x93851,a921)),x93856),x93852)),x93854))
% 25.54/25.42 [10018]~P6(x100181,x100185,x100184)+P1(f862(f862(f321(f931(x100181,x100181)),f862(f862(f244(x100181,x100181),x100182),x100183)),x100184))+~P1(f862(f862(f321(x100181),x100186),f862(f862(f94(f932(x100181,a921)),f862(f276(x100181,x100181,x100184),f862(f862(f301(x100181),x100182),f181(f932(x100181,a921))))),f862(f276(x100181,x100181,x100184),f862(f862(f301(x100181),x100183),f181(f932(x100181,a921)))))))
% 25.54/25.42 [8809]~P125(x88092)+~E(f862(f862(f73(x88092),f862(f862(f74(x88092),x88094),x88095)),x88091),f862(f862(f73(x88092),f862(f862(f74(x88092),x88093),x88095)),x88096))+E(x88091,f862(f862(f73(x88092),f862(f862(f74(x88092),f862(f862(f3(x88092),x88093),x88094)),x88095)),x88096))
% 25.54/25.42 [8810]~P125(x88101)+~E(f862(f862(f73(x88101),f862(f862(f74(x88101),x88102),x88104)),x88105),f862(f862(f73(x88101),f862(f862(f74(x88101),x88103),x88104)),x88106))+E(f862(f862(f73(x88101),f862(f862(f74(x88101),f862(f862(f3(x88101),x88102),x88103)),x88104)),x88105),x88106)
% 25.54/25.42 [8993]~P125(x89931)+E(f862(f862(f73(x89931),f862(f862(f74(x89931),x89932),x89933)),x89934),f862(f862(f73(x89931),f862(f862(f74(x89931),x89935),x89933)),x89936))+~E(x89936,f862(f862(f73(x89931),f862(f862(f74(x89931),f862(f862(f3(x89931),x89932),x89935)),x89933)),x89934))
% 25.54/25.42 [8994]~P125(x89941)+E(f862(f862(f73(x89941),f862(f862(f74(x89941),x89942),x89943)),x89944),f862(f862(f73(x89941),f862(f862(f74(x89941),x89945),x89943)),x89946))+~E(f862(f862(f73(x89941),f862(f862(f74(x89941),f862(f862(f3(x89941),x89942),x89945)),x89943)),x89944),x89946)
% 25.54/25.42 [9321]~P1(f862(f862(x93214,x93215),x93216))+~P1(f862(f862(x93213,x93215),x93216))+P1(f862(f862(f862(f862(f94(f932(x93211,f932(x93212,a921))),x93213),x93214),x93215),x93216))
% 25.54/25.42 [9586]P1(f862(f862(x95861,x95862),x95863))+P1(f862(f862(x95864,x95862),x95863))+~P1(f862(f862(f862(f862(f103(f932(x95865,f932(x95866,a921))),x95864),x95861),x95862),x95863))
% 25.54/25.42 [9880]~P126(x98801)+~P1(f862(f862(f227(x98801),f862(f862(f73(x98801),f862(f862(f74(x98801),x98804),x98805)),x98802)),f862(f862(f73(x98801),f862(f862(f74(x98801),x98803),x98805)),x98806)))+P1(f862(f862(f227(x98801),x98802),f862(f862(f73(x98801),f862(f862(f74(x98801),f862(f862(f3(x98801),x98803),x98804)),x98805)),x98806)))
% 25.54/25.42 [9881]~P126(x98811)+~P1(f862(f862(f228(x98811),f862(f862(f73(x98811),f862(f862(f74(x98811),x98814),x98815)),x98812)),f862(f862(f73(x98811),f862(f862(f74(x98811),x98813),x98815)),x98816)))+P1(f862(f862(f228(x98811),x98812),f862(f862(f73(x98811),f862(f862(f74(x98811),f862(f862(f3(x98811),x98813),x98814)),x98815)),x98816)))
% 25.54/25.42 [9905]~P126(x99051)+P1(f862(f862(f227(x99051),f862(f862(f73(x99051),f862(f862(f74(x99051),x99052),x99053)),x99054)),f862(f862(f73(x99051),f862(f862(f74(x99051),x99055),x99053)),x99056)))+~P1(f862(f862(f227(x99051),x99054),f862(f862(f73(x99051),f862(f862(f74(x99051),f862(f862(f3(x99051),x99055),x99052)),x99053)),x99056)))
% 25.54/25.42 [9906]~P126(x99061)+P1(f862(f862(f228(x99061),f862(f862(f73(x99061),f862(f862(f74(x99061),x99062),x99063)),x99064)),f862(f862(f73(x99061),f862(f862(f74(x99061),x99065),x99063)),x99066)))+~P1(f862(f862(f228(x99061),x99064),f862(f862(f73(x99061),f862(f862(f74(x99061),f862(f862(f3(x99061),x99065),x99062)),x99063)),x99066)))
% 25.54/25.42 [10010]~P126(x100101)+~P1(f862(f862(f227(x100101),f862(f862(f73(x100101),f862(f862(f74(x100101),x100102),x100104)),x100105)),f862(f862(f73(x100101),f862(f862(f74(x100101),x100103),x100104)),x100106)))+P1(f862(f862(f227(x100101),f862(f862(f73(x100101),f862(f862(f74(x100101),f862(f862(f3(x100101),x100102),x100103)),x100104)),x100105)),x100106))
% 25.54/25.42 [10011]~P126(x100111)+~P1(f862(f862(f228(x100111),f862(f862(f73(x100111),f862(f862(f74(x100111),x100112),x100114)),x100115)),f862(f862(f73(x100111),f862(f862(f74(x100111),x100113),x100114)),x100116)))+P1(f862(f862(f228(x100111),f862(f862(f73(x100111),f862(f862(f74(x100111),f862(f862(f3(x100111),x100112),x100113)),x100114)),x100115)),x100116))
% 25.54/25.42 [10057]~P126(x100571)+P1(f862(f862(f227(x100571),f862(f862(f73(x100571),f862(f862(f74(x100571),x100572),x100573)),x100574)),f862(f862(f73(x100571),f862(f862(f74(x100571),x100575),x100573)),x100576)))+~P1(f862(f862(f227(x100571),f862(f862(f73(x100571),f862(f862(f74(x100571),f862(f862(f3(x100571),x100572),x100575)),x100573)),x100574)),x100576))
% 25.54/25.42 [10058]~P126(x100581)+P1(f862(f862(f228(x100581),f862(f862(f73(x100581),f862(f862(f74(x100581),x100582),x100583)),x100584)),f862(f862(f73(x100581),f862(f862(f74(x100581),x100585),x100583)),x100586)))+~P1(f862(f862(f228(x100581),f862(f862(f73(x100581),f862(f862(f74(x100581),f862(f862(f3(x100581),x100582),x100585)),x100583)),x100584)),x100586))
% 25.54/25.42 [10223]~P72(x102232)+~P1(f862(f54(x102231),x102236))+E(f862(f862(f8(x102231,x102232),f862(f862(f20(x102231,x102232,x102232),f862(f862(f20(x102231,x102232,f932(x102232,x102232)),f862(f862(f10(a921,f932(x102232,f932(x102232,x102232)),x102231),f89(x102232)),x102233)),x102234)),x102235)),x102236),f862(f862(f73(x102232),f862(f862(f8(x102231,x102232),x102234),f862(f862(f94(f932(x102231,a921)),x102236),f862(f254(x102231),x102233)))),f862(f862(f8(x102231,x102232),x102235),f862(f862(f94(f932(x102231,a921)),x102236),f862(f72(f932(x102231,a921)),f862(f254(x102231),x102233))))))
% 25.54/25.42 [10282]P1(f862(f862(f321(x102822),x102824),x102826))+P1(f862(f862(f321(x102822),x102825),x102826))+E(f862(f303(x102821,x102822,f862(f862(f9(x102821,x102822,x102822),f862(f862(f9(x102821,x102822,f932(x102822,x102822)),f862(f862(f10(a921,f932(x102822,f932(x102822,x102822)),x102821),f89(x102822)),f862(f862(f9(x102821,f932(x102821,a921),a921),f321(x102821)),x102823))),x102824)),x102825)),x102826),f181(f932(x102821,a921)))
% 25.54/25.42 [10283]P1(f862(f862(f321(x102832),x102835),x102836))+~P1(f862(f862(f321(x102832),x102834),x102836))+E(f862(f303(x102831,x102832,f862(f862(f9(x102831,x102832,x102832),f862(f862(f9(x102831,x102832,f932(x102832,x102832)),f862(f862(f10(a921,f932(x102832,f932(x102832,x102832)),x102831),f89(x102832)),f862(f862(f9(x102831,f932(x102831,a921),a921),f321(x102831)),x102833))),x102834)),x102835)),x102836),x102833)
% 25.54/25.42 [10284]P1(f862(f862(f321(x102842),x102844),x102846))+~P1(f862(f862(f321(x102842),x102845),x102846))+E(f862(f303(x102841,x102842,f862(f862(f9(x102841,x102842,x102842),f862(f862(f9(x102841,x102842,f932(x102842,x102842)),f862(f862(f10(a921,f932(x102842,f932(x102842,x102842)),x102841),f89(x102842)),f862(f862(f9(x102841,f932(x102841,a921),a921),f321(x102841)),x102843))),x102844)),x102845)),x102846),f862(f72(f932(x102841,a921)),x102843))
% 25.54/25.42 [10285]~P1(f862(f862(f321(x102852),x102854),x102856))+~P1(f862(f862(f321(x102852),x102855),x102856))+E(f862(f303(x102851,x102852,f862(f862(f9(x102851,x102852,x102852),f862(f862(f9(x102851,x102852,f932(x102852,x102852)),f862(f862(f10(a921,f932(x102852,f932(x102852,x102852)),x102851),f89(x102852)),f862(f862(f9(x102851,f932(x102851,a921),a921),f321(x102851)),x102853))),x102854)),x102855)),x102856),f234(f932(x102851,a921)))
% 25.54/25.42 [8842]E(x88421,x88422)+~P54(x88424,x88425,x88423,x88426,x88427)+~E(f862(x88423,x88421),f862(x88423,x88422))
% 25.54/25.42 [8870]~P8(x88706,x88705,x88707,x88704,x88701)+E(f862(f862(x88701,x88702),x88703),x88704)+P1(f862(f54(x88705),x88703))
% 25.54/25.42 [8871]~P8(x88716,x88715,x88717,x88714,x88711)+E(f862(f862(x88711,x88712),x88713),x88714)+P1(f862(f54(x88715),x88713))
% 25.54/25.42 [9747]P40(x97471,x97472,x97473,x97474,x97475,f862(f862(x97473,x97476),x97477))+~E(f862(f862(x97473,x97476),x97477),x97474)+~E(x97475,f181(f932(x97471,a921)))
% 25.54/25.42 [9927]~P1(f862(x99276,x99273))+~P1(f862(f862(f321(f931(x99272,x99272)),f862(f862(f244(x99272,x99272),x99274),x99275)),f862(x99277,x99273)))+P1(f862(f862(f321(f931(f931(x99271,x99272),f931(x99271,x99272))),f862(f862(f244(f931(x99271,x99272),f931(x99271,x99272)),f862(f862(f244(x99271,x99272),x99273),x99274)),f862(f862(f244(x99271,x99272),x99273),x99275))),f272(x99271,x99272,x99276,x99277)))
% 25.54/25.42 [10347]~P40(x103472,x103477,x103473,x103476,x103471,f862(f862(x103473,x103475),x103474))+E(f862(f862(x103473,f751(x103474,x103475,x103471,x103476,x103473,x103477,x103472)),f761(x103474,x103475,x103471,x103476,x103473,x103477,x103472)),f862(f862(x103473,x103475),x103474))+E(x103471,f181(f932(x103472,a921)))
% 25.54/25.42 [10348]~P40(x103487,x103486,x103481,x103484,x103485,f862(f862(x103481,x103482),x103483))+E(f862(f862(x103481,f751(x103483,x103482,x103485,x103484,x103481,x103486,x103487)),f761(x103483,x103482,x103485,x103484,x103481,x103486,x103487)),f862(f862(x103481,x103482),x103483))+E(f862(f862(x103481,x103482),x103483),x103484)
% 25.54/25.42 [9419]~P32(x94191,x94192,x94193,x94195,x94197)+P32(x94191,x94192,x94193,f862(f862(f144(x94191),x94194),x94195),f862(f862(f144(x94192),x94196),x94197))+~P1(f862(f862(x94193,x94194),x94196))
% 25.54/25.42 [9437]P32(x94371,x94372,x94373,x94374,x94375)+~P32(x94371,x94372,x94373,f862(f862(f127(x94371),x94376),x94374),f862(f862(f127(x94372),x94377),x94375))+~E(f862(f182(f925(x94371)),x94376),f862(f182(f925(x94372)),x94377))
% 25.54/25.42 [9438]P32(x94381,x94382,x94383,x94384,x94385)+~P32(x94381,x94382,x94383,f862(f862(f127(x94381),x94384),x94386),f862(f862(f127(x94382),x94385),x94387))+~E(f862(f182(f925(x94381)),x94384),f862(f182(f925(x94382)),x94385))
% 25.54/25.42 [9652]~P32(x96521,x96522,x96523,x96525,x96527)+~P32(x96521,x96522,x96523,x96524,x96526)+P32(x96521,x96522,x96523,f862(f862(f127(x96521),x96524),x96525),f862(f862(f127(x96522),x96526),x96527))
% 25.54/25.42 [10002]~P1(f862(f59(x100021,x100024,x100025,x100026,x100023),x100027))+P1(f862(f59(x100021,x100024,x100025,x100026,f862(f862(f301(x100021),x100022),x100023)),f862(f862(x100025,x100022),x100027)))+P1(f862(f862(f321(x100021),x100022),x100023))
% 25.54/25.42 [10234]~P54(x102347,x102343,x102346,x102345,x102344)+P1(f862(x102341,x102342))+P1(f862(f862(f321(x102343),f901(x102342,x102341,x102344,x102345,x102346,x102343)),x102344))
% 25.54/25.42 [10274]~P54(x102743,x102744,x102745,x102746,x102747)+P1(f862(x102741,x102742))+~P1(f862(x102741,f862(x102746,f901(x102742,x102741,x102747,x102746,x102745,x102744))))
% 25.54/25.42 [10379]~P40(x103792,x103797,x103796,x103795,x103791,f862(f862(x103796,x103794),x103793))+E(x103791,f181(f932(x103792,a921)))+P1(f862(f862(f321(x103792),f751(x103793,x103794,x103791,x103795,x103796,x103797,x103792)),x103791))
% 25.54/25.42 [10380]~P40(x103805,x103807,x103801,x103804,x103806,f862(f862(x103801,x103802),x103803))+E(f862(f862(x103801,x103802),x103803),x103804)+P1(f862(f862(f321(x103805),f751(x103803,x103802,x103806,x103804,x103801,x103807,x103805)),x103806))
% 25.54/25.42 [10467]E(f862(f862(f244(x104671,x104672),x104673),x104674),f862(f862(f244(x104671,x104672),x104675),x104676))+P1(f862(f862(f321(f931(f931(x104671,x104672),f931(x104671,x104672))),f862(f862(f244(f931(x104671,x104672),f931(x104671,x104672)),f862(f862(f244(x104671,x104672),f849(x104677,x104674,x104673,x104676,x104675,x104672,x104671)),f850(x104677,x104674,x104673,x104676,x104675,x104672,x104671))),f862(f862(f244(x104671,x104672),x104673),x104674))),f299(f931(x104671,x104672),x104677)))+~P1(f862(f862(f321(f931(f931(x104671,x104672),f931(x104671,x104672))),f862(f862(f244(f931(x104671,x104672),f931(x104671,x104672)),f862(f862(f244(x104671,x104672),x104675),x104676)),f862(f862(f244(x104671,x104672),x104673),x104674))),f299(f931(x104671,x104672),x104677)))
% 25.54/25.42 [9115]~P19(x91154,x91155,x91156,x91157,x91151)+~P1(f862(f54(x91155),x91153))+E(f862(f862(x91151,x91152),x91153),f862(f862(f862(f58(x91154,x91155,x91156),x91152),x91157),x91153))
% 25.54/25.42 [9116]~P8(x91164,x91165,x91166,x91167,x91161)+~P1(f862(f54(x91165),x91163))+E(f862(f862(x91161,x91162),x91163),f862(f862(f862(f58(x91164,x91165,x91166),x91162),x91167),x91163))
% 25.54/25.42 [9899]~P21(x98993,x98994,x98995,x98997,x98996,x98991)+~P1(f862(f54(x98994),x98992))+E(f862(x98991,x98992),f862(f862(f862(f58(x98993,x98994,x98995),x98996),x98997),x98992))
% 25.54/25.42 [10052]P40(x100521,x100522,x100523,x100524,x100525,f862(f862(x100523,x100526),x100527))+~P40(x100521,x100522,x100523,x100524,f862(f862(f3(f932(x100521,a921)),x100525),f862(f862(f301(x100521),x100526),f181(f932(x100521,a921)))),x100527)+~P1(f862(f862(f321(x100521),x100526),x100525))
% 25.54/25.42 [10403]P1(f862(f862(x104037,f795(x104034,x104035,x104031,x104036,x104033,x104032,x104037)),f796(x104034,x104035,x104031,x104036,x104033,x104032,x104037)))+~P1(f862(f862(x104037,f862(f248(x104032,x104033),x104036)),f862(f243(x104032,x104033),x104036)))+P1(f862(x104031,f862(f862(f249(x104032,x104033,x104034),x104035),x104036)))
% 25.54/25.42 [10413]~P40(x104132,x104133,x104134,x104135,x104131,f862(f862(x104134,x104137),x104136))+P40(x104132,x104133,x104134,x104135,f862(f862(f3(f932(x104132,a921)),x104131),f862(f862(f301(x104132),f751(x104136,x104137,x104131,x104135,x104134,x104133,x104132)),f181(f932(x104132,a921)))),f761(x104136,x104137,x104131,x104135,x104134,x104133,x104132))+E(x104131,f181(f932(x104132,a921)))
% 25.54/25.42 [10414]~P40(x104145,x104146,x104141,x104144,x104147,f862(f862(x104141,x104142),x104143))+P40(x104145,x104146,x104141,x104144,f862(f862(f3(f932(x104145,a921)),x104147),f862(f862(f301(x104145),f751(x104143,x104142,x104147,x104144,x104141,x104146,x104145)),f181(f932(x104145,a921)))),f761(x104143,x104142,x104147,x104144,x104141,x104146,x104145))+E(f862(f862(x104141,x104142),x104143),x104144)
% 25.54/25.42 [10434]~P1(f862(x104341,f862(f862(x104345,f796(x104344,x104345,x104341,x104346,x104343,x104342,x104347)),f795(x104344,x104345,x104341,x104346,x104343,x104342,x104347))))+~P1(f862(f862(x104347,f862(f248(x104342,x104343),x104346)),f862(f243(x104342,x104343),x104346)))+P1(f862(x104341,f862(f862(f249(x104342,x104343,x104344),x104345),x104346)))
% 25.54/25.42 [9732]P1(f862(f862(f227(f932(f931(x97321,x97322),a921)),f862(f862(f280(x97321,x97323,x97322),x97324),x97325)),f862(f862(f280(x97321,x97323,x97322),x97326),x97327)))+~P1(f862(f862(f227(f932(f931(x97323,x97322),a921)),x97325),x97327))+~P1(f862(f862(f227(f932(f931(x97321,x97323),a921)),x97324),x97326))
% 25.54/25.42 [10461]E(f862(f862(f244(x104611,x104612),x104613),x104614),f862(f862(f244(x104611,x104612),x104615),x104616))+~P1(f862(f862(f321(f931(f931(x104611,x104612),f931(x104611,x104612))),f862(f862(f244(f931(x104611,x104612),f931(x104611,x104612)),f862(f862(f244(x104611,x104612),x104613),x104614)),f862(f862(f244(x104611,x104612),x104615),x104616))),f299(f931(x104611,x104612),x104617)))+P1(f862(f862(f321(f931(f931(x104611,x104612),f931(x104611,x104612))),f862(f862(f244(f931(x104611,x104612),f931(x104611,x104612)),f862(f862(f244(x104611,x104612),x104613),x104614)),f862(f862(f244(x104611,x104612),f849(x104617,x104616,x104615,x104614,x104613,x104612,x104611)),f850(x104617,x104616,x104615,x104614,x104613,x104612,x104611)))),x104617))
% 25.54/25.42 [10063]~P1(f862(f862(f321(x100631),x100636),x100635))+P1(f862(f59(x100631,x100632,x100633,x100634,x100635),f862(f862(x100633,x100636),x100637)))+~P1(f862(f59(x100631,x100632,x100633,x100634,f862(f862(f3(f932(x100631,a921)),x100635),f862(f862(f301(x100631),x100636),f181(f932(x100631,a921))))),x100637))
% 25.54/25.42 [10474]~P146(x104741)+~P22(f931(x104742,x104743),x104741,f862(f249(x104742,x104743,x104741),f862(f862(f9(x104742,f932(x104743,x104741),f932(x104743,x104741)),f862(f862(f10(f932(x104741,x104741),f932(f932(x104743,x104741),f932(x104743,x104741)),x104742),f10(x104741,x104741,x104743)),f862(f862(f10(x104741,f932(x104741,x104741),x104742),f74(x104741)),x104744))),x104745)),f862(f862(f246(x104742,x104743),x104746),f862(f18(f932(x104743,a921),x104742),x104747)))+E(f862(f862(f8(x104741,x104741),f25(x104741)),f862(f254(x104741),f862(f862(f10(f932(x104742,a921),a921,x104741),f80(x104742)),f862(f862(f10(f932(x104742,f932(x104743,a921)),f932(x104742,a921),x104741),f862(f10(f932(x104743,a921),a921,x104742),f80(x104743))),f862(f862(f9(x104741,f932(x104742,f932(x104743,a921)),f932(x104742,f932(x104743,a921))),f862(f862(f10(f932(x104742,f932(f932(x104743,a921),f932(x104743,a921))),f932(f932(x104742,f932(x104743,a921)),f932(x104742,f932(x104743,a921))),x104741),f20(x104742,f932(x104743,a921),f932(x104743,a921))),f862(f862(f10(f932(x104742,f932(x104743,f932(a921,a921))),f932(x104742,f932(f932(x104743,a921),f932(x104743,a921))),x104741),f862(f10(f932(x104743,f932(a921,a921)),f932(f932(x104743,a921),f932(x104743,a921)),x104742),f20(x104743,a921,a921))),f862(f862(f10(f932(x104742,f932(x104743,a921)),f932(x104742,f932(x104743,f932(a921,a921))),x104741),f862(f10(f932(x104743,a921),f932(x104743,f932(a921,a921)),x104742),f862(f10(a921,f932(a921,a921),x104743),a318))),f862(f862(f9(x104741,f932(x104742,f932(x104743,x104741)),f932(x104742,f932(x104743,a921))),f862(f862(f10(f932(f932(x104743,x104741),f932(x104743,a921)),f932(f932(x104742,f932(x104743,x104741)),f932(x104742,f932(x104743,a921))),x104741),f10(f932(x104743,x104741),f932(x104743,a921),x104742)),f862(f862(f10(f932(x104741,a921),f932(f932(x104743,x104741),f932(x104743,a921)),x104741),f10(x104741,a921,x104743)),a317))),f862(f862(f9(x104742,f932(x104743,x104741),f932(x104743,x104741)),f862(f862(f10(f932(x104741,x104741),f932(f932(x104743,x104741),f932(x104743,x104741)),x104742),f10(x104741,x104741,x104743)),f862(f862(f10(x104741,f932(x104741,x104741),x104742),f74(x104741)),x104744))),x104745)))))),f862(f862(f9(x104742,f932(x104743,a921),f932(x104743,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104743,a921),f932(x104743,a921)),x104742),f10(a921,a921,x104743)),f862(f862(f10(a921,f932(a921,a921),x104742),a318),f862(f862(f9(x104742,f932(x104742,a921),a921),f321(x104742)),x104746)))),f862(f862(f9(x104743,f932(x104743,a921),a921),f321(x104743)),x104747))))))),f862(f862(f74(x104741),f862(f862(f8(x104742,x104741),x104744),x104746)),f862(f862(f8(x104743,x104741),x104745),x104747)))
% 25.54/25.42 [9735]~P23(x97353,x97352,x97354,x97358,x97357)+~P23(x97351,x97353,x97355,x97356,x97358)+P23(x97351,x97352,f862(f66(x97353,x97352,x97351,x97354),x97355),x97356,x97357)
% 25.54/25.42 [9736]~P23(x97361,x97363,x97365,x97366,x97368)+~P23(x97363,x97362,x97364,x97368,x97367)+P23(x97361,x97362,f862(f66(x97363,x97362,x97361,x97364),x97365),x97366,x97367)
% 25.54/25.42 [9765]P23(x97651,x97652,x97653,x97654,x97655)+~P23(x97656,x97651,x97657,x97658,x97654)+~P23(x97656,x97652,f862(f66(x97651,x97652,x97656,x97653),x97657),x97658,x97655)
% 25.54/25.42 [9896]~P1(f862(f862(x98964,x98966),x98968))+~P1(f862(f862(x98965,x98968),x98967))+P1(f862(f862(f245(x98961,x98962,x98963,x98964,x98965),x98966),x98967))
% 25.54/25.42 [9897]~P1(f862(f862(x98974,x98976),x98978))+~P1(f862(f862(x98975,x98978),x98977))+P1(f862(f862(f245(x98971,x98972,x98973,x98974,x98975),x98976),x98977))
% 25.54/25.42 [9490]~P17(x94908,x94901,x94903,x94905)+~P1(f862(f54(x94908),x94906))+E(f862(f66(x94901,x94901,x94902,f862(x94903,x94904)),f862(f66(x94901,x94901,x94902,f862(x94905,x94906)),x94907)),f862(f66(x94901,x94901,x94902,f862(x94905,x94906)),f862(f66(x94901,x94901,x94902,f862(x94903,x94904)),x94907)))
% 25.54/25.42 [9887]~P20(x98877,x98872,x98875,x98878,x98876,x98871)+~P1(f862(f54(x98872),x98874))+E(f862(x98871,f862(f862(f301(x98872),x98873),x98874)),f862(f862(x98875,f862(x98876,x98873)),f862(x98871,x98874)))
% 25.54/25.42 [10008]~P22(x100082,x100084,x100086,x100088)+~P22(x100081,x100083,x100085,x100087)+P22(f931(x100081,x100082),f931(x100083,x100084),f250(x100081,x100083,x100082,x100084,x100085,x100086),f862(f862(f246(x100081,x100082),x100087),f862(f18(f932(x100082,a921),x100081),x100088)))
% 25.54/25.42 [9678]P1(f862(f862(f321(f931(x96781,x96782)),f862(f862(f244(x96781,x96782),x96783),x96784)),f862(f862(f280(x96781,x96785,x96782),x96786),x96787)))+~P1(f862(f862(f321(f931(x96781,x96785)),f862(f862(f244(x96781,x96785),x96783),x96788)),x96786))+~P1(f862(f862(f321(f931(x96785,x96782)),f862(f862(f244(x96785,x96782),x96788),x96784)),x96787))
% 25.54/25.42 [9868]~P1(f862(f862(f227(f932(f931(x98683,x98682),a921)),x98685),f862(f862(f246(x98683,x98682),x98688),f862(f18(f932(x98682,a921),x98683),x98687))))+~P1(f862(f862(f227(f932(f931(x98681,x98683),a921)),x98684),f862(f862(f246(x98681,x98683),x98686),f862(f18(f932(x98683,a921),x98681),x98688))))+P1(f862(f862(f227(f932(f931(x98681,x98682),a921)),f862(f862(f280(x98681,x98683,x98682),x98684),x98685)),f862(f862(f246(x98681,x98682),x98686),f862(f18(f932(x98682,a921),x98681),x98687))))
% 25.54/25.42 [9922]~E(x99223,x99225)+P1(f862(f862(f321(f931(f931(x99221,x99222),f931(x99221,x99222))),f862(f862(f244(f931(x99221,x99222),f931(x99221,x99222)),f862(f862(f244(x99221,x99222),x99223),x99224)),f862(f862(f244(x99221,x99222),x99225),x99226))),f311(x99221,x99222,x99227,x99228)))+~P1(f862(f862(f321(f931(x99222,x99222)),f862(f862(f244(x99222,x99222),x99224),x99226)),x99228))
% 25.54/25.42 [10027]E(x100271,x100272)+~P1(f862(f862(f321(f931(f931(x100273,x100275),f931(x100273,x100275))),f862(f862(f244(f931(x100273,x100275),f931(x100273,x100275)),f862(f862(f244(x100273,x100275),x100271),x100276)),f862(f862(f244(x100273,x100275),x100272),x100277))),f311(x100273,x100275,x100274,x100278)))+P1(f862(f862(f321(f931(x100273,x100273)),f862(f862(f244(x100273,x100273),x100271),x100272)),x100274))
% 25.54/25.42 [10042]~P1(f862(f862(f321(f931(f931(x100421,x100425),f931(x100421,x100425))),f862(f862(f244(f931(x100421,x100425),f931(x100421,x100425)),f862(f862(f244(x100421,x100425),x100422),x100426)),f862(f862(f244(x100421,x100425),x100423),x100427))),f311(x100421,x100425,x100424,x100428)))+P1(f862(f862(f321(f931(x100421,x100421)),f862(f862(f244(x100421,x100421),x100422),x100423)),x100424))+P1(f862(f862(f321(f931(x100425,x100425)),f862(f862(f244(x100425,x100425),x100426),x100427)),x100428))
% 25.54/25.42 [9957]~P21(x99577,x99575,x99571,x99578,x99572,x99574)+~P1(f862(f54(x99575),x99576))+E(f862(f862(x99571,f862(x99572,x99573)),f862(x99574,f862(f862(f3(f932(x99575,a921)),x99576),f862(f862(f301(x99575),x99573),f181(f932(x99575,a921)))))),f862(x99574,f862(f862(f301(x99575),x99573),x99576)))
% 25.54/25.42 [9443]~P1(f862(f862(f862(x94435,x94438),x94436),x94437))+~P1(f862(f862(f321(x94431),x94438),x94434))+P1(f862(f862(f862(f862(f33(x94431,f932(x94432,f932(x94433,a921))),x94434),x94435),x94436),x94437))
% 25.54/25.42 [9444]~P1(f862(f862(f862(x94445,x94448),x94446),x94447))+~P1(f862(f862(f321(x94441),x94448),x94444))+P1(f862(f862(f862(f862(f33(x94441,f932(x94442,f932(x94443,a921))),x94444),x94445),x94446),x94447))
% 25.54/25.42 [9661]P1(f862(f862(f862(x96611,x96612),x96613),x96614))+~P1(f862(f862(f321(x96615),x96612),x96616))+~P1(f862(f862(f862(f862(f32(x96615,f932(x96617,f932(x96618,a921))),x96616),x96611),x96613),x96614))
% 25.54/25.42 [9662]P1(f862(f862(f862(x96621,x96622),x96623),x96624))+~P1(f862(f862(f321(x96625),x96622),x96626))+~P1(f862(f862(f862(f862(f32(x96625,f932(x96627,f932(x96628,a921))),x96626),x96621),x96623),x96624))
% 25.54/25.42 [9663]P1(f862(f862(f862(x96631,x96632),x96633),x96634))+~P1(f862(f862(f321(x96635),x96632),x96636))+~P1(f862(f862(f862(f862(f32(x96635,f932(x96637,f932(x96638,a921))),x96636),x96631),x96633),x96634))
% 25.54/25.42 [9861]~P19(x98613,x98612,x98614,x98618,x98611)+~P1(f862(f54(x98612),x98617))+E(f862(f862(x98611,f862(f862(f20(x98612,x98613,x98613),f862(f862(f10(x98613,f932(x98613,x98613),x98612),x98614),x98615)),x98616)),x98617),f862(f862(x98614,f862(f862(x98611,x98615),x98617)),f862(f862(x98611,x98616),x98617)))
% 25.54/25.42 [10131]~E(f862(f302(x101312,x101314,x101316),x101318),x1013110)+~E(f862(f302(x101311,x101313,x101315),x101317),x101319)+E(f862(f302(f931(x101311,x101312),f931(x101313,x101314),f250(x101311,x101313,x101312,x101314,x101315,x101316)),f862(f862(f246(x101311,x101312),x101317),f862(f18(f932(x101312,a921),x101311),x101318))),f862(f862(f246(x101313,x101314),x101319),f862(f18(f932(x101314,a921),x101313),x1013110)))
% 25.54/25.42 [5051]~P46(x50511,x50512)+~P47(x50511,x50512)+~P48(x50511,x50512)+P5(x50511,x50512)
% 25.54/25.42 [5052]~P46(x50521,x50522)+~P47(x50521,x50522)+~P48(x50521,x50522)+P5(x50521,x50522)
% 25.54/25.42 [5008]~P109(x50082)+~P11(x50082,x50081)+P11(x50082,f107(x50082,x50081))+E(x50081,f106(x50082))
% 25.54/25.42 [5009]~P109(x50092)+~P11(x50092,x50091)+P11(x50092,f714(x50091,x50092))+E(x50091,f106(x50092))
% 25.54/25.42 [5258]~P3(x52582)+E(f12(x52582,x52581),f31(x52582,x52581))+E(x52581,f181(f932(x52582,a921)))+~P1(f862(f54(x52582),x52581))
% 25.54/25.42 [5259]~P3(x52592)+E(f15(x52592,x52591),f30(x52592,x52591))+E(x52591,f181(f932(x52592,a921)))+~P1(f862(f54(x52592),x52591))
% 25.54/25.42 [5418]~P109(x54182)+~P11(x54182,x54181)+E(x54181,f106(x54182))+E(f862(f862(f144(x54182),f733(x54181,x54182)),f714(x54181,x54182)),x54181)
% 25.54/25.42 [6239]~P93(x62392)+E(x62391,f181(f932(x62392,a921)))+P1(f862(f862(f227(x62392),f12(x62392,x62391)),f15(x62392,x62391)))+~P1(f862(f54(x62392),x62391))
% 25.54/25.42 [6248]~P38(x62482)+~P38(x62481)+E(x62481,x62482)+~E(f862(f302(a1,a924,a97),x62481),f862(f302(a1,a924,a97),x62482))
% 25.54/25.42 [9300]~P112(x93001)+~P1(f862(f862(f321(x93001),x93002),f102(x93001)))+P1(f862(f862(f228(x93001),f862(f862(f73(x93001),f862(f862(f73(x93001),f71(x93001)),x93002)),x93002)),f2(x93001)))+~P1(f862(f862(f228(x93001),x93002),f2(x93001)))
% 25.54/25.42 [9544]~P112(x95441)+~P1(f862(f862(f321(x95441),x95442),f102(x95441)))+~P1(f862(f862(f228(x95441),f862(f862(f73(x95441),f862(f862(f73(x95441),f71(x95441)),x95442)),x95442)),f2(x95441)))+P1(f862(f862(f228(x95441),x95442),f2(x95441)))
% 25.54/25.42 [5067]~P116(x50672)+~P146(x50672)+E(x50671,f2(a924))+E(f862(f862(f236(x50672),f2(x50672)),x50671),f2(x50672))
% 25.54/25.42 [5070]~P116(x50701)+~P146(x50701)+~E(x50702,f2(a924))+E(f862(f862(f236(x50701),f2(x50701)),x50702),f71(x50701))
% 25.54/25.42 [5244]~P141(x52442)+E(x52441,f71(x52442))+E(x52441,f862(f72(x52442),f71(x52442)))+~E(f862(f862(f74(x52442),x52441),x52441),f71(x52442))
% 25.54/25.42 [5494]~P88(x54942)+E(x54941,f2(x54942))+E(f75(x54942,x54941),f862(f72(x54942),f71(x54942)))+P1(f862(f862(f228(x54942),f2(x54942)),x54941))
% 25.54/25.42 [5691]~E(x56912,f71(a1))+~E(x56911,f71(a1))+E(f862(f862(f74(a1),x56911),x56912),f71(a1))+~P1(f862(f862(f228(a1),f2(a1)),x56911))
% 25.54/25.42 [5738]~P88(x57382)+E(f75(x57382,x57381),f71(x57382))+E(x57381,f2(x57382))+~P1(f862(f862(f228(x57382),f2(x57382)),x57381))
% 25.54/25.42 [5748]E(x57481,x57482)+~E(f862(f96(a924),x57481),f862(f96(a924),x57482))+P1(f862(a186,f862(f96(a1),x57482)))+P1(f862(a186,f862(f96(a1),x57481)))
% 25.54/25.42 [5799]~P97(x57991)+~E(x57992,f2(x57991))+E(f862(f862(f73(x57991),x57992),x57992),f2(x57991))+~P1(f862(f862(f321(x57991),x57992),f102(x57991)))
% 25.54/25.42 [5838]E(x58381,f2(a1))+~E(f862(f862(f29(a1),x58382),x58381),f2(a1))+P1(f862(f862(f228(a1),x58381),x58382))+P1(f862(f862(f228(a1),x58382),x58381))
% 25.54/25.42 [5868]E(x58681,f2(a1))+~E(f862(f862(f29(a1),x58682),x58681),f2(a1))+P1(f862(f862(f227(a1),x58682),f2(a1)))+P1(f862(f862(f228(a1),x58682),x58681))
% 25.54/25.42 [5902]E(x59021,f2(a1))+~E(f862(f862(f29(a1),x59022),x59021),f2(a1))+P1(f862(f862(f227(a1),f2(a1)),x59022))+P1(f862(f862(f228(a1),x59021),x59022))
% 25.54/25.42 [5935]E(x59351,f2(a1))+~E(f862(f862(f29(a1),x59352),x59351),f2(a1))+P1(f862(f862(f227(a1),x59352),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),x59352))
% 25.54/25.42 [5937]~P97(x59372)+E(x59371,f2(x59372))+~E(f862(f862(f73(x59372),x59371),x59371),f2(x59372))+~P1(f862(f862(f321(x59372),x59371),f102(x59372)))
% 25.54/25.42 [6008]E(f862(f96(a924),x60081),f862(f96(a924),x60082))+~E(f862(f96(a1),x60082),f2(a1))+P1(f862(a186,f862(f96(a1),x60082)))+~P1(f862(a186,f862(f96(a1),x60081)))
% 25.54/25.42 [6037]~E(f862(f96(a924),x60372),f862(f96(a924),x60371))+E(f862(f96(a1),x60371),f2(a1))+P1(f862(a186,f862(f96(a1),x60371)))+~P1(f862(a186,f862(f96(a1),x60372)))
% 25.54/25.42 [6047]~P109(x60472)+E(x60471,f181(f932(x60472,a921)))+~P1(f862(f54(x60472),x60471))+P1(f862(f862(f321(x60472),f16(x60472,x60471)),x60471))
% 25.54/25.42 [6048]~P109(x60482)+E(x60481,f181(f932(x60482,a921)))+~P1(f862(f54(x60482),x60481))+P1(f862(f862(f321(x60482),f17(x60482,x60481)),x60481))
% 25.54/25.42 [6216]~P112(x62161)+~P98(x62161)+P1(f862(f862(f227(x62161),f2(x62161)),f862(f96(x62161),x62162)))+~P1(f862(f862(f227(a1),a76),x62162))
% 25.54/25.42 [6217]~P112(x62171)+~P98(x62171)+P1(f862(f862(f228(x62171),f2(x62171)),f862(f96(x62171),x62172)))+~P1(f862(f862(f228(a1),a76),x62172))
% 25.54/25.42 [6238]~P112(x62381)+~P98(x62381)+E(f862(f69(x62381),f862(f96(x62381),x62382)),f862(f96(x62381),x62382))+P1(f862(f862(f228(x62381),f862(f96(x62381),x62382)),f2(x62381)))
% 25.54/25.42 [6271]E(x62711,x62712)+~E(f862(a97,x62711),f862(a97,x62712))+~P1(f862(f862(f227(a1),f2(a1)),x62712))+~P1(f862(f862(f227(a1),f2(a1)),x62711))
% 25.54/25.42 [6272]E(x62721,x62722)+~E(f862(a97,x62721),f862(a97,x62722))+~P1(f862(f862(f227(a1),f2(a1)),x62722))+~P1(f862(f862(f227(a1),f2(a1)),x62721))
% 25.54/25.42 [6302]~E(x63021,f2(a1))+E(f39(x63021,x63022),f862(f862(f244(a1,a1),f2(a1)),f2(a1)))+P1(f862(f862(f227(a1),f2(a1)),x63022))+~P1(f862(f862(f227(a1),f2(a1)),x63021))
% 25.54/25.42 [6467]~P98(x64672)+~P112(x64672)+~P1(f862(f862(f227(x64672),f2(x64672)),f862(f96(x64672),x64671)))+P1(f862(f862(f227(a1),a76),x64671))
% 25.54/25.42 [6468]~P98(x64682)+~P112(x64682)+~P1(f862(f862(f228(x64682),f2(x64682)),f862(f96(x64682),x64681)))+P1(f862(f862(f228(a1),a76),x64681))
% 25.54/25.42 [6473]~P112(x64731)+~P98(x64731)+P1(f862(f862(f227(x64731),f862(f96(x64731),x64732)),f2(x64731)))+~P1(f862(f862(f227(a1),x64732),a76))
% 25.54/25.42 [6474]~P112(x64741)+~P98(x64741)+P1(f862(f862(f228(x64741),f862(f96(x64741),x64742)),f2(x64741)))+~P1(f862(f862(f228(a1),x64742),a76))
% 25.54/25.42 [6793]~P98(x67932)+~P112(x67932)+~P1(f862(f862(f227(x67932),f862(f96(x67932),x67931)),f2(x67932)))+P1(f862(f862(f227(a1),x67931),a76))
% 25.54/25.42 [6794]~P98(x67942)+~P112(x67942)+~P1(f862(f862(f228(x67942),f862(f96(x67942),x67941)),f2(x67942)))+P1(f862(f862(f228(a1),x67941),a76))
% 25.54/25.42 [6884]~P112(x68841)+~P98(x68841)+E(f862(f69(x68841),f862(f96(x68841),x68842)),f862(f72(x68841),f862(f96(x68841),x68842)))+~P1(f862(f862(f228(x68841),f862(f96(x68841),x68842)),f2(x68841)))
% 25.54/25.42 [6902]E(f862(f96(a924),x69021),f862(f96(a924),x69022))+~E(f862(f96(a1),x69022),f2(a1))+~P1(f862(f862(f227(a1),f862(f96(a1),x69021)),f2(a1)))+~P1(f862(a186,f862(f96(a1),x69021)))
% 25.54/25.42 [7071]E(x70711,x70712)+~E(f862(a5,x70711),f862(a5,x70712))+~P1(f862(f862(f321(a924),x70712),f234(f932(a924,a921))))+~P1(f862(f862(f321(a924),x70711),f234(f932(a924,a921))))
% 25.54/25.42 [7297]P1(f862(f862(f227(a924),f862(a97,x72971)),f862(a97,x72972)))+~P1(f862(f862(f227(a1),f2(a1)),x72972))+~P1(f862(f862(f227(a1),f2(a1)),x72971))+~P1(f862(f862(f227(a1),x72971),x72972))
% 25.54/25.42 [7298]P1(f862(f862(f228(a924),f862(a97,x72981)),f862(a97,x72982)))+~P1(f862(f862(f227(a1),f2(a1)),x72982))+~P1(f862(f862(f227(a1),f2(a1)),x72981))+~P1(f862(f862(f228(a1),x72981),x72982))
% 25.54/25.42 [7534]~P4(x75341)+~P38(x75342)+~P1(f862(f862(f321(a1),x75341),x75342))+P1(f862(f862(f321(a924),f862(a97,x75341)),f862(f302(a1,a924,a97),x75342)))
% 25.54/25.42 [7539]~P1(f862(f862(f227(a924),f862(a97,x75391)),f862(a97,x75392)))+~P1(f862(f862(f227(a1),f2(a1)),x75392))+~P1(f862(f862(f227(a1),f2(a1)),x75391))+P1(f862(f862(f227(a1),x75391),x75392))
% 25.54/25.42 [7540]~P1(f862(f862(f228(a924),f862(a97,x75401)),f862(a97,x75402)))+~P1(f862(f862(f227(a1),f2(a1)),x75402))+~P1(f862(f862(f227(a1),f2(a1)),x75401))+P1(f862(f862(f228(a1),x75401),x75402))
% 25.54/25.42 [7788]~P109(x77882)+E(x77881,f181(f932(x77882,a921)))+~P1(f862(f54(x77882),x77881))+P1(f862(f862(f227(x77882),f13(x77882,f225(x77882),x77881)),f14(x77882,f226(x77882),x77881)))
% 25.54/25.42 [8108]~P4(x81081)+~P38(x81082)+P1(f862(f862(f321(a1),x81081),x81082))+~P1(f862(f862(f321(a924),f862(a97,x81081)),f862(f302(a1,a924,a97),x81082)))
% 25.54/25.42 [6043]~P142(x60432)+E(x60431,f2(a1))+E(f862(f72(x60432),f862(f95(x60432),f862(f72(a1),x60431))),f862(f95(x60432),x60431))+~P1(f862(f862(f228(a1),x60431),f2(a1)))
% 25.54/25.42 [6121]~P97(x61211)+~P98(x61211)+~P26(x61211,f862(f96(x61211),x61212))+P26(x61211,f862(f96(x61211),f862(f862(f73(a1),x61212),x61212)))
% 25.54/25.42 [6456]~P76(x64562)+E(x64561,f181(f932(x64562,a921)))+E(f17(x64562,f862(f302(x64562,x64562,f72(x64562)),x64561)),f862(f72(x64562),f16(x64562,x64561)))+~P1(f862(f54(x64562),x64561))
% 25.54/25.42 [6457]~P76(x64572)+E(x64571,f181(f932(x64572,a921)))+E(f16(x64572,f862(f302(x64572,x64572,f72(x64572)),x64571)),f862(f72(x64572),f17(x64572,x64571)))+~P1(f862(f54(x64572),x64571))
% 25.54/25.42 [6490]~P97(x64901)+~P98(x64901)+P26(x64901,f862(f96(x64901),x64902))+~P26(x64901,f862(f96(x64901),f862(f862(f73(a1),x64902),x64902)))
% 25.54/25.42 [6584]E(x65841,f2(a1))+E(f862(a44,f43(f862(f72(a1),x65841),f862(f72(a1),x65842))),f39(x65841,x65842))+P1(f862(f862(f227(a1),f2(a1)),x65842))+~P1(f862(f862(f227(a1),f2(a1)),x65841))
% 25.54/25.42 [7450]~P1(f862(f862(f227(a1),f2(a1)),x74501))+~P1(f862(f862(f228(a1),f2(a1)),x74502))+~P1(f862(f862(f227(a1),x74502),x74501))+P1(f862(f862(f228(a1),f2(a1)),f862(f862(f29(a1),x74501),x74502)))
% 25.54/25.42 [7863]~E(x78632,f2(a1))+E(f208(x78631,x78632),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x78632),f2(a1)))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x78631),x78632)))
% 25.54/25.42 [7864]~E(x78641,f2(a1))+E(f208(x78641,x78642),f862(f862(f244(a1,a1),f2(a1)),f71(a1)))+P1(f862(f862(f228(a1),x78642),f2(a1)))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x78641),x78642)))
% 25.54/25.42 [8899]~P38(x88992)+~P38(x88991)+P1(f862(f862(f227(f932(a924,a921)),f862(f302(a1,a924,a97),x88991)),f862(f302(a1,a924,a97),x88992)))+~P1(f862(f862(f227(f932(a1,a921)),x88991),x88992))
% 25.54/25.42 [8900]~P38(x89002)+~P38(x89001)+P1(f862(f862(f228(f932(a924,a921)),f862(f302(a1,a924,a97),x89001)),f862(f302(a1,a924,a97),x89002)))+~P1(f862(f862(f228(f932(a1,a921)),x89001),x89002))
% 25.54/25.42 [9133]~E(f737(x91332,x91331),f738(x91332,x91331))+~P1(f862(f130(x91331),f736(x91332,x91331)))+~P1(f862(f130(f925(x91331)),x91332))+P1(f862(f130(x91331),f862(f135(f925(x91331),f925(x91331),f127(x91331),f106(x91331)),x91332)))
% 25.54/25.42 [9219]~P38(x92192)+~P38(x92191)+~P1(f862(f862(f227(f932(a924,a921)),f862(f302(a1,a924,a97),x92191)),f862(f302(a1,a924,a97),x92192)))+P1(f862(f862(f227(f932(a1,a921)),x92191),x92192))
% 25.54/25.42 [9220]~P38(x92202)+~P38(x92201)+~P1(f862(f862(f228(f932(a924,a921)),f862(f302(a1,a924,a97),x92201)),f862(f302(a1,a924,a97),x92202)))+P1(f862(f862(f228(f932(a1,a921)),x92201),x92202))
% 25.54/25.42 [9226]~E(f737(x92262,x92261),f738(x92262,x92261))+~P1(f862(f130(f925(x92261)),x92262))+P1(f862(f130(x92261),f862(f135(f925(x92261),f925(x92261),f127(x92261),f106(x92261)),x92262)))+P1(f862(f862(f321(f925(x92261)),f736(x92262,x92261)),f862(f165(f925(x92261)),x92262)))
% 25.54/25.42 [9267]~P1(f862(f130(x92671),f736(x92672,x92671)))+~P1(f862(f130(f925(x92671)),x92672))+P1(f862(f130(x92671),f862(f135(f925(x92671),f925(x92671),f127(x92671),f106(x92671)),x92672)))+P1(f862(f862(f321(f925(x92671)),f738(x92672,x92671)),f862(f165(f925(x92671)),x92672)))
% 25.54/25.42 [9268]~P1(f862(f130(x92681),f736(x92682,x92681)))+~P1(f862(f130(f925(x92681)),x92682))+P1(f862(f130(x92681),f862(f135(f925(x92681),f925(x92681),f127(x92681),f106(x92681)),x92682)))+P1(f862(f862(f321(f925(x92681)),f737(x92682,x92681)),f862(f165(f925(x92681)),x92682)))
% 25.54/25.42 [9347]~P1(f862(f130(f925(x93471)),x93472))+P1(f862(f130(x93471),f862(f135(f925(x93471),f925(x93471),f127(x93471),f106(x93471)),x93472)))+P1(f862(f862(f321(f925(x93471)),f738(x93472,x93471)),f862(f165(f925(x93471)),x93472)))+P1(f862(f862(f321(f925(x93471)),f736(x93472,x93471)),f862(f165(f925(x93471)),x93472)))
% 25.54/25.42 [9348]~P1(f862(f130(f925(x93481)),x93482))+P1(f862(f130(x93481),f862(f135(f925(x93481),f925(x93481),f127(x93481),f106(x93481)),x93482)))+P1(f862(f862(f321(f925(x93481)),f737(x93482,x93481)),f862(f165(f925(x93481)),x93482)))+P1(f862(f862(f321(f925(x93481)),f736(x93482,x93481)),f862(f165(f925(x93481)),x93482)))
% 25.54/25.42 [9362]~E(f862(f862(f94(f932(x93621,a921)),f862(f165(x93621),f738(x93622,x93621))),f862(f165(x93621),f737(x93622,x93621))),f181(f932(x93621,a921)))+~P1(f862(f130(x93621),f736(x93622,x93621)))+~P1(f862(f130(f925(x93621)),x93622))+P1(f862(f130(x93621),f862(f135(f925(x93621),f925(x93621),f127(x93621),f106(x93621)),x93622)))
% 25.54/25.42 [9425]~E(f862(f862(f94(f932(x94251,a921)),f862(f165(x94251),f738(x94252,x94251))),f862(f165(x94251),f737(x94252,x94251))),f181(f932(x94251,a921)))+~P1(f862(f130(f925(x94251)),x94252))+P1(f862(f130(x94251),f862(f135(f925(x94251),f925(x94251),f127(x94251),f106(x94251)),x94252)))+P1(f862(f862(f321(f925(x94251)),f736(x94252,x94251)),f862(f165(f925(x94251)),x94252)))
% 25.54/25.42 [9705]E(x97051,f2(a1))+E(x97052,f2(a1))+E(f862(f862(f79(a1,f931(a1,a1)),f862(f862(a210,x97052),x97051)),f862(f862(f20(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f29(a1),x97052))),f862(f29(a1),x97051))),f208(x97052,x97051))+P1(f862(f862(f228(a1),x97051),f2(a1)))
% 25.54/25.42 [8440]~P98(x84402)+~P112(x84402)+~P1(f862(f862(f227(x84402),f862(f96(x84402),x84401)),f71(x84402)))+P1(f862(f862(f227(a1),x84401),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))
% 25.54/25.42 [8441]~P98(x84412)+~P112(x84412)+~P1(f862(f862(f228(x84412),f862(f96(x84412),x84411)),f71(x84412)))+P1(f862(f862(f228(a1),x84411),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))
% 25.54/25.42 [8714]~P112(x87141)+~P98(x87141)+P1(f862(f862(f227(x87141),f862(f96(x87141),x87142)),f71(x87141)))+~P1(f862(f862(f227(a1),x87142),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))
% 25.54/25.42 [8715]~P112(x87151)+~P98(x87151)+P1(f862(f862(f228(x87151),f862(f96(x87151),x87152)),f71(x87151)))+~P1(f862(f862(f228(a1),x87152),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))
% 25.54/25.42 [8928]~P98(x89282)+~P112(x89282)+~P1(f862(f862(f227(x89282),f71(x89282)),f862(f96(x89282),x89281)))+P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x89281))
% 25.54/25.42 [8929]~P98(x89292)+~P112(x89292)+~P1(f862(f862(f228(x89292),f71(x89292)),f862(f96(x89292),x89291)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x89291))
% 25.54/25.42 [9306]~P112(x93061)+~P98(x93061)+P1(f862(f862(f227(x93061),f71(x93061)),f862(f96(x93061),x93062)))+~P1(f862(f862(f227(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x93062))
% 25.54/25.42 [9307]~P112(x93071)+~P98(x93071)+P1(f862(f862(f228(x93071),f71(x93071)),f862(f96(x93071),x93072)))+~P1(f862(f862(f228(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),x93072))
% 25.54/25.42 [9834]~P141(x98342)+E(x98341,f71(x98342))+E(x98341,f862(f72(x98342),f71(x98342)))+~E(f862(f862(f236(x98342),x98341),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f71(x98342))
% 25.54/25.42 [10106]~P66(x101061)+~P98(x101061)+~P1(f862(f862(f228(x101061),f2(x101061)),x101062))+P1(f862(f862(f228(x101061),f2(x101061)),f862(f862(f281(x101061),x101062),f862(f96(x101061),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.42 [10107]~P66(x101071)+~P98(x101071)+~P1(f862(f862(f228(x101071),f2(x101071)),x101072))+P1(f862(f862(f228(x101071),f2(x101071)),f862(f862(f281(x101071),x101072),f862(f96(x101071),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.42 [10159]~P66(x101591)+~P98(x101591)+P1(f862(f862(f228(x101591),f2(x101591)),x101592))+~P1(f862(f862(f228(x101591),f2(x101591)),f862(f862(f281(x101591),x101592),f862(f96(x101591),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.42 [10441]~P142(x104412)+E(x104411,f2(a1))+P1(f862(f862(f228(a1),x104411),f2(a1)))+E(f862(f862(f249(a1,a1,x104412),f862(f862(f9(a1,f932(a1,f932(x104412,x104412)),f932(a1,x104412)),f862(f862(f10(f932(f932(x104412,x104412),x104412),f932(f932(a1,f932(x104412,x104412)),f932(a1,x104412)),a1),f10(f932(x104412,x104412),x104412,a1)),f862(f862(f10(x104412,f932(f932(x104412,x104412),x104412),a1),f79(x104412,x104412)),f95(x104412)))),f862(f862(f9(a1,f932(x104412,x104412),f932(x104412,x104412)),f862(f862(f10(f932(x104412,f932(x104412,x104412)),f932(f932(x104412,x104412),f932(x104412,x104412)),a1),f20(x104412,x104412,x104412)),f862(f862(f9(a1,f932(x104412,x104412),f932(x104412,f932(x104412,x104412))),f862(f862(f10(f932(x104412,f932(x104412,x104412)),f932(f932(x104412,x104412),f932(x104412,f932(x104412,x104412))),a1),f10(x104412,f932(x104412,x104412),x104412)),f862(f862(f10(a921,f932(x104412,f932(x104412,x104412)),a1),f89(x104412)),f862(f862(f9(a1,a1,a921),a317),f2(a1))))),f862(f862(f20(x104412,x104412,x104412),f73(x104412)),f7(x104412))))),f862(f862(f9(x104412,x104412,x104412),f862(f862(f10(x104412,f932(x104412,x104412),x104412),f73(x104412)),f862(f862(f20(x104412,x104412,x104412),f73(x104412)),f7(x104412)))),f71(x104412))))),f39(x104411,f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f95(x104412),x104411))
% 25.54/25.42 [10193]P1(f862(f862(f227(a1),x101931),f2(a1)))+P1(f862(f862(f228(a1),x101932),x101931))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x101932),x101931)))+E(f862(f36(x101931),f40(x101932,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101931))),f40(x101932,x101931))
% 25.54/25.42 [10197]P1(f862(f862(f227(a1),x101971),f2(a1)))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x101972),x101971)))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),x101972),x101971)))+E(f862(f36(x101971),f43(x101972,f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),x101971))),f43(x101972,x101971))
% 25.54/25.42 [5502]~P36(x55021,x55023)+~P49(x55021,x55023)+~P50(x55021,x55022,x55023)+P6(x55021,x55022,x55023)
% 25.54/25.42 [5503]~P36(x55031,x55033)+~P49(x55031,x55033)+~P50(x55031,x55032,x55033)+P6(x55031,x55032,x55033)
% 25.54/25.42 [5036]~P97(x50363)+~P98(x50363)+E(x50361,x50362)+~E(f862(f96(x50363),x50361),f862(f96(x50363),x50362))
% 25.54/25.42 [5512]~P47(x55121,x55122)+~P48(x55121,x55122)+P13(x55121,x55122)+~P1(f862(f862(x55122,x55123),x55123))
% 25.54/25.42 [5513]~P47(x55131,x55132)+~P48(x55131,x55132)+P13(x55131,x55132)+~P1(f862(f862(x55132,x55133),x55133))
% 25.54/25.42 [6023]P13(x60232,x60231)+E(f862(x60231,f811(x60231)),f862(x60231,f813(x60231)))+P1(f862(f862(x60231,f811(x60231)),f813(x60231)))+~P1(f862(f862(x60231,x60233),x60233))
% 25.54/25.42 [6226]~P1(f862(x62261,x62262))+~P1(f862(x62261,x62263))+~P1(f862(f862(f227(a924),x62263),f360(x62262,x62261)))+P1(f862(x62261,f2(a924)))
% 25.54/25.42 [6291]P13(x62911,x62912)+P1(f862(f862(x62912,f811(x62912)),f811(x62912)))+P1(f862(f862(x62912,f811(x62912)),f813(x62912)))+~P1(f862(f862(x62912,x62913),x62913))
% 25.54/25.42 [6292]P13(x62921,x62922)+P1(f862(f862(x62922,f811(x62922)),f813(x62922)))+P1(f862(f862(x62922,f813(x62922)),f813(x62922)))+~P1(f862(f862(x62922,x62923),x62923))
% 25.54/25.42 [6649]P149(x66492,x66491,x66493)+E(x66491,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x66493,x66491,x66492)))+P1(f862(f862(f228(a1),x66491),f2(a1)))
% 25.54/25.42 [6650]P148(x66502,x66501,x66503)+E(x66501,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x66503,x66501,x66502)))+P1(f862(f862(f228(a1),x66501),f2(a1)))
% 25.54/25.42 [6774]P148(x67741,x67742,x67743)+~P1(f862(x67741,x67743))+P1(f862(f862(f227(a1),f2(a1)),f873(x67743,x67742,x67741)))+P1(f862(f862(f228(a1),x67742),f2(a1)))
% 25.54/25.42 [6799]P149(x67991,x67992,x67993)+P1(f862(f862(f227(a1),f2(a1)),f868(x67993,x67992,x67991)))+~P1(f862(x67991,f2(a1)))+P1(f862(f862(f228(a1),x67992),f2(a1)))
% 25.54/25.42 [6827]P149(x68272,x68271,x68273)+E(x68271,f2(a1))+~P1(f862(x68272,f869(x68273,x68271,x68272)))+P1(f862(f862(f228(a1),x68271),f2(a1)))
% 25.54/25.42 [6828]P148(x68282,x68281,x68283)+E(x68281,f2(a1))+~P1(f862(x68282,f873(x68283,x68281,x68282)))+P1(f862(f862(f228(a1),x68281),f2(a1)))
% 25.54/25.42 [6926]~P3(x69261)+~P109(x69261)+~P1(f862(f862(f228(x69261),x69262),f30(x69261,x69263)))+P1(f862(f862(f228(x69261),x69262),f724(x69263,x69262,x69261)))
% 25.54/25.42 [6936]P148(x69361,x69362,x69363)+~P1(f862(x69361,x69363))+~P1(f862(x69361,f873(x69363,x69362,x69361)))+P1(f862(f862(f228(a1),x69362),f2(a1)))
% 25.54/25.42 [6969]P149(x69691,x69692,x69693)+~P1(f862(x69691,f869(x69693,x69692,x69691)))+~P1(f862(x69691,f2(a1)))+P1(f862(f862(f228(a1),x69692),f2(a1)))
% 25.54/25.42 [7217]P149(x72172,x72171,x72173)+E(x72171,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x72173,x72171,x72172)))+P1(f862(f862(f228(a1),x72171),f867(x72173,x72171,x72172)))
% 25.54/25.42 [7218]P148(x72182,x72181,x72183)+E(x72181,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x72183,x72181,x72182)))+P1(f862(f862(f228(a1),x72181),f872(x72183,x72181,x72182)))
% 25.54/25.42 [7339]P148(x73391,x73392,x73393)+~P1(f862(x73391,x73393))+P1(f862(f862(f227(a1),f2(a1)),f873(x73393,x73392,x73391)))+P1(f862(f862(f228(a1),x73392),f872(x73393,x73392,x73391)))
% 25.54/25.42 [7360]P149(x73601,x73602,x73603)+P1(f862(f862(f227(a1),f2(a1)),f868(x73603,x73602,x73601)))+P1(f862(f862(f228(a1),x73602),f867(x73603,x73602,x73601)))+~P1(f862(x73601,f2(a1)))
% 25.54/25.42 [7392]P149(x73922,x73921,x73923)+E(x73921,f2(a1))+~P1(f862(x73922,f869(x73923,x73921,x73922)))+P1(f862(f862(f228(a1),x73921),f867(x73923,x73921,x73922)))
% 25.54/25.42 [7393]P148(x73932,x73931,x73933)+E(x73931,f2(a1))+~P1(f862(x73932,f873(x73933,x73931,x73932)))+P1(f862(f862(f228(a1),x73931),f872(x73933,x73931,x73932)))
% 25.54/25.42 [7438]P149(x74382,x74381,x74383)+E(x74381,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x74383,x74381,x74382)))+~P1(f862(x74382,f871(x74383,x74381,x74382)))
% 25.54/25.42 [7439]P148(x74392,x74391,x74393)+E(x74391,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x74393,x74391,x74392)))+~P1(f862(x74392,f872(x74393,x74391,x74392)))
% 25.54/25.42 [7538]P148(x75381,x75382,x75383)+~P1(f862(x75381,x75383))+~P1(f862(x75381,f873(x75383,x75382,x75381)))+P1(f862(f862(f228(a1),x75382),f872(x75383,x75382,x75381)))
% 25.54/25.42 [7554]P149(x75541,x75542,x75543)+~P1(f862(x75541,f869(x75543,x75542,x75541)))+P1(f862(f862(f228(a1),x75542),f867(x75543,x75542,x75541)))+~P1(f862(x75541,f2(a1)))
% 25.54/25.42 [7557]P148(x75571,x75572,x75573)+~P1(f862(x75571,x75573))+P1(f862(f862(f227(a1),f2(a1)),f873(x75573,x75572,x75571)))+~P1(f862(x75571,f872(x75573,x75572,x75571)))
% 25.54/25.42 [7573]P149(x75731,x75732,x75733)+P1(f862(f862(f227(a1),f2(a1)),f868(x75733,x75732,x75731)))+~P1(f862(x75731,f871(x75733,x75732,x75731)))+~P1(f862(x75731,f2(a1)))
% 25.54/25.42 [7597]P149(x75972,x75971,x75973)+E(x75971,f2(a1))+~P1(f862(x75972,f869(x75973,x75971,x75972)))+~P1(f862(x75972,f871(x75973,x75971,x75972)))
% 25.54/25.42 [7598]P148(x75982,x75981,x75983)+E(x75981,f2(a1))+~P1(f862(x75982,f873(x75983,x75981,x75982)))+~P1(f862(x75982,f872(x75983,x75981,x75982)))
% 25.54/25.42 [7683]P148(x76831,x76832,x76833)+~P1(f862(x76831,x76833))+~P1(f862(x76831,f873(x76833,x76832,x76831)))+~P1(f862(x76831,f872(x76833,x76832,x76831)))
% 25.54/25.42 [7701]P149(x77011,x77012,x77013)+~P1(f862(x77011,f869(x77013,x77012,x77011)))+~P1(f862(x77011,f871(x77013,x77012,x77011)))+~P1(f862(x77011,f2(a1)))
% 25.54/25.42 [7747]P149(x77472,x77471,x77473)+E(x77471,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f868(x77473,x77471,x77472)))+P1(f862(f862(f227(a1),f867(x77473,x77471,x77472)),f2(a1)))
% 25.54/25.42 [7748]P148(x77482,x77481,x77483)+E(x77481,f2(a1))+P1(f862(f862(f227(a1),f2(a1)),f873(x77483,x77481,x77482)))+P1(f862(f862(f227(a1),f872(x77483,x77481,x77482)),f2(a1)))
% 25.54/25.42 [7749]~P142(x77491)+~P1(f862(f862(f321(x77491),x77493),f102(x77491)))+~P1(f862(f862(f321(x77491),x77492),f102(x77491)))+P1(f862(f862(f321(x77491),f862(f862(f3(x77491),x77492),x77493)),f102(x77491)))
% 25.54/25.42 [7750]~P142(x77501)+~P1(f862(f862(f321(x77501),x77503),f102(x77501)))+~P1(f862(f862(f321(x77501),x77502),f102(x77501)))+P1(f862(f862(f321(x77501),f862(f862(f74(x77501),x77502),x77503)),f102(x77501)))
% 25.54/25.42 [7751]~P147(x77511)+~P1(f862(f862(f321(x77511),x77513),f179(x77511)))+~P1(f862(f862(f321(x77511),x77512),f179(x77511)))+P1(f862(f862(f321(x77511),f862(f862(f74(x77511),x77512),x77513)),f179(x77511)))
% 25.54/25.42 [7752]~P142(x77521)+~P1(f862(f862(f321(x77521),x77523),f102(x77521)))+~P1(f862(f862(f321(x77521),x77522),f102(x77521)))+P1(f862(f862(f321(x77521),f862(f862(f73(x77521),x77522),x77523)),f102(x77521)))
% 25.54/25.42 [7753]~P147(x77531)+~P1(f862(f862(f321(x77531),x77533),f179(x77531)))+~P1(f862(f862(f321(x77531),x77532),f179(x77531)))+P1(f862(f862(f321(x77531),f862(f862(f73(x77531),x77532),x77533)),f179(x77531)))
% 25.54/25.42 [7754]~P87(x77541)+~P1(f862(f862(f227(x77541),x77543),f2(x77541)))+~P1(f862(f862(f227(x77541),x77542),f2(x77541)))+P1(f862(f862(f227(x77541),f862(f862(f73(x77541),x77542),x77543)),f2(x77541)))
% 25.54/25.42 [7755]~P87(x77551)+~P1(f862(f862(f227(x77551),x77553),f2(x77551)))+~P1(f862(f862(f228(x77551),x77552),f2(x77551)))+P1(f862(f862(f228(x77551),f862(f862(f73(x77551),x77552),x77553)),f2(x77551)))
% 25.54/25.42 [7756]~P87(x77561)+~P1(f862(f862(f227(x77561),x77562),f2(x77561)))+~P1(f862(f862(f228(x77561),x77563),f2(x77561)))+P1(f862(f862(f228(x77561),f862(f862(f73(x77561),x77562),x77563)),f2(x77561)))
% 25.54/25.42 [7757]~P87(x77571)+~P1(f862(f862(f228(x77571),x77573),f2(x77571)))+~P1(f862(f862(f228(x77571),x77572),f2(x77571)))+P1(f862(f862(f228(x77571),f862(f862(f73(x77571),x77572),x77573)),f2(x77571)))
% 25.54/25.42 [7784]P149(x77843,x77841,x77842)+E(x77841,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x77841),f869(x77842,x77841,x77843))),f868(x77842,x77841,x77843)),x77842)+P1(f862(f862(f228(a1),x77841),f2(a1)))
% 25.54/25.42 [7785]P148(x77853,x77851,x77852)+E(x77851,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x77851),f874(x77852,x77851,x77853))),f873(x77852,x77851,x77853)),x77852)+P1(f862(f862(f228(a1),x77851),f2(a1)))
% 25.54/25.42 [7868]P148(x78681,x78682,x78683)+~P1(f862(x78681,x78683))+P1(f862(f862(f227(a1),f2(a1)),f873(x78683,x78682,x78681)))+P1(f862(f862(f227(a1),f872(x78683,x78682,x78681)),f2(a1)))
% 25.54/25.42 [7898]P149(x78981,x78982,x78983)+P1(f862(f862(f227(a1),f2(a1)),f868(x78983,x78982,x78981)))+~P1(f862(x78981,f2(a1)))+P1(f862(f862(f227(a1),f867(x78983,x78982,x78981)),f2(a1)))
% 25.54/25.42 [7907]P148(x79073,x79071,x79072)+~P1(f862(x79073,x79072))+E(f862(f862(f73(a1),f862(f862(f74(a1),x79071),f874(x79072,x79071,x79073))),f873(x79072,x79071,x79073)),x79072)+P1(f862(f862(f228(a1),x79071),f2(a1)))
% 25.54/25.42 [7913]P149(x79132,x79131,x79133)+E(x79131,f2(a1))+~P1(f862(x79132,f869(x79133,x79131,x79132)))+P1(f862(f862(f227(a1),f867(x79133,x79131,x79132)),f2(a1)))
% 25.54/25.42 [7914]P148(x79142,x79141,x79143)+E(x79141,f2(a1))+~P1(f862(x79142,f873(x79143,x79141,x79142)))+P1(f862(f862(f227(a1),f872(x79143,x79141,x79142)),f2(a1)))
% 25.54/25.42 [7919]P149(x79193,x79191,x79192)+E(f862(f862(f73(a1),f862(f862(f74(a1),x79191),f869(x79192,x79191,x79193))),f868(x79192,x79191,x79193)),x79192)+~P1(f862(x79193,f2(a1)))+P1(f862(f862(f228(a1),x79191),f2(a1)))
% 25.54/25.42 [7975]P148(x79751,x79752,x79753)+~P1(f862(x79751,x79753))+~P1(f862(x79751,f873(x79753,x79752,x79751)))+P1(f862(f862(f227(a1),f872(x79753,x79752,x79751)),f2(a1)))
% 25.54/25.42 [7979]P149(x79791,x79792,x79793)+~P1(f862(x79791,f869(x79793,x79792,x79791)))+~P1(f862(x79791,f2(a1)))+P1(f862(f862(f227(a1),f867(x79793,x79792,x79791)),f2(a1)))
% 25.54/25.42 [8048]~P128(x80481)+~P1(f862(f862(f227(x80481),f862(f862(f74(x80481),x80483),x80482)),f2(x80481)))+P1(f862(f862(f227(x80481),x80482),f2(x80481)))+P1(f862(f862(f227(x80481),x80483),f2(x80481)))
% 25.54/25.42 [8049]~P66(x80491)+~P1(f862(f862(f227(x80491),f862(f862(f281(x80491),x80493),x80492)),f2(x80491)))+P1(f862(f862(f227(x80491),x80492),f2(x80491)))+P1(f862(f862(f227(x80491),x80493),f2(x80491)))
% 25.54/25.42 [8050]~P66(x80501)+~P1(f862(f862(f228(x80501),f862(f862(f281(x80501),x80503),x80502)),f2(x80501)))+P1(f862(f862(f228(x80501),x80502),f2(x80501)))+P1(f862(f862(f228(x80501),x80503),f2(x80501)))
% 25.54/25.42 [8165]P149(x81653,x81651,x81652)+E(x81651,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81651),f869(x81652,x81651,x81653))),f868(x81652,x81651,x81653)),x81652)+P1(f862(f862(f228(a1),x81651),f867(x81652,x81651,x81653)))
% 25.54/25.42 [8166]P148(x81663,x81661,x81662)+E(x81661,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81661),f874(x81662,x81661,x81663))),f873(x81662,x81661,x81663)),x81662)+P1(f862(f862(f228(a1),x81661),f872(x81662,x81661,x81663)))
% 25.54/25.42 [8179]P149(x81793,x81791,x81792)+E(x81791,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81791),f871(x81792,x81791,x81793))),f867(x81792,x81791,x81793)),x81792)+P1(f862(f862(f227(a1),f2(a1)),f868(x81792,x81791,x81793)))
% 25.54/25.42 [8180]P148(x81803,x81801,x81802)+E(x81801,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x81801),f875(x81802,x81801,x81803))),f872(x81802,x81801,x81803)),x81802)+P1(f862(f862(f227(a1),f2(a1)),f873(x81802,x81801,x81803)))
% 25.54/25.42 [8223]P148(x82233,x82231,x82232)+~P1(f862(x82233,x82232))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82231),f874(x82232,x82231,x82233))),f873(x82232,x82231,x82233)),x82232)+P1(f862(f862(f228(a1),x82231),f872(x82232,x82231,x82233)))
% 25.54/25.42 [8232]P149(x82323,x82321,x82322)+E(f862(f862(f73(a1),f862(f862(f74(a1),x82321),f869(x82322,x82321,x82323))),f868(x82322,x82321,x82323)),x82322)+P1(f862(f862(f228(a1),x82321),f867(x82322,x82321,x82323)))+~P1(f862(x82323,f2(a1)))
% 25.54/25.42 [8238]P148(x82383,x82381,x82382)+~P1(f862(x82383,x82382))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82381),f875(x82382,x82381,x82383))),f872(x82382,x82381,x82383)),x82382)+P1(f862(f862(f227(a1),f2(a1)),f873(x82382,x82381,x82383)))
% 25.54/25.42 [8244]P149(x82443,x82441,x82442)+E(f862(f862(f73(a1),f862(f862(f74(a1),x82441),f871(x82442,x82441,x82443))),f867(x82442,x82441,x82443)),x82442)+P1(f862(f862(f227(a1),f2(a1)),f868(x82442,x82441,x82443)))+~P1(f862(x82443,f2(a1)))
% 25.54/25.42 [8255]P149(x82553,x82551,x82552)+E(x82551,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82551),f869(x82552,x82551,x82553))),f868(x82552,x82551,x82553)),x82552)+~P1(f862(x82553,f871(x82552,x82551,x82553)))
% 25.54/25.42 [8256]P148(x82563,x82561,x82562)+E(x82561,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82561),f874(x82562,x82561,x82563))),f873(x82562,x82561,x82563)),x82562)+~P1(f862(x82563,f872(x82562,x82561,x82563)))
% 25.54/25.42 [8257]P149(x82573,x82571,x82572)+E(x82571,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82571),f871(x82572,x82571,x82573))),f867(x82572,x82571,x82573)),x82572)+~P1(f862(x82573,f869(x82572,x82571,x82573)))
% 25.54/25.42 [8258]P148(x82583,x82581,x82582)+E(x82581,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x82581),f875(x82582,x82581,x82583))),f872(x82582,x82581,x82583)),x82582)+~P1(f862(x82583,f873(x82582,x82581,x82583)))
% 25.54/25.42 [8319]P148(x83193,x83191,x83192)+~P1(f862(x83193,x83192))+E(f862(f862(f73(a1),f862(f862(f74(a1),x83191),f874(x83192,x83191,x83193))),f873(x83192,x83191,x83193)),x83192)+~P1(f862(x83193,f872(x83192,x83191,x83193)))
% 25.54/25.42 [8320]P148(x83203,x83201,x83202)+~P1(f862(x83203,x83202))+E(f862(f862(f73(a1),f862(f862(f74(a1),x83201),f875(x83202,x83201,x83203))),f872(x83202,x83201,x83203)),x83202)+~P1(f862(x83203,f873(x83202,x83201,x83203)))
% 25.54/25.42 [8333]P149(x83333,x83331,x83332)+E(f862(f862(f73(a1),f862(f862(f74(a1),x83331),f869(x83332,x83331,x83333))),f868(x83332,x83331,x83333)),x83332)+~P1(f862(x83333,f871(x83332,x83331,x83333)))+~P1(f862(x83333,f2(a1)))
% 25.54/25.42 [8334]P149(x83343,x83341,x83342)+E(f862(f862(f73(a1),f862(f862(f74(a1),x83341),f871(x83342,x83341,x83343))),f867(x83342,x83341,x83343)),x83342)+~P1(f862(x83343,f869(x83342,x83341,x83343)))+~P1(f862(x83343,f2(a1)))
% 25.54/25.42 [8433]P149(x84333,x84331,x84332)+E(x84331,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84331),f869(x84332,x84331,x84333))),f868(x84332,x84331,x84333)),x84332)+P1(f862(f862(f227(a1),f867(x84332,x84331,x84333)),f2(a1)))
% 25.54/25.42 [8434]P148(x84343,x84341,x84342)+E(x84341,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84341),f874(x84342,x84341,x84343))),f873(x84342,x84341,x84343)),x84342)+P1(f862(f862(f227(a1),f872(x84342,x84341,x84343)),f2(a1)))
% 25.54/25.42 [8473]P148(x84733,x84731,x84732)+~P1(f862(x84733,x84732))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84731),f874(x84732,x84731,x84733))),f873(x84732,x84731,x84733)),x84732)+P1(f862(f862(f227(a1),f872(x84732,x84731,x84733)),f2(a1)))
% 25.54/25.42 [8478]P149(x84783,x84781,x84782)+E(f862(f862(f73(a1),f862(f862(f74(a1),x84781),f869(x84782,x84781,x84783))),f868(x84782,x84781,x84783)),x84782)+~P1(f862(x84783,f2(a1)))+P1(f862(f862(f227(a1),f867(x84782,x84781,x84783)),f2(a1)))
% 25.54/25.42 [8614]P149(x86143,x86141,x86142)+E(x86141,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86141),f871(x86142,x86141,x86143))),f867(x86142,x86141,x86143)),x86142)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86141),f869(x86142,x86141,x86143))),f868(x86142,x86141,x86143)),x86142)
% 25.54/25.42 [8615]P148(x86153,x86151,x86152)+E(x86151,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86151),f875(x86152,x86151,x86153))),f872(x86152,x86151,x86153)),x86152)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86151),f874(x86152,x86151,x86153))),f873(x86152,x86151,x86153)),x86152)
% 25.54/25.42 [8635]P148(x86353,x86351,x86352)+~P1(f862(x86353,x86352))+E(f862(f862(f73(a1),f862(f862(f74(a1),x86351),f875(x86352,x86351,x86353))),f872(x86352,x86351,x86353)),x86352)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86351),f874(x86352,x86351,x86353))),f873(x86352,x86351,x86353)),x86352)
% 25.54/25.42 [8647]P149(x86473,x86471,x86472)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86471),f871(x86472,x86471,x86473))),f867(x86472,x86471,x86473)),x86472)+E(f862(f862(f73(a1),f862(f862(f74(a1),x86471),f869(x86472,x86471,x86473))),f868(x86472,x86471,x86473)),x86472)+~P1(f862(x86473,f2(a1)))
% 25.54/25.42 [9314]~P128(x93141)+~E(x93143,f2(x93141))+~E(x93142,f2(x93141))+P1(f862(f862(f227(x93141),f862(f862(f73(x93141),f862(f862(f74(x93141),x93142),x93142)),f862(f862(f74(x93141),x93143),x93143))),f2(x93141)))
% 25.54/25.42 [10382]~P112(x103821)+~E(x103823,f2(x103821))+~E(x103822,f2(x103821))+P1(f862(f862(f227(x103821),f862(f862(f73(x103821),f862(f862(f236(x103821),x103822),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103821),x103823),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))),f2(x103821)))
% 25.54/25.42 [4984]~E(x49843,x49841)+~P121(x49842)+E(x49841,f2(x49842))+E(f862(f862(f281(x49842),x49843),x49841),f71(x49842))
% 25.54/25.42 [5037]~P95(x50371)+~E(x50373,f181(x50371))+~E(x50372,f181(x50371))+E(f862(f862(f103(x50371),x50372),x50373),f181(x50371))
% 25.54/25.42 [5038]~P94(x50381)+~E(x50383,f234(x50381))+~E(x50382,f234(x50381))+E(f862(f862(f94(x50381),x50382),x50383),f234(x50381))
% 25.54/25.42 [5135]~P121(x51353)+E(x51351,x51352)+E(x51352,f2(x51353))+~E(f862(f862(f281(x51353),x51351),x51352),f71(x51353))
% 25.54/25.42 [5152]~P133(x51522)+E(x51521,f2(x51522))+E(x51523,f2(x51522))+~E(f862(f862(f74(x51522),x51523),x51521),f2(x51522))
% 25.54/25.42 [5153]~P133(x51532)+E(x51531,f2(x51532))+E(x51533,f2(x51532))+~E(f862(f862(f74(x51532),x51533),x51531),f2(x51532))
% 25.54/25.42 [5154]~P143(x51542)+E(x51541,f2(x51542))+E(x51543,f2(x51542))+~E(f862(f862(f74(x51542),x51543),x51541),f2(x51542))
% 25.54/25.42 [5532]~P113(x55323)+E(x55321,x55322)+E(x55321,f862(f72(x55323),x55322))+~E(f862(f862(f74(x55323),x55321),x55321),f862(f862(f74(x55323),x55322),x55322))
% 25.54/25.42 [5572]~P96(x55721)+E(f862(f72(x55721),x55722),x55723)+~E(f862(f862(f103(x55721),x55722),x55723),f234(x55721))+~E(f862(f862(f94(x55721),x55722),x55723),f181(x55721))
% 25.54/25.42 [5648]~P109(x56483)+E(x56481,x56482)+P1(f862(f862(f228(x56483),x56482),x56481))+P1(f862(f862(f228(x56483),x56481),x56482))
% 25.54/25.42 [5649]~P109(x56493)+E(x56491,x56492)+P1(f862(f862(f228(x56493),x56492),x56491))+P1(f862(f862(f228(x56493),x56491),x56492))
% 25.54/25.42 [5650]~P109(x56503)+E(x56501,x56502)+P1(f862(f862(f228(x56503),x56502),x56501))+P1(f862(f862(f228(x56503),x56501),x56502))
% 25.54/25.42 [5651]~P109(x56513)+E(x56511,x56512)+P1(f862(f862(f228(x56513),x56512),x56511))+P1(f862(f862(f228(x56513),x56511),x56512))
% 25.54/25.42 [5652]~P109(x56523)+E(x56521,x56522)+P1(f862(f862(f228(x56523),x56522),x56521))+P1(f862(f862(f228(x56523),x56521),x56522))
% 25.54/25.42 [5653]~P112(x56533)+E(x56531,x56532)+P1(f862(f862(f228(x56533),x56532),x56531))+P1(f862(f862(f228(x56533),x56531),x56532))
% 25.54/25.42 [5654]~P109(x56543)+E(x56541,x56542)+P1(f862(f862(f228(x56543),x56542),x56541))+P1(f862(f862(f228(x56543),x56541),x56542))
% 25.54/25.42 [5655]~E(x56552,x56553)+~P109(x56551)+P1(f862(f862(f228(x56551),x56552),x56553))+P1(f862(f862(f227(x56551),x56552),x56553))
% 25.54/25.42 [5830]P149(x58302,x58301,x58303)+E(x58301,f2(a1))+P1(f862(f862(f228(a1),x58301),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x58301))
% 25.54/25.42 [5831]P148(x58312,x58311,x58313)+E(x58311,f2(a1))+P1(f862(f862(f228(a1),x58311),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x58311))
% 25.54/25.42 [5856]E(x58561,x58562)+P1(f862(f862(x58563,x58561),x58562))+P1(f862(f862(f228(a924),x58562),x58561))+P1(f862(f862(f228(a924),x58561),x58562))
% 25.54/25.42 [5918]~P110(x59183)+E(x59181,x59182)+~P1(f862(f862(f227(x59183),x59182),x59181))+P1(f862(f862(f228(x59183),x59182),x59181))
% 25.54/25.42 [5919]~P109(x59193)+E(x59191,x59192)+~P1(f862(f862(f227(x59193),x59191),x59192))+P1(f862(f862(f228(x59193),x59191),x59192))
% 25.54/25.42 [5920]~P109(x59203)+E(x59201,x59202)+~P1(f862(f862(f227(x59203),x59201),x59202))+P1(f862(f862(f228(x59203),x59201),x59202))
% 25.54/25.42 [5921]~P110(x59213)+E(x59211,x59212)+~P1(f862(f862(f227(x59213),x59211),x59212))+P1(f862(f862(f228(x59213),x59211),x59212))
% 25.54/25.42 [5922]~P110(x59223)+E(x59221,x59222)+~P1(f862(f862(f227(x59223),x59221),x59222))+P1(f862(f862(f228(x59223),x59221),x59222))
% 25.54/25.42 [5923]~P110(x59233)+E(x59231,x59232)+~P1(f862(f862(f227(x59233),x59231),x59232))+P1(f862(f862(f228(x59233),x59231),x59232))
% 25.54/25.42 [5924]~P110(x59243)+E(x59241,x59242)+~P1(f862(f862(f227(x59243),x59241),x59242))+P1(f862(f862(f228(x59243),x59241),x59242))
% 25.54/25.42 [5925]~P110(x59253)+E(x59251,x59252)+~P1(f862(f862(f227(x59253),x59251),x59252))+P1(f862(f862(f228(x59253),x59251),x59252))
% 25.54/25.42 [5926]~P110(x59263)+E(x59261,x59262)+~P1(f862(f862(f227(x59263),x59261),x59262))+P1(f862(f862(f228(x59263),x59261),x59262))
% 25.54/25.42 [6040]P148(x60401,x60402,x60403)+~P1(f862(x60401,x60403))+P1(f862(f862(f228(a1),x60402),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x60402))
% 25.54/25.42 [6094]P149(x60941,x60942,x60943)+~P1(f862(x60941,f2(a1)))+P1(f862(f862(f228(a1),x60942),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x60942))
% 25.54/25.42 [6099]~P93(x60991)+E(f862(f862(f103(x60991),x60992),f12(x60991,x60993)),x60992)+~P1(f862(f54(x60991),x60993))+~P1(f862(f862(f321(x60991),x60992),x60993))
% 25.54/25.42 [6100]~P93(x61001)+E(f862(f862(f94(x61001),x61002),f15(x61001,x61003)),x61002)+~P1(f862(f54(x61001),x61003))+~P1(f862(f862(f321(x61001),x61002),x61003))
% 25.54/25.42 [6138]~P93(x61381)+E(f862(f862(f103(x61381),x61382),f15(x61381,x61383)),f15(x61381,x61383))+~P1(f862(f54(x61381),x61383))+~P1(f862(f862(f321(x61381),x61382),x61383))
% 25.54/25.42 [6139]~P93(x61391)+E(f862(f862(f94(x61391),x61392),f12(x61391,x61393)),f12(x61391,x61393))+~P1(f862(f54(x61391),x61393))+~P1(f862(f862(f321(x61391),x61392),x61393))
% 25.54/25.42 [6140]~P109(x61401)+E(f862(f862(f225(x61401),x61402),f16(x61401,x61403)),f16(x61401,x61403))+~P1(f862(f54(x61401),x61403))+~P1(f862(f862(f321(x61401),x61402),x61403))
% 25.54/25.42 [6141]~P109(x61411)+E(f862(f862(f226(x61411),x61412),f17(x61411,x61413)),f17(x61411,x61413))+~P1(f862(f54(x61411),x61413))+~P1(f862(f862(f321(x61411),x61412),x61413))
% 25.54/25.42 [6176]E(x61761,x61762)+~P110(x61763)+~P1(f862(f862(f227(x61763),x61762),x61761))+~P1(f862(f862(f227(x61763),x61761),x61762))
% 25.54/25.42 [6177]E(x61771,x61772)+~P110(x61773)+~P1(f862(f862(f227(x61773),x61772),x61771))+~P1(f862(f862(f227(x61773),x61771),x61772))
% 25.54/25.42 [6178]E(x61781,x61782)+~P110(x61783)+~P1(f862(f862(f227(x61783),x61782),x61781))+~P1(f862(f862(f227(x61783),x61781),x61782))
% 25.54/25.42 [6179]E(x61791,x61792)+~P110(x61793)+~P1(f862(f862(f227(x61793),x61792),x61791))+~P1(f862(f862(f227(x61793),x61791),x61792))
% 25.54/25.42 [6181]~E(x61811,x61812)+~P109(x61813)+~P1(f862(f862(f227(x61813),x61811),x61812))+~P1(f862(f862(f228(x61813),x61811),x61812))
% 25.54/25.42 [6319]~P91(x63191)+P1(f862(f862(f228(x63191),x63193),x63192))+~P1(f862(f862(f227(x63191),x63193),x63192))+P1(f862(f862(f227(x63191),x63192),x63193))
% 25.54/25.42 [6346]~P109(x63461)+~P1(f862(f54(x63461),x63463))+P1(f862(f862(f227(x63461),x63462),f17(x63461,x63463)))+~P1(f862(f862(f321(x63461),x63462),x63463))
% 25.54/25.42 [6393]~P109(x63931)+E(f862(f862(f225(x63931),x63932),f14(x63931,f226(x63931),x63933)),x63932)+~P1(f862(f54(x63931),x63933))+~P1(f862(f862(f321(x63931),x63932),x63933))
% 25.54/25.42 [6394]~P109(x63941)+E(f862(f862(f226(x63941),x63942),f13(x63941,f225(x63941),x63943)),x63942)+~P1(f862(f54(x63941),x63943))+~P1(f862(f862(f321(x63941),x63942),x63943))
% 25.54/25.42 [6536]E(x65361,x65362)+~E(f862(f862(f3(a924),x65361),x65363),f862(f862(f3(a924),x65362),x65363))+~P1(f862(f862(f227(a924),x65363),x65361))+~P1(f862(f862(f227(a924),x65363),x65362))
% 25.54/25.42 [6563]~P109(x65631)+~P1(f862(f54(x65631),x65632))+~P1(f862(f862(f321(x65631),x65633),x65632))+P1(f862(f862(f227(x65631),f16(x65631,x65632)),x65633))
% 25.54/25.42 [6604]E(x66041,f2(a924))+~P1(f862(f41(x66043,x66041),x66042))+P1(f862(f862(f228(a924),f2(a924)),x66041))+P1(f862(f862(f228(a924),x66041),f862(f248(a924,a924),x66042)))
% 25.54/25.42 [6628]P149(x66282,x66281,x66283)+E(x66281,f2(a1))+P1(f862(f862(f228(a1),x66281),f867(x66283,x66281,x66282)))+P1(f862(f862(f228(a1),f2(a1)),x66281))
% 25.54/25.42 [6629]P148(x66292,x66291,x66293)+E(x66291,f2(a1))+P1(f862(f862(f228(a1),x66291),f872(x66293,x66291,x66292)))+P1(f862(f862(f228(a1),f2(a1)),x66291))
% 25.54/25.42 [6630]~P109(x66301)+E(f862(f862(f225(x66301),x66302),f13(x66301,f225(x66301),x66303)),f13(x66301,f225(x66301),x66303))+~P1(f862(f54(x66301),x66303))+~P1(f862(f862(f321(x66301),x66302),x66303))
% 25.54/25.42 [6631]~P109(x66311)+E(f862(f862(f226(x66311),x66312),f14(x66311,f226(x66311),x66313)),f14(x66311,f226(x66311),x66313))+~P1(f862(f54(x66311),x66313))+~P1(f862(f862(f321(x66311),x66312),x66313))
% 25.54/25.42 [6636]~P1(f862(x66361,x66362))+P1(f862(x66361,f437(x66362,x66361,x66363)))+P1(f862(x66361,f2(a924)))+~P1(f862(f862(f228(a924),x66362),x66363))
% 25.54/25.42 [6694]~P1(f862(x66941,x66942))+~P1(f862(f54(x66943),x66942))+P1(f862(x66941,f876(x66941,x66942,x66943)))+P1(f862(x66941,f181(f932(x66943,a921))))
% 25.54/25.42 [6707]~P112(x67071)+~P98(x67071)+P1(f862(f862(f227(x67071),f862(f96(x67071),x67072)),f862(f96(x67071),x67073)))+~P1(f862(f862(f227(a1),x67072),x67073))
% 25.54/25.42 [6708]~P112(x67081)+~P98(x67081)+P1(f862(f862(f228(x67081),f862(f96(x67081),x67082)),f862(f96(x67081),x67083)))+~P1(f862(f862(f228(a1),x67082),x67083))
% 25.54/25.42 [6711]~P1(f862(x67111,x67113))+~P1(f862(f54(x67112),x67113))+P1(f862(f54(x67112),f876(x67111,x67113,x67112)))+P1(f862(x67111,f181(f932(x67112,a921))))
% 25.54/25.42 [6745]P148(x67451,x67452,x67453)+~P1(f862(x67451,x67453))+P1(f862(f862(f228(a1),x67452),f872(x67453,x67452,x67451)))+P1(f862(f862(f228(a1),f2(a1)),x67452))
% 25.54/25.42 [6780]P149(x67801,x67802,x67803)+P1(f862(f862(f228(a1),x67802),f867(x67803,x67802,x67801)))+~P1(f862(x67801,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x67802))
% 25.54/25.42 [6810]~P108(x68101)+~P99(x68101)+E(f862(f862(f225(x68101),f862(f96(x68101),x68102)),f862(f96(x68101),x68103)),f862(f96(x68101),x68103))+P1(f862(f862(f227(x68101),f862(f96(x68101),x68102)),f862(f96(x68101),x68103)))
% 25.54/25.42 [6811]~P108(x68111)+~P99(x68111)+E(f862(f862(f226(x68111),f862(f96(x68111),x68112)),f862(f96(x68111),x68113)),f862(f96(x68111),x68112))+P1(f862(f862(f227(x68111),f862(f96(x68111),x68112)),f862(f96(x68111),x68113)))
% 25.54/25.42 [6815]E(x68151,f2(a924))+~P1(f862(f41(x68153,x68151),x68152))+~P1(f862(f862(f228(a924),f2(a924)),x68151))+P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x68152)))
% 25.54/25.42 [6868]P149(x68682,x68681,x68683)+E(x68681,f2(a1))+~P1(f862(x68682,f871(x68683,x68681,x68682)))+P1(f862(f862(f228(a1),f2(a1)),x68681))
% 25.54/25.42 [6869]P148(x68692,x68691,x68693)+E(x68691,f2(a1))+~P1(f862(x68692,f872(x68693,x68691,x68692)))+P1(f862(f862(f228(a1),f2(a1)),x68691))
% 25.54/25.42 [6873]P1(f862(x68731,x68732))+~P1(f862(f54(x68733),x68732))+P1(f862(x68731,f441(x68731,x68732,x68733)))+~P1(f862(x68731,f181(f932(x68733,a921))))
% 25.54/25.42 [6893]P1(f862(x68931,x68932))+P1(f862(f54(x68933),f441(x68931,x68932,x68933)))+~P1(f862(f54(x68933),x68932))+~P1(f862(x68931,f181(f932(x68933,a921))))
% 25.54/25.42 [6957]P148(x69571,x69572,x69573)+~P1(f862(x69571,x69573))+~P1(f862(x69571,f872(x69573,x69572,x69571)))+P1(f862(f862(f228(a1),f2(a1)),x69572))
% 25.54/25.42 [6988]P149(x69881,x69882,x69883)+~P1(f862(x69881,f871(x69883,x69882,x69881)))+~P1(f862(x69881,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x69882))
% 25.54/25.42 [6999]E(x69991,f2(a924))+~P1(f862(f41(x69993,x69991),x69992))+P1(f862(f862(f227(a924),f862(f248(a924,a924),x69992)),f2(a924)))+P1(f862(f862(f228(a924),f2(a924)),x69991))
% 25.54/25.42 [7095]~P98(x70953)+~P112(x70953)+~P1(f862(f862(f227(x70953),f862(f96(x70953),x70951)),f862(f96(x70953),x70952)))+P1(f862(f862(f227(a1),x70951),x70952))
% 25.54/25.42 [7096]~P98(x70963)+~P112(x70963)+~P1(f862(f862(f228(x70963),f862(f96(x70963),x70961)),f862(f96(x70963),x70962)))+P1(f862(f862(f228(a1),x70961),x70962))
% 25.54/25.42 [7124]~P109(x71241)+~P11(x71241,x71243)+P11(x71241,f862(f862(f144(x71241),x71242),x71243))+~P1(f862(f862(f227(x71241),x71242),f717(x71243,x71242,x71241)))
% 25.54/25.42 [7125]~P109(x71251)+~P11(x71251,x71253)+P11(x71251,f862(f862(f144(x71251),x71252),x71253))+~P1(f862(f862(f227(x71251),x71252),f719(x71253,x71252,x71251)))
% 25.54/25.42 [7126]~P109(x71261)+~P11(x71261,x71263)+P11(x71261,f862(f862(f144(x71261),x71262),x71263))+~P1(f862(f862(f227(x71261),x71262),f758(x71262,x71263,x71261)))
% 25.54/25.42 [7211]P149(x72112,x72111,x72113)+E(x72111,f2(a1))+P1(f862(f862(f228(a1),x72111),f2(a1)))+P1(f862(f862(f228(a1),f868(x72113,x72111,x72112)),x72111))
% 25.54/25.42 [7212]P148(x72122,x72121,x72123)+E(x72121,f2(a1))+P1(f862(f862(f228(a1),x72121),f2(a1)))+P1(f862(f862(f228(a1),f873(x72123,x72121,x72122)),x72121))
% 25.54/25.42 [7216]~P109(x72161)+~P99(x72161)+P1(f862(f862(f227(x72161),f862(f96(x72161),x72162)),f862(f96(x72161),x72163)))+P1(f862(f862(f228(x72161),f862(f96(x72161),x72163)),f862(f96(x72161),x72162)))
% 25.54/25.42 [7248]P149(x72482,x72481,x72483)+E(x72481,f2(a1))+P1(f862(f862(f227(a1),f867(x72483,x72481,x72482)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x72481))
% 25.54/25.42 [7249]P148(x72492,x72491,x72493)+E(x72491,f2(a1))+P1(f862(f862(f227(a1),f872(x72493,x72491,x72492)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x72491))
% 25.54/25.42 [7275]~P109(x72751)+~P11(x72751,x72753)+E(f862(f862(f141(x72751,x72751,f7(x72751)),x72752),f163(x72751,x72752,x72753)),x72753)+~P1(f862(f862(f321(x72751),x72752),f862(f165(x72751),x72753)))
% 25.54/25.42 [7322]P148(x73221,x73222,x73223)+~P1(f862(x73221,x73223))+P1(f862(f862(f228(a1),x73222),f2(a1)))+P1(f862(f862(f228(a1),f873(x73223,x73222,x73221)),x73222))
% 25.54/25.42 [7328]~P108(x73281)+~P99(x73281)+E(f862(f862(f225(x73281),f862(f96(x73281),x73282)),f862(f96(x73281),x73283)),f862(f96(x73281),x73282))+~P1(f862(f862(f227(x73281),f862(f96(x73281),x73282)),f862(f96(x73281),x73283)))
% 25.54/25.42 [7329]~P108(x73291)+~P99(x73291)+E(f862(f862(f226(x73291),f862(f96(x73291),x73292)),f862(f96(x73291),x73293)),f862(f96(x73291),x73293))+~P1(f862(f862(f227(x73291),f862(f96(x73291),x73292)),f862(f96(x73291),x73293)))
% 25.54/25.42 [7343]P149(x73431,x73432,x73433)+~P1(f862(x73431,f2(a1)))+P1(f862(f862(f228(a1),x73432),f2(a1)))+P1(f862(f862(f228(a1),f868(x73433,x73432,x73431)),x73432))
% 25.54/25.42 [7353]P148(x73531,x73532,x73533)+~P1(f862(x73531,x73533))+P1(f862(f862(f227(a1),f872(x73533,x73532,x73531)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x73532))
% 25.54/25.42 [7377]P149(x73771,x73772,x73773)+~P1(f862(x73771,f2(a1)))+P1(f862(f862(f227(a1),f867(x73773,x73772,x73771)),f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x73772))
% 25.54/25.42 [7405]~P1(f862(x74051,x74052))+P1(f862(x74051,f2(a924)))+~P1(f862(f862(f228(a924),x74052),x74053))+P1(f862(f862(f228(a924),f437(x74052,x74051,x74053)),x74053))
% 25.54/25.42 [7422]~P109(x74221)+~P11(x74221,x74223)+P11(x74221,f862(f862(f144(x74221),x74222),x74223))+P1(f862(f862(f321(x74221),f717(x74223,x74222,x74221)),f862(f165(x74221),x74223)))
% 25.54/25.42 [7423]~P109(x74231)+~P11(x74231,x74233)+P11(x74231,f862(f862(f144(x74231),x74232),x74233))+P1(f862(f862(f321(x74231),f719(x74233,x74232,x74231)),f862(f165(x74231),x74233)))
% 25.54/25.42 [7424]~P109(x74241)+~P11(x74241,x74243)+P11(x74241,f862(f862(f144(x74241),x74242),x74243))+P1(f862(f862(f321(x74241),f758(x74242,x74243,x74241)),f862(f165(x74241),x74243)))
% 25.54/25.42 [7542]~P3(x75421)+~P109(x75421)+~P1(f862(f862(f228(x75421),x75423),f30(x75421,x75422)))+P1(f862(f862(f321(x75421),f724(x75422,x75423,x75421)),x75422))
% 25.54/25.42 [7699]~P3(x76991)+~P109(x76991)+~P1(f862(f862(f228(x76991),f31(x76991,x76993)),x76992))+P1(f862(f862(f321(x76991),f734(x76992,x76993,x76991)),x76993))
% 25.54/25.42 [7700]~P3(x77001)+~P109(x77001)+~P1(f862(f862(f228(x77001),f31(x77001,x77003)),x77002))+P1(f862(f862(f228(x77001),f734(x77002,x77003,x77001)),x77002))
% 25.54/25.42 [7711]P149(x77112,x77111,x77113)+E(x77111,f2(a1))+P1(f862(f862(f228(a1),x77111),f867(x77113,x77111,x77112)))+P1(f862(f862(f228(a1),f868(x77113,x77111,x77112)),x77111))
% 25.54/25.42 [7712]P148(x77122,x77121,x77123)+E(x77121,f2(a1))+P1(f862(f862(f228(a1),x77121),f872(x77123,x77121,x77122)))+P1(f862(f862(f228(a1),f873(x77123,x77121,x77122)),x77121))
% 25.54/25.42 [7807]P149(x78073,x78071,x78072)+E(x78071,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x78071),f871(x78072,x78071,x78073))),f867(x78072,x78071,x78073)),x78072)+P1(f862(f862(f228(a1),f2(a1)),x78071))
% 25.54/25.42 [7808]P148(x78083,x78081,x78082)+E(x78081,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x78081),f875(x78082,x78081,x78083))),f872(x78082,x78081,x78083)),x78082)+P1(f862(f862(f228(a1),f2(a1)),x78081))
% 25.54/25.42 [7809]~P136(x78091)+~P1(f862(f862(f227(x78091),x78092),f2(x78091)))+P1(f862(f862(f227(x78091),f862(f862(f74(x78091),x78092),x78093)),f2(x78091)))+~P1(f862(f862(f227(x78091),f2(x78091)),x78093))
% 25.54/25.42 [7810]~P136(x78101)+~P1(f862(f862(f227(x78101),x78103),f2(x78101)))+P1(f862(f862(f227(x78101),f862(f862(f74(x78101),x78102),x78103)),f2(x78101)))+~P1(f862(f862(f227(x78101),f2(x78101)),x78102))
% 25.54/25.42 [7811]~P136(x78111)+~P1(f862(f862(f227(x78111),x78113),f2(x78111)))+P1(f862(f862(f227(x78111),f862(f862(f74(x78111),x78112),x78113)),f2(x78111)))+~P1(f862(f862(f227(x78111),f2(x78111)),x78112))
% 25.54/25.42 [7812]~P136(x78121)+~P1(f862(f862(f227(x78121),x78122),f2(x78121)))+P1(f862(f862(f227(x78121),f862(f862(f74(x78121),x78122),x78123)),f2(x78121)))+~P1(f862(f862(f227(x78121),f2(x78121)),x78123))
% 25.54/25.42 [7813]~P136(x78131)+~P1(f862(f862(f227(x78131),x78132),f2(x78131)))+P1(f862(f862(f227(x78131),f862(f862(f74(x78131),x78132),x78133)),f2(x78131)))+~P1(f862(f862(f227(x78131),f2(x78131)),x78133))
% 25.54/25.42 [7814]~P128(x78141)+~P1(f862(f862(f227(x78141),x78143),f2(x78141)))+P1(f862(f862(f227(x78141),f862(f862(f74(x78141),x78142),x78143)),f2(x78141)))+~P1(f862(f862(f227(x78141),f2(x78141)),x78142))
% 25.54/25.42 [7815]~P128(x78151)+~P1(f862(f862(f227(x78151),x78152),f2(x78151)))+P1(f862(f862(f227(x78151),f862(f862(f74(x78151),x78152),x78153)),f2(x78151)))+~P1(f862(f862(f227(x78151),f2(x78151)),x78153))
% 25.54/25.42 [7816]~P66(x78161)+~P1(f862(f862(f227(x78161),x78163),f2(x78161)))+P1(f862(f862(f227(x78161),f862(f862(f281(x78161),x78162),x78163)),f2(x78161)))+~P1(f862(f862(f227(x78161),f2(x78161)),x78162))
% 25.54/25.42 [7817]~P66(x78171)+~P1(f862(f862(f227(x78171),x78172),f2(x78171)))+P1(f862(f862(f227(x78171),f862(f862(f281(x78171),x78172),x78173)),f2(x78171)))+~P1(f862(f862(f227(x78171),f2(x78171)),x78173))
% 25.54/25.42 [7818]~P67(x78181)+~P1(f862(f862(f227(x78181),x78182),f2(x78181)))+P1(f862(f862(f227(x78181),f862(f862(f281(x78181),x78182),x78183)),f2(x78181)))+~P1(f862(f862(f228(x78181),f2(x78181)),x78183))
% 25.54/25.42 [7819]~P67(x78191)+~P1(f862(f862(f228(x78191),x78193),f2(x78191)))+P1(f862(f862(f227(x78191),f862(f862(f281(x78191),x78192),x78193)),f2(x78191)))+~P1(f862(f862(f227(x78191),f2(x78191)),x78192))
% 25.54/25.42 [7820]~P135(x78201)+~P1(f862(f862(f228(x78201),x78202),f2(x78201)))+P1(f862(f862(f228(x78201),f862(f862(f74(x78201),x78202),x78203)),f2(x78201)))+~P1(f862(f862(f228(x78201),f2(x78201)),x78203))
% 25.54/25.42 [7821]~P135(x78211)+~P1(f862(f862(f228(x78211),x78213),f2(x78211)))+P1(f862(f862(f228(x78211),f862(f862(f74(x78211),x78212),x78213)),f2(x78211)))+~P1(f862(f862(f228(x78211),f2(x78211)),x78212))
% 25.54/25.42 [7822]~P135(x78221)+~P1(f862(f862(f228(x78221),x78222),f2(x78221)))+P1(f862(f862(f228(x78221),f862(f862(f74(x78221),x78222),x78223)),f2(x78221)))+~P1(f862(f862(f228(x78221),f2(x78221)),x78223))
% 25.54/25.42 [7823]~P66(x78231)+~P1(f862(f862(f228(x78231),x78233),f2(x78231)))+P1(f862(f862(f228(x78231),f862(f862(f281(x78231),x78232),x78233)),f2(x78231)))+~P1(f862(f862(f228(x78231),f2(x78231)),x78232))
% 25.54/25.42 [7824]~P66(x78241)+~P1(f862(f862(f228(x78241),x78242),f2(x78241)))+P1(f862(f862(f228(x78241),f862(f862(f281(x78241),x78242),x78243)),f2(x78241)))+~P1(f862(f862(f228(x78241),f2(x78241)),x78243))
% 25.54/25.42 [7825]~P67(x78251)+~P1(f862(f862(f228(x78251),x78253),f2(x78251)))+P1(f862(f862(f228(x78251),f862(f862(f281(x78251),x78252),x78253)),f2(x78251)))+~P1(f862(f862(f228(x78251),f2(x78251)),x78252))
% 25.54/25.42 [7826]~P67(x78261)+~P1(f862(f862(f228(x78261),x78262),f2(x78261)))+P1(f862(f862(f228(x78261),f862(f862(f281(x78261),x78262),x78263)),f2(x78261)))+~P1(f862(f862(f228(x78261),f2(x78261)),x78263))
% 25.54/25.42 [7841]P148(x78411,x78412,x78413)+~P1(f862(x78411,x78413))+P1(f862(f862(f228(a1),x78412),f872(x78413,x78412,x78411)))+P1(f862(f862(f228(a1),f873(x78413,x78412,x78411)),x78412))
% 25.54/25.42 [7854]P149(x78541,x78542,x78543)+P1(f862(f862(f228(a1),x78542),f867(x78543,x78542,x78541)))+~P1(f862(x78541,f2(a1)))+P1(f862(f862(f228(a1),f868(x78543,x78542,x78541)),x78542))
% 25.54/25.42 [7905]P149(x79052,x79051,x79053)+E(x79051,f2(a1))+~P1(f862(x79052,f871(x79053,x79051,x79052)))+P1(f862(f862(f228(a1),f868(x79053,x79051,x79052)),x79051))
% 25.54/25.42 [7906]P148(x79062,x79061,x79063)+E(x79061,f2(a1))+~P1(f862(x79062,f872(x79063,x79061,x79062)))+P1(f862(f862(f228(a1),f873(x79063,x79061,x79062)),x79061))
% 25.54/25.42 [7916]P148(x79163,x79161,x79162)+~P1(f862(x79163,x79162))+E(f862(f862(f73(a1),f862(f862(f74(a1),x79161),f875(x79162,x79161,x79163))),f872(x79162,x79161,x79163)),x79162)+P1(f862(f862(f228(a1),f2(a1)),x79161))
% 25.54/25.42 [7931]P149(x79313,x79311,x79312)+E(f862(f862(f73(a1),f862(f862(f74(a1),x79311),f871(x79312,x79311,x79313))),f867(x79312,x79311,x79313)),x79312)+~P1(f862(x79313,f2(a1)))+P1(f862(f862(f228(a1),f2(a1)),x79311))
% 25.54/25.42 [7959]~P1(f862(x79591,x79593))+~P1(f862(f54(x79592),x79593))+P1(f862(f862(f321(x79592),f877(x79591,x79593,x79592)),f876(x79591,x79593,x79592)))+P1(f862(x79591,f181(f932(x79592,a921))))
% 25.54/25.42 [7970]P148(x79701,x79702,x79703)+~P1(f862(x79701,x79703))+~P1(f862(x79701,f872(x79703,x79702,x79701)))+P1(f862(f862(f228(a1),f873(x79703,x79702,x79701)),x79702))
% 25.54/25.42 [7976]P149(x79761,x79762,x79763)+~P1(f862(x79761,f871(x79763,x79762,x79761)))+~P1(f862(x79761,f2(a1)))+P1(f862(f862(f228(a1),f868(x79763,x79762,x79761)),x79762))
% 25.54/25.42 [8043]~P99(x80431)+~P109(x80431)+~P1(f862(f862(f227(x80431),f862(f96(x80431),x80432)),f862(f96(x80431),x80433)))+~P1(f862(f862(f228(x80431),f862(f96(x80431),x80433)),f862(f96(x80431),x80432)))
% 25.54/25.42 [8079]~P128(x80791)+~P1(f862(f862(f227(x80791),f862(f862(f74(x80791),x80793),x80792)),f2(x80791)))+P1(f862(f862(f227(x80791),x80792),f2(x80791)))+P1(f862(f862(f227(x80791),f2(x80791)),x80792))
% 25.54/25.42 [8080]~P128(x80801)+~P1(f862(f862(f227(x80801),f862(f862(f74(x80801),x80802),x80803)),f2(x80801)))+P1(f862(f862(f227(x80801),x80802),f2(x80801)))+P1(f862(f862(f227(x80801),f2(x80801)),x80802))
% 25.54/25.42 [8081]~P66(x80811)+~P1(f862(f862(f227(x80811),f862(f862(f281(x80811),x80813),x80812)),f2(x80811)))+P1(f862(f862(f227(x80811),x80812),f2(x80811)))+P1(f862(f862(f227(x80811),f2(x80811)),x80812))
% 25.54/25.42 [8082]~P66(x80821)+~P1(f862(f862(f227(x80821),f862(f862(f281(x80821),x80822),x80823)),f2(x80821)))+P1(f862(f862(f227(x80821),x80822),f2(x80821)))+P1(f862(f862(f227(x80821),f2(x80821)),x80822))
% 25.54/25.42 [8083]~P66(x80831)+~P1(f862(f862(f228(x80831),f862(f862(f281(x80831),x80833),x80832)),f2(x80831)))+P1(f862(f862(f228(x80831),x80832),f2(x80831)))+P1(f862(f862(f228(x80831),f2(x80831)),x80832))
% 25.54/25.42 [8084]~P66(x80841)+~P1(f862(f862(f228(x80841),f862(f862(f281(x80841),x80842),x80843)),f2(x80841)))+P1(f862(f862(f228(x80841),x80842),f2(x80841)))+P1(f862(f862(f228(x80841),f2(x80841)),x80842))
% 25.54/25.42 [8109]~P128(x81091)+~P1(f862(f862(f227(x81091),f862(f862(f74(x81091),x81092),x81093)),f2(x81091)))+P1(f862(f862(f227(x81091),f2(x81091)),x81092))+P1(f862(f862(f227(x81091),f2(x81091)),x81093))
% 25.54/25.42 [8110]~P66(x81101)+~P1(f862(f862(f227(x81101),f862(f862(f281(x81101),x81102),x81103)),f2(x81101)))+P1(f862(f862(f227(x81101),f2(x81101)),x81102))+P1(f862(f862(f227(x81101),f2(x81101)),x81103))
% 25.54/25.42 [8111]~P66(x81111)+~P1(f862(f862(f228(x81111),f862(f862(f281(x81111),x81112),x81113)),f2(x81111)))+P1(f862(f862(f228(x81111),f2(x81111)),x81112))+P1(f862(f862(f228(x81111),f2(x81111)),x81113))
% 25.54/25.42 [8133]P149(x81332,x81331,x81333)+E(x81331,f2(a1))+P1(f862(f862(f227(a1),f867(x81333,x81331,x81332)),f2(a1)))+P1(f862(f862(f228(a1),f868(x81333,x81331,x81332)),x81331))
% 25.54/25.42 [8134]P148(x81342,x81341,x81343)+E(x81341,f2(a1))+P1(f862(f862(f227(a1),f872(x81343,x81341,x81342)),f2(a1)))+P1(f862(f862(f228(a1),f873(x81343,x81341,x81342)),x81341))
% 25.54/25.42 [8141]~P127(x81411)+~P1(f862(f862(f228(x81411),x81412),f71(x81411)))+P1(f862(f862(f228(x81411),f862(f862(f236(x81411),x81412),f862(a105,x81413))),f71(x81411)))+~P1(f862(f862(f228(x81411),f2(x81411)),x81412))
% 25.54/25.42 [8196]~P109(x81961)+~E(x81963,f106(x81961))+~P11(x81961,f862(f161(x81961),x81963))+E(f862(f135(x81961,x81961,f862(f9(x81961,x81961,x81961),f226(x81961)),x81962),f862(f161(x81961),x81963)),x81962)
% 25.54/25.42 [8200]P148(x82001,x82002,x82003)+~P1(f862(x82001,x82003))+P1(f862(f862(f227(a1),f872(x82003,x82002,x82001)),f2(a1)))+P1(f862(f862(f228(a1),f873(x82003,x82002,x82001)),x82002))
% 25.54/25.42 [8207]P149(x82071,x82072,x82073)+~P1(f862(x82071,f2(a1)))+P1(f862(f862(f227(a1),f867(x82073,x82072,x82071)),f2(a1)))+P1(f862(f862(f228(a1),f868(x82073,x82072,x82071)),x82072))
% 25.54/25.42 [8428]P149(x84283,x84281,x84282)+E(x84281,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84281),f871(x84282,x84281,x84283))),f867(x84282,x84281,x84283)),x84282)+P1(f862(f862(f228(a1),f868(x84282,x84281,x84283)),x84281))
% 25.54/25.42 [8429]P148(x84293,x84291,x84292)+E(x84291,f2(a1))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84291),f875(x84292,x84291,x84293))),f872(x84292,x84291,x84293)),x84292)+P1(f862(f862(f228(a1),f873(x84292,x84291,x84293)),x84291))
% 25.54/25.42 [8464]P148(x84643,x84641,x84642)+~P1(f862(x84643,x84642))+E(f862(f862(f73(a1),f862(f862(f74(a1),x84641),f875(x84642,x84641,x84643))),f872(x84642,x84641,x84643)),x84642)+P1(f862(f862(f228(a1),f873(x84642,x84641,x84643)),x84641))
% 25.54/25.42 [8465]~P71(x84651)+~P72(x84651)+~P38(x84653)+E(f862(f862(f8(a924,x84651),f862(f862(f10(a1,x84651,a924),x84652),f93(a1))),f862(f302(a1,a924,a97),x84653)),f862(f862(f8(a1,x84651),x84652),x84653))
% 25.54/25.42 [8466]~P71(x84661)+~P72(x84661)+~P38(x84663)+E(f862(f862(f11(a924,x84661),f862(f862(f10(a1,x84661,a924),x84662),f93(a1))),f862(f302(a1,a924,a97),x84663)),f862(f862(f11(a1,x84661),x84662),x84663))
% 25.54/25.42 [8475]P149(x84753,x84751,x84752)+E(f862(f862(f73(a1),f862(f862(f74(a1),x84751),f871(x84752,x84751,x84753))),f867(x84752,x84751,x84753)),x84752)+~P1(f862(x84753,f2(a1)))+P1(f862(f862(f228(a1),f868(x84752,x84751,x84753)),x84751))
% 25.54/25.42 [8497]~E(x84972,f2(a924))+~E(f862(f243(a924,a924),x84973),f2(a924))+~E(x84971,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x84973)),x84972)),f862(f248(a924,a924),x84973)))+P1(f862(f41(x84971,x84972),x84973))
% 25.54/25.42 [8554]P1(f862(x85541,x85542))+~P1(f862(f862(f321(x85543),f442(x85541,x85542,x85543)),f441(x85541,x85542,x85543)))+~P1(f862(f54(x85543),x85542))+~P1(f862(x85541,f181(f932(x85543,a921))))
% 25.54/25.42 [9185]P1(f862(x91851,x91852))+~P1(f862(f54(x91853),x91852))+~P1(f862(x91851,f862(f862(f301(x91853),f442(x91851,x91852,x91853)),f441(x91851,x91852,x91853))))+~P1(f862(x91851,f181(f932(x91853,a921))))
% 25.54/25.42 [9418]P1(f862(f862(f227(a1),x94181),f2(a1)))+~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x94183),x94181)),x94182)),f2(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x94182))+~P1(f862(f862(f228(a1),f2(a1)),x94183))
% 25.54/25.42 [10176]E(x101761,x101762)+~E(f862(f85(x101763),x101761),f862(f85(x101763),x101762))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101763,f932(a920,a921))),f930(a920,x101763)),a921)),x101761),f862(f254(f932(f922(f930(a919,f932(x101763,f932(a920,a921))),f930(a920,x101763)),a921)),f88(x101763))))+~P1(f862(f862(f321(f932(f922(f930(a919,f932(x101763,f932(a920,a921))),f930(a920,x101763)),a921)),x101762),f862(f254(f932(f922(f930(a919,f932(x101763,f932(a920,a921))),f930(a920,x101763)),a921)),f88(x101763))))
% 25.54/25.42 [5988]~P93(x59882)+E(x59881,f181(f932(x59882,a921)))+~P1(f862(f54(x59882),x59881))+E(f12(x59882,f862(f862(f301(x59882),x59883),x59881)),f862(f862(f94(x59882),x59883),f12(x59882,x59881)))
% 25.54/25.42 [5989]~P93(x59892)+E(x59891,f181(f932(x59892,a921)))+~P1(f862(f54(x59892),x59891))+E(f15(x59892,f862(f862(f301(x59892),x59893),x59891)),f862(f862(f103(x59892),x59893),f15(x59892,x59891)))
% 25.54/25.42 [5990]~P109(x59902)+E(x59901,f181(f932(x59902,a921)))+~P1(f862(f54(x59902),x59901))+E(f16(x59902,f862(f862(f301(x59902),x59903),x59901)),f862(f862(f225(x59902),x59903),f16(x59902,x59901)))
% 25.54/25.42 [5991]~P109(x59912)+E(x59911,f181(f932(x59912,a921)))+~P1(f862(f54(x59912),x59911))+E(f17(x59912,f862(f862(f301(x59912),x59913),x59911)),f862(f862(f226(x59912),x59913),f17(x59912,x59911)))
% 25.54/25.42 [6316]~P128(x63161)+~E(x63163,f2(x63161))+~E(x63162,f2(x63161))+E(f862(f862(f73(x63161),f862(f862(f74(x63161),x63162),x63162)),f862(f862(f74(x63161),x63163),x63163)),f2(x63161))
% 25.54/25.42 [6386]~P100(x63862)+E(x63861,f181(f932(x63862,a921)))+~P1(f862(f54(x63862),x63861))+E(f862(f56(x63862,f74(x63862)),f862(f862(f301(x63862),x63863),x63861)),f862(f862(f74(x63862),x63863),f862(f56(x63862,f74(x63862)),x63861)))
% 25.54/25.42 [6512]~P109(x65122)+E(x65121,f181(f932(x65122,a921)))+~P1(f862(f54(x65122),x65121))+E(f13(x65122,f225(x65122),f862(f862(f301(x65122),x65123),x65121)),f862(f862(f225(x65122),x65123),f13(x65122,f225(x65122),x65121)))
% 25.54/25.42 [6513]~P109(x65132)+E(x65131,f181(f932(x65132,a921)))+~P1(f862(f54(x65132),x65131))+E(f14(x65132,f226(x65132),f862(f862(f301(x65132),x65133),x65131)),f862(f862(f226(x65132),x65133),f14(x65132,f226(x65132),x65131)))
% 25.54/25.42 [6910]~P93(x69101)+~P1(f862(f54(x69101),x69103))+E(f862(f862(f57(x69101,x69101,f94(x69101)),x69102),x69103),f12(x69101,f862(f862(f301(x69101),x69102),x69103)))+P1(f862(f862(f321(x69101),x69102),x69103))
% 25.54/25.42 [6911]~P93(x69111)+~P1(f862(f54(x69111),x69113))+E(f862(f862(f57(x69111,x69111,f103(x69111)),x69112),x69113),f15(x69111,f862(f862(f301(x69111),x69112),x69113)))+P1(f862(f862(f321(x69111),x69112),x69113))
% 25.54/25.42 [6912]~P109(x69121)+~P1(f862(f54(x69121),x69123))+E(f862(f862(f57(x69121,x69121,f225(x69121)),x69122),x69123),f16(x69121,f862(f862(f301(x69121),x69122),x69123)))+P1(f862(f862(f321(x69121),x69122),x69123))
% 25.54/25.42 [6913]~P109(x69131)+~P1(f862(f54(x69131),x69133))+E(f862(f862(f57(x69131,x69131,f226(x69131)),x69132),x69133),f17(x69131,f862(f862(f301(x69131),x69132),x69133)))+P1(f862(f862(f321(x69131),x69132),x69133))
% 25.54/25.42 [7022]~P69(x70221)+~P1(f862(f54(x70221),x70223))+E(f862(f56(x70221,f74(x70221)),f862(f862(f301(x70221),x70222),x70223)),f862(f862(f57(x70221,x70221,f74(x70221)),x70222),x70223))+P1(f862(f862(f321(x70221),x70222),x70223))
% 25.54/25.42 [7037]~P109(x70371)+~P1(f862(f54(x70371),x70373))+E(f13(x70371,f225(x70371),f862(f862(f301(x70371),x70372),x70373)),f862(f862(f57(x70371,x70371,f225(x70371)),x70372),x70373))+P1(f862(f862(f321(x70371),x70372),x70373))
% 25.54/25.42 [7038]~P109(x70381)+~P1(f862(f54(x70381),x70383))+E(f14(x70381,f226(x70381),f862(f862(f301(x70381),x70382),x70383)),f862(f862(f57(x70381,x70381,f226(x70381)),x70382),x70383))+P1(f862(f862(f321(x70381),x70382),x70383))
% 25.54/25.42 [7102]~E(f862(f862(f73(a1),x71022),f862(f862(f74(a1),x71023),x71021)),x71023)+~P1(f862(f862(f228(a1),f2(a1)),x71023))+P1(f862(f862(f227(a1),f71(a1)),x71021))+~P1(f862(f862(f228(a1),x71022),x71023))
% 25.54/25.42 [7131]~E(f862(f862(f73(a1),x71312),f862(f862(f74(a1),x71313),x71311)),x71313)+P1(f862(f862(f227(a1),x71311),f71(a1)))+~P1(f862(f862(f227(a1),f2(a1)),x71312))+~P1(f862(f862(f228(a1),f2(a1)),x71313))
% 25.54/25.42 [7147]E(x71471,f2(a924))+~P1(f862(f41(x71473,x71471),x71472))+~P1(f862(f862(f228(a924),f2(a924)),x71471))+P1(f862(f862(f228(a924),f862(f248(a924,a924),x71472)),x71471))
% 25.54/25.42 [7179]~P139(x71791)+~P1(f862(f862(f227(x71791),x71792),f2(x71791)))+~P1(f862(f862(f227(x71791),x71793),f2(x71791)))+E(f862(f862(f74(x71791),f862(f69(x71791),x71792)),f862(f69(x71791),x71793)),f862(f69(x71791),f862(f862(f74(x71791),x71792),x71793)))
% 25.54/25.42 [7225]~P139(x72251)+~P1(f862(f862(f227(x72251),x72252),f2(x72251)))+E(f862(f862(f74(x72251),f862(f69(x72251),x72252)),f862(f69(x72251),x72253)),f862(f69(x72251),f862(f862(f74(x72251),x72252),x72253)))+~P1(f862(f862(f227(x72251),f2(x72251)),x72253))
% 25.54/25.42 [7226]~P139(x72261)+~P1(f862(f862(f227(x72261),x72263),f2(x72261)))+E(f862(f862(f74(x72261),f862(f69(x72261),x72262)),f862(f69(x72261),x72263)),f862(f69(x72261),f862(f862(f74(x72261),x72262),x72263)))+~P1(f862(f862(f227(x72261),f2(x72261)),x72262))
% 25.54/25.42 [7283]~P139(x72831)+E(f862(f862(f74(x72831),f862(f69(x72831),x72832)),f862(f69(x72831),x72833)),f862(f69(x72831),f862(f862(f74(x72831),x72832),x72833)))+~P1(f862(f862(f227(x72831),f2(x72831)),x72832))+~P1(f862(f862(f227(x72831),f2(x72831)),x72833))
% 25.54/25.42 [7299]~P126(x72991)+~P1(f862(f862(f227(x72991),x72993),f2(x72991)))+~P1(f862(f862(f227(x72991),x72992),f2(x72991)))+P1(f862(f862(f227(x72991),f2(x72991)),f862(f862(f74(x72991),x72992),x72993)))
% 25.54/25.42 [7300]~P126(x73001)+~P1(f862(f862(f227(x73001),x73003),f2(x73001)))+~P1(f862(f862(f227(x73001),x73002),f2(x73001)))+P1(f862(f862(f227(x73001),f2(x73001)),f862(f862(f74(x73001),x73002),x73003)))
% 25.54/25.42 [7301]~P128(x73011)+~P1(f862(f862(f227(x73011),x73013),f2(x73011)))+~P1(f862(f862(f227(x73011),x73012),f2(x73011)))+P1(f862(f862(f227(x73011),f2(x73011)),f862(f862(f74(x73011),x73012),x73013)))
% 25.54/25.42 [7302]~P66(x73021)+~P1(f862(f862(f227(x73021),x73023),f2(x73021)))+~P1(f862(f862(f227(x73021),x73022),f2(x73021)))+P1(f862(f862(f227(x73021),f2(x73021)),f862(f862(f281(x73021),x73022),x73023)))
% 25.54/25.42 [7303]~P67(x73031)+~P1(f862(f862(f228(x73031),x73033),f2(x73031)))+~P1(f862(f862(f227(x73031),x73032),f2(x73031)))+P1(f862(f862(f227(x73031),f2(x73031)),f862(f862(f281(x73031),x73032),x73033)))
% 25.54/25.42 [7304]~P128(x73041)+~P1(f862(f862(f228(x73041),x73043),f2(x73041)))+~P1(f862(f862(f228(x73041),x73042),f2(x73041)))+P1(f862(f862(f228(x73041),f2(x73041)),f862(f862(f74(x73041),x73042),x73043)))
% 25.54/25.42 [7305]~P66(x73051)+~P1(f862(f862(f228(x73051),x73053),f2(x73051)))+~P1(f862(f862(f228(x73051),x73052),f2(x73051)))+P1(f862(f862(f228(x73051),f2(x73051)),f862(f862(f281(x73051),x73052),x73053)))
% 25.54/25.42 [7306]~P67(x73061)+~P1(f862(f862(f228(x73061),x73063),f2(x73061)))+~P1(f862(f862(f228(x73061),x73062),f2(x73061)))+P1(f862(f862(f228(x73061),f2(x73061)),f862(f862(f281(x73061),x73062),x73063)))
% 25.54/25.42 [7307]~P127(x73071)+~P1(f862(f862(f228(a924),f2(a924)),x73073))+~P1(f862(f862(f228(x73071),f71(x73071)),x73072))+P1(f862(f862(f228(x73071),f71(x73071)),f862(f862(f236(x73071),x73072),x73073)))
% 25.54/25.42 [7406]~P126(x74061)+~P1(f862(f862(f227(x74061),f2(x74061)),x74063))+~P1(f862(f862(f227(x74061),f2(x74061)),x74062))+P1(f862(f862(f227(x74061),f2(x74061)),f862(f862(f74(x74061),x74062),x74063)))
% 25.54/25.42 [7407]~P136(x74071)+~P1(f862(f862(f227(x74071),f2(x74071)),x74073))+~P1(f862(f862(f227(x74071),f2(x74071)),x74072))+P1(f862(f862(f227(x74071),f2(x74071)),f862(f862(f74(x74071),x74072),x74073)))
% 25.54/25.42 [7408]~P128(x74081)+~P1(f862(f862(f227(x74081),f2(x74081)),x74083))+~P1(f862(f862(f227(x74081),f2(x74081)),x74082))+P1(f862(f862(f227(x74081),f2(x74081)),f862(f862(f74(x74081),x74082),x74083)))
% 25.54/25.42 [7409]~P87(x74091)+~P1(f862(f862(f227(x74091),f2(x74091)),x74093))+~P1(f862(f862(f227(x74091),f2(x74091)),x74092))+P1(f862(f862(f227(x74091),f2(x74091)),f862(f862(f73(x74091),x74092),x74093)))
% 25.54/25.42 [7410]~P66(x74101)+~P1(f862(f862(f227(x74101),f2(x74101)),x74103))+~P1(f862(f862(f227(x74101),f2(x74101)),x74102))+P1(f862(f862(f227(x74101),f2(x74101)),f862(f862(f281(x74101),x74102),x74103)))
% 25.54/25.42 [7411]~P67(x74111)+~P1(f862(f862(f228(x74111),f2(x74111)),x74113))+~P1(f862(f862(f227(x74111),f2(x74111)),x74112))+P1(f862(f862(f227(x74111),f2(x74111)),f862(f862(f281(x74111),x74112),x74113)))
% 25.54/25.42 [7412]~P127(x74121)+~P1(f862(f862(f228(x74121),f71(x74121)),x74123))+~P1(f862(f862(f228(x74121),f71(x74121)),x74122))+P1(f862(f862(f228(x74121),f71(x74121)),f862(f862(f74(x74121),x74122),x74123)))
% 25.54/25.42 [7413]~P135(x74131)+~P1(f862(f862(f228(x74131),f2(x74131)),x74133))+~P1(f862(f862(f228(x74131),f2(x74131)),x74132))+P1(f862(f862(f228(x74131),f2(x74131)),f862(f862(f74(x74131),x74132),x74133)))
% 25.54/25.42 [7414]~P87(x74141)+~P1(f862(f862(f227(x74141),f2(x74141)),x74143))+~P1(f862(f862(f228(x74141),f2(x74141)),x74142))+P1(f862(f862(f228(x74141),f2(x74141)),f862(f862(f73(x74141),x74142),x74143)))
% 25.54/25.42 [7415]~P87(x74151)+~P1(f862(f862(f227(x74151),f2(x74151)),x74152))+~P1(f862(f862(f228(x74151),f2(x74151)),x74153))+P1(f862(f862(f228(x74151),f2(x74151)),f862(f862(f73(x74151),x74152),x74153)))
% 25.54/25.42 [7416]~P87(x74161)+~P1(f862(f862(f228(x74161),f2(x74161)),x74163))+~P1(f862(f862(f228(x74161),f2(x74161)),x74162))+P1(f862(f862(f228(x74161),f2(x74161)),f862(f862(f73(x74161),x74162),x74163)))
% 25.54/25.42 [7417]~P66(x74171)+~P1(f862(f862(f228(x74171),f2(x74171)),x74173))+~P1(f862(f862(f228(x74171),f2(x74171)),x74172))+P1(f862(f862(f228(x74171),f2(x74171)),f862(f862(f281(x74171),x74172),x74173)))
% 25.54/25.42 [7418]~P67(x74181)+~P1(f862(f862(f228(x74181),f2(x74181)),x74183))+~P1(f862(f862(f228(x74181),f2(x74181)),x74182))+P1(f862(f862(f228(x74181),f2(x74181)),f862(f862(f281(x74181),x74182),x74183)))
% 25.54/25.42 [7499]~P93(x74991)+~P1(f862(f54(x74991),x74993))+E(f12(x74991,f862(f862(f301(x74991),x74992),x74993)),x74992)+~E(f862(f862(f3(f932(x74991,a921)),x74993),f862(f862(f301(x74991),x74992),f181(f932(x74991,a921)))),f181(f932(x74991,a921)))
% 25.54/25.42 [7500]~P93(x75001)+~P1(f862(f54(x75001),x75003))+E(f15(x75001,f862(f862(f301(x75001),x75002),x75003)),x75002)+~E(f862(f862(f3(f932(x75001,a921)),x75003),f862(f862(f301(x75001),x75002),f181(f932(x75001,a921)))),f181(f932(x75001,a921)))
% 25.54/25.42 [7501]~P109(x75011)+~P1(f862(f54(x75011),x75013))+E(f16(x75011,f862(f862(f301(x75011),x75012),x75013)),x75012)+~E(f862(f862(f3(f932(x75011,a921)),x75013),f862(f862(f301(x75011),x75012),f181(f932(x75011,a921)))),f181(f932(x75011,a921)))
% 25.54/25.42 [7502]~P109(x75021)+~P1(f862(f54(x75021),x75023))+E(f17(x75021,f862(f862(f301(x75021),x75022),x75023)),x75022)+~E(f862(f862(f3(f932(x75021,a921)),x75023),f862(f862(f301(x75021),x75022),f181(f932(x75021,a921)))),f181(f932(x75021,a921)))
% 25.54/25.42 [7504]~P128(x75041)+P1(f862(f862(f227(x75041),x75042),f2(x75041)))+P1(f862(f862(f227(x75041),f2(x75041)),x75043))+~P1(f862(f862(f227(x75041),f2(x75041)),f862(f862(f74(x75041),x75043),x75042)))
% 25.54/25.42 [7505]~P128(x75051)+P1(f862(f862(f227(x75051),x75052),f2(x75051)))+P1(f862(f862(f227(x75051),f2(x75051)),x75053))+~P1(f862(f862(f227(x75051),f2(x75051)),f862(f862(f74(x75051),x75052),x75053)))
% 25.54/25.42 [7506]~P66(x75061)+P1(f862(f862(f227(x75061),x75062),f2(x75061)))+P1(f862(f862(f227(x75061),f2(x75061)),x75063))+~P1(f862(f862(f227(x75061),f2(x75061)),f862(f862(f281(x75061),x75063),x75062)))
% 25.54/25.42 [7507]~P66(x75071)+P1(f862(f862(f227(x75071),x75072),f2(x75071)))+P1(f862(f862(f227(x75071),f2(x75071)),x75073))+~P1(f862(f862(f227(x75071),f2(x75071)),f862(f862(f281(x75071),x75072),x75073)))
% 25.54/25.42 [7508]~P128(x75081)+P1(f862(f862(f227(x75081),x75082),f2(x75081)))+P1(f862(f862(f227(x75081),f2(x75081)),x75082))+~P1(f862(f862(f227(x75081),f2(x75081)),f862(f862(f74(x75081),x75083),x75082)))
% 25.54/25.42 [7509]~P128(x75091)+P1(f862(f862(f227(x75091),x75092),f2(x75091)))+P1(f862(f862(f227(x75091),f2(x75091)),x75092))+~P1(f862(f862(f227(x75091),f2(x75091)),f862(f862(f74(x75091),x75092),x75093)))
% 25.54/25.42 [7510]~P66(x75101)+P1(f862(f862(f227(x75101),x75102),f2(x75101)))+P1(f862(f862(f227(x75101),f2(x75101)),x75102))+~P1(f862(f862(f227(x75101),f2(x75101)),f862(f862(f281(x75101),x75103),x75102)))
% 25.54/25.42 [7511]~P66(x75111)+P1(f862(f862(f227(x75111),x75112),f2(x75111)))+P1(f862(f862(f227(x75111),f2(x75111)),x75112))+~P1(f862(f862(f227(x75111),f2(x75111)),f862(f862(f281(x75111),x75112),x75113)))
% 25.54/25.42 [7512]~P66(x75121)+P1(f862(f862(f228(x75121),x75122),f2(x75121)))+P1(f862(f862(f228(x75121),f2(x75121)),x75123))+~P1(f862(f862(f228(x75121),f2(x75121)),f862(f862(f281(x75121),x75123),x75122)))
% 25.54/25.42 [7513]~P66(x75131)+P1(f862(f862(f228(x75131),x75132),f2(x75131)))+P1(f862(f862(f228(x75131),f2(x75131)),x75133))+~P1(f862(f862(f228(x75131),f2(x75131)),f862(f862(f281(x75131),x75132),x75133)))
% 25.54/25.42 [7514]~P66(x75141)+P1(f862(f862(f228(x75141),x75142),f2(x75141)))+P1(f862(f862(f228(x75141),f2(x75141)),x75142))+~P1(f862(f862(f228(x75141),f2(x75141)),f862(f862(f281(x75141),x75143),x75142)))
% 25.54/25.42 [7515]~P66(x75151)+P1(f862(f862(f228(x75151),x75152),f2(x75151)))+P1(f862(f862(f228(x75151),f2(x75151)),x75152))+~P1(f862(f862(f228(x75151),f2(x75151)),f862(f862(f281(x75151),x75152),x75153)))
% 25.54/25.42 [7588]~P1(f862(f862(f278(a924),x75881),x75883))+P1(f862(f862(f278(a924),x75881),x75882))+~P1(f862(f862(f227(a924),x75882),x75883))+~P1(f862(f862(f278(a924),x75881),f862(f862(f3(a924),x75883),x75882)))
% 25.54/25.42 [7589]~P1(f862(f862(f278(a924),x75891),x75893))+P1(f862(f862(f278(a924),x75891),x75892))+~P1(f862(f862(f227(a924),x75893),x75892))+~P1(f862(f862(f278(a924),x75891),f862(f862(f3(a924),x75892),x75893)))
% 25.54/25.42 [7605]~E(f862(f862(f94(f932(x76051,a921)),f862(f165(x76051),x76052)),f862(f165(x76051),x76053)),f181(f932(x76051,a921)))+~P1(f862(f130(x76051),x76053))+~P1(f862(f130(x76051),x76052))+P1(f862(f130(x76051),f862(f862(f127(x76051),x76052),x76053)))
% 25.54/25.42 [7606]~P109(x76061)+~P1(f862(f54(x76061),x76063))+E(f13(x76061,f225(x76061),f862(f862(f301(x76061),x76062),x76063)),x76062)+~E(f862(f862(f3(f932(x76061,a921)),x76063),f862(f862(f301(x76061),x76062),f181(f932(x76061,a921)))),f181(f932(x76061,a921)))
% 25.54/25.42 [7607]~P109(x76071)+~P1(f862(f54(x76071),x76073))+E(f14(x76071,f226(x76071),f862(f862(f301(x76071),x76072),x76073)),x76072)+~E(f862(f862(f3(f932(x76071,a921)),x76073),f862(f862(f301(x76071),x76072),f181(f932(x76071,a921)))),f181(f932(x76071,a921)))
% 25.54/25.42 [7619]~P86(x76191)+~P1(f862(f862(f227(x76191),x76192),x76193))+~P1(f862(f862(f227(x76191),f862(f72(x76191),x76192)),x76193))+P1(f862(f862(f227(x76191),f862(f69(x76191),x76192)),x76193))
% 25.54/25.42 [7620]~P86(x76201)+~P1(f862(f862(f227(x76201),x76202),x76203))+~P1(f862(f862(f227(x76201),f862(f72(x76201),x76202)),x76203))+P1(f862(f862(f227(x76201),f862(f69(x76201),x76202)),x76203))
% 25.54/25.42 [7621]~P112(x76211)+~P1(f862(f862(f228(x76211),x76212),x76213))+~P1(f862(f862(f228(x76211),f862(f72(x76211),x76212)),x76213))+P1(f862(f862(f228(x76211),f862(f69(x76211),x76212)),x76213))
% 25.54/25.42 [7688]~P135(x76881)+P1(f862(f862(f228(x76881),f2(x76881)),x76882))+~P1(f862(f862(f228(x76881),f2(x76881)),x76883))+~P1(f862(f862(f228(x76881),f2(x76881)),f862(f862(f74(x76881),x76883),x76882)))
% 25.54/25.42 [7689]~P135(x76891)+P1(f862(f862(f228(x76891),f2(x76891)),x76892))+~P1(f862(f862(f228(x76891),f2(x76891)),x76893))+~P1(f862(f862(f228(x76891),f2(x76891)),f862(f862(f74(x76891),x76892),x76893)))
% 25.54/25.42 [7990]E(x79901,x79902)+~P1(f862(f54(x79903),x79901))+~P1(f862(f862(f227(a924),f862(f28(x79903),x79901)),f862(f28(x79903),x79902)))+~P1(f862(f862(f227(f932(x79903,a921)),x79902),x79901))
% 25.54/25.42 [8059]~P1(f862(f862(f227(a924),x80592),x80591))+~P1(f862(f862(f227(a924),x80592),x80593))+~P1(f862(f862(f227(a924),x80591),x80593))+P1(f862(f862(f227(a924),f862(f862(f3(a924),x80591),x80592)),f862(f862(f3(a924),x80593),x80592)))
% 25.54/25.42 [8060]~P1(f862(f862(f227(a924),x80602),x80601))+~P1(f862(f862(f227(a924),x80602),x80603))+~P1(f862(f862(f228(a924),x80601),x80603))+P1(f862(f862(f228(a924),f862(f862(f3(a924),x80601),x80602)),f862(f862(f3(a924),x80603),x80602)))
% 25.54/25.42 [8138]~P1(f862(f862(f228(a1),x81381),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x81382))+~P1(f862(f862(f227(a1),x81382),x81383))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x81381),x81382)),f862(f862(f29(a1),x81381),x81383)))
% 25.54/25.42 [8148]~P1(f862(f862(f227(a1),f2(a1)),x81481))+~P1(f862(f862(f228(a1),f2(a1)),x81483))+~P1(f862(f862(f227(a1),x81483),x81482))+P1(f862(f862(f227(a1),f862(f862(f29(a1),x81481),x81482)),f862(f862(f29(a1),x81481),x81483)))
% 25.54/25.42 [8285]E(f862(x82851,f433(x82852,x82851,x82853)),x82852)+~P1(f862(f862(f227(a1),x82852),f862(x82851,x82853)))+P1(f862(f862(f228(a924),f434(x82852,x82851,x82853)),x82853))+~P1(f862(f862(f227(a1),f862(x82851,f2(a924))),x82852))
% 25.54/25.42 [8286]E(f862(x82861,f439(x82862,x82861,x82863)),x82862)+~P1(f862(f862(f227(a1),x82862),f862(x82861,x82863)))+P1(f862(f862(f228(a924),f440(x82862,x82861,x82863)),x82863))+~P1(f862(f862(f227(a1),f862(x82861,f2(a924))),x82862))
% 25.54/25.42 [8391]~P1(f862(f54(x83911),x83913))+~P1(f862(f862(f228(a924),f862(f28(x83911),x83912)),f862(f28(x83911),x83913)))+~P1(f862(f862(f227(f932(x83911,a921)),x83912),x83913))+P1(f862(f862(f228(f932(x83911,a921)),x83912),x83913))
% 25.54/25.42 [8418]E(f862(f862(f73(a1),f385(x84183,x84181,x84182)),f386(x84183,x84181,x84182)),x84181)+E(f862(f862(f3(a1),x84181),x84182),x84181)+~P1(f862(f862(f228(a1),f2(a1)),x84182))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x84181),f71(a1))),x84183))
% 25.54/25.42 [8419]E(f862(f862(f3(a1),f393(x84193,x84191,x84192)),f394(x84193,x84191,x84192)),x84191)+E(f862(f862(f73(a1),x84191),x84192),x84191)+~P1(f862(f862(f228(a1),f2(a1)),x84192))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x84191),f71(a1))),x84193))
% 25.54/25.42 [8470]~P1(f862(f862(f227(a924),x84703),x84701))+P1(f862(f862(f227(a924),x84701),x84702))+~P1(f862(f862(f227(a924),x84703),x84702))+~P1(f862(f862(f227(a924),f862(f862(f3(a924),x84701),x84703)),f862(f862(f3(a924),x84702),x84703)))
% 25.54/25.42 [8471]~P1(f862(f862(f227(a924),x84713),x84711))+P1(f862(f862(f228(a924),x84711),x84712))+~P1(f862(f862(f227(a924),x84713),x84712))+~P1(f862(f862(f228(a924),f862(f862(f3(a924),x84711),x84713)),f862(f862(f3(a924),x84712),x84713)))
% 25.54/25.42 [8490]~P109(x84902)+E(x84901,f106(x84902))+~P11(x84902,f862(f161(x84902),x84901))+E(f862(f135(x84902,x84902,f862(f9(x84902,x84902,x84902),f226(x84902)),x84903),f862(f161(x84902),x84901)),f862(f862(f226(x84902),f862(f862(f157(x84902),x84901),f2(a924))),x84903))
% 25.54/25.42 [8559]E(f862(f862(f3(a1),x85591),x85592),x85591)+~P1(f862(f862(f228(a1),f2(a1)),x85592))+P1(f862(f862(f321(a1),f385(x85593,x85591,x85592)),x85593))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x85591),f71(a1))),x85593))
% 25.54/25.42 [8560]E(f862(f862(f73(a1),x85601),x85602),x85601)+~P1(f862(f862(f228(a1),f2(a1)),x85602))+P1(f862(f862(f321(a1),f393(x85603,x85601,x85602)),x85603))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x85601),f71(a1))),x85603))
% 25.54/25.42 [8633]~P1(f862(f862(f227(a1),x86331),f862(x86332,x86333)))+P1(f862(f862(f228(a924),f434(x86331,x86332,x86333)),x86333))+P1(f862(f862(f227(a924),f433(x86331,x86332,x86333)),x86333))+~P1(f862(f862(f227(a1),f862(x86332,f2(a924))),x86331))
% 25.54/25.42 [8634]~P1(f862(f862(f227(a1),x86341),f862(x86342,x86343)))+P1(f862(f862(f228(a924),f440(x86341,x86342,x86343)),x86343))+P1(f862(f862(f227(a924),f439(x86341,x86342,x86343)),x86343))+~P1(f862(f862(f227(a1),f862(x86342,f2(a924))),x86341))
% 25.54/25.42 [8708]E(f862(f862(f3(a1),x87081),x87082),x87081)+~P1(f862(f862(f228(a1),f2(a1)),x87082))+P1(f862(f862(f321(a1),f386(x87083,x87081,x87082)),f296(a1,f71(a1),x87082)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x87081),f71(a1))),x87083))
% 25.54/25.42 [8709]E(f862(f862(f73(a1),x87091),x87092),x87091)+~P1(f862(f862(f228(a1),f2(a1)),x87092))+P1(f862(f862(f321(a1),f394(x87093,x87091,x87092)),f296(a1,f71(a1),x87092)))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x87091),f71(a1))),x87093))
% 25.54/25.42 [8843]~P127(x88431)+~P1(f862(f862(f228(x88431),x88432),f71(x88431)))+~P1(f862(f862(f228(x88431),f2(x88431)),x88432))+P1(f862(f862(f228(x88431),f862(f862(f74(x88431),x88432),f862(f862(f236(x88431),x88432),x88433))),f862(f862(f236(x88431),x88432),x88433)))
% 25.54/25.42 [8937]~P1(f862(x89371,x89372))+P1(f862(x89371,f2(a924)))+~P1(f862(f862(f228(a924),x89372),x89373))+~P1(f862(x89371,f38(a924,f862(a105,f437(x89372,x89371,x89373)),x89373)))
% 25.54/25.42 [9091]E(f510(x90911,x90912,x90913),f2(a924))+P1(f862(f862(x90911,x90913),x90912))+P1(f862(f862(x90911,f510(x90911,x90912,x90913)),f38(a924,f508(x90911,x90912,x90913),f510(x90911,x90912,x90913))))+~P1(f862(f307(f931(a924,a924),a212),f862(f862(f244(a924,a924),x90913),x90912)))
% 25.54/25.42 [9127]~P22(x91271,x91271,x91272,x91273)+E(f862(f302(x91271,x91271,x91272),x91273),x91273)+~P1(f862(f54(x91271),x91273))+~P1(f862(f862(f227(f932(x91271,a921)),f862(f302(x91271,x91271,x91272),x91273)),x91273))
% 25.54/25.42 [9344]P1(f862(f862(x93441,x93442),x93443))+P1(f862(f862(f228(a1),f779(x93441,x93443,x93442)),f780(x93441,x93443,x93442)))+P1(f862(f862(x93441,f779(x93441,x93443,x93442)),f862(f862(f73(a1),f780(x93441,x93443,x93442)),f71(a1))))+~P1(f862(f307(f931(a1,a1),a126),f862(f862(f244(a1,a1),x93442),x93443)))
% 25.54/25.42 [9361]P1(f862(f862(x93611,x93612),x93613))+~P1(f862(f862(f228(a1),f507(x93611,x93613,x93612)),f2(a1)))+P1(f862(f862(x93611,f862(f72(a1),f504(x93611,x93613,x93612))),f862(f72(a1),f507(x93611,x93613,x93612))))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x93612),x93613)))
% 25.54/25.42 [9550]P1(f862(f862(x95501,x95502),x95503))+P1(f862(f862(x95501,f862(f862(f73(a1),f683(x95501,x95503,x95502)),f71(a1))),f685(x95501,x95503,x95502)))+~P1(f862(f862(f227(a1),f683(x95501,x95503,x95502)),f685(x95501,x95503,x95502)))+~P1(f862(f307(f931(a1,a1),a175),f862(f862(f244(a1,a1),x95502),x95503)))
% 25.54/25.42 [9989]~P63(x99892)+~P63(x99891)+~P1(f862(f49(f931(x99891,x99892)),x99893))+P1(f862(f49(x99891),f862(f862(f10(f932(x99892,a921),a921,x99891),f49(x99892)),f862(f862(f10(f932(x99892,f931(x99891,x99892)),f932(x99892,a921),x99891),f862(f10(f931(x99891,x99892),a921,x99892),x99893)),f244(x99891,x99892)))))
% 25.54/25.42 [9990]~P63(x99902)+~P63(x99901)+~P1(f862(f50(f931(x99901,x99902)),x99903))+P1(f862(f50(x99901),f862(f862(f10(f932(x99902,a921),a921,x99901),f50(x99902)),f862(f862(f10(f932(x99902,f931(x99901,x99902)),f932(x99902,a921),x99901),f862(f10(f931(x99901,x99902),a921,x99902),x99903)),f244(x99901,x99902)))))
% 25.54/25.42 [10085]~P63(x100852)+~P63(x100851)+P1(f862(f49(f931(x100851,x100852)),x100853))+~P1(f862(f49(x100851),f862(f862(f10(f932(x100852,a921),a921,x100851),f49(x100852)),f862(f862(f10(f932(x100852,f931(x100851,x100852)),f932(x100852,a921),x100851),f862(f10(f931(x100851,x100852),a921,x100852),x100853)),f244(x100851,x100852)))))
% 25.54/25.42 [10086]~P63(x100862)+~P63(x100861)+P1(f862(f50(f931(x100861,x100862)),x100863))+~P1(f862(f50(x100861),f862(f862(f10(f932(x100862,a921),a921,x100861),f50(x100862)),f862(f862(f10(f932(x100862,f931(x100861,x100862)),f932(x100862,a921),x100861),f862(f10(f931(x100861,x100862),a921,x100862),x100863)),f244(x100861,x100862)))))
% 25.54/25.42 [10248]E(f862(x102481,f433(x102482,x102481,x102483)),x102482)+~P1(f862(f862(f227(a1),x102482),f862(x102481,x102483)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102481,f862(f862(f73(a924),f434(x102482,x102481,x102483)),f71(a924)))),f862(x102481,f434(x102482,x102481,x102483))))),f71(a1)))+~P1(f862(f862(f227(a1),f862(x102481,f2(a924))),x102482))
% 25.54/25.42 [10249]E(f862(x102491,f439(x102492,x102491,x102493)),x102492)+~P1(f862(f862(f227(a1),x102492),f862(x102491,x102493)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102491,f862(f862(f73(a924),f440(x102492,x102491,x102493)),f71(a924)))),f862(x102491,f440(x102492,x102491,x102493))))),f71(a1)))+~P1(f862(f862(f227(a1),f862(x102491,f2(a924))),x102492))
% 25.54/25.42 [10252]~P1(f862(f862(f227(a1),x102521),f862(x102522,x102523)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102522,f862(f862(f73(a924),f434(x102521,x102522,x102523)),f71(a924)))),f862(x102522,f434(x102521,x102522,x102523))))),f71(a1)))+P1(f862(f862(f227(a924),f433(x102521,x102522,x102523)),x102523))+~P1(f862(f862(f227(a1),f862(x102522,f2(a924))),x102521))
% 25.54/25.42 [10253]~P1(f862(f862(f227(a1),x102531),f862(x102532,x102533)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x102532,f862(f862(f73(a924),f440(x102531,x102532,x102533)),f71(a924)))),f862(x102532,f440(x102531,x102532,x102533))))),f71(a1)))+P1(f862(f862(f227(a924),f439(x102531,x102532,x102533)),x102533))+~P1(f862(f862(f227(a1),f862(x102532,f2(a924))),x102531))
% 25.54/25.42 [10312]E(x103121,x103122)+~E(f862(f135(f925(x103123),f925(x103123),f127(x103123),f106(x103123)),x103121),f862(f135(f925(x103123),f925(x103123),f127(x103123),f106(x103123)),x103122))+~E(f862(f182(f925(f925(x103123))),x103121),f862(f182(f925(f925(x103123))),x103122))+~P1(f862(f862(f249(f925(x103123),f925(x103123),a921),f862(f862(f9(f925(x103123),f932(f925(x103123),a924),f932(f925(x103123),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x103123),a924),f932(f925(x103123),a921)),f925(x103123)),f10(a924,a921,f925(x103123))),f862(f862(f10(a924,f932(a924,a921),f925(x103123)),a317),f182(f925(x103123))))),f182(f925(x103123)))),f709(x103122,x103121,x103123)))
% 25.54/25.42 [10313]E(x103131,x103132)+~E(f862(f135(f925(x103133),f925(x103133),f127(x103133),f106(x103133)),x103131),f862(f135(f925(x103133),f925(x103133),f127(x103133),f106(x103133)),x103132))+~E(f862(f182(f925(f925(x103133))),x103131),f862(f182(f925(f925(x103133))),x103132))+~P1(f862(f862(f249(f925(x103133),f925(x103133),a921),f862(f862(f9(f925(x103133),f932(f925(x103133),a924),f932(f925(x103133),a921)),f862(f862(f10(f932(a924,a921),f932(f932(f925(x103133),a924),f932(f925(x103133),a921)),f925(x103133)),f10(a924,a921,f925(x103133))),f862(f862(f10(a924,f932(a924,a921),f925(x103133)),a317),f182(f925(x103133))))),f182(f925(x103133)))),f710(x103131,x103132,x103133)))
% 25.54/25.42 [7010]~E(f71(a924),f2(a924))+~P1(f862(f54(x70101),x70103))+~P1(f862(f54(x70101),x70102))+E(f862(f862(f73(a924),f862(f28(x70101),x70102)),f862(f28(x70101),x70103)),f862(f28(x70101),f862(f862(f103(f932(x70101,a921)),x70102),x70103)))
% 25.54/25.42 [7425]~P104(x74251)+~P1(f862(f54(x74251),x74252))+~P1(f862(f862(f321(x74251),x74253),x74252))+P1(f862(f862(f227(x74251),f862(f56(x74251,f94(x74251)),x74252)),x74253))
% 25.54/25.42 [7426]~P109(x74261)+~P1(f862(f54(x74261),x74262))+~P1(f862(f862(f321(x74261),x74263),x74262))+P1(f862(f862(f227(x74261),f862(f56(x74261,f225(x74261)),x74262)),x74263))
% 25.54/25.42 [7681]~P1(f862(f54(x76811),x76813))+~P1(f862(f54(x76811),x76812))+~E(f862(f862(f94(f932(x76811,a921)),x76812),x76813),f181(f932(x76811,a921)))+E(f862(f862(f73(a924),f862(f28(x76811),x76812)),f862(f28(x76811),x76813)),f862(f28(x76811),f862(f862(f103(f932(x76811,a921)),x76812),x76813)))
% 25.54/25.42 [8476]~P35(x84761,x84763)+~P35(x84761,x84762)+~E(f862(f862(f94(f932(x84761,a921)),f862(f256(x84761,x84761),x84762)),f862(f275(x84761,x84761),x84763)),f181(f932(x84761,a921)))+P35(x84761,f862(f862(f103(f932(f931(x84761,x84761),a921)),x84762),x84763))
% 25.54/25.42 [8571]E(x85711,f862(f862(f29(a924),x85712),x85713))+~P1(f862(f862(f228(a924),f2(a924)),x85713))+~P1(f862(f862(f228(a924),x85712),f862(f862(f74(a924),x85713),f862(a105,x85711))))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x85713),x85711)),x85712))
% 25.54/25.42 [8706]~P1(f862(f54(x87061),x87062))+~P1(f862(f54(x87061),x87063))+E(f862(f862(f73(a924),f862(f28(x87061),x87062)),f862(f28(x87061),x87063)),f862(f28(x87061),f862(f862(f103(f932(x87061,a921)),x87062),x87063)))+P1(f862(f862(f321(x87061),f352(x87063,x87062,x87061)),f862(f862(f94(f932(x87061,a921)),x87062),x87063)))
% 25.54/25.42 [9103]~P128(x91032)+~E(x91031,f2(x91032))+~E(x91033,f2(x91032))+~P1(f862(f862(f228(x91032),f2(x91032)),f862(f862(f73(x91032),f862(f862(f74(x91032),x91033),x91033)),f862(f862(f74(x91032),x91031),x91031))))
% 25.54/25.42 [9633]~P35(x96331,x96333)+~P35(x96331,x96332)+P35(x96331,f862(f862(f103(f932(f931(x96331,x96331),a921)),x96332),x96333))+~P1(f862(f862(f227(f932(f931(x96331,x96331),a921)),f862(f862(f280(x96331,x96331,x96331),x96332),x96333)),x96332))
% 25.54/25.42 [9763]~P1(f862(x97631,x97633))+~P1(f862(f54(x97632),x97633))+P1(f862(x97631,f181(f932(x97632,a921))))+~P1(f862(x97631,f862(f862(f3(f932(x97632,a921)),f876(x97631,x97633,x97632)),f862(f862(f301(x97632),f877(x97631,x97633,x97632)),f181(f932(x97632,a921))))))
% 25.54/25.42 [8883]~P1(f862(f862(f228(a1),f2(a1)),x88833))+P1(f862(f862(f227(a1),f2(a1)),x88831))+~P1(f862(f862(f228(a1),x88832),x88833))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x88833),x88831)),x88832)))
% 25.54/25.42 [8908]~P93(x89081)+~P1(f862(f54(x89081),x89082))+E(f862(f862(f3(f932(x89081,a921)),x89082),f862(f862(f301(x89081),x89083),f181(f932(x89081,a921)))),f181(f932(x89081,a921)))+E(f862(f862(f94(x89081),x89083),f12(x89081,f862(f862(f3(f932(x89081,a921)),x89082),f862(f862(f301(x89081),x89083),f181(f932(x89081,a921)))))),f12(x89081,f862(f862(f301(x89081),x89083),x89082)))
% 25.54/25.42 [8909]~P93(x89091)+~P1(f862(f54(x89091),x89092))+E(f862(f862(f3(f932(x89091,a921)),x89092),f862(f862(f301(x89091),x89093),f181(f932(x89091,a921)))),f181(f932(x89091,a921)))+E(f862(f862(f103(x89091),x89093),f15(x89091,f862(f862(f3(f932(x89091,a921)),x89092),f862(f862(f301(x89091),x89093),f181(f932(x89091,a921)))))),f15(x89091,f862(f862(f301(x89091),x89093),x89092)))
% 25.54/25.42 [8910]~P109(x89101)+~P1(f862(f54(x89101),x89102))+E(f862(f862(f3(f932(x89101,a921)),x89102),f862(f862(f301(x89101),x89103),f181(f932(x89101,a921)))),f181(f932(x89101,a921)))+E(f862(f862(f225(x89101),x89103),f16(x89101,f862(f862(f3(f932(x89101,a921)),x89102),f862(f862(f301(x89101),x89103),f181(f932(x89101,a921)))))),f16(x89101,f862(f862(f301(x89101),x89103),x89102)))
% 25.54/25.42 [8911]~P109(x89111)+~P1(f862(f54(x89111),x89112))+E(f862(f862(f3(f932(x89111,a921)),x89112),f862(f862(f301(x89111),x89113),f181(f932(x89111,a921)))),f181(f932(x89111,a921)))+E(f862(f862(f226(x89111),x89113),f17(x89111,f862(f862(f3(f932(x89111,a921)),x89112),f862(f862(f301(x89111),x89113),f181(f932(x89111,a921)))))),f17(x89111,f862(f862(f301(x89111),x89113),x89112)))
% 25.54/25.42 [8983]~P109(x89831)+~P1(f862(f54(x89831),x89832))+E(f862(f862(f3(f932(x89831,a921)),x89832),f862(f862(f301(x89831),x89833),f181(f932(x89831,a921)))),f181(f932(x89831,a921)))+E(f862(f862(f225(x89831),x89833),f13(x89831,f225(x89831),f862(f862(f3(f932(x89831,a921)),x89832),f862(f862(f301(x89831),x89833),f181(f932(x89831,a921)))))),f13(x89831,f225(x89831),f862(f862(f301(x89831),x89833),x89832)))
% 25.54/25.42 [8984]~P109(x89841)+~P1(f862(f54(x89841),x89842))+E(f862(f862(f3(f932(x89841,a921)),x89842),f862(f862(f301(x89841),x89843),f181(f932(x89841,a921)))),f181(f932(x89841,a921)))+E(f862(f862(f226(x89841),x89843),f14(x89841,f226(x89841),f862(f862(f3(f932(x89841,a921)),x89842),f862(f862(f301(x89841),x89843),f181(f932(x89841,a921)))))),f14(x89841,f226(x89841),f862(f862(f301(x89841),x89843),x89842)))
% 25.54/25.42 [9570]E(x95701,x95702)+~E(f862(f135(f925(x95703),f925(x95703),f127(x95703),f106(x95703)),x95701),f862(f135(f925(x95703),f925(x95703),f127(x95703),f106(x95703)),x95702))+~E(f862(f182(f925(f925(x95703))),x95701),f862(f182(f925(f925(x95703))),x95702))+P1(f862(f862(f321(f931(f925(x95703),f925(x95703))),f709(x95702,x95701,x95703)),f862(f165(f931(f925(x95703),f925(x95703))),f862(f862(f174(f925(x95703),f925(x95703)),x95701),x95702))))
% 25.54/25.42 [9571]E(x95711,x95712)+~E(f862(f135(f925(x95713),f925(x95713),f127(x95713),f106(x95713)),x95711),f862(f135(f925(x95713),f925(x95713),f127(x95713),f106(x95713)),x95712))+~E(f862(f182(f925(f925(x95713))),x95711),f862(f182(f925(f925(x95713))),x95712))+P1(f862(f862(f321(f931(f925(x95713),f925(x95713))),f710(x95711,x95712,x95713)),f862(f165(f931(f925(x95713),f925(x95713))),f862(f862(f174(f925(x95713),f925(x95713)),x95712),x95711))))
% 25.54/25.42 [10421]~P102(x104212)+E(x104211,f181(f932(x104212,a921)))+~P1(f862(f54(x104212),x104211))+E(f12(x104212,f862(f254(x104212),f862(f862(f10(f932(x104212,a921),a921,x104212),f80(x104212)),f862(f862(f9(x104212,f932(x104212,a921),f932(x104212,a921)),f862(f862(f10(f932(x104212,f932(a921,a921)),f932(f932(x104212,a921),f932(x104212,a921)),x104212),f20(x104212,a921,a921)),f862(f862(f10(f932(x104212,a921),f932(x104212,f932(a921,a921)),x104212),f862(f10(a921,f932(a921,a921),x104212),a318)),f862(f862(f9(x104212,f932(x104212,x104212),f932(x104212,a921)),f862(f862(f10(f932(x104212,a921),f932(f932(x104212,x104212),f932(x104212,a921)),x104212),f10(x104212,a921,x104212)),a317)),f862(f103(x104212),x104213))))),f862(f862(f9(x104212,f932(x104212,a921),a921),f321(x104212)),x104211))))),f862(f862(f103(x104212),x104213),f12(x104212,x104211)))
% 25.54/25.42 [10422]~P102(x104222)+E(x104221,f181(f932(x104222,a921)))+~P1(f862(f54(x104222),x104221))+E(f15(x104222,f862(f254(x104222),f862(f862(f10(f932(x104222,a921),a921,x104222),f80(x104222)),f862(f862(f9(x104222,f932(x104222,a921),f932(x104222,a921)),f862(f862(f10(f932(x104222,f932(a921,a921)),f932(f932(x104222,a921),f932(x104222,a921)),x104222),f20(x104222,a921,a921)),f862(f862(f10(f932(x104222,a921),f932(x104222,f932(a921,a921)),x104222),f862(f10(a921,f932(a921,a921),x104222),a318)),f862(f862(f9(x104222,f932(x104222,x104222),f932(x104222,a921)),f862(f862(f10(f932(x104222,a921),f932(f932(x104222,x104222),f932(x104222,a921)),x104222),f10(x104222,a921,x104222)),a317)),f862(f94(x104222),x104223))))),f862(f862(f9(x104222,f932(x104222,a921),a921),f321(x104222)),x104221))))),f862(f862(f94(x104222),x104223),f15(x104222,x104221)))
% 25.54/25.42 [10423]~P77(x104232)+E(x104231,f181(f932(x104232,a921)))+~P1(f862(f54(x104232),x104231))+E(f16(x104232,f862(f254(x104232),f862(f862(f10(f932(x104232,a921),a921,x104232),f80(x104232)),f862(f862(f9(x104232,f932(x104232,a921),f932(x104232,a921)),f862(f862(f10(f932(x104232,f932(a921,a921)),f932(f932(x104232,a921),f932(x104232,a921)),x104232),f20(x104232,a921,a921)),f862(f862(f10(f932(x104232,a921),f932(x104232,f932(a921,a921)),x104232),f862(f10(a921,f932(a921,a921),x104232),a318)),f862(f862(f9(x104232,f932(x104232,x104232),f932(x104232,a921)),f862(f862(f10(f932(x104232,a921),f932(f932(x104232,x104232),f932(x104232,a921)),x104232),f10(x104232,a921,x104232)),a317)),f862(f73(x104232),x104233))))),f862(f862(f9(x104232,f932(x104232,a921),a921),f321(x104232)),x104231))))),f862(f862(f73(x104232),x104233),f16(x104232,x104231)))
% 25.54/25.42 [10424]~P77(x104242)+E(x104241,f181(f932(x104242,a921)))+~P1(f862(f54(x104242),x104241))+E(f17(x104242,f862(f254(x104242),f862(f862(f10(f932(x104242,a921),a921,x104242),f80(x104242)),f862(f862(f9(x104242,f932(x104242,a921),f932(x104242,a921)),f862(f862(f10(f932(x104242,f932(a921,a921)),f932(f932(x104242,a921),f932(x104242,a921)),x104242),f20(x104242,a921,a921)),f862(f862(f10(f932(x104242,a921),f932(x104242,f932(a921,a921)),x104242),f862(f10(a921,f932(a921,a921),x104242),a318)),f862(f862(f9(x104242,f932(x104242,x104242),f932(x104242,a921)),f862(f862(f10(f932(x104242,a921),f932(f932(x104242,x104242),f932(x104242,a921)),x104242),f10(x104242,a921,x104242)),a317)),f862(f73(x104242),x104243))))),f862(f862(f9(x104242,f932(x104242,a921),a921),f321(x104242)),x104241))))),f862(f862(f73(x104242),x104243),f17(x104242,x104241)))
% 25.54/25.42 [10425]~P109(x104252)+E(x104251,f181(f932(x104252,a921)))+~P1(f862(f54(x104252),x104251))+E(f14(x104252,f226(x104252),f862(f254(x104252),f862(f862(f10(f932(x104252,a921),a921,x104252),f80(x104252)),f862(f862(f9(x104252,f932(x104252,a921),f932(x104252,a921)),f862(f862(f10(f932(x104252,f932(a921,a921)),f932(f932(x104252,a921),f932(x104252,a921)),x104252),f20(x104252,a921,a921)),f862(f862(f10(f932(x104252,a921),f932(x104252,f932(a921,a921)),x104252),f862(f10(a921,f932(a921,a921),x104252),a318)),f862(f862(f9(x104252,f932(x104252,x104252),f932(x104252,a921)),f862(f862(f10(f932(x104252,a921),f932(f932(x104252,x104252),f932(x104252,a921)),x104252),f10(x104252,a921,x104252)),a317)),f862(f225(x104252),x104253))))),f862(f862(f9(x104252,f932(x104252,a921),a921),f321(x104252)),x104251))))),f862(f862(f225(x104252),x104253),f14(x104252,f226(x104252),x104251)))
% 25.54/25.42 [10426]~P109(x104262)+E(x104261,f181(f932(x104262,a921)))+~P1(f862(f54(x104262),x104261))+E(f13(x104262,f225(x104262),f862(f254(x104262),f862(f862(f10(f932(x104262,a921),a921,x104262),f80(x104262)),f862(f862(f9(x104262,f932(x104262,a921),f932(x104262,a921)),f862(f862(f10(f932(x104262,f932(a921,a921)),f932(f932(x104262,a921),f932(x104262,a921)),x104262),f20(x104262,a921,a921)),f862(f862(f10(f932(x104262,a921),f932(x104262,f932(a921,a921)),x104262),f862(f10(a921,f932(a921,a921),x104262),a318)),f862(f862(f9(x104262,f932(x104262,x104262),f932(x104262,a921)),f862(f862(f10(f932(x104262,a921),f932(f932(x104262,x104262),f932(x104262,a921)),x104262),f10(x104262,a921,x104262)),a317)),f862(f226(x104262),x104263))))),f862(f862(f9(x104262,f932(x104262,a921),a921),f321(x104262)),x104261))))),f862(f862(f226(x104262),x104263),f13(x104262,f225(x104262),x104261)))
% 25.54/25.42 [10152]~P112(x101521)+~E(x101523,f2(x101521))+~E(x101522,f2(x101521))+E(f862(f862(f73(x101521),f862(f862(f236(x101521),x101522),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x101521),x101523),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f2(x101521))
% 25.54/25.42 [10293]~P127(x102931)+~P1(f862(f862(f227(x102931),f2(x102931)),x102933))+P1(f862(f862(f227(x102931),x102932),x102933))+~P1(f862(f862(f227(x102931),f862(f862(f236(x102931),x102932),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102931),x102933),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.42 [10294]~P127(x102941)+~P1(f862(f862(f227(x102941),f2(x102941)),x102943))+P1(f862(f862(f228(x102941),x102942),x102943))+~P1(f862(f862(f228(x102941),f862(f862(f236(x102941),x102942),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x102941),x102943),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))))
% 25.54/25.42 [10350]~P112(x103502)+~E(x103501,f2(x103502))+~E(x103503,f2(x103502))+~P1(f862(f862(f228(x103502),f2(x103502)),f862(f862(f73(x103502),f862(f862(f236(x103502),x103503),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90))))),f862(f862(f236(x103502),x103501),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))))
% 25.54/25.42 [6891]~P5(x68913,x68912)+~P1(f862(x68911,x68914))+~P1(f862(f862(f321(x68913),x68914),f262(x68913,x68912)))+P1(f862(x68911,f825(x68911,x68912,x68913)))
% 25.54/25.42 [8818]P23(x88181,x88182,f829(x88183,x88182,x88184,x88181),x88184,x88183)+~E(f862(f28(x88181),x88184),f862(f28(x88182),x88183))+~P1(f862(f54(x88182),x88183))+~P1(f862(f54(x88181),x88184))
% 25.54/25.42 [9531]E(x95311,x95312)+~E(f650(x95311,x95312,x95314,x95313),f655(x95311,x95312,x95314,x95313))+P1(f862(f862(f321(f931(f925(x95313),f925(x95313))),f862(f862(f244(f925(x95313),f925(x95313)),x95312),x95311)),f140(x95313,x95314)))+P1(f862(f862(f321(f931(f925(x95313),f925(x95313))),f862(f862(f244(f925(x95313),f925(x95313)),x95311),x95312)),f140(x95313,x95314)))
% 25.54/25.42 [5022]~P64(x50222)+~E(x50224,f2(x50222))+~E(x50221,f2(x50222))+E(x50221,f862(f862(f281(x50222),x50223),x50224))
% 25.54/25.42 [5023]~P64(x50231)+~E(x50233,f2(x50231))+~E(x50234,f2(x50231))+E(f862(f862(f281(x50231),x50232),x50233),x50234)
% 25.54/25.42 [5143]~P64(x51432)+E(x51431,f2(x51432))+~E(x51433,f2(x51432))+~E(x51431,f862(f862(f281(x51432),x51434),x51433))
% 25.54/25.42 [5144]~P64(x51442)+E(x51441,f2(x51442))+~E(x51443,f2(x51442))+~E(f862(f862(f281(x51442),x51444),x51443),x51441)
% 25.54/25.42 [5329]~P121(x53292)+E(x53291,f2(x53292))+~E(f862(f862(f281(x53292),x53293),x53291),x53294)+E(x53293,f862(f862(f74(x53292),x53294),x53291))
% 25.54/25.42 [5330]~P121(x53302)+E(x53301,f2(x53302))+~E(f862(f862(f74(x53302),x53303),x53301),x53304)+E(x53303,f862(f862(f281(x53302),x53304),x53301))
% 25.54/25.42 [5331]~P121(x53312)+E(x53311,f2(x53312))+~E(f862(f862(f74(x53312),x53313),x53311),x53314)+E(x53313,f862(f862(f281(x53312),x53314),x53311))
% 25.54/25.42 [5332]~P64(x53322)+E(x53321,f2(x53322))+~E(f862(f862(f281(x53322),x53323),x53321),x53324)+E(x53323,f862(f862(f74(x53322),x53324),x53321))
% 25.54/25.42 [5333]~P64(x53332)+E(x53331,f2(x53332))+~E(f862(f862(f74(x53332),x53333),x53331),x53334)+E(x53333,f862(f862(f281(x53332),x53334),x53331))
% 25.54/25.42 [5334]~P121(x53342)+E(x53341,f2(x53342))+~E(x53343,f862(f862(f281(x53342),x53344),x53341))+E(f862(f862(f74(x53342),x53343),x53341),x53344)
% 25.54/25.42 [5335]~P121(x53352)+E(x53351,f2(x53352))+~E(x53353,f862(f862(f74(x53352),x53354),x53351))+E(f862(f862(f281(x53352),x53353),x53351),x53354)
% 25.54/25.42 [5336]~P121(x53362)+E(x53361,f2(x53362))+~E(x53363,f862(f862(f74(x53362),x53364),x53361))+E(f862(f862(f281(x53362),x53363),x53361),x53364)
% 25.54/25.42 [5337]~P64(x53372)+E(x53371,f2(x53372))+~E(x53373,f862(f862(f281(x53372),x53374),x53371))+E(f862(f862(f74(x53372),x53373),x53371),x53374)
% 25.54/25.42 [5338]~P64(x53382)+E(x53381,f2(x53382))+~E(x53383,f862(f862(f74(x53382),x53384),x53381))+E(f862(f862(f281(x53382),x53383),x53381),x53384)
% 25.54/25.42 [5362]~P64(x53622)+~E(x53621,f2(x53622))+~E(f862(f862(f74(x53622),x53621),x53624),x53623)+E(x53621,f862(f862(f281(x53622),x53623),x53624))
% 25.54/25.42 [5363]~P64(x53631)+~E(x53634,f2(x53631))+~E(x53632,f862(f862(f74(x53631),x53634),x53633))+E(f862(f862(f281(x53631),x53632),x53633),x53634)
% 25.54/25.42 [5440]~E(x54403,x54404)+~E(x54402,x54403)+~P110(x54401)+E(f296(x54401,x54402,x54403),f862(f862(f301(x54401),x54404),f181(f932(x54401,a921))))
% 25.54/25.42 [5643]~E(f107(x56432,x56431),x56433)+~E(f137(x56432,x56431),x56434)+E(x56431,f106(x56432))+E(f862(f862(f127(x56432),x56433),f862(f862(f144(x56432),x56434),f106(x56432))),x56431)
% 25.54/25.42 [6282]~P127(x62823)+E(x62821,x62822)+~E(f862(f862(f236(x62823),x62824),x62821),f862(f862(f236(x62823),x62824),x62822))+~P1(f862(f862(f228(x62823),f71(x62823)),x62824))
% 25.54/25.42 [6283]E(x62831,x62832)+~E(f862(f862(f301(x62833),x62834),x62831),f862(f862(f301(x62833),x62834),x62832))+P1(f862(f862(f321(x62833),x62834),x62832))+P1(f862(f862(f321(x62833),x62834),x62831))
% 25.54/25.42 [6325]E(f862(x63251,x63252),f71(a924))+~E(f862(f862(f11(x63253,a924),x63251),x63254),f71(a924))+~P1(f862(f54(x63253),x63254))+~P1(f862(f862(f321(x63253),x63252),x63254))
% 25.54/25.42 [6326]E(f862(x63261,x63262),f2(a924))+~E(f862(f862(f8(x63263,a924),x63261),x63264),f2(a924))+~P1(f862(f54(x63263),x63264))+~P1(f862(f862(f321(x63263),x63262),x63264))
% 25.54/25.42 [6547]~P110(x65471)+~P1(f862(f862(f227(x65471),x65474),x65473))+P1(f862(f862(f227(x65471),x65472),x65473))+~P1(f862(f862(f227(x65471),x65472),x65474))
% 25.54/25.42 [6548]~P91(x65481)+~P1(f862(f862(f227(x65481),x65482),x65484))+P1(f862(f862(f227(x65481),x65482),x65483))+~P1(f862(f862(f227(x65481),x65484),x65483))
% 25.54/25.42 [6549]~P110(x65491)+~P1(f862(f862(f228(x65491),x65494),x65493))+P1(f862(f862(f228(x65491),x65492),x65493))+~P1(f862(f862(f227(x65491),x65492),x65494))
% 25.54/25.42 [6550]~P110(x65501)+~P1(f862(f862(f228(x65501),x65502),x65504))+P1(f862(f862(f228(x65501),x65502),x65503))+~P1(f862(f862(f227(x65501),x65504),x65503))
% 25.54/25.42 [6551]~P110(x65511)+~P1(f862(f862(f228(x65511),x65514),x65513))+P1(f862(f862(f228(x65511),x65512),x65513))+~P1(f862(f862(f228(x65511),x65512),x65514))
% 25.54/25.42 [6552]~P91(x65521)+~P1(f862(f862(f228(x65521),x65522),x65524))+P1(f862(f862(f228(x65521),x65522),x65523))+~P1(f862(f862(f227(x65521),x65524),x65523))
% 25.54/25.42 [6553]~P91(x65531)+~P1(f862(f862(f228(x65531),x65534),x65533))+P1(f862(f862(f228(x65531),x65532),x65533))+~P1(f862(f862(f227(x65531),x65532),x65534))
% 25.54/25.42 [6554]~P91(x65541)+~P1(f862(f862(f228(x65541),x65542),x65544))+P1(f862(f862(f228(x65541),x65542),x65543))+~P1(f862(f862(f228(x65541),x65544),x65543))
% 25.54/25.42 [6555]~P119(x65551)+~P1(f862(f862(f278(x65551),x65552),x65554))+P1(f862(f862(f278(x65551),x65552),x65553))+~P1(f862(f862(f278(x65551),x65554),x65553))
% 25.54/25.42 [6637]~P33(x66374,x66373,x66372)+E(x66371,f764(x66372,x66373,x66374))+~P1(f862(x66373,x66371))+~P1(f862(f862(f321(x66374),x66371),f862(f165(x66374),x66372)))
% 25.54/25.42 [6638]~P33(x66384,x66383,x66382)+E(x66381,f775(x66382,x66383,x66384))+~P1(f862(x66383,x66381))+~P1(f862(f862(f321(x66384),x66381),f862(f165(x66384),x66382)))
% 25.54/25.42 [6786]~P3(x67861)+~P1(f862(f862(f227(x67861),x67862),f31(x67861,x67864)))+P1(f862(f862(f227(x67861),x67862),x67863))+~P1(f862(f862(f321(x67861),x67863),x67864))
% 25.54/25.42 [6928]~P109(x69281)+~P11(x69281,f862(f862(f144(x69281),x69282),x69284))+~P1(f862(f862(f321(x69281),x69283),f862(f165(x69281),x69284)))+P1(f862(f862(f227(x69281),x69282),x69283))
% 25.54/25.42 [6929]~P109(x69291)+~P11(x69291,f862(f862(f144(x69291),x69292),x69294))+~P1(f862(f862(f321(x69291),x69293),f862(f165(x69291),x69294)))+P1(f862(f862(f227(x69291),x69292),x69293))
% 25.54/25.42 [7020]~P3(x70201)+~P1(f862(f862(f227(x70201),f30(x70201,x70204)),x70203))+P1(f862(f862(f227(x70201),x70202),x70203))+~P1(f862(f862(f321(x70201),x70202),x70204))
% 25.54/25.42 [7160]~P61(x71601)+P1(f862(f862(f278(x71601),x71602),f38(x71601,x71603,x71604)))+~P1(f862(f862(f278(x71601),x71602),x71604))+~P1(f862(f862(f278(x71601),x71602),x71603))
% 25.54/25.42 [7161]~P61(x71611)+P1(f862(f862(f278(x71611),x71612),f38(x71611,x71613,x71614)))+~P1(f862(f862(f278(x71611),x71612),x71614))+~P1(f862(f862(f278(x71611),x71612),x71613))
% 25.54/25.42 [7428]~P109(x74281)+E(f862(f862(f103(f932(x74281,a921)),f862(f295(x74281,x74282),x74283)),f862(f295(x74281,x74283),x74284)),f862(f295(x74281,x74282),x74284))+~P1(f862(f862(f227(x74281),x74283),x74284))+~P1(f862(f862(f227(x74281),x74282),x74283))
% 25.54/25.42 [7473]P33(x74731,x74732,x74733)+~E(f776(x74733,x74732,x74731,x74734),x74734)+~P1(f862(x74732,x74734))+~P1(f862(f862(f321(x74731),x74734),f862(f165(x74731),x74733)))
% 25.54/25.42 [7474]P33(x74741,x74742,x74743)+~E(f783(x74743,x74742,x74741,x74744),x74744)+~P1(f862(x74742,x74744))+~P1(f862(f862(f321(x74741),x74744),f862(f165(x74741),x74743)))
% 25.54/25.42 [7517]~P61(x75171)+~P1(f862(f862(f278(x75171),x75172),f38(x75171,x75173,x75174)))+P1(f862(f862(f278(x75171),x75172),x75173))+~P1(f862(f862(f278(x75171),x75172),x75174))
% 25.54/25.42 [7518]~P61(x75181)+~P1(f862(f862(f278(x75181),x75182),f38(x75181,x75183,x75184)))+P1(f862(f862(f278(x75181),x75182),x75183))+~P1(f862(f862(f278(x75181),x75182),x75184))
% 25.54/25.42 [7553]~P109(x75531)+E(f862(f862(f103(f932(x75531,a921)),f862(f295(x75531,x75532),x75533)),f296(x75531,x75533,x75534)),f296(x75531,x75532,x75534))+~P1(f862(f862(f227(x75531),x75533),x75534))+~P1(f862(f862(f227(x75531),x75532),x75533))
% 25.54/25.42 [7615]~P109(x76151)+E(f862(f862(f103(f932(x76151,a921)),f298(x76151,x76152,x76153)),f862(f295(x76151,x76153),x76154)),f298(x76151,x76152,x76154))+~P1(f862(f862(f227(x76151),x76153),x76154))+~P1(f862(f862(f228(x76151),x76152),x76153))
% 25.54/25.42 [7632]~P109(x76321)+E(f862(f862(f103(f932(x76321,a921)),f296(x76321,x76322,x76323)),f298(x76321,x76323,x76324)),f862(f295(x76321,x76322),x76324))+~P1(f862(f862(f227(x76321),x76322),x76323))+~P1(f862(f862(f228(x76321),x76323),x76324))
% 25.54/25.42 [7662]~P109(x76621)+E(f862(f862(f103(f932(x76621,a921)),f298(x76621,x76622,x76623)),f296(x76621,x76623,x76624)),f297(x76621,x76622,x76624))+~P1(f862(f862(f227(x76621),x76623),x76624))+~P1(f862(f862(f228(x76621),x76622),x76623))
% 25.54/25.42 [7663]~P109(x76631)+E(f862(f862(f103(f932(x76631,a921)),f297(x76631,x76632,x76633)),f298(x76631,x76633,x76634)),f298(x76631,x76632,x76634))+~P1(f862(f862(f227(x76631),x76632),x76633))+~P1(f862(f862(f228(x76631),x76633),x76634))
% 25.54/25.42 [7664]~P109(x76641)+E(f862(f862(f103(f932(x76641,a921)),f297(x76641,x76642,x76643)),f297(x76641,x76643,x76644)),f297(x76641,x76642,x76644))+~P1(f862(f862(f227(x76641),x76643),x76644))+~P1(f862(f862(f227(x76641),x76642),x76643))
% 25.54/25.42 [7665]~P109(x76651)+E(f862(f862(f103(f932(x76651,a921)),f296(x76651,x76652,x76653)),f297(x76651,x76653,x76654)),f296(x76651,x76652,x76654))+~P1(f862(f862(f227(x76651),x76653),x76654))+~P1(f862(f862(f227(x76651),x76652),x76653))
% 25.54/25.42 [8460]P22(x84601,x84602,f543(x84603,x84602,x84604,x84601),x84604)+~P1(f862(f54(x84602),x84603))+~P1(f862(f54(x84601),x84604))+~P1(f862(f862(f227(a924),f862(f28(x84601),x84604)),f862(f28(x84602),x84603)))
% 25.54/25.42 [8481]P33(x84811,x84812,x84813)+~P1(f862(x84812,x84814))+P1(f862(x84812,f776(x84813,x84812,x84811,x84814)))+~P1(f862(f862(f321(x84811),x84814),f862(f165(x84811),x84813)))
% 25.54/25.42 [8482]P33(x84821,x84822,x84823)+~P1(f862(x84822,x84824))+P1(f862(x84822,f783(x84823,x84822,x84821,x84824)))+~P1(f862(f862(f321(x84821),x84824),f862(f165(x84821),x84823)))
% 25.54/25.42 [8536]~P71(x85361)+~E(f862(x85363,f374(x85363,x85364,x85362,x85361)),f71(x85361))+E(f862(f862(f862(f58(x85361,x85362,f74(x85361)),x85363),f71(x85361)),x85364),f71(x85361))+~P1(f862(f54(x85362),x85364))
% 25.54/25.42 [8807]~P127(x88071)+~P1(f862(f862(f227(x88071),f2(x88071)),x88073))+P1(f862(f862(f227(x88071),x88072),x88073))+~P1(f862(f862(f227(x88071),f862(f862(f236(x88071),x88072),f862(a105,x88074))),f862(f862(f236(x88071),x88073),f862(a105,x88074))))
% 25.54/25.42 [9128]P33(x91281,x91282,x91283)+~P1(f862(x91282,x91284))+~P1(f862(f862(f321(x91281),x91284),f862(f165(x91281),x91283)))+P1(f862(f862(f321(x91281),f776(x91283,x91282,x91281,x91284)),f862(f165(x91281),x91283)))
% 25.54/25.42 [9129]P33(x91291,x91292,x91293)+~P1(f862(x91292,x91294))+~P1(f862(f862(f321(x91291),x91294),f862(f165(x91291),x91293)))+P1(f862(f862(f321(x91291),f783(x91293,x91292,x91291,x91294)),f862(f165(x91291),x91293)))
% 25.54/25.42 [9205]~P71(x92051)+E(f862(f862(f862(f58(x92051,x92052,f74(x92051)),x92053),f71(x92051)),x92054),f71(x92051))+~P1(f862(f54(x92052),x92054))+P1(f862(f862(f321(x92052),f374(x92053,x92054,x92052,x92051)),x92054))
% 25.54/25.42 [9706]~P1(f862(f862(f227(a1),x97064),f2(a1)))+P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x97061),f38(a1,x97062,x97063))),x97064)),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x97063))+~P1(f862(f862(f228(a1),x97061),x97064))
% 25.54/25.42 [10145]~P1(f862(f54(x101451),x101452))+~P1(f862(f862(f321(x101451),x101454),x101452))+~P1(f862(f862(f321(x101451),x101453),x101452))+P1(f862(f862(f228(a924),f862(f28(x101451),f862(f862(f3(f932(x101451,a921)),f862(f862(f3(f932(x101451,a921)),x101452),f862(f862(f301(x101451),x101453),f181(f932(x101451,a921))))),f862(f862(f301(x101451),x101454),f181(f932(x101451,a921)))))),f862(f28(x101451),x101452)))
% 25.54/25.42 [7078]~P146(x70783)+~P120(x70783)+P1(f862(x70781,f858(x70782,x70781,x70783)))+~P1(f862(x70781,f862(f862(f74(x70783),x70782),x70784)))
% 25.54/25.42 [7133]~P104(x71331)+~P1(f862(f862(f227(x71331),x71332),x71334))+~P1(f862(f862(f227(x71331),x71332),x71333))+P1(f862(f862(f227(x71331),x71332),f862(f862(f94(x71331),x71333),x71334)))
% 25.54/25.42 [7134]~P104(x71341)+~P1(f862(f862(f227(x71341),x71342),x71344))+~P1(f862(f862(f227(x71341),x71342),x71343))+P1(f862(f862(f227(x71341),x71342),f862(f862(f94(x71341),x71343),x71344)))
% 25.54/25.42 [7135]~P104(x71351)+~P1(f862(f862(f227(x71351),x71352),x71354))+~P1(f862(f862(f227(x71351),x71352),x71353))+P1(f862(f862(f227(x71351),x71352),f862(f862(f94(x71351),x71353),x71354)))
% 25.54/25.42 [7136]~P109(x71361)+~P1(f862(f862(f227(x71361),x71362),x71364))+~P1(f862(f862(f227(x71361),x71362),x71363))+P1(f862(f862(f227(x71361),x71362),f862(f862(f225(x71361),x71363),x71364)))
% 25.54/25.42 [7137]~P109(x71371)+~P1(f862(f862(f227(x71371),x71372),x71374))+~P1(f862(f862(f227(x71371),x71372),x71373))+P1(f862(f862(f227(x71371),x71372),f862(f862(f225(x71371),x71373),x71374)))
% 25.54/25.42 [7138]~P109(x71381)+~P1(f862(f862(f227(x71381),x71382),x71384))+~P1(f862(f862(f227(x71381),x71382),x71383))+P1(f862(f862(f227(x71381),x71382),f862(f862(f225(x71381),x71383),x71384)))
% 25.54/25.42 [7139]~P109(x71391)+~P1(f862(f862(f228(x71391),x71392),x71394))+~P1(f862(f862(f228(x71391),x71392),x71393))+P1(f862(f862(f228(x71391),x71392),f862(f862(f225(x71391),x71393),x71394)))
% 25.54/25.42 [7159]~P65(x71592)+E(x71591,f2(x71592))+E(f862(f862(f281(x71592),f862(f862(f236(x71592),x71591),x71593)),f862(f862(f236(x71592),x71591),x71594)),f862(f862(f236(x71592),x71591),f862(f862(f3(a924),x71593),x71594)))+~P1(f862(f862(f227(a924),x71594),x71593))
% 25.54/25.42 [7204]~P109(x72041)+~P11(x72041,f862(f862(f144(x72041),x72043),x72044))+P11(x72041,f862(f862(f144(x72041),x72042),f862(f862(f144(x72041),x72043),x72044)))+~P1(f862(f862(f227(x72041),x72042),x72043))
% 25.54/25.42 [7205]~P109(x72051)+~P11(x72051,f862(f862(f144(x72051),x72053),x72054))+P11(x72051,f862(f862(f144(x72051),x72052),f862(f862(f144(x72051),x72053),x72054)))+~P1(f862(f862(f227(x72051),x72052),x72053))
% 25.54/25.42 [7241]~P87(x72411)+~P1(f862(f862(f227(x72411),f2(x72411)),x72414))+~P1(f862(f862(f227(x72411),x72412),x72413))+P1(f862(f862(f227(x72411),x72412),f862(f862(f73(x72411),x72413),x72414)))
% 25.54/25.42 [7242]~P87(x72421)+~P1(f862(f862(f227(x72421),f2(x72421)),x72423))+~P1(f862(f862(f227(x72421),x72422),x72424))+P1(f862(f862(f227(x72421),x72422),f862(f862(f73(x72421),x72423),x72424)))
% 25.54/25.42 [7243]~P127(x72431)+~P1(f862(f862(f228(x72431),f2(x72431)),x72433))+~P1(f862(f862(f228(x72431),x72432),x72434))+P1(f862(f862(f228(x72431),x72432),f862(f862(f73(x72431),x72433),x72434)))
% 25.54/25.42 [7244]~P87(x72441)+~P1(f862(f862(f227(x72441),x72442),x72444))+~P1(f862(f862(f228(x72441),f2(x72441)),x72443))+P1(f862(f862(f228(x72441),x72442),f862(f862(f73(x72441),x72443),x72444)))
% 25.54/25.42 [7245]~P87(x72451)+~P1(f862(f862(f227(x72451),f2(x72451)),x72453))+~P1(f862(f862(f228(x72451),x72452),x72454))+P1(f862(f862(f228(x72451),x72452),f862(f862(f73(x72451),x72453),x72454)))
% 25.54/25.42 [7287]~P109(x72871)+P1(f862(f862(f227(x72871),x72872),x72873))+P1(f862(f862(f227(x72871),x72872),x72874))+~P1(f862(f862(f227(x72871),x72872),f862(f862(f226(x72871),x72874),x72873)))
% 25.54/25.42 [7288]~P109(x72881)+P1(f862(f862(f228(x72881),x72882),x72883))+P1(f862(f862(f228(x72881),x72882),x72884))+~P1(f862(f862(f228(x72881),x72882),f862(f862(f226(x72881),x72884),x72883)))
% 25.54/25.42 [7586]~P110(x75862)+~P63(x75861)+~P1(f862(f862(f228(f932(x75861,x75862)),x75863),x75864))+P1(f862(f862(f227(f932(x75861,x75862)),x75863),x75864))
% 25.54/25.42 [7952]~P67(x79521)+~P1(f862(f862(f228(x79521),x79524),f2(x79521)))+~P1(f862(f862(f227(x79521),x79523),f862(f862(f281(x79521),x79522),x79524)))+P1(f862(f862(f227(x79521),x79522),f862(f862(f74(x79521),x79523),x79524)))
% 25.54/25.42 [7953]~P67(x79531)+~P1(f862(f862(f228(x79531),x79534),f2(x79531)))+~P1(f862(f862(f227(x79531),x79533),f862(f862(f74(x79531),x79532),x79534)))+P1(f862(f862(f227(x79531),x79532),f862(f862(f281(x79531),x79533),x79534)))
% 25.54/25.42 [7954]~P67(x79541)+~P1(f862(f862(f228(x79541),x79544),f2(x79541)))+~P1(f862(f862(f228(x79541),x79543),f862(f862(f281(x79541),x79542),x79544)))+P1(f862(f862(f228(x79541),x79542),f862(f862(f74(x79541),x79543),x79544)))
% 25.54/25.42 [7955]~P67(x79551)+~P1(f862(f862(f228(x79551),x79554),f2(x79551)))+~P1(f862(f862(f228(x79551),x79553),f862(f862(f74(x79551),x79552),x79554)))+P1(f862(f862(f228(x79551),x79552),f862(f862(f281(x79551),x79553),x79554)))
% 25.54/25.42 [8062]~P126(x80621)+~P1(f862(f862(f227(x80621),x80622),f2(x80621)))+~P1(f862(f862(f227(x80621),x80624),x80623))+P1(f862(f862(f227(x80621),f862(f862(f74(x80621),x80622),x80623)),f862(f862(f74(x80621),x80622),x80624)))
% 25.54/25.42 [8063]~P128(x80631)+~P1(f862(f862(f228(x80631),x80632),f2(x80631)))+~P1(f862(f862(f227(x80631),x80634),x80633))+P1(f862(f862(f227(x80631),f862(f862(f74(x80631),x80632),x80633)),f862(f862(f74(x80631),x80632),x80634)))
% 25.54/25.42 [8064]~P126(x80641)+~P1(f862(f862(f227(x80641),x80643),f2(x80641)))+~P1(f862(f862(f227(x80641),x80644),x80642))+P1(f862(f862(f227(x80641),f862(f862(f74(x80641),x80642),x80643)),f862(f862(f74(x80641),x80644),x80643)))
% 25.54/25.42 [8065]~P66(x80651)+~P1(f862(f862(f227(x80651),x80653),f2(x80651)))+~P1(f862(f862(f227(x80651),x80654),x80652))+P1(f862(f862(f227(x80651),f862(f862(f281(x80651),x80652),x80653)),f862(f862(f281(x80651),x80654),x80653)))
% 25.54/25.42 [8066]~P128(x80661)+~P1(f862(f862(f228(x80661),x80662),f2(x80661)))+~P1(f862(f862(f228(x80661),x80664),x80663))+P1(f862(f862(f228(x80661),f862(f862(f74(x80661),x80662),x80663)),f862(f862(f74(x80661),x80662),x80664)))
% 25.54/25.42 [8067]~P128(x80671)+~P1(f862(f862(f228(x80671),x80672),f2(x80671)))+~P1(f862(f862(f228(x80671),x80674),x80673))+P1(f862(f862(f228(x80671),f862(f862(f74(x80671),x80672),x80673)),f862(f862(f74(x80671),x80672),x80674)))
% 25.54/25.42 [8068]~P128(x80681)+~P1(f862(f862(f228(x80681),x80683),f2(x80681)))+~P1(f862(f862(f228(x80681),x80684),x80682))+P1(f862(f862(f228(x80681),f862(f862(f74(x80681),x80682),x80683)),f862(f862(f74(x80681),x80684),x80683)))
% 25.54/25.42 [8069]~P128(x80691)+~P1(f862(f862(f228(x80691),x80693),f2(x80691)))+~P1(f862(f862(f228(x80691),x80694),x80692))+P1(f862(f862(f228(x80691),f862(f862(f74(x80691),x80692),x80693)),f862(f862(f74(x80691),x80694),x80693)))
% 25.54/25.42 [8070]~P128(x80701)+~P1(f862(f862(f228(x80701),x80702),f2(x80701)))+~P1(f862(f862(f228(x80701),x80704),x80703))+P1(f862(f862(f228(x80701),f862(f862(f74(x80701),x80702),x80703)),f862(f862(f74(x80701),x80702),x80704)))
% 25.54/25.42 [8071]~P67(x80711)+~P1(f862(f862(f228(x80711),x80713),f2(x80711)))+~P1(f862(f862(f228(x80711),x80714),x80712))+P1(f862(f862(f228(x80711),f862(f862(f281(x80711),x80712),x80713)),f862(f862(f281(x80711),x80714),x80713)))
% 25.54/25.42 [8072]~P127(x80721)+~P1(f862(f862(f228(x80721),f71(x80721)),x80722))+~P1(f862(f862(f227(a924),x80723),x80724))+P1(f862(f862(f227(x80721),f862(f862(f236(x80721),x80722),x80723)),f862(f862(f236(x80721),x80722),x80724)))
% 25.54/25.42 [8073]~P127(x80731)+~P1(f862(f862(f227(x80731),f71(x80731)),x80732))+~P1(f862(f862(f227(a924),x80733),x80734))+P1(f862(f862(f227(x80731),f862(f862(f236(x80731),x80732),x80733)),f862(f862(f236(x80731),x80732),x80734)))
% 25.54/25.42 [8074]~P127(x80741)+~P1(f862(f862(f228(x80741),f71(x80741)),x80742))+~P1(f862(f862(f228(a924),x80743),x80744))+P1(f862(f862(f228(x80741),f862(f862(f236(x80741),x80742),x80743)),f862(f862(f236(x80741),x80742),x80744)))
% 25.54/25.42 [8075]~P127(x80751)+~P1(f862(f862(f228(x80751),f71(x80751)),x80752))+~P1(f862(f862(f228(a924),x80753),x80754))+P1(f862(f862(f228(x80751),f862(f862(f236(x80751),x80752),x80753)),f862(f862(f236(x80751),x80752),x80754)))
% 25.54/25.42 [8103]P1(f862(f862(f228(a924),f2(a924)),f862(x81031,x81032)))+~P1(f862(f54(x81033),x81034))+~P1(f862(f862(f321(x81033),x81032),x81034))+~P1(f862(f862(f228(a924),f2(a924)),f862(f862(f11(x81033,a924),x81031),x81034)))
% 25.54/25.42 [8112]~P138(x81121)+~P1(f862(f862(f227(x81121),x81123),x81124))+~P1(f862(f862(f227(x81121),f2(x81121)),x81122))+P1(f862(f862(f227(x81121),f862(f862(f74(x81121),x81122),x81123)),f862(f862(f74(x81121),x81122),x81124)))
% 25.54/25.42 [8113]~P137(x81131)+~P1(f862(f862(f227(x81131),x81133),x81134))+~P1(f862(f862(f227(x81131),f2(x81131)),x81132))+P1(f862(f862(f227(x81131),f862(f862(f74(x81131),x81132),x81133)),f862(f862(f74(x81131),x81132),x81134)))
% 25.54/25.42 [8114]~P128(x81141)+~P1(f862(f862(f228(x81141),f2(x81141)),x81142))+~P1(f862(f862(f227(x81141),x81143),x81144))+P1(f862(f862(f227(x81141),f862(f862(f74(x81141),x81142),x81143)),f862(f862(f74(x81141),x81142),x81144)))
% 25.54/25.42 [8115]~P138(x81151)+~P1(f862(f862(f227(x81151),x81152),x81154))+~P1(f862(f862(f227(x81151),f2(x81151)),x81153))+P1(f862(f862(f227(x81151),f862(f862(f74(x81151),x81152),x81153)),f862(f862(f74(x81151),x81154),x81153)))
% 25.54/25.42 [8116]~P66(x81161)+~P1(f862(f862(f227(x81161),x81162),x81164))+~P1(f862(f862(f227(x81161),f2(x81161)),x81163))+P1(f862(f862(f227(x81161),f862(f862(f281(x81161),x81162),x81163)),f862(f862(f281(x81161),x81164),x81163)))
% 25.54/25.42 [8117]~P127(x81171)+~P1(f862(f862(f227(x81171),x81172),x81174))+~P1(f862(f862(f227(x81171),f2(x81171)),x81172))+P1(f862(f862(f227(x81171),f862(f862(f236(x81171),x81172),x81173)),f862(f862(f236(x81171),x81174),x81173)))
% 25.54/25.42 [8118]~P128(x81181)+~P1(f862(f862(f228(x81181),x81183),x81184))+~P1(f862(f862(f228(x81181),f2(x81181)),x81182))+P1(f862(f862(f228(x81181),f862(f862(f74(x81181),x81182),x81183)),f862(f862(f74(x81181),x81182),x81184)))
% 25.54/25.42 [8119]~P123(x81191)+~P1(f862(f862(f228(x81191),x81193),x81194))+~P1(f862(f862(f228(x81191),f2(x81191)),x81192))+P1(f862(f862(f228(x81191),f862(f862(f74(x81191),x81192),x81193)),f862(f862(f74(x81191),x81192),x81194)))
% 25.54/25.42 [8120]~P135(x81201)+~P1(f862(f862(f228(x81201),x81203),x81204))+~P1(f862(f862(f228(x81201),f2(x81201)),x81202))+P1(f862(f862(f228(x81201),f862(f862(f74(x81201),x81202),x81203)),f862(f862(f74(x81201),x81202),x81204)))
% 25.54/25.42 [8121]~P128(x81211)+~P1(f862(f862(f228(x81211),x81212),x81214))+~P1(f862(f862(f228(x81211),f2(x81211)),x81213))+P1(f862(f862(f228(x81211),f862(f862(f74(x81211),x81212),x81213)),f862(f862(f74(x81211),x81214),x81213)))
% 25.54/25.42 [8122]~P135(x81221)+~P1(f862(f862(f228(x81221),x81222),x81224))+~P1(f862(f862(f228(x81221),f2(x81221)),x81223))+P1(f862(f862(f228(x81221),f862(f862(f74(x81221),x81222),x81223)),f862(f862(f74(x81221),x81224),x81223)))
% 25.54/25.42 [8123]~P128(x81231)+~P1(f862(f862(f228(x81231),x81233),x81234))+~P1(f862(f862(f228(x81231),f2(x81231)),x81232))+P1(f862(f862(f228(x81231),f862(f862(f74(x81231),x81232),x81233)),f862(f862(f74(x81231),x81232),x81234)))
% 25.54/25.42 [8124]~P67(x81241)+~P1(f862(f862(f228(x81241),x81242),x81244))+~P1(f862(f862(f228(x81241),f2(x81241)),x81243))+P1(f862(f862(f228(x81241),f862(f862(f281(x81241),x81242),x81243)),f862(f862(f281(x81241),x81244),x81243)))
% 25.54/25.42 [8168]~P108(x81682)+P1(f862(f862(f228(f932(x81681,x81682)),x81684),x81683))+~P1(f862(f862(f227(f932(x81681,x81682)),x81684),x81683))+P1(f862(f862(f227(f932(x81681,x81682)),x81683),x81684))
% 25.54/25.42 [8209]P1(f862(f862(f321(x82091),x82092),x82093))+P1(f862(f862(f321(x82091),x82092),x82094))+~P1(f862(f862(f227(f932(x82091,a921)),x82094),x82093))+P1(f862(f862(f228(f932(x82091,a921)),x82094),f862(f862(f301(x82091),x82092),x82093)))
% 25.54/25.42 [8322]~P113(x83222)+E(x83221,f2(x83222))+P1(f862(f862(f278(x83222),x83223),x83224))+~P1(f862(f862(f278(x83222),f862(f862(f74(x83222),x83223),x83221)),f862(f862(f74(x83222),x83224),x83221)))
% 25.54/25.42 [8323]~P113(x83232)+E(x83231,f2(x83232))+P1(f862(f862(f278(x83232),x83233),x83234))+~P1(f862(f862(f278(x83232),f862(f862(f74(x83232),x83231),x83233)),f862(f862(f74(x83232),x83231),x83234)))
% 25.54/25.42 [8372]P1(f862(f862(f321(x83721),x83722),x83723))+P1(f862(f862(f321(x83721),x83722),x83724))+~P1(f862(f862(f228(f932(x83721,a921)),x83724),f862(f862(f301(x83721),x83722),x83723)))+P1(f862(f862(f227(f932(x83721,a921)),x83724),x83723))
% 25.54/25.42 [8438]~P128(x84381)+P1(f862(f862(f228(x84381),x84383),x84382))+P1(f862(f862(f228(x84381),x84382),x84383))+~P1(f862(f862(f228(x84381),f862(f862(f74(x84381),x84384),x84382)),f862(f862(f74(x84381),x84384),x84383)))
% 25.54/25.42 [8439]~P128(x84391)+P1(f862(f862(f228(x84391),x84393),x84392))+P1(f862(f862(f228(x84391),x84392),x84393))+~P1(f862(f862(f228(x84391),f862(f862(f74(x84391),x84392),x84394)),f862(f862(f74(x84391),x84393),x84394)))
% 25.54/25.42 [8450]~P128(x84501)+P1(f862(f862(f228(x84501),x84504),f2(x84501)))+P1(f862(f862(f228(x84501),x84502),x84503))+~P1(f862(f862(f228(x84501),f862(f862(f74(x84501),x84502),x84504)),f862(f862(f74(x84501),x84503),x84504)))
% 25.54/25.42 [8451]~P128(x84511)+P1(f862(f862(f228(x84511),x84514),f2(x84511)))+P1(f862(f862(f228(x84511),x84512),x84513))+~P1(f862(f862(f228(x84511),f862(f862(f74(x84511),x84514),x84512)),f862(f862(f74(x84511),x84514),x84513)))
% 25.54/25.42 [8454]~P128(x84541)+P1(f862(f862(f228(x84541),x84542),x84543))+P1(f862(f862(f228(x84541),f2(x84541)),x84544))+~P1(f862(f862(f228(x84541),f862(f862(f74(x84541),x84544),x84543)),f862(f862(f74(x84541),x84544),x84542)))
% 25.54/25.42 [8455]~P128(x84551)+P1(f862(f862(f228(x84551),x84552),x84553))+P1(f862(f862(f228(x84551),f2(x84551)),x84554))+~P1(f862(f862(f228(x84551),f862(f862(f74(x84551),x84553),x84554)),f862(f862(f74(x84551),x84552),x84554)))
% 25.54/25.42 [8468]~P128(x84681)+P1(f862(f862(f228(x84681),x84682),f2(x84681)))+P1(f862(f862(f228(x84681),f2(x84681)),x84682))+~P1(f862(f862(f228(x84681),f862(f862(f74(x84681),x84683),x84682)),f862(f862(f74(x84681),x84684),x84682)))
% 25.54/25.42 [8469]~P128(x84691)+P1(f862(f862(f228(x84691),x84692),f2(x84691)))+P1(f862(f862(f228(x84691),f2(x84691)),x84692))+~P1(f862(f862(f228(x84691),f862(f862(f74(x84691),x84692),x84693)),f862(f862(f74(x84691),x84692),x84694)))
% 25.54/25.42 [8498]~P128(x84981)+~P1(f862(f862(f228(x84981),x84984),f2(x84981)))+P1(f862(f862(f227(x84981),x84982),x84983))+~P1(f862(f862(f227(x84981),f862(f862(f74(x84981),x84984),x84983)),f862(f862(f74(x84981),x84984),x84982)))
% 25.54/25.42 [8499]~P128(x84991)+~P1(f862(f862(f228(x84991),x84994),f2(x84991)))+P1(f862(f862(f228(x84991),x84992),x84993))+~P1(f862(f862(f228(x84991),f862(f862(f74(x84991),x84994),x84993)),f862(f862(f74(x84991),x84994),x84992)))
% 25.54/25.42 [8509]~P127(x85093)+~P1(f862(f862(f228(x85093),f71(x85093)),x85094))+P1(f862(f862(f227(a924),x85091),x85092))+~P1(f862(f862(f227(x85093),f862(f862(f236(x85093),x85094),x85091)),f862(f862(f236(x85093),x85094),x85092)))
% 25.54/25.42 [8510]~P127(x85103)+~P1(f862(f862(f228(x85103),f71(x85103)),x85104))+P1(f862(f862(f227(a924),x85101),x85102))+~P1(f862(f862(f227(x85103),f862(f862(f236(x85103),x85104),x85101)),f862(f862(f236(x85103),x85104),x85102)))
% 25.54/25.42 [8511]~P127(x85113)+~P1(f862(f862(f228(x85113),f71(x85113)),x85114))+P1(f862(f862(f228(a924),x85111),x85112))+~P1(f862(f862(f228(x85113),f862(f862(f236(x85113),x85114),x85111)),f862(f862(f236(x85113),x85114),x85112)))
% 25.54/25.42 [8512]~P127(x85123)+~P1(f862(f862(f228(x85123),f71(x85123)),x85124))+P1(f862(f862(f228(a924),x85121),x85122))+~P1(f862(f862(f228(x85123),f862(f862(f236(x85123),x85124),x85121)),f862(f862(f236(x85123),x85124),x85122)))
% 25.54/25.42 [8522]~P128(x85221)+P1(f862(f862(f227(x85221),x85222),x85223))+~P1(f862(f862(f228(x85221),f2(x85221)),x85224))+~P1(f862(f862(f227(x85221),f862(f862(f74(x85221),x85224),x85222)),f862(f862(f74(x85221),x85224),x85223)))
% 25.54/25.42 [8523]~P135(x85231)+P1(f862(f862(f227(x85231),x85232),x85233))+~P1(f862(f862(f228(x85231),f2(x85231)),x85234))+~P1(f862(f862(f227(x85231),f862(f862(f74(x85231),x85234),x85232)),f862(f862(f74(x85231),x85234),x85233)))
% 25.54/25.42 [8524]~P135(x85241)+P1(f862(f862(f227(x85241),x85242),x85243))+~P1(f862(f862(f228(x85241),f2(x85241)),x85244))+~P1(f862(f862(f227(x85241),f862(f862(f74(x85241),x85242),x85244)),f862(f862(f74(x85241),x85243),x85244)))
% 25.54/25.42 [8525]~P128(x85251)+P1(f862(f862(f228(x85251),x85252),x85253))+~P1(f862(f862(f228(x85251),f2(x85251)),x85254))+~P1(f862(f862(f228(x85251),f862(f862(f74(x85251),x85254),x85252)),f862(f862(f74(x85251),x85254),x85253)))
% 25.54/25.42 [8526]~P135(x85261)+P1(f862(f862(f228(x85261),x85262),x85263))+~P1(f862(f862(f227(x85261),f2(x85261)),x85264))+~P1(f862(f862(f228(x85261),f862(f862(f74(x85261),x85264),x85262)),f862(f862(f74(x85261),x85264),x85263)))
% 25.54/25.42 [8527]~P131(x85271)+P1(f862(f862(f228(x85271),x85272),x85273))+~P1(f862(f862(f227(x85271),f2(x85271)),x85274))+~P1(f862(f862(f228(x85271),f862(f862(f74(x85271),x85274),x85272)),f862(f862(f74(x85271),x85274),x85273)))
% 25.54/25.42 [8528]~P127(x85281)+~P1(f862(f862(f227(x85281),f2(x85281)),x85283))+P1(f862(f862(f228(x85281),x85282),x85283))+~P1(f862(f862(f228(x85281),f862(f862(f236(x85281),x85282),x85284)),f862(f862(f236(x85281),x85283),x85284)))
% 25.54/25.42 [8529]~P135(x85291)+P1(f862(f862(f228(x85291),x85292),x85293))+~P1(f862(f862(f227(x85291),f2(x85291)),x85294))+~P1(f862(f862(f228(x85291),f862(f862(f74(x85291),x85292),x85294)),f862(f862(f74(x85291),x85293),x85294)))
% 25.54/25.42 [8530]~P131(x85301)+P1(f862(f862(f228(x85301),x85302),x85303))+~P1(f862(f862(f227(x85301),f2(x85301)),x85304))+~P1(f862(f862(f228(x85301),f862(f862(f74(x85301),x85302),x85304)),f862(f862(f74(x85301),x85303),x85304)))
% 25.54/25.42 [8574]P1(f862(f862(f321(x85741),x85742),x85743))+~P1(f862(f862(f227(f932(x85741,a921)),x85743),x85744))+~P1(f862(f862(f228(f932(x85741,a921)),x85743),x85744))+P1(f862(f862(f228(f932(x85741,a921)),x85743),f862(f862(f301(x85741),x85742),x85744)))
% 25.54/25.42 [8607]~P146(x86071)+~P120(x86071)+P1(f862(f862(f278(x86071),x86072),f862(f862(f73(x86071),f858(x86072,x86073,x86071)),f2(x86071))))+~P1(f862(x86073,f862(f862(f74(x86071),x86072),x86074)))
% 25.54/25.42 [8958]E(f862(f862(f3(a1),f376(x89581,x89582,x89583,x89584)),f377(x89581,x89582,x89583,x89584)),x89584)+~P1(f862(f862(f228(a1),f2(a1)),x89583))+~P1(f862(f862(f227(a1),x89581),x89584))+P1(f862(f862(f227(a1),x89581),f862(f862(f73(a1),x89584),x89583)))
% 25.54/25.42 [8959]E(f862(f862(f3(a1),f402(x89591,x89592,x89593,x89594)),f403(x89591,x89592,x89593,x89594)),x89594)+~P1(f862(f862(f228(a1),f2(a1)),x89593))+~P1(f862(f862(f228(a1),x89591),x89594))+P1(f862(f862(f228(a1),x89591),f862(f862(f73(a1),x89594),x89593)))
% 25.54/25.42 [9111]~E(f862(f862(f157(x91111),x91113),f684(x91114,x91113,x91111,x91112)),f862(f862(f157(x91111),x91114),f684(x91114,x91113,x91111,x91112)))+E(f862(f862(f168(x91111),x91112),x91113),f862(f862(f168(x91111),x91112),x91114))+~P1(f862(f862(f227(a924),x91112),f862(f182(f925(x91111)),x91113)))+~P1(f862(f862(f227(a924),x91112),f862(f182(f925(x91111)),x91114)))
% 25.54/25.42 [9173]~P1(f862(f862(f228(a1),f2(a1)),x91733))+~P1(f862(f862(f227(a1),x91731),x91734))+P1(f862(f862(f321(a1),f376(x91731,x91732,x91733,x91734)),x91732))+P1(f862(f862(f227(a1),x91731),f862(f862(f73(a1),x91734),x91733)))
% 25.54/25.42 [9174]~P1(f862(f862(f228(a1),f2(a1)),x91743))+~P1(f862(f862(f228(a1),x91741),x91744))+P1(f862(f862(f321(a1),f402(x91741,x91742,x91743,x91744)),x91742))+P1(f862(f862(f228(a1),x91741),f862(f862(f73(a1),x91744),x91743)))
% 25.54/25.42 [9214]~P104(x92141)+~P1(f862(f54(x92141),x92143))+~P1(f862(f862(f321(x92141),x92144),x92143))+P1(f862(f862(f227(x92141),f862(f862(f57(x92141,x92141,f94(x92141)),x92142),x92143)),f862(f862(f94(x92141),x92144),x92142)))
% 25.54/25.42 [9215]~P109(x92151)+~P1(f862(f54(x92151),x92153))+~P1(f862(f862(f321(x92151),x92154),x92153))+P1(f862(f862(f227(x92151),f862(f862(f57(x92151,x92151,f225(x92151)),x92152),x92153)),f862(f862(f225(x92151),x92154),x92152)))
% 25.54/25.42 [9259]E(f862(f862(f168(x92591),x92592),x92593),f862(f862(f168(x92591),x92592),x92594))+P1(f862(f862(f228(a924),f684(x92593,x92594,x92591,x92592)),x92592))+~P1(f862(f862(f227(a924),x92592),f862(f182(f925(x92591)),x92593)))+~P1(f862(f862(f227(a924),x92592),f862(f182(f925(x92591)),x92594)))
% 25.54/25.42 [9264]~P1(f862(f862(f228(a1),f2(a1)),x92643))+~P1(f862(f862(f227(a1),x92641),x92642))+P1(f862(f862(f321(a1),f377(x92641,x92644,x92643,x92642)),f296(a1,f71(a1),x92643)))+P1(f862(f862(f227(a1),x92641),f862(f862(f73(a1),x92642),x92643)))
% 25.54/25.42 [9265]~P1(f862(f862(f228(a1),f2(a1)),x92653))+~P1(f862(f862(f228(a1),x92651),x92652))+P1(f862(f862(f321(a1),f403(x92651,x92654,x92653,x92652)),f296(a1,f71(a1),x92653)))+P1(f862(f862(f228(a1),x92651),f862(f862(f73(a1),x92652),x92653)))
% 25.54/25.42 [9592]~P103(x95921)+~P1(f862(f54(x95921),x95924))+P1(f862(f862(f321(x95921),f909(x95922,x95923,x95924,x95921)),x95924))+P1(f862(f862(f227(x95921),f862(f862(f57(x95921,x95921,f103(x95921)),x95922),x95924)),f862(f862(f103(x95921),x95923),x95922)))
% 25.54/25.42 [9593]~P109(x95931)+~P1(f862(f54(x95931),x95934))+P1(f862(f862(f321(x95931),f477(x95932,x95933,x95934,x95931)),x95934))+P1(f862(f862(f227(x95931),f862(f862(f57(x95931,x95931,f226(x95931)),x95932),x95934)),f862(f862(f226(x95931),x95933),x95932)))
% 25.54/25.42 [9722]~P103(x97221)+~P1(f862(f54(x97221),x97223))+~P1(f862(f862(f227(x97221),f909(x97222,x97224,x97223,x97221)),x97224))+P1(f862(f862(f227(x97221),f862(f862(f57(x97221,x97221,f103(x97221)),x97222),x97223)),f862(f862(f103(x97221),x97224),x97222)))
% 25.54/25.42 [9723]~P109(x97231)+~P1(f862(f54(x97231),x97233))+~P1(f862(f862(f227(x97231),f477(x97232,x97234,x97233,x97231)),x97234))+P1(f862(f862(f227(x97231),f862(f862(f57(x97231,x97231,f226(x97231)),x97232),x97233)),f862(f862(f226(x97231),x97234),x97232)))
% 25.54/25.42 [9725]~P1(f862(f862(f227(a1),f2(a1)),x97254))+~P1(f862(f862(f228(a1),f2(a1)),x97253))+~P1(f862(f862(f228(a1),x97254),x97251))+P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x97251),f38(a1,x97252,x97253))),x97254)),f862(f862(f74(a1),x97251),x97253)))
% 25.54/25.42 [10117]E(x101171,x101172)+P1(f862(f862(f321(f931(f925(x101173),f925(x101173))),f862(f862(f244(f925(x101173),f925(x101173)),x101172),x101171)),f140(x101173,x101174)))+P1(f862(f862(f321(f931(f925(x101173),f925(x101173))),f862(f862(f244(f925(x101173),f925(x101173)),x101171),x101172)),f140(x101173,x101174)))+~P1(f862(f862(f321(f931(x101173,x101173)),f862(f862(f244(x101173,x101173),f650(x101171,x101172,x101174,x101173)),f655(x101171,x101172,x101174,x101173))),x101174))
% 25.54/25.42 [10118]E(x101181,x101182)+P1(f862(f862(f321(f931(f925(x101183),f925(x101183))),f862(f862(f244(f925(x101183),f925(x101183)),x101182),x101181)),f140(x101183,x101184)))+P1(f862(f862(f321(f931(f925(x101183),f925(x101183))),f862(f862(f244(f925(x101183),f925(x101183)),x101181),x101182)),f140(x101183,x101184)))+~P1(f862(f862(f321(f931(x101183,x101183)),f862(f862(f244(x101183,x101183),f655(x101181,x101182,x101184,x101183)),f650(x101181,x101182,x101184,x101183))),x101184))
% 25.54/25.42 [7651]~P103(x76511)+~P1(f862(f862(f227(x76511),x76513),x76514))+~P1(f862(f862(f227(x76511),x76512),x76514))+P1(f862(f862(f227(x76511),f862(f862(f103(x76511),x76512),x76513)),x76514))
% 25.54/25.42 [7652]~P103(x76521)+~P1(f862(f862(f227(x76521),x76523),x76524))+~P1(f862(f862(f227(x76521),x76522),x76524))+P1(f862(f862(f227(x76521),f862(f862(f103(x76521),x76522),x76523)),x76524))
% 25.54/25.42 [7653]~P103(x76531)+~P1(f862(f862(f227(x76531),x76533),x76534))+~P1(f862(f862(f227(x76531),x76532),x76534))+P1(f862(f862(f227(x76531),f862(f862(f103(x76531),x76532),x76533)),x76534))
% 25.54/25.42 [7654]~P109(x76541)+~P1(f862(f862(f227(x76541),x76543),x76544))+~P1(f862(f862(f227(x76541),x76542),x76544))+P1(f862(f862(f227(x76541),f862(f862(f226(x76541),x76542),x76543)),x76544))
% 25.54/25.42 [7655]~P109(x76551)+~P1(f862(f862(f227(x76551),x76553),x76554))+~P1(f862(f862(f227(x76551),x76552),x76554))+P1(f862(f862(f227(x76551),f862(f862(f226(x76551),x76552),x76553)),x76554))
% 25.54/25.42 [7656]~P109(x76561)+~P1(f862(f862(f227(x76561),x76563),x76564))+~P1(f862(f862(f227(x76561),x76562),x76564))+P1(f862(f862(f227(x76561),f862(f862(f226(x76561),x76562),x76563)),x76564))
% 25.54/25.42 [7657]~P109(x76571)+~P1(f862(f862(f228(x76571),x76573),x76574))+~P1(f862(f862(f228(x76571),x76572),x76574))+P1(f862(f862(f228(x76571),f862(f862(f226(x76571),x76572),x76573)),x76574))
% 25.54/25.42 [7977]~E(x79771,x79773)+E(f132(a924,f862(f295(a924,x79771),x79772)),f862(f862(f144(a924),x79773),x79774))+~E(f132(a924,f862(f295(a924,f862(f862(f73(a924),x79771),f71(a924))),x79772)),x79774)+~P1(f862(f862(f228(a924),x79771),x79772))
% 25.54/25.42 [7985]~P109(x79851)+P1(f862(f862(f227(x79851),x79852),x79853))+P1(f862(f862(f227(x79851),x79854),x79853))+~P1(f862(f862(f227(x79851),f862(f862(f225(x79851),x79854),x79852)),x79853))
% 25.54/25.42 [7986]~P109(x79861)+P1(f862(f862(f228(x79861),x79862),x79863))+P1(f862(f862(f228(x79861),x79864),x79863))+~P1(f862(f862(f228(x79861),f862(f862(f225(x79861),x79864),x79862)),x79863))
% 25.54/25.42 [8267]~P66(x82671)+~P1(f862(f862(f228(x82671),f2(x82671)),x82673))+~P1(f862(f862(f227(x82671),x82672),f862(f862(f281(x82671),x82674),x82673)))+P1(f862(f862(f227(x82671),f862(f862(f74(x82671),x82672),x82673)),x82674))
% 25.54/25.42 [8268]~P67(x82681)+~P1(f862(f862(f228(x82681),f2(x82681)),x82683))+~P1(f862(f862(f227(x82681),x82682),f862(f862(f281(x82681),x82684),x82683)))+P1(f862(f862(f227(x82681),f862(f862(f74(x82681),x82682),x82683)),x82684))
% 25.54/25.42 [8269]~P66(x82691)+~P1(f862(f862(f228(x82691),f2(x82691)),x82693))+~P1(f862(f862(f227(x82691),x82692),f862(f862(f74(x82691),x82694),x82693)))+P1(f862(f862(f227(x82691),f862(f862(f281(x82691),x82692),x82693)),x82694))
% 25.54/25.42 [8270]~P67(x82701)+~P1(f862(f862(f228(x82701),f2(x82701)),x82703))+~P1(f862(f862(f227(x82701),x82702),f862(f862(f74(x82701),x82704),x82703)))+P1(f862(f862(f227(x82701),f862(f862(f281(x82701),x82702),x82703)),x82704))
% 25.54/25.42 [8271]~P67(x82711)+~P1(f862(f862(f228(x82711),f2(x82711)),x82713))+~P1(f862(f862(f227(x82711),x82712),f862(f862(f74(x82711),x82714),x82713)))+P1(f862(f862(f227(x82711),f862(f862(f281(x82711),x82712),x82713)),x82714))
% 25.54/25.42 [8272]~P66(x82721)+~P1(f862(f862(f228(x82721),f2(x82721)),x82723))+~P1(f862(f862(f228(x82721),x82722),f862(f862(f281(x82721),x82724),x82723)))+P1(f862(f862(f228(x82721),f862(f862(f74(x82721),x82722),x82723)),x82724))
% 25.54/25.42 [8273]~P67(x82731)+~P1(f862(f862(f228(x82731),f2(x82731)),x82733))+~P1(f862(f862(f228(x82731),x82732),f862(f862(f281(x82731),x82734),x82733)))+P1(f862(f862(f228(x82731),f862(f862(f74(x82731),x82732),x82733)),x82734))
% 25.54/25.42 [8274]~P66(x82741)+~P1(f862(f862(f228(x82741),f2(x82741)),x82743))+~P1(f862(f862(f228(x82741),x82742),f862(f862(f74(x82741),x82744),x82743)))+P1(f862(f862(f228(x82741),f862(f862(f281(x82741),x82742),x82743)),x82744))
% 25.54/25.42 [8275]~P67(x82751)+~P1(f862(f862(f228(x82751),f2(x82751)),x82753))+~P1(f862(f862(f228(x82751),x82752),f862(f862(f74(x82751),x82754),x82753)))+P1(f862(f862(f228(x82751),f862(f862(f281(x82751),x82752),x82753)),x82754))
% 25.54/25.42 [8276]~P67(x82761)+~P1(f862(f862(f228(x82761),f2(x82761)),x82763))+~P1(f862(f862(f228(x82761),x82762),f862(f862(f74(x82761),x82764),x82763)))+P1(f862(f862(f228(x82761),f862(f862(f281(x82761),x82762),x82763)),x82764))
% 25.54/25.42 [8408]~P66(x84081)+~P1(f862(f862(f228(x84081),f2(x84081)),x84084))+P1(f862(f862(f227(x84081),x84082),f862(f862(f74(x84081),x84083),x84084)))+~P1(f862(f862(f227(x84081),f862(f862(f281(x84081),x84082),x84084)),x84083))
% 25.54/25.42 [8409]~P66(x84091)+~P1(f862(f862(f228(x84091),f2(x84091)),x84094))+P1(f862(f862(f227(x84091),x84092),f862(f862(f281(x84091),x84093),x84094)))+~P1(f862(f862(f227(x84091),f862(f862(f74(x84091),x84092),x84094)),x84093))
% 25.54/25.42 [8410]~P67(x84101)+~P1(f862(f862(f228(x84101),f2(x84101)),x84104))+P1(f862(f862(f227(x84101),x84102),f862(f862(f281(x84101),x84103),x84104)))+~P1(f862(f862(f227(x84101),f862(f862(f74(x84101),x84102),x84104)),x84103))
% 25.54/25.42 [8411]~P67(x84111)+~P1(f862(f862(f228(x84111),f2(x84111)),x84114))+P1(f862(f862(f227(x84111),x84112),f862(f862(f74(x84111),x84113),x84114)))+~P1(f862(f862(f227(x84111),f862(f862(f281(x84111),x84112),x84114)),x84113))
% 25.54/25.42 [8412]~P67(x84121)+~P1(f862(f862(f228(x84121),f2(x84121)),x84124))+P1(f862(f862(f227(x84121),x84122),f862(f862(f281(x84121),x84123),x84124)))+~P1(f862(f862(f227(x84121),f862(f862(f74(x84121),x84122),x84124)),x84123))
% 25.54/25.42 [8413]~P66(x84131)+~P1(f862(f862(f228(x84131),f2(x84131)),x84134))+P1(f862(f862(f228(x84131),x84132),f862(f862(f74(x84131),x84133),x84134)))+~P1(f862(f862(f228(x84131),f862(f862(f281(x84131),x84132),x84134)),x84133))
% 25.54/25.42 [8414]~P66(x84141)+~P1(f862(f862(f228(x84141),f2(x84141)),x84144))+P1(f862(f862(f228(x84141),x84142),f862(f862(f281(x84141),x84143),x84144)))+~P1(f862(f862(f228(x84141),f862(f862(f74(x84141),x84142),x84144)),x84143))
% 25.54/25.42 [8415]~P67(x84151)+~P1(f862(f862(f228(x84151),f2(x84151)),x84154))+P1(f862(f862(f228(x84151),x84152),f862(f862(f281(x84151),x84153),x84154)))+~P1(f862(f862(f228(x84151),f862(f862(f74(x84151),x84152),x84154)),x84153))
% 25.54/25.42 [8416]~P67(x84161)+~P1(f862(f862(f228(x84161),f2(x84161)),x84164))+P1(f862(f862(f228(x84161),x84162),f862(f862(f74(x84161),x84163),x84164)))+~P1(f862(f862(f228(x84161),f862(f862(f281(x84161),x84162),x84164)),x84163))
% 25.54/25.42 [8417]~P67(x84171)+~P1(f862(f862(f228(x84171),f2(x84171)),x84174))+P1(f862(f862(f228(x84171),x84172),f862(f862(f281(x84171),x84173),x84174)))+~P1(f862(f862(f228(x84171),f862(f862(f74(x84171),x84172),x84174)),x84173))
% 25.54/25.42 [8577]~P67(x85771)+~P1(f862(f862(f228(x85771),x85773),f2(x85771)))+~P1(f862(f862(f227(x85771),f862(f862(f281(x85771),x85774),x85773)),x85772))+P1(f862(f862(f227(x85771),f862(f862(f74(x85771),x85772),x85773)),x85774))
% 25.54/25.42 [8578]~P67(x85781)+~P1(f862(f862(f228(x85781),x85783),f2(x85781)))+~P1(f862(f862(f227(x85781),f862(f862(f74(x85781),x85784),x85783)),x85782))+P1(f862(f862(f227(x85781),f862(f862(f281(x85781),x85782),x85783)),x85784))
% 25.54/25.42 [8579]~P67(x85791)+~P1(f862(f862(f228(x85791),x85793),f2(x85791)))+~P1(f862(f862(f228(x85791),f862(f862(f281(x85791),x85794),x85793)),x85792))+P1(f862(f862(f228(x85791),f862(f862(f74(x85791),x85792),x85793)),x85794))
% 25.54/25.42 [8580]~P67(x85801)+~P1(f862(f862(f228(x85801),x85803),f2(x85801)))+~P1(f862(f862(f228(x85801),f862(f862(f74(x85801),x85804),x85803)),x85802))+P1(f862(f862(f228(x85801),f862(f862(f281(x85801),x85802),x85803)),x85804))
% 25.54/25.42 [8592]~P1(f862(x85921,x85924))+~P1(f862(f862(f228(a924),x85922),f862(f862(f74(a924),x85923),f862(a105,x85924))))+P1(f862(x85921,f862(f862(f29(a924),x85922),x85923)))+~P1(f862(f862(f227(a924),f862(f862(f74(a924),x85923),x85924)),x85922))
% 25.54/25.42 [8805]~P103(x88051)+~P1(f862(f54(x88051),x88054))+~P1(f862(f862(f321(x88051),x88052),x88054))+P1(f862(f862(f227(x88051),f862(f862(f103(x88051),x88052),x88053)),f862(f862(f57(x88051,x88051,f103(x88051)),x88053),x88054)))
% 25.54/25.42 [8806]~P109(x88061)+~P1(f862(f54(x88061),x88064))+~P1(f862(f862(f321(x88061),x88062),x88064))+P1(f862(f862(f227(x88061),f862(f862(f226(x88061),x88062),x88063)),f862(f862(f57(x88061,x88061,f226(x88061)),x88063),x88064)))
% 25.54/25.42 [8960]~P1(f862(f54(x89601),x89602))+E(f862(f28(x89601),f862(f862(f3(f932(x89601,a921)),x89602),f862(f862(f301(x89601),x89603),x89604))),f862(f862(f3(a924),f862(f28(x89601),f862(f862(f3(f932(x89601,a921)),x89602),x89604))),f71(a924)))+P1(f862(f862(f321(x89601),x89603),x89604))+~P1(f862(f862(f321(x89601),x89603),x89602))
% 25.54/25.42 [9039]E(f862(f862(f73(a1),f378(x90391,x90392,x90393,x90394)),f379(x90391,x90392,x90393,x90394)),x90394)+~P1(f862(f862(f228(a1),f2(a1)),x90393))+~P1(f862(f862(f227(a1),x90394),x90391))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x90394),x90393)),x90391))
% 25.54/25.42 [9040]E(f862(f862(f73(a1),f404(x90401,x90402,x90403,x90404)),f405(x90401,x90402,x90403,x90404)),x90404)+~P1(f862(f862(f228(a1),f2(a1)),x90403))+~P1(f862(f862(f228(a1),x90404),x90401))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x90404),x90403)),x90401))
% 25.54/25.42 [9244]~P1(f862(f862(f228(a1),f2(a1)),x92443))+~P1(f862(f862(f227(a1),x92444),x92441))+P1(f862(f862(f321(a1),f378(x92441,x92442,x92443,x92444)),x92442))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x92444),x92443)),x92441))
% 25.54/25.42 [9245]~P1(f862(f862(f228(a1),f2(a1)),x92453))+~P1(f862(f862(f228(a1),x92454),x92451))+P1(f862(f862(f321(a1),f404(x92451,x92452,x92453,x92454)),x92452))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x92454),x92453)),x92451))
% 25.54/25.42 [9333]~P1(f862(f862(f228(a1),f2(a1)),x93332))+~P1(f862(f862(f227(a1),x93331),x93333))+P1(f862(f862(f321(a1),f379(x93333,x93334,x93332,x93331)),f296(a1,f71(a1),x93332)))+P1(f862(f862(f227(a1),f862(f862(f3(a1),x93331),x93332)),x93333))
% 25.54/25.42 [9334]~P1(f862(f862(f228(a1),f2(a1)),x93342))+~P1(f862(f862(f228(a1),x93341),x93343))+P1(f862(f862(f321(a1),f405(x93343,x93344,x93342,x93341)),f296(a1,f71(a1),x93342)))+P1(f862(f862(f228(a1),f862(f862(f3(a1),x93341),x93342)),x93343))
% 25.54/25.42 [9352]~P1(f862(f862(f227(a1),f2(a1)),x93524))+~P1(f862(f862(f228(a1),f2(a1)),x93523))+~P1(f862(f862(f228(a1),x93524),x93521))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x93521),f38(a1,x93522,x93523))),x93524)))
% 25.54/25.42 [9380]E(x93801,x93802)+~P37(x93803,x93804)+~P1(f862(f862(f321(f931(x93803,x93803)),f862(f862(f244(x93803,x93803),x93802),x93801)),x93804))+~P1(f862(f862(f321(f931(x93803,x93803)),f862(f862(f244(x93803,x93803),x93801),x93802)),x93804))
% 25.54/25.42 [9381]E(x93811,x93812)+~P37(x93813,x93814)+~P1(f862(f862(f321(f931(x93813,x93813)),f862(f862(f244(x93813,x93813),x93812),x93811)),x93814))+~P1(f862(f862(f321(f931(x93813,x93813)),f862(f862(f244(x93813,x93813),x93811),x93812)),x93814))
% 25.54/25.42 [9414]~P104(x94141)+~P1(f862(f54(x94141),x94144))+~P1(f862(f862(f227(x94141),x94142),f906(x94143,x94142,x94144,x94141)))+P1(f862(f862(f227(x94141),f862(f862(f94(x94141),x94142),x94143)),f862(f862(f57(x94141,x94141,f94(x94141)),x94143),x94144)))
% 25.54/25.42 [9415]~P109(x94151)+~P1(f862(f54(x94151),x94154))+~P1(f862(f862(f227(x94151),x94152),f463(x94153,x94152,x94154,x94151)))+P1(f862(f862(f227(x94151),f862(f862(f225(x94151),x94152),x94153)),f862(f862(f57(x94151,x94151,f225(x94151)),x94153),x94154)))
% 25.54/25.42 [9431]~P1(f862(f862(f227(a1),x94314),f2(a1)))+~P1(f862(f862(f228(a1),f2(a1)),x94312))+~P1(f862(f862(f228(a1),x94311),x94314))+P1(f862(f862(f228(a1),f862(f862(f74(a1),x94311),x94312)),f862(f862(f73(a1),f862(f862(f74(a1),x94311),f38(a1,x94313,x94312))),x94314)))
% 25.54/25.42 [9457]P1(f862(f54(x94571),x94572))+~P1(f862(f54(x94571),x94573))+~P1(f862(f862(f321(f932(x94571,a921)),x94572),f862(f862(f53(x94571),x94573),x94574)))+~P1(f862(f862(f227(f932(f931(x94571,x94571),a921)),x94574),f862(f862(f246(x94571,x94571),x94573),f862(f18(f932(x94571,a921),x94571),x94573))))
% 25.54/25.42 [9481]~P104(x94811)+~P1(f862(f54(x94811),x94814))+P1(f862(f862(f321(x94811),f906(x94812,x94813,x94814,x94811)),x94814))+P1(f862(f862(f227(x94811),f862(f862(f94(x94811),x94813),x94812)),f862(f862(f57(x94811,x94811,f94(x94811)),x94812),x94814)))
% 25.54/25.42 [9482]~P109(x94821)+~P1(f862(f54(x94821),x94824))+P1(f862(f862(f321(x94821),f463(x94822,x94823,x94824,x94821)),x94824))+P1(f862(f862(f227(x94821),f862(f862(f225(x94821),x94823),x94822)),f862(f862(f57(x94821,x94821,f225(x94821)),x94822),x94824)))
% 25.54/25.42 [9889]~P1(f862(f54(x98892),x98894))+~P1(f862(f54(x98891),x98893))+~P1(f862(f862(f227(a924),f862(f28(x98892),x98894)),f862(f28(x98891),x98893)))+P1(f862(f862(f227(f932(x98891,a921)),f862(f302(x98892,x98891,f543(x98893,x98891,x98894,x98892)),x98894)),x98893))
% 25.54/25.42 [9530]~P1(f862(f862(f321(x95301),x95302),x95304))+P1(f862(f862(f321(x95301),x95302),x95303))+~P1(f862(f862(f228(f932(x95301,a921)),x95304),f862(f862(f301(x95301),x95302),x95303)))+P1(f862(f862(f228(f932(x95301,a921)),f862(f862(f3(f932(x95301,a921)),x95304),f862(f862(f301(x95301),x95302),f181(f932(x95301,a921))))),x95303))
% 25.54/25.42 [9703]~P1(f862(f862(f321(x97031),x97032),x97034))+P1(f862(f862(f321(x97031),x97032),x97033))+P1(f862(f862(f228(f932(x97031,a921)),x97034),f862(f862(f301(x97031),x97032),x97033)))+~P1(f862(f862(f228(f932(x97031,a921)),f862(f862(f3(f932(x97031,a921)),x97034),f862(f862(f301(x97031),x97032),f181(f932(x97031,a921))))),x97033))
% 25.54/25.42 [9728]P1(f862(f862(f321(x97281),x97282),x97283))+~P1(f862(f862(f227(f932(x97281,a921)),x97284),x97283))+P1(f862(f862(f228(f932(x97281,a921)),x97284),f862(f862(f301(x97281),x97282),x97283)))+~P1(f862(f862(f228(f932(x97281,a921)),f862(f862(f3(f932(x97281,a921)),x97284),f862(f862(f301(x97281),x97282),f181(f932(x97281,a921))))),x97283))
% 25.54/25.42 [9733]~P1(f862(f862(f321(x97331),x97333),x97332))+~P1(f862(f862(f228(f932(x97331,a921)),x97332),x97334))+P1(f862(f862(f228(f932(x97331,a921)),x97332),f862(f862(f301(x97331),x97333),x97334)))+~P1(f862(f862(f228(f932(x97331,a921)),f862(f862(f3(f932(x97331,a921)),x97332),f862(f862(f301(x97331),x97333),f181(f932(x97331,a921))))),x97334))
% 25.54/25.42 [9749]~P1(f862(f862(f227(f932(x97491,a921)),x97492),x97494))+~P1(f862(f862(f228(f932(x97491,a921)),x97492),x97494))+P1(f862(f862(f228(f932(x97491,a921)),x97492),f862(f862(f301(x97491),x97493),x97494)))+~P1(f862(f862(f228(f932(x97491,a921)),f862(f862(f3(f932(x97491,a921)),x97492),f862(f862(f301(x97491),x97493),f181(f932(x97491,a921))))),x97494))
% 25.54/25.42 [9794]~P110(x97942)+~P63(x97941)+~P1(f862(f862(f227(f932(x97941,x97942)),x97943),x97944))+P1(f862(f50(x97941),f862(f862(f20(x97941,x97942,a921),f862(f862(f10(x97942,f932(x97942,a921),x97941),f227(x97942)),x97943)),x97944)))
% 25.54/25.42 [9938]~P110(x99382)+~P63(x99381)+P1(f862(f862(f227(f932(x99381,x99382)),x99383),x99384))+~P1(f862(f50(x99381),f862(f862(f20(x99381,x99382,a921),f862(f862(f10(x99382,f932(x99382,a921),x99381),f227(x99382)),x99383)),x99384)))
% 25.54/25.42 [10108]E(f862(f862(f157(x101081),f862(f862(f157(f925(x101081)),f172(x101081,x101082)),x101083)),x101084),f862(f862(f157(x101081),f862(f862(f157(f925(x101081)),x101082),x101084)),x101083))+~P1(f862(f862(f228(a924),x101083),f862(f182(f925(f925(x101081))),f172(x101081,x101082))))+~P11(a924,f862(f161(a924),f862(f862(f147(f925(x101081),a924),f182(f925(x101081))),x101082)))+~P1(f862(f862(f228(a924),x101084),f862(f182(f925(f925(x101081))),f862(f129(f925(x101081),f862(f862(f10(a924,a921,f925(x101081)),f862(f228(a924),x101083)),f182(f925(x101081)))),x101082))))
% 25.54/25.42 [10129]~P1(f862(f862(f321(f931(a924,a924)),x101294),x101291))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101294),x101292)),a64))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101291),x101293)),a65))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101291),f862(f862(f301(f931(a924,a924)),x101292),x101293))),a65))
% 25.54/25.42 [10130]~P1(f862(f862(f321(f931(a924,a924)),x101304),x101301))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101304),x101302)),a26))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101301),x101303)),a62))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101301),f862(f862(f301(f931(a924,a924)),x101302),x101303))),a62))
% 25.54/25.42 [10017]~P110(x100172)+~P63(x100171)+~P1(f862(f862(f228(f932(x100171,x100172)),x100173),x100174))+P1(f862(f49(x100171),f862(f862(f10(a921,a921,x100171),a314),f862(f862(f20(x100171,x100172,a921),f862(f862(f10(x100172,f932(x100172,a921),x100171),a317),x100173)),x100174))))
% 25.54/25.42 [10141]~P1(f862(f862(f321(f931(a924,a924)),x101414),x101413))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101411),x101414)),a26))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101412),x101413)),a27))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f862(f862(f301(f931(a924,a924)),x101411),x101412)),x101413)),a27))
% 25.54/25.42 [10142]~P1(f862(f862(f321(f931(a924,a924)),x101424),x101423))+~P1(f862(f862(f321(f931(f931(a924,a924),f931(a924,a924))),f862(f862(f244(f931(a924,a924),f931(a924,a924)),x101421),x101424)),a64))+~P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),x101422),x101423)),a63))+P1(f862(f862(f321(f931(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921))),f862(f862(f244(f932(f931(a924,a924),a921),f932(f931(a924,a924),a921)),f862(f862(f301(f931(a924,a924)),x101421),x101422)),x101423)),a63))
% 25.54/25.42 [6235]~P5(x62354,x62351)+~P1(f862(f862(x62351,x62352),x62355))+P1(f862(f862(x62351,x62352),x62353))+~P1(f862(f862(x62351,x62355),x62353))
% 25.54/25.42 [6236]~P47(x62364,x62361)+~P1(f862(f862(x62361,x62362),x62365))+P1(f862(f862(x62361,x62362),x62363))+~P1(f862(f862(x62361,x62365),x62363))
% 25.54/25.42 [6237]~P13(x62374,x62371)+~P1(f862(f862(x62371,x62372),x62375))+P1(f862(f862(x62371,x62372),x62373))+~P1(f862(f862(x62371,x62375),x62373))
% 25.54/25.42 [8924]~P23(x89241,x89243,x89245,x89242,x89244)+E(f862(f28(x89241),x89242),f862(f28(x89243),x89244))+~P1(f862(f54(x89243),x89244))+~P1(f862(f54(x89241),x89242))
% 25.54/25.42 [8945]~P5(x89454,x89453)+~P1(f862(x89451,x89455))+P1(f862(x89452,f837(x89452,x89451,x89453,x89454)))+P1(f862(x89451,f836(x89452,x89451,x89453,x89454)))
% 25.54/25.42 [9181]~P5(x91814,x91813)+~P1(f862(x91812,x91815))+~P1(f862(x91811,f836(x91811,x91812,x91813,x91814)))+P1(f862(x91811,f837(x91811,x91812,x91813,x91814)))
% 25.54/25.42 [9365]~P5(x93654,x93653)+~P1(f862(x93651,x93655))+P1(f862(f862(f321(x93654),f837(x93652,x93651,x93653,x93654)),f262(x93654,x93653)))+P1(f862(x93651,f836(x93652,x93651,x93653,x93654)))
% 25.54/25.42 [9488]~P5(x94881,x94884)+~P1(f862(x94883,x94885))+~P1(f862(x94882,f836(x94882,x94883,x94884,x94881)))+P1(f862(f862(f321(x94881),f837(x94882,x94883,x94884,x94881)),f262(x94881,x94884)))
% 25.54/25.42 [9783]~P36(x97831,x97834)+P1(f862(f862(f321(f931(f925(x97831),f925(x97831))),f862(f862(f244(f925(x97831),f925(x97831)),x97832),x97833)),f140(x97831,x97834)))+~P1(f862(f862(f321(f931(f925(x97831),f925(x97831))),f862(f862(f244(f925(x97831),f925(x97831)),x97832),x97835)),f140(x97831,x97834)))+~P1(f862(f862(f321(f931(f925(x97831),f925(x97831))),f862(f862(f244(f925(x97831),f925(x97831)),x97835),x97833)),f140(x97831,x97834)))
% 25.54/25.42 [5463]~P59(x54635)+E(x54631,x54632)+~E(x54633,x54634)+~E(f862(f862(f3(x54635),x54633),x54634),f862(f862(f3(x54635),x54631),x54632))
% 25.54/25.42 [5464]~P59(x54645)+E(x54641,x54642)+~E(x54643,x54644)+~E(f862(f862(f3(x54645),x54643),x54644),f862(f862(f3(x54645),x54641),x54642))
% 25.54/25.42 [6347]~P15(x63475,x63471,x63473)+E(f862(f862(x63471,x63472),f862(x63473,x63474)),f862(x63473,x63474))+~P1(f862(f54(x63475),x63474))+~P1(f862(f862(f321(x63475),x63472),x63474))
% 25.54/25.42 [6537]~P78(x65371)+~E(f862(f862(f3(x65371),x65374),x65375),f862(f862(f3(x65371),x65372),x65373))+~P1(f862(f862(f227(x65371),x65374),x65375))+P1(f862(f862(f227(x65371),x65372),x65373))
% 25.54/25.42 [6538]~P78(x65381)+~E(f862(f862(f3(x65381),x65384),x65385),f862(f862(f3(x65381),x65382),x65383))+~P1(f862(f862(f227(x65381),x65384),x65385))+P1(f862(f862(f227(x65381),x65382),x65383))
% 25.54/25.42 [6539]~P78(x65391)+~E(f862(f862(f3(x65391),x65394),x65395),f862(f862(f3(x65391),x65392),x65393))+~P1(f862(f862(f228(x65391),x65394),x65395))+P1(f862(f862(f228(x65391),x65392),x65393))
% 25.54/25.42 [6540]~P78(x65401)+~E(f862(f862(f3(x65401),x65404),x65405),f862(f862(f3(x65401),x65402),x65403))+~P1(f862(f862(f228(x65401),x65404),x65405))+P1(f862(f862(f228(x65401),x65402),x65403))
% 25.54/25.42 [7519]~E(x75192,f862(f862(f144(x75191),x75194),x75195))+P1(f862(f862(f321(f925(x75191)),x75192),f154(x75191,x75193)))+~P1(f862(f862(f321(f925(x75191)),x75195),f154(x75191,x75193)))+~P1(f862(f862(f321(x75191),x75194),x75193))
% 25.54/25.42 [7926]~E(f862(f182(f925(x79261)),x79263),f862(f182(f925(x79262)),x79264))+~E(f862(f862(f147(f931(x79261,x79262),x79262),f248(x79261,x79262)),x79265),x79264)+~E(f862(f862(f147(f931(x79261,x79262),x79261),f243(x79261,x79262)),x79265),x79263)+E(f862(f862(f174(x79261,x79262),x79263),x79264),x79265)
% 25.54/25.42 [8263]~P110(x82631)+P1(f862(f862(f228(f932(x82631,a921)),f296(x82631,x82632,x82633)),f296(x82631,x82634,x82635)))+~P1(f862(f862(f227(x82631),x82634),x82635))+P1(f862(f862(f227(x82631),x82632),x82633))
% 25.54/25.42 [8365]~P110(x83651)+P1(f862(f862(f227(f932(x83651,a921)),f296(x83651,x83652,x83653)),f296(x83651,x83654,x83655)))+~P1(f862(f862(f227(x83651),x83653),x83655))+~P1(f862(f862(f227(x83651),x83654),x83652))
% 25.54/25.42 [8484]~P109(x84841)+P1(f862(f862(f227(x84841),x84842),x84843))+P1(f862(f862(f227(x84841),x84844),x84843))+~P1(f862(f862(f227(f932(x84841,a921)),f862(f295(x84841,x84843),x84842)),f862(f295(x84841,x84844),x84845)))
% 25.54/25.42 [8485]~P109(x84851)+P1(f862(f862(f227(x84851),x84852),x84853))+P1(f862(f862(f227(x84851),x84852),x84854))+~P1(f862(f862(f227(f932(x84851,a921)),f862(f295(x84851,x84853),x84852)),f862(f295(x84851,x84855),x84854)))
% 25.54/25.42 [8721]~P110(x87211)+~P1(f862(f862(f227(f932(x87211,a921)),f296(x87211,x87214,x87212)),f296(x87211,x87215,x87213)))+P1(f862(f862(f227(x87211),x87212),x87213))+~P1(f862(f862(f227(x87211),x87214),x87212))
% 25.54/25.42 [8722]~P110(x87221)+~P1(f862(f862(f228(f932(x87221,a921)),f296(x87221,x87224,x87222)),f296(x87221,x87225,x87223)))+P1(f862(f862(f227(x87221),x87222),x87223))+~P1(f862(f862(f227(x87221),x87224),x87222))
% 25.54/25.42 [8723]~P110(x87231)+~P1(f862(f862(f227(f932(x87231,a921)),f296(x87231,x87233,x87234)),f296(x87231,x87232,x87235)))+P1(f862(f862(f227(x87231),x87232),x87233))+~P1(f862(f862(f227(x87231),x87233),x87234))
% 25.54/25.42 [8724]~P110(x87241)+~P1(f862(f862(f228(f932(x87241,a921)),f296(x87241,x87243,x87244)),f296(x87241,x87242,x87245)))+P1(f862(f862(f227(x87241),x87242),x87243))+~P1(f862(f862(f227(x87241),x87243),x87244))
% 25.54/25.42 [6234]~P15(x62342,x62345,x62343)+E(x62341,f181(f932(x62342,a921)))+~P1(f862(f54(x62342),x62341))+E(f862(x62343,f862(f862(f301(x62342),x62344),x62341)),f862(f862(x62345,x62344),f862(x62343,x62341)))
% 25.54/25.42 [7008]~E(x70081,x70082)+~E(f862(f862(f94(f932(x70083,a921)),x70084),x70085),f181(f932(x70083,a921)))+~P1(f862(f862(f321(x70083),x70082),x70085))+~P1(f862(f862(f321(x70083),x70081),x70084))
% 25.54/25.42 [7089]~P16(x70892,x70895,x70891)+~P1(f862(f54(x70892),x70894))+E(f862(x70891,f862(f862(f301(x70892),x70893),x70894)),f862(f862(f57(x70892,x70892,x70895),x70893),x70894))+P1(f862(f862(f321(x70892),x70893),x70894))
% 25.54/25.42 [7154]~P72(x71542)+~P1(f862(f54(x71541),x71545))+E(f862(f862(f8(x71541,x71542),x71543),f862(f862(f301(x71541),x71544),x71545)),f862(f862(f73(x71542),f862(x71543,x71544)),f862(f862(f8(x71541,x71542),x71543),x71545)))+P1(f862(f862(f321(x71541),x71544),x71545))
% 25.54/25.42 [7155]~P72(x71552)+~P1(f862(f54(x71551),x71555))+E(f862(f862(f8(x71551,x71552),x71553),f862(f862(f301(x71551),x71554),x71555)),f862(f862(f73(x71552),f862(x71553,x71554)),f862(f862(f8(x71551,x71552),x71553),x71555)))+P1(f862(f862(f321(x71551),x71554),x71555))
% 25.54/25.42 [7156]~P71(x71562)+~P1(f862(f54(x71561),x71565))+E(f862(f862(f11(x71561,x71562),x71563),f862(f862(f301(x71561),x71564),x71565)),f862(f862(f74(x71562),f862(x71563,x71564)),f862(f862(f11(x71561,x71562),x71563),x71565)))+P1(f862(f862(f321(x71561),x71564),x71565))
% 25.54/25.42 [7157]~P71(x71572)+~P1(f862(f54(x71571),x71575))+E(f862(f862(f11(x71571,x71572),x71573),f862(f862(f301(x71571),x71574),x71575)),f862(f862(f74(x71572),f862(x71573,x71574)),f862(f862(f11(x71571,x71572),x71573),x71575)))+P1(f862(f862(f321(x71571),x71574),x71575))
% 25.54/25.42 [7666]~P16(x76662,x76665,x76661)+~P1(f862(f54(x76662),x76664))+E(f862(x76661,f862(f862(f301(x76662),x76663),x76664)),x76663)+~E(f862(f862(f3(f932(x76662,a921)),x76664),f862(f862(f301(x76662),x76663),f181(f932(x76662,a921)))),f181(f932(x76662,a921)))
% 25.54/25.42 [7998]~P119(x79981)+~P1(f862(f862(f278(x79981),x79982),x79984))+~P1(f862(f862(f227(a924),x79983),x79985))+P1(f862(f862(f278(x79981),f862(f862(f236(x79981),x79982),x79983)),f862(f862(f236(x79981),x79984),x79985)))
% 25.54/25.42 [8027]~P61(x80271)+E(f862(f862(f29(x80271),f862(f862(f74(x80271),x80272),x80273)),f862(f862(f74(x80271),x80274),x80275)),f862(f862(f74(x80271),f862(f862(f29(x80271),x80272),x80274)),f862(f862(f29(x80271),x80273),x80275)))+~P1(f862(f862(f278(x80271),x80275),x80273))+~P1(f862(f862(f278(x80271),x80274),x80272))
% 25.54/25.42 [8031]~P103(x80311)+~P1(f862(f862(f227(x80311),x80313),x80315))+~P1(f862(f862(f227(x80311),x80312),x80314))+P1(f862(f862(f227(x80311),f862(f862(f103(x80311),x80312),x80313)),f862(f862(f103(x80311),x80314),x80315)))
% 25.54/25.42 [8032]~P104(x80321)+~P1(f862(f862(f227(x80321),x80323),x80325))+~P1(f862(f862(f227(x80321),x80322),x80324))+P1(f862(f862(f227(x80321),f862(f862(f94(x80321),x80322),x80323)),f862(f862(f94(x80321),x80324),x80325)))
% 25.54/25.42 [8033]~P85(x80331)+~P1(f862(f862(f227(x80331),x80333),x80335))+~P1(f862(f862(f227(x80331),x80332),x80334))+P1(f862(f862(f227(x80331),f862(f862(f73(x80331),x80332),x80333)),f862(f862(f73(x80331),x80334),x80335)))
% 25.54/25.42 [8034]~P109(x80341)+~P1(f862(f862(f227(x80341),x80343),x80345))+~P1(f862(f862(f227(x80341),x80342),x80344))+P1(f862(f862(f227(x80341),f862(f862(f225(x80341),x80342),x80343)),f862(f862(f225(x80341),x80344),x80345)))
% 25.54/25.42 [8035]~P109(x80351)+~P1(f862(f862(f227(x80351),x80353),x80355))+~P1(f862(f862(f227(x80351),x80352),x80354))+P1(f862(f862(f227(x80351),f862(f862(f226(x80351),x80352),x80353)),f862(f862(f226(x80351),x80354),x80355)))
% 25.54/25.42 [8036]~P83(x80361)+~P1(f862(f862(f227(x80361),x80363),x80365))+~P1(f862(f862(f228(x80361),x80362),x80364))+P1(f862(f862(f228(x80361),f862(f862(f73(x80361),x80362),x80363)),f862(f862(f73(x80361),x80364),x80365)))
% 25.54/25.42 [8037]~P83(x80371)+~P1(f862(f862(f227(x80371),x80372),x80374))+~P1(f862(f862(f228(x80371),x80373),x80375))+P1(f862(f862(f228(x80371),f862(f862(f73(x80371),x80372),x80373)),f862(f862(f73(x80371),x80374),x80375)))
% 25.54/25.42 [8038]~P83(x80381)+~P1(f862(f862(f228(x80381),x80383),x80385))+~P1(f862(f862(f228(x80381),x80382),x80384))+P1(f862(f862(f228(x80381),f862(f862(f73(x80381),x80382),x80383)),f862(f862(f73(x80381),x80384),x80385)))
% 25.54/25.42 [8039]~P119(x80391)+~P1(f862(f862(f278(x80391),x80393),x80395))+~P1(f862(f862(f278(x80391),x80392),x80394))+P1(f862(f862(f278(x80391),f862(f862(f74(x80391),x80392),x80393)),f862(f862(f74(x80391),x80394),x80395)))
% 25.54/25.42 [8177]~P144(x81775)+E(x81771,x81772)+E(x81773,x81774)+~E(f862(f862(f73(x81775),f862(f862(f74(x81775),x81773),x81771)),f862(f862(f74(x81775),x81774),x81772)),f862(f862(f73(x81775),f862(f862(f74(x81775),x81773),x81772)),f862(f862(f74(x81775),x81774),x81771)))
% 25.54/25.42 [8178]~P144(x81785)+E(x81781,x81782)+E(x81783,x81784)+~E(f862(f862(f73(x81785),f862(f862(f74(x81785),x81783),x81781)),f862(f862(f74(x81785),x81784),x81782)),f862(f862(f73(x81785),f862(f862(f74(x81785),x81783),x81782)),f862(f862(f74(x81785),x81784),x81781)))
% 25.54/25.42 [8386]~P109(x83864)+~P1(f862(f130(x83861),x83863))+P1(f862(f862(f321(x83861),x83862),f862(f165(x83861),x83863)))+P1(f862(f130(x83861),f862(f862(f141(x83861,x83864,x83865),x83862),x83863)))
% 25.54/25.42 [8531]~P59(x85311)+E(f862(f862(f3(x85311),f862(f862(f8(a924,x85311),x85312),f862(f295(a924,x85313),x85314))),f862(f862(f8(a924,x85311),x85312),f862(f295(a924,x85313),x85315))),f862(f862(f8(a924,x85311),x85312),f862(f295(a924,x85315),x85314)))+~P1(f862(f862(f227(a924),x85315),x85314))+~P1(f862(f862(f227(a924),x85313),x85315))
% 25.54/25.42 [8532]~P72(x85321)+E(f862(f862(f73(x85321),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85323),x85324))),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85324),x85325))),f862(f862(f8(a924,x85321),x85322),f862(f295(a924,x85323),x85325)))+~P1(f862(f862(f227(a924),x85324),x85325))+~P1(f862(f862(f227(a924),x85323),x85324))
% 25.54/25.42 [8865]~P65(x88652)+E(x88651,f2(x88652))+E(x88653,f2(x88652))+E(f862(f862(f281(x88652),f862(f862(f3(x88652),f862(f862(f74(x88652),x88654),x88651)),f862(f862(f74(x88652),x88655),x88653))),f862(f862(f74(x88652),x88653),x88651)),f862(f862(f3(x88652),f862(f862(f281(x88652),x88654),x88653)),f862(f862(f281(x88652),x88655),x88651)))
% 25.54/25.42 [8866]~P65(x88662)+E(x88661,f2(x88662))+E(x88663,f2(x88662))+E(f862(f862(f281(x88662),f862(f862(f73(x88662),f862(f862(f74(x88662),x88664),x88661)),f862(f862(f74(x88662),x88665),x88663))),f862(f862(f74(x88662),x88663),x88661)),f862(f862(f73(x88662),f862(f862(f281(x88662),x88664),x88663)),f862(f862(f281(x88662),x88665),x88661)))
% 25.54/25.42 [8875]~E(x88752,f862(x88753,x88751))+E(x88751,f539(x88752,x88753,x88754,x88755))+~P22(x88755,x88754,x88753,f234(f932(x88755,a921)))+~P1(f862(f862(f321(x88754),x88752),f862(f302(x88755,x88754,x88753),f234(f932(x88755,a921)))))
% 25.54/25.42 [9095]~P112(x90951)+~P1(f862(f862(f228(x90951),f862(f69(x90951),x90952)),x90954))+P1(f862(f862(f228(x90951),f862(f862(f74(x90951),f862(f69(x90951),x90952)),f862(f69(x90951),x90953))),f862(f862(f74(x90951),x90954),x90955)))+~P1(f862(f862(f228(x90951),f862(f69(x90951),x90953)),x90955))
% 25.54/25.42 [9206]~P22(x92061,x92063,x92065,x92062)+~P1(f862(f54(x92063),x92064))+P1(f862(f862(f227(a924),f862(f28(x92061),x92062)),f862(f28(x92063),x92064)))+~P1(f862(f862(f227(f932(x92063,a921)),f862(f302(x92061,x92063,x92065),x92062)),x92064))
% 25.54/25.42 [9273]~P72(x92732)+~P22(x92731,x92731,x92734,x92735)+~P1(f862(f54(x92731),x92735))+E(f862(f862(f8(x92731,x92732),f862(f66(x92731,x92732,x92731,x92733),x92734)),x92735),f862(f862(f8(x92731,x92732),x92733),f862(f302(x92731,x92731,x92734),x92735)))
% 25.54/25.42 [9274]~P71(x92742)+~P22(x92741,x92741,x92744,x92745)+~P1(f862(f54(x92741),x92745))+E(f862(f862(f11(x92741,x92742),f862(f66(x92741,x92742,x92741,x92743),x92744)),x92745),f862(f862(f11(x92741,x92742),x92743),f862(f302(x92741,x92741,x92744),x92745)))
% 25.54/25.42 [9356]~E(f540(x93562,x93564,x93561,x93563,x93565),x93565)+~E(x93562,f862(x93564,x93565))+~P22(x93563,x93561,x93564,f234(f932(x93563,a921)))+P1(f862(f862(f321(x93561),x93562),f862(f302(x93563,x93561,x93564),f234(f932(x93563,a921)))))
% 25.54/25.42 [9394]~P35(x93941,x93942)+~P1(f862(f862(f321(x93941),x93943),x93944))+~P1(f862(f862(f321(x93941),x93945),x93944))+~P1(f862(f862(f321(f931(x93941,x93941)),f862(f862(f244(x93941,x93941),x93945),f611(x93942,x93941,x93944))),x93942))
% 25.54/25.42 [9430]~P22(x94302,x94303,x94305,x94301)+E(x94301,f181(f932(x94302,a921)))+E(f862(f302(x94303,x94302,f541(x94304,x94303,x94302,x94301)),x94304),x94301)+~P1(f862(f862(f227(f932(x94303,a921)),f862(f302(x94302,x94303,x94305),x94301)),x94304))
% 25.54/25.42 [9471]~E(x94712,f862(x94711,x94715))+~P22(x94714,x94713,x94711,f234(f932(x94714,a921)))+E(f862(x94711,f540(x94712,x94711,x94713,x94714,x94715)),x94712)+P1(f862(f862(f321(x94713),x94712),f862(f302(x94714,x94713,x94711),f234(f932(x94714,a921)))))
% 25.54/25.42 [9919]~P3(x99195)+~P109(x99195)+P1(f862(f862(f321(x99191),f479(x99192,x99193,x99191,x99194,x99195)),x99193))+~P1(f862(f862(f228(x99195),x99194),f862(f862(f33(x99191,x99195),x99193),x99192)))
% 25.54/25.42 [9924]~P3(x99241)+~P109(x99241)+P1(f862(f862(f228(x99241),x99242),f862(x99243,f479(x99243,x99244,x99245,x99242,x99241))))+~P1(f862(f862(f228(x99241),x99242),f862(f862(f33(x99245,x99241),x99244),x99243)))
% 25.54/25.42 [10004]~P69(x100041)+~P1(f862(f59(x100041,x100041,f74(x100041),x100042,x100043),x100045))+P1(f862(f862(f321(x100041),x100042),x100043))+P1(f862(f59(x100041,x100041,f74(x100041),x100044,f862(f862(f301(x100041),x100042),x100043)),f862(f862(f74(x100041),x100044),x100045)))
% 25.54/25.42 [10209]~P72(x102092)+~P1(f862(f54(x102091),x102095))+E(f862(f862(f8(x102091,x102092),f862(f862(f9(x102091,x102092,x102092),f862(f862(f20(x102091,x102092,f932(x102092,x102092)),f862(f862(f10(a921,f932(x102092,f932(x102092,x102092)),x102091),f89(x102092)),f862(a317,x102093))),x102094)),f2(x102092))),x102095),f2(x102092))+P1(f862(f862(f321(x102091),x102093),x102095))
% 25.54/25.42 [10210]~P71(x102102)+~P1(f862(f54(x102101),x102105))+E(f862(f862(f11(x102101,x102102),f862(f862(f9(x102101,x102102,x102102),f862(f862(f20(x102101,x102102,f932(x102102,x102102)),f862(f862(f10(a921,f932(x102102,f932(x102102,x102102)),x102101),f89(x102102)),f862(a317,x102103))),x102104)),f71(x102102))),x102105),f71(x102102))+P1(f862(f862(f321(x102101),x102103),x102105))
% 25.54/25.42 [10211]~P72(x102112)+~P1(f862(f54(x102111),x102115))+E(f862(f862(f8(x102111,x102112),f862(f862(f9(x102111,x102112,x102112),f862(f862(f20(x102111,x102112,f932(x102112,x102112)),f862(f862(f10(a921,f932(x102112,f932(x102112,x102112)),x102111),f89(x102112)),f862(a317,x102113))),x102114)),f2(x102112))),x102115),f862(x102114,x102113))+~P1(f862(f862(f321(x102111),x102113),x102115))
% 25.54/25.42 [10212]~P71(x102122)+~P1(f862(f54(x102121),x102125))+E(f862(f862(f11(x102121,x102122),f862(f862(f9(x102121,x102122,x102122),f862(f862(f20(x102121,x102122,f932(x102122,x102122)),f862(f862(f10(a921,f932(x102122,f932(x102122,x102122)),x102121),f89(x102122)),f862(a317,x102123))),x102124)),f71(x102122))),x102125),f862(x102124,x102123))+~P1(f862(f862(f321(x102121),x102123),x102125))
% 25.54/25.42 [10266]~P72(x102662)+~P1(f862(f54(x102661),x102665))+E(f862(f862(f8(x102661,x102662),f862(f862(f9(x102661,x102662,x102662),f862(f862(f20(x102661,x102662,f932(x102662,x102662)),f862(f862(f10(a921,f932(x102662,f932(x102662,x102662)),x102661),f89(x102662)),f862(f862(f9(x102661,x102661,a921),a317),x102663))),x102664)),f2(x102662))),x102665),f2(x102662))+P1(f862(f862(f321(x102661),x102663),x102665))
% 25.54/25.42 [10267]~P71(x102672)+~P1(f862(f54(x102671),x102675))+E(f862(f862(f11(x102671,x102672),f862(f862(f9(x102671,x102672,x102672),f862(f862(f20(x102671,x102672,f932(x102672,x102672)),f862(f862(f10(a921,f932(x102672,f932(x102672,x102672)),x102671),f89(x102672)),f862(f862(f9(x102671,x102671,a921),a317),x102673))),x102674)),f71(x102672))),x102675),f71(x102672))+P1(f862(f862(f321(x102671),x102673),x102675))
% 25.54/25.42 [10269]~P72(x102692)+~P1(f862(f54(x102691),x102695))+E(f862(f862(f8(x102691,x102692),f862(f862(f9(x102691,x102692,x102692),f862(f862(f20(x102691,x102692,f932(x102692,x102692)),f862(f862(f10(a921,f932(x102692,f932(x102692,x102692)),x102691),f89(x102692)),f862(f862(f9(x102691,x102691,a921),a317),x102693))),x102694)),f2(x102692))),x102695),f862(x102694,x102693))+~P1(f862(f862(f321(x102691),x102693),x102695))
% 25.54/25.42 [10270]~P71(x102702)+~P1(f862(f54(x102701),x102705))+E(f862(f862(f11(x102701,x102702),f862(f862(f9(x102701,x102702,x102702),f862(f862(f20(x102701,x102702,f932(x102702,x102702)),f862(f862(f10(a921,f932(x102702,f932(x102702,x102702)),x102701),f89(x102702)),f862(f862(f9(x102701,x102701,a921),a317),x102703))),x102704)),f71(x102702))),x102705),f862(x102704,x102703))+~P1(f862(f862(f321(x102701),x102703),x102705))
% 25.54/25.42 [8030]~P59(x80302)+~P1(f862(f54(x80301),x80304))+E(f862(f862(f8(x80301,x80302),x80303),f862(f862(f3(f932(x80301,a921)),x80304),f862(f862(f301(x80301),x80305),f181(f932(x80301,a921))))),f862(f862(f8(x80301,x80302),x80303),x80304))+P1(f862(f862(f321(x80301),x80305),x80304))
% 25.54/25.42 [8539]~P125(x85392)+~P1(f862(f54(x85391),x85394))+E(f862(f862(f8(x85391,x85392),x85393),f862(f862(f3(f932(x85391,a921)),x85394),f862(f862(f301(x85391),x85395),f181(f932(x85391,a921))))),f862(f862(f3(x85392),f862(f862(f8(x85391,x85392),x85393),x85394)),f862(x85393,x85395)))+~P1(f862(f862(f321(x85391),x85395),x85394))
% 25.54/25.42 [8540]~P59(x85402)+~P1(f862(f54(x85401),x85404))+E(f862(f862(f8(x85401,x85402),x85403),f862(f862(f3(f932(x85401,a921)),x85404),f862(f862(f301(x85401),x85405),f181(f932(x85401,a921))))),f862(f862(f3(x85402),f862(f862(f8(x85401,x85402),x85403),x85404)),f862(x85403,x85405)))+~P1(f862(f862(f321(x85401),x85405),x85404))
% 25.54/25.42 [8552]~P119(x85521)+~P1(f862(f862(f227(a924),x85523),x85525))+~P1(f862(f862(f278(x85521),f862(f862(f236(x85521),x85522),x85525)),x85524))+P1(f862(f862(f278(x85521),f862(f862(f236(x85521),x85522),x85523)),x85524))
% 25.54/25.42 [8570]~P59(x85701)+~P1(f862(f54(x85702),x85704))+E(f862(f862(f3(x85701),f862(f862(f8(x85702,x85701),x85703),x85704)),f862(f862(f8(x85702,x85701),x85703),x85705)),f862(f862(f8(x85702,x85701),x85703),f862(f862(f3(f932(x85702,a921)),x85704),x85705)))+~P1(f862(f862(f227(f932(x85702,a921)),x85705),x85704))
% 25.54/25.42 [8589]P1(f862(f54(x85891),f862(x85892,x85893)))+~P1(f862(f54(x85894),x85895))+~P1(f862(f862(f321(x85894),x85893),x85895))+~P1(f862(f54(x85891),f862(f862(f33(x85894,f932(x85891,a921)),x85895),x85892)))
% 25.54/25.42 [9051]~P6(x90511,x90515,x90514)+~E(f862(f276(x90511,x90511,x90514),f862(f862(f301(x90511),x90512),f181(f932(x90511,a921)))),f862(f276(x90511,x90511,x90514),f862(f862(f301(x90511),x90513),f181(f932(x90511,a921)))))+~P1(f862(f862(f321(x90511),x90513),x90515))+P1(f862(f862(f321(f931(x90511,x90511)),f862(f862(f244(x90511,x90511),x90512),x90513)),x90514))
% 25.54/25.42 [9350]~P1(f862(x93501,x93505))+P1(f862(x93501,f632(x93501,x93502,x93503,x93504)))+P1(f862(x93501,f622(x93501,x93502,x93503,x93504)))+~P1(f862(f862(f321(x93504),x93505),f862(f862(f103(f932(x93504,a921)),x93503),x93502)))
% 25.54/25.42 [9535]~P1(f862(x95351,x95355))+P1(f862(x95351,f622(x95351,x95352,x95353,x95354)))+P1(f862(f862(f321(x95354),f632(x95351,x95352,x95353,x95354)),x95352))+~P1(f862(f862(f321(x95354),x95355),f862(f862(f103(f932(x95354,a921)),x95353),x95352)))
% 25.54/25.42 [9536]~P1(f862(x95361,x95365))+P1(f862(x95361,f632(x95361,x95362,x95363,x95364)))+P1(f862(f862(f321(x95364),f622(x95361,x95362,x95363,x95364)),x95363))+~P1(f862(f862(f321(x95364),x95365),f862(f862(f103(f932(x95364,a921)),x95363),x95362)))
% 25.54/25.42 [9540]P1(f862(x95401,x95402))+~P1(f862(x95401,f615(x95401,x95403,x95404,x95405)))+~P1(f862(x95401,f598(x95401,x95403,x95404,x95405)))+~P1(f862(f862(f321(x95405),x95402),f862(f862(f103(f932(x95405,a921)),x95404),x95403)))
% 25.54/25.42 [9545]~P36(x95451,x95454)+~P1(f862(f862(f321(f931(x95451,x95451)),f862(f862(f244(x95451,x95451),x95452),x95455)),x95454))+P1(f862(f862(f321(f931(x95451,x95451)),f862(f862(f244(x95451,x95451),x95452),x95453)),x95454))+~P1(f862(f862(f321(f931(x95451,x95451)),f862(f862(f244(x95451,x95451),x95455),x95453)),x95454))
% 25.54/25.42 [9546]~P36(x95461,x95464)+~P1(f862(f862(f321(f931(x95461,x95461)),f862(f862(f244(x95461,x95461),x95462),x95465)),x95464))+P1(f862(f862(f321(f931(x95461,x95461)),f862(f862(f244(x95461,x95461),x95462),x95463)),x95464))+~P1(f862(f862(f321(f931(x95461,x95461)),f862(f862(f244(x95461,x95461),x95465),x95463)),x95464))
% 25.54/25.42 [9587]E(x95871,x95872)+~P1(f862(f862(f321(f931(x95873,x95873)),f862(f862(f244(x95873,x95873),x95871),x95872)),f299(x95873,x95875)))+P1(f862(f862(f321(x95873),x95871),x95874))+~P1(f862(f862(f227(f932(f931(x95873,x95873),a921)),x95875),f862(f862(f246(x95873,x95873),x95874),f862(f18(f932(x95873,a921),x95873),x95874))))
% 25.54/25.42 [9605]P1(f862(x96051,x96052))+~P1(f862(x96051,f598(x96051,x96054,x96055,x96053)))+P1(f862(f862(f321(x96053),f615(x96051,x96054,x96055,x96053)),x96054))+~P1(f862(f862(f321(x96053),x96052),f862(f862(f103(f932(x96053,a921)),x96055),x96054)))
% 25.54/25.42 [9606]P1(f862(x96061,x96062))+~P1(f862(x96061,f615(x96061,x96064,x96065,x96063)))+P1(f862(f862(f321(x96063),f598(x96061,x96064,x96065,x96063)),x96065))+~P1(f862(f862(f321(x96063),x96062),f862(f862(f103(f932(x96063,a921)),x96065),x96064)))
% 25.54/25.42 [9673]P1(f862(x96731,x96732))+P1(f862(f862(f321(x96733),f615(x96731,x96734,x96735,x96733)),x96734))+P1(f862(f862(f321(x96733),f598(x96731,x96734,x96735,x96733)),x96735))+~P1(f862(f862(f321(x96733),x96732),f862(f862(f103(f932(x96733,a921)),x96735),x96734)))
% 25.54/25.42 [9675]~P1(f862(x96752,x96755))+P1(f862(f862(f321(x96751),f632(x96752,x96753,x96754,x96751)),x96753))+P1(f862(f862(f321(x96751),f622(x96752,x96753,x96754,x96751)),x96754))+~P1(f862(f862(f321(x96751),x96755),f862(f862(f103(f932(x96751,a921)),x96754),x96753)))
% 25.54/25.42 [9825]~P6(x98251,x98255,x98254)+~P1(f862(f862(f321(x98251),x98253),x98255))+P1(f862(f862(f321(f931(x98251,x98251)),f862(f862(f244(x98251,x98251),x98252),x98253)),x98254))+~P1(f862(f862(f227(f932(x98251,a921)),f862(f276(x98251,x98251,x98254),f862(f862(f301(x98251),x98253),f181(f932(x98251,a921))))),f862(f276(x98251,x98251,x98254),f862(f862(f301(x98251),x98252),f181(f932(x98251,a921))))))
% 25.54/25.42 [9953]~P3(x99535)+~P109(x99535)+P1(f862(f862(f321(x99531),f480(x99532,x99533,x99534,x99531,x99535)),x99534))+~P1(f862(f862(f228(x99535),f862(f862(f32(x99531,x99535),x99534),x99533)),x99532))
% 25.54/25.42 [9986]~P85(x99865)+~P81(x99865)+P1(f862(f862(f321(x99861),f701(x99862,x99863,x99864,x99861,x99865)),f862(f165(x99861),x99864)))+P1(f862(f862(f227(x99865),f862(f158(x99865),f862(f862(f147(x99861,x99865),x99863),x99864))),f862(f158(x99865),f862(f862(f147(x99861,x99865),x99862),x99864))))
% 25.54/25.42 [10097]~P3(x100971)+~P109(x100971)+P1(f862(f862(f228(x100971),f862(x100972,f480(x100973,x100972,x100974,x100975,x100971))),x100973))+~P1(f862(f862(f228(x100971),f862(f862(f32(x100975,x100971),x100974),x100972)),x100973))
% 25.54/25.42 [10227]~P85(x102271)+~P81(x102271)+~P1(f862(f862(f227(x102271),f862(x102273,f701(x102275,x102273,x102274,x102272,x102271))),f862(x102275,f701(x102275,x102273,x102274,x102272,x102271))))+P1(f862(f862(f227(x102271),f862(f158(x102271),f862(f862(f147(x102272,x102271),x102273),x102274))),f862(f158(x102271),f862(f862(f147(x102272,x102271),x102275),x102274))))
% 25.54/25.42 [8887]~P72(x88871)+~P1(f862(f54(x88874),x88875))+~P1(f862(f862(f321(x88874),x88873),x88875))+E(f862(f862(f73(x88871),f862(x88872,x88873)),f862(f862(f8(x88874,x88871),x88872),f862(f862(f3(f932(x88874,a921)),x88875),f862(f862(f301(x88874),x88873),f181(f932(x88874,a921)))))),f862(f862(f8(x88874,x88871),x88872),x88875))
% 25.54/25.42 [8888]~P72(x88881)+~P1(f862(f54(x88884),x88885))+~P1(f862(f862(f321(x88884),x88883),x88885))+E(f862(f862(f73(x88881),f862(x88882,x88883)),f862(f862(f8(x88884,x88881),x88882),f862(f862(f3(f932(x88884,a921)),x88885),f862(f862(f301(x88884),x88883),f181(f932(x88884,a921)))))),f862(f862(f8(x88884,x88881),x88882),x88885))
% 25.54/25.42 [8889]~P71(x88891)+~P1(f862(f54(x88894),x88895))+~P1(f862(f862(f321(x88894),x88893),x88895))+E(f862(f862(f74(x88891),f862(x88892,x88893)),f862(f862(f11(x88894,x88891),x88892),f862(f862(f3(f932(x88894,a921)),x88895),f862(f862(f301(x88894),x88893),f181(f932(x88894,a921)))))),f862(f862(f11(x88894,x88891),x88892),x88895))
% 25.54/25.42 [8950]~P16(x89501,x89504,x89505)+~P1(f862(f54(x89501),x89502))+E(f862(f862(f3(f932(x89501,a921)),x89502),f862(f862(f301(x89501),x89503),f181(f932(x89501,a921)))),f181(f932(x89501,a921)))+E(f862(f862(x89504,x89503),f862(x89505,f862(f862(f3(f932(x89501,a921)),x89502),f862(f862(f301(x89501),x89503),f181(f932(x89501,a921)))))),f862(x89505,f862(f862(f301(x89501),x89503),x89502)))
% 25.54/25.42 [9328]~P71(x93281)+~P1(f862(f54(x93282),x93285))+~P1(f862(f54(x93282),x93284))+E(f862(f862(f74(x93281),f862(f862(f11(x93282,x93281),x93283),f862(f862(f103(f932(x93282,a921)),x93284),x93285))),f862(f862(f11(x93282,x93281),x93283),f862(f862(f94(f932(x93282,a921)),x93284),x93285))),f862(f862(f74(x93281),f862(f862(f11(x93282,x93281),x93283),x93284)),f862(f862(f11(x93282,x93281),x93283),x93285)))
% 25.54/25.42 [9329]~P71(x93291)+~P1(f862(f54(x93292),x93295))+~P1(f862(f54(x93292),x93294))+E(f862(f862(f74(x93291),f862(f862(f11(x93292,x93291),x93293),f862(f862(f103(f932(x93292,a921)),x93294),x93295))),f862(f862(f11(x93292,x93291),x93293),f862(f862(f94(f932(x93292,a921)),x93294),x93295))),f862(f862(f74(x93291),f862(f862(f11(x93292,x93291),x93293),x93294)),f862(f862(f11(x93292,x93291),x93293),x93295)))
% 25.54/25.42 [9330]~P72(x93301)+~P1(f862(f54(x93302),x93305))+~P1(f862(f54(x93302),x93304))+E(f862(f862(f73(x93301),f862(f862(f8(x93302,x93301),x93303),f862(f862(f103(f932(x93302,a921)),x93304),x93305))),f862(f862(f8(x93302,x93301),x93303),f862(f862(f94(f932(x93302,a921)),x93304),x93305))),f862(f862(f73(x93301),f862(f862(f8(x93302,x93301),x93303),x93304)),f862(f862(f8(x93302,x93301),x93303),x93305)))
% 25.54/25.42 [9470]~P59(x94701)+~P1(f862(f54(x94702),x94705))+~P1(f862(f54(x94702),x94704))+E(f862(f862(f3(x94701),f862(f862(f73(x94701),f862(f862(f8(x94702,x94701),x94703),x94704)),f862(f862(f8(x94702,x94701),x94703),x94705))),f862(f862(f8(x94702,x94701),x94703),f862(f862(f94(f932(x94702,a921)),x94704),x94705))),f862(f862(f8(x94702,x94701),x94703),f862(f862(f103(f932(x94702,a921)),x94704),x94705)))
% 25.54/25.42 [9687]~P22(x96871,x96872,x96873,x96875)+~P22(x96871,x96872,x96873,x96874)+P22(x96871,x96872,x96873,f862(f862(f103(f932(x96871,a921)),x96874),x96875))+~E(f862(f862(f94(f932(x96872,a921)),f862(f302(x96871,x96872,x96873),f862(f862(f3(f932(x96871,a921)),x96874),x96875))),f862(f302(x96871,x96872,x96873),f862(f862(f3(f932(x96871,a921)),x96875),x96874))),f181(f932(x96872,a921)))
% 25.54/25.42 [9800]E(x98001,f2(a1))+~P1(f862(f862(f228(a1),f2(a1)),x98003))+~P1(f862(f42(x98002,x98001),f862(f862(f244(a1,a1),x98004),x98005)))+P1(f862(f42(x98002,f862(f862(f74(a1),x98001),x98003)),f862(f862(f244(a1,a1),f862(f862(f29(a1),x98004),x98003)),f862(f862(f73(a1),f862(f862(f74(a1),x98001),f38(a1,x98004,x98003))),x98005))))
% 25.54/25.42 [9808]~P1(f862(f862(f228(a924),f2(a924)),x98083))+~P1(f862(f862(f228(a924),f2(a924)),x98082))+~P1(f862(f41(x98081,x98082),f862(f862(f244(a924,a924),x98084),x98085)))+P1(f862(f41(x98081,f862(f862(f74(a924),x98082),x98083)),f862(f862(f244(a924,a924),f862(f862(f29(a924),x98084),x98083)),f862(f862(f73(a924),f862(f862(f74(a924),x98082),f38(a924,x98084,x98083))),x98085))))
% 25.54/25.42 [9857]~P71(x98571)+~P1(f862(f54(x98572),x98575))+~P1(f862(f54(x98572),x98574))+E(f862(f862(f74(x98571),f862(f862(f862(f58(x98571,x98572,f74(x98571)),x98573),f71(x98571)),f862(f862(f103(f932(x98572,a921)),x98574),x98575))),f862(f862(f862(f58(x98571,x98572,f74(x98571)),x98573),f71(x98571)),f862(f862(f94(f932(x98572,a921)),x98574),x98575))),f862(f862(f74(x98571),f862(f862(f862(f58(x98571,x98572,f74(x98571)),x98573),f71(x98571)),x98574)),f862(f862(f862(f58(x98571,x98572,f74(x98571)),x98573),f71(x98571)),x98575)))
% 25.54/25.42 [9859]~E(f862(f862(f168(x98591),x98595),x98592),f862(f862(f168(x98591),x98595),x98593))+P1(f862(f862(f321(f931(f925(x98591),f925(x98591))),f862(f862(f244(f925(x98591),f925(x98591)),x98592),x98593)),f140(x98591,x98594)))+~P1(f862(f862(f228(a924),x98595),f862(f862(f225(a924),f862(f182(f925(x98591)),x98592)),f862(f182(f925(x98591)),x98593))))+~P1(f862(f862(f321(f931(x98591,x98591)),f862(f862(f244(x98591,x98591),f862(f862(f157(x98591),x98592),x98595)),f862(f862(f157(x98591),x98593),x98595))),x98594))
% 25.54/25.42 [9975]~P85(x99755)+~P147(x99755)+P1(f862(f862(f321(x99751),f413(x99752,x99753,x99754,x99751,x99755)),x99754))+P1(f862(f862(f227(x99755),f862(f862(f8(x99751,x99755),x99753),x99754)),f862(f862(f74(x99755),f862(f93(x99755),f862(f28(x99751),x99754))),x99752)))
% 25.54/25.42 [10155]~P85(x101551)+~P147(x101551)+~P1(f862(f862(f227(x101551),f862(x101553,f413(x101555,x101553,x101554,x101552,x101551))),x101555))+P1(f862(f862(f227(x101551),f862(f862(f8(x101552,x101551),x101553),x101554)),f862(f862(f74(x101551),f862(f93(x101551),f862(f28(x101552),x101554))),x101555)))
% 25.54/25.42 [8918]E(f862(f862(f127(x89181),x89182),x89183),f862(f862(f127(x89181),x89184),x89185))+~E(f862(f862(f168(x89181),f862(f182(f925(x89181)),x89182)),x89184),x89182)+~E(f862(f862(f127(x89181),f862(f862(f131(x89181),f862(f182(f925(x89181)),x89182)),x89184)),x89185),x89183)+P1(f862(f862(f227(a924),f862(f182(f925(x89181)),x89184)),f862(f182(f925(x89181)),x89182)))
% 25.54/25.42 [9050]E(f862(f862(f127(x90501),x90502),x90503),f862(f862(f127(x90501),x90504),x90505))+~E(f862(f862(f168(x90501),f862(f182(f925(x90501)),x90502)),x90504),x90502)+~E(x90503,f862(f862(f127(x90501),f862(f862(f131(x90501),f862(f182(f925(x90501)),x90502)),x90504)),x90505))+~P1(f862(f862(f227(a924),f862(f182(f925(x90501)),x90502)),f862(f182(f925(x90501)),x90504)))
% 25.54/25.42 [10289]~P1(f862(x102895,x102894))+~P1(f862(f54(x102892),f862(f254(x102892),x102895)))+P1(f862(f54(x102891),f862(f254(x102891),f862(f862(f9(x102891,x102892,a921),x102893),x102894))))+~P1(f862(f54(x102891),f862(f254(x102891),f862(f862(f10(f932(x102892,a921),a921,x102891),f80(x102892)),f862(f862(f10(f932(x102892,a921),f932(x102892,a921),x102891),f862(f20(x102892,a921,a921),f862(f862(f10(a921,f932(a921,a921),x102892),a318),x102895))),x102893)))))
% 25.54/25.42 [10365]~P1(f862(f54(x103652),x103655))+~P1(f862(f862(f321(x103652),x103654),x103655))+P1(f862(f54(x103651),f862(f254(x103651),f862(f862(f9(x103651,x103652,a921),x103653),x103654))))+~P1(f862(f54(x103651),f862(f254(x103651),f862(f862(f10(f932(x103652,a921),a921,x103651),f80(x103652)),f862(f862(f10(f932(x103652,a921),f932(x103652,a921),x103651),f862(f20(x103652,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103652),a318),f862(f862(f9(x103652,f932(x103652,a921),a921),f321(x103652)),x103655)))),x103653)))))
% 25.54/25.42 [8701]~P17(x87015,x87011,x87016,x87012)+E(f862(f66(x87011,x87011,x87011,f862(x87012,x87013)),f862(x87012,x87014)),f862(f66(x87011,x87011,x87011,f862(x87012,x87014)),f862(x87012,x87013)))+~P1(f862(f54(x87015),x87014))+~P1(f862(f54(x87015),x87013))
% 25.54/25.42 [8086]~P22(x80861,x80862,x80864,x80863)+~E(f862(x80864,x80866),x80865)+E(f862(f70(x80861,x80862,x80863,x80864),x80865),x80866)+~P1(f862(f862(f321(x80861),x80866),x80863))
% 25.54/25.42 [8087]~P22(x80871,x80872,x80874,x80873)+~E(f862(x80874,x80876),x80875)+E(f862(f86(x80871,x80872,x80873,x80874),x80875),x80876)+~P1(f862(f862(f321(x80871),x80876),x80873))
% 25.54/25.42 [8284]~P18(x82846,x82841,x82844,x82842)+E(f862(f66(x82841,x82841,x82841,f862(x82842,x82843)),f862(x82844,x82845)),f862(x82842,x82843))+~P1(f862(f54(x82846),x82843))+~P1(f862(f862(f321(x82846),x82845),x82843))
% 25.54/25.42 [9422]E(x94221,x94222)+~E(f862(f86(x94223,x94224,x94225,x94226),x94221),f862(f86(x94223,x94224,x94225,x94226),x94222))+~P1(f862(f862(f321(x94224),x94222),f862(f302(x94223,x94224,x94226),x94225)))+~P1(f862(f862(f321(x94224),x94221),f862(f302(x94223,x94224,x94226),x94225)))
% 25.54/25.42 [9519]~P17(x95193,x95191,x95196,x95192)+E(f862(f66(x95191,x95191,x95191,f862(x95192,f862(f862(f3(f932(x95193,a921)),x95194),f862(f862(f301(x95193),x95195),f181(f932(x95193,a921)))))),f862(x95196,x95195)),f862(x95192,x95194))+~P1(f862(f54(x95193),x95194))+~P1(f862(f862(f321(x95193),x95195),x95194))
% 25.54/25.42 [7162]~P62(x71621)+~E(f38(x71621,x71623,x71624),f38(x71621,x71626,x71624))+~E(f38(x71621,x71622,x71624),f38(x71621,x71625,x71624))+E(f38(x71621,f862(f862(f3(x71621),x71622),x71623),x71624),f38(x71621,f862(f862(f3(x71621),x71625),x71626),x71624))
% 25.54/25.42 [7163]~P61(x71631)+~E(f38(x71631,x71633,x71634),f38(x71631,x71636,x71634))+~E(f38(x71631,x71632,x71634),f38(x71631,x71635,x71634))+E(f38(x71631,f862(f862(f74(x71631),x71632),x71633),x71634),f38(x71631,f862(f862(f74(x71631),x71635),x71636),x71634))
% 25.54/25.42 [7164]~P61(x71641)+~E(f38(x71641,x71643,x71644),f38(x71641,x71646,x71644))+~E(f38(x71641,x71642,x71644),f38(x71641,x71645,x71644))+E(f38(x71641,f862(f862(f73(x71641),x71642),x71643),x71644),f38(x71641,f862(f862(f73(x71641),x71645),x71646),x71644))
% 25.54/25.42 [7980]~P14(x79801,x79802,x79803)+~P1(f862(f54(x79801),x79806))+E(f862(f862(f57(x79801,x79802,x79803),x79804),f862(f862(f301(x79801),x79805),x79806)),f862(f862(f57(x79801,x79802,x79803),f862(f862(x79803,x79805),x79804)),x79806))+P1(f862(f862(f321(x79801),x79805),x79806))
% 25.54/25.42 [8045]~P3(x80451)+P1(f862(f862(f227(x80451),x80452),f862(x80453,x80454)))+~P1(f862(f862(f321(x80455),x80454),x80456))+~P1(f862(f862(f227(x80451),x80452),f862(f862(f32(x80455,x80451),x80456),x80453)))
% 25.54/25.42 [8206]~P14(x82061,x82062,x82063)+~P1(f862(f54(x82061),x82066))+E(f862(f862(f57(x82061,x82062,x82063),x82064),f862(f862(f301(x82061),x82065),x82066)),f862(f862(x82063,x82065),f862(f862(f57(x82061,x82062,x82063),x82064),x82066)))+P1(f862(f862(f321(x82061),x82065),x82066))
% 25.54/25.42 [8304]~P109(x83043)+~P1(f862(x83042,x83045))+~P11(x83043,f862(f862(f147(x83041,x83043),x83044),x83046))+E(f862(f129(x83041,x83042),f862(f862(f141(x83041,x83043,x83044),x83045),x83046)),f862(f862(f141(x83041,x83043,x83044),x83045),f862(f129(x83041,x83042),x83046)))
% 25.54/25.42 [8327]E(x83271,x83272)+E(x83273,f2(a1))+~P1(f862(f42(x83274,x83273),f862(f862(f244(a1,a1),x83275),x83272)))+~P1(f862(f42(x83274,x83273),f862(f862(f244(a1,a1),x83276),x83271)))
% 25.54/25.42 [8328]E(x83281,x83282)+E(x83283,f2(a1))+~P1(f862(f42(x83284,x83283),f862(f862(f244(a1,a1),x83282),x83285)))+~P1(f862(f42(x83284,x83283),f862(f862(f244(a1,a1),x83281),x83286)))
% 25.54/25.42 [8351]~P17(x83512,x83515,x83516,x83511)+~P1(f862(f54(x83512),x83514))+E(f862(x83511,f862(f862(f301(x83512),x83513),x83514)),f862(f66(x83515,x83515,x83515,f862(x83511,x83514)),f862(x83516,x83513)))+P1(f862(f862(f321(x83512),x83513),x83514))
% 25.54/25.42 [8573]~P18(x85735,x85731,x85736,x85732)+E(f862(f66(x85731,x85731,x85731,f862(x85732,x85733)),f862(x85732,x85734)),f862(x85732,x85733))+~P1(f862(f54(x85735),x85733))+~P1(f862(f862(f227(f932(x85735,a921)),x85734),x85733))
% 25.54/25.42 [9730]~P22(x97301,x97302,x97304,x97303)+~P1(f862(f862(f321(x97302),x97305),f862(f302(x97301,x97302,x97304),x97303)))+P1(f862(f862(f321(x97301),f862(f70(x97301,x97302,x97303,x97304),x97305)),x97306))+~P1(f862(f862(f227(f932(x97301,a921)),x97303),x97306))
% 25.54/25.42 [10109]~P72(x101092)+~E(f602(x101091,x101093,x101095,x101096,x101094,x101092),f603(x101091,x101093,x101095,x101096,x101094,x101092))+~P1(f862(f54(x101094),x101096))+E(f862(f862(f8(x101091,x101092),x101093),f862(f302(x101094,x101091,x101095),x101096)),f862(f862(f8(x101094,x101092),f862(f66(x101091,x101092,x101094,x101093),x101095)),x101096))
% 25.54/25.42 [10137]~P72(x101376)+E(f862(x101371,f602(x101372,x101373,x101371,x101374,x101375,x101376)),f862(x101371,f603(x101372,x101373,x101371,x101374,x101375,x101376)))+E(f862(f862(f8(x101372,x101376),x101373),f862(f302(x101375,x101372,x101371),x101374)),f862(f862(f8(x101375,x101376),f862(f66(x101372,x101376,x101375,x101373),x101371)),x101374))+~P1(f862(f54(x101375),x101374))
% 25.54/25.42 [10177]~P72(x101772)+~E(f862(x101773,f862(x101775,f603(x101771,x101773,x101775,x101776,x101774,x101772))),f2(x101772))+~P1(f862(f54(x101774),x101776))+E(f862(f862(f8(x101771,x101772),x101773),f862(f302(x101774,x101771,x101775),x101776)),f862(f862(f8(x101774,x101772),f862(f66(x101771,x101772,x101774,x101773),x101775)),x101776))
% 25.54/25.42 [10236]~P72(x102362)+~P1(f862(f54(x102364),x102366))+E(f862(f862(f8(x102361,x102362),x102363),f862(f302(x102364,x102361,x102365),x102366)),f862(f862(f8(x102364,x102362),f862(f66(x102361,x102362,x102364,x102363),x102365)),x102366))+P1(f862(f862(f321(x102364),f603(x102361,x102363,x102365,x102366,x102364,x102362)),x102366))
% 25.54/25.42 [10237]~P72(x102372)+~P1(f862(f54(x102374),x102376))+E(f862(f862(f8(x102371,x102372),x102373),f862(f302(x102374,x102371,x102375),x102376)),f862(f862(f8(x102374,x102372),f862(f66(x102371,x102372,x102374,x102373),x102375)),x102376))+P1(f862(f862(f321(x102374),f602(x102371,x102373,x102375,x102376,x102374,x102372)),x102376))
% 25.54/25.42 [10364]~P71(x103641)+~P1(f862(f54(x103642),x103646))+E(f862(f862(f862(f58(x103641,x103642,f74(x103641)),f862(f862(f20(x103642,f932(x103643,a921),x103641),f862(f862(f9(x103642,x103641,f932(f932(x103643,a921),x103641)),f862(f862(f10(f932(x103643,x103641),f932(x103641,f932(f932(x103643,a921),x103641)),x103642),f58(x103641,x103643,f74(x103641))),x103644)),f71(x103641))),x103645)),f71(x103641)),x103646),f862(f862(f862(f58(x103641,f931(x103642,x103643),f74(x103641)),f862(f249(x103642,x103643,x103641),x103644)),f71(x103641)),f862(f862(f246(x103642,x103643),x103646),x103645)))+P1(f862(f862(f321(x103642),f575(x103644,x103645,x103643,x103646,x103642,x103641)),x103646))
% 25.54/25.42 [10386]~P71(x103861)+~P1(f862(f54(x103862),x103866))+E(f862(f862(f862(f58(x103861,x103862,f74(x103861)),f862(f862(f20(x103862,f932(x103863,a921),x103861),f862(f862(f9(x103862,x103861,f932(f932(x103863,a921),x103861)),f862(f862(f10(f932(x103863,x103861),f932(x103861,f932(f932(x103863,a921),x103861)),x103862),f58(x103861,x103863,f74(x103861))),x103864)),f71(x103861))),x103865)),f71(x103861)),x103866),f862(f862(f862(f58(x103861,f931(x103862,x103863),f74(x103861)),f862(f249(x103862,x103863,x103861),x103864)),f71(x103861)),f862(f862(f246(x103862,x103863),x103866),x103865)))+~P1(f862(f54(x103863),f862(x103865,f575(x103864,x103865,x103863,x103866,x103862,x103861))))
% 25.54/25.42 [8483]~P18(x84832,x84835,x84836,x84831)+~P1(f862(f54(x84832),x84834))+~P1(f862(f54(x84832),x84833))+E(f862(x84831,f862(f862(f103(f932(x84832,a921)),x84833),x84834)),f862(f66(x84835,x84835,x84835,f862(x84831,x84833)),f862(x84831,x84834)))
% 25.54/25.42 [8702]~P3(x87021)+P1(f862(f862(f227(x87021),f862(x87022,x87023)),x87024))+~P1(f862(f862(f321(x87025),x87023),x87026))+~P1(f862(f862(f227(x87021),f862(f862(f33(x87025,x87021),x87026),x87022)),x87024))
% 25.54/25.42 [9136]~P22(x91362,x91361,x91363,x91366)+E(f862(f862(f94(f932(x91361,a921)),f862(f302(x91362,x91361,x91363),x91364)),f862(f302(x91362,x91361,x91363),x91365)),f862(f302(x91362,x91361,x91363),f862(f862(f94(f932(x91362,a921)),x91364),x91365)))+~P1(f862(f862(f227(f932(x91362,a921)),x91365),x91366))+~P1(f862(f862(f227(f932(x91362,a921)),x91364),x91366))
% 25.54/25.42 [9137]~P22(x91372,x91371,x91373,x91376)+E(f862(f862(f3(f932(x91371,a921)),f862(f302(x91372,x91371,x91373),x91374)),f862(f302(x91372,x91371,x91373),x91375)),f862(f302(x91372,x91371,x91373),f862(f862(f3(f932(x91372,a921)),x91374),x91375)))+~P1(f862(f862(f227(f932(x91372,a921)),x91375),x91376))+~P1(f862(f862(f227(f932(x91372,a921)),x91374),x91376))
% 25.54/25.42 [9395]E(x93951,x93952)+~P52(x93953,x93954,x93955)+~P1(f862(f862(f321(f931(x93953,x93954)),f862(f862(f244(x93953,x93954),x93956),x93952)),x93955))+~P1(f862(f862(f321(f931(x93953,x93954)),f862(f862(f244(x93953,x93954),x93956),x93951)),x93955))
% 25.54/25.42 [9396]E(x93961,x93962)+~P52(x93963,x93964,x93965)+~P1(f862(f862(f321(f931(x93963,x93964)),f862(f862(f244(x93963,x93964),x93966),x93962)),x93965))+~P1(f862(f862(f321(f931(x93963,x93964)),f862(f862(f244(x93963,x93964),x93966),x93961)),x93965))
% 25.54/25.42 [10172]~P69(x101721)+~E(f862(x101723,f384(x101724,x101726,x101723,x101725,x101722,x101721)),f862(x101726,f384(x101724,x101726,x101723,x101725,x101722,x101721)))+~P1(f862(f54(x101722),x101725))+E(f862(f862(f862(f58(x101721,x101722,f74(x101721)),x101723),x101724),x101725),f862(f862(f862(f58(x101721,x101722,f74(x101721)),x101726),x101724),x101725))
% 25.54/25.42 [10233]~P69(x102331)+~P1(f862(f54(x102332),x102335))+E(f862(f862(f862(f58(x102331,x102332,f74(x102331)),x102333),x102334),x102335),f862(f862(f862(f58(x102331,x102332,f74(x102331)),x102336),x102334),x102335))+P1(f862(f862(f321(x102332),f384(x102334,x102333,x102336,x102335,x102332,x102331)),x102335))
% 25.54/25.42 [8932]~P69(x89321)+~P1(f862(f54(x89322),x89326))+P1(f862(f862(f321(x89322),x89325),x89326))+E(f862(f862(f862(f58(x89321,x89322,f74(x89321)),x89323),x89324),f862(f862(f301(x89322),x89325),x89326)),f862(f862(f74(x89321),f862(x89323,x89325)),f862(f862(f862(f58(x89321,x89322,f74(x89321)),x89323),x89324),x89326)))
% 25.54/25.42 [8985]~P6(x89851,x89856,x89853)+~P9(x89851,f932(x89852,a921),x89853,x89855)+~P1(f862(f862(f321(x89851),x89854),x89856))+E(f862(f862(f33(x89851,f932(x89852,a921)),f862(f276(x89851,x89851,x89853),f862(f862(f301(x89851),x89854),f181(f932(x89851,a921))))),x89855),f862(x89855,x89854))
% 25.54/25.42 [9113]~P14(x91133,x91134,x91131)+~P1(f862(f54(x91133),x91136))+~P1(f862(f862(f321(x91133),x91132),x91136))+E(f862(f862(x91131,x91132),f862(f862(f57(x91133,x91134,x91131),x91135),f862(f862(f3(f932(x91133,a921)),x91136),f862(f862(f301(x91133),x91132),f181(f932(x91133,a921)))))),f862(f862(f57(x91133,x91134,x91131),x91135),x91136))
% 25.54/25.42 [9406]~P17(x94063,x94061,x94066,x94062)+~P1(f862(f54(x94063),x94065))+~P1(f862(f54(x94063),x94064))+E(f862(f66(x94061,x94061,x94061,f862(x94062,f862(f862(f103(f932(x94063,a921)),x94064),x94065))),f862(x94062,f862(f862(f94(f932(x94063,a921)),x94064),x94065))),f862(f66(x94061,x94061,x94061,f862(x94062,x94064)),f862(x94062,x94065)))
% 25.54/25.42 [9753]~E(x97533,f862(f862(f152(x97531,x97532),x97535),x97536))+P1(f862(f862(f321(f931(f925(x97531),f925(x97531))),f862(f862(f244(f925(x97531),f925(x97531)),x97532),x97533)),f150(x97531,x97534)))+~P1(f862(f862(f228(a924),x97535),f862(f182(f925(x97531)),x97532)))+~P1(f862(f862(f321(f931(x97531,x97531)),f862(f862(f244(x97531,x97531),f862(f862(f157(x97531),x97532),x97535)),x97536)),x97534))
% 25.54/25.42 [10246]~P72(x102462)+~P1(f862(f54(x102461),x102466))+P1(f862(f862(f321(x102461),f573(x102464,x102465,x102463,x102466,x102461,x102462)),x102466))+E(f862(f862(f8(x102461,x102462),f862(f862(f20(x102461,f932(x102463,a921),x102462),f862(f862(f10(f932(x102463,x102462),f932(f932(x102463,a921),x102462),x102461),f8(x102463,x102462)),x102464)),x102465)),x102466),f862(f862(f8(f931(x102461,x102463),x102462),f862(f249(x102461,x102463,x102462),x102464)),f862(f862(f246(x102461,x102463),x102466),x102465)))
% 25.54/25.42 [10247]~P71(x102472)+~P1(f862(f54(x102471),x102476))+P1(f862(f862(f321(x102471),f574(x102474,x102475,x102473,x102476,x102471,x102472)),x102476))+E(f862(f862(f11(x102471,x102472),f862(f862(f20(x102471,f932(x102473,a921),x102472),f862(f862(f10(f932(x102473,x102472),f932(f932(x102473,a921),x102472),x102471),f11(x102473,x102472)),x102474)),x102475)),x102476),f862(f862(f11(f931(x102471,x102473),x102472),f862(f249(x102471,x102473,x102472),x102474)),f862(f862(f246(x102471,x102473),x102476),x102475)))
% 25.54/25.42 [10287]~P72(x102872)+~P1(f862(f54(x102871),x102876))+~P1(f862(f54(x102873),f862(x102875,f573(x102874,x102875,x102873,x102876,x102871,x102872))))+E(f862(f862(f8(x102871,x102872),f862(f862(f20(x102871,f932(x102873,a921),x102872),f862(f862(f10(f932(x102873,x102872),f932(f932(x102873,a921),x102872),x102871),f8(x102873,x102872)),x102874)),x102875)),x102876),f862(f862(f8(f931(x102871,x102873),x102872),f862(f249(x102871,x102873,x102872),x102874)),f862(f862(f246(x102871,x102873),x102876),x102875)))
% 25.54/25.42 [10288]~P71(x102882)+~P1(f862(f54(x102881),x102886))+~P1(f862(f54(x102883),f862(x102885,f574(x102884,x102885,x102883,x102886,x102881,x102882))))+E(f862(f862(f11(x102881,x102882),f862(f862(f20(x102881,f932(x102883,a921),x102882),f862(f862(f10(f932(x102883,x102882),f932(f932(x102883,a921),x102882),x102881),f11(x102883,x102882)),x102884)),x102885)),x102886),f862(f862(f11(f931(x102881,x102883),x102882),f862(f249(x102881,x102883,x102882),x102884)),f862(f862(f246(x102881,x102883),x102886),x102885)))
% 25.54/25.42 [10268]~P71(x102682)+~P1(f862(f54(x102681),x102686))+P1(f862(f862(f321(x102681),x102683),x102686))+E(f862(f862(f11(x102681,x102682),f862(f862(f9(x102681,x102682,x102682),f862(f862(f20(x102681,x102682,f932(x102682,x102682)),f862(f862(f10(a921,f932(x102682,f932(x102682,x102682)),x102681),f89(x102682)),f862(f862(f9(x102681,x102681,a921),a317),x102683))),x102684)),x102685)),x102686),f862(f862(f236(x102682),x102685),f862(f28(x102681),x102686)))
% 25.54/25.42 [10271]~P71(x102712)+~P1(f862(f54(x102711),x102716))+~P1(f862(f862(f321(x102711),x102713),x102716))+E(f862(f862(f11(x102711,x102712),f862(f862(f9(x102711,x102712,x102712),f862(f862(f20(x102711,x102712,f932(x102712,x102712)),f862(f862(f10(a921,f932(x102712,f932(x102712,x102712)),x102711),f89(x102712)),f862(f862(f9(x102711,x102711,a921),a317),x102713))),x102714)),x102715)),x102716),f862(f862(f74(x102712),f862(x102714,x102713)),f862(f862(f236(x102712),x102715),f862(f862(f3(a924),f862(f28(x102711),x102716)),f71(a924)))))
% 25.54/25.42 [10351]~P1(f862(f54(x103511),x103515))+~P1(f862(f54(x103512),x103513))+P1(f862(f862(f321(x103512),f512(x103516,x103514,x103513,x103512,x103515,x103511)),x103513))+E(f862(f862(f8(x103511,a924),f862(f862(f10(f932(x103512,a921),a924,x103511),f28(x103512)),f862(f862(f10(f932(x103512,a921),f932(x103512,a921),x103511),f254(x103512)),f862(f862(f10(f932(x103512,a921),f932(x103512,a921),x103511),f862(f20(x103512,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103512),a318),f862(f862(f9(x103512,f932(x103512,a921),a921),f321(x103512)),x103513)))),x103514)))),x103515),f862(f862(f74(a924),x103516),f862(f28(x103512),x103513)))
% 25.54/25.42 [10352]~P1(f862(f54(x103521),x103525))+~P1(f862(f54(x103522),x103523))+P1(f862(f862(f321(x103522),f519(x103526,x103524,x103523,x103522,x103525,x103521)),x103523))+E(f862(f862(f8(x103521,a924),f862(f862(f10(f932(x103522,a921),a924,x103521),f28(x103522)),f862(f862(f10(f932(x103522,a921),f932(x103522,a921),x103521),f254(x103522)),f862(f862(f10(f932(x103522,a921),f932(x103522,a921),x103521),f862(f20(x103522,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103522),a318),f862(f862(f9(x103522,f932(x103522,a921),a921),f321(x103522)),x103523)))),x103524)))),x103525),f862(f862(f8(x103522,a924),x103526),x103523))
% 25.54/25.42 [10399]~P1(f862(f54(x103992),x103993))+~P1(f862(f54(x103991),x103995))+~E(f862(f28(x103991),f862(f254(x103991),f862(f862(f20(x103991,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103991),a318),f862(f862(f9(x103991,f932(x103991,a921),a921),f321(x103991)),x103995))),f862(f862(f9(x103991,x103992,a921),x103994),f512(x103996,x103994,x103993,x103992,x103995,x103991))))),x103996)+E(f862(f862(f8(x103991,a924),f862(f862(f10(f932(x103992,a921),a924,x103991),f28(x103992)),f862(f862(f10(f932(x103992,a921),f932(x103992,a921),x103991),f254(x103992)),f862(f862(f10(f932(x103992,a921),f932(x103992,a921),x103991),f862(f20(x103992,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103992),a318),f862(f862(f9(x103992,f932(x103992,a921),a921),f321(x103992)),x103993)))),x103994)))),x103995),f862(f862(f74(a924),x103996),f862(f28(x103992),x103993)))
% 25.54/25.42 [10401]~P1(f862(f54(x104012),x104013))+~P1(f862(f54(x104011),x104015))+~E(f862(f28(x104011),f862(f254(x104011),f862(f862(f20(x104011,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104011),a318),f862(f862(f9(x104011,f932(x104011,a921),a921),f321(x104011)),x104015))),f862(f862(f9(x104011,x104012,a921),x104014),f519(x104016,x104014,x104013,x104012,x104015,x104011))))),f862(x104016,f519(x104016,x104014,x104013,x104012,x104015,x104011)))+E(f862(f862(f8(x104011,a924),f862(f862(f10(f932(x104012,a921),a924,x104011),f28(x104012)),f862(f862(f10(f932(x104012,a921),f932(x104012,a921),x104011),f254(x104012)),f862(f862(f10(f932(x104012,a921),f932(x104012,a921),x104011),f862(f20(x104012,a921,a921),f862(f862(f10(a921,f932(a921,a921),x104012),a318),f862(f862(f9(x104012,f932(x104012,a921),a921),f321(x104012)),x104013)))),x104014)))),x104015),f862(f862(f8(x104012,a924),x104016),x104013))
% 25.54/25.42 [10032]E(x100321,x100322)+~P14(x100323,x100324,x100325)+~P1(f862(f59(x100323,x100324,x100325,x100326,x100327),x100322))+~P1(f862(f59(x100323,x100324,x100325,x100326,x100327),x100321))
% 25.54/25.42 [9676]~P32(x96761,x96762,x96763,x96765,x96767)+~P32(x96761,x96762,x96763,x96764,x96766)+P32(x96761,x96762,x96763,f862(f862(f127(x96761),x96764),x96765),f862(f862(f127(x96762),x96766),x96767))+~E(f862(f182(f925(x96761)),x96764),f862(f182(f925(x96762)),x96766))
% 25.54/25.42 [9829]P1(f862(x98291,x98292))+~P1(f862(f862(f321(x98297),x98292),f862(x98296,x98294)))+~P1(f862(x98291,f886(x98291,x98296,x98295,x98293,x98297)))+~P1(f862(f862(f321(x98293),x98294),x98295))
% 25.54/25.42 [10260]~P14(x102607,x102606,x102601)+E(f862(f862(x102601,x102602),f802(x102602,x102603,x102604,x102605,x102601,x102606,x102607)),x102603)+~P1(f862(f59(x102607,x102606,x102601,x102605,x102604),x102603))+~P1(f862(f862(f321(x102607),x102602),x102604))
% 25.54/25.42 [10275]~P54(x102753,x102754,x102755,x102756,x102757)+P1(f862(x102751,x102752))+~P1(f862(f862(f321(x102754),x102752),x102757))+~P1(f862(x102751,f862(x102755,f910(x102751,x102752,x102757,x102756,x102755,x102754))))
% 25.54/25.42 [10329]~P14(x103291,x103292,x103293)+~P1(f862(f59(x103291,x103292,x103293,x103294,x103295),x103297))+P1(f862(f59(x103291,x103292,x103293,x103294,f862(f862(f3(f932(x103291,a921)),x103295),f862(f862(f301(x103291),x103296),f181(f932(x103291,a921))))),f802(x103296,x103297,x103295,x103294,x103293,x103292,x103291)))+~P1(f862(f862(f321(x103291),x103296),x103295))
% 25.54/25.42 [9477]P23(x94771,x94772,x94773,x94774,x94775)+~P23(x94771,x94772,x94773,x94776,x94777)+~E(f862(f302(x94771,x94772,x94773),x94774),x94775)+~P1(f862(f862(f227(f932(x94771,a921)),x94774),x94776))
% 25.54/25.42 [9721]~P23(x97211,x97212,x97213,x97215,x97217)+~P23(x97211,x97212,x97213,x97214,x97216)+P23(x97211,x97212,x97213,f862(f862(f103(f932(x97211,a921)),x97214),x97215),f862(f862(f103(f932(x97212,a921)),x97216),x97217))+~E(f862(f862(f94(f932(x97212,a921)),x97216),x97217),f181(f932(x97212,a921)))
% 25.54/25.42 [9726]~P69(x97261)+~P22(x97265,x97262,x97266,x97267)+~P1(f862(f54(x97265),x97267))+E(f862(f862(f862(f58(x97261,x97262,f74(x97261)),x97263),x97264),f862(f302(x97265,x97262,x97266),x97267)),f862(f862(f862(f58(x97261,x97265,f74(x97261)),f862(f66(x97262,x97261,x97265,x97263),x97266)),x97264),x97267))
% 25.54/25.42 [9852]~E(f862(f862(f301(x98521),x98525),x98526),f862(f862(f301(x98521),x98522),x98523))+~P1(f862(f59(x98521,x98521,x98524,x98522,x98523),x98527))+P1(f862(f862(f321(x98521),x98522),x98523))+P1(f862(f55(x98521,x98524,f862(f862(f301(x98521),x98525),x98526)),x98527))
% 25.54/25.42 [9937]P1(f862(x99371,x99372))+~P1(f862(f862(f321(x99373),x99372),f862(x99374,x99377)))+~P1(f862(f862(f321(x99376),x99377),x99375))+P1(f862(f862(f321(x99373),f886(x99371,x99374,x99375,x99376,x99373)),f862(f862(f33(x99376,f932(x99373,a921)),x99375),x99374)))
% 25.54/25.42 [9954]~P22(x99542,x99541,x99545,x99544)+~P22(x99541,x99543,x99546,f862(f302(x99542,x99541,x99545),x99544))+E(f862(f862(f66(x99541,x99542,x99543,f70(x99542,x99541,x99544,x99545)),f70(x99541,x99543,f862(f302(x99542,x99541,x99545),x99544),x99546)),x99547),f862(f70(x99542,x99543,x99544,f862(f66(x99541,x99543,x99542,x99546),x99545)),x99547))+~P1(f862(f862(f321(x99543),x99547),f862(f302(x99541,x99543,x99546),f862(f302(x99542,x99541,x99545),x99544))))
% 25.54/25.42 [9955]~P22(x99552,x99551,x99555,x99554)+~P22(x99551,x99553,x99556,f862(f302(x99552,x99551,x99555),x99554))+E(f862(f862(f66(x99551,x99552,x99553,f86(x99552,x99551,x99554,x99555)),f86(x99551,x99553,f862(f302(x99552,x99551,x99555),x99554),x99556)),x99557),f862(f86(x99552,x99553,x99554,f862(f66(x99551,x99553,x99552,x99556),x99555)),x99557))+~P1(f862(f862(f321(x99553),x99557),f862(f302(x99551,x99553,x99556),f862(f302(x99552,x99551,x99555),x99554))))
% 25.54/25.42 [10261]~P14(x102617,x102616,x102611)+E(f862(f862(x102611,x102612),f880(x102613,x102614,x102612,x102615,x102611,x102616,x102617)),x102613)+P1(f862(f862(f321(x102617),x102612),x102614))+~P1(f862(f59(x102617,x102616,x102611,x102615,f862(f862(f301(x102617),x102612),x102614)),x102613))
% 25.54/25.42 [10328]~P14(x103281,x103284,x103285)+P1(f862(f59(x103281,x103284,x103285,x103286,x103283),f880(x103287,x103283,x103282,x103286,x103285,x103284,x103281)))+P1(f862(f862(f321(x103281),x103282),x103283))+~P1(f862(f59(x103281,x103284,x103285,x103286,f862(f862(f301(x103281),x103282),x103283)),x103287))
% 25.54/25.42 [10014]E(x100141,f2(a1))+~P1(f862(f42(x100143,x100141),f862(f862(f244(a1,a1),x100145),x100147)))+~P1(f862(f42(x100142,x100141),f862(f862(f244(a1,a1),x100144),x100146)))+P1(f862(f42(f862(f862(f73(a1),x100142),x100143),x100141),f862(f862(f244(a1,a1),f862(f862(f73(a1),f862(f862(f73(a1),x100144),x100145)),f862(f862(f29(a1),f862(f862(f73(a1),x100146),x100147)),x100141))),f38(a1,f862(f862(f73(a1),x100146),x100147),x100141))))
% 25.54/25.42 [10016]~P1(f862(f862(f228(a924),f2(a924)),x100163))+~P1(f862(f41(x100162,x100163),f862(f862(f244(a924,a924),x100165),x100167)))+~P1(f862(f41(x100161,x100163),f862(f862(f244(a924,a924),x100164),x100166)))+P1(f862(f41(f862(f862(f73(a924),x100161),x100162),x100163),f862(f862(f244(a924,a924),f862(f862(f73(a924),f862(f862(f73(a924),x100164),x100165)),f862(f862(f29(a924),f862(f862(f73(a924),x100166),x100167)),x100163))),f38(a924,f862(f862(f73(a924),x100166),x100167),x100163))))
% 25.54/25.42 [10398]~P72(x103982)+~P1(f862(f54(x103983),x103985))+~P1(f862(f54(x103981),x103987))+E(f862(f862(f8(x103981,x103982),f862(f862(f20(x103981,f932(x103983,a921),x103982),f862(f862(f10(f932(x103983,x103982),f932(f932(x103983,a921),x103982),x103981),f8(x103983,x103982)),x103984)),f862(f862(f10(f932(x103983,a921),f932(x103983,a921),x103981),f254(x103983)),f862(f862(f10(f932(x103983,a921),f932(x103983,a921),x103981),f862(f20(x103983,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103983),a318),f862(f862(f9(x103983,f932(x103983,a921),a921),f321(x103983)),x103985)))),x103986)))),x103987),f862(f862(f8(x103983,x103982),f862(f862(f20(x103983,f932(x103981,a921),x103982),f862(f862(f10(f932(x103981,x103982),f932(f932(x103981,a921),x103982),x103983),f8(x103981,x103982)),f862(f9(x103981,x103983,x103982),x103984))),f862(f862(f10(f932(x103981,a921),f932(x103981,a921),x103983),f254(x103981)),f862(f862(f10(f932(x103981,a921),f932(x103981,a921),x103983),f862(f20(x103981,a921,a921),f862(f862(f10(a921,f932(a921,a921),x103981),a318),f862(f862(f9(x103981,f932(x103981,a921),a921),f321(x103981)),x103987)))),f862(f9(x103981,x103983,a921),x103986))))),x103985))
% 25.54/25.42 [10349]~P19(x103498,x103497,x103496,x103495,x103491)+~E(f862(x103492,f859(x103494,x103492,x103493,x103491,x103495,x103496,x103497)),f862(x103494,f859(x103494,x103492,x103493,x103491,x103495,x103496,x103497)))+E(f862(f862(x103491,x103492),x103493),f862(f862(x103491,x103494),x103493))+~P1(f862(f54(x103497),x103493))
% 25.54/25.42 [9888]~P20(x98887,x98886,x98881,x98888,x98882,x98884)+E(f862(f862(x98881,f862(x98882,x98883)),f862(x98884,x98885)),f862(x98884,x98885))+~P1(f862(f54(x98886),x98885))+~P1(f862(f862(f321(x98886),x98883),x98885))
% 25.54/25.42 [9892]~P10(x98926,x98921,x98922,x98928,x98923,x98924)+~P6(x98926,x98927,x98928)+P9(x98921,x98922,x98923,f862(x98924,x98925))+~P1(f862(f862(f321(x98926),x98925),x98927))
% 25.54/25.42 [10371]~P19(x103718,x103715,x103717,x103716,x103711)+E(f862(f862(x103711,x103712),x103713),f862(f862(x103711,x103714),x103713))+~P1(f862(f54(x103715),x103713))+P1(f862(f862(f321(x103715),f859(x103712,x103714,x103713,x103711,x103716,x103717,x103715)),x103713))
% 25.54/25.42 [10448]~P1(f862(f862(x104481,x104486),x104485))+P1(f862(f862(x104481,f846(x104481,x104484,x104485,x104486,x104483,x104482,x104487,x104488)),f852(x104481,x104484,x104485,x104486,x104483,x104482,x104487,x104488)))+P1(f862(f862(x104481,x104482),x104483))+~P1(f862(f862(f321(f931(f931(x104488,x104487),f931(x104488,x104487))),f862(f862(f244(f931(x104488,x104487),f931(x104488,x104487)),f862(f862(f244(x104488,x104487),x104482),x104483)),f862(f862(f244(x104488,x104487),x104486),x104485))),f299(f931(x104488,x104487),x104484)))
% 25.54/25.42 [10449]~P1(f862(f862(x104491,x104496),x104495))+P1(f862(f862(x104491,f843(x104491,x104494,x104493,x104492,x104495,x104496,x104497,x104498)),f844(x104491,x104494,x104493,x104492,x104495,x104496,x104497,x104498)))+P1(f862(f862(x104491,x104492),x104493))+~P1(f862(f862(f321(f931(f931(x104498,x104497),f931(x104498,x104497))),f862(f862(f244(f931(x104498,x104497),f931(x104498,x104497)),f862(f862(f244(x104498,x104497),x104496),x104495)),f862(f862(f244(x104498,x104497),x104492),x104493))),f299(f931(x104498,x104497),x104494)))
% 25.54/25.42 [10459]~P1(f862(f862(x104591,f847(x104591,x104596,x104595,x104594,x104593,x104592,x104597,x104598)),f851(x104591,x104596,x104595,x104594,x104593,x104592,x104597,x104598)))+P1(f862(f862(x104591,x104592),x104593))+~P1(f862(f862(x104591,x104594),x104595))+~P1(f862(f862(f321(f931(f931(x104598,x104597),f931(x104598,x104597))),f862(f862(f244(f931(x104598,x104597),f931(x104598,x104597)),f862(f862(f244(x104598,x104597),x104592),x104593)),f862(f862(f244(x104598,x104597),x104594),x104595))),f299(f931(x104598,x104597),x104596)))
% 25.54/25.42 [10460]~P1(f862(f862(x104601,f845(x104601,x104606,x104603,x104602,x104605,x104604,x104607,x104608)),f848(x104601,x104606,x104603,x104602,x104605,x104604,x104607,x104608)))+P1(f862(f862(x104601,x104602),x104603))+~P1(f862(f862(x104601,x104604),x104605))+~P1(f862(f862(f321(f931(f931(x104608,x104607),f931(x104608,x104607))),f862(f862(f244(f931(x104608,x104607),f931(x104608,x104607)),f862(f862(f244(x104608,x104607),x104604),x104605)),f862(f862(f244(x104608,x104607),x104602),x104603))),f299(f931(x104608,x104607),x104606)))
% 25.54/25.42 [10473]~P1(f862(f862(x104731,x104736),x104737))+P1(f862(f862(x104731,x104732),x104733))+P1(f862(f862(f321(f931(f931(x104734,x104735),f931(x104734,x104735))),f862(f862(f244(f931(x104734,x104735),f931(x104734,x104735)),f862(f862(f244(x104734,x104735),x104736),x104737)),f862(f862(f244(x104734,x104735),f843(x104731,x104738,x104733,x104732,x104737,x104736,x104735,x104734)),f844(x104731,x104738,x104733,x104732,x104737,x104736,x104735,x104734)))),f299(f931(x104734,x104735),x104738)))+~P1(f862(f862(f321(f931(f931(x104734,x104735),f931(x104734,x104735))),f862(f862(f244(f931(x104734,x104735),f931(x104734,x104735)),f862(f862(f244(x104734,x104735),x104736),x104737)),f862(f862(f244(x104734,x104735),x104732),x104733))),f299(f931(x104734,x104735),x104738)))
% 25.54/25.42 [10475]~P1(f862(f862(x104751,x104758),x104757))+P1(f862(f862(x104751,x104752),x104753))+P1(f862(f862(f321(f931(f931(x104754,x104755),f931(x104754,x104755))),f862(f862(f244(f931(x104754,x104755),f931(x104754,x104755)),f862(f862(f244(x104754,x104755),f846(x104751,x104756,x104757,x104758,x104753,x104752,x104755,x104754)),f852(x104751,x104756,x104757,x104758,x104753,x104752,x104755,x104754))),f862(f862(f244(x104754,x104755),x104758),x104757))),f299(f931(x104754,x104755),x104756)))+~P1(f862(f862(f321(f931(f931(x104754,x104755),f931(x104754,x104755))),f862(f862(f244(f931(x104754,x104755),f931(x104754,x104755)),f862(f862(f244(x104754,x104755),x104752),x104753)),f862(f862(f244(x104754,x104755),x104758),x104757))),f299(f931(x104754,x104755),x104756)))
% 25.54/25.42 [9502]~P17(x95027,x95021,x95028,x95023)+~P1(f862(f54(x95027),x95025))+~P1(f862(f54(x95027),x95024))+E(f862(f66(x95021,x95021,x95022,f862(x95023,x95024)),f862(f66(x95021,x95021,x95022,f862(x95023,x95025)),x95026)),f862(f66(x95021,x95021,x95022,f862(x95023,x95025)),f862(f66(x95021,x95021,x95022,f862(x95023,x95024)),x95026)))
% 25.54/25.42 [9511]~P32(x95111,x95112,x95113,x95114,x95117)+P32(x95111,x95112,x95113,f862(f862(f152(x95111,x95114),x95115),x95116),f862(f862(f152(x95112,x95117),x95115),x95118))+~P1(f862(f862(x95113,x95116),x95118))+~P1(f862(f862(f228(a924),x95115),f862(f182(f925(x95111)),x95114)))
% 25.54/25.42 [9512]~P32(x95121,x95122,x95123,x95124,x95127)+P32(x95121,x95122,x95123,f862(f862(f152(x95121,x95124),x95125),x95126),f862(f862(f152(x95122,x95127),x95125),x95128))+~P1(f862(f862(x95123,x95126),x95128))+~P1(f862(f862(f228(a924),x95125),f862(f182(f925(x95122)),x95127)))
% 25.54/25.42 [9594]~P22(x95942,x95942,x95945,x95946)+~P19(x95943,x95942,x95947,x95948,x95941)+~P1(f862(f54(x95942),x95946))+E(f862(f862(x95941,f862(f66(x95942,x95943,x95942,x95944),x95945)),x95946),f862(f862(x95941,x95944),f862(f302(x95942,x95942,x95945),x95946)))
% 25.54/25.42 [9828]~P23(x98281,x98283,x98285,x98286,x98288)+~P23(x98283,x98282,x98284,x98288,x98287)+P23(x98281,x98282,f862(f66(x98283,x98282,x98281,x98284),x98285),x98286,x98287)+~P1(f862(f862(f227(f932(x98283,a921)),f862(f302(x98281,x98283,x98285),x98286)),x98288))
% 25.54/25.42 [9853]P23(x98531,x98532,x98533,x98534,x98535)+~P23(x98532,x98536,x98537,x98535,x98538)+~P23(x98531,x98536,f862(f66(x98532,x98536,x98531,x98537),x98533),x98534,x98538)+~P1(f862(f862(f227(f932(x98532,a921)),f862(f302(x98531,x98532,x98533),x98534)),x98535))
% 25.54/25.42 [9890]~P21(x98907,x98902,x98905,x98908,x98906,x98901)+~P1(f862(f54(x98902),x98904))+E(f862(x98901,f862(f862(f301(x98902),x98903),x98904)),f862(f862(x98905,f862(x98906,x98903)),f862(x98901,x98904)))+P1(f862(f862(f321(x98902),x98903),x98904))
% 25.54/25.42 [9902]~P20(x99026,x99025,x99021,x99027,x99028,x99022)+E(f862(f862(x99021,f862(x99022,x99023)),f862(x99022,x99024)),f862(x99022,x99024))+~P1(f862(f54(x99025),x99024))+~P1(f862(f862(f227(f932(x99025,a921)),x99023),x99024))
% 25.54/25.42 [9489]P1(f862(f862(f321(f931(f925(x94891),f925(x94891))),f862(f862(f244(f925(x94891),f925(x94891)),x94892),x94893)),f150(x94891,x94894)))+~E(x94893,f862(f862(f127(x94891),x94895),f862(f862(f144(x94891),x94896),x94897)))+~E(x94892,f862(f862(f127(x94891),x94895),f862(f862(f144(x94891),x94898),x94897)))+~P1(f862(f862(f321(f931(x94891,x94891)),f862(f862(f244(x94891,x94891),x94898),x94896)),x94894))
% 25.54/25.42 [9895]~P20(x98956,x98952,x98955,x98957,x98958,x98951)+~P1(f862(f54(x98952),x98954))+~P1(f862(f54(x98952),x98953))+E(f862(x98951,f862(f862(f103(f932(x98952,a921)),x98953),x98954)),f862(f862(x98955,f862(x98951,x98953)),f862(x98951,x98954)))
% 25.54/25.42 [10438]~P22(x104384,x104382,x104385,x104388)+E(f862(f862(f32(x104381,f932(x104382,a921)),x104383),f862(f862(f10(f932(x104384,a921),f932(x104382,a921),x104381),f302(x104384,x104382,x104385)),x104386)),f862(f302(x104384,x104382,x104385),f862(f862(f32(x104381,f932(x104384,a921)),x104383),x104386)))+~P1(f862(f862(f321(x104381),x104387),x104383))+P1(f862(f862(f321(x104381),f544(x104387,x104386,x104383,x104381,x104388,x104385,x104382,x104384)),x104383))
% 25.54/25.42 [10464]~P22(x104644,x104642,x104645,x104647)+E(f862(f862(f32(x104641,f932(x104642,a921)),x104643),f862(f862(f10(f932(x104644,a921),f932(x104642,a921),x104641),f302(x104644,x104642,x104645)),x104646)),f862(f302(x104644,x104642,x104645),f862(f862(f32(x104641,f932(x104644,a921)),x104643),x104646)))+~P1(f862(f862(f321(x104641),x104648),x104643))+~P1(f862(f862(f227(f932(x104644,a921)),f862(x104646,f544(x104648,x104646,x104643,x104641,x104647,x104645,x104642,x104644))),x104647))
% 25.54/25.42 [10476]~P1(f862(f862(x104761,x104768),x104767))+P1(f862(f862(x104761,x104762),x104763))+~P1(f862(f862(f321(f931(f931(x104764,x104765),f931(x104764,x104765))),f862(f862(f244(f931(x104764,x104765),f931(x104764,x104765)),f862(f862(f244(x104764,x104765),x104762),x104763)),f862(f862(f244(x104764,x104765),x104768),x104767))),f299(f931(x104764,x104765),x104766)))+P1(f862(f862(f321(f931(f931(x104764,x104765),f931(x104764,x104765))),f862(f862(f244(f931(x104764,x104765),f931(x104764,x104765)),f862(f862(f244(x104764,x104765),f847(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764)),f851(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764))),f862(f862(f244(x104764,x104765),f846(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764)),f852(x104761,x104766,x104767,x104768,x104763,x104762,x104765,x104764)))),x104766))
% 25.54/25.42 [10477]~P1(f862(f862(x104771,x104778),x104777))+P1(f862(f862(x104771,x104772),x104773))+~P1(f862(f862(f321(f931(f931(x104774,x104775),f931(x104774,x104775))),f862(f862(f244(f931(x104774,x104775),f931(x104774,x104775)),f862(f862(f244(x104774,x104775),x104778),x104777)),f862(f862(f244(x104774,x104775),x104772),x104773))),f299(f931(x104774,x104775),x104776)))+P1(f862(f862(f321(f931(f931(x104774,x104775),f931(x104774,x104775))),f862(f862(f244(f931(x104774,x104775),f931(x104774,x104775)),f862(f862(f244(x104774,x104775),f843(x104771,x104776,x104773,x104772,x104777,x104778,x104775,x104774)),f844(x104771,x104776,x104773,x104772,x104777,x104778,x104775,x104774))),f862(f862(f244(x104774,x104775),f845(x104771,x104776,x104773,x104772,x104777,x104778,x104775,x104774)),f848(x104771,x104776,x104773,x104772,x104777,x104778,x104775,x104774)))),x104776))
% 25.54/25.42 [9964]~P21(x99647,x99645,x99641,x99648,x99642,x99644)+~P1(f862(f54(x99645),x99646))+~P1(f862(f862(f321(x99645),x99643),x99646))+E(f862(f862(x99641,f862(x99642,x99643)),f862(x99644,f862(f862(f3(f932(x99645,a921)),x99646),f862(f862(f301(x99645),x99643),f181(f932(x99645,a921)))))),f862(x99644,x99646))
% 25.54/25.42 [9972]~P21(x99726,x99723,x99721,x99727,x99728,x99722)+~P1(f862(f54(x99723),x99725))+~P1(f862(f54(x99723),x99724))+E(f862(f862(x99721,f862(x99722,f862(f862(f103(f932(x99723,a921)),x99724),x99725))),f862(x99722,f862(f862(f94(f932(x99723,a921)),x99724),x99725))),f862(f862(x99721,f862(x99722,x99724)),f862(x99722,x99725)))
% 25.54/25.42 [10056]P40(x100561,x100562,x100563,x100564,x100565,f862(f862(x100563,x100566),x100567))+~P40(x100561,x100562,x100563,x100564,f862(f862(f3(f932(x100561,a921)),x100565),f862(f862(f301(x100561),x100568),f181(f932(x100561,a921)))),x100569)+~E(f862(f862(x100563,x100566),x100567),f862(f862(x100563,x100568),x100569))+~P1(f862(f862(f321(x100561),x100568),x100565))
% 25.54/25.42 [9997]~P10(x99976,x99977,x99978,x99979,x999710,x99971)+E(f862(f862(x99971,x99972),x99973),f862(f862(x99971,x99974),x99975))+~P1(f862(f862(f321(f931(x99977,x99977)),f862(f862(f244(x99977,x99977),x99973),x99975)),x999710))+~P1(f862(f862(f321(f931(x99976,x99976)),f862(f862(f244(x99976,x99976),x99972),x99974)),x99979))
% 25.54/25.42 [9752]E(x97521,f2(a1))+E(x97522,f2(a1))+E(f862(f862(f79(a1,f931(a1,a1)),f862(f862(a210,x97522),x97521)),f862(f862(f20(a1,a1,f931(a1,a1)),f862(f862(f10(a1,f932(a1,f931(a1,a1)),a1),f244(a1,a1)),f862(f29(a1),x97522))),f862(f29(a1),x97521))),f208(x97522,x97521))+P1(f862(f862(f228(a1),x97521),f2(a1)))+~P1(f862(f307(f931(a1,a1),a214),f862(f862(f244(a1,a1),x97522),x97521)))
% 25.54/25.42 [9596]~P93(x95962)+E(x95961,f181(f932(x95962,a921)))+~P1(f862(f54(x95962),x95961))+P1(f862(f862(f321(x95962),f12(x95962,x95961)),x95961))+~P1(f862(f862(f321(x95962),f862(f862(f94(x95962),f885(x95961,x95962)),f889(x95961,x95962))),f862(f862(f301(x95962),f885(x95961,x95962)),f862(f862(f301(x95962),f889(x95961,x95962)),f181(f932(x95962,a921))))))
% 25.54/25.42 [9597]~P93(x95972)+E(x95971,f181(f932(x95972,a921)))+~P1(f862(f54(x95972),x95971))+P1(f862(f862(f321(x95972),f15(x95972,x95971)),x95971))+~P1(f862(f862(f321(x95972),f862(f862(f103(x95972),f890(x95971,x95972)),f891(x95971,x95972))),f862(f862(f301(x95972),f890(x95971,x95972)),f862(f862(f301(x95972),f891(x95971,x95972)),f181(f932(x95972,a921))))))
% 25.54/25.42 [9598]~P109(x95982)+E(x95981,f181(f932(x95982,a921)))+~P1(f862(f54(x95982),x95981))+P1(f862(f862(f321(x95982),f16(x95982,x95981)),x95981))+~P1(f862(f862(f321(x95982),f862(f862(f225(x95982),f455(x95981,x95982)),f458(x95981,x95982))),f862(f862(f301(x95982),f455(x95981,x95982)),f862(f862(f301(x95982),f458(x95981,x95982)),f181(f932(x95982,a921))))))
% 25.54/25.42 [9599]~P109(x95992)+E(x95991,f181(f932(x95992,a921)))+~P1(f862(f54(x95992),x95991))+P1(f862(f862(f321(x95992),f17(x95992,x95991)),x95991))+~P1(f862(f862(f321(x95992),f862(f862(f226(x95992),f468(x95991,x95992)),f469(x95991,x95992))),f862(f862(f301(x95992),f468(x95991,x95992)),f862(f862(f301(x95992),f469(x95991,x95992)),f181(f932(x95992,a921))))))
% 25.54/25.42 [9630]~P69(x96302)+E(x96301,f181(f932(x96302,a921)))+~P1(f862(f54(x96302),x96301))+P1(f862(f862(f321(x96302),f862(f56(x96302,f74(x96302)),x96301)),x96301))+~P1(f862(f862(f321(x96302),f862(f862(f74(x96302),f903(x96301,x96302)),f904(x96301,x96302))),f862(f862(f301(x96302),f903(x96301,x96302)),f862(f862(f301(x96302),f904(x96301,x96302)),f181(f932(x96302,a921))))))
% 25.54/25.42 [9635]~P109(x96352)+E(x96351,f181(f932(x96352,a921)))+~P1(f862(f54(x96352),x96351))+P1(f862(f862(f321(x96352),f13(x96352,f225(x96352),x96351)),x96351))+~P1(f862(f862(f321(x96352),f862(f862(f225(x96352),f456(x96351,x96352)),f457(x96351,x96352))),f862(f862(f301(x96352),f456(x96351,x96352)),f862(f862(f301(x96352),f457(x96351,x96352)),f181(f932(x96352,a921))))))
% 25.54/25.42 [9636]~P109(x96362)+E(x96361,f181(f932(x96362,a921)))+~P1(f862(f54(x96362),x96361))+P1(f862(f862(f321(x96362),f14(x96362,f226(x96362),x96361)),x96361))+~P1(f862(f862(f321(x96362),f862(f862(f226(x96362),f470(x96361,x96362)),f471(x96361,x96362))),f862(f862(f301(x96362),f470(x96361,x96362)),f862(f862(f301(x96362),f471(x96361,x96362)),f181(f932(x96362,a921))))))
% 25.54/25.42 [6731]~P87(x67312)+E(x67311,f2(x67312))+~E(f862(f862(f73(x67312),x67313),x67311),f2(x67312))+~P1(f862(f862(f227(x67312),f2(x67312)),x67313))+~P1(f862(f862(f227(x67312),f2(x67312)),x67311))
% 25.54/25.42 [6732]~P87(x67322)+E(x67321,f2(x67322))+~E(f862(f862(f73(x67322),x67321),x67323),f2(x67322))+~P1(f862(f862(f227(x67322),f2(x67322)),x67323))+~P1(f862(f862(f227(x67322),f2(x67322)),x67321))
% 25.54/25.42 [7261]~P109(x72612)+~P11(x72612,x72611)+E(x72611,f106(x72612))+~P1(f862(f862(f321(x72612),x72613),f862(f165(x72612),f714(x72611,x72612))))+P1(f862(f862(f227(x72612),f733(x72611,x72612)),x72613))
% 25.54/25.42 [7433]~P109(x74331)+E(f16(x74331,x74332),x74333)+~P1(f862(f54(x74331),x74332))+~P1(f862(f862(f227(x74331),x74333),f459(x74333,x74332,x74331)))+~P1(f862(f862(f321(x74331),x74333),x74332))
% 25.54/25.42 [7467]~P109(x74671)+~P11(x74671,x74672)+~P11(x74671,x74673)+P11(x74671,f862(f862(f127(x74671),x74672),x74673))+P1(f862(f862(f321(x74671),f720(x74673,x74672,x74671)),f862(f165(x74671),x74672)))
% 25.54/25.42 [7468]~P109(x74681)+~P11(x74681,x74682)+~P11(x74681,x74683)+P11(x74681,f862(f862(f127(x74681),x74682),x74683))+P1(f862(f862(f321(x74681),f721(x74683,x74682,x74681)),f862(f165(x74681),x74683)))
% 25.54/25.42 [7532]~P109(x75321)+E(f16(x75321,x75322),x75323)+~P1(f862(f54(x75321),x75322))+P1(f862(f862(f321(x75321),f459(x75323,x75322,x75321)),x75322))+~P1(f862(f862(f321(x75321),x75323),x75322))
% 25.54/25.42 [7533]~P109(x75331)+E(f17(x75331,x75332),x75333)+~P1(f862(f54(x75331),x75332))+P1(f862(f862(f321(x75331),f465(x75333,x75332,x75331)),x75332))+~P1(f862(f862(f321(x75331),x75333),x75332))
% 25.54/25.42 [8107]~P109(x81071)+E(f17(x81071,x81072),x81073)+~P1(f862(f54(x81071),x81072))+~P1(f862(f862(f321(x81071),x81073),x81072))+~P1(f862(f862(f227(x81071),f465(x81073,x81072,x81071)),x81073))
% 25.54/25.42 [8431]~P109(x84311)+~P11(x84311,x84312)+~P11(x84311,x84313)+P11(x84311,f862(f862(f127(x84311),x84312),x84313))+~P1(f862(f862(f227(x84311),f720(x84313,x84312,x84311)),f721(x84313,x84312,x84311)))
% 25.54/25.42 [9229]~P93(x92292)+E(x92291,f181(f932(x92292,a921)))+~E(f862(f862(f94(x92292),f862(x92293,f894(x92291,x92293,x92292))),f862(x92293,f895(x92291,x92293,x92292))),f862(x92293,f862(f862(f94(x92292),f894(x92291,x92293,x92292)),f895(x92291,x92293,x92292))))+E(f12(x92292,f862(f302(x92292,x92292,x92293),x92291)),f862(x92293,f12(x92292,x92291)))+~P1(f862(f54(x92292),x92291))
% 25.54/25.42 [9230]~P93(x92302)+E(x92301,f181(f932(x92302,a921)))+~E(f862(f862(f103(x92302),f862(x92303,f896(x92301,x92303,x92302))),f862(x92303,f897(x92301,x92303,x92302))),f862(x92303,f862(f862(f103(x92302),f896(x92301,x92303,x92302)),f897(x92301,x92303,x92302))))+E(f15(x92302,f862(f302(x92302,x92302,x92303),x92301)),f862(x92303,f15(x92302,x92301)))+~P1(f862(f54(x92302),x92301))
% 25.54/25.42 [9231]~P109(x92312)+E(x92311,f181(f932(x92312,a921)))+~E(f862(f862(f225(x92312),f862(x92313,f460(x92311,x92313,x92312))),f862(x92313,f462(x92311,x92313,x92312))),f862(x92313,f862(f862(f225(x92312),f460(x92311,x92313,x92312)),f462(x92311,x92313,x92312))))+E(f16(x92312,f862(f302(x92312,x92312,x92313),x92311)),f862(x92313,f16(x92312,x92311)))+~P1(f862(f54(x92312),x92311))
% 25.54/25.42 [9232]~P109(x92322)+E(x92321,f181(f932(x92322,a921)))+~E(f862(f862(f226(x92322),f862(x92323,f473(x92321,x92323,x92322))),f862(x92323,f476(x92321,x92323,x92322))),f862(x92323,f862(f862(f226(x92322),f473(x92321,x92323,x92322)),f476(x92321,x92323,x92322))))+E(f17(x92322,f862(f302(x92322,x92322,x92323),x92321)),f862(x92323,f17(x92322,x92321)))+~P1(f862(f54(x92322),x92321))
% 25.54/25.42 [9301]~P109(x93012)+E(x93011,f181(f932(x93012,a921)))+~E(f862(f862(f225(x93012),f862(x93013,f454(x93011,x93013,x93012))),f862(x93013,f461(x93011,x93013,x93012))),f862(x93013,f862(f862(f225(x93012),f454(x93011,x93013,x93012)),f461(x93011,x93013,x93012))))+E(f13(x93012,f225(x93012),f862(f302(x93012,x93012,x93013),x93011)),f862(x93013,f13(x93012,f225(x93012),x93011)))+~P1(f862(f54(x93012),x93011))
% 25.54/25.42 [9302]~P109(x93022)+E(x93021,f181(f932(x93022,a921)))+~E(f862(f862(f226(x93022),f862(x93023,f474(x93021,x93023,x93022))),f862(x93023,f475(x93021,x93023,x93022))),f862(x93023,f862(f862(f226(x93022),f474(x93021,x93023,x93022)),f475(x93021,x93023,x93022))))+E(f14(x93022,f226(x93022),f862(f302(x93022,x93022,x93023),x93021)),f862(x93023,f14(x93022,f226(x93022),x93021)))+~P1(f862(f54(x93022),x93021))
% 25.54/25.42 [6358]~P93(x63582)+E(x63581,f181(f932(x63582,a921)))+~P1(f862(f54(x63582),x63581))+E(f12(x63582,f862(f862(f301(x63582),x63583),x63581)),f862(f862(f94(x63582),x63583),f12(x63582,x63581)))+P1(f862(f862(f321(x63582),x63583),x63581))
% 25.54/25.42 [6359]~P93(x63592)+E(x63591,f181(f932(x63592,a921)))+~P1(f862(f54(x63592),x63591))+E(f15(x63592,f862(f862(f301(x63592),x63593),x63591)),f862(f862(f103(x63592),x63593),f15(x63592,x63591)))+P1(f862(f862(f321(x63592),x63593),x63591))
% 25.54/25.42 [6360]~P109(x63602)+E(x63601,f181(f932(x63602,a921)))+~P1(f862(f54(x63602),x63601))+E(f16(x63602,f862(f862(f301(x63602),x63603),x63601)),f862(f862(f225(x63602),x63603),f16(x63602,x63601)))+P1(f862(f862(f321(x63602),x63603),x63601))
% 25.54/25.42 [6361]~P109(x63612)+E(x63611,f181(f932(x63612,a921)))+~P1(f862(f54(x63612),x63611))+E(f17(x63612,f862(f862(f301(x63612),x63613),x63611)),f862(f862(f226(x63612),x63613),f17(x63612,x63611)))+P1(f862(f862(f321(x63612),x63613),x63611))
% 25.54/25.42 [6747]~P69(x67472)+E(x67471,f181(f932(x67472,a921)))+~P1(f862(f54(x67472),x67471))+E(f862(f56(x67472,f74(x67472)),f862(f862(f301(x67472),x67473),x67471)),f862(f862(f74(x67472),x67473),f862(f56(x67472,f74(x67472)),x67471)))+P1(f862(f862(f321(x67472),x67473),x67471))
% 25.54/25.42 [6829]~P109(x68292)+E(x68291,f181(f932(x68292,a921)))+~P1(f862(f54(x68292),x68291))+E(f13(x68292,f225(x68292),f862(f862(f301(x68292),x68293),x68291)),f862(f862(f225(x68292),x68293),f13(x68292,f225(x68292),x68291)))+P1(f862(f862(f321(x68292),x68293),x68291))
% 25.54/25.42 [6830]~P109(x68302)+E(x68301,f181(f932(x68302,a921)))+~P1(f862(f54(x68302),x68301))+E(f14(x68302,f226(x68302),f862(f862(f301(x68302),x68303),x68301)),f862(f862(f226(x68302),x68303),f14(x68302,f226(x68302),x68301)))+P1(f862(f862(f321(x68302),x68303),x68301))
% 25.54/25.42 [7268]~P93(x72682)+E(f862(f862(f103(x72682),f15(x72682,x72681)),f15(x72682,x72683)),f15(x72682,x72683))+E(x72681,f181(f932(x72682,a921)))+~P1(f862(f54(x72682),x72683))+~P1(f862(f862(f227(f932(x72682,a921)),x72681),x72683))
% 25.54/25.42 [7269]~P93(x72692)+E(f862(f862(f94(x72692),f12(x72692,x72691)),f12(x72692,x72693)),f12(x72692,x72693))+E(x72691,f181(f932(x72692,a921)))+~P1(f862(f54(x72692),x72693))+~P1(f862(f862(f227(f932(x72692,a921)),x72691),x72693))
% 25.54/25.42 [7270]~P109(x72702)+E(f862(f862(f225(x72702),f16(x72702,x72701)),f16(x72702,x72703)),f16(x72702,x72703))+E(x72701,f181(f932(x72702,a921)))+~P1(f862(f54(x72702),x72703))+~P1(f862(f862(f227(f932(x72702,a921)),x72701),x72703))
% 25.54/25.42 [7271]~P109(x72712)+E(f862(f862(f226(x72712),f17(x72712,x72711)),f17(x72712,x72713)),f17(x72712,x72713))+E(x72711,f181(f932(x72712,a921)))+~P1(f862(f54(x72712),x72713))+~P1(f862(f862(f227(f932(x72712,a921)),x72711),x72713))
% 25.54/25.42 [7580]~P109(x75802)+E(x75801,f181(f932(x75802,a921)))+~P1(f862(f54(x75802),x75803))+P1(f862(f862(f227(x75802),f16(x75802,x75803)),f16(x75802,x75801)))+~P1(f862(f862(f227(f932(x75802,a921)),x75801),x75803))
% 25.54/25.42 [7581]~P109(x75812)+E(x75811,f181(f932(x75812,a921)))+~P1(f862(f54(x75812),x75813))+P1(f862(f862(f227(x75812),f17(x75812,x75811)),f17(x75812,x75813)))+~P1(f862(f862(f227(f932(x75812,a921)),x75811),x75813))
% 25.54/25.42 [7636]~P93(x76361)+E(f12(x76361,x76362),x76363)+~P1(f862(f54(x76361),x76362))+~E(f862(f862(f3(f932(x76361,a921)),x76362),f862(f862(f301(x76361),x76363),f181(f932(x76361,a921)))),f181(f932(x76361,a921)))+~P1(f862(f862(f321(x76361),x76363),x76362))
% 25.54/25.42 [7637]~P93(x76371)+E(f15(x76371,x76372),x76373)+~P1(f862(f54(x76371),x76372))+~E(f862(f862(f3(f932(x76371,a921)),x76372),f862(f862(f301(x76371),x76373),f181(f932(x76371,a921)))),f181(f932(x76371,a921)))+~P1(f862(f862(f321(x76371),x76373),x76372))
% 25.54/25.42 [7638]~P109(x76381)+E(f16(x76381,x76382),x76383)+~P1(f862(f54(x76381),x76382))+~E(f862(f862(f3(f932(x76381,a921)),x76382),f862(f862(f301(x76381),x76383),f181(f932(x76381,a921)))),f181(f932(x76381,a921)))+~P1(f862(f862(f321(x76381),x76383),x76382))
% 25.54/25.42 [7639]~P109(x76391)+E(f17(x76391,x76392),x76393)+~P1(f862(f54(x76391),x76392))+~E(f862(f862(f3(f932(x76391,a921)),x76392),f862(f862(f301(x76391),x76393),f181(f932(x76391,a921)))),f181(f932(x76391,a921)))+~P1(f862(f862(f321(x76391),x76393),x76392))
% 25.54/25.42 [7734]~P109(x77341)+E(f13(x77341,f225(x77341),x77342),x77343)+~P1(f862(f54(x77341),x77342))+~E(f862(f862(f3(f932(x77341,a921)),x77342),f862(f862(f301(x77341),x77343),f181(f932(x77341,a921)))),f181(f932(x77341,a921)))+~P1(f862(f862(f321(x77341),x77343),x77342))
% 25.54/25.42 [7735]~P109(x77351)+E(f14(x77351,f226(x77351),x77352),x77353)+~P1(f862(f54(x77351),x77352))+~E(f862(f862(f3(f932(x77351,a921)),x77352),f862(f862(f301(x77351),x77353),f181(f932(x77351,a921)))),f181(f932(x77351,a921)))+~P1(f862(f862(f321(x77351),x77353),x77352))
% 25.54/25.42 [7771]~P104(x77712)+E(x77711,f181(f932(x77712,a921)))+~P1(f862(f54(x77712),x77711))+~P1(f862(f862(f227(x77712),x77713),f892(x77713,x77711,x77712)))+P1(f862(f862(f227(x77712),x77713),f862(f56(x77712,f94(x77712)),x77711)))
% 25.54/25.42 [7772]~P109(x77722)+E(x77721,f181(f932(x77722,a921)))+~P1(f862(f54(x77722),x77721))+~P1(f862(f862(f227(x77722),x77723),f450(x77723,x77721,x77722)))+P1(f862(f862(f227(x77722),x77723),f862(f56(x77722,f225(x77722)),x77721)))
% 25.54/25.42 [7773]~P109(x77732)+E(x77731,f181(f932(x77732,a921)))+~P1(f862(f54(x77732),x77731))+~P1(f862(f862(f228(x77732),x77733),f451(x77733,x77731,x77732)))+P1(f862(f862(f228(x77732),x77733),f862(f56(x77732,f225(x77732)),x77731)))
% 25.54/25.42 [7860]~P104(x78602)+E(x78601,f181(f932(x78602,a921)))+~P1(f862(f54(x78602),x78601))+P1(f862(f862(f321(x78602),f892(x78603,x78601,x78602)),x78601))+P1(f862(f862(f227(x78602),x78603),f862(f56(x78602,f94(x78602)),x78601)))
% 25.54/25.42 [7861]~P109(x78612)+E(x78611,f181(f932(x78612,a921)))+~P1(f862(f54(x78612),x78611))+P1(f862(f862(f321(x78612),f450(x78613,x78611,x78612)),x78611))+P1(f862(f862(f227(x78612),x78613),f862(f56(x78612,f225(x78612)),x78611)))
% 25.54/25.42 [7862]~P109(x78622)+E(x78621,f181(f932(x78622,a921)))+~P1(f862(f54(x78622),x78621))+P1(f862(f862(f321(x78622),f451(x78623,x78621,x78622)),x78621))+P1(f862(f862(f228(x78622),x78623),f862(f56(x78622,f225(x78622)),x78621)))
% 25.54/25.42 [7982]~P109(x79822)+E(x79821,f181(f932(x79822,a921)))+E(f862(f862(f225(x79822),f13(x79822,f225(x79822),x79821)),f13(x79822,f225(x79822),x79823)),f13(x79822,f225(x79822),x79823))+~P1(f862(f54(x79822),x79823))+~P1(f862(f862(f227(f932(x79822,a921)),x79821),x79823))
% 25.54/25.42 [7983]~P109(x79832)+E(x79831,f181(f932(x79832,a921)))+E(f862(f862(f226(x79832),f14(x79832,f226(x79832),x79831)),f14(x79832,f226(x79832),x79833)),f14(x79832,f226(x79832),x79833))+~P1(f862(f54(x79832),x79833))+~P1(f862(f862(f227(f932(x79832,a921)),x79831),x79833))
% 25.54/25.42 [8186]~E(f370(x81861,x81863,x81862),f371(x81861,x81863,x81862))+~E(f862(f28(x81862),f372(x81861,x81863,x81862)),x81861)+E(f862(f862(f74(a924),x81861),f862(f28(f932(x81862,a921)),x81863)),f862(f28(x81862),f30(f932(x81862,a921),x81863)))+~P1(f862(f54(x81862),f30(f932(x81862,a921),x81863)))+~P1(f862(f54(f932(x81862,a921)),x81863))
% 25.54/25.42 [8370]~P109(x83702)+E(x83701,f181(f932(x83702,a921)))+~P1(f862(f54(x83702),x83703))+P1(f862(f862(f227(x83702),f862(f56(x83702,f225(x83702)),x83703)),f862(f56(x83702,f225(x83702)),x83701)))+~P1(f862(f862(f227(f932(x83702,a921)),x83701),x83703))
% 25.54/25.42 [8672]~E(f370(x86721,x86723,x86722),f371(x86721,x86723,x86722))+E(f862(f862(f74(a924),x86721),f862(f28(f932(x86722,a921)),x86723)),f862(f28(x86722),f30(f932(x86722,a921),x86723)))+P1(f862(f862(f321(f932(x86722,a921)),f372(x86721,x86723,x86722)),x86723))+~P1(f862(f54(x86722),f30(f932(x86722,a921),x86723)))+~P1(f862(f54(f932(x86722,a921)),x86723))
% 25.54/25.42 [8698]~E(f862(f28(x86982),f372(x86981,x86983,x86982)),x86981)+E(f862(f862(f74(a924),x86981),f862(f28(f932(x86982,a921)),x86983)),f862(f28(x86982),f30(f932(x86982,a921),x86983)))+P1(f862(f862(f321(f932(x86982,a921)),f371(x86981,x86983,x86982)),x86983))+~P1(f862(f54(x86982),f30(f932(x86982,a921),x86983)))+~P1(f862(f54(f932(x86982,a921)),x86983))
% 25.54/25.42 [8699]~E(f862(f28(x86992),f372(x86991,x86993,x86992)),x86991)+E(f862(f862(f74(a924),x86991),f862(f28(f932(x86992,a921)),x86993)),f862(f28(x86992),f30(f932(x86992,a921),x86993)))+P1(f862(f862(f321(f932(x86992,a921)),f370(x86991,x86993,x86992)),x86993))+~P1(f862(f54(x86992),f30(f932(x86992,a921),x86993)))+~P1(f862(f54(f932(x86992,a921)),x86993))
% 25.54/25.42 [8725]~E(f862(f28(x87252),f372(x87251,x87253,x87252)),x87251)+~E(f862(f862(f94(f932(x87252,a921)),f371(x87251,x87253,x87252)),f370(x87251,x87253,x87252)),f181(f932(x87252,a921)))+E(f862(f862(f74(a924),x87251),f862(f28(f932(x87252,a921)),x87253)),f862(f28(x87252),f30(f932(x87252,a921),x87253)))+~P1(f862(f54(f932(x87252,a921)),x87253))+~P1(f862(f54(x87252),f30(f932(x87252,a921),x87253)))
% 25.54/25.42 [8991]E(f862(f862(f74(a924),x89911),f862(f28(f932(x89912,a921)),x89913)),f862(f28(x89912),f30(f932(x89912,a921),x89913)))+P1(f862(f862(f321(f932(x89912,a921)),f372(x89911,x89913,x89912)),x89913))+P1(f862(f862(f321(f932(x89912,a921)),f371(x89911,x89913,x89912)),x89913))+~P1(f862(f54(f932(x89912,a921)),x89913))+~P1(f862(f54(x89912),f30(f932(x89912,a921),x89913)))
% 25.54/25.42 [8992]E(f862(f862(f74(a924),x89921),f862(f28(f932(x89922,a921)),x89923)),f862(f28(x89922),f30(f932(x89922,a921),x89923)))+P1(f862(f862(f321(f932(x89922,a921)),f372(x89921,x89923,x89922)),x89923))+P1(f862(f862(f321(f932(x89922,a921)),f370(x89921,x89923,x89922)),x89923))+~P1(f862(f54(f932(x89922,a921)),x89923))+~P1(f862(f54(x89922),f30(f932(x89922,a921),x89923)))
% 25.54/25.42 [9018]~E(f862(f862(f94(f932(x90182,a921)),f371(x90181,x90183,x90182)),f370(x90181,x90183,x90182)),f181(f932(x90182,a921)))+E(f862(f862(f74(a924),x90181),f862(f28(f932(x90182,a921)),x90183)),f862(f28(x90182),f30(f932(x90182,a921),x90183)))+~P1(f862(f54(f932(x90182,a921)),x90183))+P1(f862(f862(f321(f932(x90182,a921)),f372(x90181,x90183,x90182)),x90183))+~P1(f862(f54(x90182),f30(f932(x90182,a921),x90183)))
% 25.54/25.42 [9275]~P100(x92752)+E(x92751,f181(f932(x92752,a921)))+~E(f862(f862(f74(x92752),f862(x92753,f902(x92751,x92753,x92752))),f862(x92753,f905(x92751,x92753,x92752))),f862(x92753,f862(f862(f74(x92752),f902(x92751,x92753,x92752)),f905(x92751,x92753,x92752))))+~P1(f862(f54(x92752),x92751))+E(f862(f56(x92752,f74(x92752)),f862(f302(x92752,x92752,x92753),x92751)),f862(x92753,f862(f56(x92752,f74(x92752)),x92751)))
% 25.54/25.42 [10207]P1(f862(f862(x102071,x102072),x102073))+P1(f862(f862(f228(a1),f501(x102071,x102073,x102072)),f503(x102071,x102073,x102072)))+P1(f862(f862(f227(a1),f503(x102071,x102073,x102072)),f2(a1)))+P1(f862(f862(x102071,f501(x102071,x102073,x102072)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f503(x102071,x102073,x102072))))+~P1(f862(f307(f931(a1,a1),a51),f862(f862(f244(a1,a1),x102072),x102073)))
% 25.54/25.42 [10213]P1(f862(f862(x102131,x102132),x102133))+P1(f862(f862(f227(a1),f500(x102131,x102133,x102132)),f2(a1)))+P1(f862(f862(x102131,f499(x102131,x102133,x102132)),f862(f862(f74(a1),f862(f96(a1),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f500(x102131,x102133,x102132))))+P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f499(x102131,x102133,x102132)),f500(x102131,x102133,x102132))))+~P1(f862(f307(f931(a1,a1),a45),f862(f862(f244(a1,a1),x102132),x102133)))
% 25.54/25.42 [8157]~P112(x81571)+~P1(f862(f862(f227(x81571),x81572),f71(x81571)))+~P1(f862(f862(f227(x81571),f2(x81571)),x81572))+~P1(f862(f862(f227(x81571),f2(x81571)),x81573))+P1(f862(f862(f227(x81571),f862(f862(f74(x81571),x81572),x81573)),x81573))
% 25.54/25.42 [8158]~P112(x81581)+~P1(f862(f862(f227(x81581),x81583),f71(x81581)))+~P1(f862(f862(f227(x81581),f2(x81581)),x81583))+~P1(f862(f862(f227(x81581),f2(x81581)),x81582))+P1(f862(f862(f227(x81581),f862(f862(f74(x81581),x81582),x81583)),x81582))
% 25.54/25.42 [8516]~P109(x85162)+E(x85161,f181(f932(x85162,a921)))+~P1(f862(f54(x85162),x85161))+P1(f862(f862(f321(x85162),f452(x85163,x85161,x85162)),x85161))+~P1(f862(f862(f227(x85162),f862(f56(x85162,f225(x85162)),x85161)),x85163))
% 25.54/25.42 [8517]~P109(x85172)+E(x85171,f181(f932(x85172,a921)))+~P1(f862(f54(x85172),x85171))+P1(f862(f862(f321(x85172),f453(x85173,x85171,x85172)),x85171))+~P1(f862(f862(f228(x85172),f862(f56(x85172,f225(x85172)),x85171)),x85173))
% 25.54/25.42 [8518]~P109(x85182)+E(x85181,f181(f932(x85182,a921)))+~P1(f862(f54(x85182),x85181))+P1(f862(f862(f227(x85182),f452(x85183,x85181,x85182)),x85183))+~P1(f862(f862(f227(x85182),f862(f56(x85182,f225(x85182)),x85181)),x85183))
% 25.54/25.42 [8519]~P109(x85192)+E(x85191,f181(f932(x85192,a921)))+~P1(f862(f54(x85192),x85191))+P1(f862(f862(f228(x85192),f453(x85193,x85191,x85192)),x85193))+~P1(f862(f862(f228(x85192),f862(f56(x85192,f225(x85192)),x85191)),x85193))
% 25.54/25.42 [8606]~P1(f862(x86061,x86063))+P1(f862(x86061,f388(x86061,x86062)))+P1(f862(x86061,f387(x86061,x86062)))+~P1(f862(f862(f228(a1),f2(a1)),x86062))+P1(f862(x86061,f862(f862(f3(a1),f387(x86061,x86062)),f862(f862(f74(a1),f389(x86061,x86062)),x86062))))
% 25.54/25.42 [8827]~P1(f862(x88271,x88273))+P1(f862(x88271,f387(x88271,x88272)))+~P1(f862(f862(f228(a1),f2(a1)),x88272))+P1(f862(f862(f321(a1),f388(x88271,x88272)),f296(a1,f71(a1),x88272)))+P1(f862(x88271,f862(f862(f3(a1),f387(x88271,x88272)),f862(f862(f74(a1),f389(x88271,x88272)),x88272))))
% 25.54/25.42 [9042]~P1(f862(x90421,x90423))+~P1(f862(x90421,f387(x90421,x90422)))+P1(f862(x90421,f388(x90421,x90422)))+~P1(f862(f862(f228(a1),f2(a1)),x90422))+~P1(f862(x90421,f862(f862(f3(a1),f387(x90421,x90422)),f862(f862(f74(a1),f389(x90421,x90422)),x90422))))
% 25.54/25.42 [9166]~P1(f862(x91661,x91663))+~P1(f862(x91661,f387(x91661,x91662)))+~P1(f862(f862(f228(a1),f2(a1)),x91662))+P1(f862(f862(f321(a1),f388(x91661,x91662)),f296(a1,f71(a1),x91662)))+~P1(f862(x91661,f862(f862(f3(a1),f387(x91661,x91662)),f862(f862(f74(a1),f389(x91661,x91662)),x91662))))
% 25.54/25.42 [8946]~P93(x89461)+~P1(f862(f54(x89461),x89462))+E(f862(f862(f3(f932(x89461,a921)),x89462),f862(f862(f301(x89461),x89463),f181(f932(x89461,a921)))),f181(f932(x89461,a921)))+~P1(f862(f862(f321(x89461),x89463),x89462))+E(f862(f862(f94(x89461),x89463),f12(x89461,f862(f862(f3(f932(x89461,a921)),x89462),f862(f862(f301(x89461),x89463),f181(f932(x89461,a921)))))),f12(x89461,x89462))
% 25.54/25.42 [8947]~P93(x89471)+~P1(f862(f54(x89471),x89472))+E(f862(f862(f3(f932(x89471,a921)),x89472),f862(f862(f301(x89471),x89473),f181(f932(x89471,a921)))),f181(f932(x89471,a921)))+~P1(f862(f862(f321(x89471),x89473),x89472))+E(f862(f862(f103(x89471),x89473),f15(x89471,f862(f862(f3(f932(x89471,a921)),x89472),f862(f862(f301(x89471),x89473),f181(f932(x89471,a921)))))),f15(x89471,x89472))
% 25.54/25.42 [8948]~P109(x89481)+~P1(f862(f54(x89481),x89482))+E(f862(f862(f3(f932(x89481,a921)),x89482),f862(f862(f301(x89481),x89483),f181(f932(x89481,a921)))),f181(f932(x89481,a921)))+~P1(f862(f862(f321(x89481),x89483),x89482))+E(f862(f862(f225(x89481),x89483),f16(x89481,f862(f862(f3(f932(x89481,a921)),x89482),f862(f862(f301(x89481),x89483),f181(f932(x89481,a921)))))),f16(x89481,x89482))
% 25.54/25.42 [8949]~P109(x89491)+~P1(f862(f54(x89491),x89492))+E(f862(f862(f3(f932(x89491,a921)),x89492),f862(f862(f301(x89491),x89493),f181(f932(x89491,a921)))),f181(f932(x89491,a921)))+~P1(f862(f862(f321(x89491),x89493),x89492))+E(f862(f862(f226(x89491),x89493),f17(x89491,f862(f862(f3(f932(x89491,a921)),x89492),f862(f862(f301(x89491),x89493),f181(f932(x89491,a921)))))),f17(x89491,x89492))
% 25.54/25.42 [9011]~P109(x90111)+~P1(f862(f54(x90111),x90112))+E(f862(f862(f3(f932(x90111,a921)),x90112),f862(f862(f301(x90111),x90113),f181(f932(x90111,a921)))),f181(f932(x90111,a921)))+~P1(f862(f862(f321(x90111),x90113),x90112))+E(f862(f862(f225(x90111),x90113),f13(x90111,f225(x90111),f862(f862(f3(f932(x90111,a921)),x90112),f862(f862(f301(x90111),x90113),f181(f932(x90111,a921)))))),f13(x90111,f225(x90111),x90112))
% 25.54/25.42 [9012]~P109(x90121)+~P1(f862(f54(x90121),x90122))+E(f862(f862(f3(f932(x90121,a921)),x90122),f862(f862(f301(x90121),x90123),f181(f932(x90121,a921)))),f181(f932(x90121,a921)))+~P1(f862(f862(f321(x90121),x90123),x90122))+E(f862(f862(f226(x90121),x90123),f14(x90121,f226(x90121),f862(f862(f3(f932(x90121,a921)),x90122),f862(f862(f301(x90121),x90123),f181(f932(x90121,a921)))))),f14(x90121,f226(x90121),x90122))
% 25.54/25.42 [9028]~P93(x90281)+~P1(f862(f54(x90281),x90283))+~P1(f862(f54(x90281),x90282))+E(f862(f862(f94(f932(x90281,a921)),x90282),x90283),f181(f932(x90281,a921)))+E(f862(f862(f103(x90281),f15(x90281,f862(f862(f103(f932(x90281,a921)),x90282),x90283))),f15(x90281,f862(f862(f94(f932(x90281,a921)),x90282),x90283))),f862(f862(f103(x90281),f15(x90281,x90282)),f15(x90281,x90283)))
% 25.54/25.42 [9029]~P93(x90291)+~P1(f862(f54(x90291),x90293))+~P1(f862(f54(x90291),x90292))+E(f862(f862(f94(f932(x90291,a921)),x90292),x90293),f181(f932(x90291,a921)))+E(f862(f862(f94(x90291),f12(x90291,f862(f862(f103(f932(x90291,a921)),x90292),x90293))),f12(x90291,f862(f862(f94(f932(x90291,a921)),x90292),x90293))),f862(f862(f94(x90291),f12(x90291,x90292)),f12(x90291,x90293)))
% 25.54/25.42 [9030]~P109(x90301)+~P1(f862(f54(x90301),x90303))+~P1(f862(f54(x90301),x90302))+E(f862(f862(f94(f932(x90301,a921)),x90302),x90303),f181(f932(x90301,a921)))+E(f862(f862(f225(x90301),f16(x90301,f862(f862(f103(f932(x90301,a921)),x90302),x90303))),f16(x90301,f862(f862(f94(f932(x90301,a921)),x90302),x90303))),f862(f862(f225(x90301),f16(x90301,x90302)),f16(x90301,x90303)))
% 25.54/25.42 [9031]~P109(x90311)+~P1(f862(f54(x90311),x90313))+~P1(f862(f54(x90311),x90312))+E(f862(f862(f94(f932(x90311,a921)),x90312),x90313),f181(f932(x90311,a921)))+E(f862(f862(f226(x90311),f17(x90311,f862(f862(f103(f932(x90311,a921)),x90312),x90313))),f17(x90311,f862(f862(f94(f932(x90311,a921)),x90312),x90313))),f862(f862(f226(x90311),f17(x90311,x90312)),f17(x90311,x90313)))
% 25.54/25.42 [9247]~P109(x92471)+~P1(f862(f54(x92471),x92473))+~P1(f862(f54(x92471),x92472))+E(f862(f862(f94(f932(x92471,a921)),x92472),x92473),f181(f932(x92471,a921)))+E(f862(f862(f225(x92471),f13(x92471,f225(x92471),f862(f862(f103(f932(x92471,a921)),x92472),x92473))),f13(x92471,f225(x92471),f862(f862(f94(f932(x92471,a921)),x92472),x92473))),f862(f862(f225(x92471),f13(x92471,f225(x92471),x92472)),f13(x92471,f225(x92471),x92473)))
% 25.54/25.42 [9248]~P109(x92481)+~P1(f862(f54(x92481),x92483))+~P1(f862(f54(x92481),x92482))+E(f862(f862(f94(f932(x92481,a921)),x92482),x92483),f181(f932(x92481,a921)))+E(f862(f862(f226(x92481),f14(x92481,f226(x92481),f862(f862(f103(f932(x92481,a921)),x92482),x92483))),f14(x92481,f226(x92481),f862(f862(f94(f932(x92481,a921)),x92482),x92483))),f862(f862(f226(x92481),f14(x92481,f226(x92481),x92482)),f14(x92481,f226(x92481),x92483)))
% 25.54/25.42 [10053]~P127(x100533)+E(x100531,x100532)+~P1(f862(f862(f227(x100533),f2(x100533)),x100532))+~P1(f862(f862(f227(x100533),f2(x100533)),x100531))+~E(f862(f862(f236(x100533),x100531),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))),f862(f862(f236(x100533),x100532),f862(f96(a924),f862(f862(f73(a1),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)),f862(f862(f3(a1),f862(f862(f73(a1),a76),a76)),a90)))))
% 25.54/25.42 [5269]~P64(x52691)+~P99(x52691)+~E(x52694,f2(x52691))+~E(f862(f96(x52691),x52692),f2(x52691))+E(f862(f96(x52691),x52692),f862(f862(f281(x52691),x52693),x52694))
% 25.54/25.42 [5270]~P64(x52701)+~P99(x52701)+~E(x52703,f2(x52701))+~E(f862(f96(x52701),x52704),f2(x52701))+E(f862(f862(f281(x52701),x52702),x52703),f862(f96(x52701),x52704))
% 25.54/25.42 [5359]~P64(x53592)+~P99(x53592)+~E(x53591,f2(x53592))+~E(f862(f96(x53592),x53594),f2(x53592))+E(x53591,f862(f862(f281(x53592),x53593),f862(f96(x53592),x53594)))
% 25.54/25.42 [5360]~P64(x53601)+~P99(x53601)+~E(x53604,f2(x53601))+~E(f862(f96(x53601),x53603),f2(x53601))+E(f862(f862(f281(x53601),x53602),f862(f96(x53601),x53603)),x53604)
% 25.54/25.42 [5393]~P64(x53931)+~P99(x53931)+~E(x53933,f2(x53931))+E(f862(f96(x53931),x53932),f2(x53931))+~E(f862(f96(x53931),x53932),f862(f862(f281(x53931),x53934),x53933))
% 25.54/25.42 [5394]~P64(x53941)+~P99(x53941)+~E(x53943,f2(x53941))+E(f862(f96(x53941),x53942),f2(x53941))+~E(f862(f862(f281(x53941),x53944),x53943),f862(f96(x53941),x53942))
% 25.54/25.42 [5560]~P64(x55602)+~P99(x55602)+E(x55601,f2(x55602))+~E(f862(f96(x55602),x55603),f2(x55602))+~E(x55601,f862(f862(f281(x55602),x55604),f862(f96(x55602),x55603)))
% 25.54/25.42 [5561]~P64(x55612)+~P99(x55612)+E(x55611,f2(x55612))+~E(f862(f96(x55612),x55613),f2(x55612))+~E(f862(f862(f281(x55612),x55614),f862(f96(x55612),x55613)),x55611)
% 25.54/25.42 [5794]~P64(x57942)+~P99(x57942)+~E(x57941,f2(x57942))+E(x57941,f862(f862(f281(x57942),x57943),f862(f96(x57942),x57944)))+~E(f862(f862(f74(x57942),x57941),f862(f96(x57942),x57944)),x57943)
% 25.54/25.42 [5795]~P64(x57951)+~P99(x57951)+~E(x57954,f2(x57951))+~E(x57952,f862(f862(f74(x57951),x57954),f862(f96(x57951),x57953)))+E(f862(f862(f281(x57951),x57952),f862(f96(x57951),x57953)),x57954)
% 25.54/25.42 [5860]~P64(x58601)+~P99(x58601)+E(f862(f96(x58601),x58602),f2(x58601))+~E(f862(f862(f281(x58601),x58603),f862(f96(x58601),x58602)),x58604)+E(x58603,f862(f862(f74(x58601),x58604),f862(f96(x58601),x58602)))
% 25.54/25.42 [5861]~P64(x58611)+~P99(x58611)+E(f862(f96(x58611),x58612),f2(x58611))+~E(f862(f862(f74(x58611),x58613),f862(f96(x58611),x58612)),x58614)+E(x58613,f862(f862(f281(x58611),x58614),f862(f96(x58611),x58612)))
% 25.54/25.42 [5862]~P64(x58621)+~P99(x58621)+E(f862(f96(x58621),x58622),f2(x58621))+~E(x58623,f862(f862(f281(x58621),x58624),f862(f96(x58621),x58622)))+E(f862(f862(f74(x58621),x58623),f862(f96(x58621),x58622)),x58624)
% 25.54/25.42 [5863]~P64(x58631)+~P99(x58631)+E(f862(f96(x58631),x58632),f2(x58631))+~E(x58633,f862(f862(f74(x58631),x58634),f862(f96(x58631),x58632)))+E(f862(f862(f281(x58631),x58633),f862(f96(x58631),x58632)),x58634)
% 25.54/25.42 [6078]~P61(x60782)+E(x60781,f2(x60782))+~E(f862(f862(f29(x60782),x60783),x60781),x60784)+E(x60783,f862(f862(f74(x60782),x60784),x60781))+~P1(f862(f862(f278(x60782),x60781),x60783))
% 25.54/25.42 [6079]~P61(x60792)+E(x60791,f2(x60792))+~E(x60793,f862(f862(f74(x60792),x60794),x60791))+E(f862(f862(f29(x60792),x60793),x60791),x60794)+~P1(f862(f862(f278(x60792),x60791),x60793))
% 25.54/25.42 [6542]E(f335(x65421,x65422,x65423),x65424)+E(f862(x65421,x65424),f2(a924))+~E(f862(f862(f8(x65423,a924),x65421),x65422),f71(a924))+~P1(f862(f54(x65423),x65422))+~P1(f862(f862(f321(x65423),x65424),x65422))
% 25.54/25.42 [6607]E(f333(x66071,x66072,x66073),x66074)+E(f862(x66071,x66074),f2(a924))+~E(f862(f862(f8(x66073,a924),x66071),x66072),f862(a105,f2(a924)))+~P1(f862(f54(x66073),x66072))+~P1(f862(f862(f321(x66073),x66074),x66072))
% 25.54/25.42 [6716]~P3(x67161)+~P109(x67161)+P1(f862(f862(f228(x67161),x67162),f30(x67161,x67163)))+~P1(f862(f862(f228(x67161),x67162),x67164))+~P1(f862(f862(f321(x67161),x67164),x67163))
% 25.54/25.42 [6887]~P3(x68871)+~P109(x68871)+~P1(f862(f862(f228(x68871),x68874),x68873))+P1(f862(f862(f228(x68871),f31(x68871,x68872)),x68873))+~P1(f862(f862(f321(x68871),x68874),x68872))
% 25.54/25.42 [7146]~P127(x71463)+E(x71461,x71462)+~E(f862(f862(f236(x71463),x71461),f862(a105,x71464)),f862(f862(f236(x71463),x71462),f862(a105,x71464)))+~P1(f862(f862(f227(x71463),f2(x71463)),x71462))+~P1(f862(f862(f227(x71463),f2(x71463)),x71461))
% 25.54/25.42 [7359]~E(f342(x73592,x73593,x73591,x73594),x73594)+~E(f862(x73592,x73594),f71(a924))+E(f862(f862(f8(x73591,a924),x73592),x73593),f71(a924))+~P1(f862(f54(x73591),x73593))+~P1(f862(f862(f321(x73591),x73594),x73593))
% 25.54/25.42 [7366]~P119(x73664)+~P133(x73664)+E(f862(x73661,f337(x73661,x73662,x73663,x73664)),f2(x73664))+~E(f862(f862(f11(x73663,x73664),x73661),x73662),f2(x73664))+~P1(f862(f54(x73663),x73662))
% 25.54/25.42 [7457]~E(f334(x74572,x74573,x74571,x74574),x74574)+~E(f862(x74572,x74574),f862(a105,f2(a924)))+E(f862(f862(f8(x74571,a924),x74572),x74573),f862(a105,f2(a924)))+~P1(f862(f54(x74571),x74573))+~P1(f862(f862(f321(x74571),x74574),x74573))
% 25.54/25.42 [8199]~E(f862(x81992,x81994),f71(a924))+~E(f862(x81992,f342(x81992,x81993,x81991,x81994)),f2(a924))+E(f862(f862(f8(x81991,a924),x81992),x81993),f71(a924))+~P1(f862(f54(x81991),x81993))+~P1(f862(f862(f321(x81991),x81994),x81993))
% 25.54/25.42 [8237]~E(f862(x82372,x82374),f862(a105,f2(a924)))+~E(f862(x82372,f334(x82372,x82373,x82371,x82374)),f2(a924))+E(f862(f862(f8(x82371,a924),x82372),x82373),f862(a105,f2(a924)))+~P1(f862(f54(x82371),x82373))+~P1(f862(f862(f321(x82371),x82374),x82373))
% 25.54/25.42 [8325]~P146(x83252)+~P120(x83252)+~P1(f862(x83251,x83254))+~P1(f862(f862(f278(x83252),x83253),f862(f862(f73(x83252),x83254),f2(x83252))))+P1(f862(x83251,f862(f862(f74(x83252),x83253),f860(x83253,x83251,x83252))))
% 25.54/25.42 [8794]~P109(x87941)+~P11(x87941,x87944)+P11(x87941,x87942)+~E(x87942,f862(f862(f144(x87941),x87943),x87944))+~P1(f862(f862(f227(x87941),x87943),f735(x87942,x87941,x87944,x87943)))
% 25.54/25.42 [8831]E(x88311,x88312)+E(f862(f862(f3(a1),f390(x88313,x88312,x88314,x88311)),f391(x88313,x88312,x88314,x88311)),x88311)+~E(f862(f862(f73(a1),x88311),x88314),x88312)+~P1(f862(f862(f228(a1),f2(a1)),x88314))+~P1(f862(f862(f321(a1),x88312),x88313))
% 25.54/25.42 [8832]E(x88321,x88322)+E(f862(f862(f73(a1),f396(x88323,x88322,x88324,x88321)),f397(x88323,x88322,x88324,x88321)),x88321)+~E(f862(f862(f3(a1),x88321),x88324),x88322)+~P1(f862(f862(f228(a1),f2(a1)),x88324))+~P1(f862(f862(f321(a1),x88322),x88323))
% 25.54/25.42 [9026]E(f862(x90261,f443(x90262,x90261,x90263,x90264)),x90262)+P1(f862(f862(f227(a924),x90264),f444(x90262,x90261,x90263,x90264)))+~P1(f862(f862(f227(a1),x90262),f862(x90261,x90263)))+~P1(f862(f862(f228(a924),x90264),x90263))+~P1(f862(f862(f227(a1),f862(x90261,x90264)),x90262))
% 25.54/25.42 [9027]~P109(x90271)+~P11(x90271,x90273)+P11(x90271,x90272)+~E(x90272,f862(f862(f144(x90271),x90274),x90273))+P1(f862(f862(f321(x90271),f735(x90272,x90271,x90273,x90274)),f862(f165(x90271),x90273)))
% 25.54/25.42 [9046]~P119(x90464)+~P133(x90464)+~E(f862(f862(f11(x90461,x90464),x90462),x90463),f2(x90464))+~P1(f862(f54(x90461),x90463))+P1(f862(f862(f321(x90461),f337(x90462,x90463,x90461,x90464)),x90463))
% 25.54/25.42 [9084]~E(f862(x90842,x90844),f71(a924))+E(f862(f862(f8(x90841,a924),x90842),x90843),f71(a924))+~P1(f862(f54(x90841),x90843))+~P1(f862(f862(f321(x90841),x90844),x90843))+P1(f862(f862(f321(x90841),f342(x90842,x90843,x90841,x90844)),x90843))
% 25.54/25.42 [9096]E(x90961,x90962)+~E(f862(f862(f73(a1),x90962),x90964),x90961)+~P1(f862(f862(f228(a1),f2(a1)),x90964))+~P1(f862(f862(f321(a1),x90961),x90963))+P1(f862(f862(f321(a1),f390(x90963,x90961,x90964,x90962)),x90963))
% 25.54/25.42 [9097]E(x90971,x90972)+~E(f862(f862(f3(a1),x90972),x90974),x90971)+~P1(f862(f862(f228(a1),f2(a1)),x90974))+~P1(f862(f862(f321(a1),x90971),x90973))+P1(f862(f862(f321(a1),f396(x90973,x90971,x90974,x90972)),x90973))
% 25.54/25.42 [9099]~E(f862(x90992,x90994),f862(a105,f2(a924)))+E(f862(f862(f8(x90991,a924),x90992),x90993),f862(a105,f2(a924)))+~P1(f862(f54(x90991),x90993))+~P1(f862(f862(f321(x90991),x90994),x90993))+P1(f862(f862(f321(x90991),f334(x90992,x90993,x90991,x90994)),x90993))
% 25.54/25.42 [9104]P56(x91042,x91043,x91044,x91041)+E(x91041,f181(f932(x91042,a921)))+~P1(f862(f54(x91042),x91044))+~P1(f862(f54(x91042),x91041))+P1(f862(f862(f321(x91042),f803(x91043,x91041,x91044,x91042)),x91044))
% 25.54/25.42 [9105]P56(x91052,x91053,x91054,x91051)+E(x91051,f181(f932(x91052,a921)))+~P1(f862(f54(x91052),x91054))+~P1(f862(f54(x91052),x91051))+P1(f862(f862(f321(x91052),f550(x91051,x91054,x91053,x91052)),x91054))
% 25.54/25.42 [9106]P56(x91062,x91063,x91064,x91061)+E(x91061,f181(f932(x91062,a921)))+~P1(f862(f54(x91062),x91064))+~P1(f862(f54(x91062),x91061))+P1(f862(f862(f321(x91062),f804(x91061,x91064,x91063,x91062)),x91064))
% 25.54/25.42 [9179]E(x91791,x91792)+~E(f862(f862(f73(a1),x91792),x91794),x91791)+~P1(f862(f862(f228(a1),f2(a1)),x91794))+~P1(f862(f862(f321(a1),x91791),x91793))+P1(f862(f862(f321(a1),f391(x91793,x91791,x91794,x91792)),f296(a1,f71(a1),x91794)))
% 25.54/25.42 [9180]E(x91801,x91802)+~E(f862(f862(f3(a1),x91802),x91804),x91801)+~P1(f862(f862(f228(a1),f2(a1)),x91804))+~P1(f862(f862(f321(a1),x91801),x91803))+P1(f862(f862(f321(a1),f397(x91803,x91801,x91804,x91802)),f296(a1,f71(a1),x91804)))
% 25.54/25.42 [9253]P1(f862(f862(f227(a924),x92531),f443(x92532,x92533,x92534,x92531)))+~P1(f862(f862(f227(a1),x92532),f862(x92533,x92534)))+P1(f862(f862(f227(a924),x92531),f444(x92532,x92533,x92534,x92531)))+~P1(f862(f862(f228(a924),x92531),x92534))+~P1(f862(f862(f227(a1),f862(x92533,x92531)),x92532))
% 25.54/25.42 [9369]E(f862(x93691,f443(x93692,x93691,x93693,x93694)),x93692)+~P1(f862(f862(f227(a1),x93692),f862(x93691,x93693)))+P1(f862(f862(f228(a924),f444(x93692,x93691,x93693,x93694)),x93693))+~P1(f862(f862(f228(a924),x93694),x93693))+~P1(f862(f862(f227(a1),f862(x93691,x93694)),x93692))
% 25.54/25.42 [9499]~P1(f862(f862(f227(a1),x94992),f862(x94993,x94994)))+P1(f862(f862(f227(a924),x94991),f444(x94992,x94993,x94994,x94991)))+P1(f862(f862(f227(a924),f443(x94992,x94993,x94994,x94991)),x94994))+~P1(f862(f862(f228(a924),x94991),x94994))+~P1(f862(f862(f227(a1),f862(x94993,x94991)),x94992))
% 25.54/25.42 [9500]~P1(f862(f862(f227(a1),x95002),f862(x95003,x95004)))+P1(f862(f862(f227(a924),x95001),f443(x95002,x95003,x95004,x95001)))+P1(f862(f862(f228(a924),f444(x95002,x95003,x95004,x95001)),x95004))+~P1(f862(f862(f228(a924),x95001),x95004))+~P1(f862(f862(f227(a1),f862(x95003,x95001)),x95002))
% 25.54/25.42 [9611]~P1(f862(f862(f227(a1),x96111),f862(x96112,x96113)))+P1(f862(f862(f228(a924),f444(x96111,x96112,x96113,x96114)),x96113))+~P1(f862(f862(f228(a924),x96114),x96113))+~P1(f862(f862(f227(a1),f862(x96112,x96114)),x96111))+P1(f862(f862(f227(a924),f443(x96111,x96112,x96113,x96114)),x96113))
% 25.54/25.42 [9699]E(x96991,f181(f932(x96992,a921)))+~P1(f862(f54(x96992),x96994))+~P1(f862(f54(x96992),x96991))+P1(f862(f862(f321(f931(f932(x96992,a921),f932(x96992,a921))),f862(f862(f244(f932(x96992,a921),f932(x96992,a921)),x96994),x96991)),f310(x96992,x96993)))+P1(f862(f862(f321(x96992),f559(x96993,x96991,x96994,x96992)),x96994))
% 25.54/25.42 [9700]E(x97001,f181(f932(x97002,a921)))+~P1(f862(f54(x97002),x97004))+~P1(f862(f54(x97002),x97001))+P1(f862(f862(f321(f931(f932(x97002,a921),f932(x97002,a921))),f862(f862(f244(f932(x97002,a921),f932(x97002,a921)),x97004),x97001)),f310(x97002,x97003)))+P1(f862(f862(f321(x97002),f617(x97003,x97001,x97004,x97002)),x97004))
% 25.54/25.42 [10366]E(f862(x103661,f443(x103662,x103661,x103663,x103664)),x103662)+~P1(f862(f862(f227(a1),x103662),f862(x103661,x103663)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103661,f862(f862(f73(a924),f444(x103662,x103661,x103663,x103664)),f71(a924)))),f862(x103661,f444(x103662,x103661,x103663,x103664))))),f71(a1)))+~P1(f862(f862(f228(a924),x103664),x103663))+~P1(f862(f862(f227(a1),f862(x103661,x103664)),x103662))
% 25.54/25.42 [10367]~P1(f862(f862(f227(a1),x103672),f862(x103673,x103674)))+P1(f862(f862(f227(a924),x103671),f443(x103672,x103673,x103674,x103671)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103673,f862(f862(f73(a924),f444(x103672,x103673,x103674,x103671)),f71(a924)))),f862(x103673,f444(x103672,x103673,x103674,x103671))))),f71(a1)))+~P1(f862(f862(f228(a924),x103671),x103674))+~P1(f862(f862(f227(a1),f862(x103673,x103671)),x103672))
% 25.54/25.42 [10368]~P1(f862(f862(f227(a1),x103681),f862(x103682,x103683)))+~P1(f862(f862(f227(a1),f862(f69(a1),f862(f862(f3(a1),f862(x103682,f862(f862(f73(a924),f444(x103681,x103682,x103683,x103684)),f71(a924)))),f862(x103682,f444(x103681,x103682,x103683,x103684))))),f71(a1)))+~P1(f862(f862(f228(a924),x103684),x103683))+~P1(f862(f862(f227(a1),f862(x103682,x103684)),x103681))+P1(f862(f862(f227(a924),f443(x103681,x103682,x103683,x103684)),x103683))
% 25.54/25.42 [5818]~P64(x58182)+~P99(x58182)+E(x58181,f2(x58182))+~E(f862(f862(f281(x58182),x58183),x58181),f862(f96(x58182),x58184))+E(x58183,f862(f862(f74(x58182),f862(f96(x58182),x58184)),x58181))
% 25.54/25.42 [5819]~P64(x58192)+~P99(x58192)+E(x58191,f2(x58192))+~E(f862(f96(x58192),x58193),f862(f862(f281(x58192),x58194),x58191))+E(f862(f862(f74(x58192),f862(f96(x58192),x58193)),x58191),x58194)
% 25.54/25.42 [5974]~P64(x59742)+~P99(x59742)+E(x59741,f2(x59742))+E(f862(f96(x59742),x59743),f862(f862(f281(x59742),x59744),x59741))+~E(f862(f862(f74(x59742),f862(f96(x59742),x59743)),x59741),x59744)
% 25.54/25.42 [5975]~P64(x59752)+~P99(x59752)+E(x59751,f2(x59752))+E(f862(f862(f281(x59752),x59753),x59751),f862(f96(x59752),x59754))+~E(x59753,f862(f862(f74(x59752),f862(f96(x59752),x59754)),x59751))
% 25.54/25.42 [6114]~P64(x61141)+~P99(x61141)+~E(f862(f96(x61141),x61142),f2(x61141))+E(f862(f96(x61141),x61142),f862(f862(f281(x61141),x61143),x61144))+~E(f862(f862(f74(x61141),f862(f96(x61141),x61142)),x61144),x61143)
% 25.54/25.42 [6115]~P64(x61151)+~P99(x61151)+~E(f862(f96(x61151),x61154),f2(x61151))+E(f862(f862(f281(x61151),x61152),x61153),f862(f96(x61151),x61154))+~E(x61152,f862(f862(f74(x61151),f862(f96(x61151),x61154)),x61153))
% 25.54/25.42 [7419]~P66(x74191)+P1(f862(f862(f228(x74191),x74192),f2(x74191)))+~P1(f862(f862(f227(x74191),x74193),f2(x74191)))+P1(f862(f862(f228(x74191),f2(x74191)),x74192))+P1(f862(f862(f227(x74191),x74193),f862(f862(f281(x74191),x74194),x74192)))
% 25.54/25.42 [7420]~P66(x74201)+P1(f862(f862(f228(x74201),x74202),f2(x74201)))+~P1(f862(f862(f228(x74201),x74203),f2(x74201)))+P1(f862(f862(f228(x74201),f2(x74201)),x74202))+P1(f862(f862(f228(x74201),x74203),f862(f862(f281(x74201),x74204),x74202)))
% 25.54/25.42 [7672]~P66(x76721)+P1(f862(f862(f227(x76721),x76722),f2(x76721)))+P1(f862(f862(f228(x76721),x76723),f2(x76721)))+P1(f862(f862(f228(x76721),f2(x76721)),x76723))+~P1(f862(f862(f227(x76721),x76722),f862(f862(f281(x76721),x76724),x76723)))
% 25.54/25.42 [7673]~P66(x76731)+P1(f862(f862(f228(x76731),x76732),f2(x76731)))+P1(f862(f862(f228(x76731),x76733),f2(x76731)))+P1(f862(f862(f228(x76731),f2(x76731)),x76733))+~P1(f862(f862(f228(x76731),x76732),f862(f862(f281(x76731),x76734),x76733)))
% 25.54/25.42 [7791]E(x77911,x77912)+~E(f862(f862(f157(x77913),x77914),x77911),f862(f862(f157(x77913),x77914),x77912))+~P1(f862(f130(x77913),x77914))+~P1(f862(f862(f228(a924),x77912),f862(f182(f925(x77913)),x77914)))+~P1(f862(f862(f228(a924),x77911),f862(f182(f925(x77913)),x77914)))
% 25.54/25.42 [7792]E(x77921,x77922)+~E(f862(f862(f157(x77923),x77924),x77921),f862(f862(f157(x77923),x77924),x77922))+~P1(f862(f130(x77923),x77924))+~P1(f862(f862(f228(a924),x77922),f862(f182(f925(x77923)),x77924)))+~P1(f862(f862(f228(a924),x77921),f862(f182(f925(x77923)),x77924)))
% 25.54/25.42 [8159]~P66(x81591)+~P1(f862(f862(f227(x81591),x81593),f2(x81591)))+P1(f862(f862(f228(x81591),f2(x81591)),x81592))+~P1(f862(f862(f227(x81591),x81594),f862(f862(f74(x81591),x81593),x81592)))+P1(f862(f862(f227(x81591),x81593),f862(f862(f281(x81591),x81594),x81592)))
% 25.54/25.42 [8160]~P66(x81601)+~P1(f862(f862(f228(x81601),x81603),f2(x81601)))+P1(f862(f862(f228(x81601),f2(x81601)),x81602))+~P1(f862(f862(f228(x81601),x81604),f862(f862(f74(x81601),x81603),x81602)))+P1(f862(f862(f228(x81601),x81603),f862(f862(f281(x81601),x81604),x81602)))
% 25.54/25.42 [8161]~P66(x81611)+~P1(f862(f862(f228(x81611),x81612),f2(x81611)))+P1(f862(f862(f228(x81611),f2(x81611)),x81612))+~P1(f862(f862(f227(x81611),x81614),f862(f862(f74(x81611),x81613),x81612)))+P1(f862(f862(f227(x81611),x81613),f862(f862(f281(x81611),x81614),x81612)))
% 25.54/25.42 [8162]~P66(x81621)+~P1(f862(f862(f228(x81621),x81622),f2(x81621)))+P1(f862(f862(f228(x81621),f2(x81621)),x81622))+~P1(f862(f862(f227(x81621),x81624),f862(f862(f281(x81621),x81623),x81622)))+P1(f862(f862(f227(x81621),x81623),f862(f862(f74(x81621),x81624),x81622)))
% 25.54/25.42 [8163]~P66(x81631)+~P1(f862(f862(f228(x81631),x81632),f2(x81631)))+P1(f862(f862(f228(x81631),f2(x81631)),x81632))+~P1(f862(f862(f228(x81631),x81634),f862(f862(f74(x81631),x81633),x81632)))+P1(f862(f862(f228(x81631),x81633),f862(f862(f281(x81631),x81634),x81632)))
% 25.54/25.42 [8164]~P66(x81641)+~P1(f862(f862(f228(x81641),x81642),f2(x81641)))+P1(f862(f862(f228(x81641),f2(x81641)),x81642))+~P1(f862(f862(f228(x81641),x81644),f862(f862(f281(x81641),x81643),x81642)))+P1(f862(f862(f228(x81641),x81643),f862(f862(f74(x81641),x81644),x81642)))
% 25.54/25.42 [8292]~P61(x82921)+~P1(f862(f862(f278(x82921),x82923),x82924))+~P1(f862(f862(f278(x82921),x82923),x82922))+~P1(f862(f862(f278(x82921),x82922),x82924))+P1(f862(f862(f278(x82921),f862(f862(f29(x82921),x82922),x82923)),f862(f862(f29(x82921),x82924),x82923)))
% 25.54/25.42 [8307]~P109(x83071)+~P11(x83071,x83072)+~P1(f862(f862(f227(a924),x83073),x83074))+P1(f862(f862(f227(x83071),f862(f862(f157(x83071),x83072),x83073)),f862(f862(f157(x83071),x83072),x83074)))+~P1(f862(f862(f228(a924),x83074),f862(f182(f925(x83071)),x83072)))
% 25.54/25.42 [8308]~P109(x83081)+~P11(x83081,x83082)+~P1(f862(f862(f227(a924),x83083),x83084))+P1(f862(f862(f227(x83081),f862(f862(f157(x83081),x83082),x83083)),f862(f862(f157(x83081),x83082),x83084)))+~P1(f862(f862(f228(a924),x83084),f862(f182(f925(x83081)),x83082)))
% 25.54/25.42 [8361]~P127(x83611)+~P1(f862(f862(f227(x83611),x83612),f71(x83611)))+~P1(f862(f862(f227(x83611),f2(x83611)),x83612))+~P1(f862(f862(f227(a924),x83614),x83613))+P1(f862(f862(f227(x83611),f862(f862(f236(x83611),x83612),x83613)),f862(f862(f236(x83611),x83612),x83614)))
% 25.54/25.42 [8362]~P127(x83621)+~P1(f862(f862(f228(x83621),x83622),f71(x83621)))+~P1(f862(f862(f228(x83621),f2(x83621)),x83622))+~P1(f862(f862(f228(a924),x83624),x83623))+P1(f862(f862(f228(x83621),f862(f862(f236(x83621),x83622),x83623)),f862(f862(f236(x83621),x83622),x83624)))
% 25.54/25.42 [8363]~P127(x83631)+~P1(f862(f862(f227(x83631),f2(x83631)),x83632))+~P1(f862(f862(f228(a924),f2(a924)),x83633))+~P1(f862(f862(f228(x83631),x83632),x83634))+P1(f862(f862(f228(x83631),f862(f862(f236(x83631),x83632),x83633)),f862(f862(f236(x83631),x83634),x83633)))
% 25.54/25.42 [8382]~P109(x83821)+~P11(x83821,f862(f161(x83821),x83822))+~P1(f862(f862(f227(a924),x83824),x83823))+P1(f862(f862(f227(x83821),f862(f862(f157(x83821),x83822),x83823)),f862(f862(f157(x83821),x83822),x83824)))+~P1(f862(f862(f228(a924),x83823),f862(f182(f925(x83821)),x83822)))
% 25.54/25.42 [8613]~P61(x86131)+P1(f862(f862(f278(x86131),x86132),x86133))+~P1(f862(f862(f278(x86131),x86134),x86133))+~P1(f862(f862(f278(x86131),x86134),x86132))+~P1(f862(f862(f278(x86131),f862(f862(f29(x86131),x86132),x86134)),f862(f862(f29(x86131),x86133),x86134)))
% 25.54/25.42 [8628]~P66(x86281)+~P1(f862(f862(f227(x86281),x86282),f2(x86281)))+~P1(f862(f862(f227(x86281),x86283),x86284))+~P1(f862(f862(f228(x86281),f2(x86281)),f862(f862(f74(x86281),x86283),x86284)))+P1(f862(f862(f227(x86281),f862(f862(f281(x86281),x86282),x86283)),f862(f862(f281(x86281),x86282),x86284)))
% 25.54/25.42 [8629]~P67(x86291)+~P1(f862(f862(f228(x86291),x86292),f2(x86291)))+~P1(f862(f862(f228(x86291),x86293),x86294))+~P1(f862(f862(f228(x86291),f2(x86291)),f862(f862(f74(x86291),x86293),x86294)))+P1(f862(f862(f228(x86291),f862(f862(f281(x86291),x86292),x86293)),f862(f862(f281(x86291),x86292),x86294)))
% 25.54/25.42 [8638]~P67(x86381)+~P1(f862(f862(f227(x86381),x86384),x86383))+~P1(f862(f862(f227(x86381),f2(x86381)),x86382))+~P1(f862(f862(f228(x86381),f2(x86381)),f862(f862(f74(x86381),x86383),x86384)))+P1(f862(f862(f227(x86381),f862(f862(f281(x86381),x86382),x86383)),f862(f862(f281(x86381),x86382),x86384)))
% 25.54/25.42 [8639]~P67(x86391)+~P1(f862(f862(f228(x86391),x86394),x86393))+~P1(f862(f862(f228(x86391),f2(x86391)),x86392))+~P1(f862(f862(f228(x86391),f2(x86391)),f862(f862(f74(x86391),x86393),x86394)))+P1(f862(f862(f228(x86391),f862(f862(f281(x86391),x86392),x86393)),f862(f862(f281(x86391),x86392),x86394)))
% 25.54/25.42 [8741]P1(f862(x87411,x87412))+~P1(f862(f54(x87414),x87412))+P1(f862(x87411,f893(x87411,x87413,x87412,x87414)))+~P1(f862(x87411,f181(f932(x87414,a921))))+~P1(f862(f862(f227(f932(x87414,a921)),x87412),x87413))
% 25.54/25.42 [8750]P1(f862(x87501,x87502))+P1(f862(f54(x87503),f893(x87501,x87504,x87502,x87503)))+~P1(f862(f54(x87503),x87502))+~P1(f862(x87501,f181(f932(x87503,a921))))+~P1(f862(f862(f227(f932(x87503,a921)),x87502),x87504))
% 25.54/25.42 [9020]E(f862(f862(f73(a1),f398(x90201,x90202,x90203,x90204)),f399(x90201,x90202,x90203,x90204)),x90204)+~P1(f862(f862(f228(a1),f2(a1)),x90203))+~P1(f862(f862(f228(a1),x90202),x90204))+~P1(f862(f862(f321(a1),x90202),x90201))+P1(f862(f862(f228(a1),x90202),f862(f862(f3(a1),x90204),x90203)))
% 25.54/25.42 [9235]~P1(f862(f862(f228(a1),f2(a1)),x92353))+~P1(f862(f862(f228(a1),x92352),x92354))+~P1(f862(f862(f321(a1),x92352),x92351))+P1(f862(f862(f321(a1),f398(x92351,x92352,x92353,x92354)),x92351))+P1(f862(f862(f228(a1),x92352),f862(f862(f3(a1),x92354),x92353)))
% 25.54/25.42 [9246]P1(f862(x92461,x92462))+~P1(f862(f54(x92463),x92462))+P1(f862(f862(f321(x92463),f898(x92461,x92464,x92462,x92463)),x92464))+~P1(f862(x92461,f181(f932(x92463,a921))))+~P1(f862(f862(f227(f932(x92463,a921)),x92462),x92464))
% 25.54/25.42 [9263]E(f862(f862(f73(a1),f380(x92631,x92632,x92633,x92634)),f381(x92631,x92632,x92633,x92634)),x92634)+~P1(f862(f862(f228(a1),f2(a1)),x92633))+~P1(f862(f862(f227(a1),x92632),x92634))+P1(f862(f862(f227(a1),x92632),f862(f862(f3(a1),x92634),x92633)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x92632),f71(a1))),x92631))
% 25.54/25.42 [9318]~P1(f862(f862(f228(a1),f2(a1)),x93183))+~P1(f862(f862(f228(a1),x93181),x93182))+~P1(f862(f862(f321(a1),x93181),x93184))+P1(f862(f862(f321(a1),f399(x93184,x93181,x93183,x93182)),f296(a1,f71(a1),x93183)))+P1(f862(f862(f228(a1),x93181),f862(f862(f3(a1),x93182),x93183)))
% 25.54/25.42 [9345]~P72(x93452)+~E(f784(x93453,x93454,x93451,x93452),f785(x93453,x93454,x93451,x93452))+~P1(f862(f54(x93451),f786(x93453,x93454,x93451,x93452)))+E(f862(f862(f8(f932(x93451,a921),x93452),f862(f8(x93451,x93452),x93453)),x93454),f862(f862(f8(x93451,x93452),x93453),f30(f932(x93451,a921),x93454)))+~P1(f862(f54(f932(x93451,a921)),x93454))
% 25.54/25.42 [9349]~P72(x93492)+~E(f862(x93493,f787(x93493,x93494,x93491,x93492)),f2(x93492))+~P1(f862(f54(x93491),f786(x93493,x93494,x93491,x93492)))+E(f862(f862(f8(f932(x93491,a921),x93492),f862(f8(x93491,x93492),x93493)),x93494),f862(f862(f8(x93491,x93492),x93493),f30(f932(x93491,a921),x93494)))+~P1(f862(f54(f932(x93491,a921)),x93494))
% 25.54/25.42 [9413]~P1(f862(f862(f228(a1),f2(a1)),x94133))+~P1(f862(f862(f227(a1),x94132),x94134))+P1(f862(f862(f321(a1),f380(x94131,x94132,x94133,x94134)),x94131))+P1(f862(f862(f227(a1),x94132),f862(f862(f3(a1),x94134),x94133)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x94132),f71(a1))),x94131))
% 25.54/25.42 [9458]~P1(f862(f862(f228(a1),f2(a1)),x94583))+~P1(f862(f862(f227(a1),x94581),x94582))+P1(f862(f862(f321(a1),f381(x94584,x94581,x94583,x94582)),f296(a1,f71(a1),x94583)))+P1(f862(f862(f227(a1),x94581),f862(f862(f3(a1),x94582),x94583)))+~P1(f862(f862(f321(a1),f862(f862(f3(a1),x94581),f71(a1))),x94584))
% 25.54/25.42 [9479]~P72(x94792)+~E(f784(x94793,x94794,x94791,x94792),f785(x94793,x94794,x94791,x94792))+E(f862(f862(f8(f932(x94791,a921),x94792),f862(f8(x94791,x94792),x94793)),x94794),f862(f862(f8(x94791,x94792),x94793),f30(f932(x94791,a921),x94794)))+P1(f862(f862(f321(f932(x94791,a921)),f786(x94793,x94794,x94791,x94792)),x94794))+~P1(f862(f54(f932(x94791,a921)),x94794))
% 25.54/25.42 [9484]~P72(x94842)+~E(f862(x94843,f787(x94843,x94844,x94841,x94842)),f2(x94842))+E(f862(f862(f8(f932(x94841,a921),x94842),f862(f8(x94841,x94842),x94843)),x94844),f862(f862(f8(x94841,x94842),x94843),f30(f932(x94841,a921),x94844)))+P1(f862(f862(f321(f932(x94841,a921)),f786(x94843,x94844,x94841,x94842)),x94844))+~P1(f862(f54(f932(x94841,a921)),x94844))
% 25.54/25.42 [9588]~P72(x95882)+~P1(f862(f54(x95881),f786(x95883,x95884,x95881,x95882)))+E(f862(f862(f8(f932(x95881,a921),x95882),f862(f8(x95881,x95882),x95883)),x95884),f862(f862(f8(x95881,x95882),x95883),f30(f932(x95881,a921),x95884)))+P1(f862(f862(f321(f932(x95881,a921)),f785(x95883,x95884,x95881,x95882)),x95884))+~P1(f862(f54(f932(x95881,a921)),x95884))
% 25.54/25.42 [9589]~P72(x95892)+~P1(f862(f54(x95891),f786(x95893,x95894,x95891,x95892)))+E(f862(f862(f8(f932(x95891,a921),x95892),f862(f8(x95891,x95892),x95893)),x95894),f862(f862(f8(x95891,x95892),x95893),f30(f932(x95891,a921),x95894)))+P1(f862(f862(f321(f932(x95891,a921)),f784(x95893,x95894,x95891,x95892)),x95894))+~P1(f862(f54(f932(x95891,a921)),x95894))
% 25.54/25.42 [9668]~P72(x96682)+E(f862(f862(f8(f932(x96681,a921),x96682),f862(f8(x96681,x96682),x96683)),x96684),f862(f862(f8(x96681,x96682),x96683),f30(f932(x96681,a921),x96684)))+P1(f862(f862(f321(f932(x96681,a921)),f786(x96683,x96684,x96681,x96682)),x96684))+P1(f862(f862(f321(f932(x96681,a921)),f785(x96683,x96684,x96681,x96682)),x96684))+~P1(f862(f54(f932(x96681,a921)),x96684))
% 25.54/25.42 [9669]~P72(x96692)+E(f862(f862(f8(f932(x96691,a921),x96692),f862(f8(x96691,x96692),x96693)),x96694),f862(f862(f8(x96691,x96692),x96693),f30(f932(x96691,a921),x96694)))+P1(f862(f862(f321(f932(x96691,a921)),f786(x96693,x96694,x96691,x96692)),x96694))+P1(f862(f862(f321(f932(x96691,a921)),f784(x96693,x96694,x96691,x96692)),x96694))+~P1(f862(f54(f932(x96691,a921)),x96694))
% 25.54/25.42 [9688]~P72(x96882)+P1(f862(f862(f321(x96881),f787(x96883,x96884,x96881,x96882)),f785(x96883,x96884,x96881,x96882)))+~P1(f862(f54(x96881),f786(x96883,x96884,x96881,x96882)))+E(f862(f862(f8(f932(x96881,a921),x96882),f862(f8(x96881,x96882),x96883)),x96884),f862(f862(f8(x96881,x96882),x96883),f30(f932(x96881,a921),x96884)))+~P1(f862(f54(f932(x96881,a921)),x96884))
% 25.54/25.42 [9689]~P72(x96892)+P1(f862(f862(f321(x96891),f787(x96893,x96894,x96891,x96892)),f784(x96893,x96894,x96891,x96892)))+~P1(f862(f54(x96891),f786(x96893,x96894,x96891,x96892)))+E(f862(f862(f8(f932(x96891,a921),x96892),f862(f8(x96891,x96892),x96893)),x96894),f862(f862(f8(x96891,x96892),x96893),f30(f932(x96891,a921),x96894)))+~P1(f862(f54(f932(x96891,a921)),x96894))
% 25.54/25.42 [9702]P1(f862(x97021,x97022))+~P1(f862(f862(f321(x97023),f898(x97021,x97024,x97022,x97023)),f893(x97021,x97024,x97022,x97023)))+~P1(f862(f54(x97023),x97022))+~P1(f862(x97021,f181(f932(x97023,a921))))+~P1(f862(f862(f227(f932(x97023,a921)),x97022),x97024))
% 25.54/25.42 [9739]~P72(x97392)+P1(f862(f862(f321(x97391),f787(x97393,x97394,x97391,x97392)),f785(x97393,x97394,x97391,x97392)))+E(f862(f862(f8(f932(x97391,a921),x97392),f862(f8(x97391,x97392),x97393)),x97394),f862(f862(f8(x97391,x97392),x97393),f30(f932(x97391,a921),x97394)))+P1(f862(f862(f321(f932(x97391,a921)),f786(x97393,x97394,x97391,x97392)),x97394))+~P1(f862(f54(f932(x97391,a921)),x97394))
% 25.54/25.42 [9740]~P72(x97402)+P1(f862(f862(f321(x97401),f787(x97403,x97404,x97401,x97402)),f784(x97403,x97404,x97401,x97402)))+E(f862(f862(f8(f932(x97401,a921),x97402),f862(f8(x97401,x97402),x97403)),x97404),f862(f862(f8(x97401,x97402),x97403),f30(f932(x97401,a921),x97404)))+P1(f862(f862(f321(f932(x97401,a921)),f786(x97403,x97404,x97401,x97402)),x97404))+~P1(f862(f54(f932(x97401,a921)),x97404))
% 25.54/25.42 [9916]P1(f862(x99161,x99162))+~P1(f862(f54(x99163),x99162))+~P1(f862(x99161,f862(f862(f301(x99163),f898(x99161,x99164,x99162,x99163)),f893(x99161,x99164,x99162,x99163))))+~P1(f862(x99161,f181(f932(x99163,a921))))+~P1(f862(f862(f227(f932(x99163,a921)),x99162),x99164))
% 25.54/25.42 [7927]~P66(x79271)+P1(f862(f862(f228(x79271),x79272),f2(x79271)))+~P1(f862(f862(f227(x79271),f2(x79271)),x79274))+P1(f862(f862(f228(x79271),f2(x79271)),x79272))+P1(f862(f862(f227(x79271),f862(f862(f281(x79271),x79273),x79272)),x79274))
% 25.54/25.42 [7928]~P66(x79281)+P1(f862(f862(f228(x79281),x79282),f2(x79281)))+P1(f862(f862(f228(x79281),f2(x79281)),x79282))+~P1(f862(f862(f228(x79281),f2(x79281)),x79284))+P1(f862(f862(f228(x79281),f862(f862(f281(x79281),x79283),x79282)),x79284))
% 25.54/25.42 [8212]~P1(f862(f862(f227(a1),x82124),f2(a1)))+~E(x82122,f862(f862(f73(a1),f862(f862(f74(a1),x82121),x82123)),x82124))+P1(f862(f862(f228(a1),f2(a1)),x82121))+~P1(f862(f862(f228(a1),x82121),x82124))+P1(f862(f42(x82122,x82121),f862(f862(f244(a1,a1),x82123),x82124)))
% 25.54/25.42 [8246]~P1(f862(x82461,x82464))+P1(f862(x82461,f407(x82462,x82461,x82463)))+~P1(f862(f862(f227(a1),f2(a1)),x82462))+~P1(f862(f862(f228(a1),f2(a1)),x82463))+P1(f862(x82461,f862(f862(f3(a1),x82464),f862(f862(f74(a1),x82462),x82463))))
% 25.54/25.42 [8247]~P1(f862(x82471,x82474))+P1(f862(x82471,f408(x82472,x82471,x82473)))+~P1(f862(f862(f227(a1),f2(a1)),x82472))+~P1(f862(f862(f228(a1),f2(a1)),x82473))+P1(f862(x82471,f862(f862(f73(a1),x82474),f862(f862(f74(a1),x82472),x82473))))
% 25.54/25.42 [8248]~P66(x82481)+P1(f862(f862(f228(x82481),x82482),f2(x82481)))+P1(f862(f862(f228(x82481),f2(x82481)),x82482))+P1(f862(f862(f227(x82481),f2(x82481)),x82483))+~P1(f862(f862(f227(x82481),f862(f862(f281(x82481),x82484),x82482)),x82483))
% 25.54/25.42 [8249]~P66(x82491)+P1(f862(f862(f228(x82491),x82492),f2(x82491)))+P1(f862(f862(f228(x82491),f2(x82491)),x82492))+P1(f862(f862(f228(x82491),f2(x82491)),x82493))+~P1(f862(f862(f228(x82491),f862(f862(f281(x82491),x82494),x82492)),x82493))
% 25.54/25.42 [8303]~E(x83031,f862(f862(f73(a1),f862(f862(f74(a1),x83032),x83033)),x83034))+~P1(f862(f862(f227(a1),f2(a1)),x83034))+~P1(f862(f862(f228(a1),f2(a1)),x83032))+~P1(f862(f862(f228(a1),x83034),x83032))+P1(f862(f42(x83031,x83032),f862(f862(f244(a1,a1),x83033),x83034)))
% 25.54/25.42 [8421]~P66(x84211)+P1(f862(f862(f228(x84211),x84212),f2(x84211)))+~P1(f862(f862(f227(x84211),f2(x84211)),x84214))+~P1(f862(f862(f227(x84211),x84213),f862(f862(f74(x84211),x84214),x84212)))+P1(f862(f862(f227(x84211),f862(f862(f281(x84211),x84213),x84212)),x84214))
% 25.54/25.42 [8422]~P66(x84221)+P1(f862(f862(f228(x84221),x84222),f2(x84221)))+~P1(f862(f862(f228(x84221),f2(x84221)),x84224))+~P1(f862(f862(f228(x84221),x84223),f862(f862(f74(x84221),x84224),x84222)))+P1(f862(f862(f228(x84221),f862(f862(f281(x84221),x84223),x84222)),x84224))
% 25.54/25.42 [8506]~P66(x85061)+P1(f862(f862(f228(x85061),x85062),f2(x85061)))+~P1(f862(f862(f227(x85061),x85063),f2(x85061)))+P1(f862(f862(f227(x85061),x85063),f862(f862(f281(x85061),x85064),x85062)))+~P1(f862(f862(f227(x85061),f862(f862(f74(x85061),x85063),x85062)),x85064))
% 25.54/25.42 [8507]~P66(x85071)+P1(f862(f862(f228(x85071),x85072),f2(x85071)))+~P1(f862(f862(f228(x85071),x85073),f2(x85071)))+P1(f862(f862(f228(x85071),x85073),f862(f862(f281(x85071),x85074),x85072)))+~P1(f862(f862(f228(x85071),f862(f862(f74(x85071),x85073),x85072)),x85074))
% 25.54/25.42 [8661]~P66(x86611)+~P1(f862(f862(f228(x86611),x86612),f2(x86611)))+P1(f862(f862(f228(x86611),f2(x86611)),x86612))+~P1(f862(f862(f227(x86611),f862(f862(f281(x86611),x86614),x86612)),x86613))+P1(f862(f862(f227(x86611),f862(f862(f74(x86611),x86613),x86612)),x86614))
% 25.54/25.42 [8662]~P66(x86621)+~P1(f862(f862(f228(x86621),x86622),f2(x86621)))+P1(f862(f862(f228(x86621),f2(x86621)),x86622))+~P1(f862(f862(f227(x86621),f862(f862(f74(x86621),x86624),x86622)),x86623))+P1(f862(f862(f227(x86621),f862(f862(f281(x86621),x86623),x86622)),x86624))
% 25.54/25.42 [8663]~P66(x86631)+~P1(f862(f862(f228(x86631),x86632),f2(x86631)))+P1(f862(f862(f228(x86631),f2(x86631)),x86632))+~P1(f862(f862(f228(x86631),f862(f862(f281(x86631),x86634),x86632)),x86633))+P1(f862(f862(f228(x86631),f862(f862(f74(x86631),x86633),x86632)),x86634))
% 25.54/25.42 [8664]~P66(x86641)+~P1(f862(f862(f228(x86641),x86642),f2(x86641)))+P1(f862(f862(f228(x86641),f2(x86641)),x86642))+~P1(f862(f862(f228(x86641),f862(f862(f74(x86641),x86644),x86642)),x86643))+P1(f862(f862(f228(x86641),f862(f862(f281(x86641),x86643),x86642)),x86644))
% 25.54/25.42 [8680]~P66(x86801)+~P1(f862(f862(f227(x86801),f2(x86801)),x86804))+P1(f862(f862(f228(x86801),f2(x86801)),x86802))+~P1(f862(f862(f227(x86801),f862(f862(f74(x86801),x86804),x86802)),x86803))+P1(f862(f862(f227(x86801),f862(f862(f281(x86801),x86803),x86802)),x86804))
% 25.54/25.42 [8681]~P66(x86811)+~P1(f862(f862(f228(x86811),f2(x86811)),x86814))+P1(f862(f862(f228(x86811),f2(x86811)),x86812))+~P1(f862(f862(f228(x86811),f862(f862(f74(x86811),x86814),x86812)),x86813))+P1(f862(f862(f228(x86811),f862(f862(f281(x86811),x86813),x86812)),x86814))
% 25.54/25.42 [8735]~P66(x87351)+~P99(x87351)+~P1(f862(f862(f228(x87351),f2(x87351)),x87354))+~P1(f862(f862(f227(x87351),f862(f862(f281(x87351),x87352),x87354)),f862(f96(x87351),x87353)))+P1(f862(f862(f227(x87351),x87352),f862(f862(f74(x87351),f862(f96(x87351),x87353)),x87354)))
% 25.54/25.42 [8736]~P66(x87361)+~P99(x87361)+~P1(f862(f862(f228(x87361),f2(x87361)),x87364))+~P1(f862(f862(f228(x87361),f862(f862(f281(x87361),x87362),x87364)),f862(f96(x87361),x87363)))+P1(f862(f862(f228(x87361),x87362),f862(f862(f74(x87361),f862(f96(x87361),x87363)),x87364)))
% 25.54/25.42 [8742]~P66(x87421)+~P99(x87421)+~P1(f862(f862(f228(x87421),f2(x87421)),x87423))+P1(f862(f862(f227(x87421),f862(f862(f281(x87421),x87422),x87423)),f862(f96(x87421),x87424)))+~P1(f862(f862(f227(x87421),x87422),f862(f862(f74(x87421),f862(f96(x87421),x87424)),x87423)))
% 25.54/25.42 [8743]~P66(x87431)+~P99(x87431)+~P1(f862(f862(f228(x87431),f2(x87431)),x87433))+P1(f862(f862(f228(x87431),f862(f862(f281(x87431),x87432),x87433)),f862(f96(x87431),x87434)))+~P1(f862(f862(f228(x87431),x87432),f862(f862(f74(x87431),f862(f96(x87431),x87434)),x87433)))
% 25.54/25.42 [8759]~P66(x87591)+~P1(f862(f862(f228(x87591),x87594),f2(x87591)))+~P1(f862(f862(f227(x87591),x87593),f862(f862(f74(x87591),x87592),x87594)))+P1(f862(f862(f227(x87591),x87592),f862(f862(f281(x87591),x87593),x87594)))+~P1(f862(f862(f227(x87591),f862(f862(f74(x87591),x87592),x87594)),x87593))
% 25.54/25.42 [8760]~P66(x87601)+~P1(f862(f862(f227(x87601),x87602),f2(x87601)))+~P1(f862(f862(f227(x87601),x87603),f862(f862(f74(x87601),x87602),x87604)))+P1(f862(f862(f227(x87601),x87602),f862(f862(f281(x87601),x87603),x87604)))+~P1(f862(f862(f227(x87601),f862(f862(f74(x87601),x87602),x87604)),x87603))
% 25.54/25.42 [8761]~P66(x87611)+~P1(f862(f862(f228(x87611),x87614),f2(x87611)))+~P1(f862(f862(f228(x87611),x87613),f862(f862(f74(x87611),x87612),x87614)))+P1(f862(f862(f228(x87611),x87612),f862(f862(f281(x87611),x87613),x87614)))+~P1(f862(f862(f228(x87611),f862(f862(f74(x87611),x87612),x87614)),x87613))
% 25.54/25.42 [8762]~P66(x87621)+~P1(f862(f862(f228(x87621),x87622),f2(x87621)))+~P1(f862(f862(f228(x87621),x87623),f862(f862(f74(x87621),x87622),x87624)))+P1(f862(f862(f228(x87621),x87622),f862(f862(f281(x87621),x87623),x87624)))+~P1(f862(f862(f228(x87621),f862(f862(f74(x87621),x87622),x87624)),x87623))
% 25.54/25.42 [8811]~P66(x88111)+~P99(x88111)+~P1(f862(f862(f228(x88111),f2(x88111)),f862(f96(x88111),x88113)))+~P1(f862(f862(f227(x88111),x88112),f862(f862(f281(x88111),x88114),f862(f96(x88111),x88113))))+P1(f862(f862(f227(x88111),f862(f862(f74(x88111),x88112),f862(f96(x88111),x88113))),x88114))
% 25.54/25.42 [8812]~P66(x88121)+~P99(x88121)+~P1(f862(f862(f228(x88121),f2(x88121)),f862(f96(x88121),x88123)))+~P1(f862(f862(f227(x88121),x88122),f862(f862(f74(x88121),x88124),f862(f96(x88121),x88123))))+P1(f862(f862(f227(x88121),f862(f862(f281(x88121),x88122),f862(f96(x88121),x88123))),x88124))
% 25.54/25.42 [8813]~P66(x88131)+~P99(x88131)+~P1(f862(f862(f228(x88131),f2(x88131)),f862(f96(x88131),x88133)))+~P1(f862(f862(f228(x88131),x88132),f862(f862(f281(x88131),x88134),f862(f96(x88131),x88133))))+P1(f862(f862(f228(x88131),f862(f862(f74(x88131),x88132),f862(f96(x88131),x88133))),x88134))
% 25.54/25.42 [8814]~P66(x88141)+~P99(x88141)+~P1(f862(f862(f228(x88141),f2(x88141)),f862(f96(x88141),x88143)))+~P1(f862(f862(f228(x88141),x88142),f862(f862(f74(x88141),x88144),f862(f96(x88141),x88143))))+P1(f862(f862(f228(x88141),f862(f862(f281(x88141),x88142),f862(f96(x88141),x88143))),x88144))
% 25.54/25.42 [8884]~P66(x88841)+~P1(f862(f862(f228(x88841),x88843),f2(x88841)))+~P1(f862(f862(f227(x88841),x88842),f862(f862(f74(x88841),x88844),x88843)))+~P1(f862(f862(f227(x88841),f862(f862(f74(x88841),x88844),x88843)),x88842))+P1(f862(f862(f227(x88841),f862(f862(f281(x88841),x88842),x88843)),x88844))
% 25.54/25.42 [8885]~P66(x88851)+~P1(f862(f862(f228(x88851),x88853),f2(x88851)))+~P1(f862(f862(f228(x88851),x88852),f862(f862(f74(x88851),x88854),x88853)))+~P1(f862(f862(f228(x88851),f862(f862(f74(x88851),x88854),x88853)),x88852))+P1(f862(f862(f228(x88851),f862(f862(f281(x88851),x88852),x88853)),x88854))
% 25.54/25.42 [8903]~P66(x89031)+~P1(f862(f862(f227(x89031),f2(x89031)),x89034))+~P1(f862(f862(f227(x89031),x89032),f862(f862(f74(x89031),x89034),x89033)))+~P1(f862(f862(f227(x89031),f862(f862(f74(x89031),x89034),x89033)),x89032))+P1(f862(f862(f227(x89031),f862(f862(f281(x89031),x89032),x89033)),x89034))
% 25.54/25.42 [8904]~P66(x89041)+~P1(f862(f862(f228(x89041),f2(x89041)),x89044))+~P1(f862(f862(f228(x89041),x89042),f862(f862(f74(x89041),x89044),x89043)))+~P1(f862(f862(f228(x89041),f862(f862(f74(x89041),x89044),x89043)),x89042))+P1(f862(f862(f228(x89041),f862(f862(f281(x89041),x89042),x89043)),x89044))
% 25.54/25.42 [8938]~P66(x89381)+~P99(x89381)+~P1(f862(f862(f228(x89381),f2(x89381)),f862(f96(x89381),x89384)))+P1(f862(f862(f227(x89381),x89382),f862(f862(f74(x89381),x89383),f862(f96(x89381),x89384))))+~P1(f862(f862(f227(x89381),f862(f862(f281(x89381),x89382),f862(f96(x89381),x89384))),x89383))
% 25.54/25.42 [8939]~P66(x89391)+~P99(x89391)+~P1(f862(f862(f228(x89391),f2(x89391)),f862(f96(x89391),x89394)))+P1(f862(f862(f227(x89391),x89392),f862(f862(f281(x89391),x89393),f862(f96(x89391),x89394))))+~P1(f862(f862(f227(x89391),f862(f862(f74(x89391),x89392),f862(f96(x89391),x89394))),x89393))
% 25.54/25.42 [8940]~P66(x89401)+~P99(x89401)+~P1(f862(f862(f228(x89401),f2(x89401)),f862(f96(x89401),x89404)))+P1(f862(f862(f228(x89401),x89402),f862(f862(f74(x89401),x89403),f862(f96(x89401),x89404))))+~P1(f862(f862(f228(x89401),f862(f862(f281(x89401),x89402),f862(f96(x89401),x89404))),x89403))
% 25.54/25.42 [8941]~P66(x89411)+~P99(x89411)+~P1(f862(f862(f228(x89411),f2(x89411)),f862(f96(x89411),x89414)))+P1(f862(f862(f228(x89411),x89412),f862(f862(f281(x89411),x89413),f862(f96(x89411),x89414))))+~P1(f862(f862(f228(x89411),f862(f862(f74(x89411),x89412),f862(f96(x89411),x89414))),x89413))
% 25.54/25.42 [9089]E(f862(f862(f3(a1),f400(x90891,x90892,x90893,x90894)),f401(x90891,x90892,x90893,x90894)),x90894)+~P1(f862(f862(f228(a1),f2(a1)),x90893))+~P1(f862(f862(f321(a1),x90892),x90891))+~P1(f862(f862(f228(a1),x90894),x90892))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x90894),x90893)),x90892))
% 25.54/25.42 [9160]~P1(f862(x91601,x91602))+~P1(f862(f862(f227(a1),f2(a1)),x91603))+~P1(f862(f862(f228(a1),f2(a1)),x91604))+~P1(f862(x91601,f862(f862(f3(a1),f407(x91603,x91601,x91604)),x91604)))+P1(f862(x91601,f862(f862(f3(a1),x91602),f862(f862(f74(a1),x91603),x91604))))
% 25.54/25.42 [9161]~P1(f862(x91611,x91612))+~P1(f862(f862(f227(a1),f2(a1)),x91613))+~P1(f862(f862(f228(a1),f2(a1)),x91614))+~P1(f862(x91611,f862(f862(f73(a1),f408(x91613,x91611,x91614)),x91614)))+P1(f862(x91611,f862(f862(f73(a1),x91612),f862(f862(f74(a1),x91613),x91614))))
% 25.54/25.42 [9312]~P1(f862(f862(f228(a1),f2(a1)),x93123))+~P1(f862(f862(f321(a1),x93122),x93121))+~P1(f862(f862(f228(a1),x93124),x93122))+P1(f862(f862(f321(a1),f400(x93121,x93122,x93123,x93124)),x93121))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x93124),x93123)),x93122))
% 25.54/25.42 [9332]E(f862(f862(f3(a1),f382(x93321,x93322,x93323,x93324)),f383(x93321,x93322,x93323,x93324)),x93324)+~P1(f862(f862(f228(a1),f2(a1)),x93323))+~P1(f862(f862(f227(a1),x93324),x93322))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x93322),f71(a1))),x93321))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x93324),x93323)),x93322))
% 25.54/25.42 [9360]~P1(f862(f862(f228(a1),f2(a1)),x93602))+~P1(f862(f862(f321(a1),x93603),x93604))+~P1(f862(f862(f228(a1),x93601),x93603))+P1(f862(f862(f321(a1),f401(x93604,x93603,x93602,x93601)),f296(a1,f71(a1),x93602)))+P1(f862(f862(f228(a1),f862(f862(f73(a1),x93601),x93602)),x93603))
% 25.54/25.42 [9450]~P1(f862(f862(f228(a1),f2(a1)),x94503))+~P1(f862(f862(f227(a1),x94504),x94502))+P1(f862(f862(f321(a1),f382(x94501,x94502,x94503,x94504)),x94501))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x94502),f71(a1))),x94501))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x94504),x94503)),x94502))
% 25.54/25.42 [9495]~P1(f862(f862(f228(a1),f2(a1)),x94952))+~P1(f862(f862(f227(a1),x94951),x94953))+P1(f862(f862(f321(a1),f383(x94954,x94953,x94952,x94951)),f296(a1,f71(a1),x94952)))+~P1(f862(f862(f321(a1),f862(f862(f73(a1),x94953),f71(a1))),x94954))+P1(f862(f862(f227(a1),f862(f862(f73(a1),x94951),x94952)),x94953))
% 25.54/25.42 [9793]~P35(x97931,x97933)+~P24(x97931,x97934)+P35(x97931,f862(f862(f103(f932(f931(x97931,x97931),a921)),x97932),x97933))+~P1(f862(f862(f227(f932(f931(x97931,x97931),a921)),x97932),f862(f243(f932(f931(x97931,x97931),a921),f932(f931(x97931,x97931),a921)),x97934)))+~P1(f862(f862(f227(f932(f931(x97931,x97931),a921)),x97933),f862(f248(f932(f931(x97931,x97931),a921),f932(f931(x97931,x97931),a921)),x97934)))
% 25.54/25.42 [10175]~P16(x101752,x101754,x101753)+E(x101751,f181(f932(x101752,a921)))+~P1(f862(f54(x101752),x101751))+P1(f862(f862(f321(x101752),f862(x101753,x101751)),x101751))+~P1(f862(f862(f321(x101752),f862(f862(x101754,f881(x101751,x101753,x101754,x101752)),f882(x101751,x101753,x101754,x101752))),f862(f862(f301(x101752),f881(x101751,x101753,x101754,x101752)),f862(f862(f301(x101752),f882(x101751,x101753,x101754,x101752)),f181(f932(x101752,a921))))))
% 25.54/25.42 [8926]~P66(x89261)+~P99(x89261)+~P1(f862(f862(f228(x89261),f2(x89261)),x89263))+~P1(f862(f862(f227(x89261),f862(f96(x89261),x89262)),f862(f862(f281(x89261),x89264),x89263)))+P1(f862(f862(f227(x89261),f862(f862(f74(x89261),f862(f96(x89261),x89262)),x89263)),x89264))
% 25.54/25.42 [8927]~P66(x89271)+~P99(x89271)+~P1(f862(f862(f228(x89271),f2(x89271)),x89273))+~P1(f862(f862(f228(x89271),f862(f96(x89271),x89272)),f862(f862(f281(x89271),x89274),x89273)))+P1(f862(f862(f228(x89271),f862(f862(f74(x89271),f862(f96(x89271),x89272)),x89273)),x89274))
% 25.54/25.42 [9092]~P66(x90921)+~P99(x90921)+~P1(f862(f862(f228(x90921),f2(x90921)),x90924))+P1(f862(f862(f227(x90921),f862(f96(x90921),x90922)),f862(f862(f281(x90921),x90923),x90924)))+~P1(f862(f862(f227(x90921),f862(f862(f74(x90921),f862(f96(x90921),x90922)),x90924)),x90923))
% 25.54/25.42 [9093]~P66(x90931)+~P99(x90931)+~P1(f862(f862(f228(x90931),f2(x90931)),x90934))+P1(f862(f862(f228(x90931),f862(f96(x90931),x90932)),f862(f862(f281(x90931),x90933),x90934)))+~P1(f862(f862(f228(x90931),f862(f862(f74(x90931),f862(f96(x90931),x90932)),x90934)),x90933))
% 25.54/25.42 [10111]~P110(x101112)+~P63(x101111)+~P1(f862(f862(f227(f932(x101111,x101112)),x101113),x101114))+P1(f862(f862(f228(f932(x101111,x101112)),x101113),x101114))+~P1(f862(f49(x101111),f862(f862(f10(a921,a921,x101111),a314),f862(f862(f20(x101111,x101112,a921),f862(f862(f10(x101112,f932(x101112,a921),x101111),a317),x101113)),x101114))))
% 25.54/25.42 [9708]~P52(x97081,x97081,x97084)+P1(f862(f862(f321(f931(x97081,x97081)),f862(f862(f244(x97081,x97081),x97082),x97083)),f299(x97081,x97084)))+P1(f862(f862(f321(f931(x97081,x97081)),f862(f862(f244(x97081,x97081),x97083),x97082)),f299(x97081,x97084)))+~P1(f862(f862(f321(f931(x97081,x97081)),f862(f862(f244(x97081,x97081),x97085),x97082)),f299(x97081,x97084)))+~P1(f862(f862(f321(f931(x97081,x97081)),f862(f862(f244(x97081,x97081),x97085),x97083)),f299(x97081,x97084)))
% 25.54/25.42 [5808]E(x58081,f2(a924))+~E(f862(f28(x58082),x58085),x58081)+E(f862(f28(x58082),x58083),f862(a105,x58081))+~E(x58083,f862(f862(f301(x58082),x58084),x58085))+P1(f862(f862(f321(x58082),x58084),x58085))
% 25.54/25.42 [5930]~P65(x59302)+E(x59301,f2(x59302))+E(x59303,f2(x59302))+~E(f862(f862(f281(x59302),x59304),x59303),f862(f862(f281(x59302),x59305),x59301))+E(f862(f862(f74(x59302),x59304),x59301),f862(f862(f74(x59302),x59305),x59303))
% 25.54/25.42 [5931]~P65(x59312)+E(x59311,f2(x59312))+E(x59313,f2(x59312))+~E(f862(f862(f74(x59312),x59314),x59313),f862(f862(f74(x59312),x59315),x59311))+E(f862(f862(f281(x59312),x59314),x59311),f862(f862(f281(x59312),x59315),x59313))
% 25.54/25.42 [6009]~E(f862(f28(x60091),x60095),x60093)+~E(x60095,f181(f932(x60091,a921)))+E(f862(f28(x60091),x60092),f862(a105,x60093))+~E(x60092,f862(f862(f301(x60091),x60094),x60095))+P1(f862(f862(f321(x60091),x60094),x60095))
% 25.54/25.42 [6246]~P119(x62462)+~E(f862(x62463,x62465),f2(x62462))+E(f862(f862(f11(x62461,x62462),x62463),x62464),f2(x62462))+~P1(f862(f54(x62461),x62464))+~P1(f862(f862(f321(x62461),x62465),x62464))
% 25.54/25.42 [6618]~P109(x66183)+E(x66181,x66182)+~E(f862(f295(x66183,x66184),x66181),f862(f295(x66183,x66185),x66182))+~P1(f862(f862(f228(x66183),x66185),x66182))+~P1(f862(f862(f228(x66183),x66184),x66181))
% 25.54/25.42 [6619]~P109(x66193)+E(x66191,x66192)+~E(f862(f295(x66193,x66191),x66194),f862(f295(x66193,x66192),x66195))+~P1(f862(f862(f228(x66193),x66192),x66195))+~P1(f862(f862(f228(x66193),x66191),x66194))
% 25.54/25.42 [6620]~P109(x66203)+E(x66201,x66202)+~E(f862(f295(x66203,x66204),x66201),f862(f295(x66203,x66205),x66202))+~P1(f862(f862(f228(x66203),x66205),x66202))+~P1(f862(f862(f228(x66203),x66204),x66201))
% 25.54/25.42 [6621]~P109(x66213)+E(x66211,x66212)+~E(f862(f295(x66213,x66211),x66214),f862(f295(x66213,x66212),x66215))+~P1(f862(f862(f228(x66213),x66212),x66215))+~P1(f862(f862(f228(x66213),x66211),x66214))
% 25.54/25.42 [7690]~P109(x76901)+~P11(x76901,f862(f862(f127(x76901),x76904),x76905))+~P1(f862(f862(f321(x76901),x76903),f862(f165(x76901),x76905)))+~P1(f862(f862(f321(x76901),x76902),f862(f165(x76901),x76904)))+P1(f862(f862(f227(x76901),x76902),x76903))
% 25.54/25.42 [8796]~P110(x87961)+~P1(f862(f862(f228(f932(x87961,a921)),f296(x87961,x87965,x87962)),f296(x87961,x87964,x87963)))+~P1(f862(f862(f227(x87961),x87965),x87962))+P1(f862(f862(f228(x87961),x87962),x87963))+P1(f862(f862(f228(x87961),x87964),x87965))
% 25.54/25.42 [10219]~P15(x102192,x102195,x102193)+E(x102191,f181(f932(x102192,a921)))+~E(f862(f862(x102195,f862(x102194,f899(x102191,x102194,x102193,x102195,x102192))),f862(x102194,f900(x102191,x102194,x102193,x102195,x102192))),f862(x102194,f862(f862(x102195,f899(x102191,x102194,x102193,x102195,x102192)),f900(x102191,x102194,x102193,x102195,x102192))))+E(f862(x102193,f862(f302(x102192,x102192,x102194),x102191)),f862(x102194,f862(x102193,x102191)))+~P1(f862(f54(x102192),x102191))
% 25.54/25.42 [6617]~P16(x66172,x66175,x66173)+E(x66171,f181(f932(x66172,a921)))+~P1(f862(f54(x66172),x66171))+E(f862(x66173,f862(f862(f301(x66172),x66174),x66171)),f862(f862(x66175,x66174),f862(x66173,x66171)))+P1(f862(f862(f321(x66172),x66174),x66171))
% 25.54/25.42 [7448]~P15(x74482,x74483,x74484)+E(f862(f862(x74483,f862(x74484,x74481)),f862(x74484,x74485)),f862(x74484,x74485))+E(x74481,f181(f932(x74482,a921)))+~P1(f862(f54(x74482),x74485))+~P1(f862(f862(f227(f932(x74482,a921)),x74481),x74485))
% 25.54/25.42 [7827]~P16(x78274,x78275,x78271)+E(f862(x78271,x78272),x78273)+~P1(f862(f54(x78274),x78272))+~E(f862(f862(f3(f932(x78274,a921)),x78272),f862(f862(f301(x78274),x78273),f181(f932(x78274,a921)))),f181(f932(x78274,a921)))+~P1(f862(f862(f321(x78274),x78273),x78272))
% 25.54/25.42 [8716]~P71(x87161)+~P120(x87161)+~P1(f862(f54(x87162),x87165))+P1(f862(f862(f278(x87161),f862(f862(f11(x87162,x87161),x87163),x87164)),f862(f862(f11(x87162,x87161),x87163),x87165)))+~P1(f862(f862(f227(f932(x87162,a921)),x87164),x87165))
% 25.54/25.42 [8766]E(x87661,x87662)+~P6(x87663,x87664,x87665)+E(f862(f862(f94(f932(x87663,a921)),x87661),x87662),f181(f932(x87663,a921)))+~P1(f862(f862(f321(f932(x87663,a921)),x87662),f862(f862(f53(x87663),x87664),x87665)))+~P1(f862(f862(f321(f932(x87663,a921)),x87661),f862(f862(f53(x87663),x87664),x87665)))
% 25.54/25.42 [9237]~P22(x92371,x92373,x92375,x92372)+~P1(f862(f54(x92373),x92374))+~P1(f862(f54(x92371),x92372))+P1(f862(f862(f227(a924),f862(f28(x92371),x92372)),f862(f28(x92373),x92374)))+~P1(f862(f862(f227(f932(x92373,a921)),f862(f302(x92371,x92373,x92375),x92372)),x92374))
% 25.54/25.42 [9581]~P72(x95812)+~E(f862(x95813,f365(x95813,x95814,x95815,x95811,x95812)),f2(x95812))+E(f862(f862(f8(x95811,x95812),x95813),x95814),f862(f862(f8(x95811,x95812),x95813),x95815))+~P1(f862(f54(x95811),x95815))+~P1(f862(f862(f227(f932(x95811,a921)),x95814),x95815))
% 25.54/25.42 [9582]~P72(x95822)+~E(f862(x95823,f366(x95823,x95824,x95825,x95821,x95822)),f2(x95822))+E(f862(f862(f8(x95821,x95822),x95823),x95824),f862(f862(f8(x95821,x95822),x95823),x95825))+~P1(f862(f54(x95821),x95825))+~P1(f862(f862(f227(f932(x95821,a921)),x95824),x95825))
% 25.54/25.42 [9583]~P71(x95832)+~E(f862(x95833,f916(x95833,x95834,x95835,x95831,x95832)),f71(x95832))+E(f862(f862(f11(x95831,x95832),x95833),x95834),f862(f862(f11(x95831,x95832),x95833),x95835))+~P1(f862(f54(x95831),x95835))+~P1(f862(f862(f227(f932(x95831,a921)),x95834),x95835))
% 25.54/25.42 [9584]~P71(x95842)+~E(f862(x95843,f330(x95843,x95844,x95845,x95841,x95842)),f71(x95842))+E(f862(f862(f11(x95841,x95842),x95843),x95844),f862(f862(f11(x95841,x95842),x95843),x95845))+~P1(f862(f54(x95841),x95845))+~P1(f862(f862(f227(f932(x95841,a921)),x95844),x95845))
% 25.54/25.42 [10061]~P87(x100611)+~P1(f862(f54(x100612),x100615))+~P1(f862(f862(f227(x100611),f2(x100611)),f862(x100613,f355(x100613,x100614,x100615,x100612,x100611))))+P1(f862(f862(f227(x100611),f862(f862(f8(x100612,x100611),x100613),x100614)),f862(f862(f8(x100612,x100611),x100613),x100615)))+~P1(f862(f862(f227(f932(x100612,a921)),x100614),x100615))
% 25.54/25.42 [7687]E(x76871,f2(a924))+P1(f862(x76872,x76873))+~E(x76874,f862(f862(f73(a924),f862(f862(f74(a924),x76871),x76873)),x76875))+~P1(f862(f862(f228(a924),x76875),x76871))+~P1(f862(x76872,f862(f862(f29(a924),x76874),x76871)))
% 25.54/25.42 [7765]E(x77651,f2(a924))+P1(f862(x77652,x77653))+~P1(f862(x77652,f38(a924,x77654,x77651)))+~E(x77654,f862(f862(f73(a924),f862(f862(f74(a924),x77651),x77655)),x77653))+~P1(f862(f862(f228(a924),x77653),x77651))
% 25.54/25.42 [8058]~P65(x80583)+E(f862(x80581,x80582),f2(x80583))+~P1(f862(f54(x80584),x80585))+E(f862(f862(f11(x80584,x80583),x80581),f862(f862(f3(f932(x80584,a921)),x80585),f862(f862(f301(x80584),x80582),f181(f932(x80584,a921))))),f862(f862(f11(x80584,x80583),x80581),x80585))+P1(f862(f862(f321(x80584),x80582),x80585))
% 25.54/25.42 [8461]~P72(x84611)+~P1(f862(f54(x84612),x84615))+~P1(f862(f54(x84612),x84614))+~E(f862(f862(f94(f932(x84612,a921)),x84614),x84615),f181(f932(x84612,a921)))+E(f862(f862(f73(x84611),f862(f862(f8(x84612,x84611),x84613),x84614)),f862(f862(f8(x84612,x84611),x84613),x84615)),f862(f862(f8(x84612,x84611),x84613),f862(f862(f103(f932(x84612,a921)),x84614),x84615)))
% 25.54/25.42 [8462]~P71(x84621)+~P1(f862(f54(x84622),x84625))+~P1(f862(f54(x84622),x84624))+~E(f862(f862(f94(f932(x84622,a921)),x84624),x84625),f181(f932(x84622,a921)))+E(f862(f862(f74(x84621),f862(f862(f11(x84622,x84621),x84623),x84624)),f862(f862(f11(x84622,x84621),x84623),x84625)),f862(f862(f11(x84622,x84621),x84623),f862(f862(f103(f932(x84622,a921)),x84624),x84625)))
% 25.54/25.42 [8463]~P71(x84631)+~P1(f862(f54(x84632),x84635))+~P1(f862(f54(x84632),x84634))+~E(f862(f862(f94(f932(x84632,a921)),x84634),x84635),f181(f932(x84632,a921)))+E(f862(f862(f74(x84631),f862(f862(f11(x84632,x84631),x84633),x84634)),f862(f862(f11(x84632,x84631),x84633),x84635)),f862(f862(f11(x84632,x84631),x84633),f862(f862(f103(f932(x84632,a921)),x84634),x84635)))
% 25.54/25.42 [8562]~P65(x85623)+E(f862(x85621,x85622),f2(x85623))+~P1(f862(f54(x85624),x85625))+E(f862(f862(f11(x85624,x85623),x85621),f862(f862(f3(f932(x85624,a921)),x85625),f862(f862(f301(x85624),x85622),f181(f932(x85624,a921))))),f862(f862(f281(x85623),f862(f862(f11(x85624,x85623),x85621),x85625)),f862(x85621,x85622)))+~P1(f862(f862(f321(x85624),x85622),x85625))
% 25.54/25.42 [9107]~P6(x91071,x91075,x91074)+~E(f862(f276(x91071,x91071,x91074),f862(f862(f301(x91071),x91072),f181(f932(x91071,a921)))),f862(f276(x91071,x91071,x91074),f862(f862(f301(x91071),x91073),f181(f932(x91071,a921)))))+~P1(f862(f862(f321(x91071),x91073),x91075))+~P1(f862(f862(f321(x91071),x91072),x91075))+P1(f862(f862(f321(f931(x91071,x91071)),f862(f862(f244(x91071,x91071),x91072),x91073)),x91074))
% 25.54/25.42 [9108]~P6(x91081,x91085,x91084)+~E(f862(f276(x91081,x91081,x91084),f862(f862(f301(x91081),x91082),f181(f932(x91081,a921)))),f862(f276(x91081,x91081,x91084),f862(f862(f301(x91081),x91083),f181(f932(x91081,a921)))))+~P1(f862(f862(f321(x91081),x91083),x91085))+~P1(f862(f862(f321(x91081),x91082),x91085))+P1(f862(f862(f321(f931(x91081,x91081)),f862(f862(f244(x91081,x91081),x91082),x91083)),x91084))
% 25.54/25.42 [9200]~P6(x92001,x92005,x92002)+E(f862(f276(x92001,x92001,x92002),f862(f862(f301(x92001),x92003),f181(f932(x92001,a921)))),f862(f276(x92001,x92001,x92002),f862(f862(f301(x92001),x92004),f181(f932(x92001,a921)))))+~P1(f862(f862(f321(x92001),x92004),x92005))+~P1(f862(f862(f321(x92001),x92003),x92005))+~P1(f862(f862(f321(f931(x92001,x92001)),f862(f862(f244(x92001,x92001),x92003),x92004)),x92002))
% 25.54/25.42 [9288]~P6(x92881,x92885,x92884)+~E(f862(f862(f53(x92881),f862(f862(f301(x92881),x92882),f181(f932(x92881,a921)))),x92884),f862(f862(f53(x92881),f862(f862(f301(x92881),x92883),f181(f932(x92881,a921)))),x92884))+~P1(f862(f862(f321(x92881),x92883),x92885))+~P1(f862(f862(f321(x92881),x92882),x92885))+P1(f862(f862(f321(f931(x92881,x92881)),f862(f862(f244(x92881,x92881),x92882),x92883)),x92884))
% 25.54/25.42 [9311]~P6(x93111,x93115,x93113)+E(f862(f862(f53(x93111),f862(f862(f301(x93111),x93112),f181(f932(x93111,a921)))),x93113),f862(f862(f53(x93111),f862(f862(f301(x93111),x93114),f181(f932(x93111,a921)))),x93113))+~P1(f862(f862(f321(x93111),x93114),x93115))+~P1(f862(f862(f321(x93111),x93112),x93115))+~P1(f862(f862(f321(f931(x93111,x93111)),f862(f862(f244(x93111,x93111),x93112),x93114)),x93113))
% 25.54/25.42 [9610]~P71(x96101)+~P1(f862(f54(x96102),x96105))+~P1(f862(f54(x96102),x96104))+~E(f862(f862(f94(f932(x96102,a921)),x96104),x96105),f181(f932(x96102,a921)))+E(f862(f862(f74(x96101),f862(f862(f862(f58(x96101,x96102,f74(x96101)),x96103),f71(x96101)),x96104)),f862(f862(f862(f58(x96101,x96102,f74(x96101)),x96103),f71(x96101)),x96105)),f862(f862(f862(f58(x96101,x96102,f74(x96101)),x96103),f71(x96101)),f862(f862(f103(f932(x96102,a921)),x96104),x96105)))
% 25.54/25.42 [9621]~P72(x96211)+~E(f862(x96213,f353(x96213,x96215,x96214,x96212,x96211)),f2(x96211))+~P1(f862(f54(x96212),x96214))+~P1(f862(f54(x96212),x96215))+E(f862(f862(f73(x96211),f862(f862(f8(x96212,x96211),x96213),x96214)),f862(f862(f8(x96212,x96211),x96213),x96215)),f862(f862(f8(x96212,x96211),x96213),f862(f862(f103(f932(x96212,a921)),x96214),x96215)))
% 25.54/25.42 [9622]~P72(x96221)+~E(f862(x96223,f356(x96223,x96225,x96224,x96222,x96221)),f2(x96221))+~P1(f862(f54(x96222),x96224))+~P1(f862(f54(x96222),x96225))+E(f862(f862(f73(x96221),f862(f862(f8(x96222,x96221),x96223),x96224)),f862(f862(f8(x96222,x96221),x96223),x96225)),f862(f862(f8(x96222,x96221),x96223),f862(f862(f103(f932(x96222,a921)),x96224),x96225)))
% 25.54/25.42 [9623]~P71(x96231)+~E(f862(x96233,f917(x96233,x96235,x96234,x96232,x96231)),f71(x96231))+~P1(f862(f54(x96232),x96234))+~P1(f862(f54(x96232),x96235))+E(f862(f862(f74(x96231),f862(f862(f11(x96232,x96231),x96233),x96234)),f862(f862(f11(x96232,x96231),x96233),x96235)),f862(f862(f11(x96232,x96231),x96233),f862(f862(f103(f932(x96232,a921)),x96234),x96235)))
% 25.54/25.42 [9624]~P71(x96241)+~E(f862(x96243,f918(x96243,x96245,x96244,x96242,x96241)),f71(x96241))+~P1(f862(f54(x96242),x96244))+~P1(f862(f54(x96242),x96245))+E(f862(f862(f74(x96241),f862(f862(f11(x96242,x96241),x96243),x96244)),f862(f862(f11(x96242,x96241),x96243),x96245)),f862(f862(f11(x96242,x96241),x96243),f862(f862(f103(f932(x96242,a921)),x96244),x96245)))
% 25.54/25.42 [9836]~P71(x98361)+~E(f862(x98363,f354(x98363,x98365,x98364,x98362,x98361)),f71(x98361))+~P1(f862(f54(x98362),x98364))+~P1(f862(f54(x98362),x98365))+E(f862(f862(f74(x98361),f862(f862(f862(f58(x98361,x98362,f74(x98361)),x98363),f71(x98361)),x98364)),f862(f862(f862(f58(x98361,x98362,f74(x98361)),x98363),f71(x98361)),x98365)),f862(f862(f862(f58(x98361,x98362,f74(x98361)),x98363),f71(x98361)),f862(f862(f103(f932(x98362,a921)),x98364),x98365)))
% 25.54/25.42 [9947]~P72(x99472)+E(f862(f862(f8(x99471,x99472),x99473),x99474),f862(f862(f8(x99471,x99472),x99473),x99475))+~P1(f862(f54(x99471),x99475))+~P1(f862(f862(f227(f932(x99471,a921)),x99474),x99475))+P1(f862(f862(f321(x99471),f365(x99473,x99474,x99475,x99471,x99472)),f862(f862(f3(f932(x99471,a921)),x99475),x99474)))
% 25.54/25.42 [9948]~P72(x99482)+E(f862(f862(f8(x99481,x99482),x99483),x99484),f862(f862(f8(x99481,x99482),x99483),x99485))+~P1(f862(f54(x99481),x99485))+~P1(f862(f862(f227(f932(x99481,a921)),x99484),x99485))+P1(f862(f862(f321(x99481),f366(x99483,x99484,x99485,x99481,x99482)),f862(f862(f3(f932(x99481,a921)),x99485),x99484)))
% 25.54/25.42 [9949]~P71(x99492)+E(f862(f862(f11(x99491,x99492),x99493),x99494),f862(f862(f11(x99491,x99492),x99493),x99495))+~P1(f862(f54(x99491),x99495))+~P1(f862(f862(f227(f932(x99491,a921)),x99494),x99495))+P1(f862(f862(f321(x99491),f916(x99493,x99494,x99495,x99491,x99492)),f862(f862(f3(f932(x99491,a921)),x99495),x99494)))
% 25.54/25.42 [9950]~P71(x99502)+E(f862(f862(f11(x99501,x99502),x99503),x99504),f862(f862(f11(x99501,x99502),x99503),x99505))+~P1(f862(f54(x99501),x99505))+~P1(f862(f862(f227(f932(x99501,a921)),x99504),x99505))+P1(f862(f862(f321(x99501),f330(x99503,x99504,x99505,x99501,x99502)),f862(f862(f3(f932(x99501,a921)),x99505),x99504)))
% 25.54/25.42 [9968]~P72(x99681)+~P1(f862(f54(x99682),x99684))+~P1(f862(f54(x99682),x99685))+E(f862(f862(f73(x99681),f862(f862(f8(x99682,x99681),x99683),x99684)),f862(f862(f8(x99682,x99681),x99683),x99685)),f862(f862(f8(x99682,x99681),x99683),f862(f862(f103(f932(x99682,a921)),x99684),x99685)))+P1(f862(f862(f321(x99682),f353(x99683,x99685,x99684,x99682,x99681)),f862(f862(f94(f932(x99682,a921)),x99684),x99685)))
% 25.54/25.42 [9969]~P72(x99691)+~P1(f862(f54(x99692),x99694))+~P1(f862(f54(x99692),x99695))+E(f862(f862(f73(x99691),f862(f862(f8(x99692,x99691),x99693),x99694)),f862(f862(f8(x99692,x99691),x99693),x99695)),f862(f862(f8(x99692,x99691),x99693),f862(f862(f103(f932(x99692,a921)),x99694),x99695)))+P1(f862(f862(f321(x99692),f356(x99693,x99695,x99694,x99692,x99691)),f862(f862(f94(f932(x99692,a921)),x99694),x99695)))
% 25.54/25.42 [9970]~P71(x99701)+~P1(f862(f54(x99702),x99704))+~P1(f862(f54(x99702),x99705))+E(f862(f862(f74(x99701),f862(f862(f11(x99702,x99701),x99703),x99704)),f862(f862(f11(x99702,x99701),x99703),x99705)),f862(f862(f11(x99702,x99701),x99703),f862(f862(f103(f932(x99702,a921)),x99704),x99705)))+P1(f862(f862(f321(x99702),f917(x99703,x99705,x99704,x99702,x99701)),f862(f862(f94(f932(x99702,a921)),x99704),x99705)))
% 25.54/25.42 [9971]~P71(x99711)+~P1(f862(f54(x99712),x99714))+~P1(f862(f54(x99712),x99715))+E(f862(f862(f74(x99711),f862(f862(f11(x99712,x99711),x99713),x99714)),f862(f862(f11(x99712,x99711),x99713),x99715)),f862(f862(f11(x99712,x99711),x99713),f862(f862(f103(f932(x99712,a921)),x99714),x99715)))+P1(f862(f862(f321(x99712),f918(x99713,x99715,x99714,x99712,x99711)),f862(f862(f94(f932(x99712,a921)),x99714),x99715)))
% 25.54/25.42 [9978]~P87(x99785)+~P1(f862(f54(x99781),x99784))+P1(f862(f862(f227(x99785),f862(f862(f8(x99781,x99785),x99782),x99783)),f862(f862(f8(x99781,x99785),x99782),x99784)))+~P1(f862(f862(f227(f932(x99781,a921)),x99783),x99784))+P1(f862(f862(f321(x99781),f355(x99782,x99783,x99784,x99781,x99785)),f862(f862(f3(f932(x99781,a921)),x99784),x99783)))
% 25.54/25.42 [10023]~P71(x100231)+~P1(f862(f54(x100232),x100234))+~P1(f862(f54(x100232),x100235))+E(f862(f862(f74(x100231),f862(f862(f862(f58(x100231,x100232,f74(x100231)),x100233),f71(x100231)),x100234)),f862(f862(f862(f58(x100231,x100232,f74(x100231)),x100233),f71(x100231)),x100235)),f862(f862(f862(f58(x100231,x100232,f74(x100231)),x100233),f71(x100231)),f862(f862(f103(f932(x100232,a921)),x100234),x100235)))+P1(f862(f862(f321(x100232),f354(x100233,x100235,x100234,x100232,x100231)),f862(f862(f94(f932(x100232,a921)),x100234),x100235)))
% 25.54/25.42 [8976]~P16(x89761,x89764,x89765)+~P1(f862(f54(x89761),x89762))+E(f862(f862(f3(f932(x89761,a921)),x89762),f862(f862(f301(x89761),x89763),f181(f932(x89761,a921)))),f181(f932(x89761,a921)))+~P1(f862(f862(f321(x89761),x89763),x89762))+E(f862(f862(x89764,x89763),f862(x89765,f862(f862(f3(f932(x89761,a921)),x89762),f862(f862(f301(x89761),x89763),f181(f932(x89761,a921)))))),f862(x89765,x89762))
% 25.54/25.42 [9056]~P16(x90561,x90564,x90565)+~P1(f862(f54(x90561),x90563))+~P1(f862(f54(x90561),x90562))+E(f862(f862(f94(f932(x90561,a921)),x90562),x90563),f181(f932(x90561,a921)))+E(f862(f862(x90564,f862(x90565,f862(f862(f103(f932(x90561,a921)),x90562),x90563))),f862(x90565,f862(f862(f94(f932(x90561,a921)),x90562),x90563))),f862(f862(x90564,f862(x90565,x90562)),f862(x90565,x90563)))
% 25.54/25.42 [9626]~P1(f862(f862(f227(a1),x96264),f2(a1)))+~P1(f862(f862(f228(a1),x96263),x96265))+P1(f862(f862(f227(a1),x96261),x96262))+~P1(f862(f862(f228(a1),x96263),x96264))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x96263),x96262)),x96265)),f862(f862(f73(a1),f862(f862(f74(a1),x96263),x96261)),x96264)))
% 25.54/25.42 [9628]~P1(f862(f862(f227(a1),f2(a1)),x96285))+P1(f862(f862(f227(a1),x96281),x96282))+~P1(f862(f862(f228(a1),x96283),x96284))+~P1(f862(f862(f228(a1),x96285),x96284))+~P1(f862(f862(f227(a1),f862(f862(f73(a1),f862(f862(f74(a1),x96284),x96281)),x96285)),f862(f862(f73(a1),f862(f862(f74(a1),x96284),x96282)),x96283)))
% 25.54/25.42 [9745]~P65(x97455)+E(f862(x97451,f367(x97451,x97452,x97453,x97454,x97455)),f2(x97455))+~P1(f862(f54(x97454),x97453))+~P1(f862(f54(x97454),x97452))+E(f862(f862(f281(x97455),f862(f862(f74(x97455),f862(f862(f11(x97454,x97455),x97451),x97453)),f862(f862(f11(x97454,x97455),x97451),x97452))),f862(f862(f11(x97454,x97455),x97451),f862(f862(f94(f932(x97454,a921)),x97453),x97452))),f862(f862(f11(x97454,x97455),x97451),f862(f862(f103(f932(x97454,a921)),x97453),x97452)))
% 25.54/25.42 [10015]~P65(x100151)+~P1(f862(f54(x100152),x100154))+~P1(f862(f54(x100152),x100155))+E(f862(f862(f281(x100151),f862(f862(f74(x100151),f862(f862(f11(x100152,x100151),x100153),x100154)),f862(f862(f11(x100152,x100151),x100153),x100155))),f862(f862(f11(x100152,x100151),x100153),f862(f862(f94(f932(x100152,a921)),x100154),x100155))),f862(f862(f11(x100152,x100151),x100153),f862(f862(f103(f932(x100152,a921)),x100154),x100155)))+P1(f862(f862(f321(x100152),f367(x100153,x100155,x100154,x100152,x100151)),f862(f862(f94(f932(x100152,a921)),x100154),x100155)))
% 25.54/25.42 [9331]E(f862(f862(f127(x93311),x93312),x93313),f862(f862(f127(x93311),x93314),x93315))+~E(f862(f862(f168(x93311),f862(f182(f925(x93311)),x93314)),x93312),x93314)+~E(f862(f862(f168(x93311),f862(f182(f925(x93311)),x93312)),x93314),x93312)+~E(x93315,f862(f862(f127(x93311),f862(f862(f131(x93311),f862(f182(f925(x93311)),x93314)),x93312)),x93313))+~E(f862(f862(f127(x93311),f862(f862(f131(x93311),f862(f182(f925(x93311)),x93312)),x93314)),x93315),x93313)
% 25.54/25.42 [9743]~P109(x97432)+E(f862(f862(f141(x97431,x97432,x97433),x97434),f163(x97431,x97434,x97435)),x97435)+~P11(x97432,f862(f862(f147(x97431,x97432),x97433),x97435))+~P1(f862(f862(f321(x97431),x97434),f862(f165(x97431),x97435)))+~E(f862(f134(x97431),f862(f129(x97431,f862(f862(f10(x97432,a921,x97431),f862(a317,f862(x97433,x97434))),x97433)),x97435)),x97434)
% 25.54/25.42 [10079]~P69(x100791)+~P1(f862(f59(x100791,x100791,f74(x100791),x100792,x100793),x100795))+~P1(f862(f862(f321(x100791),x100794),x100793))+P1(f862(f862(f321(x100791),x100792),x100793))+P1(f862(f59(x100791,x100791,f74(x100791),x100794,f862(f862(f301(x100791),x100792),f862(f862(f3(f932(x100791,a921)),x100793),f862(f862(f301(x100791),x100794),f181(f932(x100791,a921)))))),x100795))
% 25.54/25.42 [7453]E(x74531,x74532)+~P22(x74534,x74535,x74533,x74536)+~E(f862(x74533,x74531),f862(x74533,x74532))+~P1(f862(f862(f321(x74534),x74532),x74536))+~P1(f862(f862(f321(x74534),x74531),x74536))
% 25.54/25.42 [7454]E(x74541,x74542)+~P22(x74544,x74545,x74543,x74546)+~E(f862(x74543,x74541),f862(x74543,x74542))+~P1(f862(f862(f321(x74544),x74542),x74546))+~P1(f862(f862(f321(x74544),x74541),x74546))
% 25.54/25.42 [7455]E(x74551,x74552)+~P22(x74554,x74555,x74553,x74556)+~E(f862(x74553,x74551),f862(x74553,x74552))+~P1(f862(f862(f321(x74554),x74552),x74556))+~P1(f862(f862(f321(x74554),x74551),x74556))
% 25.54/25.42 [7456]E(x74561,x74562)+~P22(x74564,x74565,x74563,x74566)+~E(f862(x74563,x74561),f862(x74563,x74562))+~P1(f862(f862(f321(x74564),x74562),x74566))+~P1(f862(f862(f321(x74564),x74561),x74566))
% 25.54/25.42 [6710]~P144(x67104)+E(x67101,x67102)+~E(x67105,x67106)+E(x67103,f2(x67104))+~E(f862(f862(f73(x67104),x67105),f862(f862(f74(x67104),x67103),x67101)),f862(f862(f73(x67104),x67106),f862(f862(f74(x67104),x67103),x67102)))
% 25.54/25.42 [7744]~P3(x77441)+~P109(x77441)+~P1(f862(f862(f228(x77441),x77442),f862(x77445,x77446)))+~P1(f862(f862(f321(x77443),x77446),x77444))+P1(f862(f862(f228(x77441),x77442),f862(f862(f33(x77443,x77441),x77444),x77445)))
% 25.54/25.42 [10075]~P22(x100752,x100751,x100753,x100754)+~P22(x100751,x100752,x100756,x100755)+P23(x100751,x100752,f830(x100753,x100754,x100755,x100756,x100752,x100751),x100755,x100754)+~P1(f862(f862(f227(f932(x100752,a921)),f862(f302(x100751,x100752,x100756),x100755)),x100754))+~P1(f862(f862(f227(f932(x100751,a921)),f862(f302(x100752,x100751,x100753),x100754)),x100755))
% 25.54/25.42 [8432]~P3(x84321)+~P109(x84321)+~P1(f862(f862(f228(x84321),f862(x84324,x84326)),x84325))+~P1(f862(f862(f321(x84322),x84326),x84323))+P1(f862(f862(f228(x84321),f862(f862(f32(x84322,x84321),x84323),x84324)),x84325))
% 25.54/25.42 [8687]~P17(x86872,x86875,x86876,x86871)+~P1(f862(f54(x86872),x86874))+~P1(f862(f54(x86872),x86873))+~E(f862(f862(f94(f932(x86872,a921)),x86873),x86874),f181(f932(x86872,a921)))+E(f862(x86871,f862(f862(f103(f932(x86872,a921)),x86873),x86874)),f862(f66(x86875,x86875,x86875,f862(x86871,x86873)),f862(x86871,x86874)))
% 25.54/25.42 [10277]~P71(x102771)+~E(f820(x102774,x102775,x102773,x102776,x102772,x102771),f821(x102774,x102775,x102773,x102776,x102772,x102771))+~P1(f862(f54(x102772),x102776))+E(f862(f862(f862(f58(x102771,x102772,f74(x102771)),f862(f862(f10(f932(x102773,a921),x102771,x102772),f862(f862(f58(x102771,x102773,f74(x102771)),x102774),f71(x102771))),x102775)),f71(x102771)),x102776),f862(f862(f862(f58(x102771,x102773,f74(x102771)),x102774),f71(x102771)),f862(f862(f33(x102772,f932(x102773,a921)),x102776),x102775)))+P1(f862(f862(f321(x102772),f819(x102774,x102775,x102773,x102776,x102772,x102771)),x102776))
% 25.54/25.42 [10307]~P71(x103071)+~E(f820(x103074,x103075,x103073,x103076,x103072,x103071),f821(x103074,x103075,x103073,x103076,x103072,x103071))+~P1(f862(f54(x103072),x103076))+E(f862(f862(f862(f58(x103071,x103072,f74(x103071)),f862(f862(f10(f932(x103073,a921),x103071,x103072),f862(f862(f58(x103071,x103073,f74(x103071)),x103074),f71(x103071))),x103075)),f71(x103071)),x103076),f862(f862(f862(f58(x103071,x103073,f74(x103071)),x103074),f71(x103071)),f862(f862(f33(x103072,f932(x103073,a921)),x103076),x103075)))+~P1(f862(f54(x103073),f862(x103075,f819(x103074,x103075,x103073,x103076,x103072,x103071))))
% 25.54/25.42 [10310]~P71(x103101)+~P1(f862(f54(x103102),x103106))+E(f862(f862(f862(f58(x103101,x103102,f74(x103101)),f862(f862(f10(f932(x103103,a921),x103101,x103102),f862(f862(f58(x103101,x103103,f74(x103101)),x103104),f71(x103101))),x103105)),f71(x103101)),x103106),f862(f862(f862(f58(x103101,x103103,f74(x103101)),x103104),f71(x103101)),f862(f862(f33(x103102,f932(x103103,a921)),x103106),x103105)))+P1(f862(f862(f321(x103102),f819(x103104,x103105,x103103,x103106,x103102,x103101)),x103106))+P1(f862(f862(f321(x103102),f821(x103104,x103105,x103103,x103106,x103102,x103101)),x103106))
% 25.54/25.42 [10311]~P71(x103111)+~P1(f862(f54(x103112),x103116))+E(f862(f862(f862(f58(x103111,x103112,f74(x103111)),f862(f862(f10(f932(x103113,a921),x103111,x103112),f862(f862(f58(x103111,x103113,f74(x103111)),x103114),f71(x103111))),x103115)),f71(x103111)),x103116),f862(f862(f862(f58(x103111,x103113,f74(x103111)),x103114),f71(x103111)),f862(f862(f33(x103112,f932(x103113,a921)),x103116),x103115)))+P1(f862(f862(f321(x103112),f819(x103114,x103115,x103113,x103116,x103112,x103111)),x103116))+P1(f862(f862(f321(x103112),f820(x103114,x103115,x103113,x103116,x103112,x103111)),x103116))
% 25.54/25.42 [10330]~P71(x103301)+~P1(f862(f54(x103302),x103306))+E(f862(f862(f862(f58(x103301,x103302,f74(x103301)),f862(f862(f10(f932(x103303,a921),x103301,x103302),f862(f862(f58(x103301,x103303,f74(x103301)),x103304),f71(x103301))),x103305)),f71(x103301)),x103306),f862(f862(f862(f58(x103301,x103303,f74(x103301)),x103304),f71(x103301)),f862(f862(f33(x103302,f932(x103303,a921)),x103306),x103305)))+P1(f862(f862(f321(x103302),f821(x103304,x103305,x103303,x103306,x103302,x103301)),x103306))+~P1(f862(f54(x103303),f862(x103305,f819(x103304,x103305,x103303,x103306,x103302,x103301))))
% 25.54/25.42 [10331]~P71(x103311)+~P1(f862(f54(x103312),x103316))+E(f862(f862(f862(f58(x103311,x103312,f74(x103311)),f862(f862(f10(f932(x103313,a921),x103311,x103312),f862(f862(f58(x103311,x103313,f74(x103311)),x103314),f71(x103311))),x103315)),f71(x103311)),x103316),f862(f862(f862(f58(x103311,x103313,f74(x103311)),x103314),f71(x103311)),f862(f862(f33(x103312,f932(x103313,a921)),x103316),x103315)))+P1(f862(f862(f321(x103312),f820(x103314,x103315,x103313,x103316,x103312,x103311)),x103316))+~P1(f862(f54(x103313),f862(x103315,f819(x103314,x103315,x103313,x103316,x103312,x103311))))
% 25.54/25.42 [10342]~P71(x103421)+~E(f862(f862(f94(f932(x103423,a921)),f862(x103425,f821(x103424,x103425,x103423,x103426,x103422,x103421))),f862(x103425,f820(x103424,x103425,x103423,x103426,x103422,x103421))),f181(f932(x103423,a921)))+~P1(f862(f54(x103422),x103426))+E(f862(f862(f862(f58(x103421,x103422,f74(x103421)),f862(f862(f10(f932(x103423,a921),x103421,x103422),f862(f862(f58(x103421,x103423,f74(x103421)),x103424),f71(x103421))),x103425)),f71(x103421)),x103426),f862(f862(f862(f58(x103421,x103423,f74(x103421)),x103424),f71(x103421)),f862(f862(f33(x103422,f932(x103423,a921)),x103426),x103425)))+P1(f862(f862(f321(x103422),f819(x103424,x103425,x103423,x103426,x103422,x103421)),x103426))
% 25.54/25.42 [10353]~P71(x103531)+~E(f862(f862(f94(f932(x103533,a921)),f862(x103535,f821(x103534,x103535,x103533,x103536,x103532,x103531))),f862(x103535,f820(x103534,x103535,x103533,x103536,x103532,x103531))),f181(f932(x103533,a921)))+~P1(f862(f54(x103532),x103536))+E(f862(f862(f862(f58(x103531,x103532,f74(x103531)),f862(f862(f10(f932(x103533,a921),x103531,x103532),f862(f862(f58(x103531,x103533,f74(x103531)),x103534),f71(x103531))),x103535)),f71(x103531)),x103536),f862(f862(f862(f58(x103531,x103533,f74(x103531)),x103534),f71(x103531)),f862(f862(f33(x103532,f932(x103533,a921)),x103536),x103535)))+~P1(f862(f54(x103533),f862(x103535,f819(x103534,x103535,x103533,x103536,x103532,x103531))))
% 25.54/25.42 [9420]~P120(x94201)+~P118(x94201)+~P1(f862(f862(f278(x94201),x94202),x94205))+~P1(f862(f862(f278(x94201),x94202),f862(f862(f73(x94201),x94203),x94206)))+P1(f862(f862(f278(x94201),x94202),f862(f862(f73(x94201),f862(f862(f3(x94201),x94203),f862(f862(f74(x94201),x94204),x94205))),x94206)))
% 25.54/25.42 [9421]~P120(x94211)+~P118(x94211)+~P1(f862(f862(f278(x94211),x94212),x94215))+~P1(f862(f862(f278(x94211),x94212),f862(f862(f73(x94211),x94213),x94216)))+P1(f862(f862(f278(x94211),x94212),f862(f862(f73(x94211),f862(f862(f3(x94211),x94213),f862(f862(f74(x94211),x94214),x94215))),x94216)))
% 25.54/25.42 [9614]~P120(x96141)+~P118(x96141)+~P1(f862(f862(f278(x96141),x96142),x96145))+P1(f862(f862(f278(x96141),x96142),f862(f862(f73(x96141),x96143),x96144)))+~P1(f862(f862(f278(x96141),x96142),f862(f862(f73(x96141),f862(f862(f3(x96141),x96143),f862(f862(f74(x96141),x96146),x96145))),x96144)))
% 25.54/25.42 [9615]~P120(x96151)+~P118(x96151)+~P1(f862(f862(f278(x96151),x96152),x96155))+P1(f862(f862(f278(x96151),x96152),f862(f862(f73(x96151),x96153),x96154)))+~P1(f862(f862(f278(x96151),x96152),f862(f862(f73(x96151),f862(f862(f3(x96151),x96153),f862(f862(f74(x96151),x96156),x96155))),x96154)))
% 25.54/25.42 [9024]E(x90241,x90242)+~P54(x90244,x90245,x90246,x90243,x90247)+~E(f862(x90243,x90241),f862(x90243,x90242))+~P1(f862(f862(f321(x90245),x90242),x90247))+~P1(f862(f862(f321(x90245),x90241),x90247))
% 25.54/25.42 [9742]~P23(x97421,x97422,x97423,x97425,x97427)+~P23(x97421,x97422,x97423,x97424,x97426)+P23(x97421,x97422,x97423,f862(f862(f103(f932(x97421,a921)),x97424),x97425),f862(f862(f103(f932(x97422,a921)),x97426),x97427))+~E(f862(f862(f94(f932(x97422,a921)),x97426),x97427),f181(f932(x97422,a921)))+~E(f862(f862(f94(f932(x97421,a921)),x97424),x97425),f181(f932(x97421,a921)))
% 25.54/25.42 [10318]~P1(f862(x103182,x103184))+~E(x103185,f862(f129(x103181,x103182),x103187))+E(f862(f129(x103181,x103182),x103183),f862(f862(f144(x103181),x103184),x103185))+~E(x103183,f862(f862(f127(x103181),x103186),f862(f862(f144(x103181),x103184),x103187)))+P1(f862(x103182,f754(x103185,x103184,x103183,x103182,x103181,x103186,x103187)))
% 25.54/25.42 [10319]~P1(f862(x103194,x103192))+~E(x103193,f862(f129(x103191,x103194),x103197))+E(f862(f862(f144(x103191),x103192),x103193),f862(f129(x103191,x103194),x103195))+~E(x103195,f862(f862(f127(x103191),x103196),f862(f862(f144(x103191),x103192),x103197)))+P1(f862(x103194,f755(x103195,x103194,x103193,x103192,x103191,x103196,x103197)))
% 25.54/25.42 [10369]~P1(f862(x103692,x103694))+~E(x103695,f862(f129(x103691,x103692),x103697))+E(f862(f129(x103691,x103692),x103693),f862(f862(f144(x103691),x103694),x103695))+~E(x103693,f862(f862(f127(x103691),x103696),f862(f862(f144(x103691),x103694),x103697)))+P1(f862(f862(f321(x103691),f754(x103695,x103694,x103693,x103692,x103691,x103696,x103697)),f862(f165(x103691),x103696)))
% 25.54/25.42 [10370]~P1(f862(x103704,x103702))+~E(x103703,f862(f129(x103701,x103704),x103707))+E(f862(f862(f144(x103701),x103702),x103703),f862(f129(x103701,x103704),x103705))+~E(x103705,f862(f862(f127(x103701),x103706),f862(f862(f144(x103701),x103702),x103707)))+P1(f862(f862(f321(x103701),f755(x103705,x103704,x103703,x103702,x103701,x103706,x103707)),f862(f165(x103701),x103706)))
% 25.54/25.42 [10374]~P6(x103741,x103747,x103746)+~P9(x103741,f932(x103745,a921),x103746,x103744)+P1(f862(f862(f321(x103741),f532(x103742,x103743,x103744,x103745,x103746,x103747,x103741)),x103747))+~P1(f862(f862(f321(f932(x103741,a921)),x103743),f862(f862(f53(x103741),x103747),x103746)))+P1(f862(f862(f321(f932(x103745,a921)),f862(f862(f33(x103741,f932(x103745,a921)),x103743),x103744)),x103742))
% 25.54/25.42 [10429]~P6(x104292,x104296,x104297)+~P9(x104292,f932(x104291,a921),x104297,x104294)+~P1(f862(f862(f321(f932(x104292,a921)),x104293),f862(f862(f53(x104292),x104296),x104297)))+~P1(f862(f862(f321(f932(x104291,a921)),f862(x104294,f532(x104295,x104293,x104294,x104291,x104297,x104296,x104292))),x104295))+P1(f862(f862(f321(f932(x104291,a921)),f862(f862(f33(x104292,f932(x104291,a921)),x104293),x104294)),x104295))
% 25.54/25.42 [8605]~P71(x86052)+~P22(x86051,x86055,x86058,x86054)+~E(x86053,f862(f66(x86055,x86052,x86051,x86056),x86058))+~E(x86057,f862(f302(x86051,x86055,x86058),x86054))+E(f862(f862(f11(x86051,x86052),x86053),x86054),f862(f862(f11(x86055,x86052),x86056),x86057))
% 25.54/25.42 [10433]~P71(x104332)+~P22(x104335,x104331,x104338,x104337)+~E(f862(x104336,f605(x104333,x104336,x104334,x104337,x104338,x104331,x104335,x104332)),f862(f862(f66(x104331,x104332,x104335,x104333),x104338),f605(x104333,x104336,x104334,x104337,x104338,x104331,x104335,x104332)))+~E(x104334,f862(f302(x104335,x104331,x104338),x104337))+E(f862(f862(f11(x104331,x104332),x104333),x104334),f862(f862(f11(x104335,x104332),x104336),x104337))
% 25.54/25.42 [10436]~P72(x104362)+~P22(x104361,x104365,x104368,x104364)+~E(x104367,f862(f302(x104361,x104365,x104368),x104364))+E(f862(f862(f8(x104361,x104362),x104363),x104364),f862(f862(f8(x104365,x104362),x104366),x104367))+P1(f862(f862(f321(x104361),f619(x104366,x104363,x104367,x104364,x104368,x104365,x104361,x104362)),x104364))
% 25.54/25.42 [10437]~P71(x104372)+~P22(x104371,x104375,x104378,x104374)+~E(x104377,f862(f302(x104371,x104375,x104378),x104374))+E(f862(f862(f11(x104371,x104372),x104373),x104374),f862(f862(f11(x104375,x104372),x104376),x104377))+P1(f862(f862(f321(x104371),f605(x104376,x104373,x104377,x104374,x104378,x104375,x104371,x104372)),x104374))
% 25.54/25.42 [10442]~P72(x104422)+~P22(x104425,x104421,x104428,x104427)+~E(x104424,f862(f302(x104425,x104421,x104428),x104427))+~E(f862(x104426,f619(x104423,x104426,x104424,x104427,x104428,x104421,x104425,x104422)),f862(x104423,f862(x104428,f619(x104423,x104426,x104424,x104427,x104428,x104421,x104425,x104422))))+E(f862(f862(f8(x104421,x104422),x104423),x104424),f862(f862(f8(x104425,x104422),x104426),x104427))
% 25.54/25.42 [9910]~P21(x99106,x99102,x99105,x99107,x99108,x99101)+~P1(f862(f54(x99102),x99104))+~P1(f862(f54(x99102),x99103))+~E(f862(f862(f94(f932(x99102,a921)),x99103),x99104),f181(f932(x99102,a921)))+E(f862(x99101,f862(f862(f103(f932(x99102,a921)),x99103),x99104)),f862(f862(x99105,f862(x99101,x99103)),f862(x99101,x99104)))
% 25.54/25.42 [10304]~P21(x103048,x103042,x103045,x103047,x103046,x103041)+~E(f862(x103046,f908(x103044,x103043,x103041,x103046,x103047,x103045,x103042)),x103047)+~P1(f862(f54(x103042),x103043))+~P1(f862(f54(x103042),x103044))+E(f862(x103041,f862(f862(f103(f932(x103042,a921)),x103043),x103044)),f862(f862(x103045,f862(x103041,x103043)),f862(x103041,x103044)))
% 25.54/25.42 [10381]~P21(x103818,x103812,x103815,x103817,x103816,x103811)+~P1(f862(f54(x103812),x103813))+~P1(f862(f54(x103812),x103814))+E(f862(x103811,f862(f862(f103(f932(x103812,a921)),x103813),x103814)),f862(f862(x103815,f862(x103811,x103813)),f862(x103811,x103814)))+P1(f862(f862(f321(x103812),f908(x103814,x103813,x103811,x103816,x103817,x103815,x103812)),f862(f862(f94(f932(x103812,a921)),x103813),x103814)))
% 25.54/25.42 [10066]~P6(x100664,x100668,x100665)+~P6(x100661,x100669,x100663)+~P10(x100661,x100664,f932(x100662,a921),x100663,x100665,x100667)+P9(x100661,f932(x100662,a921),x100663,f862(f862(f10(f932(x100664,f932(x100662,a921)),f932(x100662,a921),x100661),f862(f33(x100664,f932(x100662,a921)),f862(f276(x100664,x100664,x100665),f862(f862(f301(x100664),x100666),f181(f932(x100664,a921)))))),x100667))+~P1(f862(f862(f321(x100664),x100666),x100668))
% 25.54/25.42 [5603]~P109(x56033)+~P11(x56033,x56031)+E(x56031,f731(x56032,x56033))+~E(f862(f165(x56033),x56031),x56032)+~P1(f862(f54(x56033),x56032))+~P1(f862(f130(x56033),x56031))
% 25.54/25.42 [7447]P13(x74471,x74472)+~E(f862(x74472,f811(x74472)),f862(x74472,f813(x74472)))+~P1(f862(f862(x74472,f811(x74472)),f811(x74472)))+~P1(f862(f862(x74472,f811(x74472)),f813(x74472)))+~P1(f862(f862(x74472,f813(x74472)),f813(x74472)))+~P1(f862(f862(x74472,x74473),x74473))
% 25.54/25.42 [5227]~P133(x52272)+~P134(x52272)+~P145(x52272)+~P116(x52272)+E(x52271,f2(x52272))+~E(f862(f862(f236(x52272),x52271),x52273),f2(x52272))
% 25.54/25.42 [5228]~P133(x52282)+~P134(x52282)+~P145(x52282)+~P116(x52282)+~E(x52281,f2(a924))+~E(f862(f862(f236(x52282),x52283),x52281),f2(x52282))
% 25.54/25.42 [6692]~P87(x66921)+~E(x66923,f2(x66921))+~E(x66922,f2(x66921))+E(f862(f862(f73(x66921),x66922),x66923),f2(x66921))+~P1(f862(f862(f227(x66921),f2(x66921)),x66923))+~P1(f862(f862(f227(x66921),f2(x66921)),x66922))
% 25.54/25.42 [9076]E(x90761,f2(a924))+~E(x90762,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x90763)),x90761)),f862(f248(a924,a924),x90763)))+P1(f862(f41(x90762,x90761),x90763))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x90763)),f2(a924)))+P1(f862(f862(f228(a924),f2(a924)),x90761))+~P1(f862(f862(f228(a924),x90761),f862(f248(a924,a924),x90763)))
% 25.54/25.42 [9094]~E(f862(f243(a924,a924),x90943),f2(a924))+~E(x90941,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x90943)),x90942)),f862(f248(a924,a924),x90943)))+P1(f862(f41(x90941,x90942),x90943))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x90943)),f2(a924)))+P1(f862(f862(f228(a924),f2(a924)),x90942))+~P1(f862(f862(f228(a924),x90942),f862(f248(a924,a924),x90943)))
% 25.54/25.42 [9102]E(x91021,f2(a924))+~E(x91022,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x91023)),x91021)),f862(f248(a924,a924),x91023)))+P1(f862(f41(x91022,x91021),x91023))+~P1(f862(f862(f228(a924),f2(a924)),x91021))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x91023)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x91023)),x91021))
% 25.54/25.42 [9120]~E(f862(f243(a924,a924),x91203),f2(a924))+~E(x91201,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x91203)),x91202)),f862(f248(a924,a924),x91203)))+P1(f862(f41(x91201,x91202),x91203))+~P1(f862(f862(f228(a924),f2(a924)),x91202))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x91203)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x91203)),x91202))
% 25.54/25.42 [7072]~P93(x70722)+E(x70721,f181(f932(x70722,a921)))+E(x70723,f181(f932(x70722,a921)))+~P1(f862(f54(x70722),x70721))+~P1(f862(f54(x70722),x70723))+E(f12(x70722,f862(f862(f103(f932(x70722,a921)),x70723),x70721)),f862(f862(f94(x70722),f12(x70722,x70723)),f12(x70722,x70721)))
% 25.54/25.42 [7073]~P93(x70732)+E(x70731,f181(f932(x70732,a921)))+E(x70733,f181(f932(x70732,a921)))+~P1(f862(f54(x70732),x70731))+~P1(f862(f54(x70732),x70733))+E(f15(x70732,f862(f862(f103(f932(x70732,a921)),x70733),x70731)),f862(f862(f103(x70732),f15(x70732,x70733)),f15(x70732,x70731)))
% 25.54/25.42 [7074]~P109(x70742)+E(x70741,f181(f932(x70742,a921)))+E(x70743,f181(f932(x70742,a921)))+~P1(f862(f54(x70742),x70741))+~P1(f862(f54(x70742),x70743))+E(f16(x70742,f862(f862(f103(f932(x70742,a921)),x70743),x70741)),f862(f862(f225(x70742),f16(x70742,x70743)),f16(x70742,x70741)))
% 25.54/25.42 [7075]~P109(x70752)+E(x70751,f181(f932(x70752,a921)))+E(x70753,f181(f932(x70752,a921)))+~P1(f862(f54(x70752),x70751))+~P1(f862(f54(x70752),x70753))+E(f17(x70752,f862(f862(f103(f932(x70752,a921)),x70753),x70751)),f862(f862(f226(x70752),f17(x70752,x70753)),f17(x70752,x70751)))
% 25.54/25.42 [7718]~P100(x77182)+E(x77181,f181(f932(x77182,a921)))+E(x77183,f181(f932(x77182,a921)))+~P1(f862(f54(x77182),x77181))+~P1(f862(f54(x77182),x77183))+E(f862(f862(f74(x77182),f862(f56(x77182,f74(x77182)),x77183)),f862(f56(x77182,f74(x77182)),x77181)),f862(f56(x77182,f74(x77182)),f862(f862(f103(f932(x77182,a921)),x77183),x77181)))
% 25.54/25.42 [7881]~P109(x78812)+E(x78811,f181(f932(x78812,a921)))+E(x78813,f181(f932(x78812,a921)))+~P1(f862(f54(x78812),x78811))+~P1(f862(f54(x78812),x78813))+E(f862(f862(f225(x78812),f13(x78812,f225(x78812),x78813)),f13(x78812,f225(x78812),x78811)),f13(x78812,f225(x78812),f862(f862(f103(f932(x78812,a921)),x78813),x78811)))
% 25.54/25.42 [7882]~P109(x78822)+E(x78821,f181(f932(x78822,a921)))+E(x78823,f181(f932(x78822,a921)))+~P1(f862(f54(x78822),x78821))+~P1(f862(f54(x78822),x78823))+E(f862(f862(f226(x78822),f14(x78822,f226(x78822),x78823)),f14(x78822,f226(x78822),x78821)),f14(x78822,f226(x78822),f862(f862(f103(f932(x78822,a921)),x78823),x78821)))
% 25.54/25.42 [8925]~P1(f862(x89251,x89253))+P1(f862(x89251,f392(x89251,x89252)))+P1(f862(x89251,f387(x89251,x89252)))+~P1(f862(f862(f228(a1),f2(a1)),x89252))+~P1(f862(f862(f321(a1),x89253),f296(a1,f71(a1),x89252)))+P1(f862(x89251,f862(f862(f3(a1),f387(x89251,x89252)),f862(f862(f74(a1),f389(x89251,x89252)),x89252))))
% 25.54/25.42 [9228]~P1(f862(x92281,x92283))+~P1(f862(x92281,f387(x92281,x92282)))+P1(f862(x92281,f392(x92281,x92282)))+~P1(f862(f862(f228(a1),f2(a1)),x92282))+~P1(f862(f862(f321(a1),x92283),f296(a1,f71(a1),x92282)))+~P1(f862(x92281,f862(f862(f3(a1),f387(x92281,x92282)),f862(f862(f74(a1),f389(x92281,x92282)),x92282))))
% 25.54/25.42 [10469]~P102(x104692)+E(x104691,f181(f932(x104692,a921)))+E(x104693,f181(f932(x104692,a921)))+~P1(f862(f54(x104692),x104691))+~P1(f862(f54(x104692),x104693))+E(f12(x104692,f862(f254(x104692),f862(f862(f10(f932(x104692,a921),a921,x104692),f80(x104692)),f862(f862(f10(f932(x104692,f932(x104692,a921)),f932(x104692,a921),x104692),f862(f10(f932(x104692,a921),a921,x104692),f80(x104692))),f862(f862(f9(x104692,f932(x104692,f932(x104692,a921)),f932(x104692,f932(x104692,a921))),f862(f862(f10(f932(x104692,f932(f932(x104692,a921),f932(x104692,a921))),f932(f932(x104692,f932(x104692,a921)),f932(x104692,f932(x104692,a921))),x104692),f20(x104692,f932(x104692,a921),f932(x104692,a921))),f862(f862(f10(f932(x104692,f932(x104692,f932(a921,a921))),f932(x104692,f932(f932(x104692,a921),f932(x104692,a921))),x104692),f862(f10(f932(x104692,f932(a921,a921)),f932(f932(x104692,a921),f932(x104692,a921)),x104692),f20(x104692,a921,a921))),f862(f862(f10(f932(x104692,f932(x104692,a921)),f932(x104692,f932(x104692,f932(a921,a921))),x104692),f862(f10(f932(x104692,a921),f932(x104692,f932(a921,a921)),x104692),f862(f10(a921,f932(a921,a921),x104692),a318))),f862(f862(f9(x104692,f932(x104692,f932(x104692,x104692)),f932(x104692,f932(x104692,a921))),f862(f862(f10(f932(f932(x104692,x104692),f932(x104692,a921)),f932(f932(x104692,f932(x104692,x104692)),f932(x104692,f932(x104692,a921))),x104692),f10(f932(x104692,x104692),f932(x104692,a921),x104692)),f862(f862(f10(f932(x104692,a921),f932(f932(x104692,x104692),f932(x104692,a921)),x104692),f10(x104692,a921,x104692)),a317))),f103(x104692)))))),f862(f862(f9(x104692,f932(x104692,a921),f932(x104692,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104692,a921),f932(x104692,a921)),x104692),f10(a921,a921,x104692)),f862(f862(f10(a921,f932(a921,a921),x104692),a318),f862(f862(f9(x104692,f932(x104692,a921),a921),f321(x104692)),x104693)))),f862(f862(f9(x104692,f932(x104692,a921),a921),f321(x104692)),x104691))))))),f862(f862(f103(x104692),f12(x104692,x104693)),f12(x104692,x104691)))
% 25.54/25.42 [10470]~P102(x104702)+E(x104701,f181(f932(x104702,a921)))+E(x104703,f181(f932(x104702,a921)))+~P1(f862(f54(x104702),x104701))+~P1(f862(f54(x104702),x104703))+E(f15(x104702,f862(f254(x104702),f862(f862(f10(f932(x104702,a921),a921,x104702),f80(x104702)),f862(f862(f10(f932(x104702,f932(x104702,a921)),f932(x104702,a921),x104702),f862(f10(f932(x104702,a921),a921,x104702),f80(x104702))),f862(f862(f9(x104702,f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,a921))),f862(f862(f10(f932(x104702,f932(f932(x104702,a921),f932(x104702,a921))),f932(f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,a921))),x104702),f20(x104702,f932(x104702,a921),f932(x104702,a921))),f862(f862(f10(f932(x104702,f932(x104702,f932(a921,a921))),f932(x104702,f932(f932(x104702,a921),f932(x104702,a921))),x104702),f862(f10(f932(x104702,f932(a921,a921)),f932(f932(x104702,a921),f932(x104702,a921)),x104702),f20(x104702,a921,a921))),f862(f862(f10(f932(x104702,f932(x104702,a921)),f932(x104702,f932(x104702,f932(a921,a921))),x104702),f862(f10(f932(x104702,a921),f932(x104702,f932(a921,a921)),x104702),f862(f10(a921,f932(a921,a921),x104702),a318))),f862(f862(f9(x104702,f932(x104702,f932(x104702,x104702)),f932(x104702,f932(x104702,a921))),f862(f862(f10(f932(f932(x104702,x104702),f932(x104702,a921)),f932(f932(x104702,f932(x104702,x104702)),f932(x104702,f932(x104702,a921))),x104702),f10(f932(x104702,x104702),f932(x104702,a921),x104702)),f862(f862(f10(f932(x104702,a921),f932(f932(x104702,x104702),f932(x104702,a921)),x104702),f10(x104702,a921,x104702)),a317))),f94(x104702)))))),f862(f862(f9(x104702,f932(x104702,a921),f932(x104702,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104702,a921),f932(x104702,a921)),x104702),f10(a921,a921,x104702)),f862(f862(f10(a921,f932(a921,a921),x104702),a318),f862(f862(f9(x104702,f932(x104702,a921),a921),f321(x104702)),x104703)))),f862(f862(f9(x104702,f932(x104702,a921),a921),f321(x104702)),x104701))))))),f862(f862(f94(x104702),f15(x104702,x104703)),f15(x104702,x104701)))
% 25.54/25.42 [10471]~P109(x104712)+E(x104711,f181(f932(x104712,a921)))+E(x104713,f181(f932(x104712,a921)))+~P1(f862(f54(x104712),x104711))+~P1(f862(f54(x104712),x104713))+E(f14(x104712,f226(x104712),f862(f254(x104712),f862(f862(f10(f932(x104712,a921),a921,x104712),f80(x104712)),f862(f862(f10(f932(x104712,f932(x104712,a921)),f932(x104712,a921),x104712),f862(f10(f932(x104712,a921),a921,x104712),f80(x104712))),f862(f862(f9(x104712,f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,a921))),f862(f862(f10(f932(x104712,f932(f932(x104712,a921),f932(x104712,a921))),f932(f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,a921))),x104712),f20(x104712,f932(x104712,a921),f932(x104712,a921))),f862(f862(f10(f932(x104712,f932(x104712,f932(a921,a921))),f932(x104712,f932(f932(x104712,a921),f932(x104712,a921))),x104712),f862(f10(f932(x104712,f932(a921,a921)),f932(f932(x104712,a921),f932(x104712,a921)),x104712),f20(x104712,a921,a921))),f862(f862(f10(f932(x104712,f932(x104712,a921)),f932(x104712,f932(x104712,f932(a921,a921))),x104712),f862(f10(f932(x104712,a921),f932(x104712,f932(a921,a921)),x104712),f862(f10(a921,f932(a921,a921),x104712),a318))),f862(f862(f9(x104712,f932(x104712,f932(x104712,x104712)),f932(x104712,f932(x104712,a921))),f862(f862(f10(f932(f932(x104712,x104712),f932(x104712,a921)),f932(f932(x104712,f932(x104712,x104712)),f932(x104712,f932(x104712,a921))),x104712),f10(f932(x104712,x104712),f932(x104712,a921),x104712)),f862(f862(f10(f932(x104712,a921),f932(f932(x104712,x104712),f932(x104712,a921)),x104712),f10(x104712,a921,x104712)),a317))),f225(x104712)))))),f862(f862(f9(x104712,f932(x104712,a921),f932(x104712,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104712,a921),f932(x104712,a921)),x104712),f10(a921,a921,x104712)),f862(f862(f10(a921,f932(a921,a921),x104712),a318),f862(f862(f9(x104712,f932(x104712,a921),a921),f321(x104712)),x104713)))),f862(f862(f9(x104712,f932(x104712,a921),a921),f321(x104712)),x104711))))))),f862(f862(f225(x104712),f14(x104712,f226(x104712),x104713)),f14(x104712,f226(x104712),x104711)))
% 25.54/25.42 [10472]~P109(x104722)+E(x104721,f181(f932(x104722,a921)))+E(x104723,f181(f932(x104722,a921)))+~P1(f862(f54(x104722),x104721))+~P1(f862(f54(x104722),x104723))+E(f13(x104722,f225(x104722),f862(f254(x104722),f862(f862(f10(f932(x104722,a921),a921,x104722),f80(x104722)),f862(f862(f10(f932(x104722,f932(x104722,a921)),f932(x104722,a921),x104722),f862(f10(f932(x104722,a921),a921,x104722),f80(x104722))),f862(f862(f9(x104722,f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,a921))),f862(f862(f10(f932(x104722,f932(f932(x104722,a921),f932(x104722,a921))),f932(f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,a921))),x104722),f20(x104722,f932(x104722,a921),f932(x104722,a921))),f862(f862(f10(f932(x104722,f932(x104722,f932(a921,a921))),f932(x104722,f932(f932(x104722,a921),f932(x104722,a921))),x104722),f862(f10(f932(x104722,f932(a921,a921)),f932(f932(x104722,a921),f932(x104722,a921)),x104722),f20(x104722,a921,a921))),f862(f862(f10(f932(x104722,f932(x104722,a921)),f932(x104722,f932(x104722,f932(a921,a921))),x104722),f862(f10(f932(x104722,a921),f932(x104722,f932(a921,a921)),x104722),f862(f10(a921,f932(a921,a921),x104722),a318))),f862(f862(f9(x104722,f932(x104722,f932(x104722,x104722)),f932(x104722,f932(x104722,a921))),f862(f862(f10(f932(f932(x104722,x104722),f932(x104722,a921)),f932(f932(x104722,f932(x104722,x104722)),f932(x104722,f932(x104722,a921))),x104722),f10(f932(x104722,x104722),f932(x104722,a921),x104722)),f862(f862(f10(f932(x104722,a921),f932(f932(x104722,x104722),f932(x104722,a921)),x104722),f10(x104722,a921,x104722)),a317))),f226(x104722)))))),f862(f862(f9(x104722,f932(x104722,a921),f932(x104722,a921)),f862(f862(f10(f932(a921,a921),f932(f932(x104722,a921),f932(x104722,a921)),x104722),f10(a921,a921,x104722)),f862(f862(f10(a921,f932(a921,a921),x104722),a318),f862(f862(f9(x104722,f932(x104722,a921),a921),f321(x104722)),x104723)))),f862(f862(f9(x104722,f932(x104722,a921),a921),f321(x104722)),x104721))))))),f862(f862(f226(x104722),f13(x104722,f225(x104722),x104723)),f13(x104722,f225(x104722),x104721)))
% 25.54/25.42 [7402]~P127(x74023)+E(x74021,x74022)+~E(f862(f862(f236(x74023),x74021),x74024),f862(f862(f236(x74023),x74022),x74024))+~P1(f862(f862(f227(x74023),f2(x74023)),x74022))+~P1(f862(f862(f227(x74023),f2(x74023)),x74021))+~P1(f862(f862(f228(a924),f2(a924)),x74024))
% 25.54/25.42 [8233]~P66(x82331)+~P99(x82331)+P1(f862(f862(f228(x82331),x82332),f2(x82331)))+P1(f862(f862(f228(x82331),f2(x82331)),x82332))+P1(f862(f862(f227(x82331),f862(f862(f281(x82331),x82333),x82332)),f862(f96(x82331),x82334)))+~P1(f862(f862(f227(x82331),f2(x82331)),f862(f96(x82331),x82334)))
% 25.54/25.42 [8234]~P66(x82341)+~P99(x82341)+P1(f862(f862(f228(x82341),x82342),f2(x82341)))+P1(f862(f862(f228(x82341),f2(x82341)),x82342))+P1(f862(f862(f228(x82341),f862(f862(f281(x82341),x82343),x82342)),f862(f96(x82341),x82344)))+~P1(f862(f862(f228(x82341),f2(x82341)),f862(f96(x82341),x82344)))
% 25.54/25.42 [8479]~P66(x84791)+~P99(x84791)+P1(f862(f862(f228(x84791),x84792),f2(x84791)))+P1(f862(f862(f228(x84791),f2(x84791)),x84792))+~P1(f862(f862(f227(x84791),f862(f862(f281(x84791),x84794),x84792)),f862(f96(x84791),x84793)))+P1(f862(f862(f227(x84791),f2(x84791)),f862(f96(x84791),x84793)))
% 25.54/25.42 [8480]~P66(x84801)+~P99(x84801)+P1(f862(f862(f228(x84801),x84802),f2(x84801)))+P1(f862(f862(f228(x84801),f2(x84801)),x84802))+~P1(f862(f862(f228(x84801),f862(f862(f281(x84801),x84804),x84802)),f862(f96(x84801),x84803)))+P1(f862(f862(f228(x84801),f2(x84801)),f862(f96(x84801),x84803)))
% 25.54/25.42 [7678]~P109(x76782)+E(x76781,f181(f932(x76782,a921)))+~P1(f862(f54(x76782),x76781))+~P1(f862(f862(f321(x76782),x76784),x76781))+P1(f862(f862(f227(x76782),x76783),x76784))+~P1(f862(f862(f227(x76782),x76783),f862(f56(x76782,f225(x76782)),x76781)))
% 25.54/25.42 [7679]~P104(x76792)+E(x76791,f181(f932(x76792,a921)))+~P1(f862(f54(x76792),x76791))+~P1(f862(f862(f321(x76792),x76794),x76791))+P1(f862(f862(f227(x76792),x76793),x76794))+~P1(f862(f862(f227(x76792),x76793),f862(f56(x76792,f94(x76792)),x76791)))
% 25.54/25.42 [7680]~P109(x76802)+E(x76801,f181(f932(x76802,a921)))+~P1(f862(f54(x76802),x76801))+~P1(f862(f862(f321(x76802),x76804),x76801))+P1(f862(f862(f228(x76802),x76803),x76804))+~P1(f862(f862(f228(x76802),x76803),f862(f56(x76802,f225(x76802)),x76801)))
% 25.54/25.42 [8187]~P66(x81871)+~P99(x81871)+P1(f862(f862(f228(x81871),f862(f96(x81871),x81872)),f2(x81871)))+~P1(f862(f862(f227(x81871),x81873),f2(x81871)))+P1(f862(f862(f228(x81871),f2(x81871)),f862(f96(x81871),x81872)))+P1(f862(f862(f227(x81871),x81873),f862(f862(f281(x81871),x81874),f862(f96(x81871),x81872))))
% 25.54/25.42 [8188]~P66(x81881)+~P99(x81881)+P1(f862(f862(f228(x81881),f862(f96(x81881),x81882)),f2(x81881)))+~P1(f862(f862(f228(x81881),x81883),f2(x81881)))+P1(f862(f862(f228(x81881),f2(x81881)),f862(f96(x81881),x81882)))+P1(f862(f862(f228(x81881),x81883),f862(f862(f281(x81881),x81884),f862(f96(x81881),x81882))))
% 25.54/25.42 [8201]~P66(x82011)+~P99(x82011)+P1(f862(f862(f228(x82011),x82012),f2(x82011)))+~P1(f862(f862(f227(x82011),f862(f96(x82011),x82013)),f2(x82011)))+P1(f862(f862(f228(x82011),f2(x82011)),x82012))+P1(f862(f862(f227(x82011),f862(f96(x82011),x82013)),f862(f862(f281(x82011),x82014),x82012)))
% 25.54/25.42 [8202]~P66(x82021)+~P99(x82021)+P1(f862(f862(f228(x82021),x82022),f2(x82021)))+~P1(f862(f862(f228(x82021),f862(f96(x82021),x82023)),f2(x82021)))+P1(f862(f862(f228(x82021),f2(x82021)),x82022))+P1(f862(f862(f228(x82021),f862(f96(x82021),x82023)),f862(f862(f281(x82021),x82024),x82022)))
% 25.54/25.42 [8353]~P66(x83531)+~P99(x83531)+P1(f862(f862(f228(x83531),x83532),f2(x83531)))+P1(f862(f862(f227(x83531),f862(f96(x83531),x83533)),f2(x83531)))+P1(f862(f862(f228(x83531),f2(x83531)),x83532))+~P1(f862(f862(f227(x83531),f862(f96(x83531),x83533)),f862(f862(f281(x83531),x83534),x83532)))
% 25.54/25.42 [8354]~P66(x83541)+~P99(x83541)+P1(f862(f862(f228(x83541),x83542),f2(x83541)))+P1(f862(f862(f228(x83541),f862(f96(x83541),x83543)),f2(x83541)))+P1(f862(f862(f228(x83541),f2(x83541)),x83542))+~P1(f862(f862(f228(x83541),f862(f96(x83541),x83543)),f862(f862(f281(x83541),x83544),x83542)))
% 25.54/25.42 [8426]~P66(x84261)+~P99(x84261)+P1(f862(f862(f227(x84261),x84262),f2(x84261)))+P1(f862(f862(f228(x84261),f862(f96(x84261),x84263)),f2(x84261)))+P1(f862(f862(f228(x84261),f2(x84261)),f862(f96(x84261),x84263)))+~P1(f862(f862(f227(x84261),x84262),f862(f862(f281(x84261),x84264),f862(f96(x84261),x84263))))
% 25.54/25.42 [8427]~P66(x84271)+~P99(x84271)+P1(f862(f862(f228(x84271),x84272),f2(x84271)))+P1(f862(f862(f228(x84271),f862(f96(x84271),x84273)),f2(x84271)))+P1(f862(f862(f228(x84271),f2(x84271)),f862(f96(x84271),x84273)))+~P1(f862(f862(f228(x84271),x84272),f862(f862(f281(x84271),x84274),f862(f96(x84271),x84273))))
% 25.54/25.42 [8620]~P66(x86201)+~P99(x86201)+~P1(f862(f862(f227(x86201),x86203),f2(x86201)))+P1(f862(f862(f228(x86201),f2(x86201)),f862(f96(x86201),x86202)))+~P1(f862(f862(f227(x86201),x86204),f862(f862(f74(x86201),x86203),f862(f96(x86201),x86202))))+P1(f862(f862(f227(x86201),x86203),f862(f862(f281(x86201),x86204),f862(f96(x86201),x86202))))
% 25.54/25.42 [8621]~P66(x86211)+~P99(x86211)+~P1(f862(f862(f228(x86211),x86213),f2(x86211)))+P1(f862(f862(f228(x86211),f2(x86211)),f862(f96(x86211),x86212)))+~P1(f862(f862(f228(x86211),x86214),f862(f862(f74(x86211),x86213),f862(f96(x86211),x86212))))+P1(f862(f862(f228(x86211),x86213),f862(f862(f281(x86211),x86214),f862(f96(x86211),x86212))))
% 25.54/25.42 [8789]~P66(x87891)+~P99(x87891)+~P1(f862(f862(f228(x87891),f862(f96(x87891),x87892)),f2(x87891)))+P1(f862(f862(f228(x87891),f2(x87891)),f862(f96(x87891),x87892)))+~P1(f862(f862(f227(x87891),x87894),f862(f862(f74(x87891),x87893),f862(f96(x87891),x87892))))+P1(f862(f862(f227(x87891),x87893),f862(f862(f281(x87891),x87894),f862(f96(x87891),x87892))))
% 25.54/25.42 [8790]~P66(x87901)+~P99(x87901)+~P1(f862(f862(f228(x87901),f862(f96(x87901),x87902)),f2(x87901)))+P1(f862(f862(f228(x87901),f2(x87901)),f862(f96(x87901),x87902)))+~P1(f862(f862(f227(x87901),x87904),f862(f862(f281(x87901),x87903),f862(f96(x87901),x87902))))+P1(f862(f862(f227(x87901),x87903),f862(f862(f74(x87901),x87904),f862(f96(x87901),x87902))))
% 25.54/25.42 [8791]~P66(x87911)+~P99(x87911)+~P1(f862(f862(f228(x87911),f862(f96(x87911),x87912)),f2(x87911)))+P1(f862(f862(f228(x87911),f2(x87911)),f862(f96(x87911),x87912)))+~P1(f862(f862(f228(x87911),x87914),f862(f862(f74(x87911),x87913),f862(f96(x87911),x87912))))+P1(f862(f862(f228(x87911),x87913),f862(f862(f281(x87911),x87914),f862(f96(x87911),x87912))))
% 25.54/25.42 [8792]~P66(x87921)+~P99(x87921)+~P1(f862(f862(f228(x87921),f862(f96(x87921),x87922)),f2(x87921)))+P1(f862(f862(f228(x87921),f2(x87921)),f862(f96(x87921),x87922)))+~P1(f862(f862(f228(x87921),x87924),f862(f862(f281(x87921),x87923),f862(f96(x87921),x87922))))+P1(f862(f862(f228(x87921),x87923),f862(f862(f74(x87921),x87924),f862(f96(x87921),x87922))))
% 25.54/25.42 [7584]E(x75841,f2(a1))+E(f862(f862(f29(a1),x75842),x75841),x75843)+~P1(f862(f862(f227(a1),x75844),f2(a1)))+~E(x75842,f862(f862(f73(a1),f862(f862(f74(a1),x75841),x75843)),x75844))+P1(f862(f862(f228(a1),f2(a1)),x75841))+~P1(f862(f862(f228(a1),x75841),x75844))
% 25.54/25.42 [7602]E(f38(a1,x76022,x76021),x76023)+E(x76021,f2(a1))+~P1(f862(f862(f227(a1),x76023),f2(a1)))+~E(x76022,f862(f862(f73(a1),f862(f862(f74(a1),x76021),x76024)),x76023))+P1(f862(f862(f228(a1),f2(a1)),x76021))+~P1(f862(f862(f228(a1),x76021),x76023))
% 25.54/25.42 [7717]E(x77171,f2(a1))+E(f862(f862(f29(a1),x77172),x77171),x77173)+~E(x77172,f862(f862(f73(a1),f862(f862(f74(a1),x77171),x77173)),x77174))+~P1(f862(f862(f227(a1),f2(a1)),x77174))+~P1(f862(f862(f228(a1),f2(a1)),x77171))+~P1(f862(f862(f228(a1),x77174),x77171))
% 25.54/25.42 [7740]E(f38(a1,x77402,x77401),x77403)+E(x77401,f2(a1))+~E(x77402,f862(f862(f73(a1),f862(f862(f74(a1),x77401),x77404)),x77403))+~P1(f862(f862(f227(a1),f2(a1)),x77403))+~P1(f862(f862(f228(a1),f2(a1)),x77401))+~P1(f862(f862(f228(a1),x77403),x77401))
% 25.54/25.42 [7885]~P109(x78852)+E(x78851,f181(f932(x78852,a921)))+~P1(f862(f54(x78852),x78851))+~P1(f862(f862(f227(x78852),x78854),x78853))+~P1(f862(f862(f321(x78852),x78854),x78851))+P1(f862(f862(f227(x78852),f862(f56(x78852,f225(x78852)),x78851)),x78853))
% 25.54/25.42 [7886]~P109(x78862)+E(x78861,f181(f932(x78862,a921)))+~P1(f862(f54(x78862),x78861))+~P1(f862(f862(f228(x78862),x78864),x78863))+~P1(f862(f862(f321(x78862),x78864),x78861))+P1(f862(f862(f228(x78862),f862(f56(x78862,f225(x78862)),x78861)),x78863))
% 25.54/25.42 [8456]~P1(f862(f862(f227(a1),x84564),f2(a1)))+~E(x84561,f862(f862(f73(a1),f862(f862(f74(a1),x84562),x84563)),x84564))+~P1(f862(f862(f227(a1),f2(a1)),x84564))+~P1(f862(f862(f228(a1),x84564),x84562))+~P1(f862(f862(f228(a1),x84562),x84564))+P1(f862(f42(x84561,x84562),f862(f862(f244(a1,a1),x84563),x84564)))
% 25.54/25.42 [8581]~P66(x85811)+~P99(x85811)+P1(f862(f862(f228(x85811),f862(f96(x85811),x85812)),f2(x85811)))+~P1(f862(f862(f227(x85811),f2(x85811)),x85814))+P1(f862(f862(f228(x85811),f2(x85811)),f862(f96(x85811),x85812)))+P1(f862(f862(f227(x85811),f862(f862(f281(x85811),x85813),f862(f96(x85811),x85812))),x85814))
% 25.54/25.42 [8582]~P66(x85821)+~P99(x85821)+P1(f862(f862(f228(x85821),f862(f96(x85821),x85822)),f2(x85821)))+~P1(f862(f862(f228(x85821),f2(x85821)),x85824))+P1(f862(f862(f228(x85821),f2(x85821)),f862(f96(x85821),x85822)))+P1(f862(f862(f228(x85821),f862(f862(f281(x85821),x85823),f862(f96(x85821),x85822))),x85824))
% 25.54/25.42 [8695]~P66(x86951)+~P99(x86951)+~P1(f862(f862(f228(x86951),x86952),f2(x86951)))+P1(f862(f862(f228(x86951),f2(x86951)),x86952))+~P1(f862(f862(f227(x86951),f862(f96(x86951),x86954)),f862(f862(f281(x86951),x86953),x86952)))+P1(f862(f862(f227(x86951),x86953),f862(f862(f74(x86951),f862(f96(x86951),x86954)),x86952)))
% 25.54/25.42 [8696]~P66(x86961)+~P99(x86961)+~P1(f862(f862(f228(x86961),x86962),f2(x86961)))+P1(f862(f862(f228(x86961),f2(x86961)),x86962))+~P1(f862(f862(f228(x86961),f862(f96(x86961),x86964)),f862(f862(f281(x86961),x86963),x86962)))+P1(f862(f862(f228(x86961),x86963),f862(f862(f74(x86961),f862(f96(x86961),x86964)),x86962)))
% 25.54/25.42 [8733]~P66(x87331)+~P99(x87331)+~P1(f862(f862(f228(x87331),x87332),f2(x87331)))+P1(f862(f862(f228(x87331),f2(x87331)),x87332))+P1(f862(f862(f227(x87331),f862(f96(x87331),x87333)),f862(f862(f281(x87331),x87334),x87332)))+~P1(f862(f862(f227(x87331),x87334),f862(f862(f74(x87331),f862(f96(x87331),x87333)),x87332)))
% 25.54/25.42 [8734]~P66(x87341)+~P99(x87341)+~P1(f862(f862(f228(x87341),x87342),f2(x87341)))+P1(f862(f862(f228(x87341),f2(x87341)),x87342))+P1(f862(f862(f228(x87341),f862(f96(x87341),x87343)),f862(f862(f281(x87341),x87344),x87342)))+~P1(f862(f862(f228(x87341),x87344),f862(f862(f74(x87341),f862(f96(x87341),x87343)),x87342)))
% 25.54/25.42 [8829]~P66(x88291)+~P99(x88291)+P1(f862(f862(f228(x88291),f862(f96(x88291),x88293)),f2(x88291)))+P1(f862(f862(f227(x88291),f2(x88291)),x88292))+P1(f862(f862(f228(x88291),f2(x88291)),f862(f96(x88291),x88293)))+~P1(f862(f862(f227(x88291),f862(f862(f281(x88291),x88294),f862(f96(x88291),x88293))),x88292))
% 25.54/25.42 [8830]~P66(x88301)+~P99(x88301)+P1(f862(f862(f228(x88301),f862(f96(x88301),x88303)),f2(x88301)))+P1(f862(f862(f228(x88301),f2(x88301)),x88302))+P1(f862(f862(f228(x88301),f2(x88301)),f862(f96(x88301),x88303)))+~P1(f862(f862(f228(x88301),f862(f862(f281(x88301),x88304),f862(f96(x88301),x88303))),x88302))
% 25.54/25.42 [8881]~P66(x88811)+~P99(x88811)+~P1(f862(f862(f227(x88811),f862(f96(x88811),x88813)),f2(x88811)))+P1(f862(f862(f228(x88811),f2(x88811)),x88812))+P1(f862(f862(f227(x88811),f862(f96(x88811),x88813)),f862(f862(f281(x88811),x88814),x88812)))+~P1(f862(f862(f227(x88811),x88814),f862(f862(f74(x88811),f862(f96(x88811),x88813)),x88812)))
% 25.54/25.42 [8882]~P66(x88821)+~P99(x88821)+~P1(f862(f862(f228(x88821),f862(f96(x88821),x88823)),f2(x88821)))+P1(f862(f862(f228(x88821),f2(x88821)),x88822))+P1(f862(f862(f228(x88821),f862(f96(x88821),x88823)),f862(f862(f281(x88821),x88824),x88822)))+~P1(f862(f862(f228(x88821),x88824),f862(f862(f74(x88821),f862(f96(x88821),x88823)),x88822)))
% 25.54/25.42 [8890]~P66(x88901)+~P99(x88901)+P1(f862(f862(f228(x88901),x88902),f2(x88901)))+P1(f862(f862(f227(x88901),f862(f862(f281(x88901),x88903),x88902)),f862(f96(x88901),x88904)))+~P1(f862(f862(f227(x88901),f2(x88901)),f862(f96(x88901),x88904)))+~P1(f862(f862(f227(x88901),x88903),f862(f862(f74(x88901),f862(f96(x88901),x88904)),x88902)))
% 25.54/25.42 [8891]~P66(x88911)+~P99(x88911)+P1(f862(f862(f228(x88911),x88912),f2(x88911)))+P1(f862(f862(f228(x88911),f862(f862(f281(x88911),x88913),x88912)),f862(f96(x88911),x88914)))+~P1(f862(f862(f228(x88911),f2(x88911)),f862(f96(x88911),x88914)))+~P1(f862(f862(f228(x88911),x88913),f862(f862(f74(x88911),f862(f96(x88911),x88914)),x88912)))
% 25.54/25.42 [8912]~P66(x89121)+~P99(x89121)+P1(f862(f862(f228(x89121),f862(f96(x89121),x89122)),f2(x89121)))+~P1(f862(f862(f227(x89121),f2(x89121)),x89124))+~P1(f862(f862(f227(x89121),x89123),f862(f862(f74(x89121),x89124),f862(f96(x89121),x89122))))+P1(f862(f862(f227(x89121),f862(f862(f281(x89121),x89123),f862(f96(x89121),x89122))),x89124))
% 25.54/25.42 [8913]~P66(x89131)+~P99(x89131)+P1(f862(f862(f228(x89131),f862(f96(x89131),x89132)),f2(x89131)))+~P1(f862(f862(f228(x89131),f2(x89131)),x89134))+~P1(f862(f862(f228(x89131),x89133),f862(f862(f74(x89131),x89134),f862(f96(x89131),x89132))))+P1(f862(f862(f228(x89131),f862(f862(f281(x89131),x89133),f862(f96(x89131),x89132))),x89134))
% 25.54/25.42 [9005]~P66(x90051)+~P99(x90051)+P1(f862(f862(f228(x90051),f862(f96(x90051),x90052)),f2(x90051)))+~P1(f862(f862(f227(x90051),x90053),f2(x90051)))+P1(f862(f862(f227(x90051),x90053),f862(f862(f281(x90051),x90054),f862(f96(x90051),x90052))))+~P1(f862(f862(f227(x90051),f862(f862(f74(x90051),x90053),f862(f96(x90051),x90052))),x90054))
% 25.54/25.42 [9006]~P66(x90061)+~P99(x90061)+P1(f862(f862(f228(x90061),f862(f96(x90061),x90062)),f2(x90061)))+~P1(f862(f862(f228(x90061),x90063),f2(x90061)))+P1(f862(f862(f228(x90061),x90063),f862(f862(f281(x90061),x90064),f862(f96(x90061),x90062))))+~P1(f862(f862(f228(x90061),f862(f862(f74(x90061),x90063),f862(f96(x90061),x90062))),x90064))
% 25.54/25.42 [9125]~P66(x91251)+~P99(x91251)+~P1(f862(f862(f227(x91251),f2(x91251)),x91254))+P1(f862(f862(f228(x91251),f2(x91251)),f862(f96(x91251),x91252)))+~P1(f862(f862(f227(x91251),f862(f862(f74(x91251),x91254),f862(f96(x91251),x91252))),x91253))+P1(f862(f862(f227(x91251),f862(f862(f281(x91251),x91253),f862(f96(x91251),x91252))),x91254))
% 25.54/25.42 [9126]~P66(x91261)+~P99(x91261)+~P1(f862(f862(f228(x91261),f2(x91261)),x91264))+P1(f862(f862(f228(x91261),f2(x91261)),f862(f96(x91261),x91262)))+~P1(f862(f862(f228(x91261),f862(f862(f74(x91261),x91264),f862(f96(x91261),x91262))),x91263))+P1(f862(f862(f228(x91261),f862(f862(f281(x91261),x91263),f862(f96(x91261),x91262))),x91264))
% 25.54/25.42 [9182]~P66(x91821)+~P99(x91821)+~P1(f862(f862(f227(x91821),x91822),f2(x91821)))+P1(f862(f862(f227(x91821),x91822),f862(f862(f281(x91821),x91823),f862(f96(x91821),x91824))))+~P1(f862(f862(f227(x91821),x91823),f862(f862(f74(x91821),x91822),f862(f96(x91821),x91824))))+~P1(f862(f862(f227(x91821),f862(f862(f74(x91821),x91822),f862(f96(x91821),x91824))),x91823))
% 25.54/25.42 [9183]~P66(x91831)+~P99(x91831)+~P1(f862(f862(f228(x91831),x91832),f2(x91831)))+P1(f862(f862(f228(x91831),x91832),f862(f862(f281(x91831),x91833),f862(f96(x91831),x91834))))+~P1(f862(f862(f228(x91831),x91833),f862(f862(f74(x91831),x91832),f862(f96(x91831),x91834))))+~P1(f862(f862(f228(x91831),f862(f862(f74(x91831),x91832),f862(f96(x91831),x91834))),x91833))
% 25.54/25.42 [9210]~P66(x92101)+~P99(x92101)+~P1(f862(f862(f228(x92101),f862(f96(x92101),x92102)),f2(x92101)))+P1(f862(f862(f228(x92101),f2(x92101)),f862(f96(x92101),x92102)))+~P1(f862(f862(f227(x92101),f862(f862(f281(x92101),x92104),f862(f96(x92101),x92102))),x92103))+P1(f862(f862(f227(x92101),f862(f862(f74(x92101),x92103),f862(f96(x92101),x92102))),x92104))
% 25.54/25.42 [9211]~P66(x92111)+~P99(x92111)+~P1(f862(f862(f228(x92111),f862(f96(x92111),x92112)),f2(x92111)))+P1(f862(f862(f228(x92111),f2(x92111)),f862(f96(x92111),x92112)))+~P1(f862(f862(f227(x92111),f862(f862(f74(x92111),x92114),f862(f96(x92111),x92112))),x92113))+P1(f862(f862(f227(x92111),f862(f862(f281(x92111),x92113),f862(f96(x92111),x92112))),x92114))
% 25.54/25.42 [9212]~P66(x92121)+~P99(x92121)+~P1(f862(f862(f228(x92121),f862(f96(x92121),x92122)),f2(x92121)))+P1(f862(f862(f228(x92121),f2(x92121)),f862(f96(x92121),x92122)))+~P1(f862(f862(f228(x92121),f862(f862(f281(x92121),x92124),f862(f96(x92121),x92122))),x92123))+P1(f862(f862(f228(x92121),f862(f862(f74(x92121),x92123),f862(f96(x92121),x92122))),x92124))
% 25.54/25.42 [9213]~P66(x92131)+~P99(x92131)+~P1(f862(f862(f228(x92131),f862(f96(x92131),x92132)),f2(x92131)))+P1(f862(f862(f228(x92131),f2(x92131)),f862(f96(x92131),x92132)))+~P1(f862(f862(f228(x92131),f862(f862(f74(x92131),x92134),f862(f96(x92131),x92132))),x92133))+P1(f862(f862(f228(x92131),f862(f862(f281(x92131),x92133),f862(f96(x92131),x92132))),x92134))
% 25.54/25.42 [9289]~P66(x92891)+~P99(x92891)+~P1(f862(f862(f228(x92891),f862(f96(x92891),x92894)),f2(x92891)))+P1(f862(f862(f227(x92891),x92892),f862(f862(f281(x92891),x92893),f862(f96(x92891),x92894))))+~P1(f862(f862(f227(x92891),x92893),f862(f862(f74(x92891),x92892),f862(f96(x92891),x92894))))+~P1(f862(f862(f227(x92891),f862(f862(f74(x92891),x92892),f862(f96(x92891),x92894))),x92893))
% 25.54/25.42 [9290]~P66(x92901)+~P99(x92901)+~P1(f862(f862(f228(x92901),f862(f96(x92901),x92904)),f2(x92901)))+P1(f862(f862(f228(x92901),x92902),f862(f862(f281(x92901),x92903),f862(f96(x92901),x92904))))+~P1(f862(f862(f228(x92901),x92903),f862(f862(f74(x92901),x92902),f862(f96(x92901),x92904))))+~P1(f862(f862(f228(x92901),f862(f862(f74(x92901),x92902),f862(f96(x92901),x92904))),x92903))
% 25.54/25.42 [9336]~P66(x93361)+~P99(x93361)+~P1(f862(f862(f227(x93361),f2(x93361)),x93364))+~P1(f862(f862(f227(x93361),x93362),f862(f862(f74(x93361),x93364),f862(f96(x93361),x93363))))+~P1(f862(f862(f227(x93361),f862(f862(f74(x93361),x93364),f862(f96(x93361),x93363))),x93362))+P1(f862(f862(f227(x93361),f862(f862(f281(x93361),x93362),f862(f96(x93361),x93363))),x93364))
% 25.54/25.42 [9337]~P66(x93371)+~P99(x93371)+~P1(f862(f862(f228(x93371),f2(x93371)),x93374))+~P1(f862(f862(f228(x93371),x93372),f862(f862(f74(x93371),x93374),f862(f96(x93371),x93373))))+~P1(f862(f862(f228(x93371),f862(f862(f74(x93371),x93374),f862(f96(x93371),x93373))),x93372))+P1(f862(f862(f228(x93371),f862(f862(f281(x93371),x93372),f862(f96(x93371),x93373))),x93374))
% 25.54/25.42 [9372]~P66(x93721)+~P99(x93721)+~P1(f862(f862(f228(x93721),f862(f96(x93721),x93723)),f2(x93721)))+~P1(f862(f862(f227(x93721),x93722),f862(f862(f74(x93721),x93724),f862(f96(x93721),x93723))))+~P1(f862(f862(f227(x93721),f862(f862(f74(x93721),x93724),f862(f96(x93721),x93723))),x93722))+P1(f862(f862(f227(x93721),f862(f862(f281(x93721),x93722),f862(f96(x93721),x93723))),x93724))
% 25.54/25.42 [9373]~P66(x93731)+~P99(x93731)+~P1(f862(f862(f228(x93731),f862(f96(x93731),x93733)),f2(x93731)))+~P1(f862(f862(f228(x93731),x93732),f862(f862(f74(x93731),x93734),f862(f96(x93731),x93733))))+~P1(f862(f862(f228(x93731),f862(f862(f74(x93731),x93734),f862(f96(x93731),x93733))),x93732))+P1(f862(f862(f228(x93731),f862(f862(f281(x93731),x93732),f862(f96(x93731),x93733))),x93734))
% 25.54/25.42 [9071]~P66(x90711)+~P99(x90711)+~P1(f862(f862(f228(x90711),x90712),f2(x90711)))+~P1(f862(f862(f227(x90711),f862(f862(f281(x90711),x90714),x90712)),f862(f96(x90711),x90713)))+P1(f862(f862(f228(x90711),f2(x90711)),x90712))+P1(f862(f862(f227(x90711),f862(f862(f74(x90711),f862(f96(x90711),x90713)),x90712)),x90714))
% 25.54/25.42 [9072]~P66(x90721)+~P99(x90721)+~P1(f862(f862(f228(x90721),x90722),f2(x90721)))+~P1(f862(f862(f228(x90721),f862(f862(f281(x90721),x90724),x90722)),f862(f96(x90721),x90723)))+P1(f862(f862(f228(x90721),f2(x90721)),x90722))+P1(f862(f862(f228(x90721),f862(f862(f74(x90721),f862(f96(x90721),x90723)),x90722)),x90724))
% 25.54/25.42 [9186]~P66(x91861)+~P99(x91861)+~P1(f862(f862(f228(x91861),x91862),f2(x91861)))+P1(f862(f862(f228(x91861),f2(x91861)),x91862))+P1(f862(f862(f227(x91861),f862(f862(f281(x91861),x91863),x91862)),f862(f96(x91861),x91864)))+~P1(f862(f862(f227(x91861),f862(f862(f74(x91861),f862(f96(x91861),x91864)),x91862)),x91863))
% 25.54/25.42 [9187]~P66(x91871)+~P99(x91871)+~P1(f862(f862(f228(x91871),x91872),f2(x91871)))+P1(f862(f862(f228(x91871),f2(x91871)),x91872))+P1(f862(f862(f228(x91871),f862(f862(f281(x91871),x91873),x91872)),f862(f96(x91871),x91874)))+~P1(f862(f862(f228(x91871),f862(f862(f74(x91871),f862(f96(x91871),x91874)),x91872)),x91873))
% 25.54/25.42 [9224]~P66(x92241)+~P99(x92241)+P1(f862(f862(f228(x92241),x92242),f2(x92241)))+~P1(f862(f862(f227(x92241),f862(f96(x92241),x92243)),f2(x92241)))+P1(f862(f862(f227(x92241),f862(f96(x92241),x92243)),f862(f862(f281(x92241),x92244),x92242)))+~P1(f862(f862(f227(x92241),f862(f862(f74(x92241),f862(f96(x92241),x92243)),x92242)),x92244))
% 25.54/25.42 [9225]~P66(x92251)+~P99(x92251)+P1(f862(f862(f228(x92251),x92252),f2(x92251)))+~P1(f862(f862(f228(x92251),f862(f96(x92251),x92253)),f2(x92251)))+P1(f862(f862(f228(x92251),f862(f96(x92251),x92253)),f862(f862(f281(x92251),x92254),x92252)))+~P1(f862(f862(f228(x92251),f862(f862(f74(x92251),f862(f96(x92251),x92253)),x92252)),x92254))
% 25.54/25.42 [9240]~P66(x92401)+~P99(x92401)+P1(f862(f862(f228(x92401),f2(x92401)),x92402))+P1(f862(f862(f227(x92401),f862(f862(f281(x92401),x92403),x92402)),f862(f96(x92401),x92404)))+~P1(f862(f862(f227(x92401),f2(x92401)),f862(f96(x92401),x92404)))+~P1(f862(f862(f227(x92401),f862(f862(f74(x92401),f862(f96(x92401),x92404)),x92402)),x92403))
% 25.54/25.42 [9241]~P66(x92411)+~P99(x92411)+P1(f862(f862(f228(x92411),f2(x92411)),x92412))+P1(f862(f862(f228(x92411),f862(f862(f281(x92411),x92413),x92412)),f862(f96(x92411),x92414)))+~P1(f862(f862(f228(x92411),f2(x92411)),f862(f96(x92411),x92414)))+~P1(f862(f862(f228(x92411),f862(f862(f74(x92411),f862(f96(x92411),x92414)),x92412)),x92413))
% 25.54/25.42 [9404]~P66(x94041)+~P99(x94041)+~P1(f862(f862(f228(x94041),x94044),f2(x94041)))+P1(f862(f862(f227(x94041),f862(f96(x94041),x94042)),f862(f862(f281(x94041),x94043),x94044)))+~P1(f862(f862(f227(x94041),x94043),f862(f862(f74(x94041),f862(f96(x94041),x94042)),x94044)))+~P1(f862(f862(f227(x94041),f862(f862(f74(x94041),f862(f96(x94041),x94042)),x94044)),x94043))
% 25.54/25.42 [9405]~P66(x94051)+~P99(x94051)+~P1(f862(f862(f228(x94051),x94054),f2(x94051)))+P1(f862(f862(f228(x94051),f862(f96(x94051),x94052)),f862(f862(f281(x94051),x94053),x94054)))+~P1(f862(f862(f228(x94051),x94053),f862(f862(f74(x94051),f862(f96(x94051),x94052)),x94054)))+~P1(f862(f862(f228(x94051),f862(f862(f74(x94051),f862(f96(x94051),x94052)),x94054)),x94053))
% 25.54/25.42 [9439]~P66(x94391)+~P99(x94391)+~P1(f862(f862(f228(x94391),x94393),f2(x94391)))+P1(f862(f862(f227(x94391),f862(f862(f281(x94391),x94392),x94393)),f862(f96(x94391),x94394)))+~P1(f862(f862(f227(x94391),x94392),f862(f862(f74(x94391),f862(f96(x94391),x94394)),x94393)))+~P1(f862(f862(f227(x94391),f862(f862(f74(x94391),f862(f96(x94391),x94394)),x94393)),x94392))
% 25.54/25.42 [9440]~P66(x94401)+~P99(x94401)+~P1(f862(f862(f228(x94401),x94403),f2(x94401)))+P1(f862(f862(f228(x94401),f862(f862(f281(x94401),x94402),x94403)),f862(f96(x94401),x94404)))+~P1(f862(f862(f228(x94401),x94402),f862(f862(f74(x94401),f862(f96(x94401),x94404)),x94403)))+~P1(f862(f862(f228(x94401),f862(f862(f74(x94401),f862(f96(x94401),x94404)),x94403)),x94402))
% 25.54/25.42 [9460]~P66(x94601)+~P99(x94601)+~P1(f862(f862(f227(x94601),f862(f96(x94601),x94602)),f2(x94601)))+P1(f862(f862(f227(x94601),f862(f96(x94601),x94602)),f862(f862(f281(x94601),x94603),x94604)))+~P1(f862(f862(f227(x94601),x94603),f862(f862(f74(x94601),f862(f96(x94601),x94602)),x94604)))+~P1(f862(f862(f227(x94601),f862(f862(f74(x94601),f862(f96(x94601),x94602)),x94604)),x94603))
% 25.54/25.42 [9461]~P66(x94611)+~P99(x94611)+~P1(f862(f862(f228(x94611),f862(f96(x94611),x94612)),f2(x94611)))+P1(f862(f862(f228(x94611),f862(f96(x94611),x94612)),f862(f862(f281(x94611),x94613),x94614)))+~P1(f862(f862(f228(x94611),x94613),f862(f862(f74(x94611),f862(f96(x94611),x94612)),x94614)))+~P1(f862(f862(f228(x94611),f862(f862(f74(x94611),f862(f96(x94611),x94612)),x94614)),x94613))
% 25.54/25.42 [9465]~P66(x94651)+~P99(x94651)+P1(f862(f862(f227(x94651),f862(f862(f281(x94651),x94652),x94653)),f862(f96(x94651),x94654)))+~P1(f862(f862(f227(x94651),f2(x94651)),f862(f96(x94651),x94654)))+~P1(f862(f862(f227(x94651),x94652),f862(f862(f74(x94651),f862(f96(x94651),x94654)),x94653)))+~P1(f862(f862(f227(x94651),f862(f862(f74(x94651),f862(f96(x94651),x94654)),x94653)),x94652))
% 25.54/25.42 [9466]~P66(x94661)+~P99(x94661)+P1(f862(f862(f228(x94661),f862(f862(f281(x94661),x94662),x94663)),f862(f96(x94661),x94664)))+~P1(f862(f862(f228(x94661),f2(x94661)),f862(f96(x94661),x94664)))+~P1(f862(f862(f228(x94661),x94662),f862(f862(f74(x94661),f862(f96(x94661),x94664)),x94663)))+~P1(f862(f862(f228(x94661),f862(f862(f74(x94661),f862(f96(x94661),x94664)),x94663)),x94662))
% 25.54/25.42 [6263]~P119(x62632)+~P133(x62632)+~E(f862(x62633,x62635),f2(x62632))+E(f862(f862(f11(x62631,x62632),x62633),x62634),f2(x62632))+~P1(f862(f54(x62631),x62634))+~P1(f862(f862(f321(x62631),x62635),x62634))
% 25.54/25.42 [8625]~P110(x86251)+P1(f862(f862(f228(f932(x86251,a921)),f296(x86251,x86252,x86253)),f296(x86251,x86254,x86255)))+~P1(f862(f862(f227(x86251),x86254),x86252))+~P1(f862(f862(f227(x86251),x86254),x86255))+~P1(f862(f862(f227(x86251),x86253),x86255))+~P1(f862(f862(f228(x86251),x86253),x86255))
% 25.54/25.42 [8626]~P110(x86261)+P1(f862(f862(f228(f932(x86261,a921)),f296(x86261,x86262,x86263)),f296(x86261,x86264,x86265)))+~P1(f862(f862(f227(x86261),x86263),x86265))+~P1(f862(f862(f227(x86261),x86264),x86265))+~P1(f862(f862(f227(x86261),x86264),x86262))+~P1(f862(f862(f228(x86261),x86264),x86262))
% 25.54/25.42 [9491]P56(x94912,x94913,x94914,x94911)+E(x94911,f181(f932(x94912,a921)))+~P1(f862(f54(x94912),x94914))+~P1(f862(f54(x94912),x94911))+~P1(f862(f862(x94913,f550(x94911,x94914,x94913,x94912)),x94915))+~P1(f862(f862(f321(x94912),x94915),x94911))
% 25.54/25.42 [9492]P56(x94922,x94923,x94924,x94921)+E(x94921,f181(f932(x94922,a921)))+~P1(f862(f54(x94922),x94924))+~P1(f862(f54(x94922),x94921))+~P1(f862(f862(x94923,f803(x94923,x94921,x94924,x94922)),x94925))+~P1(f862(f862(f321(x94922),x94925),x94921))
% 25.54/25.42 [9493]P56(x94932,x94933,x94934,x94931)+E(x94931,f181(f932(x94932,a921)))+~P1(f862(f54(x94932),x94934))+~P1(f862(f54(x94932),x94931))+~P1(f862(f862(x94933,f804(x94931,x94934,x94933,x94932)),x94935))+~P1(f862(f862(f321(x94932),x94935),x94931))
% 25.54/25.42 [9644]~E(x96443,x96445)+~P71(x96441)+~P72(x96441)+~P38(x96443)+E(f862(f862(f8(a1,x96441),x96442),x96443),f862(f862(f8(a1,x96441),x96444),x96445))+P1(f862(f862(f227(a1),f2(a1)),f549(x96442,x96444,x96443,x96445,x96441)))
% 25.54/25.42 [9645]~E(x96453,x96455)+~P71(x96451)+~P72(x96451)+~P38(x96453)+E(f862(f862(f11(a1,x96451),x96452),x96453),f862(f862(f11(a1,x96451),x96454),x96455))+P1(f862(f862(f227(a1),f2(a1)),f514(x96452,x96454,x96453,x96455,x96451)))
% 25.54/25.42 [9819]~E(x98195,x98193)+~P71(x98191)+~P72(x98191)+~P38(x98195)+~E(f862(x98192,f549(x98194,x98192,x98195,x98193,x98191)),f862(x98194,f549(x98194,x98192,x98195,x98193,x98191)))+E(f862(f862(f8(a1,x98191),x98192),x98193),f862(f862(f8(a1,x98191),x98194),x98195))
% 25.54/25.42 [9820]~E(x98205,x98203)+~P71(x98201)+~P72(x98201)+~P38(x98205)+~E(f862(x98202,f514(x98204,x98202,x98205,x98203,x98201)),f862(x98204,f514(x98204,x98202,x98205,x98203,x98201)))+E(f862(f862(f11(a1,x98201),x98202),x98203),f862(f862(f11(a1,x98201),x98204),x98205))
% 25.54/25.42 [9908]~P78(x99083)+E(f862(x99081,x99082),f2(x99083))+~E(f862(f862(f8(x99084,x99083),x99081),x99085),f2(x99083))+~P1(f862(f54(x99084),x99085))+P1(f862(f862(f321(x99084),f516(x99082,x99081,x99085,x99084,x99083)),x99085))+~P1(f862(f862(f321(x99084),x99082),x99085))
% 25.54/25.42 [10037]~P78(x100373)+E(f862(x100371,x100372),f2(x100373))+~E(f862(f862(f8(x100374,x100373),x100371),x100375),f2(x100373))+~P1(f862(f54(x100374),x100375))+~P1(f862(f862(f321(x100374),x100372),x100375))+~P1(f862(f862(f227(x100373),f2(x100373)),f862(x100371,f516(x100372,x100371,x100375,x100374,x100373))))
% 25.54/25.42 [8541]~P138(x85411)+~P1(f862(f862(f227(x85411),x85413),x85415))+~P1(f862(f862(f227(x85411),x85412),x85414))+~P1(f862(f862(f227(x85411),f2(x85411)),x85413))+~P1(f862(f862(f227(x85411),f2(x85411)),x85414))+P1(f862(f862(f227(x85411),f862(f862(f74(x85411),x85412),x85413)),f862(f862(f74(x85411),x85414),x85415)))
% 25.54/25.42 [8542]~P138(x85421)+~P1(f862(f862(f227(x85421),x85423),x85425))+~P1(f862(f862(f227(x85421),x85422),x85424))+~P1(f862(f862(f227(x85421),f2(x85421)),x85423))+~P1(f862(f862(f227(x85421),f2(x85421)),x85422))+P1(f862(f862(f227(x85421),f862(f862(f74(x85421),x85422),x85423)),f862(f862(f74(x85421),x85424),x85425)))
% 25.54/25.42 [8543]~P67(x85431)+~P1(f862(f862(f228(x85431),f2(x85431)),x85435))+~P1(f862(f862(f227(x85431),x85435),x85433))+~P1(f862(f862(f227(x85431),x85432),x85434))+~P1(f862(f862(f227(x85431),f2(x85431)),x85432))+P1(f862(f862(f227(x85431),f862(f862(f281(x85431),x85432),x85433)),f862(f862(f281(x85431),x85434),x85435)))
% 25.54/25.42 [8544]~P135(x85441)+~P1(f862(f862(f227(x85441),x85443),x85445))+~P1(f862(f862(f227(x85441),f2(x85441)),x85442))+~P1(f862(f862(f228(x85441),x85442),x85444))+~P1(f862(f862(f228(x85441),f2(x85441)),x85443))+P1(f862(f862(f228(x85441),f862(f862(f74(x85441),x85442),x85443)),f862(f862(f74(x85441),x85444),x85445)))
% 25.54/25.42 [8545]~P135(x85451)+~P1(f862(f862(f227(x85451),x85452),x85454))+~P1(f862(f862(f227(x85451),f2(x85451)),x85453))+~P1(f862(f862(f228(x85451),x85453),x85455))+~P1(f862(f862(f228(x85451),f2(x85451)),x85452))+P1(f862(f862(f228(x85451),f862(f862(f74(x85451),x85452),x85453)),f862(f862(f74(x85451),x85454),x85455)))
% 25.54/25.42 [8546]~P135(x85461)+~P1(f862(f862(f227(x85461),f2(x85461)),x85463))+~P1(f862(f862(f227(x85461),f2(x85461)),x85462))+~P1(f862(f862(f228(x85461),x85463),x85465))+~P1(f862(f862(f228(x85461),x85462),x85464))+P1(f862(f862(f228(x85461),f862(f862(f74(x85461),x85462),x85463)),f862(f862(f74(x85461),x85464),x85465)))
% 25.54/25.42 [8547]~P135(x85471)+~P1(f862(f862(f227(x85471),f2(x85471)),x85473))+~P1(f862(f862(f228(x85471),x85473),x85475))+~P1(f862(f862(f228(x85471),x85472),x85474))+~P1(f862(f862(f228(x85471),f2(x85471)),x85474))+P1(f862(f862(f228(x85471),f862(f862(f74(x85471),x85472),x85473)),f862(f862(f74(x85471),x85474),x85475)))
% 25.54/25.42 [8548]~P67(x85481)+~P1(f862(f862(f227(x85481),x85485),x85483))+~P1(f862(f862(f227(x85481),f2(x85481)),x85482))+~P1(f862(f862(f228(x85481),x85482),x85484))+~P1(f862(f862(f228(x85481),f2(x85481)),x85485))+P1(f862(f862(f228(x85481),f862(f862(f281(x85481),x85482),x85483)),f862(f862(f281(x85481),x85484),x85485)))
% 25.54/25.42 [8549]~P67(x85491)+~P1(f862(f862(f227(x85491),x85492),x85494))+~P1(f862(f862(f228(x85491),x85495),x85493))+~P1(f862(f862(f228(x85491),f2(x85491)),x85495))+~P1(f862(f862(f228(x85491),f2(x85491)),x85492))+P1(f862(f862(f228(x85491),f862(f862(f281(x85491),x85492),x85493)),f862(f862(f281(x85491),x85494),x85495)))
% 25.54/25.42 [9951]~P72(x99515)+~P83(x99515)+E(x99511,f181(f932(x99512,a921)))+~P1(f862(f54(x99512),x99511))+P1(f862(f862(f321(x99512),f907(x99513,x99514,x99511,x99512,x99515)),x99511))+P1(f862(f862(f228(x99515),f862(f862(f8(x99512,x99515),x99514),x99511)),f862(f862(f8(x99512,x99515),x99513),x99511)))
% 25.54/25.42 [10062]~P72(x100621)+~P85(x100621)+~P1(f862(f54(x100622),x100625))+~P1(f862(f862(f227(x100621),f2(x100621)),f862(x100623,f361(x100623,x100624,x100625,x100622,x100621))))+P1(f862(f862(f227(x100621),f862(f862(f8(x100622,x100621),x100623),x100624)),f862(f862(f8(x100622,x100621),x100623),x100625)))+~P1(f862(f862(f227(f932(x100622,a921)),x100624),x100625))
% 25.54/25.42 [10224]~P72(x102243)+~P83(x102243)+E(x102241,f181(f932(x102242,a921)))+~P1(f862(f54(x102242),x102241))+~P1(f862(f862(f228(x102243),f862(x102244,f907(x102245,x102244,x102241,x102242,x102243))),f862(x102245,f907(x102245,x102244,x102241,x102242,x102243))))+P1(f862(f862(f228(x102243),f862(f862(f8(x102242,x102243),x102244),x102241)),f862(f862(f8(x102242,x102243),x102245),x102241)))
% 25.54/25.42 [7255]~P15(x72552,x72555,x72554)+E(x72551,f181(f932(x72552,a921)))+E(x72553,f181(f932(x72552,a921)))+~P1(f862(f54(x72552),x72551))+~P1(f862(f54(x72552),x72553))+E(f862(x72554,f862(f862(f103(f932(x72552,a921)),x72553),x72551)),f862(f862(x72555,f862(x72554,x72553)),f862(x72554,x72551)))
% 25.54/25.42 [7851]~P149(x78511,x78514,x78513)+P1(f862(x78511,x78512))+~P1(f862(f862(f228(a1),x78514),f2(a1)))+~P1(f862(f862(f227(a1),x78515),f2(a1)))+~E(x78513,f862(f862(f73(a1),f862(f862(f74(a1),x78514),x78512)),x78515))+~P1(f862(f862(f228(a1),x78514),x78515))
% 25.54/25.42 [7852]~P148(x78521,x78524,x78523)+P1(f862(x78521,x78522))+~P1(f862(f862(f228(a1),x78524),f2(a1)))+~P1(f862(f862(f227(a1),x78522),f2(a1)))+~E(x78523,f862(f862(f73(a1),f862(f862(f74(a1),x78524),x78525)),x78522))+~P1(f862(f862(f228(a1),x78524),x78522))
% 25.54/25.42 [7894]~P149(x78941,x78944,x78943)+P1(f862(x78941,x78942))+~E(x78943,f862(f862(f73(a1),f862(f862(f74(a1),x78944),x78942)),x78945))+~P1(f862(f862(f227(a1),f2(a1)),x78945))+~P1(f862(f862(f228(a1),f2(a1)),x78944))+~P1(f862(f862(f228(a1),x78945),x78944))
% 25.54/25.42 [7895]~P148(x78951,x78954,x78953)+P1(f862(x78951,x78952))+~E(x78953,f862(f862(f73(a1),f862(f862(f74(a1),x78954),x78955)),x78952))+~P1(f862(f862(f227(a1),f2(a1)),x78952))+~P1(f862(f862(f228(a1),f2(a1)),x78954))+~P1(f862(f862(f228(a1),x78952),x78954))
% 25.54/25.42 [8837]P1(f862(f862(x88371,x88372),x88373))+~P1(f862(f862(x88371,f862(f862(f29(a1),x88374),x88375)),f38(a1,x88374,x88375)))+~P1(f862(f862(f228(a1),x88375),f2(a1)))+~P1(f862(f862(f227(a1),x88373),f2(a1)))+~E(x88374,f862(f862(f73(a1),f862(f862(f74(a1),x88375),x88372)),x88373))+~P1(f862(f862(f228(a1),x88375),x88373))
% 25.54/25.42 [8846]P1(f862(f862(x88461,x88462),x88463))+~P1(f862(f862(x88461,f862(f862(f29(a1),x88464),x88465)),f38(a1,x88464,x88465)))+~E(x88464,f862(f862(f73(a1),f862(f862(f74(a1),x88465),x88462)),x88463))+~P1(f862(f862(f227(a1),f2(a1)),x88463))+~P1(f862(f862(f228(a1),f2(a1)),x88465))+~P1(f862(f862(f228(a1),x88463),x88465))
% 25.54/25.42 [9110]E(x91101,x91102)+~P53(x91103,x91105,x91104)+~P1(f862(f862(f321(x91103),x91102),x91105))+~P1(f862(f862(f321(x91103),x91101),x91105))+P1(f862(f862(f321(f931(x91103,x91103)),f862(f862(f244(x91103,x91103),x91101),x91102)),x91104))+P1(f862(f862(f321(f931(x91103,x91103)),f862(f862(f244(x91103,x91103),x91102),x91101)),x91104))
% 25.54/25.42 [9979]~P72(x99795)+~P85(x99795)+~P1(f862(f54(x99791),x99794))+P1(f862(f862(f227(x99795),f862(f862(f8(x99791,x99795),x99792),x99793)),f862(f862(f8(x99791,x99795),x99792),x99794)))+~P1(f862(f862(f227(f932(x99791,a921)),x99793),x99794))+P1(f862(f862(f321(x99791),f361(x99792,x99793,x99794,x99791,x99795)),f862(f862(f3(f932(x99791,a921)),x99794),x99793)))
% 25.54/25.42 [10070]E(x100701,f181(f932(x100702,a921)))+~P1(f862(f54(x100702),x100703))+~P1(f862(f54(x100702),x100701))+P1(f862(f862(f321(f931(f932(x100702,a921),f932(x100702,a921))),f862(f862(f244(f932(x100702,a921),f932(x100702,a921)),x100703),x100701)),f310(x100702,x100704)))+~P1(f862(f862(f321(x100702),x100705),x100701))+~P1(f862(f862(f321(f931(x100702,x100702)),f862(f862(f244(x100702,x100702),f559(x100704,x100701,x100703,x100702)),x100705)),x100704))
% 25.54/25.42 [10071]E(x100711,f181(f932(x100712,a921)))+~P1(f862(f54(x100712),x100713))+~P1(f862(f54(x100712),x100711))+P1(f862(f862(f321(f931(f932(x100712,a921),f932(x100712,a921))),f862(f862(f244(f932(x100712,a921),f932(x100712,a921)),x100713),x100711)),f310(x100712,x100714)))+~P1(f862(f862(f321(x100712),x100715),x100711))+~P1(f862(f862(f321(f931(x100712,x100712)),f862(f862(f244(x100712,x100712),f617(x100714,x100711,x100713,x100712)),x100715)),x100714))
% 25.54/25.42 [10228]~P78(x102281)+~E(f862(f862(f8(x102285,x102281),x102282),x102286),x102284)+~P1(f862(f54(x102285),x102286))+P1(f862(f862(f321(x102285),f520(x102283,x102284,x102282,x102286,x102285,x102281)),x102286))+P1(f862(f862(f227(x102281),f862(x102282,x102283)),x102284))+~P1(f862(f862(f321(x102285),x102283),x102286))
% 25.54/25.42 [10272]~P78(x102721)+~E(f862(f862(f8(x102725,x102721),x102722),x102726),x102724)+~P1(f862(f54(x102725),x102726))+~P1(f862(f862(f321(x102725),x102723),x102726))+~P1(f862(f862(f227(x102721),f2(x102721)),f862(x102722,f520(x102723,x102724,x102722,x102726,x102725,x102721))))+P1(f862(f862(f227(x102721),f862(x102722,x102723)),x102724))
% 25.54/25.42 [10416]~E(x104165,x104168)+~E(x104164,x104167)+~P108(x104161)+~P72(x104162)+E(f862(f862(f8(x104161,x104162),x104163),f862(f295(x104161,x104164),x104165)),f862(f862(f8(x104161,x104162),x104166),f862(f295(x104161,x104167),x104168)))+P1(f862(f862(f227(x104161),x104164),f911(x104163,x104166,x104165,x104168,x104164,x104167,x104161,x104162)))
% 25.54/25.42 [10432]~E(x104327,x104324)+~E(x104328,x104325)+~P108(x104321)+~P72(x104322)+~E(f862(x104323,f911(x104326,x104323,x104328,x104325,x104327,x104324,x104321,x104322)),f862(x104326,f911(x104326,x104323,x104328,x104325,x104327,x104324,x104321,x104322)))+E(f862(f862(f8(x104321,x104322),x104323),f862(f295(x104321,x104324),x104325)),f862(f862(f8(x104321,x104322),x104326),f862(f295(x104321,x104327),x104328)))
% 25.54/25.42 [10435]~E(x104354,x104357)+~E(x104355,x104358)+~P108(x104351)+~P72(x104352)+E(f862(f862(f8(x104351,x104352),x104353),f862(f295(x104351,x104354),x104355)),f862(f862(f8(x104351,x104352),x104356),f862(f295(x104351,x104357),x104358)))+P1(f862(f862(f228(x104351),f911(x104353,x104356,x104355,x104358,x104354,x104357,x104351,x104352)),x104355))
% 25.54/25.42 [10077]~P6(x100775,x100779,x100776)+~P6(x100771,x1007710,x100773)+~P10(x100771,x100775,f932(x100772,a921),x100773,x100776,x100778)+~P1(f862(f862(f321(x100775),x100777),x100779))+~P1(f862(f862(f321(x100771),x100774),x1007710))+E(f862(f862(f33(x100771,f932(x100772,a921)),f862(f276(x100771,x100771,x100773),f862(f862(f301(x100771),x100774),f181(f932(x100771,a921))))),f862(f862(f10(f932(x100775,f932(x100772,a921)),f932(x100772,a921),x100771),f862(f33(x100775,f932(x100772,a921)),f862(f276(x100775,x100775,x100776),f862(f862(f301(x100775),x100777),f181(f932(x100775,a921)))))),x100778)),f862(f862(x100778,x100774),x100777))
% 25.54/25.42 [5779]~P109(x57793)+~P11(x57793,x57792)+~P11(x57793,x57791)+E(x57791,x57792)+~E(f862(f165(x57793),x57791),f862(f165(x57793),x57792))+~P1(f862(f130(x57793),x57792))+~P1(f862(f130(x57793),x57791))
% 25.54/25.42 [5099]~P133(x50992)+~P134(x50992)+~P145(x50992)+~P116(x50992)+~E(x50993,f2(x50992))+E(x50991,f2(a924))+E(f862(f862(f236(x50992),x50993),x50991),f2(x50992))
% 25.54/25.42 [9367]E(x93671,f2(a924))+~E(x93672,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x93673)),x93671)),f862(f248(a924,a924),x93673)))+P1(f862(f41(x93672,x93671),x93673))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x93673)),f2(a924)))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x93673)))+~P1(f862(f862(f228(a924),x93671),f862(f248(a924,a924),x93673)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x93673)),x93671))
% 25.54/25.42 [9375]~E(f862(f243(a924,a924),x93753),f2(a924))+~E(x93751,f862(f862(f73(a924),f862(f862(f74(a924),f862(f243(a924,a924),x93753)),x93752)),f862(f248(a924,a924),x93753)))+P1(f862(f41(x93751,x93752),x93753))+~P1(f862(f862(f227(a924),f862(f248(a924,a924),x93753)),f2(a924)))+~P1(f862(f862(f227(a924),f2(a924)),f862(f248(a924,a924),x93753)))+~P1(f862(f862(f228(a924),x93752),f862(f248(a924,a924),x93753)))+~P1(f862(f862(f228(a924),f862(f248(a924,a924),x93753)),x93752))
% 25.54/25.42 [7730]~P93(x77302)+E(x77301,f181(f932(x77302,a921)))+E(x77303,f181(f932(x77302,a921)))+~P1(f862(f54(x77302),x77301))+~P1(f862(f54(x77302),x77303))+~E(f862(f862(f94(f932(x77302,a921)),x77303),x77301),f181(f932(x77302,a921)))+E(f12(x77302,f862(f862(f103(f932(x77302,a921)),x77303),x77301)),f862(f862(f94(x77302),f12(x77302,x77303)),f12(x77302,x77301)))
% 25.54/25.42 [7731]~P93(x77312)+E(x77311,f181(f932(x77312,a921)))+E(x77313,f181(f932(x77312,a921)))+~P1(f862(f54(x77312),x77311))+~P1(f862(f54(x77312),x77313))+~E(f862(f862(f94(f932(x77312,a921)),x77313),x77311),f181(f932(x77312,a921)))+E(f15(x77312,f862(f862(f103(f932(x77312,a921)),x77313),x77311)),f862(f862(f103(x77312),f15(x77312,x77313)),f15(x77312,x77311)))
% 25.54/25.42 [7732]~P109(x77322)+E(x77321,f181(f932(x77322,a921)))+E(x77323,f181(f932(x77322,a921)))+~P1(f862(f54(x77322),x77321))+~P1(f862(f54(x77322),x77323))+~E(f862(f862(f94(f932(x77322,a921)),x77323),x77321),f181(f932(x77322,a921)))+E(f16(x77322,f862(f862(f103(f932(x77322,a921)),x77323),x77321)),f862(f862(f225(x77322),f16(x77322,x77323)),f16(x77322,x77321)))
% 25.54/25.42 [7733]~P109(x77332)+E(x77331,f181(f932(x77332,a921)))+E(x77333,f181(f932(x77332,a921)))+~P1(f862(f54(x77332),x77331))+~P1(f862(f54(x77332),x77333))+~E(f862(f862(f94(f932(x77332,a921)),x77333),x77331),f181(f932(x77332,a921)))+E(f17(x77332,f862(f862(f103(f932(x77332,a921)),x77333),x77331)),f862(f862(f226(x77332),f17(x77332,x77333)),f17(x77332,x77331)))
% 25.54/25.42 [8208]~P69(x82082)+E(x82081,f181(f932(x82082,a921)))+E(x82083,f181(f932(x82082,a921)))+~P1(f862(f54(x82082),x82081))+~P1(f862(f54(x82082),x82083))+~E(f862(f862(f94(f932(x82082,a921)),x82083),x82081),f181(f932(x82082,a921)))+E(f862(f862(f74(x82082),f862(f56(x82082,f74(x82082)),x82083)),f862(f56(x82082,f74(x82082)),x82081)),f862(f56(x82082,f74(x82082)),f862(f862(f103(f932(x82082,a921)),x82083),x82081)))
% 25.54/25.42 [8281]~P109(x82812)+E(x82811,f181(f932(x82812,a921)))+E(x82813,f181(f932(x82812,a921)))+~P1(f862(f54(x82812),x82811))+~P1(f862(f54(x82812),x82813))+~E(f862(f862(f94(f932(x82812,a921)),x82813),x82811),f181(f932(x82812,a921)))+E(f862(f862(f225(x82812),f13(x82812,f225(x82812),x82813)),f13(x82812,f225(x82812),x82811)),f13(x82812,f225(x82812),f862(f862(f103(f932(x82812,a921)),x82813),x82811)))
% 25.54/25.42 [8282]~P109(x82822)+E(x82821,f181(f932(x82822,a921)))+E(x82823,f181(f932(x82822,a921)))+~P1(f862(f54(x82822),x82821))+~P1(f862(f54(x82822),x82823))+~E(f862(f862(f94(f932(x82822,a921)),x82823),x82821),f181(f932(x82822,a921)))+E(f862(f862(f226(x82822),f14(x82822,f226(x82822),x82823)),f14(x82822,f226(x82822),x82821)),f14(x82822,f226(x82822),f862(f862(f103(f932(x82822,a921)),x82823),x82821)))
% 25.54/25.42 [7988]E(x79881,f2(a1))+E(f862(f862(f29(a1),x79882),x79881),x79883)+~P1(f862(f862(f227(a1),x79884),f2(a1)))+~E(x79882,f862(f862(f73(a1),f862(f862(f74(a1),x79881),x79883)),x79884))+~P1(f862(f862(f227(a1),f2(a1)),x79884))+~P1(f862(f862(f228(a1),x79884),x79881))+~P1(f862(f862(f228(a1),x79881),x79884))
% 25.54/25.42 [7996]E(f38(a1,x79962,x79961),x79963)+E(x79961,f2(a1))+~P1(f862(f862(f227(a1),x79963),f2(a1)))+~E(x79962,f862(f862(f73(a1),f862(f862(f74(a1),x79961),x79964)),x79963))+~P1(f862(f862(f227(a1),f2(a1)),x79963))+~P1(f862(f862(f228(a1),x79963),x79961))+~P1(f862(f862(f228(a1),x79961),x79963))
% 25.54/25.42 [7039]~P61(x70392)+E(x70391,f2(x70392))+E(x70393,f2(x70392))+~E(f862(f862(f29(x70392),x70394),x70393),f862(f862(f29(x70392),x70395),x70391))+E(f862(f862(f74(x70392),x70394),x70391),f862(f862(f74(x70392),x70393),x70395))+~P1(f862(f862(f278(x70392),x70391),x70395))+~P1(f862(f862(f278(x70392),x70393),x70394))
% 25.54/25.42 [7040]~P61(x70402)+E(x70401,f2(x70402))+E(x70403,f2(x70402))+~E(f862(f862(f74(x70402),x70404),x70403),f862(f862(f74(x70402),x70401),x70405))+E(f862(f862(f29(x70402),x70404),x70401),f862(f862(f29(x70402),x70405),x70403))+~P1(f862(f862(f278(x70402),x70401),x70404))+~P1(f862(f862(f278(x70402),x70403),x70405))
% 25.54/25.42 [7903]~P16(x79032,x79035,x79034)+E(x79031,f181(f932(x79032,a921)))+E(x79033,f181(f932(x79032,a921)))+~P1(f862(f54(x79032),x79031))+~P1(f862(f54(x79032),x79033))+~E(f862(f862(f94(f932(x79032,a921)),x79033),x79031),f181(f932(x79032,a921)))+E(f862(x79034,f862(f862(f103(f932(x79032,a921)),x79033),x79031)),f862(f862(x79035,f862(x79034,x79033)),f862(x79034,x79031)))
% 25.54/25.42 [9617]~P22(x96173,x96171,x96175,x96174)+~P22(x96171,x96173,x96176,x96172)+E(f862(f28(x96171),x96172),f862(f28(x96173),x96174))+~P1(f862(f54(x96173),x96174))+~P1(f862(f54(x96171),x96172))+~P1(f862(f862(f227(f932(x96173,a921)),f862(f302(x96171,x96173,x96176),x96172)),x96174))+~P1(f862(f862(f227(f932(x96171,a921)),f862(f302(x96173,x96171,x96175),x96174)),x96172))
% 25.54/25.42 [9557]~P1(f862(f862(f228(a1),f862(f862(f73(a1),f862(f862(f74(a1),x95575),x95571)),x95576)),f2(a1)))+~E(f862(f862(f73(a1),f862(f862(f74(a1),x95573),x95572)),x95574),f862(f862(f73(a1),f862(f862(f74(a1),x95575),x95571)),x95576))+~P1(f862(f862(f227(a1),f2(a1)),x95576))+~P1(f862(f862(f228(a1),f2(a1)),x95575))+~P1(f862(f862(f227(a1),x95575),x95573))+~P1(f862(f862(f228(a1),x95574),x95573))+P1(f862(f862(f227(a1),x95571),x95572))
% 25.54/25.42 [9317]~E(f862(f862(f73(a1),f862(f862(f74(a1),x93173),x93171)),x93174),f862(f862(f73(a1),f862(f862(f74(a1),x93175),x93172)),x93176))+~P1(f862(f862(f227(a1),f2(a1)),x93174))+~P1(f862(f862(f228(a1),f2(a1)),x93175))+~P1(f862(f862(f227(a1),x93175),x93173))+~P1(f862(f862(f228(a1),x93176),x93175))+P1(f862(f862(f227(a1),x93171),x93172))+~P1(f862(f862(f227(a1),f2(a1)),f862(f862(f73(a1),f862(f862(f74(a1),x93175),x93172)),x93176)))
% 25.54/25.42 [9496]~P132(x94961)+~E(f862(f862(f73(x94961),x94962),x94964),f71(x94961))+~P1(f862(f862(f227(x94961),x94965),x94966))+~P1(f862(f862(f227(x94961),x94963),x94966))+~P1(f862(f862(f227(x94961),f2(x94961)),x94964))+~P1(f862(f862(f227(x94961),f2(x94961)),x94962))+P1(f862(f862(f227(x94961),f862(f862(f73(x94961),f862(f862(f74(x94961),x94962),x94963)),f862(f862(f74(x94961),x94964),x94965))),x94966))
% 25.54/25.42 [9497]~P130(x94971)+~E(f862(f862(f73(x94971),x94972),x94974),f71(x94971))+~P1(f862(f862(f227(x94971),f2(x94971)),x94974))+~P1(f862(f862(f227(x94971),f2(x94971)),x94972))+~P1(f862(f862(f228(x94971),x94975),x94976))+~P1(f862(f862(f228(x94971),x94973),x94976))+P1(f862(f862(f228(x94971),f862(f862(f73(x94971),f862(f862(f74(x94971),x94972),x94973)),f862(f862(f74(x94971),x94974),x94975))),x94976))
% 25.54/25.42 [10321]~P6(x103217,x103216,x103215)+E(x103211,x103212)+~P9(x103217,f932(x103214,a921),x103215,x103213)+E(f862(x103213,f530(x103211,x103212,x103213,x103214,x103215,x103216,x103217)),f862(x103213,f531(x103211,x103212,x103213,x103214,x103215,x103216,x103217)))+~E(f862(f862(f33(x103217,f932(x103214,a921)),x103211),x103213),f862(f862(f33(x103217,f932(x103214,a921)),x103212),x103213))+~P1(f862(f862(f321(f932(x103217,a921)),x103212),f862(f862(f53(x103217),x103216),x103215)))+~P1(f862(f862(f321(f932(x103217,a921)),x103211),f862(f862(f53(x103217),x103216),x103215)))
% 25.54/25.42 [10372]~P6(x103723,x103727,x103726)+E(x103721,x103722)+~P9(x103723,f932(x103725,a921),x103726,x103724)+~E(f862(f862(f33(x103723,f932(x103725,a921)),x103721),x103724),f862(f862(f33(x103723,f932(x103725,a921)),x103722),x103724))+P1(f862(f862(f321(x103723),f531(x103721,x103722,x103724,x103725,x103726,x103727,x103723)),x103727))+~P1(f862(f862(f321(f932(x103723,a921)),x103722),f862(f862(f53(x103723),x103727),x103726)))+~P1(f862(f862(f321(f932(x103723,a921)),x103721),f862(f862(f53(x103723),x103727),x103726)))
% 25.54/25.42 [10373]~P6(x103733,x103737,x103736)+E(x103731,x103732)+~P9(x103733,f932(x103735,a921),x103736,x103734)+~E(f862(f862(f33(x103733,f932(x103735,a921)),x103731),x103734),f862(f862(f33(x103733,f932(x103735,a921)),x103732),x103734))+P1(f862(f862(f321(x103733),f530(x103731,x103732,x103734,x103735,x103736,x103737,x103733)),x103737))+~P1(f862(f862(f321(f932(x103733,a921)),x103732),f862(f862(f53(x103733),x103737),x103736)))+~P1(f862(f862(f321(f932(x103733,a921)),x103731),f862(f862(f53(x103733),x103737),x103736)))
% 25.54/25.42 [10451]E(x104511,x104512)+~P6(x104513,x104516,x104517)+~P9(x104513,f932(x104514,a921),x104517,x104515)+~E(f862(f862(f33(x104513,f932(x104514,a921)),x104511),x104515),f862(f862(f33(x104513,f932(x104514,a921)),x104512),x104515))+~P1(f862(f862(f321(f931(x104513,x104513)),f862(f862(f244(x104513,x104513),f531(x104511,x104512,x104515,x104514,x104517,x104516,x104513)),f530(x104511,x104512,x104515,x104514,x104517,x104516,x104513))),x104517))+~P1(f862(f862(f321(f932(x104513,a921)),x104512),f862(f862(f53(x104513),x104516),x104517)))+~P1(f862(f862(f321(f932(x104513,a921)),x104511),f862(f862(f53(x104513),x104516),x104517)))
% 25.54/25.42 [9316]~P6(x93161,x93167,x93164)+~E(x93165,x93166)+~P1(f862(f862(f321(x93161),x93163),x93166))+~P1(f862(f862(f321(x93161),x93162),x93165))+~P1(f862(f862(f321(f932(x93161,a921)),x93166),f862(f862(f53(x93161),x93167),x93164)))+~P1(f862(f862(f321(f932(x93161,a921)),x93165),f862(f862(f53(x93161),x93167),x93164)))+P1(f862(f862(f321(f931(x93161,x93161)),f862(f862(f244(x93161,x93161),x93162),x93163)),x93164))
% 25.54/25.42 [9454]E(x94541,x94542)+~P6(x94543,x94544,x94545)+~P1(f862(f862(f321(x94543),x94546),x94542))+~P1(f862(f862(f321(x94543),x94547),x94541))+~P1(f862(f862(f321(f932(x94543,a921)),x94542),f862(f862(f53(x94543),x94544),x94545)))+~P1(f862(f862(f321(f932(x94543,a921)),x94541),f862(f862(f53(x94543),x94544),x94545)))+~P1(f862(f862(f321(f931(x94543,x94543)),f862(f862(f244(x94543,x94543),x94547),x94546)),x94545))
% 25.54/25.42 [9455]E(x94551,x94552)+~P6(x94553,x94554,x94555)+~P1(f862(f862(f321(x94553),x94556),x94552))+~P1(f862(f862(f321(x94553),x94557),x94551))+~P1(f862(f862(f321(f932(x94553,a921)),x94552),f862(f862(f53(x94553),x94554),x94555)))+~P1(f862(f862(f321(f932(x94553,a921)),x94551),f862(f862(f53(x94553),x94554),x94555)))+~P1(f862(f862(f321(f931(x94553,x94553)),f862(f862(f244(x94553,x94553),x94557),x94556)),x94555))
% 25.54/25.42 [10478]~P6(x104789,x104788,x104787)+~P6(x104781,x1047811,x1047810)+~P10(x104781,x104789,f932(x104786,a921),x1047810,x104787,x104785)+P1(f862(f862(f321(x104781),f533(x104782,x104783,x104784,x104785,x104786,x104787,x104788,x104789,x1047810,x1047811,x104781)),x1047811))+~P1(f862(f862(f321(f932(x104789,a921)),x104783),f862(f862(f53(x104789),x104788),x104787)))+~P1(f862(f862(f321(f932(x104781,a921)),x104784),f862(f862(f53(x104781),x1047811),x1047810)))+P1(f862(f862(f321(f932(x104786,a921)),f862(f862(f33(x104781,f932(x104786,a921)),x104784),f862(f862(f10(f932(x104789,f932(x104786,a921)),f932(x104786,a921),x104781),f862(f33(x104789,f932(x104786,a921)),x104783)),x104785))),x104782))
% 25.54/25.42 [10479]~P6(x1047911,x1047910,x104799)+~P6(x104791,x104798,x104797)+~P10(x1047911,x104791,f932(x104796,a921),x104799,x104797,x104795)+P1(f862(f862(f321(x104791),f534(x104792,x104793,x104794,x104795,x104796,x104797,x104798,x104791,x104799,x1047910,x1047911)),x104798))+~P1(f862(f862(f321(f932(x1047911,a921)),x104794),f862(f862(f53(x1047911),x1047910),x104799)))+~P1(f862(f862(f321(f932(x104791,a921)),x104793),f862(f862(f53(x104791),x104798),x104797)))+P1(f862(f862(f321(f932(x104796,a921)),f862(f862(f33(x1047911,f932(x104796,a921)),x104794),f862(f862(f10(f932(x104791,f932(x104796,a921)),f932(x104796,a921),x1047911),f862(f33(x104791,f932(x104796,a921)),x104793)),x104795))),x104792))
% 25.54/25.42 [10480]~P6(x104802,x104808,x104809)+~P6(x104804,x1048010,x1048011)+~P10(x104802,x104804,f932(x104801,a921),x104809,x1048011,x104806)+~P1(f862(f862(f321(f932(x104802,a921)),x104803),f862(f862(f53(x104802),x104808),x104809)))+~P1(f862(f862(f321(f932(x104804,a921)),x104805),f862(f862(f53(x104804),x1048010),x1048011)))+~P1(f862(f862(f321(f932(x104801,a921)),f862(f862(x104806,f533(x104807,x104805,x104803,x104806,x104801,x1048011,x1048010,x104804,x104809,x104808,x104802)),f534(x104807,x104805,x104803,x104806,x104801,x1048011,x1048010,x104804,x104809,x104808,x104802))),x104807))+P1(f862(f862(f321(f932(x104801,a921)),f862(f862(f33(x104802,f932(x104801,a921)),x104803),f862(f862(f10(f932(x104804,f932(x104801,a921)),f932(x104801,a921),x104802),f862(f33(x104804,f932(x104801,a921)),x104805)),x104806))),x104807))
% 25.54/25.42 [9353]E(x93531,x93532)+~P109(x93534)+~P22(x93533,x93534,x93535,f862(f862(f103(f932(x93533,a921)),f862(f165(x93533),x93531)),f862(f165(x93533),x93532)))+~E(f862(f165(x93533),x93531),f862(f165(x93533),x93532))+~P11(x93534,f862(f862(f147(x93533,x93534),x93535),x93532))+~P11(x93534,f862(f862(f147(x93533,x93534),x93535),x93531))+~P1(f862(f130(x93534),f862(f862(f147(x93533,x93534),x93535),x93532)))+~P1(f862(f130(x93534),f862(f862(f147(x93533,x93534),x93535),x93531)))
% 25.54/25.42 %EqnAxiom
% 25.54/25.42 [1]E(x11,x11)
% 25.54/25.42 [2]E(x22,x21)+~E(x21,x22)
% 25.54/25.42 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 25.54/25.42 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 25.54/25.42 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 25.54/25.42 [6]~E(x61,x62)+E(f93(x61),f93(x62))
% 25.54/25.42 [7]~E(x71,x72)+E(f181(x71),f181(x72))
% 25.54/25.42 [8]~E(x81,x82)+E(f862(x81,x83),f862(x82,x83))
% 25.54/25.42 [9]~E(x91,x92)+E(f862(x93,x91),f862(x93,x92))
% 25.54/25.42 [10]~E(x101,x102)+E(f94(x101),f94(x102))
% 25.54/25.42 [11]~E(x111,x112)+E(f225(x111),f225(x112))
% 25.54/25.42 [12]~E(x121,x122)+E(f103(x121),f103(x122))
% 25.54/25.42 [13]~E(x131,x132)+E(f226(x131),f226(x132))
% 25.54/25.42 [14]~E(x141,x142)+E(f95(x141),f95(x142))
% 25.54/25.42 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 25.54/25.42 [16]~E(x161,x162)+E(f77(x161),f77(x162))
% 25.54/25.42 [17]~E(x171,x172)+E(f925(x171),f925(x172))
% 25.54/25.42 [18]~E(x181,x182)+E(f931(x181,x183),f931(x182,x183))
% 25.54/25.42 [19]~E(x191,x192)+E(f931(x193,x191),f931(x193,x192))
% 25.54/25.42 [20]~E(x201,x202)+E(f932(x201,x203),f932(x202,x203))
% 25.54/25.42 [21]~E(x211,x212)+E(f932(x213,x211),f932(x213,x212))
% 25.54/25.42 [22]~E(x221,x222)+E(f71(x221),f71(x222))
% 25.54/25.42 [23]~E(x231,x232)+E(f534(x231,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f534(x232,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 25.54/25.42 [24]~E(x241,x242)+E(f534(x243,x241,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f534(x243,x242,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412))
% 25.54/25.42 [25]~E(x251,x252)+E(f534(x253,x254,x251,x255,x256,x257,x258,x259,x2510,x2511,x2512),f534(x253,x254,x252,x255,x256,x257,x258,x259,x2510,x2511,x2512))
% 25.54/25.42 [26]~E(x261,x262)+E(f534(x263,x264,x265,x261,x266,x267,x268,x269,x2610,x2611,x2612),f534(x263,x264,x265,x262,x266,x267,x268,x269,x2610,x2611,x2612))
% 25.54/25.42 [27]~E(x271,x272)+E(f534(x273,x274,x275,x276,x271,x277,x278,x279,x2710,x2711,x2712),f534(x273,x274,x275,x276,x272,x277,x278,x279,x2710,x2711,x2712))
% 25.54/25.42 [28]~E(x281,x282)+E(f534(x283,x284,x285,x286,x287,x281,x288,x289,x2810,x2811,x2812),f534(x283,x284,x285,x286,x287,x282,x288,x289,x2810,x2811,x2812))
% 25.54/25.42 [29]~E(x291,x292)+E(f534(x293,x294,x295,x296,x297,x298,x291,x299,x2910,x2911,x2912),f534(x293,x294,x295,x296,x297,x298,x292,x299,x2910,x2911,x2912))
% 25.54/25.42 [30]~E(x301,x302)+E(f534(x303,x304,x305,x306,x307,x308,x309,x301,x3010,x3011,x3012),f534(x303,x304,x305,x306,x307,x308,x309,x302,x3010,x3011,x3012))
% 25.54/25.42 [31]~E(x311,x312)+E(f534(x313,x314,x315,x316,x317,x318,x319,x3110,x311,x3111,x3112),f534(x313,x314,x315,x316,x317,x318,x319,x3110,x312,x3111,x3112))
% 25.54/25.42 [32]~E(x321,x322)+E(f534(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x321,x3212),f534(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x322,x3212))
% 25.54/25.42 [33]~E(x331,x332)+E(f534(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x331),f534(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x332))
% 25.54/25.42 [34]~E(x341,x342)+E(f9(x341,x343,x344),f9(x342,x343,x344))
% 25.54/25.42 [35]~E(x351,x352)+E(f9(x353,x351,x354),f9(x353,x352,x354))
% 25.54/25.42 [36]~E(x361,x362)+E(f9(x363,x364,x361),f9(x363,x364,x362))
% 25.54/25.42 [37]~E(x371,x372)+E(f6(x371),f6(x372))
% 25.54/25.42 [38]~E(x381,x382)+E(f533(x381,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f533(x382,x383,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812))
% 25.54/25.42 [39]~E(x391,x392)+E(f533(x393,x391,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912),f533(x393,x392,x394,x395,x396,x397,x398,x399,x3910,x3911,x3912))
% 25.54/25.42 [40]~E(x401,x402)+E(f533(x403,x404,x401,x405,x406,x407,x408,x409,x4010,x4011,x4012),f533(x403,x404,x402,x405,x406,x407,x408,x409,x4010,x4011,x4012))
% 25.54/25.42 [41]~E(x411,x412)+E(f533(x413,x414,x415,x411,x416,x417,x418,x419,x4110,x4111,x4112),f533(x413,x414,x415,x412,x416,x417,x418,x419,x4110,x4111,x4112))
% 25.54/25.42 [42]~E(x421,x422)+E(f533(x423,x424,x425,x426,x421,x427,x428,x429,x4210,x4211,x4212),f533(x423,x424,x425,x426,x422,x427,x428,x429,x4210,x4211,x4212))
% 25.54/25.42 [43]~E(x431,x432)+E(f533(x433,x434,x435,x436,x437,x431,x438,x439,x4310,x4311,x4312),f533(x433,x434,x435,x436,x437,x432,x438,x439,x4310,x4311,x4312))
% 25.54/25.42 [44]~E(x441,x442)+E(f533(x443,x444,x445,x446,x447,x448,x441,x449,x4410,x4411,x4412),f533(x443,x444,x445,x446,x447,x448,x442,x449,x4410,x4411,x4412))
% 25.54/25.42 [45]~E(x451,x452)+E(f533(x453,x454,x455,x456,x457,x458,x459,x451,x4510,x4511,x4512),f533(x453,x454,x455,x456,x457,x458,x459,x452,x4510,x4511,x4512))
% 25.54/25.42 [46]~E(x461,x462)+E(f533(x463,x464,x465,x466,x467,x468,x469,x4610,x461,x4611,x4612),f533(x463,x464,x465,x466,x467,x468,x469,x4610,x462,x4611,x4612))
% 25.54/25.42 [47]~E(x471,x472)+E(f533(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x471,x4712),f533(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x472,x4712))
% 25.54/25.42 [48]~E(x481,x482)+E(f533(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x481),f533(x483,x484,x485,x486,x487,x488,x489,x4810,x4811,x4812,x482))
% 25.54/25.42 [49]~E(x491,x492)+E(f321(x491),f321(x492))
% 25.54/25.42 [50]~E(x501,x502)+E(f104(x501),f104(x502))
% 25.54/25.42 [51]~E(x511,x512)+E(f73(x511),f73(x512))
% 25.54/25.42 [52]~E(x521,x522)+E(f923(x521),f923(x522))
% 25.54/25.42 [53]~E(x531,x532)+E(f928(x531),f928(x532))
% 25.54/25.42 [54]~E(x541,x542)+E(f228(x541),f228(x542))
% 25.54/25.42 [55]~E(x551,x552)+E(f926(x551),f926(x552))
% 25.54/25.42 [56]~E(x561,x562)+E(f234(x561),f234(x562))
% 25.54/25.42 [57]~E(x571,x572)+E(f18(x571,x573),f18(x572,x573))
% 25.54/25.42 [58]~E(x581,x582)+E(f18(x583,x581),f18(x583,x582))
% 25.54/25.42 [59]~E(x591,x592)+E(f38(x591,x593,x594),f38(x592,x593,x594))
% 25.54/25.42 [60]~E(x601,x602)+E(f38(x603,x601,x604),f38(x603,x602,x604))
% 25.54/25.42 [61]~E(x611,x612)+E(f38(x613,x614,x611),f38(x613,x614,x612))
% 25.54/25.42 [62]~E(x621,x622)+E(f867(x621,x623,x624),f867(x622,x623,x624))
% 25.54/25.42 [63]~E(x631,x632)+E(f867(x633,x631,x634),f867(x633,x632,x634))
% 25.54/25.42 [64]~E(x641,x642)+E(f867(x643,x644,x641),f867(x643,x644,x642))
% 25.54/25.42 [65]~E(x651,x652)+E(f72(x651),f72(x652))
% 25.54/25.42 [66]~E(x661,x662)+E(f144(x661),f144(x662))
% 25.54/25.42 [67]~E(x671,x672)+E(f96(x671),f96(x672))
% 25.54/25.42 [68]~E(x681,x682)+E(f165(x681),f165(x682))
% 25.54/25.42 [69]~E(x691,x692)+E(f182(x691),f182(x692))
% 25.54/25.42 [70]~E(x701,x702)+E(f227(x701),f227(x702))
% 25.54/25.42 [71]~E(x711,x712)+E(f281(x711),f281(x712))
% 25.54/25.42 [72]~E(x721,x722)+E(f10(x721,x723,x724),f10(x722,x723,x724))
% 25.54/25.42 [73]~E(x731,x732)+E(f10(x733,x731,x734),f10(x733,x732,x734))
% 25.54/25.42 [74]~E(x741,x742)+E(f10(x743,x744,x741),f10(x743,x744,x742))
% 25.54/25.42 [75]~E(x751,x752)+E(f54(x751),f54(x752))
% 25.54/25.42 [76]~E(x761,x762)+E(f276(x761,x763,x764),f276(x762,x763,x764))
% 25.54/25.42 [77]~E(x771,x772)+E(f276(x773,x771,x774),f276(x773,x772,x774))
% 25.54/25.42 [78]~E(x781,x782)+E(f276(x783,x784,x781),f276(x783,x784,x782))
% 25.54/25.42 [79]~E(x791,x792)+E(f74(x791),f74(x792))
% 25.54/25.42 [80]~E(x801,x802)+E(f33(x801,x803),f33(x802,x803))
% 25.54/25.42 [81]~E(x811,x812)+E(f33(x813,x811),f33(x813,x812))
% 25.54/25.42 [82]~E(x821,x822)+E(f146(x821,x823),f146(x822,x823))
% 25.54/25.42 [83]~E(x831,x832)+E(f146(x833,x831),f146(x833,x832))
% 25.54/25.42 [84]~E(x841,x842)+E(f371(x841,x843,x844),f371(x842,x843,x844))
% 25.54/25.42 [85]~E(x851,x852)+E(f371(x853,x851,x854),f371(x853,x852,x854))
% 25.54/25.42 [86]~E(x861,x862)+E(f371(x863,x864,x861),f371(x863,x864,x862))
% 25.54/25.42 [87]~E(x871,x872)+E(f278(x871),f278(x872))
% 25.54/25.42 [88]~E(x881,x882)+E(f446(x881,x883,x884,x885),f446(x882,x883,x884,x885))
% 25.54/25.42 [89]~E(x891,x892)+E(f446(x893,x891,x894,x895),f446(x893,x892,x894,x895))
% 25.54/25.42 [90]~E(x901,x902)+E(f446(x903,x904,x901,x905),f446(x903,x904,x902,x905))
% 25.54/25.42 [91]~E(x911,x912)+E(f446(x913,x914,x915,x911),f446(x913,x914,x915,x912))
% 25.54/25.42 [92]~E(x921,x922)+E(f69(x921),f69(x922))
% 25.54/25.42 [93]~E(x931,x932)+E(f171(x931,x933),f171(x932,x933))
% 25.54/25.42 [94]~E(x941,x942)+E(f171(x943,x941),f171(x943,x942))
% 25.54/25.42 [95]~E(x951,x952)+E(f53(x951),f53(x952))
% 25.54/25.42 [96]~E(x961,x962)+E(f295(x961,x963),f295(x962,x963))
% 25.54/25.42 [97]~E(x971,x972)+E(f295(x973,x971),f295(x973,x972))
% 25.54/25.42 [98]~E(x981,x982)+E(f66(x981,x983,x984,x985),f66(x982,x983,x984,x985))
% 25.54/25.42 [99]~E(x991,x992)+E(f66(x993,x991,x994,x995),f66(x993,x992,x994,x995))
% 25.54/25.42 [100]~E(x1001,x1002)+E(f66(x1003,x1004,x1001,x1005),f66(x1003,x1004,x1002,x1005))
% 25.54/25.42 [101]~E(x1011,x1012)+E(f66(x1013,x1014,x1015,x1011),f66(x1013,x1014,x1015,x1012))
% 25.54/25.42 [102]~E(x1021,x1022)+E(f137(x1021,x1023),f137(x1022,x1023))
% 25.54/25.42 [103]~E(x1031,x1032)+E(f137(x1033,x1031),f137(x1033,x1032))
% 25.54/25.42 [104]~E(x1041,x1042)+E(f20(x1041,x1043,x1044),f20(x1042,x1043,x1044))
% 25.54/25.42 [105]~E(x1051,x1052)+E(f20(x1053,x1051,x1054),f20(x1053,x1052,x1054))
% 25.54/25.42 [106]~E(x1061,x1062)+E(f20(x1063,x1064,x1061),f20(x1063,x1064,x1062))
% 25.54/25.42 [107]~E(x1071,x1072)+E(f930(x1071,x1073),f930(x1072,x1073))
% 25.54/25.42 [108]~E(x1081,x1082)+E(f930(x1083,x1081),f930(x1083,x1082))
% 25.54/25.42 [109]~E(x1091,x1092)+E(f127(x1091),f127(x1092))
% 25.54/25.42 [110]~E(x1101,x1102)+E(f187(x1101,x1103),f187(x1102,x1103))
% 25.54/25.42 [111]~E(x1111,x1112)+E(f187(x1113,x1111),f187(x1113,x1112))
% 25.54/25.42 [112]~E(x1121,x1122)+E(f302(x1121,x1123,x1124),f302(x1122,x1123,x1124))
% 25.54/25.42 [113]~E(x1131,x1132)+E(f302(x1133,x1131,x1134),f302(x1133,x1132,x1134))
% 25.54/25.42 [114]~E(x1141,x1142)+E(f302(x1143,x1144,x1141),f302(x1143,x1144,x1142))
% 25.54/25.42 [115]~E(x1151,x1152)+E(f28(x1151),f28(x1152))
% 25.54/25.42 [116]~E(x1161,x1162)+E(f158(x1161),f158(x1162))
% 25.54/25.42 [117]~E(x1171,x1172)+E(f30(x1171,x1173),f30(x1172,x1173))
% 25.54/25.42 [118]~E(x1181,x1182)+E(f30(x1183,x1181),f30(x1183,x1182))
% 25.54/25.42 [119]~E(x1191,x1192)+E(f134(x1191),f134(x1192))
% 25.54/25.42 [120]~E(x1201,x1202)+E(f254(x1201),f254(x1202))
% 25.54/25.42 [121]~E(x1211,x1212)+E(f296(x1211,x1213,x1214),f296(x1212,x1213,x1214))
% 25.54/25.42 [122]~E(x1221,x1222)+E(f296(x1223,x1221,x1224),f296(x1223,x1222,x1224))
% 25.54/25.42 [123]~E(x1231,x1232)+E(f296(x1233,x1234,x1231),f296(x1233,x1234,x1232))
% 25.54/25.42 [124]~E(x1241,x1242)+E(f147(x1241,x1243),f147(x1242,x1243))
% 25.54/25.42 [125]~E(x1251,x1252)+E(f147(x1253,x1251),f147(x1253,x1252))
% 25.54/25.42 [126]~E(x1261,x1262)+E(f243(x1261,x1263),f243(x1262,x1263))
% 25.54/25.42 [127]~E(x1271,x1272)+E(f243(x1273,x1271),f243(x1273,x1272))
% 25.54/25.42 [128]~E(x1281,x1282)+E(f17(x1281,x1283),f17(x1282,x1283))
% 25.54/25.42 [129]~E(x1291,x1292)+E(f17(x1293,x1291),f17(x1293,x1292))
% 25.54/25.42 [130]~E(x1301,x1302)+E(f29(x1301),f29(x1302))
% 25.54/25.42 [131]~E(x1311,x1312)+E(f307(x1311,x1313),f307(x1312,x1313))
% 25.54/25.42 [132]~E(x1321,x1322)+E(f307(x1323,x1321),f307(x1323,x1322))
% 25.54/25.42 [133]~E(x1331,x1332)+E(f244(x1331,x1333),f244(x1332,x1333))
% 25.54/25.42 [134]~E(x1341,x1342)+E(f244(x1343,x1341),f244(x1343,x1342))
% 25.54/25.42 [135]~E(x1351,x1352)+E(f559(x1351,x1353,x1354,x1355),f559(x1352,x1353,x1354,x1355))
% 25.54/25.42 [136]~E(x1361,x1362)+E(f559(x1363,x1361,x1364,x1365),f559(x1363,x1362,x1364,x1365))
% 25.54/25.42 [137]~E(x1371,x1372)+E(f559(x1373,x1374,x1371,x1375),f559(x1373,x1374,x1372,x1375))
% 25.54/25.42 [138]~E(x1381,x1382)+E(f559(x1383,x1384,x1385,x1381),f559(x1383,x1384,x1385,x1382))
% 25.54/25.42 [139]~E(x1391,x1392)+E(f119(x1391,x1393,x1394),f119(x1392,x1393,x1394))
% 25.54/25.42 [140]~E(x1401,x1402)+E(f119(x1403,x1401,x1404),f119(x1403,x1402,x1404))
% 25.54/25.42 [141]~E(x1411,x1412)+E(f119(x1413,x1414,x1411),f119(x1413,x1414,x1412))
% 25.54/25.42 [142]~E(x1421,x1422)+E(f636(x1421,x1423,x1424,x1425,x1426),f636(x1422,x1423,x1424,x1425,x1426))
% 25.54/25.42 [143]~E(x1431,x1432)+E(f636(x1433,x1431,x1434,x1435,x1436),f636(x1433,x1432,x1434,x1435,x1436))
% 25.54/25.42 [144]~E(x1441,x1442)+E(f636(x1443,x1444,x1441,x1445,x1446),f636(x1443,x1444,x1442,x1445,x1446))
% 25.54/25.42 [145]~E(x1451,x1452)+E(f636(x1453,x1454,x1455,x1451,x1456),f636(x1453,x1454,x1455,x1452,x1456))
% 25.54/25.42 [146]~E(x1461,x1462)+E(f636(x1463,x1464,x1465,x1466,x1461),f636(x1463,x1464,x1465,x1466,x1462))
% 25.54/25.42 [147]~E(x1471,x1472)+E(f98(x1471),f98(x1472))
% 25.54/25.42 [148]~E(x1481,x1482)+E(f99(x1481),f99(x1482))
% 25.54/25.42 [149]~E(x1491,x1492)+E(f320(x1491),f320(x1492))
% 25.54/25.42 [150]~E(x1501,x1502)+E(f8(x1501,x1503),f8(x1502,x1503))
% 25.54/25.42 [151]~E(x1511,x1512)+E(f8(x1513,x1511),f8(x1513,x1512))
% 25.54/25.42 [152]~E(x1521,x1522)+E(f587(x1521),f587(x1522))
% 25.54/25.42 [153]~E(x1531,x1532)+E(f153(x1531,x1533),f153(x1532,x1533))
% 25.54/25.42 [154]~E(x1541,x1542)+E(f153(x1543,x1541),f153(x1543,x1542))
% 25.54/25.42 [155]~E(x1551,x1552)+E(f150(x1551,x1553),f150(x1552,x1553))
% 25.54/25.42 [156]~E(x1561,x1562)+E(f150(x1563,x1561),f150(x1563,x1562))
% 25.54/25.42 [157]~E(x1571,x1572)+E(f233(x1571,x1573),f233(x1572,x1573))
% 25.54/25.42 [158]~E(x1581,x1582)+E(f233(x1583,x1581),f233(x1583,x1582))
% 25.54/25.42 [159]~E(x1591,x1592)+E(f42(x1591,x1593),f42(x1592,x1593))
% 25.54/25.42 [160]~E(x1601,x1602)+E(f42(x1603,x1601),f42(x1603,x1602))
% 25.54/25.42 [161]~E(x1611,x1612)+E(f157(x1611),f157(x1612))
% 25.54/25.42 [162]~E(x1621,x1622)+E(f248(x1621,x1623),f248(x1622,x1623))
% 25.54/25.42 [163]~E(x1631,x1632)+E(f248(x1633,x1631),f248(x1633,x1632))
% 25.54/25.42 [164]~E(x1641,x1642)+E(f790(x1641,x1643,x1644,x1645,x1646,x1647,x1648),f790(x1642,x1643,x1644,x1645,x1646,x1647,x1648))
% 25.54/25.42 [165]~E(x1651,x1652)+E(f790(x1653,x1651,x1654,x1655,x1656,x1657,x1658),f790(x1653,x1652,x1654,x1655,x1656,x1657,x1658))
% 25.54/25.42 [166]~E(x1661,x1662)+E(f790(x1663,x1664,x1661,x1665,x1666,x1667,x1668),f790(x1663,x1664,x1662,x1665,x1666,x1667,x1668))
% 25.54/25.42 [167]~E(x1671,x1672)+E(f790(x1673,x1674,x1675,x1671,x1676,x1677,x1678),f790(x1673,x1674,x1675,x1672,x1676,x1677,x1678))
% 25.54/25.42 [168]~E(x1681,x1682)+E(f790(x1683,x1684,x1685,x1686,x1681,x1687,x1688),f790(x1683,x1684,x1685,x1686,x1682,x1687,x1688))
% 25.54/25.42 [169]~E(x1691,x1692)+E(f790(x1693,x1694,x1695,x1696,x1697,x1691,x1698),f790(x1693,x1694,x1695,x1696,x1697,x1692,x1698))
% 25.54/25.42 [170]~E(x1701,x1702)+E(f790(x1703,x1704,x1705,x1706,x1707,x1708,x1701),f790(x1703,x1704,x1705,x1706,x1707,x1708,x1702))
% 25.54/25.42 [171]~E(x1711,x1712)+E(f11(x1711,x1713),f11(x1712,x1713))
% 25.54/25.42 [172]~E(x1721,x1722)+E(f11(x1723,x1721),f11(x1723,x1722))
% 25.54/25.42 [173]~E(x1731,x1732)+E(f301(x1731),f301(x1732))
% 25.54/25.42 [174]~E(x1741,x1742)+E(f7(x1741),f7(x1742))
% 25.54/25.42 [175]~E(x1751,x1752)+E(f359(x1751,x1753),f359(x1752,x1753))
% 25.54/25.42 [176]~E(x1761,x1762)+E(f359(x1763,x1761),f359(x1763,x1762))
% 25.54/25.42 [177]~E(x1771,x1772)+E(f310(x1771,x1773),f310(x1772,x1773))
% 25.54/25.42 [178]~E(x1781,x1782)+E(f310(x1783,x1781),f310(x1783,x1782))
% 25.54/25.42 [179]~E(x1791,x1792)+E(f208(x1791,x1793),f208(x1792,x1793))
% 25.54/25.42 [180]~E(x1801,x1802)+E(f208(x1803,x1801),f208(x1803,x1802))
% 25.54/25.42 [181]~E(x1811,x1812)+E(f784(x1811,x1813,x1814,x1815),f784(x1812,x1813,x1814,x1815))
% 25.54/25.42 [182]~E(x1821,x1822)+E(f784(x1823,x1821,x1824,x1825),f784(x1823,x1822,x1824,x1825))
% 25.54/25.42 [183]~E(x1831,x1832)+E(f784(x1833,x1834,x1831,x1835),f784(x1833,x1834,x1832,x1835))
% 25.54/25.42 [184]~E(x1841,x1842)+E(f784(x1843,x1844,x1845,x1841),f784(x1843,x1844,x1845,x1842))
% 25.54/25.42 [185]~E(x1851,x1852)+E(f249(x1851,x1853,x1854),f249(x1852,x1853,x1854))
% 25.54/25.42 [186]~E(x1861,x1862)+E(f249(x1863,x1861,x1864),f249(x1863,x1862,x1864))
% 25.54/25.42 [187]~E(x1871,x1872)+E(f249(x1873,x1874,x1871),f249(x1873,x1874,x1872))
% 25.54/25.42 [188]~E(x1881,x1882)+E(f391(x1881,x1883,x1884,x1885),f391(x1882,x1883,x1884,x1885))
% 25.54/25.42 [189]~E(x1891,x1892)+E(f391(x1893,x1891,x1894,x1895),f391(x1893,x1892,x1894,x1895))
% 25.54/25.42 [190]~E(x1901,x1902)+E(f391(x1903,x1904,x1901,x1905),f391(x1903,x1904,x1902,x1905))
% 25.54/25.42 [191]~E(x1911,x1912)+E(f391(x1913,x1914,x1915,x1911),f391(x1913,x1914,x1915,x1912))
% 25.54/25.42 [192]~E(x1921,x1922)+E(f298(x1921,x1923,x1924),f298(x1922,x1923,x1924))
% 25.54/25.42 [193]~E(x1931,x1932)+E(f298(x1933,x1931,x1934),f298(x1933,x1932,x1934))
% 25.54/25.42 [194]~E(x1941,x1942)+E(f298(x1943,x1944,x1941),f298(x1943,x1944,x1942))
% 25.54/25.42 [195]~E(x1951,x1952)+E(f106(x1951),f106(x1952))
% 25.54/25.42 [196]~E(x1961,x1962)+E(f236(x1961),f236(x1962))
% 25.54/25.42 [197]~E(x1971,x1972)+E(f75(x1971,x1973),f75(x1972,x1973))
% 25.54/25.42 [198]~E(x1981,x1982)+E(f75(x1983,x1981),f75(x1983,x1982))
% 25.54/25.42 [199]~E(x1991,x1992)+E(f297(x1991,x1993,x1994),f297(x1992,x1993,x1994))
% 25.54/25.42 [200]~E(x2001,x2002)+E(f297(x2003,x2001,x2004),f297(x2003,x2002,x2004))
% 25.54/25.42 [201]~E(x2011,x2012)+E(f297(x2013,x2014,x2011),f297(x2013,x2014,x2012))
% 25.54/25.42 [202]~E(x2021,x2022)+E(f163(x2021,x2023,x2024),f163(x2022,x2023,x2024))
% 25.54/25.42 [203]~E(x2031,x2032)+E(f163(x2033,x2031,x2034),f163(x2033,x2032,x2034))
% 25.54/25.42 [204]~E(x2041,x2042)+E(f163(x2043,x2044,x2041),f163(x2043,x2044,x2042))
% 25.54/25.42 [205]~E(x2051,x2052)+E(f32(x2051,x2053),f32(x2052,x2053))
% 25.54/25.42 [206]~E(x2061,x2062)+E(f32(x2063,x2061),f32(x2063,x2062))
% 25.54/25.42 [207]~E(x2071,x2072)+E(f12(x2071,x2073),f12(x2072,x2073))
% 25.54/25.42 [208]~E(x2081,x2082)+E(f12(x2083,x2081),f12(x2083,x2082))
% 25.54/25.42 [209]~E(x2091,x2092)+E(f250(x2091,x2093,x2094,x2095,x2096,x2097),f250(x2092,x2093,x2094,x2095,x2096,x2097))
% 25.54/25.42 [210]~E(x2101,x2102)+E(f250(x2103,x2101,x2104,x2105,x2106,x2107),f250(x2103,x2102,x2104,x2105,x2106,x2107))
% 25.54/25.42 [211]~E(x2111,x2112)+E(f250(x2113,x2114,x2111,x2115,x2116,x2117),f250(x2113,x2114,x2112,x2115,x2116,x2117))
% 25.54/25.42 [212]~E(x2121,x2122)+E(f250(x2123,x2124,x2125,x2121,x2126,x2127),f250(x2123,x2124,x2125,x2122,x2126,x2127))
% 25.54/25.42 [213]~E(x2131,x2132)+E(f250(x2133,x2134,x2135,x2136,x2131,x2137),f250(x2133,x2134,x2135,x2136,x2132,x2137))
% 25.54/25.42 [214]~E(x2141,x2142)+E(f250(x2143,x2144,x2145,x2146,x2147,x2141),f250(x2143,x2144,x2145,x2146,x2147,x2142))
% 25.54/25.42 [215]~E(x2151,x2152)+E(f129(x2151,x2153),f129(x2152,x2153))
% 25.54/25.42 [216]~E(x2161,x2162)+E(f129(x2163,x2161),f129(x2163,x2162))
% 25.54/25.42 [217]~E(x2171,x2172)+E(f311(x2171,x2173,x2174,x2175),f311(x2172,x2173,x2174,x2175))
% 25.54/25.42 [218]~E(x2181,x2182)+E(f311(x2183,x2181,x2184,x2185),f311(x2183,x2182,x2184,x2185))
% 25.54/25.42 [219]~E(x2191,x2192)+E(f311(x2193,x2194,x2191,x2195),f311(x2193,x2194,x2192,x2195))
% 25.54/25.42 [220]~E(x2201,x2202)+E(f311(x2203,x2204,x2205,x2201),f311(x2203,x2204,x2205,x2202))
% 25.54/25.42 [221]~E(x2211,x2212)+E(f277(x2211,x2213),f277(x2212,x2213))
% 25.54/25.42 [222]~E(x2221,x2222)+E(f277(x2223,x2221),f277(x2223,x2222))
% 25.54/25.42 [223]~E(x2231,x2232)+E(f79(x2231,x2233),f79(x2232,x2233))
% 25.54/25.42 [224]~E(x2241,x2242)+E(f79(x2243,x2241),f79(x2243,x2242))
% 25.54/25.42 [225]~E(x2251,x2252)+E(f80(x2251),f80(x2252))
% 25.54/25.42 [226]~E(x2261,x2262)+E(f443(x2261,x2263,x2264,x2265),f443(x2262,x2263,x2264,x2265))
% 25.54/25.42 [227]~E(x2271,x2272)+E(f443(x2273,x2271,x2274,x2275),f443(x2273,x2272,x2274,x2275))
% 25.54/25.42 [228]~E(x2281,x2282)+E(f443(x2283,x2284,x2281,x2285),f443(x2283,x2284,x2282,x2285))
% 25.54/25.42 [229]~E(x2291,x2292)+E(f443(x2293,x2294,x2295,x2291),f443(x2293,x2294,x2295,x2292))
% 25.54/25.42 [230]~E(x2301,x2302)+E(f423(x2301),f423(x2302))
% 25.54/25.42 [231]~E(x2311,x2312)+E(f57(x2311,x2313,x2314),f57(x2312,x2313,x2314))
% 25.54/25.42 [232]~E(x2321,x2322)+E(f57(x2323,x2321,x2324),f57(x2323,x2322,x2324))
% 25.54/25.42 [233]~E(x2331,x2332)+E(f57(x2333,x2334,x2331),f57(x2333,x2334,x2332))
% 25.54/25.42 [234]~E(x2341,x2342)+E(f275(x2341,x2343),f275(x2342,x2343))
% 25.54/25.42 [235]~E(x2351,x2352)+E(f275(x2353,x2351),f275(x2353,x2352))
% 25.54/25.42 [236]~E(x2361,x2362)+E(f31(x2361,x2363),f31(x2362,x2363))
% 25.54/25.42 [237]~E(x2371,x2372)+E(f31(x2373,x2371),f31(x2373,x2372))
% 25.54/25.42 [238]~E(x2381,x2382)+E(f131(x2381),f131(x2382))
% 25.54/25.42 [239]~E(x2391,x2392)+E(f287(x2391,x2393,x2394,x2395),f287(x2392,x2393,x2394,x2395))
% 25.54/25.42 [240]~E(x2401,x2402)+E(f287(x2403,x2401,x2404,x2405),f287(x2403,x2402,x2404,x2405))
% 25.54/25.42 [241]~E(x2411,x2412)+E(f287(x2413,x2414,x2411,x2415),f287(x2413,x2414,x2412,x2415))
% 25.54/25.42 [242]~E(x2421,x2422)+E(f287(x2423,x2424,x2425,x2421),f287(x2423,x2424,x2425,x2422))
% 25.54/25.42 [243]~E(x2431,x2432)+E(f739(x2431,x2433,x2434,x2435,x2436,x2437,x2438,x2439),f739(x2432,x2433,x2434,x2435,x2436,x2437,x2438,x2439))
% 25.54/25.42 [244]~E(x2441,x2442)+E(f739(x2443,x2441,x2444,x2445,x2446,x2447,x2448,x2449),f739(x2443,x2442,x2444,x2445,x2446,x2447,x2448,x2449))
% 25.54/25.42 [245]~E(x2451,x2452)+E(f739(x2453,x2454,x2451,x2455,x2456,x2457,x2458,x2459),f739(x2453,x2454,x2452,x2455,x2456,x2457,x2458,x2459))
% 25.54/25.42 [246]~E(x2461,x2462)+E(f739(x2463,x2464,x2465,x2461,x2466,x2467,x2468,x2469),f739(x2463,x2464,x2465,x2462,x2466,x2467,x2468,x2469))
% 25.54/25.42 [247]~E(x2471,x2472)+E(f739(x2473,x2474,x2475,x2476,x2471,x2477,x2478,x2479),f739(x2473,x2474,x2475,x2476,x2472,x2477,x2478,x2479))
% 25.54/25.42 [248]~E(x2481,x2482)+E(f739(x2483,x2484,x2485,x2486,x2487,x2481,x2488,x2489),f739(x2483,x2484,x2485,x2486,x2487,x2482,x2488,x2489))
% 25.54/25.42 [249]~E(x2491,x2492)+E(f739(x2493,x2494,x2495,x2496,x2497,x2498,x2491,x2499),f739(x2493,x2494,x2495,x2496,x2497,x2498,x2492,x2499))
% 25.54/25.42 [250]~E(x2501,x2502)+E(f739(x2503,x2504,x2505,x2506,x2507,x2508,x2509,x2501),f739(x2503,x2504,x2505,x2506,x2507,x2508,x2509,x2502))
% 25.54/25.42 [251]~E(x2511,x2512)+E(f869(x2511,x2513,x2514),f869(x2512,x2513,x2514))
% 25.54/25.42 [252]~E(x2521,x2522)+E(f869(x2523,x2521,x2524),f869(x2523,x2522,x2524))
% 25.54/25.42 [253]~E(x2531,x2532)+E(f869(x2533,x2534,x2531),f869(x2533,x2534,x2532))
% 25.54/25.42 [254]~E(x2541,x2542)+E(f771(x2541,x2543,x2544),f771(x2542,x2543,x2544))
% 25.54/25.42 [255]~E(x2551,x2552)+E(f771(x2553,x2551,x2554),f771(x2553,x2552,x2554))
% 25.54/25.42 [256]~E(x2561,x2562)+E(f771(x2563,x2564,x2561),f771(x2563,x2564,x2562))
% 25.54/25.42 [257]~E(x2571,x2572)+E(f135(x2571,x2573,x2574,x2575),f135(x2572,x2573,x2574,x2575))
% 25.54/25.42 [258]~E(x2581,x2582)+E(f135(x2583,x2581,x2584,x2585),f135(x2583,x2582,x2584,x2585))
% 25.54/25.42 [259]~E(x2591,x2592)+E(f135(x2593,x2594,x2591,x2595),f135(x2593,x2594,x2592,x2595))
% 25.54/25.42 [260]~E(x2601,x2602)+E(f135(x2603,x2604,x2605,x2601),f135(x2603,x2604,x2605,x2602))
% 25.54/25.42 [261]~E(x2611,x2612)+E(f299(x2611,x2613),f299(x2612,x2613))
% 25.54/25.42 [262]~E(x2621,x2622)+E(f299(x2623,x2621),f299(x2623,x2622))
% 25.54/25.42 [263]~E(x2631,x2632)+E(f240(x2631,x2633),f240(x2632,x2633))
% 25.54/25.42 [264]~E(x2641,x2642)+E(f240(x2643,x2641),f240(x2643,x2642))
% 25.54/25.42 [265]~E(x2651,x2652)+E(f68(x2651,x2653,x2654,x2655,x2656),f68(x2652,x2653,x2654,x2655,x2656))
% 25.54/25.42 [266]~E(x2661,x2662)+E(f68(x2663,x2661,x2664,x2665,x2666),f68(x2663,x2662,x2664,x2665,x2666))
% 25.54/25.42 [267]~E(x2671,x2672)+E(f68(x2673,x2674,x2671,x2675,x2676),f68(x2673,x2674,x2672,x2675,x2676))
% 25.54/25.42 [268]~E(x2681,x2682)+E(f68(x2683,x2684,x2685,x2681,x2686),f68(x2683,x2684,x2685,x2682,x2686))
% 25.54/25.42 [269]~E(x2691,x2692)+E(f68(x2693,x2694,x2695,x2696,x2691),f68(x2693,x2694,x2695,x2696,x2692))
% 25.54/25.42 [270]~E(x2701,x2702)+E(f107(x2701,x2703),f107(x2702,x2703))
% 25.54/25.42 [271]~E(x2711,x2712)+E(f107(x2713,x2711),f107(x2713,x2712))
% 25.54/25.42 [272]~E(x2721,x2722)+E(f899(x2721,x2723,x2724,x2725,x2726),f899(x2722,x2723,x2724,x2725,x2726))
% 25.54/25.42 [273]~E(x2731,x2732)+E(f899(x2733,x2731,x2734,x2735,x2736),f899(x2733,x2732,x2734,x2735,x2736))
% 25.54/25.42 [274]~E(x2741,x2742)+E(f899(x2743,x2744,x2741,x2745,x2746),f899(x2743,x2744,x2742,x2745,x2746))
% 25.54/25.42 [275]~E(x2751,x2752)+E(f899(x2753,x2754,x2755,x2751,x2756),f899(x2753,x2754,x2755,x2752,x2756))
% 25.54/25.42 [276]~E(x2761,x2762)+E(f899(x2763,x2764,x2765,x2766,x2761),f899(x2763,x2764,x2765,x2766,x2762))
% 25.54/25.42 [277]~E(x2771,x2772)+E(f483(x2771,x2773,x2774,x2775,x2776),f483(x2772,x2773,x2774,x2775,x2776))
% 25.54/25.42 [278]~E(x2781,x2782)+E(f483(x2783,x2781,x2784,x2785,x2786),f483(x2783,x2782,x2784,x2785,x2786))
% 25.54/25.42 [279]~E(x2791,x2792)+E(f483(x2793,x2794,x2791,x2795,x2796),f483(x2793,x2794,x2792,x2795,x2796))
% 25.54/25.42 [280]~E(x2801,x2802)+E(f483(x2803,x2804,x2805,x2801,x2806),f483(x2803,x2804,x2805,x2802,x2806))
% 25.54/25.42 [281]~E(x2811,x2812)+E(f483(x2813,x2814,x2815,x2816,x2811),f483(x2813,x2814,x2815,x2816,x2812))
% 25.54/25.42 [282]~E(x2821,x2822)+E(f145(x2821,x2823),f145(x2822,x2823))
% 25.54/25.42 [283]~E(x2831,x2832)+E(f145(x2833,x2831),f145(x2833,x2832))
% 25.54/25.42 [284]~E(x2841,x2842)+E(f168(x2841),f168(x2842))
% 25.54/25.42 [285]~E(x2851,x2852)+E(f184(x2851),f184(x2852))
% 25.54/25.42 [286]~E(x2861,x2862)+E(f102(x2861),f102(x2862))
% 25.54/25.42 [287]~E(x2871,x2872)+E(f108(x2871),f108(x2872))
% 25.54/25.42 [288]~E(x2881,x2882)+E(f655(x2881,x2883,x2884,x2885),f655(x2882,x2883,x2884,x2885))
% 25.54/25.42 [289]~E(x2891,x2892)+E(f655(x2893,x2891,x2894,x2895),f655(x2893,x2892,x2894,x2895))
% 25.54/25.42 [290]~E(x2901,x2902)+E(f655(x2903,x2904,x2901,x2905),f655(x2903,x2904,x2902,x2905))
% 25.54/25.42 [291]~E(x2911,x2912)+E(f655(x2913,x2914,x2915,x2911),f655(x2913,x2914,x2915,x2912))
% 25.54/25.42 [292]~E(x2921,x2922)+E(f475(x2921,x2923,x2924),f475(x2922,x2923,x2924))
% 25.54/25.42 [293]~E(x2931,x2932)+E(f475(x2933,x2931,x2934),f475(x2933,x2932,x2934))
% 25.54/25.42 [294]~E(x2941,x2942)+E(f475(x2943,x2944,x2941),f475(x2943,x2944,x2942))
% 25.54/25.42 [295]~E(x2951,x2952)+E(f929(x2951,x2953),f929(x2952,x2953))
% 25.54/25.42 [296]~E(x2961,x2962)+E(f929(x2963,x2961),f929(x2963,x2962))
% 25.54/25.42 [297]~E(x2971,x2972)+E(f170(x2971,x2973,x2974),f170(x2972,x2973,x2974))
% 25.54/25.42 [298]~E(x2981,x2982)+E(f170(x2983,x2981,x2984),f170(x2983,x2982,x2984))
% 25.54/25.42 [299]~E(x2991,x2992)+E(f170(x2993,x2994,x2991),f170(x2993,x2994,x2992))
% 25.54/25.42 [300]~E(x3001,x3002)+E(f161(x3001),f161(x3002))
% 25.54/25.42 [301]~E(x3011,x3012)+E(f160(x3011),f160(x3012))
% 25.54/25.42 [302]~E(x3021,x3022)+E(f84(x3021),f84(x3022))
% 25.54/25.42 [303]~E(x3031,x3032)+E(f300(x3031),f300(x3032))
% 25.54/25.42 [304]~E(x3041,x3042)+E(f152(x3041,x3043),f152(x3042,x3043))
% 25.54/25.42 [305]~E(x3051,x3052)+E(f152(x3053,x3051),f152(x3053,x3052))
% 25.54/25.42 [306]~E(x3061,x3062)+E(f140(x3061,x3063),f140(x3062,x3063))
% 25.54/25.42 [307]~E(x3071,x3072)+E(f140(x3073,x3071),f140(x3073,x3072))
% 25.54/25.42 [308]~E(x3081,x3082)+E(f164(x3081),f164(x3082))
% 25.54/25.42 [309]~E(x3091,x3092)+E(f36(x3091),f36(x3092))
% 25.54/25.42 [310]~E(x3101,x3102)+E(f162(x3101,x3103,x3104),f162(x3102,x3103,x3104))
% 25.54/25.42 [311]~E(x3111,x3112)+E(f162(x3113,x3111,x3114),f162(x3113,x3112,x3114))
% 25.54/25.42 [312]~E(x3121,x3122)+E(f162(x3123,x3124,x3121),f162(x3123,x3124,x3122))
% 25.54/25.42 [313]~E(x3131,x3132)+E(f86(x3131,x3133,x3134,x3135),f86(x3132,x3133,x3134,x3135))
% 25.54/25.42 [314]~E(x3141,x3142)+E(f86(x3143,x3141,x3144,x3145),f86(x3143,x3142,x3144,x3145))
% 25.54/25.42 [315]~E(x3151,x3152)+E(f86(x3153,x3154,x3151,x3155),f86(x3153,x3154,x3152,x3155))
% 25.54/25.42 [316]~E(x3161,x3162)+E(f86(x3163,x3164,x3165,x3161),f86(x3163,x3164,x3165,x3162))
% 25.54/25.42 [317]~E(x3171,x3172)+E(f274(x3171),f274(x3172))
% 25.54/25.42 [318]~E(x3181,x3182)+E(f293(x3181),f293(x3182))
% 25.54/25.42 [319]~E(x3191,x3192)+E(f780(x3191,x3193,x3194),f780(x3192,x3193,x3194))
% 25.54/25.42 [320]~E(x3201,x3202)+E(f780(x3203,x3201,x3204),f780(x3203,x3202,x3204))
% 25.54/25.42 [321]~E(x3211,x3212)+E(f780(x3213,x3214,x3211),f780(x3213,x3214,x3212))
% 25.54/25.42 [322]~E(x3221,x3222)+E(f136(x3221,x3223),f136(x3222,x3223))
% 25.54/25.42 [323]~E(x3231,x3232)+E(f136(x3233,x3231),f136(x3233,x3232))
% 25.54/25.42 [324]~E(x3241,x3242)+E(f132(x3241,x3243),f132(x3242,x3243))
% 25.54/25.42 [325]~E(x3251,x3252)+E(f132(x3253,x3251),f132(x3253,x3252))
% 25.54/25.42 [326]~E(x3261,x3262)+E(f58(x3261,x3263,x3264),f58(x3262,x3263,x3264))
% 25.54/25.42 [327]~E(x3271,x3272)+E(f58(x3273,x3271,x3274),f58(x3273,x3272,x3274))
% 25.54/25.42 [328]~E(x3281,x3282)+E(f58(x3283,x3284,x3281),f58(x3283,x3284,x3282))
% 25.54/25.42 [329]~E(x3291,x3292)+E(f246(x3291,x3293),f246(x3292,x3293))
% 25.54/25.42 [330]~E(x3301,x3302)+E(f246(x3303,x3301),f246(x3303,x3302))
% 25.54/25.42 [331]~E(x3311,x3312)+E(f917(x3311,x3313,x3314,x3315,x3316),f917(x3312,x3313,x3314,x3315,x3316))
% 25.54/25.42 [332]~E(x3321,x3322)+E(f917(x3323,x3321,x3324,x3325,x3326),f917(x3323,x3322,x3324,x3325,x3326))
% 25.54/25.42 [333]~E(x3331,x3332)+E(f917(x3333,x3334,x3331,x3335,x3336),f917(x3333,x3334,x3332,x3335,x3336))
% 25.54/25.42 [334]~E(x3341,x3342)+E(f917(x3343,x3344,x3345,x3341,x3346),f917(x3343,x3344,x3345,x3342,x3346))
% 25.54/25.42 [335]~E(x3351,x3352)+E(f917(x3353,x3354,x3355,x3356,x3351),f917(x3353,x3354,x3355,x3356,x3352))
% 25.54/25.42 [336]~E(x3361,x3362)+E(f519(x3361,x3363,x3364,x3365,x3366,x3367),f519(x3362,x3363,x3364,x3365,x3366,x3367))
% 25.54/25.42 [337]~E(x3371,x3372)+E(f519(x3373,x3371,x3374,x3375,x3376,x3377),f519(x3373,x3372,x3374,x3375,x3376,x3377))
% 25.54/25.42 [338]~E(x3381,x3382)+E(f519(x3383,x3384,x3381,x3385,x3386,x3387),f519(x3383,x3384,x3382,x3385,x3386,x3387))
% 25.54/25.42 [339]~E(x3391,x3392)+E(f519(x3393,x3394,x3395,x3391,x3396,x3397),f519(x3393,x3394,x3395,x3392,x3396,x3397))
% 25.54/25.42 [340]~E(x3401,x3402)+E(f519(x3403,x3404,x3405,x3406,x3401,x3407),f519(x3403,x3404,x3405,x3406,x3402,x3407))
% 25.54/25.42 [341]~E(x3411,x3412)+E(f519(x3413,x3414,x3415,x3416,x3417,x3411),f519(x3413,x3414,x3415,x3416,x3417,x3412))
% 25.54/25.42 [342]~E(x3421,x3422)+E(f235(x3421,x3423,x3424),f235(x3422,x3423,x3424))
% 25.54/25.42 [343]~E(x3431,x3432)+E(f235(x3433,x3431,x3434),f235(x3433,x3432,x3434))
% 25.54/25.42 [344]~E(x3441,x3442)+E(f235(x3443,x3444,x3441),f235(x3443,x3444,x3442))
% 25.54/25.42 [345]~E(x3451,x3452)+E(f452(x3451,x3453,x3454),f452(x3452,x3453,x3454))
% 25.54/25.42 [346]~E(x3461,x3462)+E(f452(x3463,x3461,x3464),f452(x3463,x3462,x3464))
% 25.54/25.42 [347]~E(x3471,x3472)+E(f452(x3473,x3474,x3471),f452(x3473,x3474,x3472))
% 25.54/25.42 [348]~E(x3481,x3482)+E(f312(x3481,x3483),f312(x3482,x3483))
% 25.54/25.42 [349]~E(x3491,x3492)+E(f312(x3493,x3491),f312(x3493,x3492))
% 25.54/25.42 [350]~E(x3501,x3502)+E(f872(x3501,x3503,x3504),f872(x3502,x3503,x3504))
% 25.54/25.42 [351]~E(x3511,x3512)+E(f872(x3513,x3511,x3514),f872(x3513,x3512,x3514))
% 25.54/25.42 [352]~E(x3521,x3522)+E(f872(x3523,x3524,x3521),f872(x3523,x3524,x3522))
% 25.54/25.42 [353]~E(x3531,x3532)+E(f880(x3531,x3533,x3534,x3535,x3536,x3537,x3538),f880(x3532,x3533,x3534,x3535,x3536,x3537,x3538))
% 25.54/25.42 [354]~E(x3541,x3542)+E(f880(x3543,x3541,x3544,x3545,x3546,x3547,x3548),f880(x3543,x3542,x3544,x3545,x3546,x3547,x3548))
% 25.54/25.42 [355]~E(x3551,x3552)+E(f880(x3553,x3554,x3551,x3555,x3556,x3557,x3558),f880(x3553,x3554,x3552,x3555,x3556,x3557,x3558))
% 25.54/25.42 [356]~E(x3561,x3562)+E(f880(x3563,x3564,x3565,x3561,x3566,x3567,x3568),f880(x3563,x3564,x3565,x3562,x3566,x3567,x3568))
% 25.54/25.42 [357]~E(x3571,x3572)+E(f880(x3573,x3574,x3575,x3576,x3571,x3577,x3578),f880(x3573,x3574,x3575,x3576,x3572,x3577,x3578))
% 25.54/25.42 [358]~E(x3581,x3582)+E(f880(x3583,x3584,x3585,x3586,x3587,x3581,x3588),f880(x3583,x3584,x3585,x3586,x3587,x3582,x3588))
% 25.54/25.42 [359]~E(x3591,x3592)+E(f880(x3593,x3594,x3595,x3596,x3597,x3598,x3591),f880(x3593,x3594,x3595,x3596,x3597,x3598,x3592))
% 25.54/25.42 [360]~E(x3601,x3602)+E(f375(x3601,x3603,x3604),f375(x3602,x3603,x3604))
% 25.54/25.42 [361]~E(x3611,x3612)+E(f375(x3613,x3611,x3614),f375(x3613,x3612,x3614))
% 25.54/25.42 [362]~E(x3621,x3622)+E(f375(x3623,x3624,x3621),f375(x3623,x3624,x3622))
% 25.54/25.42 [363]~E(x3631,x3632)+E(f251(x3631,x3633,x3634,x3635),f251(x3632,x3633,x3634,x3635))
% 25.54/25.42 [364]~E(x3641,x3642)+E(f251(x3643,x3641,x3644,x3645),f251(x3643,x3642,x3644,x3645))
% 25.54/25.42 [365]~E(x3651,x3652)+E(f251(x3653,x3654,x3651,x3655),f251(x3653,x3654,x3652,x3655))
% 25.54/25.42 [366]~E(x3661,x3662)+E(f251(x3663,x3664,x3665,x3661),f251(x3663,x3664,x3665,x3662))
% 25.54/25.42 [367]~E(x3671,x3672)+E(f13(x3671,x3673,x3674),f13(x3672,x3673,x3674))
% 25.54/25.42 [368]~E(x3681,x3682)+E(f13(x3683,x3681,x3684),f13(x3683,x3682,x3684))
% 25.54/25.42 [369]~E(x3691,x3692)+E(f13(x3693,x3694,x3691),f13(x3693,x3694,x3692))
% 25.54/25.42 [370]~E(x3701,x3702)+E(f15(x3701,x3703),f15(x3702,x3703))
% 25.54/25.42 [371]~E(x3711,x3712)+E(f15(x3713,x3711),f15(x3713,x3712))
% 25.54/25.42 [372]~E(x3721,x3722)+E(f190(x3721,x3723,x3724,x3725),f190(x3722,x3723,x3724,x3725))
% 25.54/25.42 [373]~E(x3731,x3732)+E(f190(x3733,x3731,x3734,x3735),f190(x3733,x3732,x3734,x3735))
% 25.54/25.42 [374]~E(x3741,x3742)+E(f190(x3743,x3744,x3741,x3745),f190(x3743,x3744,x3742,x3745))
% 25.54/25.42 [375]~E(x3751,x3752)+E(f190(x3753,x3754,x3755,x3751),f190(x3753,x3754,x3755,x3752))
% 25.54/25.42 [376]~E(x3761,x3762)+E(f783(x3761,x3763,x3764,x3765),f783(x3762,x3763,x3764,x3765))
% 25.54/25.42 [377]~E(x3771,x3772)+E(f783(x3773,x3771,x3774,x3775),f783(x3773,x3772,x3774,x3775))
% 25.54/25.42 [378]~E(x3781,x3782)+E(f783(x3783,x3784,x3781,x3785),f783(x3783,x3784,x3782,x3785))
% 25.54/25.42 [379]~E(x3791,x3792)+E(f783(x3793,x3794,x3795,x3791),f783(x3793,x3794,x3795,x3792))
% 25.54/25.42 [380]~E(x3801,x3802)+E(f292(x3801),f292(x3802))
% 25.54/25.42 [381]~E(x3811,x3812)+E(f256(x3811,x3813),f256(x3812,x3813))
% 25.54/25.42 [382]~E(x3821,x3822)+E(f256(x3823,x3821),f256(x3823,x3822))
% 25.54/25.42 [383]~E(x3831,x3832)+E(f138(x3831,x3833),f138(x3832,x3833))
% 25.54/25.42 [384]~E(x3841,x3842)+E(f138(x3843,x3841),f138(x3843,x3842))
% 25.54/25.42 [385]~E(x3851,x3852)+E(f141(x3851,x3853,x3854),f141(x3852,x3853,x3854))
% 25.54/25.42 [386]~E(x3861,x3862)+E(f141(x3863,x3861,x3864),f141(x3863,x3862,x3864))
% 25.54/25.42 [387]~E(x3871,x3872)+E(f141(x3873,x3874,x3871),f141(x3873,x3874,x3872))
% 25.54/25.42 [388]~E(x3881,x3882)+E(f744(x3881,x3883,x3884),f744(x3882,x3883,x3884))
% 25.54/25.42 [389]~E(x3891,x3892)+E(f744(x3893,x3891,x3894),f744(x3893,x3892,x3894))
% 25.54/25.42 [390]~E(x3901,x3902)+E(f744(x3903,x3904,x3901),f744(x3903,x3904,x3902))
% 25.54/25.42 [391]~E(x3911,x3912)+E(f637(x3911,x3913,x3914,x3915),f637(x3912,x3913,x3914,x3915))
% 25.54/25.42 [392]~E(x3921,x3922)+E(f637(x3923,x3921,x3924,x3925),f637(x3923,x3922,x3924,x3925))
% 25.54/25.42 [393]~E(x3931,x3932)+E(f637(x3933,x3934,x3931,x3935),f637(x3933,x3934,x3932,x3935))
% 25.54/25.42 [394]~E(x3941,x3942)+E(f637(x3943,x3944,x3945,x3941),f637(x3943,x3944,x3945,x3942))
% 25.54/25.42 [395]~E(x3951,x3952)+E(f112(x3951),f112(x3952))
% 25.54/25.42 [396]~E(x3961,x3962)+E(f113(x3961,x3963),f113(x3962,x3963))
% 25.54/25.42 [397]~E(x3971,x3972)+E(f113(x3973,x3971),f113(x3973,x3972))
% 25.54/25.42 [398]~E(x3981,x3982)+E(f868(x3981,x3983,x3984),f868(x3982,x3983,x3984))
% 25.54/25.42 [399]~E(x3991,x3992)+E(f868(x3993,x3991,x3994),f868(x3993,x3992,x3994))
% 25.54/25.42 [400]~E(x4001,x4002)+E(f868(x4003,x4004,x4001),f868(x4003,x4004,x4002))
% 25.54/25.42 [401]~E(x4011,x4012)+E(f736(x4011,x4013),f736(x4012,x4013))
% 25.54/25.42 [402]~E(x4021,x4022)+E(f736(x4023,x4021),f736(x4023,x4022))
% 25.54/25.42 [403]~E(x4031,x4032)+E(f813(x4031),f813(x4032))
% 25.54/25.42 [404]~E(x4041,x4042)+E(f753(x4041,x4043,x4044,x4045,x4046),f753(x4042,x4043,x4044,x4045,x4046))
% 25.54/25.42 [405]~E(x4051,x4052)+E(f753(x4053,x4051,x4054,x4055,x4056),f753(x4053,x4052,x4054,x4055,x4056))
% 25.54/25.42 [406]~E(x4061,x4062)+E(f753(x4063,x4064,x4061,x4065,x4066),f753(x4063,x4064,x4062,x4065,x4066))
% 25.54/25.42 [407]~E(x4071,x4072)+E(f753(x4073,x4074,x4075,x4071,x4076),f753(x4073,x4074,x4075,x4072,x4076))
% 25.54/25.42 [408]~E(x4081,x4082)+E(f753(x4083,x4084,x4085,x4086,x4081),f753(x4083,x4084,x4085,x4086,x4082))
% 25.54/25.42 [409]~E(x4091,x4092)+E(f78(x4091,x4093),f78(x4092,x4093))
% 25.54/25.42 [410]~E(x4101,x4102)+E(f78(x4103,x4101),f78(x4103,x4102))
% 25.54/25.42 [411]~E(x4111,x4112)+E(f605(x4111,x4113,x4114,x4115,x4116,x4117,x4118,x4119),f605(x4112,x4113,x4114,x4115,x4116,x4117,x4118,x4119))
% 25.54/25.42 [412]~E(x4121,x4122)+E(f605(x4123,x4121,x4124,x4125,x4126,x4127,x4128,x4129),f605(x4123,x4122,x4124,x4125,x4126,x4127,x4128,x4129))
% 25.54/25.42 [413]~E(x4131,x4132)+E(f605(x4133,x4134,x4131,x4135,x4136,x4137,x4138,x4139),f605(x4133,x4134,x4132,x4135,x4136,x4137,x4138,x4139))
% 25.54/25.42 [414]~E(x4141,x4142)+E(f605(x4143,x4144,x4145,x4141,x4146,x4147,x4148,x4149),f605(x4143,x4144,x4145,x4142,x4146,x4147,x4148,x4149))
% 25.54/25.42 [415]~E(x4151,x4152)+E(f605(x4153,x4154,x4155,x4156,x4151,x4157,x4158,x4159),f605(x4153,x4154,x4155,x4156,x4152,x4157,x4158,x4159))
% 25.54/25.42 [416]~E(x4161,x4162)+E(f605(x4163,x4164,x4165,x4166,x4167,x4161,x4168,x4169),f605(x4163,x4164,x4165,x4166,x4167,x4162,x4168,x4169))
% 25.54/25.42 [417]~E(x4171,x4172)+E(f605(x4173,x4174,x4175,x4176,x4177,x4178,x4171,x4179),f605(x4173,x4174,x4175,x4176,x4177,x4178,x4172,x4179))
% 25.54/25.42 [418]~E(x4181,x4182)+E(f605(x4183,x4184,x4185,x4186,x4187,x4188,x4189,x4181),f605(x4183,x4184,x4185,x4186,x4187,x4188,x4189,x4182))
% 25.54/25.42 [419]~E(x4191,x4192)+E(f83(x4191,x4193),f83(x4192,x4193))
% 25.54/25.42 [420]~E(x4201,x4202)+E(f83(x4203,x4201),f83(x4203,x4202))
% 25.54/25.42 [421]~E(x4211,x4212)+E(f490(x4211,x4213,x4214),f490(x4212,x4213,x4214))
% 25.54/25.42 [422]~E(x4221,x4222)+E(f490(x4223,x4221,x4224),f490(x4223,x4222,x4224))
% 25.54/25.42 [423]~E(x4231,x4232)+E(f490(x4233,x4234,x4231),f490(x4233,x4234,x4232))
% 25.54/25.42 [424]~E(x4241,x4242)+E(f748(x4241,x4243,x4244,x4245,x4246),f748(x4242,x4243,x4244,x4245,x4246))
% 25.54/25.42 [425]~E(x4251,x4252)+E(f748(x4253,x4251,x4254,x4255,x4256),f748(x4253,x4252,x4254,x4255,x4256))
% 25.54/25.42 [426]~E(x4261,x4262)+E(f748(x4263,x4264,x4261,x4265,x4266),f748(x4263,x4264,x4262,x4265,x4266))
% 25.54/25.42 [427]~E(x4271,x4272)+E(f748(x4273,x4274,x4275,x4271,x4276),f748(x4273,x4274,x4275,x4272,x4276))
% 25.54/25.42 [428]~E(x4281,x4282)+E(f748(x4283,x4284,x4285,x4286,x4281),f748(x4283,x4284,x4285,x4286,x4282))
% 25.54/25.42 [429]~E(x4291,x4292)+E(f255(x4291,x4293),f255(x4292,x4293))
% 25.54/25.42 [430]~E(x4301,x4302)+E(f255(x4303,x4301),f255(x4303,x4302))
% 25.54/25.42 [431]~E(x4311,x4312)+E(f280(x4311,x4313,x4314),f280(x4312,x4313,x4314))
% 25.54/25.42 [432]~E(x4321,x4322)+E(f280(x4323,x4321,x4324),f280(x4323,x4322,x4324))
% 25.54/25.42 [433]~E(x4331,x4332)+E(f280(x4333,x4334,x4331),f280(x4333,x4334,x4332))
% 25.54/25.42 [434]~E(x4341,x4342)+E(f176(x4341,x4343),f176(x4342,x4343))
% 25.54/25.42 [435]~E(x4351,x4352)+E(f176(x4353,x4351),f176(x4353,x4352))
% 25.54/25.42 [436]~E(x4361,x4362)+E(f143(x4361,x4363,x4364,x4365),f143(x4362,x4363,x4364,x4365))
% 25.54/25.42 [437]~E(x4371,x4372)+E(f143(x4373,x4371,x4374,x4375),f143(x4373,x4372,x4374,x4375))
% 25.54/25.42 [438]~E(x4381,x4382)+E(f143(x4383,x4384,x4381,x4385),f143(x4383,x4384,x4382,x4385))
% 25.54/25.42 [439]~E(x4391,x4392)+E(f143(x4393,x4394,x4395,x4391),f143(x4393,x4394,x4395,x4392))
% 25.54/25.42 [440]~E(x4401,x4402)+E(f326(x4401),f326(x4402))
% 25.54/25.42 [441]~E(x4411,x4412)+E(f14(x4411,x4413,x4414),f14(x4412,x4413,x4414))
% 25.54/25.42 [442]~E(x4421,x4422)+E(f14(x4423,x4421,x4424),f14(x4423,x4422,x4424))
% 25.54/25.42 [443]~E(x4431,x4432)+E(f14(x4433,x4434,x4431),f14(x4433,x4434,x4432))
% 25.54/25.42 [444]~E(x4441,x4442)+E(f258(x4441,x4443),f258(x4442,x4443))
% 25.54/25.42 [445]~E(x4451,x4452)+E(f258(x4453,x4451),f258(x4453,x4452))
% 25.54/25.42 [446]~E(x4461,x4462)+E(f154(x4461,x4463),f154(x4462,x4463))
% 25.54/25.42 [447]~E(x4471,x4472)+E(f154(x4473,x4471),f154(x4473,x4472))
% 25.54/25.42 [448]~E(x4481,x4482)+E(f568(x4481,x4483,x4484,x4485),f568(x4482,x4483,x4484,x4485))
% 25.54/25.42 [449]~E(x4491,x4492)+E(f568(x4493,x4491,x4494,x4495),f568(x4493,x4492,x4494,x4495))
% 25.54/25.42 [450]~E(x4501,x4502)+E(f568(x4503,x4504,x4501,x4505),f568(x4503,x4504,x4502,x4505))
% 25.54/25.42 [451]~E(x4511,x4512)+E(f568(x4513,x4514,x4515,x4511),f568(x4513,x4514,x4515,x4512))
% 25.54/25.42 [452]~E(x4521,x4522)+E(f16(x4521,x4523),f16(x4522,x4523))
% 25.54/25.42 [453]~E(x4531,x4532)+E(f16(x4533,x4531),f16(x4533,x4532))
% 25.54/25.42 [454]~E(x4541,x4542)+E(f294(x4541),f294(x4542))
% 25.54/25.42 [455]~E(x4551,x4552)+E(f584(x4551,x4553,x4554,x4555,x4556,x4557,x4558,x4559),f584(x4552,x4553,x4554,x4555,x4556,x4557,x4558,x4559))
% 25.54/25.42 [456]~E(x4561,x4562)+E(f584(x4563,x4561,x4564,x4565,x4566,x4567,x4568,x4569),f584(x4563,x4562,x4564,x4565,x4566,x4567,x4568,x4569))
% 25.54/25.42 [457]~E(x4571,x4572)+E(f584(x4573,x4574,x4571,x4575,x4576,x4577,x4578,x4579),f584(x4573,x4574,x4572,x4575,x4576,x4577,x4578,x4579))
% 25.54/25.42 [458]~E(x4581,x4582)+E(f584(x4583,x4584,x4585,x4581,x4586,x4587,x4588,x4589),f584(x4583,x4584,x4585,x4582,x4586,x4587,x4588,x4589))
% 25.54/25.42 [459]~E(x4591,x4592)+E(f584(x4593,x4594,x4595,x4596,x4591,x4597,x4598,x4599),f584(x4593,x4594,x4595,x4596,x4592,x4597,x4598,x4599))
% 25.54/25.42 [460]~E(x4601,x4602)+E(f584(x4603,x4604,x4605,x4606,x4607,x4601,x4608,x4609),f584(x4603,x4604,x4605,x4606,x4607,x4602,x4608,x4609))
% 25.54/25.42 [461]~E(x4611,x4612)+E(f584(x4613,x4614,x4615,x4616,x4617,x4618,x4611,x4619),f584(x4613,x4614,x4615,x4616,x4617,x4618,x4612,x4619))
% 25.54/25.42 [462]~E(x4621,x4622)+E(f584(x4623,x4624,x4625,x4626,x4627,x4628,x4629,x4621),f584(x4623,x4624,x4625,x4626,x4627,x4628,x4629,x4622))
% 25.54/25.42 [463]~E(x4631,x4632)+E(f908(x4631,x4633,x4634,x4635,x4636,x4637,x4638),f908(x4632,x4633,x4634,x4635,x4636,x4637,x4638))
% 25.54/25.42 [464]~E(x4641,x4642)+E(f908(x4643,x4641,x4644,x4645,x4646,x4647,x4648),f908(x4643,x4642,x4644,x4645,x4646,x4647,x4648))
% 25.54/25.42 [465]~E(x4651,x4652)+E(f908(x4653,x4654,x4651,x4655,x4656,x4657,x4658),f908(x4653,x4654,x4652,x4655,x4656,x4657,x4658))
% 25.54/25.42 [466]~E(x4661,x4662)+E(f908(x4663,x4664,x4665,x4661,x4666,x4667,x4668),f908(x4663,x4664,x4665,x4662,x4666,x4667,x4668))
% 25.54/25.42 [467]~E(x4671,x4672)+E(f908(x4673,x4674,x4675,x4676,x4671,x4677,x4678),f908(x4673,x4674,x4675,x4676,x4672,x4677,x4678))
% 25.54/25.42 [468]~E(x4681,x4682)+E(f908(x4683,x4684,x4685,x4686,x4687,x4681,x4688),f908(x4683,x4684,x4685,x4686,x4687,x4682,x4688))
% 25.54/25.42 [469]~E(x4691,x4692)+E(f908(x4693,x4694,x4695,x4696,x4697,x4698,x4691),f908(x4693,x4694,x4695,x4696,x4697,x4698,x4692))
% 25.54/25.42 [470]~E(x4701,x4702)+E(f922(x4701,x4703),f922(x4702,x4703))
% 25.54/25.42 [471]~E(x4711,x4712)+E(f922(x4713,x4711),f922(x4713,x4712))
% 25.54/25.42 [472]~E(x4721,x4722)+E(f238(x4721,x4723,x4724,x4725,x4726,x4727),f238(x4722,x4723,x4724,x4725,x4726,x4727))
% 25.54/25.42 [473]~E(x4731,x4732)+E(f238(x4733,x4731,x4734,x4735,x4736,x4737),f238(x4733,x4732,x4734,x4735,x4736,x4737))
% 25.54/25.42 [474]~E(x4741,x4742)+E(f238(x4743,x4744,x4741,x4745,x4746,x4747),f238(x4743,x4744,x4742,x4745,x4746,x4747))
% 25.54/25.42 [475]~E(x4751,x4752)+E(f238(x4753,x4754,x4755,x4751,x4756,x4757),f238(x4753,x4754,x4755,x4752,x4756,x4757))
% 25.54/25.42 [476]~E(x4761,x4762)+E(f238(x4763,x4764,x4765,x4766,x4761,x4767),f238(x4763,x4764,x4765,x4766,x4762,x4767))
% 25.54/25.42 [477]~E(x4771,x4772)+E(f238(x4773,x4774,x4775,x4776,x4777,x4771),f238(x4773,x4774,x4775,x4776,x4777,x4772))
% 25.54/25.42 [478]~E(x4781,x4782)+E(f89(x4781),f89(x4782))
% 25.54/25.42 [479]~E(x4791,x4792)+E(f191(x4791,x4793,x4794,x4795),f191(x4792,x4793,x4794,x4795))
% 25.54/25.42 [480]~E(x4801,x4802)+E(f191(x4803,x4801,x4804,x4805),f191(x4803,x4802,x4804,x4805))
% 25.54/25.42 [481]~E(x4811,x4812)+E(f191(x4813,x4814,x4811,x4815),f191(x4813,x4814,x4812,x4815))
% 25.54/25.42 [482]~E(x4821,x4822)+E(f191(x4823,x4824,x4825,x4821),f191(x4823,x4824,x4825,x4822))
% 25.54/25.42 [483]~E(x4831,x4832)+E(f308(x4831,x4833),f308(x4832,x4833))
% 25.54/25.42 [484]~E(x4841,x4842)+E(f308(x4843,x4841),f308(x4843,x4842))
% 25.54/25.42 [485]~E(x4851,x4852)+E(f751(x4851,x4853,x4854,x4855,x4856,x4857,x4858),f751(x4852,x4853,x4854,x4855,x4856,x4857,x4858))
% 25.54/25.42 [486]~E(x4861,x4862)+E(f751(x4863,x4861,x4864,x4865,x4866,x4867,x4868),f751(x4863,x4862,x4864,x4865,x4866,x4867,x4868))
% 25.54/25.42 [487]~E(x4871,x4872)+E(f751(x4873,x4874,x4871,x4875,x4876,x4877,x4878),f751(x4873,x4874,x4872,x4875,x4876,x4877,x4878))
% 25.54/25.42 [488]~E(x4881,x4882)+E(f751(x4883,x4884,x4885,x4881,x4886,x4887,x4888),f751(x4883,x4884,x4885,x4882,x4886,x4887,x4888))
% 25.54/25.42 [489]~E(x4891,x4892)+E(f751(x4893,x4894,x4895,x4896,x4891,x4897,x4898),f751(x4893,x4894,x4895,x4896,x4892,x4897,x4898))
% 25.54/25.42 [490]~E(x4901,x4902)+E(f751(x4903,x4904,x4905,x4906,x4907,x4901,x4908),f751(x4903,x4904,x4905,x4906,x4907,x4902,x4908))
% 25.54/25.42 [491]~E(x4911,x4912)+E(f751(x4913,x4914,x4915,x4916,x4917,x4918,x4911),f751(x4913,x4914,x4915,x4916,x4917,x4918,x4912))
% 25.54/25.42 [492]~E(x4921,x4922)+E(f303(x4921,x4923,x4924),f303(x4922,x4923,x4924))
% 25.54/25.42 [493]~E(x4931,x4932)+E(f303(x4933,x4931,x4934),f303(x4933,x4932,x4934))
% 25.54/25.42 [494]~E(x4941,x4942)+E(f303(x4943,x4944,x4941),f303(x4943,x4944,x4942))
% 25.54/25.42 [495]~E(x4951,x4952)+E(f156(x4951,x4953,x4954,x4955),f156(x4952,x4953,x4954,x4955))
% 25.54/25.42 [496]~E(x4961,x4962)+E(f156(x4963,x4961,x4964,x4965),f156(x4963,x4962,x4964,x4965))
% 25.54/25.42 [497]~E(x4971,x4972)+E(f156(x4973,x4974,x4971,x4975),f156(x4973,x4974,x4972,x4975))
% 25.54/25.42 [498]~E(x4981,x4982)+E(f156(x4983,x4984,x4985,x4981),f156(x4983,x4984,x4985,x4982))
% 25.54/25.42 [499]~E(x4991,x4992)+E(f444(x4991,x4993,x4994,x4995),f444(x4992,x4993,x4994,x4995))
% 25.54/25.42 [500]~E(x5001,x5002)+E(f444(x5003,x5001,x5004,x5005),f444(x5003,x5002,x5004,x5005))
% 25.54/25.42 [501]~E(x5011,x5012)+E(f444(x5013,x5014,x5011,x5015),f444(x5013,x5014,x5012,x5015))
% 25.54/25.42 [502]~E(x5021,x5022)+E(f444(x5023,x5024,x5025,x5021),f444(x5023,x5024,x5025,x5022))
% 25.54/25.42 [503]~E(x5031,x5032)+E(f174(x5031,x5033),f174(x5032,x5033))
% 25.54/25.42 [504]~E(x5041,x5042)+E(f174(x5043,x5041),f174(x5043,x5042))
% 25.54/25.42 [505]~E(x5051,x5052)+E(f722(x5051,x5053),f722(x5052,x5053))
% 25.54/25.42 [506]~E(x5061,x5062)+E(f722(x5063,x5061),f722(x5063,x5062))
% 25.54/25.42 [507]~E(x5071,x5072)+E(f49(x5071),f49(x5072))
% 25.54/25.42 [508]~E(x5081,x5082)+E(f172(x5081,x5083),f172(x5082,x5083))
% 25.54/25.42 [509]~E(x5091,x5092)+E(f172(x5093,x5091),f172(x5093,x5092))
% 25.54/25.42 [510]~E(x5101,x5102)+E(f111(x5101,x5103,x5104),f111(x5102,x5103,x5104))
% 25.54/25.42 [511]~E(x5111,x5112)+E(f111(x5113,x5111,x5114),f111(x5113,x5112,x5114))
% 25.54/25.42 [512]~E(x5121,x5122)+E(f111(x5123,x5124,x5121),f111(x5123,x5124,x5122))
% 25.54/25.42 [513]~E(x5131,x5132)+E(f886(x5131,x5133,x5134,x5135,x5136),f886(x5132,x5133,x5134,x5135,x5136))
% 25.54/25.42 [514]~E(x5141,x5142)+E(f886(x5143,x5141,x5144,x5145,x5146),f886(x5143,x5142,x5144,x5145,x5146))
% 25.54/25.42 [515]~E(x5151,x5152)+E(f886(x5153,x5154,x5151,x5155,x5156),f886(x5153,x5154,x5152,x5155,x5156))
% 25.54/25.42 [516]~E(x5161,x5162)+E(f886(x5163,x5164,x5165,x5161,x5166),f886(x5163,x5164,x5165,x5162,x5166))
% 25.54/25.42 [517]~E(x5171,x5172)+E(f886(x5173,x5174,x5175,x5176,x5171),f886(x5173,x5174,x5175,x5176,x5172))
% 25.54/25.42 [518]~E(x5181,x5182)+E(f286(x5181,x5183,x5184),f286(x5182,x5183,x5184))
% 25.54/25.42 [519]~E(x5191,x5192)+E(f286(x5193,x5191,x5194),f286(x5193,x5192,x5194))
% 25.54/25.42 [520]~E(x5201,x5202)+E(f286(x5203,x5204,x5201),f286(x5203,x5204,x5202))
% 25.54/25.42 [521]~E(x5211,x5212)+E(f306(x5211),f306(x5212))
% 25.54/25.42 [522]~E(x5221,x5222)+E(f455(x5221,x5223),f455(x5222,x5223))
% 25.54/25.42 [523]~E(x5231,x5232)+E(f455(x5233,x5231),f455(x5233,x5232))
% 25.54/25.42 [524]~E(x5241,x5242)+E(f728(x5241,x5243,x5244),f728(x5242,x5243,x5244))
% 25.54/25.42 [525]~E(x5251,x5252)+E(f728(x5253,x5251,x5254),f728(x5253,x5252,x5254))
% 25.54/25.42 [526]~E(x5261,x5262)+E(f728(x5263,x5264,x5261),f728(x5263,x5264,x5262))
% 25.54/25.42 [527]~E(x5271,x5272)+E(f445(x5271,x5273,x5274,x5275),f445(x5272,x5273,x5274,x5275))
% 25.54/25.42 [528]~E(x5281,x5282)+E(f445(x5283,x5281,x5284,x5285),f445(x5283,x5282,x5284,x5285))
% 25.54/25.42 [529]~E(x5291,x5292)+E(f445(x5293,x5294,x5291,x5295),f445(x5293,x5294,x5292,x5295))
% 25.54/25.42 [530]~E(x5301,x5302)+E(f445(x5303,x5304,x5305,x5301),f445(x5303,x5304,x5305,x5302))
% 25.54/25.42 [531]~E(x5311,x5312)+E(f345(x5311,x5313),f345(x5312,x5313))
% 25.54/25.42 [532]~E(x5321,x5322)+E(f345(x5323,x5321),f345(x5323,x5322))
% 25.54/25.42 [533]~E(x5331,x5332)+E(f67(x5331,x5333),f67(x5332,x5333))
% 25.54/25.42 [534]~E(x5341,x5342)+E(f67(x5343,x5341),f67(x5343,x5342))
% 25.54/25.42 [535]~E(x5351,x5352)+E(f810(x5351,x5353),f810(x5352,x5353))
% 25.54/25.42 [536]~E(x5361,x5362)+E(f810(x5363,x5361),f810(x5363,x5362))
% 25.54/25.42 [537]~E(x5371,x5372)+E(f434(x5371,x5373,x5374),f434(x5372,x5373,x5374))
% 25.54/25.42 [538]~E(x5381,x5382)+E(f434(x5383,x5381,x5384),f434(x5383,x5382,x5384))
% 25.54/25.42 [539]~E(x5391,x5392)+E(f434(x5393,x5394,x5391),f434(x5393,x5394,x5392))
% 25.54/25.42 [540]~E(x5401,x5402)+E(f374(x5401,x5403,x5404,x5405),f374(x5402,x5403,x5404,x5405))
% 25.54/25.42 [541]~E(x5411,x5412)+E(f374(x5413,x5411,x5414,x5415),f374(x5413,x5412,x5414,x5415))
% 25.54/25.42 [542]~E(x5421,x5422)+E(f374(x5423,x5424,x5421,x5425),f374(x5423,x5424,x5422,x5425))
% 25.54/25.42 [543]~E(x5431,x5432)+E(f374(x5433,x5434,x5435,x5431),f374(x5433,x5434,x5435,x5432))
% 25.54/25.42 [544]~E(x5441,x5442)+E(f842(x5441,x5443,x5444,x5445,x5446,x5447),f842(x5442,x5443,x5444,x5445,x5446,x5447))
% 25.54/25.42 [545]~E(x5451,x5452)+E(f842(x5453,x5451,x5454,x5455,x5456,x5457),f842(x5453,x5452,x5454,x5455,x5456,x5457))
% 25.54/25.42 [546]~E(x5461,x5462)+E(f842(x5463,x5464,x5461,x5465,x5466,x5467),f842(x5463,x5464,x5462,x5465,x5466,x5467))
% 25.54/25.42 [547]~E(x5471,x5472)+E(f842(x5473,x5474,x5475,x5471,x5476,x5477),f842(x5473,x5474,x5475,x5472,x5476,x5477))
% 25.54/25.42 [548]~E(x5481,x5482)+E(f842(x5483,x5484,x5485,x5486,x5481,x5487),f842(x5483,x5484,x5485,x5486,x5482,x5487))
% 25.54/25.42 [549]~E(x5491,x5492)+E(f842(x5493,x5494,x5495,x5496,x5497,x5491),f842(x5493,x5494,x5495,x5496,x5497,x5492))
% 25.54/25.42 [550]~E(x5501,x5502)+E(f56(x5501,x5503),f56(x5502,x5503))
% 25.54/25.42 [551]~E(x5511,x5512)+E(f56(x5513,x5511),f56(x5513,x5512))
% 25.54/25.42 [552]~E(x5521,x5522)+E(f169(x5521,x5523,x5524),f169(x5522,x5523,x5524))
% 25.54/25.42 [553]~E(x5531,x5532)+E(f169(x5533,x5531,x5534),f169(x5533,x5532,x5534))
% 25.54/25.42 [554]~E(x5541,x5542)+E(f169(x5543,x5544,x5541),f169(x5543,x5544,x5542))
% 25.54/25.42 [555]~E(x5551,x5552)+E(f514(x5551,x5553,x5554,x5555,x5556),f514(x5552,x5553,x5554,x5555,x5556))
% 25.54/25.42 [556]~E(x5561,x5562)+E(f514(x5563,x5561,x5564,x5565,x5566),f514(x5563,x5562,x5564,x5565,x5566))
% 25.54/25.42 [557]~E(x5571,x5572)+E(f514(x5573,x5574,x5571,x5575,x5576),f514(x5573,x5574,x5572,x5575,x5576))
% 25.54/25.42 [558]~E(x5581,x5582)+E(f514(x5583,x5584,x5585,x5581,x5586),f514(x5583,x5584,x5585,x5582,x5586))
% 25.54/25.42 [559]~E(x5591,x5592)+E(f514(x5593,x5594,x5595,x5596,x5591),f514(x5593,x5594,x5595,x5596,x5592))
% 25.54/25.42 [560]~E(x5601,x5602)+E(f437(x5601,x5603,x5604),f437(x5602,x5603,x5604))
% 25.54/25.42 [561]~E(x5611,x5612)+E(f437(x5613,x5611,x5614),f437(x5613,x5612,x5614))
% 25.54/25.42 [562]~E(x5621,x5622)+E(f437(x5623,x5624,x5621),f437(x5623,x5624,x5622))
% 25.54/25.42 [563]~E(x5631,x5632)+E(f34(x5631),f34(x5632))
% 25.54/25.42 [564]~E(x5641,x5642)+E(f839(x5641,x5643,x5644,x5645,x5646),f839(x5642,x5643,x5644,x5645,x5646))
% 25.54/25.42 [565]~E(x5651,x5652)+E(f839(x5653,x5651,x5654,x5655,x5656),f839(x5653,x5652,x5654,x5655,x5656))
% 25.54/25.42 [566]~E(x5661,x5662)+E(f839(x5663,x5664,x5661,x5665,x5666),f839(x5663,x5664,x5662,x5665,x5666))
% 25.54/25.42 [567]~E(x5671,x5672)+E(f839(x5673,x5674,x5675,x5671,x5676),f839(x5673,x5674,x5675,x5672,x5676))
% 25.54/25.42 [568]~E(x5681,x5682)+E(f839(x5683,x5684,x5685,x5686,x5681),f839(x5683,x5684,x5685,x5686,x5682))
% 25.54/25.42 [569]~E(x5691,x5692)+E(f791(x5691,x5693,x5694,x5695,x5696,x5697,x5698),f791(x5692,x5693,x5694,x5695,x5696,x5697,x5698))
% 25.54/25.42 [570]~E(x5701,x5702)+E(f791(x5703,x5701,x5704,x5705,x5706,x5707,x5708),f791(x5703,x5702,x5704,x5705,x5706,x5707,x5708))
% 25.54/25.42 [571]~E(x5711,x5712)+E(f791(x5713,x5714,x5711,x5715,x5716,x5717,x5718),f791(x5713,x5714,x5712,x5715,x5716,x5717,x5718))
% 25.54/25.42 [572]~E(x5721,x5722)+E(f791(x5723,x5724,x5725,x5721,x5726,x5727,x5728),f791(x5723,x5724,x5725,x5722,x5726,x5727,x5728))
% 25.54/25.42 [573]~E(x5731,x5732)+E(f791(x5733,x5734,x5735,x5736,x5731,x5737,x5738),f791(x5733,x5734,x5735,x5736,x5732,x5737,x5738))
% 25.54/25.42 [574]~E(x5741,x5742)+E(f791(x5743,x5744,x5745,x5746,x5747,x5741,x5748),f791(x5743,x5744,x5745,x5746,x5747,x5742,x5748))
% 25.54/25.42 [575]~E(x5751,x5752)+E(f791(x5753,x5754,x5755,x5756,x5757,x5758,x5751),f791(x5753,x5754,x5755,x5756,x5757,x5758,x5752))
% 25.54/25.42 [576]~E(x5761,x5762)+E(f741(x5761,x5763,x5764,x5765),f741(x5762,x5763,x5764,x5765))
% 25.54/25.42 [577]~E(x5771,x5772)+E(f741(x5773,x5771,x5774,x5775),f741(x5773,x5772,x5774,x5775))
% 25.54/25.42 [578]~E(x5781,x5782)+E(f741(x5783,x5784,x5781,x5785),f741(x5783,x5784,x5782,x5785))
% 25.54/25.42 [579]~E(x5791,x5792)+E(f741(x5793,x5794,x5795,x5791),f741(x5793,x5794,x5795,x5792))
% 25.54/25.42 [580]~E(x5801,x5802)+E(f836(x5801,x5803,x5804,x5805),f836(x5802,x5803,x5804,x5805))
% 25.54/25.42 [581]~E(x5811,x5812)+E(f836(x5813,x5811,x5814,x5815),f836(x5813,x5812,x5814,x5815))
% 25.54/25.42 [582]~E(x5821,x5822)+E(f836(x5823,x5824,x5821,x5825),f836(x5823,x5824,x5822,x5825))
% 25.54/25.42 [583]~E(x5831,x5832)+E(f836(x5833,x5834,x5835,x5831),f836(x5833,x5834,x5835,x5832))
% 25.54/25.42 [584]~E(x5841,x5842)+E(f699(x5841,x5843,x5844),f699(x5842,x5843,x5844))
% 25.54/25.42 [585]~E(x5851,x5852)+E(f699(x5853,x5851,x5854),f699(x5853,x5852,x5854))
% 25.54/25.42 [586]~E(x5861,x5862)+E(f699(x5863,x5864,x5861),f699(x5863,x5864,x5862))
% 25.54/25.42 [587]~E(x5871,x5872)+E(f183(x5871,x5873,x5874,x5875),f183(x5872,x5873,x5874,x5875))
% 25.54/25.42 [588]~E(x5881,x5882)+E(f183(x5883,x5881,x5884,x5885),f183(x5883,x5882,x5884,x5885))
% 25.54/25.42 [589]~E(x5891,x5892)+E(f183(x5893,x5894,x5891,x5895),f183(x5893,x5894,x5892,x5895))
% 25.54/25.42 [590]~E(x5901,x5902)+E(f183(x5903,x5904,x5905,x5901),f183(x5903,x5904,x5905,x5902))
% 25.54/25.42 [591]~E(x5911,x5912)+E(f555(x5911,x5913,x5914,x5915),f555(x5912,x5913,x5914,x5915))
% 25.54/25.42 [592]~E(x5921,x5922)+E(f555(x5923,x5921,x5924,x5925),f555(x5923,x5922,x5924,x5925))
% 25.54/25.42 [593]~E(x5931,x5932)+E(f555(x5933,x5934,x5931,x5935),f555(x5933,x5934,x5932,x5935))
% 25.54/25.42 [594]~E(x5941,x5942)+E(f555(x5943,x5944,x5945,x5941),f555(x5943,x5944,x5945,x5942))
% 25.54/25.42 [595]~E(x5951,x5952)+E(f713(x5951,x5953),f713(x5952,x5953))
% 25.54/25.42 [596]~E(x5961,x5962)+E(f713(x5963,x5961),f713(x5963,x5962))
% 25.54/25.42 [597]~E(x5971,x5972)+E(f116(x5971),f116(x5972))
% 25.54/25.42 [598]~E(x5981,x5982)+E(f676(x5981,x5983,x5984,x5985),f676(x5982,x5983,x5984,x5985))
% 25.54/25.42 [599]~E(x5991,x5992)+E(f676(x5993,x5991,x5994,x5995),f676(x5993,x5992,x5994,x5995))
% 25.54/25.42 [600]~E(x6001,x6002)+E(f676(x6003,x6004,x6001,x6005),f676(x6003,x6004,x6002,x6005))
% 25.54/25.42 [601]~E(x6011,x6012)+E(f676(x6013,x6014,x6015,x6011),f676(x6013,x6014,x6015,x6012))
% 25.54/25.42 [602]~E(x6021,x6022)+E(f40(x6021,x6023),f40(x6022,x6023))
% 25.54/25.42 [603]~E(x6031,x6032)+E(f40(x6033,x6031),f40(x6033,x6032))
% 25.54/25.42 [604]~E(x6041,x6042)+E(f494(x6041,x6043,x6044,x6045,x6046,x6047,x6048),f494(x6042,x6043,x6044,x6045,x6046,x6047,x6048))
% 25.54/25.42 [605]~E(x6051,x6052)+E(f494(x6053,x6051,x6054,x6055,x6056,x6057,x6058),f494(x6053,x6052,x6054,x6055,x6056,x6057,x6058))
% 25.54/25.42 [606]~E(x6061,x6062)+E(f494(x6063,x6064,x6061,x6065,x6066,x6067,x6068),f494(x6063,x6064,x6062,x6065,x6066,x6067,x6068))
% 25.54/25.42 [607]~E(x6071,x6072)+E(f494(x6073,x6074,x6075,x6071,x6076,x6077,x6078),f494(x6073,x6074,x6075,x6072,x6076,x6077,x6078))
% 25.54/25.42 [608]~E(x6081,x6082)+E(f494(x6083,x6084,x6085,x6086,x6081,x6087,x6088),f494(x6083,x6084,x6085,x6086,x6082,x6087,x6088))
% 25.54/25.42 [609]~E(x6091,x6092)+E(f494(x6093,x6094,x6095,x6096,x6097,x6091,x6098),f494(x6093,x6094,x6095,x6096,x6097,x6092,x6098))
% 25.54/25.42 [610]~E(x6101,x6102)+E(f494(x6103,x6104,x6105,x6106,x6107,x6108,x6101),f494(x6103,x6104,x6105,x6106,x6107,x6108,x6102))
% 25.54/25.42 [611]~E(x6111,x6112)+E(f603(x6111,x6113,x6114,x6115,x6116,x6117),f603(x6112,x6113,x6114,x6115,x6116,x6117))
% 25.54/25.42 [612]~E(x6121,x6122)+E(f603(x6123,x6121,x6124,x6125,x6126,x6127),f603(x6123,x6122,x6124,x6125,x6126,x6127))
% 25.54/25.42 [613]~E(x6131,x6132)+E(f603(x6133,x6134,x6131,x6135,x6136,x6137),f603(x6133,x6134,x6132,x6135,x6136,x6137))
% 25.54/25.42 [614]~E(x6141,x6142)+E(f603(x6143,x6144,x6145,x6141,x6146,x6147),f603(x6143,x6144,x6145,x6142,x6146,x6147))
% 25.54/25.42 [615]~E(x6151,x6152)+E(f603(x6153,x6154,x6155,x6156,x6151,x6157),f603(x6153,x6154,x6155,x6156,x6152,x6157))
% 25.54/25.42 [616]~E(x6161,x6162)+E(f603(x6163,x6164,x6165,x6166,x6167,x6161),f603(x6163,x6164,x6165,x6166,x6167,x6162))
% 25.54/25.42 [617]~E(x6171,x6172)+E(f85(x6171),f85(x6172))
% 25.54/25.42 [618]~E(x6181,x6182)+E(f588(x6181,x6183),f588(x6182,x6183))
% 25.54/25.42 [619]~E(x6191,x6192)+E(f588(x6193,x6191),f588(x6193,x6192))
% 25.54/25.42 [620]~E(x6201,x6202)+E(f130(x6201),f130(x6202))
% 25.54/25.42 [621]~E(x6211,x6212)+E(f118(x6211,x6213),f118(x6212,x6213))
% 25.54/25.42 [622]~E(x6221,x6222)+E(f118(x6223,x6221),f118(x6223,x6222))
% 25.54/25.42 [623]~E(x6231,x6232)+E(f793(x6231,x6233,x6234),f793(x6232,x6233,x6234))
% 25.54/25.42 [624]~E(x6241,x6242)+E(f793(x6243,x6241,x6244),f793(x6243,x6242,x6244))
% 25.54/25.42 [625]~E(x6251,x6252)+E(f793(x6253,x6254,x6251),f793(x6253,x6254,x6252))
% 25.54/25.42 [626]~E(x6261,x6262)+E(f61(x6261,x6263,x6264),f61(x6262,x6263,x6264))
% 25.54/25.42 [627]~E(x6271,x6272)+E(f61(x6273,x6271,x6274),f61(x6273,x6272,x6274))
% 25.54/25.42 [628]~E(x6281,x6282)+E(f61(x6283,x6284,x6281),f61(x6283,x6284,x6282))
% 25.54/25.42 [629]~E(x6291,x6292)+E(f855(x6291,x6293,x6294,x6295,x6296,x6297),f855(x6292,x6293,x6294,x6295,x6296,x6297))
% 25.54/25.42 [630]~E(x6301,x6302)+E(f855(x6303,x6301,x6304,x6305,x6306,x6307),f855(x6303,x6302,x6304,x6305,x6306,x6307))
% 25.54/25.42 [631]~E(x6311,x6312)+E(f855(x6313,x6314,x6311,x6315,x6316,x6317),f855(x6313,x6314,x6312,x6315,x6316,x6317))
% 25.54/25.42 [632]~E(x6321,x6322)+E(f855(x6323,x6324,x6325,x6321,x6326,x6327),f855(x6323,x6324,x6325,x6322,x6326,x6327))
% 25.54/25.42 [633]~E(x6331,x6332)+E(f855(x6333,x6334,x6335,x6336,x6331,x6337),f855(x6333,x6334,x6335,x6336,x6332,x6337))
% 25.54/25.42 [634]~E(x6341,x6342)+E(f855(x6343,x6344,x6345,x6346,x6347,x6341),f855(x6343,x6344,x6345,x6346,x6347,x6342))
% 25.54/25.42 [635]~E(x6351,x6352)+E(f689(x6351,x6353,x6354,x6355,x6356),f689(x6352,x6353,x6354,x6355,x6356))
% 25.54/25.42 [636]~E(x6361,x6362)+E(f689(x6363,x6361,x6364,x6365,x6366),f689(x6363,x6362,x6364,x6365,x6366))
% 25.54/25.42 [637]~E(x6371,x6372)+E(f689(x6373,x6374,x6371,x6375,x6376),f689(x6373,x6374,x6372,x6375,x6376))
% 25.54/25.42 [638]~E(x6381,x6382)+E(f689(x6383,x6384,x6385,x6381,x6386),f689(x6383,x6384,x6385,x6382,x6386))
% 25.54/25.42 [639]~E(x6391,x6392)+E(f689(x6393,x6394,x6395,x6396,x6391),f689(x6393,x6394,x6395,x6396,x6392))
% 25.54/25.42 [640]~E(x6401,x6402)+E(f133(x6401,x6403,x6404),f133(x6402,x6403,x6404))
% 25.54/25.42 [641]~E(x6411,x6412)+E(f133(x6413,x6411,x6414),f133(x6413,x6412,x6414))
% 25.54/25.42 [642]~E(x6421,x6422)+E(f133(x6423,x6424,x6421),f133(x6423,x6424,x6422))
% 25.54/25.42 [643]~E(x6431,x6432)+E(f148(x6431,x6433,x6434),f148(x6432,x6433,x6434))
% 25.54/25.42 [644]~E(x6441,x6442)+E(f148(x6443,x6441,x6444),f148(x6443,x6442,x6444))
% 25.54/25.42 [645]~E(x6451,x6452)+E(f148(x6453,x6454,x6451),f148(x6453,x6454,x6452))
% 25.54/25.42 [646]~E(x6461,x6462)+E(f41(x6461,x6463),f41(x6462,x6463))
% 25.54/25.42 [647]~E(x6471,x6472)+E(f41(x6473,x6471),f41(x6473,x6472))
% 25.54/25.42 [648]~E(x6481,x6482)+E(f202(x6481,x6483,x6484,x6485),f202(x6482,x6483,x6484,x6485))
% 25.54/25.42 [649]~E(x6491,x6492)+E(f202(x6493,x6491,x6494,x6495),f202(x6493,x6492,x6494,x6495))
% 25.54/25.42 [650]~E(x6501,x6502)+E(f202(x6503,x6504,x6501,x6505),f202(x6503,x6504,x6502,x6505))
% 25.54/25.42 [651]~E(x6511,x6512)+E(f202(x6513,x6514,x6515,x6511),f202(x6513,x6514,x6515,x6512))
% 25.54/25.42 [652]~E(x6521,x6522)+E(f518(x6521,x6523,x6524,x6525),f518(x6522,x6523,x6524,x6525))
% 25.54/25.42 [653]~E(x6531,x6532)+E(f518(x6533,x6531,x6534,x6535),f518(x6533,x6532,x6534,x6535))
% 25.54/25.42 [654]~E(x6541,x6542)+E(f518(x6543,x6544,x6541,x6545),f518(x6543,x6544,x6542,x6545))
% 25.54/25.42 [655]~E(x6551,x6552)+E(f518(x6553,x6554,x6555,x6551),f518(x6553,x6554,x6555,x6552))
% 25.54/25.42 [656]~E(x6561,x6562)+E(f247(x6561,x6563,x6564,x6565),f247(x6562,x6563,x6564,x6565))
% 25.54/25.42 [657]~E(x6571,x6572)+E(f247(x6573,x6571,x6574,x6575),f247(x6573,x6572,x6574,x6575))
% 25.54/25.42 [658]~E(x6581,x6582)+E(f247(x6583,x6584,x6581,x6585),f247(x6583,x6584,x6582,x6585))
% 25.54/25.42 [659]~E(x6591,x6592)+E(f247(x6593,x6594,x6595,x6591),f247(x6593,x6594,x6595,x6592))
% 25.54/25.42 [660]~E(x6601,x6602)+E(f476(x6601,x6603,x6604),f476(x6602,x6603,x6604))
% 25.54/25.42 [661]~E(x6611,x6612)+E(f476(x6613,x6611,x6614),f476(x6613,x6612,x6614))
% 25.54/25.42 [662]~E(x6621,x6622)+E(f476(x6623,x6624,x6621),f476(x6623,x6624,x6622))
% 25.54/25.42 [663]~E(x6631,x6632)+E(f179(x6631),f179(x6632))
% 25.54/25.42 [664]~E(x6641,x6642)+E(f564(x6641,x6643,x6644,x6645),f564(x6642,x6643,x6644,x6645))
% 25.54/25.42 [665]~E(x6651,x6652)+E(f564(x6653,x6651,x6654,x6655),f564(x6653,x6652,x6654,x6655))
% 25.54/25.42 [666]~E(x6661,x6662)+E(f564(x6663,x6664,x6661,x6665),f564(x6663,x6664,x6662,x6665))
% 25.54/25.42 [667]~E(x6671,x6672)+E(f564(x6673,x6674,x6675,x6671),f564(x6673,x6674,x6675,x6672))
% 25.54/25.42 [668]~E(x6681,x6682)+E(f812(x6681,x6683,x6684,x6685),f812(x6682,x6683,x6684,x6685))
% 25.54/25.42 [669]~E(x6691,x6692)+E(f812(x6693,x6691,x6694,x6695),f812(x6693,x6692,x6694,x6695))
% 25.54/25.42 [670]~E(x6701,x6702)+E(f812(x6703,x6704,x6701,x6705),f812(x6703,x6704,x6702,x6705))
% 25.54/25.42 [671]~E(x6711,x6712)+E(f812(x6713,x6714,x6715,x6711),f812(x6713,x6714,x6715,x6712))
% 25.54/25.42 [672]~E(x6721,x6722)+E(f351(x6721,x6723,x6724),f351(x6722,x6723,x6724))
% 25.54/25.42 [673]~E(x6731,x6732)+E(f351(x6733,x6731,x6734),f351(x6733,x6732,x6734))
% 25.54/25.42 [674]~E(x6741,x6742)+E(f351(x6743,x6744,x6741),f351(x6743,x6744,x6742))
% 25.54/25.42 [675]~E(x6751,x6752)+E(f435(x6751,x6753,x6754,x6755),f435(x6752,x6753,x6754,x6755))
% 25.54/25.42 [676]~E(x6761,x6762)+E(f435(x6763,x6761,x6764,x6765),f435(x6763,x6762,x6764,x6765))
% 25.54/25.42 [677]~E(x6771,x6772)+E(f435(x6773,x6774,x6771,x6775),f435(x6773,x6774,x6772,x6775))
% 25.54/25.42 [678]~E(x6781,x6782)+E(f435(x6783,x6784,x6785,x6781),f435(x6783,x6784,x6785,x6782))
% 25.54/25.42 [679]~E(x6791,x6792)+E(f560(x6791,x6793,x6794,x6795),f560(x6792,x6793,x6794,x6795))
% 25.54/25.42 [680]~E(x6801,x6802)+E(f560(x6803,x6801,x6804,x6805),f560(x6803,x6802,x6804,x6805))
% 25.54/25.42 [681]~E(x6811,x6812)+E(f560(x6813,x6814,x6811,x6815),f560(x6813,x6814,x6812,x6815))
% 25.54/25.42 [682]~E(x6821,x6822)+E(f560(x6823,x6824,x6825,x6821),f560(x6823,x6824,x6825,x6822))
% 25.54/25.42 [683]~E(x6831,x6832)+E(f601(x6831,x6833,x6834,x6835,x6836,x6837),f601(x6832,x6833,x6834,x6835,x6836,x6837))
% 25.54/25.42 [684]~E(x6841,x6842)+E(f601(x6843,x6841,x6844,x6845,x6846,x6847),f601(x6843,x6842,x6844,x6845,x6846,x6847))
% 25.54/25.42 [685]~E(x6851,x6852)+E(f601(x6853,x6854,x6851,x6855,x6856,x6857),f601(x6853,x6854,x6852,x6855,x6856,x6857))
% 25.54/25.42 [686]~E(x6861,x6862)+E(f601(x6863,x6864,x6865,x6861,x6866,x6867),f601(x6863,x6864,x6865,x6862,x6866,x6867))
% 25.54/25.42 [687]~E(x6871,x6872)+E(f601(x6873,x6874,x6875,x6876,x6871,x6877),f601(x6873,x6874,x6875,x6876,x6872,x6877))
% 25.54/25.42 [688]~E(x6881,x6882)+E(f601(x6883,x6884,x6885,x6886,x6887,x6881),f601(x6883,x6884,x6885,x6886,x6887,x6882))
% 25.54/25.42 [689]~E(x6891,x6892)+E(f279(x6891,x6893),f279(x6892,x6893))
% 25.54/25.42 [690]~E(x6901,x6902)+E(f279(x6903,x6901),f279(x6903,x6902))
% 25.54/25.42 [691]~E(x6911,x6912)+E(f360(x6911,x6913),f360(x6912,x6913))
% 25.54/25.42 [692]~E(x6921,x6922)+E(f360(x6923,x6921),f360(x6923,x6922))
% 25.54/25.42 [693]~E(x6931,x6932)+E(f492(x6931,x6933,x6934,x6935,x6936,x6937,x6938),f492(x6932,x6933,x6934,x6935,x6936,x6937,x6938))
% 25.54/25.42 [694]~E(x6941,x6942)+E(f492(x6943,x6941,x6944,x6945,x6946,x6947,x6948),f492(x6943,x6942,x6944,x6945,x6946,x6947,x6948))
% 25.54/25.42 [695]~E(x6951,x6952)+E(f492(x6953,x6954,x6951,x6955,x6956,x6957,x6958),f492(x6953,x6954,x6952,x6955,x6956,x6957,x6958))
% 25.54/25.42 [696]~E(x6961,x6962)+E(f492(x6963,x6964,x6965,x6961,x6966,x6967,x6968),f492(x6963,x6964,x6965,x6962,x6966,x6967,x6968))
% 25.54/25.42 [697]~E(x6971,x6972)+E(f492(x6973,x6974,x6975,x6976,x6971,x6977,x6978),f492(x6973,x6974,x6975,x6976,x6972,x6977,x6978))
% 25.54/25.42 [698]~E(x6981,x6982)+E(f492(x6983,x6984,x6985,x6986,x6987,x6981,x6988),f492(x6983,x6984,x6985,x6986,x6987,x6982,x6988))
% 25.54/25.42 [699]~E(x6991,x6992)+E(f492(x6993,x6994,x6995,x6996,x6997,x6998,x6991),f492(x6993,x6994,x6995,x6996,x6997,x6998,x6992))
% 25.54/25.42 [700]~E(x7001,x7002)+E(f372(x7001,x7003,x7004),f372(x7002,x7003,x7004))
% 25.54/25.42 [701]~E(x7011,x7012)+E(f372(x7013,x7011,x7014),f372(x7013,x7012,x7014))
% 25.54/25.42 [702]~E(x7021,x7022)+E(f372(x7023,x7024,x7021),f372(x7023,x7024,x7022))
% 25.54/25.42 [703]~E(x7031,x7032)+E(f686(x7031,x7033,x7034,x7035,x7036),f686(x7032,x7033,x7034,x7035,x7036))
% 25.54/25.42 [704]~E(x7041,x7042)+E(f686(x7043,x7041,x7044,x7045,x7046),f686(x7043,x7042,x7044,x7045,x7046))
% 25.54/25.42 [705]~E(x7051,x7052)+E(f686(x7053,x7054,x7051,x7055,x7056),f686(x7053,x7054,x7052,x7055,x7056))
% 25.54/25.42 [706]~E(x7061,x7062)+E(f686(x7063,x7064,x7065,x7061,x7066),f686(x7063,x7064,x7065,x7062,x7066))
% 25.54/25.42 [707]~E(x7071,x7072)+E(f686(x7073,x7074,x7075,x7076,x7071),f686(x7073,x7074,x7075,x7076,x7072))
% 25.54/25.42 [708]~E(x7081,x7082)+E(f856(x7081,x7083,x7084,x7085,x7086,x7087),f856(x7082,x7083,x7084,x7085,x7086,x7087))
% 25.54/25.42 [709]~E(x7091,x7092)+E(f856(x7093,x7091,x7094,x7095,x7096,x7097),f856(x7093,x7092,x7094,x7095,x7096,x7097))
% 25.54/25.42 [710]~E(x7101,x7102)+E(f856(x7103,x7104,x7101,x7105,x7106,x7107),f856(x7103,x7104,x7102,x7105,x7106,x7107))
% 25.54/25.42 [711]~E(x7111,x7112)+E(f856(x7113,x7114,x7115,x7111,x7116,x7117),f856(x7113,x7114,x7115,x7112,x7116,x7117))
% 25.54/25.42 [712]~E(x7121,x7122)+E(f856(x7123,x7124,x7125,x7126,x7121,x7127),f856(x7123,x7124,x7125,x7126,x7122,x7127))
% 25.54/25.42 [713]~E(x7131,x7132)+E(f856(x7133,x7134,x7135,x7136,x7137,x7131),f856(x7133,x7134,x7135,x7136,x7137,x7132))
% 25.54/25.42 [714]~E(x7141,x7142)+E(f260(x7141,x7143),f260(x7142,x7143))
% 25.54/25.42 [715]~E(x7151,x7152)+E(f260(x7153,x7151),f260(x7153,x7152))
% 25.54/25.42 [716]~E(x7161,x7162)+E(f348(x7161,x7163,x7164),f348(x7162,x7163,x7164))
% 25.54/25.42 [717]~E(x7171,x7172)+E(f348(x7173,x7171,x7174),f348(x7173,x7172,x7174))
% 25.54/25.42 [718]~E(x7181,x7182)+E(f348(x7183,x7184,x7181),f348(x7183,x7184,x7182))
% 25.54/25.42 [719]~E(x7191,x7192)+E(f149(x7191,x7193,x7194,x7195),f149(x7192,x7193,x7194,x7195))
% 25.54/25.42 [720]~E(x7201,x7202)+E(f149(x7203,x7201,x7204,x7205),f149(x7203,x7202,x7204,x7205))
% 25.54/25.42 [721]~E(x7211,x7212)+E(f149(x7213,x7214,x7211,x7215),f149(x7213,x7214,x7212,x7215))
% 25.54/25.42 [722]~E(x7221,x7222)+E(f149(x7223,x7224,x7225,x7221),f149(x7223,x7224,x7225,x7222))
% 25.54/25.42 [723]~E(x7231,x7232)+E(f666(x7231,x7233,x7234,x7235),f666(x7232,x7233,x7234,x7235))
% 25.54/25.42 [724]~E(x7241,x7242)+E(f666(x7243,x7241,x7244,x7245),f666(x7243,x7242,x7244,x7245))
% 25.54/25.42 [725]~E(x7251,x7252)+E(f666(x7253,x7254,x7251,x7255),f666(x7253,x7254,x7252,x7255))
% 25.54/25.42 [726]~E(x7261,x7262)+E(f666(x7263,x7264,x7265,x7261),f666(x7263,x7264,x7265,x7262))
% 25.54/25.42 [727]~E(x7271,x7272)+E(f70(x7271,x7273,x7274,x7275),f70(x7272,x7273,x7274,x7275))
% 25.54/25.42 [728]~E(x7281,x7282)+E(f70(x7283,x7281,x7284,x7285),f70(x7283,x7282,x7284,x7285))
% 25.54/25.42 [729]~E(x7291,x7292)+E(f70(x7293,x7294,x7291,x7295),f70(x7293,x7294,x7292,x7295))
% 25.54/25.42 [730]~E(x7301,x7302)+E(f70(x7303,x7304,x7305,x7301),f70(x7303,x7304,x7305,x7302))
% 25.54/25.42 [731]~E(x7311,x7312)+E(f887(x7311,x7313,x7314,x7315,x7316),f887(x7312,x7313,x7314,x7315,x7316))
% 25.54/25.42 [732]~E(x7321,x7322)+E(f887(x7323,x7321,x7324,x7325,x7326),f887(x7323,x7322,x7324,x7325,x7326))
% 25.54/25.42 [733]~E(x7331,x7332)+E(f887(x7333,x7334,x7331,x7335,x7336),f887(x7333,x7334,x7332,x7335,x7336))
% 25.54/25.42 [734]~E(x7341,x7342)+E(f887(x7343,x7344,x7345,x7341,x7346),f887(x7343,x7344,x7345,x7342,x7346))
% 25.54/25.42 [735]~E(x7351,x7352)+E(f887(x7353,x7354,x7355,x7356,x7351),f887(x7353,x7354,x7355,x7356,x7352))
% 25.54/25.42 [736]~E(x7361,x7362)+E(f649(x7361,x7363),f649(x7362,x7363))
% 25.54/25.42 [737]~E(x7371,x7372)+E(f649(x7373,x7371),f649(x7373,x7372))
% 25.54/25.42 [738]~E(x7381,x7382)+E(f871(x7381,x7383,x7384),f871(x7382,x7383,x7384))
% 25.54/25.42 [739]~E(x7391,x7392)+E(f871(x7393,x7391,x7394),f871(x7393,x7392,x7394))
% 25.54/25.42 [740]~E(x7401,x7402)+E(f871(x7403,x7404,x7401),f871(x7403,x7404,x7402))
% 25.54/25.42 [741]~E(x7411,x7412)+E(f472(x7411,x7413,x7414),f472(x7412,x7413,x7414))
% 25.54/25.42 [742]~E(x7421,x7422)+E(f472(x7423,x7421,x7424),f472(x7423,x7422,x7424))
% 25.54/25.42 [743]~E(x7431,x7432)+E(f472(x7433,x7434,x7431),f472(x7433,x7434,x7432))
% 25.54/25.42 [744]~E(x7441,x7442)+E(f625(x7441,x7443,x7444),f625(x7442,x7443,x7444))
% 25.54/25.42 [745]~E(x7451,x7452)+E(f625(x7453,x7451,x7454),f625(x7453,x7452,x7454))
% 25.54/25.42 [746]~E(x7461,x7462)+E(f625(x7463,x7464,x7461),f625(x7463,x7464,x7462))
% 25.54/25.42 [747]~E(x7471,x7472)+E(f888(x7471,x7473,x7474,x7475,x7476),f888(x7472,x7473,x7474,x7475,x7476))
% 25.54/25.42 [748]~E(x7481,x7482)+E(f888(x7483,x7481,x7484,x7485,x7486),f888(x7483,x7482,x7484,x7485,x7486))
% 25.54/25.42 [749]~E(x7491,x7492)+E(f888(x7493,x7494,x7491,x7495,x7496),f888(x7493,x7494,x7492,x7495,x7496))
% 25.54/25.42 [750]~E(x7501,x7502)+E(f888(x7503,x7504,x7505,x7501,x7506),f888(x7503,x7504,x7505,x7502,x7506))
% 25.54/25.42 [751]~E(x7511,x7512)+E(f888(x7513,x7514,x7515,x7516,x7511),f888(x7513,x7514,x7515,x7516,x7512))
% 25.54/25.42 [752]~E(x7521,x7522)+E(f503(x7521,x7523,x7524),f503(x7522,x7523,x7524))
% 25.54/25.42 [753]~E(x7531,x7532)+E(f503(x7533,x7531,x7534),f503(x7533,x7532,x7534))
% 25.54/25.42 [754]~E(x7541,x7542)+E(f503(x7543,x7544,x7541),f503(x7543,x7544,x7542))
% 25.54/25.42 [755]~E(x7551,x7552)+E(f801(x7551,x7553,x7554),f801(x7552,x7553,x7554))
% 25.54/25.42 [756]~E(x7561,x7562)+E(f801(x7563,x7561,x7564),f801(x7563,x7562,x7564))
% 25.54/25.42 [757]~E(x7571,x7572)+E(f801(x7573,x7574,x7571),f801(x7573,x7574,x7572))
% 25.54/25.42 [758]~E(x7581,x7582)+E(f532(x7581,x7583,x7584,x7585,x7586,x7587,x7588),f532(x7582,x7583,x7584,x7585,x7586,x7587,x7588))
% 25.54/25.42 [759]~E(x7591,x7592)+E(f532(x7593,x7591,x7594,x7595,x7596,x7597,x7598),f532(x7593,x7592,x7594,x7595,x7596,x7597,x7598))
% 25.54/25.42 [760]~E(x7601,x7602)+E(f532(x7603,x7604,x7601,x7605,x7606,x7607,x7608),f532(x7603,x7604,x7602,x7605,x7606,x7607,x7608))
% 25.54/25.42 [761]~E(x7611,x7612)+E(f532(x7613,x7614,x7615,x7611,x7616,x7617,x7618),f532(x7613,x7614,x7615,x7612,x7616,x7617,x7618))
% 25.54/25.42 [762]~E(x7621,x7622)+E(f532(x7623,x7624,x7625,x7626,x7621,x7627,x7628),f532(x7623,x7624,x7625,x7626,x7622,x7627,x7628))
% 25.54/25.42 [763]~E(x7631,x7632)+E(f532(x7633,x7634,x7635,x7636,x7637,x7631,x7638),f532(x7633,x7634,x7635,x7636,x7637,x7632,x7638))
% 25.54/25.42 [764]~E(x7641,x7642)+E(f532(x7643,x7644,x7645,x7646,x7647,x7648,x7641),f532(x7643,x7644,x7645,x7646,x7647,x7648,x7642))
% 25.54/25.42 [765]~E(x7651,x7652)+E(f725(x7651,x7653,x7654),f725(x7652,x7653,x7654))
% 25.54/25.42 [766]~E(x7661,x7662)+E(f725(x7663,x7661,x7664),f725(x7663,x7662,x7664))
% 25.54/25.42 [767]~E(x7671,x7672)+E(f725(x7673,x7674,x7671),f725(x7673,x7674,x7672))
% 25.54/25.42 [768]~E(x7681,x7682)+E(f442(x7681,x7683,x7684),f442(x7682,x7683,x7684))
% 25.54/25.42 [769]~E(x7691,x7692)+E(f442(x7693,x7691,x7694),f442(x7693,x7692,x7694))
% 25.54/25.42 [770]~E(x7701,x7702)+E(f442(x7703,x7704,x7701),f442(x7703,x7704,x7702))
% 25.54/25.42 [771]~E(x7711,x7712)+E(f680(x7711,x7713,x7714),f680(x7712,x7713,x7714))
% 25.54/25.42 [772]~E(x7721,x7722)+E(f680(x7723,x7721,x7724),f680(x7723,x7722,x7724))
% 25.54/25.42 [773]~E(x7731,x7732)+E(f680(x7733,x7734,x7731),f680(x7733,x7734,x7732))
% 25.54/25.42 [774]~E(x7741,x7742)+E(f488(x7741,x7743,x7744,x7745,x7746),f488(x7742,x7743,x7744,x7745,x7746))
% 25.54/25.42 [775]~E(x7751,x7752)+E(f488(x7753,x7751,x7754,x7755,x7756),f488(x7753,x7752,x7754,x7755,x7756))
% 25.54/25.42 [776]~E(x7761,x7762)+E(f488(x7763,x7764,x7761,x7765,x7766),f488(x7763,x7764,x7762,x7765,x7766))
% 25.54/25.42 [777]~E(x7771,x7772)+E(f488(x7773,x7774,x7775,x7771,x7776),f488(x7773,x7774,x7775,x7772,x7776))
% 25.54/25.42 [778]~E(x7781,x7782)+E(f488(x7783,x7784,x7785,x7786,x7781),f488(x7783,x7784,x7785,x7786,x7782))
% 25.54/25.42 [779]~E(x7791,x7792)+E(f799(x7791,x7793,x7794),f799(x7792,x7793,x7794))
% 25.54/25.42 [780]~E(x7801,x7802)+E(f799(x7803,x7801,x7804),f799(x7803,x7802,x7804))
% 25.54/25.42 [781]~E(x7811,x7812)+E(f799(x7813,x7814,x7811),f799(x7813,x7814,x7812))
% 25.54/25.42 [782]~E(x7821,x7822)+E(f537(x7821,x7823,x7824,x7825),f537(x7822,x7823,x7824,x7825))
% 25.54/25.42 [783]~E(x7831,x7832)+E(f537(x7833,x7831,x7834,x7835),f537(x7833,x7832,x7834,x7835))
% 25.54/25.42 [784]~E(x7841,x7842)+E(f537(x7843,x7844,x7841,x7845),f537(x7843,x7844,x7842,x7845))
% 25.54/25.42 [785]~E(x7851,x7852)+E(f537(x7853,x7854,x7855,x7851),f537(x7853,x7854,x7855,x7852))
% 25.54/25.42 [786]~E(x7861,x7862)+E(f473(x7861,x7863,x7864),f473(x7862,x7863,x7864))
% 25.54/25.42 [787]~E(x7871,x7872)+E(f473(x7873,x7871,x7874),f473(x7873,x7872,x7874))
% 25.54/25.42 [788]~E(x7881,x7882)+E(f473(x7883,x7884,x7881),f473(x7883,x7884,x7882))
% 25.54/25.42 [789]~E(x7891,x7892)+E(f766(x7891,x7893,x7894),f766(x7892,x7893,x7894))
% 25.54/25.42 [790]~E(x7901,x7902)+E(f766(x7903,x7901,x7904),f766(x7903,x7902,x7904))
% 25.54/25.42 [791]~E(x7911,x7912)+E(f766(x7913,x7914,x7911),f766(x7913,x7914,x7912))
% 25.54/25.42 [792]~E(x7921,x7922)+E(f824(x7921,x7923,x7924),f824(x7922,x7923,x7924))
% 25.54/25.42 [793]~E(x7931,x7932)+E(f824(x7933,x7931,x7934),f824(x7933,x7932,x7934))
% 25.54/25.42 [794]~E(x7941,x7942)+E(f824(x7943,x7944,x7941),f824(x7943,x7944,x7942))
% 25.54/25.42 [795]~E(x7951,x7952)+E(f421(x7951,x7953,x7954),f421(x7952,x7953,x7954))
% 25.54/25.42 [796]~E(x7961,x7962)+E(f421(x7963,x7961,x7964),f421(x7963,x7962,x7964))
% 25.54/25.42 [797]~E(x7971,x7972)+E(f421(x7973,x7974,x7971),f421(x7973,x7974,x7972))
% 25.54/25.42 [798]~E(x7981,x7982)+E(f697(x7981,x7983,x7984),f697(x7982,x7983,x7984))
% 25.54/25.42 [799]~E(x7991,x7992)+E(f697(x7993,x7991,x7994),f697(x7993,x7992,x7994))
% 25.54/25.42 [800]~E(x8001,x8002)+E(f697(x8003,x8004,x8001),f697(x8003,x8004,x8002))
% 25.54/25.42 [801]~E(x8011,x8012)+E(f702(x8011,x8013),f702(x8012,x8013))
% 25.54/25.42 [802]~E(x8021,x8022)+E(f702(x8023,x8021),f702(x8023,x8022))
% 25.54/25.42 [803]~E(x8031,x8032)+E(f846(x8031,x8033,x8034,x8035,x8036,x8037,x8038,x8039),f846(x8032,x8033,x8034,x8035,x8036,x8037,x8038,x8039))
% 25.54/25.42 [804]~E(x8041,x8042)+E(f846(x8043,x8041,x8044,x8045,x8046,x8047,x8048,x8049),f846(x8043,x8042,x8044,x8045,x8046,x8047,x8048,x8049))
% 25.54/25.42 [805]~E(x8051,x8052)+E(f846(x8053,x8054,x8051,x8055,x8056,x8057,x8058,x8059),f846(x8053,x8054,x8052,x8055,x8056,x8057,x8058,x8059))
% 25.54/25.42 [806]~E(x8061,x8062)+E(f846(x8063,x8064,x8065,x8061,x8066,x8067,x8068,x8069),f846(x8063,x8064,x8065,x8062,x8066,x8067,x8068,x8069))
% 25.54/25.42 [807]~E(x8071,x8072)+E(f846(x8073,x8074,x8075,x8076,x8071,x8077,x8078,x8079),f846(x8073,x8074,x8075,x8076,x8072,x8077,x8078,x8079))
% 25.54/25.42 [808]~E(x8081,x8082)+E(f846(x8083,x8084,x8085,x8086,x8087,x8081,x8088,x8089),f846(x8083,x8084,x8085,x8086,x8087,x8082,x8088,x8089))
% 25.54/25.42 [809]~E(x8091,x8092)+E(f846(x8093,x8094,x8095,x8096,x8097,x8098,x8091,x8099),f846(x8093,x8094,x8095,x8096,x8097,x8098,x8092,x8099))
% 25.54/25.42 [810]~E(x8101,x8102)+E(f846(x8103,x8104,x8105,x8106,x8107,x8108,x8109,x8101),f846(x8103,x8104,x8105,x8106,x8107,x8108,x8109,x8102))
% 25.54/25.42 [811]~E(x8111,x8112)+E(f900(x8111,x8113,x8114,x8115,x8116),f900(x8112,x8113,x8114,x8115,x8116))
% 25.54/25.42 [812]~E(x8121,x8122)+E(f900(x8123,x8121,x8124,x8125,x8126),f900(x8123,x8122,x8124,x8125,x8126))
% 25.54/25.42 [813]~E(x8131,x8132)+E(f900(x8133,x8134,x8131,x8135,x8136),f900(x8133,x8134,x8132,x8135,x8136))
% 25.54/25.42 [814]~E(x8141,x8142)+E(f900(x8143,x8144,x8145,x8141,x8146),f900(x8143,x8144,x8145,x8142,x8146))
% 25.54/25.42 [815]~E(x8151,x8152)+E(f900(x8153,x8154,x8155,x8156,x8151),f900(x8153,x8154,x8155,x8156,x8152))
% 25.54/25.42 [816]~E(x8161,x8162)+E(f845(x8161,x8163,x8164,x8165,x8166,x8167,x8168,x8169),f845(x8162,x8163,x8164,x8165,x8166,x8167,x8168,x8169))
% 25.54/25.42 [817]~E(x8171,x8172)+E(f845(x8173,x8171,x8174,x8175,x8176,x8177,x8178,x8179),f845(x8173,x8172,x8174,x8175,x8176,x8177,x8178,x8179))
% 25.54/25.42 [818]~E(x8181,x8182)+E(f845(x8183,x8184,x8181,x8185,x8186,x8187,x8188,x8189),f845(x8183,x8184,x8182,x8185,x8186,x8187,x8188,x8189))
% 25.54/25.42 [819]~E(x8191,x8192)+E(f845(x8193,x8194,x8195,x8191,x8196,x8197,x8198,x8199),f845(x8193,x8194,x8195,x8192,x8196,x8197,x8198,x8199))
% 25.54/25.42 [820]~E(x8201,x8202)+E(f845(x8203,x8204,x8205,x8206,x8201,x8207,x8208,x8209),f845(x8203,x8204,x8205,x8206,x8202,x8207,x8208,x8209))
% 25.54/25.42 [821]~E(x8211,x8212)+E(f845(x8213,x8214,x8215,x8216,x8217,x8211,x8218,x8219),f845(x8213,x8214,x8215,x8216,x8217,x8212,x8218,x8219))
% 25.54/25.42 [822]~E(x8221,x8222)+E(f845(x8223,x8224,x8225,x8226,x8227,x8228,x8221,x8229),f845(x8223,x8224,x8225,x8226,x8227,x8228,x8222,x8229))
% 25.54/25.42 [823]~E(x8231,x8232)+E(f845(x8233,x8234,x8235,x8236,x8237,x8238,x8239,x8231),f845(x8233,x8234,x8235,x8236,x8237,x8238,x8239,x8232))
% 25.54/25.42 [824]~E(x8241,x8242)+E(f428(x8241,x8243),f428(x8242,x8243))
% 25.54/25.42 [825]~E(x8251,x8252)+E(f428(x8253,x8251),f428(x8253,x8252))
% 25.54/25.42 [826]~E(x8261,x8262)+E(f159(x8261,x8263,x8264),f159(x8262,x8263,x8264))
% 25.54/25.42 [827]~E(x8271,x8272)+E(f159(x8273,x8271,x8274),f159(x8273,x8272,x8274))
% 25.54/25.42 [828]~E(x8281,x8282)+E(f159(x8283,x8284,x8281),f159(x8283,x8284,x8282))
% 25.54/25.42 [829]~E(x8291,x8292)+E(f527(x8291),f527(x8292))
% 25.54/25.42 [830]~E(x8301,x8302)+E(f125(x8301,x8303),f125(x8302,x8303))
% 25.54/25.42 [831]~E(x8311,x8312)+E(f125(x8313,x8311),f125(x8313,x8312))
% 25.54/25.42 [832]~E(x8321,x8322)+E(f46(x8321,x8323),f46(x8322,x8323))
% 25.54/25.42 [833]~E(x8331,x8332)+E(f46(x8333,x8331),f46(x8333,x8332))
% 25.54/25.42 [834]~E(x8341,x8342)+E(f530(x8341,x8343,x8344,x8345,x8346,x8347,x8348),f530(x8342,x8343,x8344,x8345,x8346,x8347,x8348))
% 25.54/25.42 [835]~E(x8351,x8352)+E(f530(x8353,x8351,x8354,x8355,x8356,x8357,x8358),f530(x8353,x8352,x8354,x8355,x8356,x8357,x8358))
% 25.54/25.42 [836]~E(x8361,x8362)+E(f530(x8363,x8364,x8361,x8365,x8366,x8367,x8368),f530(x8363,x8364,x8362,x8365,x8366,x8367,x8368))
% 25.54/25.42 [837]~E(x8371,x8372)+E(f530(x8373,x8374,x8375,x8371,x8376,x8377,x8378),f530(x8373,x8374,x8375,x8372,x8376,x8377,x8378))
% 25.54/25.42 [838]~E(x8381,x8382)+E(f530(x8383,x8384,x8385,x8386,x8381,x8387,x8388),f530(x8383,x8384,x8385,x8386,x8382,x8387,x8388))
% 25.54/25.42 [839]~E(x8391,x8392)+E(f530(x8393,x8394,x8395,x8396,x8397,x8391,x8398),f530(x8393,x8394,x8395,x8396,x8397,x8392,x8398))
% 25.54/25.42 [840]~E(x8401,x8402)+E(f530(x8403,x8404,x8405,x8406,x8407,x8408,x8401),f530(x8403,x8404,x8405,x8406,x8407,x8408,x8402))
% 25.54/25.42 [841]~E(x8411,x8412)+E(f779(x8411,x8413,x8414),f779(x8412,x8413,x8414))
% 25.54/25.42 [842]~E(x8421,x8422)+E(f779(x8423,x8421,x8424),f779(x8423,x8422,x8424))
% 25.54/25.42 [843]~E(x8431,x8432)+E(f779(x8433,x8434,x8431),f779(x8433,x8434,x8432))
% 25.54/25.42 [844]~E(x8441,x8442)+E(f591(x8441,x8443,x8444,x8445),f591(x8442,x8443,x8444,x8445))
% 25.54/25.42 [845]~E(x8451,x8452)+E(f591(x8453,x8451,x8454,x8455),f591(x8453,x8452,x8454,x8455))
% 25.54/25.42 [846]~E(x8461,x8462)+E(f591(x8463,x8464,x8461,x8465),f591(x8463,x8464,x8462,x8465))
% 25.54/25.42 [847]~E(x8471,x8472)+E(f591(x8473,x8474,x8475,x8471),f591(x8473,x8474,x8475,x8472))
% 25.54/25.42 [848]~E(x8481,x8482)+E(f397(x8481,x8483,x8484,x8485),f397(x8482,x8483,x8484,x8485))
% 25.54/25.42 [849]~E(x8491,x8492)+E(f397(x8493,x8491,x8494,x8495),f397(x8493,x8492,x8494,x8495))
% 25.54/25.42 [850]~E(x8501,x8502)+E(f397(x8503,x8504,x8501,x8505),f397(x8503,x8504,x8502,x8505))
% 25.54/25.42 [851]~E(x8511,x8512)+E(f397(x8513,x8514,x8515,x8511),f397(x8513,x8514,x8515,x8512))
% 25.54/25.42 [852]~E(x8521,x8522)+E(f389(x8521,x8523),f389(x8522,x8523))
% 25.54/25.42 [853]~E(x8531,x8532)+E(f389(x8533,x8531),f389(x8533,x8532))
% 25.54/25.42 [854]~E(x8541,x8542)+E(f879(x8541,x8543),f879(x8542,x8543))
% 25.54/25.42 [855]~E(x8551,x8552)+E(f879(x8553,x8551),f879(x8553,x8552))
% 25.54/25.42 [856]~E(x8561,x8562)+E(f831(x8561,x8563,x8564,x8565,x8566),f831(x8562,x8563,x8564,x8565,x8566))
% 25.54/25.42 [857]~E(x8571,x8572)+E(f831(x8573,x8571,x8574,x8575,x8576),f831(x8573,x8572,x8574,x8575,x8576))
% 25.54/25.42 [858]~E(x8581,x8582)+E(f831(x8583,x8584,x8581,x8585,x8586),f831(x8583,x8584,x8582,x8585,x8586))
% 25.54/25.42 [859]~E(x8591,x8592)+E(f831(x8593,x8594,x8595,x8591,x8596),f831(x8593,x8594,x8595,x8592,x8596))
% 25.54/25.42 [860]~E(x8601,x8602)+E(f831(x8603,x8604,x8605,x8606,x8601),f831(x8603,x8604,x8605,x8606,x8602))
% 25.54/25.42 [861]~E(x8611,x8612)+E(f245(x8611,x8613,x8614,x8615,x8616),f245(x8612,x8613,x8614,x8615,x8616))
% 25.54/25.42 [862]~E(x8621,x8622)+E(f245(x8623,x8621,x8624,x8625,x8626),f245(x8623,x8622,x8624,x8625,x8626))
% 25.54/25.42 [863]~E(x8631,x8632)+E(f245(x8633,x8634,x8631,x8635,x8636),f245(x8633,x8634,x8632,x8635,x8636))
% 25.54/25.42 [864]~E(x8641,x8642)+E(f245(x8643,x8644,x8645,x8641,x8646),f245(x8643,x8644,x8645,x8642,x8646))
% 25.54/25.42 [865]~E(x8651,x8652)+E(f245(x8653,x8654,x8655,x8656,x8651),f245(x8653,x8654,x8655,x8656,x8652))
% 25.54/25.42 [866]~E(x8661,x8662)+E(f635(x8661,x8663,x8664,x8665,x8666),f635(x8662,x8663,x8664,x8665,x8666))
% 25.54/25.42 [867]~E(x8671,x8672)+E(f635(x8673,x8671,x8674,x8675,x8676),f635(x8673,x8672,x8674,x8675,x8676))
% 25.54/25.42 [868]~E(x8681,x8682)+E(f635(x8683,x8684,x8681,x8685,x8686),f635(x8683,x8684,x8682,x8685,x8686))
% 25.54/25.42 [869]~E(x8691,x8692)+E(f635(x8693,x8694,x8695,x8691,x8696),f635(x8693,x8694,x8695,x8692,x8696))
% 25.54/25.42 [870]~E(x8701,x8702)+E(f635(x8703,x8704,x8705,x8706,x8701),f635(x8703,x8704,x8705,x8706,x8702))
% 25.54/25.42 [871]~E(x8711,x8712)+E(f651(x8711,x8713),f651(x8712,x8713))
% 25.54/25.42 [872]~E(x8721,x8722)+E(f651(x8723,x8721),f651(x8723,x8722))
% 25.54/25.42 [873]~E(x8731,x8732)+E(f705(x8731,x8733,x8734,x8735,x8736),f705(x8732,x8733,x8734,x8735,x8736))
% 25.54/25.42 [874]~E(x8741,x8742)+E(f705(x8743,x8741,x8744,x8745,x8746),f705(x8743,x8742,x8744,x8745,x8746))
% 25.54/25.42 [875]~E(x8751,x8752)+E(f705(x8753,x8754,x8751,x8755,x8756),f705(x8753,x8754,x8752,x8755,x8756))
% 25.54/25.42 [876]~E(x8761,x8762)+E(f705(x8763,x8764,x8765,x8761,x8766),f705(x8763,x8764,x8765,x8762,x8766))
% 25.54/25.42 [877]~E(x8771,x8772)+E(f705(x8773,x8774,x8775,x8776,x8771),f705(x8773,x8774,x8775,x8776,x8772))
% 25.54/25.42 [878]~E(x8781,x8782)+E(f837(x8781,x8783,x8784,x8785),f837(x8782,x8783,x8784,x8785))
% 25.54/25.42 [879]~E(x8791,x8792)+E(f837(x8793,x8791,x8794,x8795),f837(x8793,x8792,x8794,x8795))
% 25.54/25.42 [880]~E(x8801,x8802)+E(f837(x8803,x8804,x8801,x8805),f837(x8803,x8804,x8802,x8805))
% 25.54/25.42 [881]~E(x8811,x8812)+E(f837(x8813,x8814,x8815,x8811),f837(x8813,x8814,x8815,x8812))
% 25.54/25.42 [882]~E(x8821,x8822)+E(f803(x8821,x8823,x8824,x8825),f803(x8822,x8823,x8824,x8825))
% 25.54/25.42 [883]~E(x8831,x8832)+E(f803(x8833,x8831,x8834,x8835),f803(x8833,x8832,x8834,x8835))
% 25.54/25.42 [884]~E(x8841,x8842)+E(f803(x8843,x8844,x8841,x8845),f803(x8843,x8844,x8842,x8845))
% 25.54/25.42 [885]~E(x8851,x8852)+E(f803(x8853,x8854,x8855,x8851),f803(x8853,x8854,x8855,x8852))
% 25.54/25.42 [886]~E(x8861,x8862)+E(f39(x8861,x8863),f39(x8862,x8863))
% 25.54/25.42 [887]~E(x8871,x8872)+E(f39(x8873,x8871),f39(x8873,x8872))
% 25.54/25.42 [888]~E(x8881,x8882)+E(f420(x8881,x8883,x8884),f420(x8882,x8883,x8884))
% 25.54/25.42 [889]~E(x8891,x8892)+E(f420(x8893,x8891,x8894),f420(x8893,x8892,x8894))
% 25.54/25.42 [890]~E(x8901,x8902)+E(f420(x8903,x8904,x8901),f420(x8903,x8904,x8902))
% 25.54/25.42 [891]~E(x8911,x8912)+E(f188(x8911,x8913,x8914,x8915),f188(x8912,x8913,x8914,x8915))
% 25.54/25.42 [892]~E(x8921,x8922)+E(f188(x8923,x8921,x8924,x8925),f188(x8923,x8922,x8924,x8925))
% 25.54/25.42 [893]~E(x8931,x8932)+E(f188(x8933,x8934,x8931,x8935),f188(x8933,x8934,x8932,x8935))
% 25.54/25.42 [894]~E(x8941,x8942)+E(f188(x8943,x8944,x8945,x8941),f188(x8943,x8944,x8945,x8942))
% 25.54/25.42 [895]~E(x8951,x8952)+E(f775(x8951,x8953,x8954),f775(x8952,x8953,x8954))
% 25.54/25.42 [896]~E(x8961,x8962)+E(f775(x8963,x8961,x8964),f775(x8963,x8962,x8964))
% 25.54/25.42 [897]~E(x8971,x8972)+E(f775(x8973,x8974,x8971),f775(x8973,x8974,x8972))
% 25.54/25.42 [898]~E(x8981,x8982)+E(f386(x8981,x8983,x8984),f386(x8982,x8983,x8984))
% 25.54/25.42 [899]~E(x8991,x8992)+E(f386(x8993,x8991,x8994),f386(x8993,x8992,x8994))
% 25.54/25.42 [900]~E(x9001,x9002)+E(f386(x9003,x9004,x9001),f386(x9003,x9004,x9002))
% 25.54/25.42 [901]~E(x9011,x9012)+E(f151(x9011,x9013),f151(x9012,x9013))
% 25.54/25.42 [902]~E(x9021,x9022)+E(f151(x9023,x9021),f151(x9023,x9022))
% 25.54/25.42 [903]~E(x9031,x9032)+E(f510(x9031,x9033,x9034),f510(x9032,x9033,x9034))
% 25.54/25.42 [904]~E(x9041,x9042)+E(f510(x9043,x9041,x9044),f510(x9043,x9042,x9044))
% 25.54/25.42 [905]~E(x9051,x9052)+E(f510(x9053,x9054,x9051),f510(x9053,x9054,x9052))
% 25.54/25.42 [906]~E(x9061,x9062)+E(f712(x9061,x9063),f712(x9062,x9063))
% 25.54/25.42 [907]~E(x9071,x9072)+E(f712(x9073,x9071),f712(x9073,x9072))
% 25.54/25.42 [908]~E(x9081,x9082)+E(f262(x9081,x9083),f262(x9082,x9083))
% 25.54/25.42 [909]~E(x9091,x9092)+E(f262(x9093,x9091),f262(x9093,x9092))
% 25.54/25.42 [910]~E(x9101,x9102)+E(f764(x9101,x9103,x9104),f764(x9102,x9103,x9104))
% 25.54/25.42 [911]~E(x9111,x9112)+E(f764(x9113,x9111,x9114),f764(x9113,x9112,x9114))
% 25.54/25.42 [912]~E(x9121,x9122)+E(f764(x9123,x9124,x9121),f764(x9123,x9124,x9122))
% 25.54/25.42 [913]~E(x9131,x9132)+E(f531(x9131,x9133,x9134,x9135,x9136,x9137,x9138),f531(x9132,x9133,x9134,x9135,x9136,x9137,x9138))
% 25.54/25.42 [914]~E(x9141,x9142)+E(f531(x9143,x9141,x9144,x9145,x9146,x9147,x9148),f531(x9143,x9142,x9144,x9145,x9146,x9147,x9148))
% 25.54/25.42 [915]~E(x9151,x9152)+E(f531(x9153,x9154,x9151,x9155,x9156,x9157,x9158),f531(x9153,x9154,x9152,x9155,x9156,x9157,x9158))
% 25.54/25.42 [916]~E(x9161,x9162)+E(f531(x9163,x9164,x9165,x9161,x9166,x9167,x9168),f531(x9163,x9164,x9165,x9162,x9166,x9167,x9168))
% 25.54/25.42 [917]~E(x9171,x9172)+E(f531(x9173,x9174,x9175,x9176,x9171,x9177,x9178),f531(x9173,x9174,x9175,x9176,x9172,x9177,x9178))
% 25.54/25.42 [918]~E(x9181,x9182)+E(f531(x9183,x9184,x9185,x9186,x9187,x9181,x9188),f531(x9183,x9184,x9185,x9186,x9187,x9182,x9188))
% 25.54/25.42 [919]~E(x9191,x9192)+E(f531(x9193,x9194,x9195,x9196,x9197,x9198,x9191),f531(x9193,x9194,x9195,x9196,x9197,x9198,x9192))
% 25.54/25.42 [920]~E(x9201,x9202)+E(f370(x9201,x9203,x9204),f370(x9202,x9203,x9204))
% 25.54/25.42 [921]~E(x9211,x9212)+E(f370(x9213,x9211,x9214),f370(x9213,x9212,x9214))
% 25.54/25.42 [922]~E(x9221,x9222)+E(f370(x9223,x9224,x9221),f370(x9223,x9224,x9222))
% 25.54/25.42 [923]~E(x9231,x9232)+E(f440(x9231,x9233,x9234),f440(x9232,x9233,x9234))
% 25.54/25.42 [924]~E(x9241,x9242)+E(f440(x9243,x9241,x9244),f440(x9243,x9242,x9244))
% 25.54/25.42 [925]~E(x9251,x9252)+E(f440(x9253,x9254,x9251),f440(x9253,x9254,x9252))
% 25.54/25.42 [926]~E(x9261,x9262)+E(f583(x9261,x9263,x9264,x9265,x9266,x9267,x9268,x9269),f583(x9262,x9263,x9264,x9265,x9266,x9267,x9268,x9269))
% 25.54/25.42 [927]~E(x9271,x9272)+E(f583(x9273,x9271,x9274,x9275,x9276,x9277,x9278,x9279),f583(x9273,x9272,x9274,x9275,x9276,x9277,x9278,x9279))
% 25.54/25.42 [928]~E(x9281,x9282)+E(f583(x9283,x9284,x9281,x9285,x9286,x9287,x9288,x9289),f583(x9283,x9284,x9282,x9285,x9286,x9287,x9288,x9289))
% 25.54/25.42 [929]~E(x9291,x9292)+E(f583(x9293,x9294,x9295,x9291,x9296,x9297,x9298,x9299),f583(x9293,x9294,x9295,x9292,x9296,x9297,x9298,x9299))
% 25.54/25.42 [930]~E(x9301,x9302)+E(f583(x9303,x9304,x9305,x9306,x9301,x9307,x9308,x9309),f583(x9303,x9304,x9305,x9306,x9302,x9307,x9308,x9309))
% 25.54/25.42 [931]~E(x9311,x9312)+E(f583(x9313,x9314,x9315,x9316,x9317,x9311,x9318,x9319),f583(x9313,x9314,x9315,x9316,x9317,x9312,x9318,x9319))
% 25.54/25.42 [932]~E(x9321,x9322)+E(f583(x9323,x9324,x9325,x9326,x9327,x9328,x9321,x9329),f583(x9323,x9324,x9325,x9326,x9327,x9328,x9322,x9329))
% 25.54/25.42 [933]~E(x9331,x9332)+E(f583(x9333,x9334,x9335,x9336,x9337,x9338,x9339,x9331),f583(x9333,x9334,x9335,x9336,x9337,x9338,x9339,x9332))
% 25.54/25.42 [934]~E(x9341,x9342)+E(f417(x9341,x9343,x9344),f417(x9342,x9343,x9344))
% 25.54/25.42 [935]~E(x9351,x9352)+E(f417(x9353,x9351,x9354),f417(x9353,x9352,x9354))
% 25.54/25.42 [936]~E(x9361,x9362)+E(f417(x9363,x9364,x9361),f417(x9363,x9364,x9362))
% 25.54/25.42 [937]~E(x9371,x9372)+E(f339(x9371,x9373,x9374),f339(x9372,x9373,x9374))
% 25.54/25.42 [938]~E(x9381,x9382)+E(f339(x9383,x9381,x9384),f339(x9383,x9382,x9384))
% 25.54/25.42 [939]~E(x9391,x9392)+E(f339(x9393,x9394,x9391),f339(x9393,x9394,x9392))
% 25.54/25.42 [940]~E(x9401,x9402)+E(f542(x9401,x9403),f542(x9402,x9403))
% 25.54/25.42 [941]~E(x9411,x9412)+E(f542(x9413,x9411),f542(x9413,x9412))
% 25.54/25.42 [942]~E(x9421,x9422)+E(f859(x9421,x9423,x9424,x9425,x9426,x9427,x9428),f859(x9422,x9423,x9424,x9425,x9426,x9427,x9428))
% 25.54/25.42 [943]~E(x9431,x9432)+E(f859(x9433,x9431,x9434,x9435,x9436,x9437,x9438),f859(x9433,x9432,x9434,x9435,x9436,x9437,x9438))
% 25.54/25.42 [944]~E(x9441,x9442)+E(f859(x9443,x9444,x9441,x9445,x9446,x9447,x9448),f859(x9443,x9444,x9442,x9445,x9446,x9447,x9448))
% 25.54/25.42 [945]~E(x9451,x9452)+E(f859(x9453,x9454,x9455,x9451,x9456,x9457,x9458),f859(x9453,x9454,x9455,x9452,x9456,x9457,x9458))
% 25.54/25.42 [946]~E(x9461,x9462)+E(f859(x9463,x9464,x9465,x9466,x9461,x9467,x9468),f859(x9463,x9464,x9465,x9466,x9462,x9467,x9468))
% 25.54/25.42 [947]~E(x9471,x9472)+E(f859(x9473,x9474,x9475,x9476,x9477,x9471,x9478),f859(x9473,x9474,x9475,x9476,x9477,x9472,x9478))
% 25.54/25.42 [948]~E(x9481,x9482)+E(f859(x9483,x9484,x9485,x9486,x9487,x9488,x9481),f859(x9483,x9484,x9485,x9486,x9487,x9488,x9482))
% 25.54/25.42 [949]~E(x9491,x9492)+E(f536(x9491,x9493,x9494),f536(x9492,x9493,x9494))
% 25.54/25.42 [950]~E(x9501,x9502)+E(f536(x9503,x9501,x9504),f536(x9503,x9502,x9504))
% 25.54/25.42 [951]~E(x9511,x9512)+E(f536(x9513,x9514,x9511),f536(x9513,x9514,x9512))
% 25.54/25.42 [952]~E(x9521,x9522)+E(f834(x9521,x9523,x9524,x9525),f834(x9522,x9523,x9524,x9525))
% 25.54/25.42 [953]~E(x9531,x9532)+E(f834(x9533,x9531,x9534,x9535),f834(x9533,x9532,x9534,x9535))
% 25.54/25.42 [954]~E(x9541,x9542)+E(f834(x9543,x9544,x9541,x9545),f834(x9543,x9544,x9542,x9545))
% 25.54/25.42 [955]~E(x9551,x9552)+E(f834(x9553,x9554,x9555,x9551),f834(x9553,x9554,x9555,x9552))
% 25.54/25.42 [956]~E(x9561,x9562)+E(f55(x9561,x9563,x9564),f55(x9562,x9563,x9564))
% 25.54/25.42 [957]~E(x9571,x9572)+E(f55(x9573,x9571,x9574),f55(x9573,x9572,x9574))
% 25.54/25.42 [958]~E(x9581,x9582)+E(f55(x9583,x9584,x9581),f55(x9583,x9584,x9582))
% 25.54/25.42 [959]~E(x9591,x9592)+E(f224(x9591,x9593,x9594,x9595),f224(x9592,x9593,x9594,x9595))
% 25.54/25.42 [960]~E(x9601,x9602)+E(f224(x9603,x9601,x9604,x9605),f224(x9603,x9602,x9604,x9605))
% 25.54/25.42 [961]~E(x9611,x9612)+E(f224(x9613,x9614,x9611,x9615),f224(x9613,x9614,x9612,x9615))
% 25.54/25.42 [962]~E(x9621,x9622)+E(f224(x9623,x9624,x9625,x9621),f224(x9623,x9624,x9625,x9622))
% 25.54/25.42 [963]~E(x9631,x9632)+E(f738(x9631,x9633),f738(x9632,x9633))
% 25.54/25.42 [964]~E(x9641,x9642)+E(f738(x9643,x9641),f738(x9643,x9642))
% 25.54/25.42 [965]~E(x9651,x9652)+E(f576(x9651,x9653,x9654,x9655,x9656),f576(x9652,x9653,x9654,x9655,x9656))
% 25.54/25.42 [966]~E(x9661,x9662)+E(f576(x9663,x9661,x9664,x9665,x9666),f576(x9663,x9662,x9664,x9665,x9666))
% 25.54/25.42 [967]~E(x9671,x9672)+E(f576(x9673,x9674,x9671,x9675,x9676),f576(x9673,x9674,x9672,x9675,x9676))
% 25.54/25.42 [968]~E(x9681,x9682)+E(f576(x9683,x9684,x9685,x9681,x9686),f576(x9683,x9684,x9685,x9682,x9686))
% 25.54/25.42 [969]~E(x9691,x9692)+E(f576(x9693,x9694,x9695,x9696,x9691),f576(x9693,x9694,x9695,x9696,x9692))
% 25.54/25.42 [970]~E(x9701,x9702)+E(f615(x9701,x9703,x9704,x9705),f615(x9702,x9703,x9704,x9705))
% 25.54/25.42 [971]~E(x9711,x9712)+E(f615(x9713,x9711,x9714,x9715),f615(x9713,x9712,x9714,x9715))
% 25.54/25.42 [972]~E(x9721,x9722)+E(f615(x9723,x9724,x9721,x9725),f615(x9723,x9724,x9722,x9725))
% 25.54/25.42 [973]~E(x9731,x9732)+E(f615(x9733,x9734,x9735,x9731),f615(x9733,x9734,x9735,x9732))
% 25.54/25.42 [974]~E(x9741,x9742)+E(f59(x9741,x9743,x9744,x9745,x9746),f59(x9742,x9743,x9744,x9745,x9746))
% 25.54/25.42 [975]~E(x9751,x9752)+E(f59(x9753,x9751,x9754,x9755,x9756),f59(x9753,x9752,x9754,x9755,x9756))
% 25.54/25.42 [976]~E(x9761,x9762)+E(f59(x9763,x9764,x9761,x9765,x9766),f59(x9763,x9764,x9762,x9765,x9766))
% 25.54/25.42 [977]~E(x9771,x9772)+E(f59(x9773,x9774,x9775,x9771,x9776),f59(x9773,x9774,x9775,x9772,x9776))
% 25.54/25.42 [978]~E(x9781,x9782)+E(f59(x9783,x9784,x9785,x9786,x9781),f59(x9783,x9784,x9785,x9786,x9782))
% 25.54/25.42 [979]~E(x9791,x9792)+E(f185(x9791,x9793),f185(x9792,x9793))
% 25.54/25.42 [980]~E(x9801,x9802)+E(f185(x9803,x9801),f185(x9803,x9802))
% 25.54/25.42 [981]~E(x9811,x9812)+E(f786(x9811,x9813,x9814,x9815),f786(x9812,x9813,x9814,x9815))
% 25.54/25.42 [982]~E(x9821,x9822)+E(f786(x9823,x9821,x9824,x9825),f786(x9823,x9822,x9824,x9825))
% 25.54/25.42 [983]~E(x9831,x9832)+E(f786(x9833,x9834,x9831,x9835),f786(x9833,x9834,x9832,x9835))
% 25.54/25.42 [984]~E(x9841,x9842)+E(f786(x9843,x9844,x9845,x9841),f786(x9843,x9844,x9845,x9842))
% 25.54/25.42 [985]~E(x9851,x9852)+E(f114(x9851,x9853),f114(x9852,x9853))
% 25.54/25.42 [986]~E(x9861,x9862)+E(f114(x9863,x9861),f114(x9863,x9862))
% 25.54/25.42 [987]~E(x9871,x9872)+E(f429(x9871,x9873,x9874),f429(x9872,x9873,x9874))
% 25.54/25.42 [988]~E(x9881,x9882)+E(f429(x9883,x9881,x9884),f429(x9883,x9882,x9884))
% 25.54/25.42 [989]~E(x9891,x9892)+E(f429(x9893,x9894,x9891),f429(x9893,x9894,x9892))
% 25.54/25.42 [990]~E(x9901,x9902)+E(f646(x9901,x9903),f646(x9902,x9903))
% 25.54/25.42 [991]~E(x9911,x9912)+E(f646(x9913,x9911),f646(x9913,x9912))
% 25.54/25.42 [992]~E(x9921,x9922)+E(f573(x9921,x9923,x9924,x9925,x9926,x9927),f573(x9922,x9923,x9924,x9925,x9926,x9927))
% 25.54/25.42 [993]~E(x9931,x9932)+E(f573(x9933,x9931,x9934,x9935,x9936,x9937),f573(x9933,x9932,x9934,x9935,x9936,x9937))
% 25.54/25.42 [994]~E(x9941,x9942)+E(f573(x9943,x9944,x9941,x9945,x9946,x9947),f573(x9943,x9944,x9942,x9945,x9946,x9947))
% 25.54/25.42 [995]~E(x9951,x9952)+E(f573(x9953,x9954,x9955,x9951,x9956,x9957),f573(x9953,x9954,x9955,x9952,x9956,x9957))
% 25.54/25.42 [996]~E(x9961,x9962)+E(f573(x9963,x9964,x9965,x9966,x9961,x9967),f573(x9963,x9964,x9965,x9966,x9962,x9967))
% 25.54/25.42 [997]~E(x9971,x9972)+E(f573(x9973,x9974,x9975,x9976,x9977,x9971),f573(x9973,x9974,x9975,x9976,x9977,x9972))
% 25.54/25.42 [998]~E(x9981,x9982)+E(f692(x9981,x9983,x9984,x9985),f692(x9982,x9983,x9984,x9985))
% 25.54/25.42 [999]~E(x9991,x9992)+E(f692(x9993,x9991,x9994,x9995),f692(x9993,x9992,x9994,x9995))
% 25.54/25.42 [1000]~E(x10001,x10002)+E(f692(x10003,x10004,x10001,x10005),f692(x10003,x10004,x10002,x10005))
% 25.54/25.42 [1001]~E(x10011,x10012)+E(f692(x10013,x10014,x10015,x10011),f692(x10013,x10014,x10015,x10012))
% 25.54/25.42 [1002]~E(x10021,x10022)+E(f43(x10021,x10023),f43(x10022,x10023))
% 25.54/25.42 [1003]~E(x10031,x10032)+E(f43(x10033,x10031),f43(x10033,x10032))
% 25.54/25.42 [1004]~E(x10041,x10042)+E(f313(x10041,x10043,x10044),f313(x10042,x10043,x10044))
% 25.54/25.42 [1005]~E(x10051,x10052)+E(f313(x10053,x10051,x10054),f313(x10053,x10052,x10054))
% 25.54/25.42 [1006]~E(x10061,x10062)+E(f313(x10063,x10064,x10061),f313(x10063,x10064,x10062))
% 25.54/25.42 [1007]~E(x10071,x10072)+E(f357(x10071),f357(x10072))
% 25.54/25.42 [1008]~E(x10081,x10082)+E(f523(x10081,x10083,x10084),f523(x10082,x10083,x10084))
% 25.54/25.42 [1009]~E(x10091,x10092)+E(f523(x10093,x10091,x10094),f523(x10093,x10092,x10094))
% 25.54/25.42 [1010]~E(x10101,x10102)+E(f523(x10103,x10104,x10101),f523(x10103,x10104,x10102))
% 25.54/25.42 [1011]~E(x10111,x10112)+E(f241(x10111,x10113,x10114),f241(x10112,x10113,x10114))
% 25.54/25.42 [1012]~E(x10121,x10122)+E(f241(x10123,x10121,x10124),f241(x10123,x10122,x10124))
% 25.54/25.42 [1013]~E(x10131,x10132)+E(f241(x10133,x10134,x10131),f241(x10133,x10134,x10132))
% 25.54/25.42 [1014]~E(x10141,x10142)+E(f755(x10141,x10143,x10144,x10145,x10146,x10147,x10148),f755(x10142,x10143,x10144,x10145,x10146,x10147,x10148))
% 25.54/25.42 [1015]~E(x10151,x10152)+E(f755(x10153,x10151,x10154,x10155,x10156,x10157,x10158),f755(x10153,x10152,x10154,x10155,x10156,x10157,x10158))
% 25.54/25.42 [1016]~E(x10161,x10162)+E(f755(x10163,x10164,x10161,x10165,x10166,x10167,x10168),f755(x10163,x10164,x10162,x10165,x10166,x10167,x10168))
% 25.54/25.42 [1017]~E(x10171,x10172)+E(f755(x10173,x10174,x10175,x10171,x10176,x10177,x10178),f755(x10173,x10174,x10175,x10172,x10176,x10177,x10178))
% 25.54/25.42 [1018]~E(x10181,x10182)+E(f755(x10183,x10184,x10185,x10186,x10181,x10187,x10188),f755(x10183,x10184,x10185,x10186,x10182,x10187,x10188))
% 25.54/25.42 [1019]~E(x10191,x10192)+E(f755(x10193,x10194,x10195,x10196,x10197,x10191,x10198),f755(x10193,x10194,x10195,x10196,x10197,x10192,x10198))
% 25.54/25.42 [1020]~E(x10201,x10202)+E(f755(x10203,x10204,x10205,x10206,x10207,x10208,x10201),f755(x10203,x10204,x10205,x10206,x10207,x10208,x10202))
% 25.54/25.42 [1021]~E(x10211,x10212)+E(f873(x10211,x10213,x10214),f873(x10212,x10213,x10214))
% 25.54/25.42 [1022]~E(x10221,x10222)+E(f873(x10223,x10221,x10224),f873(x10223,x10222,x10224))
% 25.54/25.42 [1023]~E(x10231,x10232)+E(f873(x10233,x10234,x10231),f873(x10233,x10234,x10232))
% 25.54/25.42 [1024]~E(x10241,x10242)+E(f513(x10241,x10243),f513(x10242,x10243))
% 25.54/25.42 [1025]~E(x10251,x10252)+E(f513(x10253,x10251),f513(x10253,x10252))
% 25.54/25.42 [1026]~E(x10261,x10262)+E(f216(x10261,x10263,x10264,x10265,x10266),f216(x10262,x10263,x10264,x10265,x10266))
% 25.54/25.42 [1027]~E(x10271,x10272)+E(f216(x10273,x10271,x10274,x10275,x10276),f216(x10273,x10272,x10274,x10275,x10276))
% 25.54/25.42 [1028]~E(x10281,x10282)+E(f216(x10283,x10284,x10281,x10285,x10286),f216(x10283,x10284,x10282,x10285,x10286))
% 25.54/25.42 [1029]~E(x10291,x10292)+E(f216(x10293,x10294,x10295,x10291,x10296),f216(x10293,x10294,x10295,x10292,x10296))
% 25.54/25.42 [1030]~E(x10301,x10302)+E(f216(x10303,x10304,x10305,x10306,x10301),f216(x10303,x10304,x10305,x10306,x10302))
% 25.54/25.42 [1031]~E(x10311,x10312)+E(f619(x10311,x10313,x10314,x10315,x10316,x10317,x10318,x10319),f619(x10312,x10313,x10314,x10315,x10316,x10317,x10318,x10319))
% 25.54/25.42 [1032]~E(x10321,x10322)+E(f619(x10323,x10321,x10324,x10325,x10326,x10327,x10328,x10329),f619(x10323,x10322,x10324,x10325,x10326,x10327,x10328,x10329))
% 25.54/25.42 [1033]~E(x10331,x10332)+E(f619(x10333,x10334,x10331,x10335,x10336,x10337,x10338,x10339),f619(x10333,x10334,x10332,x10335,x10336,x10337,x10338,x10339))
% 25.54/25.42 [1034]~E(x10341,x10342)+E(f619(x10343,x10344,x10345,x10341,x10346,x10347,x10348,x10349),f619(x10343,x10344,x10345,x10342,x10346,x10347,x10348,x10349))
% 25.54/25.42 [1035]~E(x10351,x10352)+E(f619(x10353,x10354,x10355,x10356,x10351,x10357,x10358,x10359),f619(x10353,x10354,x10355,x10356,x10352,x10357,x10358,x10359))
% 25.54/25.42 [1036]~E(x10361,x10362)+E(f619(x10363,x10364,x10365,x10366,x10367,x10361,x10368,x10369),f619(x10363,x10364,x10365,x10366,x10367,x10362,x10368,x10369))
% 25.54/25.42 [1037]~E(x10371,x10372)+E(f619(x10373,x10374,x10375,x10376,x10377,x10378,x10371,x10379),f619(x10373,x10374,x10375,x10376,x10377,x10378,x10372,x10379))
% 25.54/25.42 [1038]~E(x10381,x10382)+E(f619(x10383,x10384,x10385,x10386,x10387,x10388,x10389,x10381),f619(x10383,x10384,x10385,x10386,x10387,x10388,x10389,x10382))
% 25.54/25.42 [1039]~E(x10391,x10392)+E(f305(x10391,x10393,x10394,x10395),f305(x10392,x10393,x10394,x10395))
% 25.54/25.42 [1040]~E(x10401,x10402)+E(f305(x10403,x10401,x10404,x10405),f305(x10403,x10402,x10404,x10405))
% 25.54/25.42 [1041]~E(x10411,x10412)+E(f305(x10413,x10414,x10411,x10415),f305(x10413,x10414,x10412,x10415))
% 25.54/25.42 [1042]~E(x10421,x10422)+E(f305(x10423,x10424,x10425,x10421),f305(x10423,x10424,x10425,x10422))
% 25.54/25.42 [1043]~E(x10431,x10432)+E(f631(x10431,x10433,x10434),f631(x10432,x10433,x10434))
% 25.54/25.42 [1044]~E(x10441,x10442)+E(f631(x10443,x10441,x10444),f631(x10443,x10442,x10444))
% 25.54/25.42 [1045]~E(x10451,x10452)+E(f631(x10453,x10454,x10451),f631(x10453,x10454,x10452))
% 25.54/25.42 [1046]~E(x10461,x10462)+E(f882(x10461,x10463,x10464,x10465),f882(x10462,x10463,x10464,x10465))
% 25.54/25.42 [1047]~E(x10471,x10472)+E(f882(x10473,x10471,x10474,x10475),f882(x10473,x10472,x10474,x10475))
% 25.54/25.42 [1048]~E(x10481,x10482)+E(f882(x10483,x10484,x10481,x10485),f882(x10483,x10484,x10482,x10485))
% 25.54/25.42 [1049]~E(x10491,x10492)+E(f882(x10493,x10494,x10495,x10491),f882(x10493,x10494,x10495,x10492))
% 25.54/25.42 [1050]~E(x10501,x10502)+E(f173(x10501),f173(x10502))
% 25.54/25.42 [1051]~E(x10511,x10512)+E(f640(x10511,x10513,x10514,x10515,x10516),f640(x10512,x10513,x10514,x10515,x10516))
% 25.54/25.42 [1052]~E(x10521,x10522)+E(f640(x10523,x10521,x10524,x10525,x10526),f640(x10523,x10522,x10524,x10525,x10526))
% 25.54/25.42 [1053]~E(x10531,x10532)+E(f640(x10533,x10534,x10531,x10535,x10536),f640(x10533,x10534,x10532,x10535,x10536))
% 25.54/25.42 [1054]~E(x10541,x10542)+E(f640(x10543,x10544,x10545,x10541,x10546),f640(x10543,x10544,x10545,x10542,x10546))
% 25.54/25.42 [1055]~E(x10551,x10552)+E(f640(x10553,x10554,x10555,x10556,x10551),f640(x10553,x10554,x10555,x10556,x10552))
% 25.54/25.42 [1056]~E(x10561,x10562)+E(f754(x10561,x10563,x10564,x10565,x10566,x10567,x10568),f754(x10562,x10563,x10564,x10565,x10566,x10567,x10568))
% 25.54/25.42 [1057]~E(x10571,x10572)+E(f754(x10573,x10571,x10574,x10575,x10576,x10577,x10578),f754(x10573,x10572,x10574,x10575,x10576,x10577,x10578))
% 25.54/25.42 [1058]~E(x10581,x10582)+E(f754(x10583,x10584,x10581,x10585,x10586,x10587,x10588),f754(x10583,x10584,x10582,x10585,x10586,x10587,x10588))
% 25.54/25.42 [1059]~E(x10591,x10592)+E(f754(x10593,x10594,x10595,x10591,x10596,x10597,x10598),f754(x10593,x10594,x10595,x10592,x10596,x10597,x10598))
% 25.54/25.42 [1060]~E(x10601,x10602)+E(f754(x10603,x10604,x10605,x10606,x10601,x10607,x10608),f754(x10603,x10604,x10605,x10606,x10602,x10607,x10608))
% 25.54/25.42 [1061]~E(x10611,x10612)+E(f754(x10613,x10614,x10615,x10616,x10617,x10611,x10618),f754(x10613,x10614,x10615,x10616,x10617,x10612,x10618))
% 25.54/25.42 [1062]~E(x10621,x10622)+E(f754(x10623,x10624,x10625,x10626,x10627,x10628,x10621),f754(x10623,x10624,x10625,x10626,x10627,x10628,x10622))
% 25.54/25.42 [1063]~E(x10631,x10632)+E(f724(x10631,x10633,x10634),f724(x10632,x10633,x10634))
% 25.54/25.42 [1064]~E(x10641,x10642)+E(f724(x10643,x10641,x10644),f724(x10643,x10642,x10644))
% 25.54/25.42 [1065]~E(x10651,x10652)+E(f724(x10653,x10654,x10651),f724(x10653,x10654,x10652))
% 25.54/25.42 [1066]~E(x10661,x10662)+E(f827(x10661,x10663),f827(x10662,x10663))
% 25.54/25.42 [1067]~E(x10671,x10672)+E(f827(x10673,x10671),f827(x10673,x10672))
% 25.54/25.42 [1068]~E(x10681,x10682)+E(f714(x10681,x10683),f714(x10682,x10683))
% 25.54/25.42 [1069]~E(x10691,x10692)+E(f714(x10693,x10691),f714(x10693,x10692))
% 25.54/25.42 [1070]~E(x10701,x10702)+E(f209(x10701,x10703),f209(x10702,x10703))
% 25.54/25.42 [1071]~E(x10711,x10712)+E(f209(x10713,x10711),f209(x10713,x10712))
% 25.54/25.42 [1072]~E(x10721,x10722)+E(f264(x10721,x10723),f264(x10722,x10723))
% 25.54/25.42 [1073]~E(x10731,x10732)+E(f264(x10733,x10731),f264(x10733,x10732))
% 25.54/25.42 [1074]~E(x10741,x10742)+E(f586(x10741,x10743,x10744,x10745,x10746,x10747),f586(x10742,x10743,x10744,x10745,x10746,x10747))
% 25.54/25.42 [1075]~E(x10751,x10752)+E(f586(x10753,x10751,x10754,x10755,x10756,x10757),f586(x10753,x10752,x10754,x10755,x10756,x10757))
% 25.54/25.42 [1076]~E(x10761,x10762)+E(f586(x10763,x10764,x10761,x10765,x10766,x10767),f586(x10763,x10764,x10762,x10765,x10766,x10767))
% 25.54/25.42 [1077]~E(x10771,x10772)+E(f586(x10773,x10774,x10775,x10771,x10776,x10777),f586(x10773,x10774,x10775,x10772,x10776,x10777))
% 25.54/25.42 [1078]~E(x10781,x10782)+E(f586(x10783,x10784,x10785,x10786,x10781,x10787),f586(x10783,x10784,x10785,x10786,x10782,x10787))
% 25.54/25.42 [1079]~E(x10791,x10792)+E(f586(x10793,x10794,x10795,x10796,x10797,x10791),f586(x10793,x10794,x10795,x10796,x10797,x10792))
% 25.54/25.42 [1080]~E(x10801,x10802)+E(f283(x10801,x10803),f283(x10802,x10803))
% 25.54/25.42 [1081]~E(x10811,x10812)+E(f283(x10813,x10811),f283(x10813,x10812))
% 25.54/25.42 [1082]~E(x10821,x10822)+E(f800(x10821,x10823,x10824,x10825),f800(x10822,x10823,x10824,x10825))
% 25.54/25.42 [1083]~E(x10831,x10832)+E(f800(x10833,x10831,x10834,x10835),f800(x10833,x10832,x10834,x10835))
% 25.54/25.42 [1084]~E(x10841,x10842)+E(f800(x10843,x10844,x10841,x10845),f800(x10843,x10844,x10842,x10845))
% 25.54/25.42 [1085]~E(x10851,x10852)+E(f800(x10853,x10854,x10855,x10851),f800(x10853,x10854,x10855,x10852))
% 25.54/25.42 [1086]~E(x10861,x10862)+E(f704(x10861,x10863,x10864,x10865),f704(x10862,x10863,x10864,x10865))
% 25.54/25.42 [1087]~E(x10871,x10872)+E(f704(x10873,x10871,x10874,x10875),f704(x10873,x10872,x10874,x10875))
% 25.54/25.42 [1088]~E(x10881,x10882)+E(f704(x10883,x10884,x10881,x10885),f704(x10883,x10884,x10882,x10885))
% 25.54/25.42 [1089]~E(x10891,x10892)+E(f704(x10893,x10894,x10895,x10891),f704(x10893,x10894,x10895,x10892))
% 25.54/25.42 [1090]~E(x10901,x10902)+E(f468(x10901,x10903),f468(x10902,x10903))
% 25.54/25.42 [1091]~E(x10911,x10912)+E(f468(x10913,x10911),f468(x10913,x10912))
% 25.54/25.42 [1092]~E(x10921,x10922)+E(f597(x10921,x10923,x10924),f597(x10922,x10923,x10924))
% 25.54/25.42 [1093]~E(x10931,x10932)+E(f597(x10933,x10931,x10934),f597(x10933,x10932,x10934))
% 25.54/25.42 [1094]~E(x10941,x10942)+E(f597(x10943,x10944,x10941),f597(x10943,x10944,x10942))
% 25.54/25.42 [1095]~E(x10951,x10952)+E(f708(x10951,x10953),f708(x10952,x10953))
% 25.54/25.42 [1096]~E(x10961,x10962)+E(f708(x10963,x10961),f708(x10963,x10962))
% 25.54/25.42 [1097]~E(x10971,x10972)+E(f669(x10971,x10973,x10974),f669(x10972,x10973,x10974))
% 25.54/25.42 [1098]~E(x10981,x10982)+E(f669(x10983,x10981,x10984),f669(x10983,x10982,x10984))
% 25.54/25.42 [1099]~E(x10991,x10992)+E(f669(x10993,x10994,x10991),f669(x10993,x10994,x10992))
% 25.54/25.42 [1100]~E(x11001,x11002)+E(f52(x11001,x11003,x11004,x11005),f52(x11002,x11003,x11004,x11005))
% 25.54/25.42 [1101]~E(x11011,x11012)+E(f52(x11013,x11011,x11014,x11015),f52(x11013,x11012,x11014,x11015))
% 25.54/25.42 [1102]~E(x11021,x11022)+E(f52(x11023,x11024,x11021,x11025),f52(x11023,x11024,x11022,x11025))
% 25.54/25.42 [1103]~E(x11031,x11032)+E(f52(x11033,x11034,x11035,x11031),f52(x11033,x11034,x11035,x11032))
% 25.54/25.42 [1104]~E(x11041,x11042)+E(f916(x11041,x11043,x11044,x11045,x11046),f916(x11042,x11043,x11044,x11045,x11046))
% 25.54/25.42 [1105]~E(x11051,x11052)+E(f916(x11053,x11051,x11054,x11055,x11056),f916(x11053,x11052,x11054,x11055,x11056))
% 25.54/25.42 [1106]~E(x11061,x11062)+E(f916(x11063,x11064,x11061,x11065,x11066),f916(x11063,x11064,x11062,x11065,x11066))
% 25.54/25.42 [1107]~E(x11071,x11072)+E(f916(x11073,x11074,x11075,x11071,x11076),f916(x11073,x11074,x11075,x11072,x11076))
% 25.54/25.42 [1108]~E(x11081,x11082)+E(f916(x11083,x11084,x11085,x11086,x11081),f916(x11083,x11084,x11085,x11086,x11082))
% 25.54/25.42 [1109]~E(x11091,x11092)+E(f746(x11091,x11093),f746(x11092,x11093))
% 25.54/25.42 [1110]~E(x11101,x11102)+E(f746(x11103,x11101),f746(x11103,x11102))
% 25.54/25.42 [1111]~E(x11111,x11112)+E(f273(x11111),f273(x11112))
% 25.54/25.42 [1112]~E(x11121,x11122)+E(f464(x11121,x11123,x11124),f464(x11122,x11123,x11124))
% 25.54/25.42 [1113]~E(x11131,x11132)+E(f464(x11133,x11131,x11134),f464(x11133,x11132,x11134))
% 25.54/25.42 [1114]~E(x11141,x11142)+E(f464(x11143,x11144,x11141),f464(x11143,x11144,x11142))
% 25.54/25.42 [1115]~E(x11151,x11152)+E(f516(x11151,x11153,x11154,x11155,x11156),f516(x11152,x11153,x11154,x11155,x11156))
% 25.54/25.42 [1116]~E(x11161,x11162)+E(f516(x11163,x11161,x11164,x11165,x11166),f516(x11163,x11162,x11164,x11165,x11166))
% 25.54/25.42 [1117]~E(x11171,x11172)+E(f516(x11173,x11174,x11171,x11175,x11176),f516(x11173,x11174,x11172,x11175,x11176))
% 25.54/25.42 [1118]~E(x11181,x11182)+E(f516(x11183,x11184,x11185,x11181,x11186),f516(x11183,x11184,x11185,x11182,x11186))
% 25.54/25.42 [1119]~E(x11191,x11192)+E(f516(x11193,x11194,x11195,x11196,x11191),f516(x11193,x11194,x11195,x11196,x11192))
% 25.54/25.42 [1120]~E(x11201,x11202)+E(f60(x11201,x11203,x11204),f60(x11202,x11203,x11204))
% 25.54/25.42 [1121]~E(x11211,x11212)+E(f60(x11213,x11211,x11214),f60(x11213,x11212,x11214))
% 25.54/25.42 [1122]~E(x11221,x11222)+E(f60(x11223,x11224,x11221),f60(x11223,x11224,x11222))
% 25.54/25.42 [1123]~E(x11231,x11232)+E(f121(x11231,x11233),f121(x11232,x11233))
% 25.54/25.42 [1124]~E(x11241,x11242)+E(f121(x11243,x11241),f121(x11243,x11242))
% 25.54/25.42 [1125]~E(x11251,x11252)+E(f592(x11251,x11253),f592(x11252,x11253))
% 25.54/25.42 [1126]~E(x11261,x11262)+E(f592(x11263,x11261),f592(x11263,x11262))
% 25.54/25.42 [1127]~E(x11271,x11272)+E(f639(x11271,x11273,x11274,x11275,x11276),f639(x11272,x11273,x11274,x11275,x11276))
% 25.54/25.42 [1128]~E(x11281,x11282)+E(f639(x11283,x11281,x11284,x11285,x11286),f639(x11283,x11282,x11284,x11285,x11286))
% 25.54/25.42 [1129]~E(x11291,x11292)+E(f639(x11293,x11294,x11291,x11295,x11296),f639(x11293,x11294,x11292,x11295,x11296))
% 25.54/25.42 [1130]~E(x11301,x11302)+E(f639(x11303,x11304,x11305,x11301,x11306),f639(x11303,x11304,x11305,x11302,x11306))
% 25.54/25.42 [1131]~E(x11311,x11312)+E(f639(x11313,x11314,x11315,x11316,x11311),f639(x11313,x11314,x11315,x11316,x11312))
% 25.54/25.42 [1132]~E(x11321,x11322)+E(f580(x11321,x11323,x11324),f580(x11322,x11323,x11324))
% 25.54/25.42 [1133]~E(x11331,x11332)+E(f580(x11333,x11331,x11334),f580(x11333,x11332,x11334))
% 25.54/25.42 [1134]~E(x11341,x11342)+E(f580(x11343,x11344,x11341),f580(x11343,x11344,x11342))
% 25.54/25.42 [1135]~E(x11351,x11352)+E(f667(x11351,x11353,x11354),f667(x11352,x11353,x11354))
% 25.54/25.42 [1136]~E(x11361,x11362)+E(f667(x11363,x11361,x11364),f667(x11363,x11362,x11364))
% 25.54/25.42 [1137]~E(x11371,x11372)+E(f667(x11373,x11374,x11371),f667(x11373,x11374,x11372))
% 25.54/25.42 [1138]~E(x11381,x11382)+E(f785(x11381,x11383,x11384,x11385),f785(x11382,x11383,x11384,x11385))
% 25.54/25.42 [1139]~E(x11391,x11392)+E(f785(x11393,x11391,x11394,x11395),f785(x11393,x11392,x11394,x11395))
% 25.54/25.42 [1140]~E(x11401,x11402)+E(f785(x11403,x11404,x11401,x11405),f785(x11403,x11404,x11402,x11405))
% 25.54/25.42 [1141]~E(x11411,x11412)+E(f785(x11413,x11414,x11415,x11411),f785(x11413,x11414,x11415,x11412))
% 25.54/25.42 [1142]~E(x11421,x11422)+E(f511(x11421,x11423,x11424,x11425),f511(x11422,x11423,x11424,x11425))
% 25.54/25.42 [1143]~E(x11431,x11432)+E(f511(x11433,x11431,x11434,x11435),f511(x11433,x11432,x11434,x11435))
% 25.54/25.42 [1144]~E(x11441,x11442)+E(f511(x11443,x11444,x11441,x11445),f511(x11443,x11444,x11442,x11445))
% 25.54/25.42 [1145]~E(x11451,x11452)+E(f511(x11453,x11454,x11455,x11451),f511(x11453,x11454,x11455,x11452))
% 25.54/25.42 [1146]~E(x11461,x11462)+E(f874(x11461,x11463,x11464),f874(x11462,x11463,x11464))
% 25.54/25.42 [1147]~E(x11471,x11472)+E(f874(x11473,x11471,x11474),f874(x11473,x11472,x11474))
% 25.54/25.42 [1148]~E(x11481,x11482)+E(f874(x11483,x11484,x11481),f874(x11483,x11484,x11482))
% 25.54/25.42 [1149]~E(x11491,x11492)+E(f142(x11491,x11493,x11494,x11495,x11496),f142(x11492,x11493,x11494,x11495,x11496))
% 25.54/25.42 [1150]~E(x11501,x11502)+E(f142(x11503,x11501,x11504,x11505,x11506),f142(x11503,x11502,x11504,x11505,x11506))
% 25.54/25.42 [1151]~E(x11511,x11512)+E(f142(x11513,x11514,x11511,x11515,x11516),f142(x11513,x11514,x11512,x11515,x11516))
% 25.54/25.42 [1152]~E(x11521,x11522)+E(f142(x11523,x11524,x11525,x11521,x11526),f142(x11523,x11524,x11525,x11522,x11526))
% 25.54/25.42 [1153]~E(x11531,x11532)+E(f142(x11533,x11534,x11535,x11536,x11531),f142(x11533,x11534,x11535,x11536,x11532))
% 25.54/25.42 [1154]~E(x11541,x11542)+E(f661(x11541,x11543,x11544,x11545,x11546),f661(x11542,x11543,x11544,x11545,x11546))
% 25.54/25.42 [1155]~E(x11551,x11552)+E(f661(x11553,x11551,x11554,x11555,x11556),f661(x11553,x11552,x11554,x11555,x11556))
% 25.54/25.42 [1156]~E(x11561,x11562)+E(f661(x11563,x11564,x11561,x11565,x11566),f661(x11563,x11564,x11562,x11565,x11566))
% 25.54/25.42 [1157]~E(x11571,x11572)+E(f661(x11573,x11574,x11575,x11571,x11576),f661(x11573,x11574,x11575,x11572,x11576))
% 25.54/25.42 [1158]~E(x11581,x11582)+E(f661(x11583,x11584,x11585,x11586,x11581),f661(x11583,x11584,x11585,x11586,x11582))
% 25.54/25.42 [1159]~E(x11591,x11592)+E(f88(x11591),f88(x11592))
% 25.54/25.42 [1160]~E(x11601,x11602)+E(f742(x11601,x11603,x11604,x11605,x11606),f742(x11602,x11603,x11604,x11605,x11606))
% 25.54/25.42 [1161]~E(x11611,x11612)+E(f742(x11613,x11611,x11614,x11615,x11616),f742(x11613,x11612,x11614,x11615,x11616))
% 25.54/25.42 [1162]~E(x11621,x11622)+E(f742(x11623,x11624,x11621,x11625,x11626),f742(x11623,x11624,x11622,x11625,x11626))
% 25.54/25.42 [1163]~E(x11631,x11632)+E(f742(x11633,x11634,x11635,x11631,x11636),f742(x11633,x11634,x11635,x11632,x11636))
% 25.54/25.42 [1164]~E(x11641,x11642)+E(f742(x11643,x11644,x11645,x11646,x11641),f742(x11643,x11644,x11645,x11646,x11642))
% 25.54/25.42 [1165]~E(x11651,x11652)+E(f323(x11651),f323(x11652))
% 25.54/25.42 [1166]~E(x11661,x11662)+E(f398(x11661,x11663,x11664,x11665),f398(x11662,x11663,x11664,x11665))
% 25.54/25.42 [1167]~E(x11671,x11672)+E(f398(x11673,x11671,x11674,x11675),f398(x11673,x11672,x11674,x11675))
% 25.54/25.42 [1168]~E(x11681,x11682)+E(f398(x11683,x11684,x11681,x11685),f398(x11683,x11684,x11682,x11685))
% 25.54/25.42 [1169]~E(x11691,x11692)+E(f398(x11693,x11694,x11695,x11691),f398(x11693,x11694,x11695,x11692))
% 25.54/25.42 [1170]~E(x11701,x11702)+E(f330(x11701,x11703,x11704,x11705,x11706),f330(x11702,x11703,x11704,x11705,x11706))
% 25.54/25.42 [1171]~E(x11711,x11712)+E(f330(x11713,x11711,x11714,x11715,x11716),f330(x11713,x11712,x11714,x11715,x11716))
% 25.54/25.42 [1172]~E(x11721,x11722)+E(f330(x11723,x11724,x11721,x11725,x11726),f330(x11723,x11724,x11722,x11725,x11726))
% 25.54/25.42 [1173]~E(x11731,x11732)+E(f330(x11733,x11734,x11735,x11731,x11736),f330(x11733,x11734,x11735,x11732,x11736))
% 25.54/25.42 [1174]~E(x11741,x11742)+E(f330(x11743,x11744,x11745,x11746,x11741),f330(x11743,x11744,x11745,x11746,x11742))
% 25.54/25.42 [1175]~E(x11751,x11752)+E(f329(x11751,x11753),f329(x11752,x11753))
% 25.54/25.42 [1176]~E(x11761,x11762)+E(f329(x11763,x11761),f329(x11763,x11762))
% 25.54/25.42 [1177]~E(x11771,x11772)+E(f50(x11771),f50(x11772))
% 25.54/25.42 [1178]~E(x11781,x11782)+E(f167(x11781,x11783,x11784),f167(x11782,x11783,x11784))
% 25.54/25.42 [1179]~E(x11791,x11792)+E(f167(x11793,x11791,x11794),f167(x11793,x11792,x11794))
% 25.54/25.42 [1180]~E(x11801,x11802)+E(f167(x11803,x11804,x11801),f167(x11803,x11804,x11802))
% 25.54/25.42 [1181]~E(x11811,x11812)+E(f903(x11811,x11813),f903(x11812,x11813))
% 25.54/25.42 [1182]~E(x11821,x11822)+E(f903(x11823,x11821),f903(x11823,x11822))
% 25.54/25.42 [1183]~E(x11831,x11832)+E(f394(x11831,x11833,x11834),f394(x11832,x11833,x11834))
% 25.54/25.42 [1184]~E(x11841,x11842)+E(f394(x11843,x11841,x11844),f394(x11843,x11842,x11844))
% 25.54/25.42 [1185]~E(x11851,x11852)+E(f394(x11853,x11854,x11851),f394(x11853,x11854,x11852))
% 25.54/25.42 [1186]~E(x11861,x11862)+E(f128(x11861),f128(x11862))
% 25.54/25.42 [1187]~E(x11871,x11872)+E(f730(x11871,x11873,x11874,x11875),f730(x11872,x11873,x11874,x11875))
% 25.54/25.42 [1188]~E(x11881,x11882)+E(f730(x11883,x11881,x11884,x11885),f730(x11883,x11882,x11884,x11885))
% 25.54/25.42 [1189]~E(x11891,x11892)+E(f730(x11893,x11894,x11891,x11895),f730(x11893,x11894,x11892,x11895))
% 25.54/25.42 [1190]~E(x11901,x11902)+E(f730(x11903,x11904,x11905,x11901),f730(x11903,x11904,x11905,x11902))
% 25.54/25.42 [1191]~E(x11911,x11912)+E(f885(x11911,x11913),f885(x11912,x11913))
% 25.54/25.42 [1192]~E(x11921,x11922)+E(f885(x11923,x11921),f885(x11923,x11922))
% 25.54/25.42 [1193]~E(x11931,x11932)+E(f538(x11931,x11933,x11934,x11935),f538(x11932,x11933,x11934,x11935))
% 25.54/25.42 [1194]~E(x11941,x11942)+E(f538(x11943,x11941,x11944,x11945),f538(x11943,x11942,x11944,x11945))
% 25.54/25.42 [1195]~E(x11951,x11952)+E(f538(x11953,x11954,x11951,x11955),f538(x11953,x11954,x11952,x11955))
% 25.54/25.42 [1196]~E(x11961,x11962)+E(f538(x11963,x11964,x11965,x11961),f538(x11963,x11964,x11965,x11962))
% 25.54/25.42 [1197]~E(x11971,x11972)+E(f694(x11971,x11973,x11974,x11975,x11976),f694(x11972,x11973,x11974,x11975,x11976))
% 25.54/25.42 [1198]~E(x11981,x11982)+E(f694(x11983,x11981,x11984,x11985,x11986),f694(x11983,x11982,x11984,x11985,x11986))
% 25.54/25.42 [1199]~E(x11991,x11992)+E(f694(x11993,x11994,x11991,x11995,x11996),f694(x11993,x11994,x11992,x11995,x11996))
% 25.54/25.42 [1200]~E(x12001,x12002)+E(f694(x12003,x12004,x12005,x12001,x12006),f694(x12003,x12004,x12005,x12002,x12006))
% 25.54/25.42 [1201]~E(x12011,x12012)+E(f694(x12013,x12014,x12015,x12016,x12011),f694(x12013,x12014,x12015,x12016,x12012))
% 25.54/25.43 [1202]~E(x12021,x12022)+E(f851(x12021,x12023,x12024,x12025,x12026,x12027,x12028,x12029),f851(x12022,x12023,x12024,x12025,x12026,x12027,x12028,x12029))
% 25.54/25.43 [1203]~E(x12031,x12032)+E(f851(x12033,x12031,x12034,x12035,x12036,x12037,x12038,x12039),f851(x12033,x12032,x12034,x12035,x12036,x12037,x12038,x12039))
% 25.54/25.43 [1204]~E(x12041,x12042)+E(f851(x12043,x12044,x12041,x12045,x12046,x12047,x12048,x12049),f851(x12043,x12044,x12042,x12045,x12046,x12047,x12048,x12049))
% 25.54/25.43 [1205]~E(x12051,x12052)+E(f851(x12053,x12054,x12055,x12051,x12056,x12057,x12058,x12059),f851(x12053,x12054,x12055,x12052,x12056,x12057,x12058,x12059))
% 25.54/25.43 [1206]~E(x12061,x12062)+E(f851(x12063,x12064,x12065,x12066,x12061,x12067,x12068,x12069),f851(x12063,x12064,x12065,x12066,x12062,x12067,x12068,x12069))
% 25.54/25.43 [1207]~E(x12071,x12072)+E(f851(x12073,x12074,x12075,x12076,x12077,x12071,x12078,x12079),f851(x12073,x12074,x12075,x12076,x12077,x12072,x12078,x12079))
% 25.54/25.43 [1208]~E(x12081,x12082)+E(f851(x12083,x12084,x12085,x12086,x12087,x12088,x12081,x12089),f851(x12083,x12084,x12085,x12086,x12087,x12088,x12082,x12089))
% 25.54/25.43 [1209]~E(x12091,x12092)+E(f851(x12093,x12094,x12095,x12096,x12097,x12098,x12099,x12091),f851(x12093,x12094,x12095,x12096,x12097,x12098,x12099,x12092))
% 25.54/25.43 [1210]~E(x12101,x12102)+E(f87(x12101),f87(x12102))
% 25.54/25.43 [1211]~E(x12111,x12112)+E(f439(x12111,x12113,x12114),f439(x12112,x12113,x12114))
% 25.54/25.43 [1212]~E(x12121,x12122)+E(f439(x12123,x12121,x12124),f439(x12123,x12122,x12124))
% 25.54/25.43 [1213]~E(x12131,x12132)+E(f439(x12133,x12134,x12131),f439(x12133,x12134,x12132))
% 25.54/25.43 [1214]~E(x12141,x12142)+E(f627(x12141,x12143,x12144),f627(x12142,x12143,x12144))
% 25.54/25.43 [1215]~E(x12151,x12152)+E(f627(x12153,x12151,x12154),f627(x12153,x12152,x12154))
% 25.54/25.43 [1216]~E(x12161,x12162)+E(f627(x12163,x12164,x12161),f627(x12163,x12164,x12162))
% 25.54/25.43 [1217]~E(x12171,x12172)+E(f854(x12171,x12173,x12174,x12175,x12176,x12177),f854(x12172,x12173,x12174,x12175,x12176,x12177))
% 25.54/25.43 [1218]~E(x12181,x12182)+E(f854(x12183,x12181,x12184,x12185,x12186,x12187),f854(x12183,x12182,x12184,x12185,x12186,x12187))
% 25.54/25.43 [1219]~E(x12191,x12192)+E(f854(x12193,x12194,x12191,x12195,x12196,x12197),f854(x12193,x12194,x12192,x12195,x12196,x12197))
% 25.54/25.43 [1220]~E(x12201,x12202)+E(f854(x12203,x12204,x12205,x12201,x12206,x12207),f854(x12203,x12204,x12205,x12202,x12206,x12207))
% 25.54/25.43 [1221]~E(x12211,x12212)+E(f854(x12213,x12214,x12215,x12216,x12211,x12217),f854(x12213,x12214,x12215,x12216,x12212,x12217))
% 25.54/25.43 [1222]~E(x12221,x12222)+E(f854(x12223,x12224,x12225,x12226,x12227,x12221),f854(x12223,x12224,x12225,x12226,x12227,x12222))
% 25.54/25.43 [1223]~E(x12231,x12232)+E(f701(x12231,x12233,x12234,x12235,x12236),f701(x12232,x12233,x12234,x12235,x12236))
% 25.54/25.43 [1224]~E(x12241,x12242)+E(f701(x12243,x12241,x12244,x12245,x12246),f701(x12243,x12242,x12244,x12245,x12246))
% 25.54/25.43 [1225]~E(x12251,x12252)+E(f701(x12253,x12254,x12251,x12255,x12256),f701(x12253,x12254,x12252,x12255,x12256))
% 25.54/25.43 [1226]~E(x12261,x12262)+E(f701(x12263,x12264,x12265,x12261,x12266),f701(x12263,x12264,x12265,x12262,x12266))
% 25.54/25.43 [1227]~E(x12271,x12272)+E(f701(x12273,x12274,x12275,x12276,x12271),f701(x12273,x12274,x12275,x12276,x12272))
% 25.54/25.43 [1228]~E(x12281,x12282)+E(f757(x12281,x12283,x12284),f757(x12282,x12283,x12284))
% 25.54/25.43 [1229]~E(x12291,x12292)+E(f757(x12293,x12291,x12294),f757(x12293,x12292,x12294))
% 25.54/25.43 [1230]~E(x12301,x12302)+E(f757(x12303,x12304,x12301),f757(x12303,x12304,x12302))
% 25.54/25.43 [1231]~E(x12311,x12312)+E(f660(x12311,x12313,x12314,x12315,x12316),f660(x12312,x12313,x12314,x12315,x12316))
% 25.54/25.43 [1232]~E(x12321,x12322)+E(f660(x12323,x12321,x12324,x12325,x12326),f660(x12323,x12322,x12324,x12325,x12326))
% 25.54/25.43 [1233]~E(x12331,x12332)+E(f660(x12333,x12334,x12331,x12335,x12336),f660(x12333,x12334,x12332,x12335,x12336))
% 25.54/25.43 [1234]~E(x12341,x12342)+E(f660(x12343,x12344,x12345,x12341,x12346),f660(x12343,x12344,x12345,x12342,x12346))
% 25.54/25.43 [1235]~E(x12351,x12352)+E(f660(x12353,x12354,x12355,x12356,x12351),f660(x12353,x12354,x12355,x12356,x12352))
% 25.54/25.43 [1236]~E(x12361,x12362)+E(f47(x12361,x12363),f47(x12362,x12363))
% 25.54/25.43 [1237]~E(x12371,x12372)+E(f47(x12373,x12371),f47(x12373,x12372))
% 25.54/25.43 [1238]~E(x12381,x12382)+E(f124(x12381,x12383,x12384,x12385),f124(x12382,x12383,x12384,x12385))
% 25.54/25.43 [1239]~E(x12391,x12392)+E(f124(x12393,x12391,x12394,x12395),f124(x12393,x12392,x12394,x12395))
% 25.54/25.43 [1240]~E(x12401,x12402)+E(f124(x12403,x12404,x12401,x12405),f124(x12403,x12404,x12402,x12405))
% 25.54/25.43 [1241]~E(x12411,x12412)+E(f124(x12413,x12414,x12415,x12411),f124(x12413,x12414,x12415,x12412))
% 25.54/25.43 [1242]~E(x12421,x12422)+E(f622(x12421,x12423,x12424,x12425),f622(x12422,x12423,x12424,x12425))
% 25.54/25.43 [1243]~E(x12431,x12432)+E(f622(x12433,x12431,x12434,x12435),f622(x12433,x12432,x12434,x12435))
% 25.54/25.43 [1244]~E(x12441,x12442)+E(f622(x12443,x12444,x12441,x12445),f622(x12443,x12444,x12442,x12445))
% 25.54/25.43 [1245]~E(x12451,x12452)+E(f622(x12453,x12454,x12455,x12451),f622(x12453,x12454,x12455,x12452))
% 25.54/25.43 [1246]~E(x12461,x12462)+E(f671(x12461,x12463,x12464,x12465),f671(x12462,x12463,x12464,x12465))
% 25.54/25.43 [1247]~E(x12471,x12472)+E(f671(x12473,x12471,x12474,x12475),f671(x12473,x12472,x12474,x12475))
% 25.54/25.43 [1248]~E(x12481,x12482)+E(f671(x12483,x12484,x12481,x12485),f671(x12483,x12484,x12482,x12485))
% 25.54/25.43 [1249]~E(x12491,x12492)+E(f671(x12493,x12494,x12495,x12491),f671(x12493,x12494,x12495,x12492))
% 25.54/25.43 [1250]~E(x12501,x12502)+E(f458(x12501,x12503),f458(x12502,x12503))
% 25.54/25.43 [1251]~E(x12511,x12512)+E(f458(x12513,x12511),f458(x12513,x12512))
% 25.54/25.43 [1252]~E(x12521,x12522)+E(f355(x12521,x12523,x12524,x12525,x12526),f355(x12522,x12523,x12524,x12525,x12526))
% 25.54/25.43 [1253]~E(x12531,x12532)+E(f355(x12533,x12531,x12534,x12535,x12536),f355(x12533,x12532,x12534,x12535,x12536))
% 25.54/25.43 [1254]~E(x12541,x12542)+E(f355(x12543,x12544,x12541,x12545,x12546),f355(x12543,x12544,x12542,x12545,x12546))
% 25.54/25.43 [1255]~E(x12551,x12552)+E(f355(x12553,x12554,x12555,x12551,x12556),f355(x12553,x12554,x12555,x12552,x12556))
% 25.54/25.43 [1256]~E(x12561,x12562)+E(f355(x12563,x12564,x12565,x12566,x12561),f355(x12563,x12564,x12565,x12566,x12562))
% 25.54/25.43 [1257]~E(x12571,x12572)+E(f193(x12571),f193(x12572))
% 25.54/25.43 [1258]~E(x12581,x12582)+E(f816(x12581,x12583,x12584),f816(x12582,x12583,x12584))
% 25.54/25.43 [1259]~E(x12591,x12592)+E(f816(x12593,x12591,x12594),f816(x12593,x12592,x12594))
% 25.54/25.43 [1260]~E(x12601,x12602)+E(f816(x12603,x12604,x12601),f816(x12603,x12604,x12602))
% 25.54/25.43 [1261]~E(x12611,x12612)+E(f192(x12611,x12613),f192(x12612,x12613))
% 25.54/25.43 [1262]~E(x12621,x12622)+E(f192(x12623,x12621),f192(x12623,x12622))
% 25.54/25.43 [1263]~E(x12631,x12632)+E(f198(x12631,x12633,x12634,x12635),f198(x12632,x12633,x12634,x12635))
% 25.54/25.43 [1264]~E(x12641,x12642)+E(f198(x12643,x12641,x12644,x12645),f198(x12643,x12642,x12644,x12645))
% 25.54/25.43 [1265]~E(x12651,x12652)+E(f198(x12653,x12654,x12651,x12655),f198(x12653,x12654,x12652,x12655))
% 25.54/25.43 [1266]~E(x12661,x12662)+E(f198(x12663,x12664,x12665,x12661),f198(x12663,x12664,x12665,x12662))
% 25.54/25.43 [1267]~E(x12671,x12672)+E(f122(x12671),f122(x12672))
% 25.54/25.43 [1268]~E(x12681,x12682)+E(f499(x12681,x12683,x12684),f499(x12682,x12683,x12684))
% 25.54/25.43 [1269]~E(x12691,x12692)+E(f499(x12693,x12691,x12694),f499(x12693,x12692,x12694))
% 25.54/25.43 [1270]~E(x12701,x12702)+E(f499(x12703,x12704,x12701),f499(x12703,x12704,x12702))
% 25.54/25.43 [1271]~E(x12711,x12712)+E(f48(x12711,x12713,x12714),f48(x12712,x12713,x12714))
% 25.54/25.43 [1272]~E(x12721,x12722)+E(f48(x12723,x12721,x12724),f48(x12723,x12722,x12724))
% 25.54/25.43 [1273]~E(x12731,x12732)+E(f48(x12733,x12734,x12731),f48(x12733,x12734,x12732))
% 25.54/25.43 [1274]~E(x12741,x12742)+E(f416(x12741,x12743,x12744),f416(x12742,x12743,x12744))
% 25.54/25.43 [1275]~E(x12751,x12752)+E(f416(x12753,x12751,x12754),f416(x12753,x12752,x12754))
% 25.54/25.43 [1276]~E(x12761,x12762)+E(f416(x12763,x12764,x12761),f416(x12763,x12764,x12762))
% 25.54/25.43 [1277]~E(x12771,x12772)+E(f612(x12771,x12773,x12774),f612(x12772,x12773,x12774))
% 25.54/25.43 [1278]~E(x12781,x12782)+E(f612(x12783,x12781,x12784),f612(x12783,x12782,x12784))
% 25.54/25.43 [1279]~E(x12791,x12792)+E(f612(x12793,x12794,x12791),f612(x12793,x12794,x12792))
% 25.54/25.43 [1280]~E(x12801,x12802)+E(f441(x12801,x12803,x12804),f441(x12802,x12803,x12804))
% 25.54/25.43 [1281]~E(x12811,x12812)+E(f441(x12813,x12811,x12814),f441(x12813,x12812,x12814))
% 25.54/25.43 [1282]~E(x12821,x12822)+E(f441(x12823,x12824,x12821),f441(x12823,x12824,x12822))
% 25.54/25.43 [1283]~E(x12831,x12832)+E(f833(x12831,x12833,x12834),f833(x12832,x12833,x12834))
% 25.54/25.43 [1284]~E(x12841,x12842)+E(f833(x12843,x12841,x12844),f833(x12843,x12842,x12844))
% 25.54/25.43 [1285]~E(x12851,x12852)+E(f833(x12853,x12854,x12851),f833(x12853,x12854,x12852))
% 25.54/25.43 [1286]~E(x12861,x12862)+E(f425(x12861),f425(x12862))
% 25.54/25.43 [1287]~E(x12871,x12872)+E(f857(x12871,x12873,x12874,x12875,x12876,x12877),f857(x12872,x12873,x12874,x12875,x12876,x12877))
% 25.54/25.43 [1288]~E(x12881,x12882)+E(f857(x12883,x12881,x12884,x12885,x12886,x12887),f857(x12883,x12882,x12884,x12885,x12886,x12887))
% 25.54/25.43 [1289]~E(x12891,x12892)+E(f857(x12893,x12894,x12891,x12895,x12896,x12897),f857(x12893,x12894,x12892,x12895,x12896,x12897))
% 25.54/25.43 [1290]~E(x12901,x12902)+E(f857(x12903,x12904,x12905,x12901,x12906,x12907),f857(x12903,x12904,x12905,x12902,x12906,x12907))
% 25.54/25.43 [1291]~E(x12911,x12912)+E(f857(x12913,x12914,x12915,x12916,x12911,x12917),f857(x12913,x12914,x12915,x12916,x12912,x12917))
% 25.54/25.43 [1292]~E(x12921,x12922)+E(f857(x12923,x12924,x12925,x12926,x12927,x12921),f857(x12923,x12924,x12925,x12926,x12927,x12922))
% 25.54/25.43 [1293]~E(x12931,x12932)+E(f529(x12931,x12933,x12934),f529(x12932,x12933,x12934))
% 25.54/25.43 [1294]~E(x12941,x12942)+E(f529(x12943,x12941,x12944),f529(x12943,x12942,x12944))
% 25.54/25.43 [1295]~E(x12951,x12952)+E(f529(x12953,x12954,x12951),f529(x12953,x12954,x12952))
% 25.54/25.43 [1296]~E(x12961,x12962)+E(f546(x12961,x12963,x12964),f546(x12962,x12963,x12964))
% 25.54/25.43 [1297]~E(x12971,x12972)+E(f546(x12973,x12971,x12974),f546(x12973,x12972,x12974))
% 25.54/25.43 [1298]~E(x12981,x12982)+E(f546(x12983,x12984,x12981),f546(x12983,x12984,x12982))
% 25.54/25.43 [1299]~E(x12991,x12992)+E(f770(x12991,x12993,x12994),f770(x12992,x12993,x12994))
% 25.54/25.43 [1300]~E(x13001,x13002)+E(f770(x13003,x13001,x13004),f770(x13003,x13002,x13004))
% 25.54/25.43 [1301]~E(x13011,x13012)+E(f770(x13013,x13014,x13011),f770(x13013,x13014,x13012))
% 25.54/25.43 [1302]~E(x13021,x13022)+E(f402(x13021,x13023,x13024,x13025),f402(x13022,x13023,x13024,x13025))
% 25.54/25.43 [1303]~E(x13031,x13032)+E(f402(x13033,x13031,x13034,x13035),f402(x13033,x13032,x13034,x13035))
% 25.54/25.43 [1304]~E(x13041,x13042)+E(f402(x13043,x13044,x13041,x13045),f402(x13043,x13044,x13042,x13045))
% 25.54/25.43 [1305]~E(x13051,x13052)+E(f402(x13053,x13054,x13055,x13051),f402(x13053,x13054,x13055,x13052))
% 25.54/25.43 [1306]~E(x13061,x13062)+E(f758(x13061,x13063,x13064),f758(x13062,x13063,x13064))
% 25.54/25.43 [1307]~E(x13071,x13072)+E(f758(x13073,x13071,x13074),f758(x13073,x13072,x13074))
% 25.54/25.43 [1308]~E(x13081,x13082)+E(f758(x13083,x13084,x13081),f758(x13083,x13084,x13082))
% 25.54/25.43 [1309]~E(x13091,x13092)+E(f166(x13091,x13093,x13094),f166(x13092,x13093,x13094))
% 25.54/25.43 [1310]~E(x13101,x13102)+E(f166(x13103,x13101,x13104),f166(x13103,x13102,x13104))
% 25.54/25.43 [1311]~E(x13111,x13112)+E(f166(x13113,x13114,x13111),f166(x13113,x13114,x13112))
% 25.54/25.43 [1312]~E(x13121,x13122)+E(f772(x13121,x13123,x13124),f772(x13122,x13123,x13124))
% 25.54/25.43 [1313]~E(x13131,x13132)+E(f772(x13133,x13131,x13134),f772(x13133,x13132,x13134))
% 25.54/25.43 [1314]~E(x13141,x13142)+E(f772(x13143,x13144,x13141),f772(x13143,x13144,x13142))
% 25.54/25.43 [1315]~E(x13151,x13152)+E(f774(x13151,x13153,x13154),f774(x13152,x13153,x13154))
% 25.54/25.43 [1316]~E(x13161,x13162)+E(f774(x13163,x13161,x13164),f774(x13163,x13162,x13164))
% 25.54/25.43 [1317]~E(x13171,x13172)+E(f774(x13173,x13174,x13171),f774(x13173,x13174,x13172))
% 25.54/25.43 [1318]~E(x13181,x13182)+E(f589(x13181,x13183),f589(x13182,x13183))
% 25.54/25.43 [1319]~E(x13191,x13192)+E(f589(x13193,x13191),f589(x13193,x13192))
% 25.54/25.43 [1320]~E(x13201,x13202)+E(f109(x13201,x13203,x13204),f109(x13202,x13203,x13204))
% 25.54/25.43 [1321]~E(x13211,x13212)+E(f109(x13213,x13211,x13214),f109(x13213,x13212,x13214))
% 25.54/25.43 [1322]~E(x13221,x13222)+E(f109(x13223,x13224,x13221),f109(x13223,x13224,x13222))
% 25.54/25.43 [1323]~E(x13231,x13232)+E(f331(x13231,x13233),f331(x13232,x13233))
% 25.54/25.43 [1324]~E(x13241,x13242)+E(f331(x13243,x13241),f331(x13243,x13242))
% 25.54/25.43 [1325]~E(x13251,x13252)+E(f199(x13251,x13253,x13254,x13255),f199(x13252,x13253,x13254,x13255))
% 25.54/25.43 [1326]~E(x13261,x13262)+E(f199(x13263,x13261,x13264,x13265),f199(x13263,x13262,x13264,x13265))
% 25.54/25.43 [1327]~E(x13271,x13272)+E(f199(x13273,x13274,x13271,x13275),f199(x13273,x13274,x13272,x13275))
% 25.54/25.43 [1328]~E(x13281,x13282)+E(f199(x13283,x13284,x13285,x13281),f199(x13283,x13284,x13285,x13282))
% 25.54/25.43 [1329]~E(x13291,x13292)+E(f632(x13291,x13293,x13294,x13295),f632(x13292,x13293,x13294,x13295))
% 25.54/25.43 [1330]~E(x13301,x13302)+E(f632(x13303,x13301,x13304,x13305),f632(x13303,x13302,x13304,x13305))
% 25.54/25.43 [1331]~E(x13311,x13312)+E(f632(x13313,x13314,x13311,x13315),f632(x13313,x13314,x13312,x13315))
% 25.54/25.43 [1332]~E(x13321,x13322)+E(f632(x13323,x13324,x13325,x13321),f632(x13323,x13324,x13325,x13322))
% 25.54/25.43 [1333]~E(x13331,x13332)+E(f342(x13331,x13333,x13334,x13335),f342(x13332,x13333,x13334,x13335))
% 25.54/25.43 [1334]~E(x13341,x13342)+E(f342(x13343,x13341,x13344,x13345),f342(x13343,x13342,x13344,x13345))
% 25.54/25.43 [1335]~E(x13351,x13352)+E(f342(x13353,x13354,x13351,x13355),f342(x13353,x13354,x13352,x13355))
% 25.54/25.43 [1336]~E(x13361,x13362)+E(f342(x13363,x13364,x13365,x13361),f342(x13363,x13364,x13365,x13362))
% 25.54/25.43 [1337]~E(x13371,x13372)+E(f819(x13371,x13373,x13374,x13375,x13376,x13377),f819(x13372,x13373,x13374,x13375,x13376,x13377))
% 25.54/25.43 [1338]~E(x13381,x13382)+E(f819(x13383,x13381,x13384,x13385,x13386,x13387),f819(x13383,x13382,x13384,x13385,x13386,x13387))
% 25.54/25.43 [1339]~E(x13391,x13392)+E(f819(x13393,x13394,x13391,x13395,x13396,x13397),f819(x13393,x13394,x13392,x13395,x13396,x13397))
% 25.54/25.43 [1340]~E(x13401,x13402)+E(f819(x13403,x13404,x13405,x13401,x13406,x13407),f819(x13403,x13404,x13405,x13402,x13406,x13407))
% 25.54/25.43 [1341]~E(x13411,x13412)+E(f819(x13413,x13414,x13415,x13416,x13411,x13417),f819(x13413,x13414,x13415,x13416,x13412,x13417))
% 25.54/25.43 [1342]~E(x13421,x13422)+E(f819(x13423,x13424,x13425,x13426,x13427,x13421),f819(x13423,x13424,x13425,x13426,x13427,x13422))
% 25.54/25.43 [1343]~E(x13431,x13432)+E(f832(x13431,x13433,x13434,x13435,x13436),f832(x13432,x13433,x13434,x13435,x13436))
% 25.54/25.43 [1344]~E(x13441,x13442)+E(f832(x13443,x13441,x13444,x13445,x13446),f832(x13443,x13442,x13444,x13445,x13446))
% 25.54/25.43 [1345]~E(x13451,x13452)+E(f832(x13453,x13454,x13451,x13455,x13456),f832(x13453,x13454,x13452,x13455,x13456))
% 25.54/25.43 [1346]~E(x13461,x13462)+E(f832(x13463,x13464,x13465,x13461,x13466),f832(x13463,x13464,x13465,x13462,x13466))
% 25.54/25.43 [1347]~E(x13471,x13472)+E(f832(x13473,x13474,x13475,x13476,x13471),f832(x13473,x13474,x13475,x13476,x13472))
% 25.54/25.43 [1348]~E(x13481,x13482)+E(f123(x13481,x13483,x13484,x13485),f123(x13482,x13483,x13484,x13485))
% 25.54/25.43 [1349]~E(x13491,x13492)+E(f123(x13493,x13491,x13494,x13495),f123(x13493,x13492,x13494,x13495))
% 25.54/25.43 [1350]~E(x13501,x13502)+E(f123(x13503,x13504,x13501,x13505),f123(x13503,x13504,x13502,x13505))
% 25.54/25.43 [1351]~E(x13511,x13512)+E(f123(x13513,x13514,x13515,x13511),f123(x13513,x13514,x13515,x13512))
% 25.54/25.43 [1352]~E(x13521,x13522)+E(f480(x13521,x13523,x13524,x13525,x13526),f480(x13522,x13523,x13524,x13525,x13526))
% 25.54/25.43 [1353]~E(x13531,x13532)+E(f480(x13533,x13531,x13534,x13535,x13536),f480(x13533,x13532,x13534,x13535,x13536))
% 25.54/25.43 [1354]~E(x13541,x13542)+E(f480(x13543,x13544,x13541,x13545,x13546),f480(x13543,x13544,x13542,x13545,x13546))
% 25.54/25.43 [1355]~E(x13551,x13552)+E(f480(x13553,x13554,x13555,x13551,x13556),f480(x13553,x13554,x13555,x13552,x13556))
% 25.54/25.43 [1356]~E(x13561,x13562)+E(f480(x13563,x13564,x13565,x13566,x13561),f480(x13563,x13564,x13565,x13566,x13562))
% 25.54/25.43 [1357]~E(x13571,x13572)+E(f459(x13571,x13573,x13574),f459(x13572,x13573,x13574))
% 25.54/25.43 [1358]~E(x13581,x13582)+E(f459(x13583,x13581,x13584),f459(x13583,x13582,x13584))
% 25.54/25.43 [1359]~E(x13591,x13592)+E(f459(x13593,x13594,x13591),f459(x13593,x13594,x13592))
% 25.54/25.43 [1360]~E(x13601,x13602)+E(f644(x13601,x13603,x13604,x13605,x13606),f644(x13602,x13603,x13604,x13605,x13606))
% 25.54/25.43 [1361]~E(x13611,x13612)+E(f644(x13613,x13611,x13614,x13615,x13616),f644(x13613,x13612,x13614,x13615,x13616))
% 25.54/25.43 [1362]~E(x13621,x13622)+E(f644(x13623,x13624,x13621,x13625,x13626),f644(x13623,x13624,x13622,x13625,x13626))
% 25.54/25.43 [1363]~E(x13631,x13632)+E(f644(x13633,x13634,x13635,x13631,x13636),f644(x13633,x13634,x13635,x13632,x13636))
% 25.54/25.43 [1364]~E(x13641,x13642)+E(f644(x13643,x13644,x13645,x13646,x13641),f644(x13643,x13644,x13645,x13646,x13642))
% 25.54/25.43 [1365]~E(x13651,x13652)+E(f901(x13651,x13653,x13654,x13655,x13656,x13657),f901(x13652,x13653,x13654,x13655,x13656,x13657))
% 25.54/25.43 [1366]~E(x13661,x13662)+E(f901(x13663,x13661,x13664,x13665,x13666,x13667),f901(x13663,x13662,x13664,x13665,x13666,x13667))
% 25.54/25.43 [1367]~E(x13671,x13672)+E(f901(x13673,x13674,x13671,x13675,x13676,x13677),f901(x13673,x13674,x13672,x13675,x13676,x13677))
% 25.54/25.43 [1368]~E(x13681,x13682)+E(f901(x13683,x13684,x13685,x13681,x13686,x13687),f901(x13683,x13684,x13685,x13682,x13686,x13687))
% 25.54/25.43 [1369]~E(x13691,x13692)+E(f901(x13693,x13694,x13695,x13696,x13691,x13697),f901(x13693,x13694,x13695,x13696,x13692,x13697))
% 25.54/25.43 [1370]~E(x13701,x13702)+E(f901(x13703,x13704,x13705,x13706,x13707,x13701),f901(x13703,x13704,x13705,x13706,x13707,x13702))
% 25.54/25.43 [1371]~E(x13711,x13712)+E(f362(x13711,x13713),f362(x13712,x13713))
% 25.54/25.43 [1372]~E(x13721,x13722)+E(f362(x13723,x13721),f362(x13723,x13722))
% 25.54/25.43 [1373]~E(x13731,x13732)+E(f433(x13731,x13733,x13734),f433(x13732,x13733,x13734))
% 25.54/25.43 [1374]~E(x13741,x13742)+E(f433(x13743,x13741,x13744),f433(x13743,x13742,x13744))
% 25.54/25.43 [1375]~E(x13751,x13752)+E(f433(x13753,x13754,x13751),f433(x13753,x13754,x13752))
% 25.54/25.43 [1376]~E(x13761,x13762)+E(f896(x13761,x13763,x13764),f896(x13762,x13763,x13764))
% 25.54/25.43 [1377]~E(x13771,x13772)+E(f896(x13773,x13771,x13774),f896(x13773,x13772,x13774))
% 25.54/25.43 [1378]~E(x13781,x13782)+E(f896(x13783,x13784,x13781),f896(x13783,x13784,x13782))
% 25.54/25.43 [1379]~E(x13791,x13792)+E(f377(x13791,x13793,x13794,x13795),f377(x13792,x13793,x13794,x13795))
% 25.54/25.43 [1380]~E(x13801,x13802)+E(f377(x13803,x13801,x13804,x13805),f377(x13803,x13802,x13804,x13805))
% 25.54/25.43 [1381]~E(x13811,x13812)+E(f377(x13813,x13814,x13811,x13815),f377(x13813,x13814,x13812,x13815))
% 25.54/25.43 [1382]~E(x13821,x13822)+E(f377(x13823,x13824,x13825,x13821),f377(x13823,x13824,x13825,x13822))
% 25.54/25.43 [1383]~E(x13831,x13832)+E(f875(x13831,x13833,x13834),f875(x13832,x13833,x13834))
% 25.54/25.43 [1384]~E(x13841,x13842)+E(f875(x13843,x13841,x13844),f875(x13843,x13842,x13844))
% 25.54/25.43 [1385]~E(x13851,x13852)+E(f875(x13853,x13854,x13851),f875(x13853,x13854,x13852))
% 25.54/25.43 [1386]~E(x13861,x13862)+E(f430(x13861,x13863,x13864),f430(x13862,x13863,x13864))
% 25.54/25.43 [1387]~E(x13871,x13872)+E(f430(x13873,x13871,x13874),f430(x13873,x13872,x13874))
% 25.54/25.43 [1388]~E(x13881,x13882)+E(f430(x13883,x13884,x13881),f430(x13883,x13884,x13882))
% 25.54/25.43 [1389]~E(x13891,x13892)+E(f21(x13891,x13893,x13894,x13895),f21(x13892,x13893,x13894,x13895))
% 25.54/25.43 [1390]~E(x13901,x13902)+E(f21(x13903,x13901,x13904,x13905),f21(x13903,x13902,x13904,x13905))
% 25.54/25.43 [1391]~E(x13911,x13912)+E(f21(x13913,x13914,x13911,x13915),f21(x13913,x13914,x13912,x13915))
% 25.54/25.43 [1392]~E(x13921,x13922)+E(f21(x13923,x13924,x13925,x13921),f21(x13923,x13924,x13925,x13922))
% 25.54/25.43 [1393]~E(x13931,x13932)+E(f710(x13931,x13933,x13934),f710(x13932,x13933,x13934))
% 25.54/25.43 [1394]~E(x13941,x13942)+E(f710(x13943,x13941,x13944),f710(x13943,x13942,x13944))
% 25.54/25.43 [1395]~E(x13951,x13952)+E(f710(x13953,x13954,x13951),f710(x13953,x13954,x13952))
% 25.54/25.43 [1396]~E(x13961,x13962)+E(f502(x13961,x13963,x13964),f502(x13962,x13963,x13964))
% 25.54/25.43 [1397]~E(x13971,x13972)+E(f502(x13973,x13971,x13974),f502(x13973,x13972,x13974))
% 25.54/25.43 [1398]~E(x13981,x13982)+E(f502(x13983,x13984,x13981),f502(x13983,x13984,x13982))
% 25.54/25.43 [1399]~E(x13991,x13992)+E(f456(x13991,x13993),f456(x13992,x13993))
% 25.54/25.43 [1400]~E(x14001,x14002)+E(f456(x14003,x14001),f456(x14003,x14002))
% 25.54/25.43 [1401]~E(x14011,x14012)+E(f912(x14011,x14013),f912(x14012,x14013))
% 25.54/25.43 [1402]~E(x14021,x14022)+E(f912(x14023,x14021),f912(x14023,x14022))
% 25.54/25.43 [1403]~E(x14031,x14032)+E(f662(x14031,x14033,x14034,x14035,x14036),f662(x14032,x14033,x14034,x14035,x14036))
% 25.54/25.43 [1404]~E(x14041,x14042)+E(f662(x14043,x14041,x14044,x14045,x14046),f662(x14043,x14042,x14044,x14045,x14046))
% 25.54/25.43 [1405]~E(x14051,x14052)+E(f662(x14053,x14054,x14051,x14055,x14056),f662(x14053,x14054,x14052,x14055,x14056))
% 25.54/25.43 [1406]~E(x14061,x14062)+E(f662(x14063,x14064,x14065,x14061,x14066),f662(x14063,x14064,x14065,x14062,x14066))
% 25.54/25.43 [1407]~E(x14071,x14072)+E(f662(x14073,x14074,x14075,x14076,x14071),f662(x14073,x14074,x14075,x14076,x14072))
% 25.54/25.43 [1408]~E(x14081,x14082)+E(f737(x14081,x14083),f737(x14082,x14083))
% 25.54/25.43 [1409]~E(x14091,x14092)+E(f737(x14093,x14091),f737(x14093,x14092))
% 25.54/25.43 [1410]~E(x14101,x14102)+E(f285(x14101,x14103,x14104),f285(x14102,x14103,x14104))
% 25.54/25.43 [1411]~E(x14111,x14112)+E(f285(x14113,x14111,x14114),f285(x14113,x14112,x14114))
% 25.54/25.43 [1412]~E(x14121,x14122)+E(f285(x14123,x14124,x14121),f285(x14123,x14124,x14122))
% 25.54/25.43 [1413]~E(x14131,x14132)+E(f378(x14131,x14133,x14134,x14135),f378(x14132,x14133,x14134,x14135))
% 25.54/25.43 [1414]~E(x14141,x14142)+E(f378(x14143,x14141,x14144,x14145),f378(x14143,x14142,x14144,x14145))
% 25.54/25.43 [1415]~E(x14151,x14152)+E(f378(x14153,x14154,x14151,x14155),f378(x14153,x14154,x14152,x14155))
% 25.54/25.43 [1416]~E(x14161,x14162)+E(f378(x14163,x14164,x14165,x14161),f378(x14163,x14164,x14165,x14162))
% 25.54/25.43 [1417]~E(x14171,x14172)+E(f852(x14171,x14173,x14174,x14175,x14176,x14177,x14178,x14179),f852(x14172,x14173,x14174,x14175,x14176,x14177,x14178,x14179))
% 25.54/25.43 [1418]~E(x14181,x14182)+E(f852(x14183,x14181,x14184,x14185,x14186,x14187,x14188,x14189),f852(x14183,x14182,x14184,x14185,x14186,x14187,x14188,x14189))
% 25.54/25.43 [1419]~E(x14191,x14192)+E(f852(x14193,x14194,x14191,x14195,x14196,x14197,x14198,x14199),f852(x14193,x14194,x14192,x14195,x14196,x14197,x14198,x14199))
% 25.54/25.43 [1420]~E(x14201,x14202)+E(f852(x14203,x14204,x14205,x14201,x14206,x14207,x14208,x14209),f852(x14203,x14204,x14205,x14202,x14206,x14207,x14208,x14209))
% 25.54/25.43 [1421]~E(x14211,x14212)+E(f852(x14213,x14214,x14215,x14216,x14211,x14217,x14218,x14219),f852(x14213,x14214,x14215,x14216,x14212,x14217,x14218,x14219))
% 25.54/25.43 [1422]~E(x14221,x14222)+E(f852(x14223,x14224,x14225,x14226,x14227,x14221,x14228,x14229),f852(x14223,x14224,x14225,x14226,x14227,x14222,x14228,x14229))
% 25.54/25.43 [1423]~E(x14231,x14232)+E(f852(x14233,x14234,x14235,x14236,x14237,x14238,x14231,x14239),f852(x14233,x14234,x14235,x14236,x14237,x14238,x14232,x14239))
% 25.54/25.43 [1424]~E(x14241,x14242)+E(f852(x14243,x14244,x14245,x14246,x14247,x14248,x14249,x14241),f852(x14243,x14244,x14245,x14246,x14247,x14248,x14249,x14242))
% 25.54/25.43 [1425]~E(x14251,x14252)+E(f602(x14251,x14253,x14254,x14255,x14256,x14257),f602(x14252,x14253,x14254,x14255,x14256,x14257))
% 25.54/25.43 [1426]~E(x14261,x14262)+E(f602(x14263,x14261,x14264,x14265,x14266,x14267),f602(x14263,x14262,x14264,x14265,x14266,x14267))
% 25.54/25.43 [1427]~E(x14271,x14272)+E(f602(x14273,x14274,x14271,x14275,x14276,x14277),f602(x14273,x14274,x14272,x14275,x14276,x14277))
% 25.54/25.43 [1428]~E(x14281,x14282)+E(f602(x14283,x14284,x14285,x14281,x14286,x14287),f602(x14283,x14284,x14285,x14282,x14286,x14287))
% 25.54/25.43 [1429]~E(x14291,x14292)+E(f602(x14293,x14294,x14295,x14296,x14291,x14297),f602(x14293,x14294,x14295,x14296,x14292,x14297))
% 25.54/25.43 [1430]~E(x14301,x14302)+E(f602(x14303,x14304,x14305,x14306,x14307,x14301),f602(x14303,x14304,x14305,x14306,x14307,x14302))
% 25.54/25.43 [1431]~E(x14311,x14312)+E(f787(x14311,x14313,x14314,x14315),f787(x14312,x14313,x14314,x14315))
% 25.54/25.43 [1432]~E(x14321,x14322)+E(f787(x14323,x14321,x14324,x14325),f787(x14323,x14322,x14324,x14325))
% 25.54/25.43 [1433]~E(x14331,x14332)+E(f787(x14333,x14334,x14331,x14335),f787(x14333,x14334,x14332,x14335))
% 25.54/25.43 [1434]~E(x14341,x14342)+E(f787(x14343,x14344,x14345,x14341),f787(x14343,x14344,x14345,x14342))
% 25.54/25.43 [1435]~E(x14351,x14352)+E(f479(x14351,x14353,x14354,x14355,x14356),f479(x14352,x14353,x14354,x14355,x14356))
% 25.54/25.43 [1436]~E(x14361,x14362)+E(f479(x14363,x14361,x14364,x14365,x14366),f479(x14363,x14362,x14364,x14365,x14366))
% 25.54/25.43 [1437]~E(x14371,x14372)+E(f479(x14373,x14374,x14371,x14375,x14376),f479(x14373,x14374,x14372,x14375,x14376))
% 25.54/25.43 [1438]~E(x14381,x14382)+E(f479(x14383,x14384,x14385,x14381,x14386),f479(x14383,x14384,x14385,x14382,x14386))
% 25.54/25.43 [1439]~E(x14391,x14392)+E(f479(x14393,x14394,x14395,x14396,x14391),f479(x14393,x14394,x14395,x14396,x14392))
% 25.54/25.43 [1440]~E(x14401,x14402)+E(f407(x14401,x14403,x14404),f407(x14402,x14403,x14404))
% 25.54/25.43 [1441]~E(x14411,x14412)+E(f407(x14413,x14411,x14414),f407(x14413,x14412,x14414))
% 25.54/25.43 [1442]~E(x14421,x14422)+E(f407(x14423,x14424,x14421),f407(x14423,x14424,x14422))
% 25.54/25.43 [1443]~E(x14431,x14432)+E(f213(x14431,x14433,x14434,x14435),f213(x14432,x14433,x14434,x14435))
% 25.54/25.43 [1444]~E(x14441,x14442)+E(f213(x14443,x14441,x14444,x14445),f213(x14443,x14442,x14444,x14445))
% 25.54/25.43 [1445]~E(x14451,x14452)+E(f213(x14453,x14454,x14451,x14455),f213(x14453,x14454,x14452,x14455))
% 25.54/25.43 [1446]~E(x14461,x14462)+E(f213(x14463,x14464,x14465,x14461),f213(x14463,x14464,x14465,x14462))
% 25.54/25.43 [1447]~E(x14471,x14472)+E(f838(x14471,x14473,x14474,x14475,x14476),f838(x14472,x14473,x14474,x14475,x14476))
% 25.54/25.43 [1448]~E(x14481,x14482)+E(f838(x14483,x14481,x14484,x14485,x14486),f838(x14483,x14482,x14484,x14485,x14486))
% 25.54/25.43 [1449]~E(x14491,x14492)+E(f838(x14493,x14494,x14491,x14495,x14496),f838(x14493,x14494,x14492,x14495,x14496))
% 25.54/25.43 [1450]~E(x14501,x14502)+E(f838(x14503,x14504,x14505,x14501,x14506),f838(x14503,x14504,x14505,x14502,x14506))
% 25.54/25.43 [1451]~E(x14511,x14512)+E(f838(x14513,x14514,x14515,x14516,x14511),f838(x14513,x14514,x14515,x14516,x14512))
% 25.54/25.43 [1452]~E(x14521,x14522)+E(f847(x14521,x14523,x14524,x14525,x14526,x14527,x14528,x14529),f847(x14522,x14523,x14524,x14525,x14526,x14527,x14528,x14529))
% 25.54/25.43 [1453]~E(x14531,x14532)+E(f847(x14533,x14531,x14534,x14535,x14536,x14537,x14538,x14539),f847(x14533,x14532,x14534,x14535,x14536,x14537,x14538,x14539))
% 25.54/25.43 [1454]~E(x14541,x14542)+E(f847(x14543,x14544,x14541,x14545,x14546,x14547,x14548,x14549),f847(x14543,x14544,x14542,x14545,x14546,x14547,x14548,x14549))
% 25.54/25.43 [1455]~E(x14551,x14552)+E(f847(x14553,x14554,x14555,x14551,x14556,x14557,x14558,x14559),f847(x14553,x14554,x14555,x14552,x14556,x14557,x14558,x14559))
% 25.54/25.43 [1456]~E(x14561,x14562)+E(f847(x14563,x14564,x14565,x14566,x14561,x14567,x14568,x14569),f847(x14563,x14564,x14565,x14566,x14562,x14567,x14568,x14569))
% 25.54/25.43 [1457]~E(x14571,x14572)+E(f847(x14573,x14574,x14575,x14576,x14577,x14571,x14578,x14579),f847(x14573,x14574,x14575,x14576,x14577,x14572,x14578,x14579))
% 25.54/25.43 [1458]~E(x14581,x14582)+E(f847(x14583,x14584,x14585,x14586,x14587,x14588,x14581,x14589),f847(x14583,x14584,x14585,x14586,x14587,x14588,x14582,x14589))
% 25.54/25.43 [1459]~E(x14591,x14592)+E(f847(x14593,x14594,x14595,x14596,x14597,x14598,x14599,x14591),f847(x14593,x14594,x14595,x14596,x14597,x14598,x14599,x14592))
% 25.54/25.43 [1460]~E(x14601,x14602)+E(f387(x14601,x14603),f387(x14602,x14603))
% 25.54/25.43 [1461]~E(x14611,x14612)+E(f387(x14613,x14611),f387(x14613,x14612))
% 25.54/25.43 [1462]~E(x14621,x14622)+E(f721(x14621,x14623,x14624),f721(x14622,x14623,x14624))
% 25.54/25.43 [1463]~E(x14631,x14632)+E(f721(x14633,x14631,x14634),f721(x14633,x14632,x14634))
% 25.54/25.43 [1464]~E(x14641,x14642)+E(f721(x14643,x14644,x14641),f721(x14643,x14644,x14642))
% 25.54/25.43 [1465]~E(x14651,x14652)+E(f890(x14651,x14653),f890(x14652,x14653))
% 25.54/25.43 [1466]~E(x14661,x14662)+E(f890(x14663,x14661),f890(x14663,x14662))
% 25.54/25.43 [1467]~E(x14671,x14672)+E(f729(x14671,x14673,x14674,x14675),f729(x14672,x14673,x14674,x14675))
% 25.54/25.43 [1468]~E(x14681,x14682)+E(f729(x14683,x14681,x14684,x14685),f729(x14683,x14682,x14684,x14685))
% 25.54/25.43 [1469]~E(x14691,x14692)+E(f729(x14693,x14694,x14691,x14695),f729(x14693,x14694,x14692,x14695))
% 25.54/25.43 [1470]~E(x14701,x14702)+E(f729(x14703,x14704,x14705,x14701),f729(x14703,x14704,x14705,x14702))
% 25.54/25.43 [1471]~E(x14711,x14712)+E(f613(x14711,x14713,x14714,x14715,x14716,x14717),f613(x14712,x14713,x14714,x14715,x14716,x14717))
% 25.54/25.43 [1472]~E(x14721,x14722)+E(f613(x14723,x14721,x14724,x14725,x14726,x14727),f613(x14723,x14722,x14724,x14725,x14726,x14727))
% 25.54/25.43 [1473]~E(x14731,x14732)+E(f613(x14733,x14734,x14731,x14735,x14736,x14737),f613(x14733,x14734,x14732,x14735,x14736,x14737))
% 25.54/25.43 [1474]~E(x14741,x14742)+E(f613(x14743,x14744,x14745,x14741,x14746,x14747),f613(x14743,x14744,x14745,x14742,x14746,x14747))
% 25.54/25.43 [1475]~E(x14751,x14752)+E(f613(x14753,x14754,x14755,x14756,x14751,x14757),f613(x14753,x14754,x14755,x14756,x14752,x14757))
% 25.54/25.43 [1476]~E(x14761,x14762)+E(f613(x14763,x14764,x14765,x14766,x14767,x14761),f613(x14763,x14764,x14765,x14766,x14767,x14762))
% 25.54/25.43 [1477]~E(x14771,x14772)+E(f253(x14771,x14773,x14774,x14775,x14776),f253(x14772,x14773,x14774,x14775,x14776))
% 25.54/25.43 [1478]~E(x14781,x14782)+E(f253(x14783,x14781,x14784,x14785,x14786),f253(x14783,x14782,x14784,x14785,x14786))
% 25.54/25.43 [1479]~E(x14791,x14792)+E(f253(x14793,x14794,x14791,x14795,x14796),f253(x14793,x14794,x14792,x14795,x14796))
% 25.54/25.43 [1480]~E(x14801,x14802)+E(f253(x14803,x14804,x14805,x14801,x14806),f253(x14803,x14804,x14805,x14802,x14806))
% 25.54/25.43 [1481]~E(x14811,x14812)+E(f253(x14813,x14814,x14815,x14816,x14811),f253(x14813,x14814,x14815,x14816,x14812))
% 25.54/25.43 [1482]~E(x14821,x14822)+E(f870(x14821,x14823,x14824,x14825,x14826),f870(x14822,x14823,x14824,x14825,x14826))
% 25.54/25.43 [1483]~E(x14831,x14832)+E(f870(x14833,x14831,x14834,x14835,x14836),f870(x14833,x14832,x14834,x14835,x14836))
% 25.54/25.43 [1484]~E(x14841,x14842)+E(f870(x14843,x14844,x14841,x14845,x14846),f870(x14843,x14844,x14842,x14845,x14846))
% 25.54/25.43 [1485]~E(x14851,x14852)+E(f870(x14853,x14854,x14855,x14851,x14856),f870(x14853,x14854,x14855,x14852,x14856))
% 25.54/25.43 [1486]~E(x14861,x14862)+E(f870(x14863,x14864,x14865,x14866,x14861),f870(x14863,x14864,x14865,x14866,x14862))
% 25.54/25.43 [1487]~E(x14871,x14872)+E(f675(x14871,x14873,x14874,x14875),f675(x14872,x14873,x14874,x14875))
% 25.54/25.43 [1488]~E(x14881,x14882)+E(f675(x14883,x14881,x14884,x14885),f675(x14883,x14882,x14884,x14885))
% 25.54/25.43 [1489]~E(x14891,x14892)+E(f675(x14893,x14894,x14891,x14895),f675(x14893,x14894,x14892,x14895))
% 25.54/25.43 [1490]~E(x14901,x14902)+E(f675(x14903,x14904,x14905,x14901),f675(x14903,x14904,x14905,x14902))
% 25.54/25.43 [1491]~E(x14911,x14912)+E(f794(x14911,x14913),f794(x14912,x14913))
% 25.54/25.43 [1492]~E(x14921,x14922)+E(f794(x14923,x14921),f794(x14923,x14922))
% 25.54/25.43 [1493]~E(x14931,x14932)+E(f349(x14931,x14933),f349(x14932,x14933))
% 25.54/25.43 [1494]~E(x14941,x14942)+E(f349(x14943,x14941),f349(x14943,x14942))
% 25.54/25.43 [1495]~E(x14951,x14952)+E(f220(x14951,x14953),f220(x14952,x14953))
% 25.54/25.43 [1496]~E(x14961,x14962)+E(f220(x14963,x14961),f220(x14963,x14962))
% 25.54/25.43 [1497]~E(x14971,x14972)+E(f703(x14971,x14973,x14974),f703(x14972,x14973,x14974))
% 25.54/25.43 [1498]~E(x14981,x14982)+E(f703(x14983,x14981,x14984),f703(x14983,x14982,x14984))
% 25.54/25.43 [1499]~E(x14991,x14992)+E(f703(x14993,x14994,x14991),f703(x14993,x14994,x14992))
% 25.54/25.43 [1500]~E(x15001,x15002)+E(f117(x15001),f117(x15002))
% 25.54/25.43 [1501]~E(x15011,x15012)+E(f272(x15011,x15013,x15014,x15015),f272(x15012,x15013,x15014,x15015))
% 25.54/25.43 [1502]~E(x15021,x15022)+E(f272(x15023,x15021,x15024,x15025),f272(x15023,x15022,x15024,x15025))
% 25.54/25.43 [1503]~E(x15031,x15032)+E(f272(x15033,x15034,x15031,x15035),f272(x15033,x15034,x15032,x15035))
% 25.54/25.43 [1504]~E(x15041,x15042)+E(f272(x15043,x15044,x15045,x15041),f272(x15043,x15044,x15045,x15042))
% 25.54/25.43 [1505]~E(x15051,x15052)+E(f506(x15051,x15053,x15054),f506(x15052,x15053,x15054))
% 25.54/25.43 [1506]~E(x15061,x15062)+E(f506(x15063,x15061,x15064),f506(x15063,x15062,x15064))
% 25.54/25.43 [1507]~E(x15071,x15072)+E(f506(x15073,x15074,x15071),f506(x15073,x15074,x15072))
% 25.54/25.43 [1508]~E(x15081,x15082)+E(f347(x15081,x15083),f347(x15082,x15083))
% 25.54/25.43 [1509]~E(x15091,x15092)+E(f347(x15093,x15091),f347(x15093,x15092))
% 25.54/25.43 [1510]~E(x15101,x15102)+E(f866(x15101),f866(x15102))
% 25.54/25.43 [1511]~E(x15111,x15112)+E(f484(x15111,x15113,x15114,x15115,x15116),f484(x15112,x15113,x15114,x15115,x15116))
% 25.54/25.43 [1512]~E(x15121,x15122)+E(f484(x15123,x15121,x15124,x15125,x15126),f484(x15123,x15122,x15124,x15125,x15126))
% 25.54/25.43 [1513]~E(x15131,x15132)+E(f484(x15133,x15134,x15131,x15135,x15136),f484(x15133,x15134,x15132,x15135,x15136))
% 25.54/25.43 [1514]~E(x15141,x15142)+E(f484(x15143,x15144,x15145,x15141,x15146),f484(x15143,x15144,x15145,x15142,x15146))
% 25.54/25.43 [1515]~E(x15151,x15152)+E(f484(x15153,x15154,x15155,x15156,x15151),f484(x15153,x15154,x15155,x15156,x15152))
% 25.54/25.43 [1516]~E(x15161,x15162)+E(f781(x15161,x15163,x15164,x15165,x15166),f781(x15162,x15163,x15164,x15165,x15166))
% 25.54/25.43 [1517]~E(x15171,x15172)+E(f781(x15173,x15171,x15174,x15175,x15176),f781(x15173,x15172,x15174,x15175,x15176))
% 25.54/25.43 [1518]~E(x15181,x15182)+E(f781(x15183,x15184,x15181,x15185,x15186),f781(x15183,x15184,x15182,x15185,x15186))
% 25.54/25.43 [1519]~E(x15191,x15192)+E(f781(x15193,x15194,x15195,x15191,x15196),f781(x15193,x15194,x15195,x15192,x15196))
% 25.54/25.43 [1520]~E(x15201,x15202)+E(f781(x15203,x15204,x15205,x15206,x15201),f781(x15203,x15204,x15205,x15206,x15202))
% 25.54/25.43 [1521]~E(x15211,x15212)+E(f778(x15211,x15213,x15214,x15215),f778(x15212,x15213,x15214,x15215))
% 25.54/25.43 [1522]~E(x15221,x15222)+E(f778(x15223,x15221,x15224,x15225),f778(x15223,x15222,x15224,x15225))
% 25.54/25.43 [1523]~E(x15231,x15232)+E(f778(x15233,x15234,x15231,x15235),f778(x15233,x15234,x15232,x15235))
% 25.54/25.43 [1524]~E(x15241,x15242)+E(f778(x15243,x15244,x15245,x15241),f778(x15243,x15244,x15245,x15242))
% 25.54/25.43 [1525]~E(x15251,x15252)+E(f139(x15251,x15253),f139(x15252,x15253))
% 25.54/25.43 [1526]~E(x15261,x15262)+E(f139(x15263,x15261),f139(x15263,x15262))
% 25.54/25.43 [1527]~E(x15271,x15272)+E(f35(x15271),f35(x15272))
% 25.54/25.43 [1528]~E(x15281,x15282)+E(f229(x15281,x15283),f229(x15282,x15283))
% 25.54/25.43 [1529]~E(x15291,x15292)+E(f229(x15293,x15291),f229(x15293,x15292))
% 25.54/25.43 [1530]~E(x15301,x15302)+E(f889(x15301,x15303),f889(x15302,x15303))
% 25.54/25.43 [1531]~E(x15311,x15312)+E(f889(x15313,x15311),f889(x15313,x15312))
% 25.54/25.43 [1532]~E(x15321,x15322)+E(f23(x15321,x15323),f23(x15322,x15323))
% 25.54/25.43 [1533]~E(x15331,x15332)+E(f23(x15333,x15331),f23(x15333,x15332))
% 25.54/25.43 [1534]~E(x15341,x15342)+E(f223(x15341,x15343,x15344),f223(x15342,x15343,x15344))
% 25.54/25.43 [1535]~E(x15351,x15352)+E(f223(x15353,x15351,x15354),f223(x15353,x15352,x15354))
% 25.54/25.43 [1536]~E(x15361,x15362)+E(f223(x15363,x15364,x15361),f223(x15363,x15364,x15362))
% 25.54/25.43 [1537]~E(x15371,x15372)+E(f110(x15371,x15373,x15374),f110(x15372,x15373,x15374))
% 25.54/25.43 [1538]~E(x15381,x15382)+E(f110(x15383,x15381,x15384),f110(x15383,x15382,x15384))
% 25.54/25.43 [1539]~E(x15391,x15392)+E(f110(x15393,x15394,x15391),f110(x15393,x15394,x15392))
% 25.54/25.43 [1540]~E(x15401,x15402)+E(f263(x15401,x15403,x15404,x15405),f263(x15402,x15403,x15404,x15405))
% 25.54/25.43 [1541]~E(x15411,x15412)+E(f263(x15413,x15411,x15414,x15415),f263(x15413,x15412,x15414,x15415))
% 25.54/25.43 [1542]~E(x15421,x15422)+E(f263(x15423,x15424,x15421,x15425),f263(x15423,x15424,x15422,x15425))
% 25.54/25.43 [1543]~E(x15431,x15432)+E(f263(x15433,x15434,x15435,x15431),f263(x15433,x15434,x15435,x15432))
% 25.54/25.43 [1544]~E(x15441,x15442)+E(f647(x15441,x15443,x15444,x15445),f647(x15442,x15443,x15444,x15445))
% 25.54/25.43 [1545]~E(x15451,x15452)+E(f647(x15453,x15451,x15454,x15455),f647(x15453,x15452,x15454,x15455))
% 25.54/25.43 [1546]~E(x15461,x15462)+E(f647(x15463,x15464,x15461,x15465),f647(x15463,x15464,x15462,x15465))
% 25.54/25.43 [1547]~E(x15471,x15472)+E(f647(x15473,x15474,x15475,x15471),f647(x15473,x15474,x15475,x15472))
% 25.54/25.43 [1548]~E(x15481,x15482)+E(f841(x15481,x15483,x15484),f841(x15482,x15483,x15484))
% 25.54/25.43 [1549]~E(x15491,x15492)+E(f841(x15493,x15491,x15494),f841(x15493,x15492,x15494))
% 25.54/25.43 [1550]~E(x15501,x15502)+E(f841(x15503,x15504,x15501),f841(x15503,x15504,x15502))
% 25.54/25.43 [1551]~E(x15511,x15512)+E(f575(x15511,x15513,x15514,x15515,x15516,x15517),f575(x15512,x15513,x15514,x15515,x15516,x15517))
% 25.54/25.43 [1552]~E(x15521,x15522)+E(f575(x15523,x15521,x15524,x15525,x15526,x15527),f575(x15523,x15522,x15524,x15525,x15526,x15527))
% 25.54/25.43 [1553]~E(x15531,x15532)+E(f575(x15533,x15534,x15531,x15535,x15536,x15537),f575(x15533,x15534,x15532,x15535,x15536,x15537))
% 25.54/25.43 [1554]~E(x15541,x15542)+E(f575(x15543,x15544,x15545,x15541,x15546,x15547),f575(x15543,x15544,x15545,x15542,x15546,x15547))
% 25.54/25.43 [1555]~E(x15551,x15552)+E(f575(x15553,x15554,x15555,x15556,x15551,x15557),f575(x15553,x15554,x15555,x15556,x15552,x15557))
% 25.54/25.43 [1556]~E(x15561,x15562)+E(f575(x15563,x15564,x15565,x15566,x15567,x15561),f575(x15563,x15564,x15565,x15566,x15567,x15562))
% 25.54/25.43 [1557]~E(x15571,x15572)+E(f668(x15571,x15573,x15574),f668(x15572,x15573,x15574))
% 25.54/25.43 [1558]~E(x15581,x15582)+E(f668(x15583,x15581,x15584),f668(x15583,x15582,x15584))
% 25.54/25.43 [1559]~E(x15591,x15592)+E(f668(x15593,x15594,x15591),f668(x15593,x15594,x15592))
% 25.54/25.43 [1560]~E(x15601,x15602)+E(f681(x15601,x15603),f681(x15602,x15603))
% 25.54/25.43 [1561]~E(x15611,x15612)+E(f681(x15613,x15611),f681(x15613,x15612))
% 25.54/25.43 [1562]~E(x15621,x15622)+E(f905(x15621,x15623,x15624),f905(x15622,x15623,x15624))
% 25.54/25.43 [1563]~E(x15631,x15632)+E(f905(x15633,x15631,x15634),f905(x15633,x15632,x15634))
% 25.54/25.43 [1564]~E(x15641,x15642)+E(f905(x15643,x15644,x15641),f905(x15643,x15644,x15642))
% 25.54/25.43 [1565]~E(x15651,x15652)+E(f674(x15651,x15653,x15654,x15655),f674(x15652,x15653,x15654,x15655))
% 25.54/25.43 [1566]~E(x15661,x15662)+E(f674(x15663,x15661,x15664,x15665),f674(x15663,x15662,x15664,x15665))
% 25.54/25.43 [1567]~E(x15671,x15672)+E(f674(x15673,x15674,x15671,x15675),f674(x15673,x15674,x15672,x15675))
% 25.54/25.43 [1568]~E(x15681,x15682)+E(f674(x15683,x15684,x15685,x15681),f674(x15683,x15684,x15685,x15682))
% 25.54/25.43 [1569]~E(x15691,x15692)+E(f804(x15691,x15693,x15694,x15695),f804(x15692,x15693,x15694,x15695))
% 25.54/25.43 [1570]~E(x15701,x15702)+E(f804(x15703,x15701,x15704,x15705),f804(x15703,x15702,x15704,x15705))
% 25.54/25.43 [1571]~E(x15711,x15712)+E(f804(x15713,x15714,x15711,x15715),f804(x15713,x15714,x15712,x15715))
% 25.54/25.43 [1572]~E(x15721,x15722)+E(f804(x15723,x15724,x15725,x15721),f804(x15723,x15724,x15725,x15722))
% 25.54/25.43 [1573]~E(x15731,x15732)+E(f731(x15731,x15733),f731(x15732,x15733))
% 25.54/25.43 [1574]~E(x15741,x15742)+E(f731(x15743,x15741),f731(x15743,x15742))
% 25.54/25.43 [1575]~E(x15751,x15752)+E(f907(x15751,x15753,x15754,x15755,x15756),f907(x15752,x15753,x15754,x15755,x15756))
% 25.54/25.43 [1576]~E(x15761,x15762)+E(f907(x15763,x15761,x15764,x15765,x15766),f907(x15763,x15762,x15764,x15765,x15766))
% 25.54/25.43 [1577]~E(x15771,x15772)+E(f907(x15773,x15774,x15771,x15775,x15776),f907(x15773,x15774,x15772,x15775,x15776))
% 25.54/25.43 [1578]~E(x15781,x15782)+E(f907(x15783,x15784,x15785,x15781,x15786),f907(x15783,x15784,x15785,x15782,x15786))
% 25.54/25.43 [1579]~E(x15791,x15792)+E(f907(x15793,x15794,x15795,x15796,x15791),f907(x15793,x15794,x15795,x15796,x15792))
% 25.54/25.43 [1580]~E(x15801,x15802)+E(f338(x15801,x15803,x15804),f338(x15802,x15803,x15804))
% 25.54/25.43 [1581]~E(x15811,x15812)+E(f338(x15813,x15811,x15814),f338(x15813,x15812,x15814))
% 25.54/25.43 [1582]~E(x15821,x15822)+E(f338(x15823,x15824,x15821),f338(x15823,x15824,x15822))
% 25.54/25.43 [1583]~E(x15831,x15832)+E(f821(x15831,x15833,x15834,x15835,x15836,x15837),f821(x15832,x15833,x15834,x15835,x15836,x15837))
% 25.54/25.43 [1584]~E(x15841,x15842)+E(f821(x15843,x15841,x15844,x15845,x15846,x15847),f821(x15843,x15842,x15844,x15845,x15846,x15847))
% 25.54/25.43 [1585]~E(x15851,x15852)+E(f821(x15853,x15854,x15851,x15855,x15856,x15857),f821(x15853,x15854,x15852,x15855,x15856,x15857))
% 25.54/25.43 [1586]~E(x15861,x15862)+E(f821(x15863,x15864,x15865,x15861,x15866,x15867),f821(x15863,x15864,x15865,x15862,x15866,x15867))
% 25.54/25.43 [1587]~E(x15871,x15872)+E(f821(x15873,x15874,x15875,x15876,x15871,x15877),f821(x15873,x15874,x15875,x15876,x15872,x15877))
% 25.54/25.43 [1588]~E(x15881,x15882)+E(f821(x15883,x15884,x15885,x15886,x15887,x15881),f821(x15883,x15884,x15885,x15886,x15887,x15882))
% 25.54/25.43 [1589]~E(x15891,x15892)+E(f337(x15891,x15893,x15894,x15895),f337(x15892,x15893,x15894,x15895))
% 25.54/25.43 [1590]~E(x15901,x15902)+E(f337(x15903,x15901,x15904,x15905),f337(x15903,x15902,x15904,x15905))
% 25.54/25.43 [1591]~E(x15911,x15912)+E(f337(x15913,x15914,x15911,x15915),f337(x15913,x15914,x15912,x15915))
% 25.54/25.43 [1592]~E(x15921,x15922)+E(f337(x15923,x15924,x15925,x15921),f337(x15923,x15924,x15925,x15922))
% 25.54/25.43 [1593]~E(x15931,x15932)+E(f716(x15931,x15933),f716(x15932,x15933))
% 25.54/25.43 [1594]~E(x15941,x15942)+E(f716(x15943,x15941),f716(x15943,x15942))
% 25.54/25.43 [1595]~E(x15951,x15952)+E(f685(x15951,x15953,x15954),f685(x15952,x15953,x15954))
% 25.54/25.43 [1596]~E(x15961,x15962)+E(f685(x15963,x15961,x15964),f685(x15963,x15962,x15964))
% 25.54/25.43 [1597]~E(x15971,x15972)+E(f685(x15973,x15974,x15971),f685(x15973,x15974,x15972))
% 25.54/25.43 [1598]~E(x15981,x15982)+E(f332(x15981,x15983),f332(x15982,x15983))
% 25.54/25.43 [1599]~E(x15991,x15992)+E(f332(x15993,x15991),f332(x15993,x15992))
% 25.54/25.43 [1600]~E(x16001,x16002)+E(f593(x16001,x16003,x16004,x16005),f593(x16002,x16003,x16004,x16005))
% 25.54/25.43 [1601]~E(x16011,x16012)+E(f593(x16013,x16011,x16014,x16015),f593(x16013,x16012,x16014,x16015))
% 25.54/25.43 [1602]~E(x16021,x16022)+E(f593(x16023,x16024,x16021,x16025),f593(x16023,x16024,x16022,x16025))
% 25.54/25.43 [1603]~E(x16031,x16032)+E(f593(x16033,x16034,x16035,x16031),f593(x16033,x16034,x16035,x16032))
% 25.54/25.43 [1604]~E(x16041,x16042)+E(f582(x16041,x16043,x16044),f582(x16042,x16043,x16044))
% 25.54/25.43 [1605]~E(x16051,x16052)+E(f582(x16053,x16051,x16054),f582(x16053,x16052,x16054))
% 25.54/25.43 [1606]~E(x16061,x16062)+E(f582(x16063,x16064,x16061),f582(x16063,x16064,x16062))
% 25.54/25.43 [1607]~E(x16071,x16072)+E(f469(x16071,x16073),f469(x16072,x16073))
% 25.54/25.43 [1608]~E(x16081,x16082)+E(f469(x16083,x16081),f469(x16083,x16082))
% 25.54/25.43 [1609]~E(x16091,x16092)+E(f405(x16091,x16093,x16094,x16095),f405(x16092,x16093,x16094,x16095))
% 25.54/25.43 [1610]~E(x16101,x16102)+E(f405(x16103,x16101,x16104,x16105),f405(x16103,x16102,x16104,x16105))
% 25.54/25.43 [1611]~E(x16111,x16112)+E(f405(x16113,x16114,x16111,x16115),f405(x16113,x16114,x16112,x16115))
% 25.54/25.43 [1612]~E(x16121,x16122)+E(f405(x16123,x16124,x16125,x16121),f405(x16123,x16124,x16125,x16122))
% 25.54/25.43 [1613]~E(x16131,x16132)+E(f558(x16131,x16133,x16134,x16135),f558(x16132,x16133,x16134,x16135))
% 25.54/25.43 [1614]~E(x16141,x16142)+E(f558(x16143,x16141,x16144,x16145),f558(x16143,x16142,x16144,x16145))
% 25.54/25.43 [1615]~E(x16151,x16152)+E(f558(x16153,x16154,x16151,x16155),f558(x16153,x16154,x16152,x16155))
% 25.54/25.43 [1616]~E(x16161,x16162)+E(f558(x16163,x16164,x16165,x16161),f558(x16163,x16164,x16165,x16162))
% 25.54/25.43 [1617]~E(x16171,x16172)+E(f628(x16171,x16173,x16174,x16175),f628(x16172,x16173,x16174,x16175))
% 25.54/25.43 [1618]~E(x16181,x16182)+E(f628(x16183,x16181,x16184,x16185),f628(x16183,x16182,x16184,x16185))
% 25.54/25.43 [1619]~E(x16191,x16192)+E(f628(x16193,x16194,x16191,x16195),f628(x16193,x16194,x16192,x16195))
% 25.54/25.43 [1620]~E(x16201,x16202)+E(f628(x16203,x16204,x16205,x16201),f628(x16203,x16204,x16205,x16202))
% 25.54/25.43 [1621]~E(x16211,x16212)+E(f796(x16211,x16213,x16214,x16215,x16216,x16217,x16218),f796(x16212,x16213,x16214,x16215,x16216,x16217,x16218))
% 25.54/25.43 [1622]~E(x16221,x16222)+E(f796(x16223,x16221,x16224,x16225,x16226,x16227,x16228),f796(x16223,x16222,x16224,x16225,x16226,x16227,x16228))
% 25.54/25.43 [1623]~E(x16231,x16232)+E(f796(x16233,x16234,x16231,x16235,x16236,x16237,x16238),f796(x16233,x16234,x16232,x16235,x16236,x16237,x16238))
% 25.54/25.43 [1624]~E(x16241,x16242)+E(f796(x16243,x16244,x16245,x16241,x16246,x16247,x16248),f796(x16243,x16244,x16245,x16242,x16246,x16247,x16248))
% 25.54/25.43 [1625]~E(x16251,x16252)+E(f796(x16253,x16254,x16255,x16256,x16251,x16257,x16258),f796(x16253,x16254,x16255,x16256,x16252,x16257,x16258))
% 25.54/25.43 [1626]~E(x16261,x16262)+E(f796(x16263,x16264,x16265,x16266,x16267,x16261,x16268),f796(x16263,x16264,x16265,x16266,x16267,x16262,x16268))
% 25.54/25.43 [1627]~E(x16271,x16272)+E(f796(x16273,x16274,x16275,x16276,x16277,x16278,x16271),f796(x16273,x16274,x16275,x16276,x16277,x16278,x16272))
% 25.54/25.43 [1628]~E(x16281,x16282)+E(f691(x16281,x16283,x16284,x16285),f691(x16282,x16283,x16284,x16285))
% 25.54/25.43 [1629]~E(x16291,x16292)+E(f691(x16293,x16291,x16294,x16295),f691(x16293,x16292,x16294,x16295))
% 25.54/25.43 [1630]~E(x16301,x16302)+E(f691(x16303,x16304,x16301,x16305),f691(x16303,x16304,x16302,x16305))
% 25.54/25.43 [1631]~E(x16311,x16312)+E(f691(x16313,x16314,x16315,x16311),f691(x16313,x16314,x16315,x16312))
% 25.54/25.43 [1632]~E(x16321,x16322)+E(f835(x16321,x16323,x16324,x16325),f835(x16322,x16323,x16324,x16325))
% 25.54/25.43 [1633]~E(x16331,x16332)+E(f835(x16333,x16331,x16334,x16335),f835(x16333,x16332,x16334,x16335))
% 25.54/25.43 [1634]~E(x16341,x16342)+E(f835(x16343,x16344,x16341,x16345),f835(x16343,x16344,x16342,x16345))
% 25.54/25.43 [1635]~E(x16351,x16352)+E(f835(x16353,x16354,x16355,x16351),f835(x16353,x16354,x16355,x16352))
% 25.54/25.43 [1636]~E(x16361,x16362)+E(f664(x16361,x16363,x16364),f664(x16362,x16363,x16364))
% 25.54/25.43 [1637]~E(x16371,x16372)+E(f664(x16373,x16371,x16374),f664(x16373,x16372,x16374))
% 25.54/25.43 [1638]~E(x16381,x16382)+E(f664(x16383,x16384,x16381),f664(x16383,x16384,x16382))
% 25.54/25.43 [1639]~E(x16391,x16392)+E(f217(x16391,x16393,x16394,x16395,x16396),f217(x16392,x16393,x16394,x16395,x16396))
% 25.54/25.43 [1640]~E(x16401,x16402)+E(f217(x16403,x16401,x16404,x16405,x16406),f217(x16403,x16402,x16404,x16405,x16406))
% 25.54/25.43 [1641]~E(x16411,x16412)+E(f217(x16413,x16414,x16411,x16415,x16416),f217(x16413,x16414,x16412,x16415,x16416))
% 25.54/25.43 [1642]~E(x16421,x16422)+E(f217(x16423,x16424,x16425,x16421,x16426),f217(x16423,x16424,x16425,x16422,x16426))
% 25.54/25.43 [1643]~E(x16431,x16432)+E(f217(x16433,x16434,x16435,x16436,x16431),f217(x16433,x16434,x16435,x16436,x16432))
% 25.54/25.43 [1644]~E(x16441,x16442)+E(f541(x16441,x16443,x16444,x16445),f541(x16442,x16443,x16444,x16445))
% 25.54/25.43 [1645]~E(x16451,x16452)+E(f541(x16453,x16451,x16454,x16455),f541(x16453,x16452,x16454,x16455))
% 25.54/25.43 [1646]~E(x16461,x16462)+E(f541(x16463,x16464,x16461,x16465),f541(x16463,x16464,x16462,x16465))
% 25.54/25.43 [1647]~E(x16471,x16472)+E(f541(x16473,x16474,x16475,x16471),f541(x16473,x16474,x16475,x16472))
% 25.54/25.43 [1648]~E(x16481,x16482)+E(f415(x16481,x16483),f415(x16482,x16483))
% 25.54/25.43 [1649]~E(x16491,x16492)+E(f415(x16493,x16491),f415(x16493,x16492))
% 25.54/25.43 [1650]~E(x16501,x16502)+E(f690(x16501,x16503,x16504,x16505),f690(x16502,x16503,x16504,x16505))
% 25.54/25.43 [1651]~E(x16511,x16512)+E(f690(x16513,x16511,x16514,x16515),f690(x16513,x16512,x16514,x16515))
% 25.54/25.43 [1652]~E(x16521,x16522)+E(f690(x16523,x16524,x16521,x16525),f690(x16523,x16524,x16522,x16525))
% 25.54/25.43 [1653]~E(x16531,x16532)+E(f690(x16533,x16534,x16535,x16531),f690(x16533,x16534,x16535,x16532))
% 25.54/25.43 [1654]~E(x16541,x16542)+E(f572(x16541,x16543,x16544,x16545),f572(x16542,x16543,x16544,x16545))
% 25.54/25.43 [1655]~E(x16551,x16552)+E(f572(x16553,x16551,x16554,x16555),f572(x16553,x16552,x16554,x16555))
% 25.54/25.43 [1656]~E(x16561,x16562)+E(f572(x16563,x16564,x16561,x16565),f572(x16563,x16564,x16562,x16565))
% 25.54/25.43 [1657]~E(x16571,x16572)+E(f572(x16573,x16574,x16575,x16571),f572(x16573,x16574,x16575,x16572))
% 25.54/25.43 [1658]~E(x16581,x16582)+E(f797(x16581,x16583),f797(x16582,x16583))
% 25.54/25.43 [1659]~E(x16591,x16592)+E(f797(x16593,x16591),f797(x16593,x16592))
% 25.54/25.43 [1660]~E(x16601,x16602)+E(f178(x16601,x16603,x16604,x16605),f178(x16602,x16603,x16604,x16605))
% 25.54/25.43 [1661]~E(x16611,x16612)+E(f178(x16613,x16611,x16614,x16615),f178(x16613,x16612,x16614,x16615))
% 25.54/25.43 [1662]~E(x16621,x16622)+E(f178(x16623,x16624,x16621,x16625),f178(x16623,x16624,x16622,x16625))
% 25.54/25.43 [1663]~E(x16631,x16632)+E(f178(x16633,x16634,x16635,x16631),f178(x16633,x16634,x16635,x16632))
% 25.54/25.43 [1664]~E(x16641,x16642)+E(f291(x16641,x16643,x16644,x16645,x16646),f291(x16642,x16643,x16644,x16645,x16646))
% 25.54/25.43 [1665]~E(x16651,x16652)+E(f291(x16653,x16651,x16654,x16655,x16656),f291(x16653,x16652,x16654,x16655,x16656))
% 25.54/25.43 [1666]~E(x16661,x16662)+E(f291(x16663,x16664,x16661,x16665,x16666),f291(x16663,x16664,x16662,x16665,x16666))
% 25.54/25.43 [1667]~E(x16671,x16672)+E(f291(x16673,x16674,x16675,x16671,x16676),f291(x16673,x16674,x16675,x16672,x16676))
% 25.54/25.43 [1668]~E(x16681,x16682)+E(f291(x16683,x16684,x16685,x16686,x16681),f291(x16683,x16684,x16685,x16686,x16682))
% 25.54/25.43 [1669]~E(x16691,x16692)+E(f340(x16691,x16693,x16694),f340(x16692,x16693,x16694))
% 25.54/25.43 [1670]~E(x16701,x16702)+E(f340(x16703,x16701,x16704),f340(x16703,x16702,x16704))
% 25.54/25.43 [1671]~E(x16711,x16712)+E(f340(x16713,x16714,x16711),f340(x16713,x16714,x16712))
% 25.54/25.43 [1672]~E(x16721,x16722)+E(f207(x16721,x16723),f207(x16722,x16723))
% 25.54/25.43 [1673]~E(x16731,x16732)+E(f207(x16733,x16731),f207(x16733,x16732))
% 25.54/25.43 [1674]~E(x16741,x16742)+E(f520(x16741,x16743,x16744,x16745,x16746,x16747),f520(x16742,x16743,x16744,x16745,x16746,x16747))
% 25.54/25.43 [1675]~E(x16751,x16752)+E(f520(x16753,x16751,x16754,x16755,x16756,x16757),f520(x16753,x16752,x16754,x16755,x16756,x16757))
% 25.54/25.43 [1676]~E(x16761,x16762)+E(f520(x16763,x16764,x16761,x16765,x16766,x16767),f520(x16763,x16764,x16762,x16765,x16766,x16767))
% 25.54/25.43 [1677]~E(x16771,x16772)+E(f520(x16773,x16774,x16775,x16771,x16776,x16777),f520(x16773,x16774,x16775,x16772,x16776,x16777))
% 25.54/25.43 [1678]~E(x16781,x16782)+E(f520(x16783,x16784,x16785,x16786,x16781,x16787),f520(x16783,x16784,x16785,x16786,x16782,x16787))
% 25.54/25.43 [1679]~E(x16791,x16792)+E(f520(x16793,x16794,x16795,x16796,x16797,x16791),f520(x16793,x16794,x16795,x16796,x16797,x16792))
% 25.54/25.43 [1680]~E(x16801,x16802)+E(f324(x16801),f324(x16802))
% 25.54/25.43 [1681]~E(x16811,x16812)+E(f607(x16811,x16813,x16814),f607(x16812,x16813,x16814))
% 25.54/25.43 [1682]~E(x16821,x16822)+E(f607(x16823,x16821,x16824),f607(x16823,x16822,x16824))
% 25.54/25.43 [1683]~E(x16831,x16832)+E(f607(x16833,x16834,x16831),f607(x16833,x16834,x16832))
% 25.54/25.43 [1684]~E(x16841,x16842)+E(f453(x16841,x16843,x16844),f453(x16842,x16843,x16844))
% 25.54/25.43 [1685]~E(x16851,x16852)+E(f453(x16853,x16851,x16854),f453(x16853,x16852,x16854))
% 25.54/25.43 [1686]~E(x16861,x16862)+E(f453(x16863,x16864,x16861),f453(x16863,x16864,x16862))
% 25.54/25.43 [1687]~E(x16871,x16872)+E(f422(x16871,x16873,x16874),f422(x16872,x16873,x16874))
% 25.54/25.43 [1688]~E(x16881,x16882)+E(f422(x16883,x16881,x16884),f422(x16883,x16882,x16884))
% 25.54/25.43 [1689]~E(x16891,x16892)+E(f422(x16893,x16894,x16891),f422(x16893,x16894,x16892))
% 25.54/25.43 [1690]~E(x16901,x16902)+E(f474(x16901,x16903,x16904),f474(x16902,x16903,x16904))
% 25.54/25.43 [1691]~E(x16911,x16912)+E(f474(x16913,x16911,x16914),f474(x16913,x16912,x16914))
% 25.54/25.43 [1692]~E(x16921,x16922)+E(f474(x16923,x16924,x16921),f474(x16923,x16924,x16922))
% 25.54/25.43 [1693]~E(x16931,x16932)+E(f552(x16931,x16933,x16934,x16935),f552(x16932,x16933,x16934,x16935))
% 25.54/25.43 [1694]~E(x16941,x16942)+E(f552(x16943,x16941,x16944,x16945),f552(x16943,x16942,x16944,x16945))
% 25.54/25.43 [1695]~E(x16951,x16952)+E(f552(x16953,x16954,x16951,x16955),f552(x16953,x16954,x16952,x16955))
% 25.54/25.43 [1696]~E(x16961,x16962)+E(f552(x16963,x16964,x16965,x16961),f552(x16963,x16964,x16965,x16962))
% 25.54/25.43 [1697]~E(x16971,x16972)+E(f610(x16971,x16973),f610(x16972,x16973))
% 25.54/25.43 [1698]~E(x16981,x16982)+E(f610(x16983,x16981),f610(x16983,x16982))
% 25.54/25.43 [1699]~E(x16991,x16992)+E(f353(x16991,x16993,x16994,x16995,x16996),f353(x16992,x16993,x16994,x16995,x16996))
% 25.54/25.43 [1700]~E(x17001,x17002)+E(f353(x17003,x17001,x17004,x17005,x17006),f353(x17003,x17002,x17004,x17005,x17006))
% 25.54/25.43 [1701]~E(x17011,x17012)+E(f353(x17013,x17014,x17011,x17015,x17016),f353(x17013,x17014,x17012,x17015,x17016))
% 25.54/25.43 [1702]~E(x17021,x17022)+E(f353(x17023,x17024,x17025,x17021,x17026),f353(x17023,x17024,x17025,x17022,x17026))
% 25.54/25.43 [1703]~E(x17031,x17032)+E(f353(x17033,x17034,x17035,x17036,x17031),f353(x17033,x17034,x17035,x17036,x17032))
% 25.54/25.43 [1704]~E(x17041,x17042)+E(f682(x17041,x17043,x17044),f682(x17042,x17043,x17044))
% 25.54/25.43 [1705]~E(x17051,x17052)+E(f682(x17053,x17051,x17054),f682(x17053,x17052,x17054))
% 25.54/25.43 [1706]~E(x17061,x17062)+E(f682(x17063,x17064,x17061),f682(x17063,x17064,x17062))
% 25.54/25.43 [1707]~E(x17071,x17072)+E(f470(x17071,x17073),f470(x17072,x17073))
% 25.54/25.43 [1708]~E(x17081,x17082)+E(f470(x17083,x17081),f470(x17083,x17082))
% 25.54/25.43 [1709]~E(x17091,x17092)+E(f507(x17091,x17093,x17094),f507(x17092,x17093,x17094))
% 25.54/25.43 [1710]~E(x17101,x17102)+E(f507(x17103,x17101,x17104),f507(x17103,x17102,x17104))
% 25.54/25.43 [1711]~E(x17111,x17112)+E(f507(x17113,x17114,x17111),f507(x17113,x17114,x17112))
% 25.54/25.43 [1712]~E(x17121,x17122)+E(f466(x17121,x17123,x17124,x17125),f466(x17122,x17123,x17124,x17125))
% 25.54/25.43 [1713]~E(x17131,x17132)+E(f466(x17133,x17131,x17134,x17135),f466(x17133,x17132,x17134,x17135))
% 25.54/25.43 [1714]~E(x17141,x17142)+E(f466(x17143,x17144,x17141,x17145),f466(x17143,x17144,x17142,x17145))
% 25.54/25.43 [1715]~E(x17151,x17152)+E(f466(x17153,x17154,x17155,x17151),f466(x17153,x17154,x17155,x17152))
% 25.54/25.43 [1716]~E(x17161,x17162)+E(f715(x17161,x17163),f715(x17162,x17163))
% 25.54/25.43 [1717]~E(x17171,x17172)+E(f715(x17173,x17171),f715(x17173,x17172))
% 25.54/25.43 [1718]~E(x17181,x17182)+E(f782(x17181,x17183,x17184,x17185),f782(x17182,x17183,x17184,x17185))
% 25.54/25.43 [1719]~E(x17191,x17192)+E(f782(x17193,x17191,x17194,x17195),f782(x17193,x17192,x17194,x17195))
% 25.54/25.43 [1720]~E(x17201,x17202)+E(f782(x17203,x17204,x17201,x17205),f782(x17203,x17204,x17202,x17205))
% 25.54/25.43 [1721]~E(x17211,x17212)+E(f782(x17213,x17214,x17215,x17211),f782(x17213,x17214,x17215,x17212))
% 25.54/25.43 [1722]~E(x17221,x17222)+E(f670(x17221,x17223,x17224),f670(x17222,x17223,x17224))
% 25.54/25.43 [1723]~E(x17231,x17232)+E(f670(x17233,x17231,x17234),f670(x17233,x17232,x17234))
% 25.54/25.43 [1724]~E(x17241,x17242)+E(f670(x17243,x17244,x17241),f670(x17243,x17244,x17242))
% 25.54/25.43 [1725]~E(x17251,x17252)+E(f155(x17251,x17253),f155(x17252,x17253))
% 25.54/25.43 [1726]~E(x17261,x17262)+E(f155(x17263,x17261),f155(x17263,x17262))
% 25.54/25.43 [1727]~E(x17271,x17272)+E(f848(x17271,x17273,x17274,x17275,x17276,x17277,x17278,x17279),f848(x17272,x17273,x17274,x17275,x17276,x17277,x17278,x17279))
% 25.54/25.43 [1728]~E(x17281,x17282)+E(f848(x17283,x17281,x17284,x17285,x17286,x17287,x17288,x17289),f848(x17283,x17282,x17284,x17285,x17286,x17287,x17288,x17289))
% 25.54/25.43 [1729]~E(x17291,x17292)+E(f848(x17293,x17294,x17291,x17295,x17296,x17297,x17298,x17299),f848(x17293,x17294,x17292,x17295,x17296,x17297,x17298,x17299))
% 25.54/25.43 [1730]~E(x17301,x17302)+E(f848(x17303,x17304,x17305,x17301,x17306,x17307,x17308,x17309),f848(x17303,x17304,x17305,x17302,x17306,x17307,x17308,x17309))
% 25.54/25.43 [1731]~E(x17311,x17312)+E(f848(x17313,x17314,x17315,x17316,x17311,x17317,x17318,x17319),f848(x17313,x17314,x17315,x17316,x17312,x17317,x17318,x17319))
% 25.54/25.43 [1732]~E(x17321,x17322)+E(f848(x17323,x17324,x17325,x17326,x17327,x17321,x17328,x17329),f848(x17323,x17324,x17325,x17326,x17327,x17322,x17328,x17329))
% 25.54/25.43 [1733]~E(x17331,x17332)+E(f848(x17333,x17334,x17335,x17336,x17337,x17338,x17331,x17339),f848(x17333,x17334,x17335,x17336,x17337,x17338,x17332,x17339))
% 25.54/25.43 [1734]~E(x17341,x17342)+E(f848(x17343,x17344,x17345,x17346,x17347,x17348,x17349,x17341),f848(x17343,x17344,x17345,x17346,x17347,x17348,x17349,x17342))
% 25.54/25.43 [1735]~E(x17351,x17352)+E(f910(x17351,x17353,x17354,x17355,x17356,x17357),f910(x17352,x17353,x17354,x17355,x17356,x17357))
% 25.54/25.43 [1736]~E(x17361,x17362)+E(f910(x17363,x17361,x17364,x17365,x17366,x17367),f910(x17363,x17362,x17364,x17365,x17366,x17367))
% 25.54/25.43 [1737]~E(x17371,x17372)+E(f910(x17373,x17374,x17371,x17375,x17376,x17377),f910(x17373,x17374,x17372,x17375,x17376,x17377))
% 25.54/25.43 [1738]~E(x17381,x17382)+E(f910(x17383,x17384,x17385,x17381,x17386,x17387),f910(x17383,x17384,x17385,x17382,x17386,x17387))
% 25.54/25.43 [1739]~E(x17391,x17392)+E(f910(x17393,x17394,x17395,x17396,x17391,x17397),f910(x17393,x17394,x17395,x17396,x17392,x17397))
% 25.54/25.43 [1740]~E(x17401,x17402)+E(f910(x17403,x17404,x17405,x17406,x17407,x17401),f910(x17403,x17404,x17405,x17406,x17407,x17402))
% 25.54/25.43 [1741]~E(x17411,x17412)+E(f500(x17411,x17413,x17414),f500(x17412,x17413,x17414))
% 25.54/25.43 [1742]~E(x17421,x17422)+E(f500(x17423,x17421,x17424),f500(x17423,x17422,x17424))
% 25.54/25.43 [1743]~E(x17431,x17432)+E(f500(x17433,x17434,x17431),f500(x17433,x17434,x17432))
% 25.54/25.43 [1744]~E(x17441,x17442)+E(f177(x17441,x17443,x17444),f177(x17442,x17443,x17444))
% 25.54/25.43 [1745]~E(x17451,x17452)+E(f177(x17453,x17451,x17454),f177(x17453,x17452,x17454))
% 25.54/25.43 [1746]~E(x17461,x17462)+E(f177(x17463,x17464,x17461),f177(x17463,x17464,x17462))
% 25.54/25.43 [1747]~E(x17471,x17472)+E(f270(x17471),f270(x17472))
% 25.54/25.43 [1748]~E(x17481,x17482)+E(f396(x17481,x17483,x17484,x17485),f396(x17482,x17483,x17484,x17485))
% 25.54/25.43 [1749]~E(x17491,x17492)+E(f396(x17493,x17491,x17494,x17495),f396(x17493,x17492,x17494,x17495))
% 25.54/25.43 [1750]~E(x17501,x17502)+E(f396(x17503,x17504,x17501,x17505),f396(x17503,x17504,x17502,x17505))
% 25.54/25.43 [1751]~E(x17511,x17512)+E(f396(x17513,x17514,x17515,x17511),f396(x17513,x17514,x17515,x17512))
% 25.54/25.43 [1752]~E(x17521,x17522)+E(f892(x17521,x17523,x17524),f892(x17522,x17523,x17524))
% 25.54/25.43 [1753]~E(x17531,x17532)+E(f892(x17533,x17531,x17534),f892(x17533,x17532,x17534))
% 25.54/25.43 [1754]~E(x17541,x17542)+E(f892(x17543,x17544,x17541),f892(x17543,x17544,x17542))
% 25.54/25.43 [1755]~E(x17551,x17552)+E(f379(x17551,x17553,x17554,x17555),f379(x17552,x17553,x17554,x17555))
% 25.54/25.43 [1756]~E(x17561,x17562)+E(f379(x17563,x17561,x17564,x17565),f379(x17563,x17562,x17564,x17565))
% 25.54/25.43 [1757]~E(x17571,x17572)+E(f379(x17573,x17574,x17571,x17575),f379(x17573,x17574,x17572,x17575))
% 25.54/25.43 [1758]~E(x17581,x17582)+E(f379(x17583,x17584,x17585,x17581),f379(x17583,x17584,x17585,x17582))
% 25.54/25.43 [1759]~E(x17591,x17592)+E(f408(x17591,x17593,x17594),f408(x17592,x17593,x17594))
% 25.54/25.43 [1760]~E(x17601,x17602)+E(f408(x17603,x17601,x17604),f408(x17603,x17602,x17604))
% 25.54/25.43 [1761]~E(x17611,x17612)+E(f408(x17613,x17614,x17611),f408(x17613,x17614,x17612))
% 25.54/25.43 [1762]~E(x17621,x17622)+E(f776(x17621,x17623,x17624,x17625),f776(x17622,x17623,x17624,x17625))
% 25.54/25.43 [1763]~E(x17631,x17632)+E(f776(x17633,x17631,x17634,x17635),f776(x17633,x17632,x17634,x17635))
% 25.54/25.43 [1764]~E(x17641,x17642)+E(f776(x17643,x17644,x17641,x17645),f776(x17643,x17644,x17642,x17645))
% 25.54/25.43 [1765]~E(x17651,x17652)+E(f776(x17653,x17654,x17655,x17651),f776(x17653,x17654,x17655,x17652))
% 25.54/25.43 [1766]~E(x17661,x17662)+E(f683(x17661,x17663,x17664),f683(x17662,x17663,x17664))
% 25.54/25.43 [1767]~E(x17671,x17672)+E(f683(x17673,x17671,x17674),f683(x17673,x17672,x17674))
% 25.54/25.43 [1768]~E(x17681,x17682)+E(f683(x17683,x17684,x17681),f683(x17683,x17684,x17682))
% 25.54/25.43 [1769]~E(x17691,x17692)+E(f709(x17691,x17693,x17694),f709(x17692,x17693,x17694))
% 25.54/25.43 [1770]~E(x17701,x17702)+E(f709(x17703,x17701,x17704),f709(x17703,x17702,x17704))
% 25.54/25.43 [1771]~E(x17711,x17712)+E(f709(x17713,x17714,x17711),f709(x17713,x17714,x17712))
% 25.54/25.43 [1772]~E(x17721,x17722)+E(f726(x17721,x17723,x17724,x17725,x17726),f726(x17722,x17723,x17724,x17725,x17726))
% 25.54/25.43 [1773]~E(x17731,x17732)+E(f726(x17733,x17731,x17734,x17735,x17736),f726(x17733,x17732,x17734,x17735,x17736))
% 25.54/25.43 [1774]~E(x17741,x17742)+E(f726(x17743,x17744,x17741,x17745,x17746),f726(x17743,x17744,x17742,x17745,x17746))
% 25.54/25.43 [1775]~E(x17751,x17752)+E(f726(x17753,x17754,x17755,x17751,x17756),f726(x17753,x17754,x17755,x17752,x17756))
% 25.54/25.43 [1776]~E(x17761,x17762)+E(f726(x17763,x17764,x17765,x17766,x17761),f726(x17763,x17764,x17765,x17766,x17762))
% 25.54/25.43 [1777]~E(x17771,x17772)+E(f727(x17771,x17773),f727(x17772,x17773))
% 25.54/25.43 [1778]~E(x17781,x17782)+E(f727(x17783,x17781),f727(x17783,x17782))
% 25.54/25.43 [1779]~E(x17791,x17792)+E(f290(x17791,x17793,x17794,x17795),f290(x17792,x17793,x17794,x17795))
% 25.54/25.43 [1780]~E(x17801,x17802)+E(f290(x17803,x17801,x17804,x17805),f290(x17803,x17802,x17804,x17805))
% 25.54/25.43 [1781]~E(x17811,x17812)+E(f290(x17813,x17814,x17811,x17815),f290(x17813,x17814,x17812,x17815))
% 25.54/25.43 [1782]~E(x17821,x17822)+E(f290(x17823,x17824,x17825,x17821),f290(x17823,x17824,x17825,x17822))
% 25.54/25.43 [1783]~E(x17831,x17832)+E(f672(x17831,x17833),f672(x17832,x17833))
% 25.54/25.43 [1784]~E(x17841,x17842)+E(f672(x17843,x17841),f672(x17843,x17842))
% 25.54/25.43 [1785]~E(x17851,x17852)+E(f515(x17851,x17853,x17854),f515(x17852,x17853,x17854))
% 25.54/25.43 [1786]~E(x17861,x17862)+E(f515(x17863,x17861,x17864),f515(x17863,x17862,x17864))
% 25.54/25.43 [1787]~E(x17871,x17872)+E(f515(x17873,x17874,x17871),f515(x17873,x17874,x17872))
% 25.54/25.43 [1788]~E(x17881,x17882)+E(f344(x17881,x17883),f344(x17882,x17883))
% 25.54/25.43 [1789]~E(x17891,x17892)+E(f344(x17893,x17891),f344(x17893,x17892))
% 25.54/25.43 [1790]~E(x17901,x17902)+E(f878(x17901,x17903,x17904,x17905),f878(x17902,x17903,x17904,x17905))
% 25.54/25.43 [1791]~E(x17911,x17912)+E(f878(x17913,x17911,x17914,x17915),f878(x17913,x17912,x17914,x17915))
% 25.54/25.43 [1792]~E(x17921,x17922)+E(f878(x17923,x17924,x17921,x17925),f878(x17923,x17924,x17922,x17925))
% 25.54/25.43 [1793]~E(x17931,x17932)+E(f878(x17933,x17934,x17935,x17931),f878(x17933,x17934,x17935,x17932))
% 25.54/25.43 [1794]~E(x17941,x17942)+E(f659(x17941,x17943,x17944,x17945),f659(x17942,x17943,x17944,x17945))
% 25.54/25.43 [1795]~E(x17951,x17952)+E(f659(x17953,x17951,x17954,x17955),f659(x17953,x17952,x17954,x17955))
% 25.54/25.43 [1796]~E(x17961,x17962)+E(f659(x17963,x17964,x17961,x17965),f659(x17963,x17964,x17962,x17965))
% 25.54/25.43 [1797]~E(x17971,x17972)+E(f659(x17973,x17974,x17975,x17971),f659(x17973,x17974,x17975,x17972))
% 25.54/25.43 [1798]~E(x17981,x17982)+E(f700(x17981,x17983,x17984,x17985,x17986),f700(x17982,x17983,x17984,x17985,x17986))
% 25.54/25.43 [1799]~E(x17991,x17992)+E(f700(x17993,x17991,x17994,x17995,x17996),f700(x17993,x17992,x17994,x17995,x17996))
% 25.54/25.43 [1800]~E(x18001,x18002)+E(f700(x18003,x18004,x18001,x18005,x18006),f700(x18003,x18004,x18002,x18005,x18006))
% 25.54/25.43 [1801]~E(x18011,x18012)+E(f700(x18013,x18014,x18015,x18011,x18016),f700(x18013,x18014,x18015,x18012,x18016))
% 25.54/25.43 [1802]~E(x18021,x18022)+E(f700(x18023,x18024,x18025,x18026,x18021),f700(x18023,x18024,x18025,x18026,x18022))
% 25.54/25.43 [1803]~E(x18031,x18032)+E(f688(x18031,x18033,x18034,x18035,x18036),f688(x18032,x18033,x18034,x18035,x18036))
% 25.54/25.43 [1804]~E(x18041,x18042)+E(f688(x18043,x18041,x18044,x18045,x18046),f688(x18043,x18042,x18044,x18045,x18046))
% 25.54/25.43 [1805]~E(x18051,x18052)+E(f688(x18053,x18054,x18051,x18055,x18056),f688(x18053,x18054,x18052,x18055,x18056))
% 25.54/25.43 [1806]~E(x18061,x18062)+E(f688(x18063,x18064,x18065,x18061,x18066),f688(x18063,x18064,x18065,x18062,x18066))
% 25.54/25.43 [1807]~E(x18071,x18072)+E(f688(x18073,x18074,x18075,x18076,x18071),f688(x18073,x18074,x18075,x18076,x18072))
% 25.54/25.43 [1808]~E(x18081,x18082)+E(f242(x18081,x18083,x18084),f242(x18082,x18083,x18084))
% 25.54/25.43 [1809]~E(x18091,x18092)+E(f242(x18093,x18091,x18094),f242(x18093,x18092,x18094))
% 25.54/25.43 [1810]~E(x18101,x18102)+E(f242(x18103,x18104,x18101),f242(x18103,x18104,x18102))
% 25.54/25.43 [1811]~E(x18111,x18112)+E(f505(x18111,x18113,x18114),f505(x18112,x18113,x18114))
% 25.54/25.43 [1812]~E(x18121,x18122)+E(f505(x18123,x18121,x18124),f505(x18123,x18122,x18124))
% 25.54/25.43 [1813]~E(x18131,x18132)+E(f505(x18133,x18134,x18131),f505(x18133,x18134,x18132))
% 25.54/25.43 [1814]~E(x18141,x18142)+E(f432(x18141),f432(x18142))
% 25.54/25.43 [1815]~E(x18151,x18152)+E(f540(x18151,x18153,x18154,x18155,x18156),f540(x18152,x18153,x18154,x18155,x18156))
% 25.54/25.43 [1816]~E(x18161,x18162)+E(f540(x18163,x18161,x18164,x18165,x18166),f540(x18163,x18162,x18164,x18165,x18166))
% 25.54/25.43 [1817]~E(x18171,x18172)+E(f540(x18173,x18174,x18171,x18175,x18176),f540(x18173,x18174,x18172,x18175,x18176))
% 25.54/25.43 [1818]~E(x18181,x18182)+E(f540(x18183,x18184,x18185,x18181,x18186),f540(x18183,x18184,x18185,x18182,x18186))
% 25.54/25.43 [1819]~E(x18191,x18192)+E(f540(x18193,x18194,x18195,x18196,x18191),f540(x18193,x18194,x18195,x18196,x18192))
% 25.54/25.43 [1820]~E(x18201,x18202)+E(f565(x18201,x18203,x18204,x18205),f565(x18202,x18203,x18204,x18205))
% 25.54/25.43 [1821]~E(x18211,x18212)+E(f565(x18213,x18211,x18214,x18215),f565(x18213,x18212,x18214,x18215))
% 25.54/25.43 [1822]~E(x18221,x18222)+E(f565(x18223,x18224,x18221,x18225),f565(x18223,x18224,x18222,x18225))
% 25.54/25.43 [1823]~E(x18231,x18232)+E(f565(x18233,x18234,x18235,x18231),f565(x18233,x18234,x18235,x18232))
% 25.54/25.43 [1824]~E(x18241,x18242)+E(f618(x18241,x18243,x18244),f618(x18242,x18243,x18244))
% 25.54/25.43 [1825]~E(x18251,x18252)+E(f618(x18253,x18251,x18254),f618(x18253,x18252,x18254))
% 25.54/25.43 [1826]~E(x18261,x18262)+E(f618(x18263,x18264,x18261),f618(x18263,x18264,x18262))
% 25.54/25.43 [1827]~E(x18271,x18272)+E(f120(x18271,x18273,x18274,x18275,x18276),f120(x18272,x18273,x18274,x18275,x18276))
% 25.54/25.43 [1828]~E(x18281,x18282)+E(f120(x18283,x18281,x18284,x18285,x18286),f120(x18283,x18282,x18284,x18285,x18286))
% 25.54/25.43 [1829]~E(x18291,x18292)+E(f120(x18293,x18294,x18291,x18295,x18296),f120(x18293,x18294,x18292,x18295,x18296))
% 25.54/25.43 [1830]~E(x18301,x18302)+E(f120(x18303,x18304,x18305,x18301,x18306),f120(x18303,x18304,x18305,x18302,x18306))
% 25.54/25.43 [1831]~E(x18311,x18312)+E(f120(x18313,x18314,x18315,x18316,x18311),f120(x18313,x18314,x18315,x18316,x18312))
% 25.54/25.43 [1832]~E(x18321,x18322)+E(f367(x18321,x18323,x18324,x18325,x18326),f367(x18322,x18323,x18324,x18325,x18326))
% 25.54/25.43 [1833]~E(x18331,x18332)+E(f367(x18333,x18331,x18334,x18335,x18336),f367(x18333,x18332,x18334,x18335,x18336))
% 25.54/25.43 [1834]~E(x18341,x18342)+E(f367(x18343,x18344,x18341,x18345,x18346),f367(x18343,x18344,x18342,x18345,x18346))
% 25.54/25.43 [1835]~E(x18351,x18352)+E(f367(x18353,x18354,x18355,x18351,x18356),f367(x18353,x18354,x18355,x18352,x18356))
% 25.54/25.43 [1836]~E(x18361,x18362)+E(f367(x18363,x18364,x18365,x18366,x18361),f367(x18363,x18364,x18365,x18366,x18362))
% 25.54/25.43 [1837]~E(x18371,x18372)+E(f579(x18371,x18373,x18374),f579(x18372,x18373,x18374))
% 25.54/25.43 [1838]~E(x18381,x18382)+E(f579(x18383,x18381,x18384),f579(x18383,x18382,x18384))
% 25.54/25.43 [1839]~E(x18391,x18392)+E(f579(x18393,x18394,x18391),f579(x18393,x18394,x18392))
% 25.54/25.43 [1840]~E(x18401,x18402)+E(f288(x18401,x18403,x18404,x18405,x18406),f288(x18402,x18403,x18404,x18405,x18406))
% 25.54/25.43 [1841]~E(x18411,x18412)+E(f288(x18413,x18411,x18414,x18415,x18416),f288(x18413,x18412,x18414,x18415,x18416))
% 25.54/25.43 [1842]~E(x18421,x18422)+E(f288(x18423,x18424,x18421,x18425,x18426),f288(x18423,x18424,x18422,x18425,x18426))
% 25.54/25.43 [1843]~E(x18431,x18432)+E(f288(x18433,x18434,x18435,x18431,x18436),f288(x18433,x18434,x18435,x18432,x18436))
% 25.54/25.43 [1844]~E(x18441,x18442)+E(f288(x18443,x18444,x18445,x18446,x18441),f288(x18443,x18444,x18445,x18446,x18442))
% 25.54/25.43 [1845]~E(x18451,x18452)+E(f205(x18451),f205(x18452))
% 25.54/25.43 [1846]~E(x18461,x18462)+E(f798(x18461,x18463),f798(x18462,x18463))
% 25.54/25.43 [1847]~E(x18471,x18472)+E(f798(x18473,x18471),f798(x18473,x18472))
% 25.54/25.43 [1848]~E(x18481,x18482)+E(f656(x18481),f656(x18482))
% 25.54/25.43 [1849]~E(x18491,x18492)+E(f578(x18491,x18493),f578(x18492,x18493))
% 25.54/25.43 [1850]~E(x18501,x18502)+E(f578(x18503,x18501),f578(x18503,x18502))
% 25.54/25.43 [1851]~E(x18511,x18512)+E(f368(x18511,x18513,x18514),f368(x18512,x18513,x18514))
% 25.54/25.43 [1852]~E(x18521,x18522)+E(f368(x18523,x18521,x18524),f368(x18523,x18522,x18524))
% 25.54/25.43 [1853]~E(x18531,x18532)+E(f368(x18533,x18534,x18531),f368(x18533,x18534,x18532))
% 25.54/25.43 [1854]~E(x18541,x18542)+E(f802(x18541,x18543,x18544,x18545,x18546,x18547,x18548),f802(x18542,x18543,x18544,x18545,x18546,x18547,x18548))
% 25.54/25.43 [1855]~E(x18551,x18552)+E(f802(x18553,x18551,x18554,x18555,x18556,x18557,x18558),f802(x18553,x18552,x18554,x18555,x18556,x18557,x18558))
% 25.54/25.43 [1856]~E(x18561,x18562)+E(f802(x18563,x18564,x18561,x18565,x18566,x18567,x18568),f802(x18563,x18564,x18562,x18565,x18566,x18567,x18568))
% 25.54/25.43 [1857]~E(x18571,x18572)+E(f802(x18573,x18574,x18575,x18571,x18576,x18577,x18578),f802(x18573,x18574,x18575,x18572,x18576,x18577,x18578))
% 25.54/25.43 [1858]~E(x18581,x18582)+E(f802(x18583,x18584,x18585,x18586,x18581,x18587,x18588),f802(x18583,x18584,x18585,x18586,x18582,x18587,x18588))
% 25.54/25.43 [1859]~E(x18591,x18592)+E(f802(x18593,x18594,x18595,x18596,x18597,x18591,x18598),f802(x18593,x18594,x18595,x18596,x18597,x18592,x18598))
% 25.54/25.43 [1860]~E(x18601,x18602)+E(f802(x18603,x18604,x18605,x18606,x18607,x18608,x18601),f802(x18603,x18604,x18605,x18606,x18607,x18608,x18602))
% 25.54/25.43 [1861]~E(x18611,x18612)+E(f760(x18611,x18613,x18614),f760(x18612,x18613,x18614))
% 25.54/25.43 [1862]~E(x18621,x18622)+E(f760(x18623,x18621,x18624),f760(x18623,x18622,x18624))
% 25.54/25.43 [1863]~E(x18631,x18632)+E(f760(x18633,x18634,x18631),f760(x18633,x18634,x18632))
% 25.54/25.43 [1864]~E(x18641,x18642)+E(f747(x18641,x18643,x18644,x18645),f747(x18642,x18643,x18644,x18645))
% 25.54/25.43 [1865]~E(x18651,x18652)+E(f747(x18653,x18651,x18654,x18655),f747(x18653,x18652,x18654,x18655))
% 25.54/25.43 [1866]~E(x18661,x18662)+E(f747(x18663,x18664,x18661,x18665),f747(x18663,x18664,x18662,x18665))
% 25.54/25.43 [1867]~E(x18671,x18672)+E(f747(x18673,x18674,x18675,x18671),f747(x18673,x18674,x18675,x18672))
% 25.54/25.43 [1868]~E(x18681,x18682)+E(f194(x18681),f194(x18682))
% 25.54/25.43 [1869]~E(x18691,x18692)+E(f487(x18691,x18693,x18694,x18695),f487(x18692,x18693,x18694,x18695))
% 25.54/25.43 [1870]~E(x18701,x18702)+E(f487(x18703,x18701,x18704,x18705),f487(x18703,x18702,x18704,x18705))
% 25.54/25.43 [1871]~E(x18711,x18712)+E(f487(x18713,x18714,x18711,x18715),f487(x18713,x18714,x18712,x18715))
% 25.54/25.43 [1872]~E(x18721,x18722)+E(f487(x18723,x18724,x18725,x18721),f487(x18723,x18724,x18725,x18722))
% 25.54/25.43 [1873]~E(x18731,x18732)+E(f521(x18731,x18733,x18734,x18735,x18736),f521(x18732,x18733,x18734,x18735,x18736))
% 25.54/25.43 [1874]~E(x18741,x18742)+E(f521(x18743,x18741,x18744,x18745,x18746),f521(x18743,x18742,x18744,x18745,x18746))
% 25.54/25.43 [1875]~E(x18751,x18752)+E(f521(x18753,x18754,x18751,x18755,x18756),f521(x18753,x18754,x18752,x18755,x18756))
% 25.54/25.43 [1876]~E(x18761,x18762)+E(f521(x18763,x18764,x18765,x18761,x18766),f521(x18763,x18764,x18765,x18762,x18766))
% 25.54/25.43 [1877]~E(x18771,x18772)+E(f521(x18773,x18774,x18775,x18776,x18771),f521(x18773,x18774,x18775,x18776,x18772))
% 25.54/25.43 [1878]~E(x18781,x18782)+E(f211(x18781,x18783),f211(x18782,x18783))
% 25.54/25.43 [1879]~E(x18791,x18792)+E(f211(x18793,x18791),f211(x18793,x18792))
% 25.54/25.43 [1880]~E(x18801,x18802)+E(f365(x18801,x18803,x18804,x18805,x18806),f365(x18802,x18803,x18804,x18805,x18806))
% 25.54/25.43 [1881]~E(x18811,x18812)+E(f365(x18813,x18811,x18814,x18815,x18816),f365(x18813,x18812,x18814,x18815,x18816))
% 25.54/25.43 [1882]~E(x18821,x18822)+E(f365(x18823,x18824,x18821,x18825,x18826),f365(x18823,x18824,x18822,x18825,x18826))
% 25.54/25.43 [1883]~E(x18831,x18832)+E(f365(x18833,x18834,x18835,x18831,x18836),f365(x18833,x18834,x18835,x18832,x18836))
% 25.54/25.43 [1884]~E(x18841,x18842)+E(f365(x18843,x18844,x18845,x18846,x18841),f365(x18843,x18844,x18845,x18846,x18842))
% 25.54/25.43 [1885]~E(x18851,x18852)+E(f454(x18851,x18853,x18854),f454(x18852,x18853,x18854))
% 25.54/25.43 [1886]~E(x18861,x18862)+E(f454(x18863,x18861,x18864),f454(x18863,x18862,x18864))
% 25.54/25.43 [1887]~E(x18871,x18872)+E(f454(x18873,x18874,x18871),f454(x18873,x18874,x18872))
% 25.54/25.43 [1888]~E(x18881,x18882)+E(f419(x18881),f419(x18882))
% 25.54/25.43 [1889]~E(x18891,x18892)+E(f630(x18891,x18893),f630(x18892,x18893))
% 25.54/25.43 [1890]~E(x18901,x18902)+E(f630(x18903,x18901),f630(x18903,x18902))
% 25.54/25.43 [1891]~E(x18911,x18912)+E(f806(x18911),f806(x18912))
% 25.54/25.43 [1892]~E(x18921,x18922)+E(f600(x18921,x18923,x18924,x18925,x18926,x18927),f600(x18922,x18923,x18924,x18925,x18926,x18927))
% 25.54/25.43 [1893]~E(x18931,x18932)+E(f600(x18933,x18931,x18934,x18935,x18936,x18937),f600(x18933,x18932,x18934,x18935,x18936,x18937))
% 25.54/25.43 [1894]~E(x18941,x18942)+E(f600(x18943,x18944,x18941,x18945,x18946,x18947),f600(x18943,x18944,x18942,x18945,x18946,x18947))
% 25.54/25.43 [1895]~E(x18951,x18952)+E(f600(x18953,x18954,x18955,x18951,x18956,x18957),f600(x18953,x18954,x18955,x18952,x18956,x18957))
% 25.54/25.43 [1896]~E(x18961,x18962)+E(f600(x18963,x18964,x18965,x18966,x18961,x18967),f600(x18963,x18964,x18965,x18966,x18962,x18967))
% 25.54/25.43 [1897]~E(x18971,x18972)+E(f600(x18973,x18974,x18975,x18976,x18977,x18971),f600(x18973,x18974,x18975,x18976,x18977,x18972))
% 25.54/25.43 [1898]~E(x18981,x18982)+E(f904(x18981,x18983),f904(x18982,x18983))
% 25.54/25.43 [1899]~E(x18991,x18992)+E(f904(x18993,x18991),f904(x18993,x18992))
% 25.54/25.43 [1900]~E(x19001,x19002)+E(f599(x19001,x19003,x19004,x19005,x19006,x19007),f599(x19002,x19003,x19004,x19005,x19006,x19007))
% 25.54/25.43 [1901]~E(x19011,x19012)+E(f599(x19013,x19011,x19014,x19015,x19016,x19017),f599(x19013,x19012,x19014,x19015,x19016,x19017))
% 25.54/25.43 [1902]~E(x19021,x19022)+E(f599(x19023,x19024,x19021,x19025,x19026,x19027),f599(x19023,x19024,x19022,x19025,x19026,x19027))
% 25.54/25.43 [1903]~E(x19031,x19032)+E(f599(x19033,x19034,x19035,x19031,x19036,x19037),f599(x19033,x19034,x19035,x19032,x19036,x19037))
% 25.54/25.43 [1904]~E(x19041,x19042)+E(f599(x19043,x19044,x19045,x19046,x19041,x19047),f599(x19043,x19044,x19045,x19046,x19042,x19047))
% 25.54/25.43 [1905]~E(x19051,x19052)+E(f599(x19053,x19054,x19055,x19056,x19057,x19051),f599(x19053,x19054,x19055,x19056,x19057,x19052))
% 25.54/25.43 [1906]~E(x19061,x19062)+E(f431(x19061,x19063),f431(x19062,x19063))
% 25.54/25.43 [1907]~E(x19071,x19072)+E(f431(x19073,x19071),f431(x19073,x19072))
% 25.54/25.43 [1908]~E(x19081,x19082)+E(f718(x19081,x19083,x19084),f718(x19082,x19083,x19084))
% 25.54/25.43 [1909]~E(x19091,x19092)+E(f718(x19093,x19091,x19094),f718(x19093,x19092,x19094))
% 25.54/25.43 [1910]~E(x19101,x19102)+E(f718(x19103,x19104,x19101),f718(x19103,x19104,x19102))
% 25.54/25.43 [1911]~E(x19111,x19112)+E(f594(x19111,x19113,x19114,x19115),f594(x19112,x19113,x19114,x19115))
% 25.54/25.43 [1912]~E(x19121,x19122)+E(f594(x19123,x19121,x19124,x19125),f594(x19123,x19122,x19124,x19125))
% 25.54/25.43 [1913]~E(x19131,x19132)+E(f594(x19133,x19134,x19131,x19135),f594(x19133,x19134,x19132,x19135))
% 25.54/25.43 [1914]~E(x19141,x19142)+E(f594(x19143,x19144,x19145,x19141),f594(x19143,x19144,x19145,x19142))
% 25.54/25.43 [1915]~E(x19151,x19152)+E(f911(x19151,x19153,x19154,x19155,x19156,x19157,x19158,x19159),f911(x19152,x19153,x19154,x19155,x19156,x19157,x19158,x19159))
% 25.54/25.43 [1916]~E(x19161,x19162)+E(f911(x19163,x19161,x19164,x19165,x19166,x19167,x19168,x19169),f911(x19163,x19162,x19164,x19165,x19166,x19167,x19168,x19169))
% 25.54/25.43 [1917]~E(x19171,x19172)+E(f911(x19173,x19174,x19171,x19175,x19176,x19177,x19178,x19179),f911(x19173,x19174,x19172,x19175,x19176,x19177,x19178,x19179))
% 25.54/25.43 [1918]~E(x19181,x19182)+E(f911(x19183,x19184,x19185,x19181,x19186,x19187,x19188,x19189),f911(x19183,x19184,x19185,x19182,x19186,x19187,x19188,x19189))
% 25.54/25.43 [1919]~E(x19191,x19192)+E(f911(x19193,x19194,x19195,x19196,x19191,x19197,x19198,x19199),f911(x19193,x19194,x19195,x19196,x19192,x19197,x19198,x19199))
% 25.54/25.43 [1920]~E(x19201,x19202)+E(f911(x19203,x19204,x19205,x19206,x19207,x19201,x19208,x19209),f911(x19203,x19204,x19205,x19206,x19207,x19202,x19208,x19209))
% 25.54/25.43 [1921]~E(x19211,x19212)+E(f911(x19213,x19214,x19215,x19216,x19217,x19218,x19211,x19219),f911(x19213,x19214,x19215,x19216,x19217,x19218,x19212,x19219))
% 25.54/25.43 [1922]~E(x19221,x19222)+E(f911(x19223,x19224,x19225,x19226,x19227,x19228,x19229,x19221),f911(x19223,x19224,x19225,x19226,x19227,x19228,x19229,x19222))
% 25.54/25.43 [1923]~E(x19231,x19232)+E(f350(x19231,x19233),f350(x19232,x19233))
% 25.54/25.43 [1924]~E(x19241,x19242)+E(f350(x19243,x19241),f350(x19243,x19242))
% 25.54/25.43 [1925]~E(x19251,x19252)+E(f844(x19251,x19253,x19254,x19255,x19256,x19257,x19258,x19259),f844(x19252,x19253,x19254,x19255,x19256,x19257,x19258,x19259))
% 25.54/25.43 [1926]~E(x19261,x19262)+E(f844(x19263,x19261,x19264,x19265,x19266,x19267,x19268,x19269),f844(x19263,x19262,x19264,x19265,x19266,x19267,x19268,x19269))
% 25.54/25.43 [1927]~E(x19271,x19272)+E(f844(x19273,x19274,x19271,x19275,x19276,x19277,x19278,x19279),f844(x19273,x19274,x19272,x19275,x19276,x19277,x19278,x19279))
% 25.54/25.43 [1928]~E(x19281,x19282)+E(f844(x19283,x19284,x19285,x19281,x19286,x19287,x19288,x19289),f844(x19283,x19284,x19285,x19282,x19286,x19287,x19288,x19289))
% 25.54/25.43 [1929]~E(x19291,x19292)+E(f844(x19293,x19294,x19295,x19296,x19291,x19297,x19298,x19299),f844(x19293,x19294,x19295,x19296,x19292,x19297,x19298,x19299))
% 25.54/25.43 [1930]~E(x19301,x19302)+E(f844(x19303,x19304,x19305,x19306,x19307,x19301,x19308,x19309),f844(x19303,x19304,x19305,x19306,x19307,x19302,x19308,x19309))
% 25.54/25.43 [1931]~E(x19311,x19312)+E(f844(x19313,x19314,x19315,x19316,x19317,x19318,x19311,x19319),f844(x19313,x19314,x19315,x19316,x19317,x19318,x19312,x19319))
% 25.54/25.43 [1932]~E(x19321,x19322)+E(f844(x19323,x19324,x19325,x19326,x19327,x19328,x19329,x19321),f844(x19323,x19324,x19325,x19326,x19327,x19328,x19329,x19322))
% 25.54/25.43 [1933]~E(x19331,x19332)+E(f643(x19331,x19333,x19334,x19335,x19336),f643(x19332,x19333,x19334,x19335,x19336))
% 25.54/25.43 [1934]~E(x19341,x19342)+E(f643(x19343,x19341,x19344,x19345,x19346),f643(x19343,x19342,x19344,x19345,x19346))
% 25.54/25.43 [1935]~E(x19351,x19352)+E(f643(x19353,x19354,x19351,x19355,x19356),f643(x19353,x19354,x19352,x19355,x19356))
% 25.54/25.43 [1936]~E(x19361,x19362)+E(f643(x19363,x19364,x19365,x19361,x19366),f643(x19363,x19364,x19365,x19362,x19366))
% 25.54/25.43 [1937]~E(x19371,x19372)+E(f643(x19373,x19374,x19375,x19376,x19371),f643(x19373,x19374,x19375,x19376,x19372))
% 25.54/25.43 [1938]~E(x19381,x19382)+E(f598(x19381,x19383,x19384,x19385),f598(x19382,x19383,x19384,x19385))
% 25.54/25.43 [1939]~E(x19391,x19392)+E(f598(x19393,x19391,x19394,x19395),f598(x19393,x19392,x19394,x19395))
% 25.54/25.43 [1940]~E(x19401,x19402)+E(f598(x19403,x19404,x19401,x19405),f598(x19403,x19404,x19402,x19405))
% 25.54/25.43 [1941]~E(x19411,x19412)+E(f598(x19413,x19414,x19415,x19411),f598(x19413,x19414,x19415,x19412))
% 25.54/25.43 [1942]~E(x19421,x19422)+E(f678(x19421,x19423,x19424),f678(x19422,x19423,x19424))
% 25.54/25.43 [1943]~E(x19431,x19432)+E(f678(x19433,x19431,x19434),f678(x19433,x19432,x19434))
% 25.54/25.43 [1944]~E(x19441,x19442)+E(f678(x19443,x19444,x19441),f678(x19443,x19444,x19442))
% 25.54/25.43 [1945]~E(x19451,x19452)+E(f498(x19451,x19453,x19454),f498(x19452,x19453,x19454))
% 25.54/25.43 [1946]~E(x19461,x19462)+E(f498(x19463,x19461,x19464),f498(x19463,x19462,x19464))
% 25.54/25.43 [1947]~E(x19471,x19472)+E(f498(x19473,x19474,x19471),f498(x19473,x19474,x19472))
% 25.54/25.43 [1948]~E(x19481,x19482)+E(f735(x19481,x19483,x19484,x19485),f735(x19482,x19483,x19484,x19485))
% 25.54/25.43 [1949]~E(x19491,x19492)+E(f735(x19493,x19491,x19494,x19495),f735(x19493,x19492,x19494,x19495))
% 25.54/25.43 [1950]~E(x19501,x19502)+E(f735(x19503,x19504,x19501,x19505),f735(x19503,x19504,x19502,x19505))
% 25.54/25.43 [1951]~E(x19511,x19512)+E(f735(x19513,x19514,x19515,x19511),f735(x19513,x19514,x19515,x19512))
% 25.54/25.43 [1952]~E(x19521,x19522)+E(f645(x19521,x19523,x19524,x19525),f645(x19522,x19523,x19524,x19525))
% 25.54/25.43 [1953]~E(x19531,x19532)+E(f645(x19533,x19531,x19534,x19535),f645(x19533,x19532,x19534,x19535))
% 25.54/25.43 [1954]~E(x19541,x19542)+E(f645(x19543,x19544,x19541,x19545),f645(x19543,x19544,x19542,x19545))
% 25.54/25.43 [1955]~E(x19551,x19552)+E(f645(x19553,x19554,x19555,x19551),f645(x19553,x19554,x19555,x19552))
% 25.54/25.43 [1956]~E(x19561,x19562)+E(f894(x19561,x19563,x19564),f894(x19562,x19563,x19564))
% 25.54/25.43 [1957]~E(x19571,x19572)+E(f894(x19573,x19571,x19574),f894(x19573,x19572,x19574))
% 25.54/25.43 [1958]~E(x19581,x19582)+E(f894(x19583,x19584,x19581),f894(x19583,x19584,x19582))
% 25.54/25.43 [1959]~E(x19591,x19592)+E(f734(x19591,x19593,x19594),f734(x19592,x19593,x19594))
% 25.54/25.43 [1960]~E(x19601,x19602)+E(f734(x19603,x19601,x19604),f734(x19603,x19602,x19604))
% 25.54/25.43 [1961]~E(x19611,x19612)+E(f734(x19613,x19614,x19611),f734(x19613,x19614,x19612))
% 25.54/25.43 [1962]~E(x19621,x19622)+E(f509(x19621,x19623,x19624,x19625),f509(x19622,x19623,x19624,x19625))
% 25.54/25.43 [1963]~E(x19631,x19632)+E(f509(x19633,x19631,x19634,x19635),f509(x19633,x19632,x19634,x19635))
% 25.54/25.43 [1964]~E(x19641,x19642)+E(f509(x19643,x19644,x19641,x19645),f509(x19643,x19644,x19642,x19645))
% 25.54/25.43 [1965]~E(x19651,x19652)+E(f509(x19653,x19654,x19655,x19651),f509(x19653,x19654,x19655,x19652))
% 25.54/25.43 [1966]~E(x19661,x19662)+E(f539(x19661,x19663,x19664,x19665),f539(x19662,x19663,x19664,x19665))
% 25.54/25.43 [1967]~E(x19671,x19672)+E(f539(x19673,x19671,x19674,x19675),f539(x19673,x19672,x19674,x19675))
% 25.54/25.43 [1968]~E(x19681,x19682)+E(f539(x19683,x19684,x19681,x19685),f539(x19683,x19684,x19682,x19685))
% 25.54/25.43 [1969]~E(x19691,x19692)+E(f539(x19693,x19694,x19695,x19691),f539(x19693,x19694,x19695,x19692))
% 25.54/25.43 [1970]~E(x19701,x19702)+E(f400(x19701,x19703,x19704,x19705),f400(x19702,x19703,x19704,x19705))
% 25.54/25.43 [1971]~E(x19711,x19712)+E(f400(x19713,x19711,x19714,x19715),f400(x19713,x19712,x19714,x19715))
% 25.54/25.43 [1972]~E(x19721,x19722)+E(f400(x19723,x19724,x19721,x19725),f400(x19723,x19724,x19722,x19725))
% 25.54/25.43 [1973]~E(x19731,x19732)+E(f400(x19733,x19734,x19735,x19731),f400(x19733,x19734,x19735,x19732))
% 25.54/25.43 [1974]~E(x19741,x19742)+E(f380(x19741,x19743,x19744,x19745),f380(x19742,x19743,x19744,x19745))
% 25.54/25.43 [1975]~E(x19751,x19752)+E(f380(x19753,x19751,x19754,x19755),f380(x19753,x19752,x19754,x19755))
% 25.54/25.43 [1976]~E(x19761,x19762)+E(f380(x19763,x19764,x19761,x19765),f380(x19763,x19764,x19762,x19765))
% 25.54/25.43 [1977]~E(x19771,x19772)+E(f380(x19773,x19774,x19775,x19771),f380(x19773,x19774,x19775,x19772))
% 25.54/25.43 [1978]~E(x19781,x19782)+E(f585(x19781,x19783,x19784),f585(x19782,x19783,x19784))
% 25.54/25.43 [1979]~E(x19791,x19792)+E(f585(x19793,x19791,x19794),f585(x19793,x19792,x19794))
% 25.54/25.43 [1980]~E(x19801,x19802)+E(f585(x19803,x19804,x19801),f585(x19803,x19804,x19802))
% 25.54/25.43 [1981]~E(x19811,x19812)+E(f549(x19811,x19813,x19814,x19815,x19816),f549(x19812,x19813,x19814,x19815,x19816))
% 25.54/25.43 [1982]~E(x19821,x19822)+E(f549(x19823,x19821,x19824,x19825,x19826),f549(x19823,x19822,x19824,x19825,x19826))
% 25.54/25.43 [1983]~E(x19831,x19832)+E(f549(x19833,x19834,x19831,x19835,x19836),f549(x19833,x19834,x19832,x19835,x19836))
% 25.54/25.43 [1984]~E(x19841,x19842)+E(f549(x19843,x19844,x19845,x19841,x19846),f549(x19843,x19844,x19845,x19842,x19846))
% 25.54/25.43 [1985]~E(x19851,x19852)+E(f549(x19853,x19854,x19855,x19856,x19851),f549(x19853,x19854,x19855,x19856,x19852))
% 25.54/25.43 [1986]~E(x19861,x19862)+E(f335(x19861,x19863,x19864),f335(x19862,x19863,x19864))
% 25.54/25.43 [1987]~E(x19871,x19872)+E(f335(x19873,x19871,x19874),f335(x19873,x19872,x19874))
% 25.54/25.43 [1988]~E(x19881,x19882)+E(f335(x19883,x19884,x19881),f335(x19883,x19884,x19882))
% 25.54/25.43 [1989]~E(x19891,x19892)+E(f761(x19891,x19893,x19894,x19895,x19896,x19897,x19898),f761(x19892,x19893,x19894,x19895,x19896,x19897,x19898))
% 25.54/25.43 [1990]~E(x19901,x19902)+E(f761(x19903,x19901,x19904,x19905,x19906,x19907,x19908),f761(x19903,x19902,x19904,x19905,x19906,x19907,x19908))
% 25.54/25.43 [1991]~E(x19911,x19912)+E(f761(x19913,x19914,x19911,x19915,x19916,x19917,x19918),f761(x19913,x19914,x19912,x19915,x19916,x19917,x19918))
% 25.54/25.43 [1992]~E(x19921,x19922)+E(f761(x19923,x19924,x19925,x19921,x19926,x19927,x19928),f761(x19923,x19924,x19925,x19922,x19926,x19927,x19928))
% 25.54/25.43 [1993]~E(x19931,x19932)+E(f761(x19933,x19934,x19935,x19936,x19931,x19937,x19938),f761(x19933,x19934,x19935,x19936,x19932,x19937,x19938))
% 25.54/25.43 [1994]~E(x19941,x19942)+E(f761(x19943,x19944,x19945,x19946,x19947,x19941,x19948),f761(x19943,x19944,x19945,x19946,x19947,x19942,x19948))
% 25.54/25.43 [1995]~E(x19951,x19952)+E(f761(x19953,x19954,x19955,x19956,x19957,x19958,x19951),f761(x19953,x19954,x19955,x19956,x19957,x19958,x19952))
% 25.54/25.43 [1996]~E(x19961,x19962)+E(f413(x19961,x19963,x19964,x19965,x19966),f413(x19962,x19963,x19964,x19965,x19966))
% 25.54/25.43 [1997]~E(x19971,x19972)+E(f413(x19973,x19971,x19974,x19975,x19976),f413(x19973,x19972,x19974,x19975,x19976))
% 25.54/25.43 [1998]~E(x19981,x19982)+E(f413(x19983,x19984,x19981,x19985,x19986),f413(x19983,x19984,x19982,x19985,x19986))
% 25.54/25.43 [1999]~E(x19991,x19992)+E(f413(x19993,x19994,x19995,x19991,x19996),f413(x19993,x19994,x19995,x19992,x19996))
% 25.54/25.43 [2000]~E(x20001,x20002)+E(f413(x20003,x20004,x20005,x20006,x20001),f413(x20003,x20004,x20005,x20006,x20002))
% 25.54/25.43 [2001]~E(x20011,x20012)+E(f626(x20011,x20013,x20014),f626(x20012,x20013,x20014))
% 25.54/25.43 [2002]~E(x20021,x20022)+E(f626(x20023,x20021,x20024),f626(x20023,x20022,x20024))
% 25.54/25.43 [2003]~E(x20031,x20032)+E(f626(x20033,x20034,x20031),f626(x20033,x20034,x20032))
% 25.54/25.43 [2004]~E(x20041,x20042)+E(f230(x20041,x20043),f230(x20042,x20043))
% 25.54/25.43 [2005]~E(x20051,x20052)+E(f230(x20053,x20051),f230(x20053,x20052))
% 25.54/25.43 [2006]~E(x20061,x20062)+E(f195(x20061,x20063),f195(x20062,x20063))
% 25.54/25.43 [2007]~E(x20071,x20072)+E(f195(x20073,x20071),f195(x20073,x20072))
% 25.54/25.43 [2008]~E(x20081,x20082)+E(f554(x20081,x20083,x20084),f554(x20082,x20083,x20084))
% 25.54/25.43 [2009]~E(x20091,x20092)+E(f554(x20093,x20091,x20094),f554(x20093,x20092,x20094))
% 25.54/25.43 [2010]~E(x20101,x20102)+E(f554(x20103,x20104,x20101),f554(x20103,x20104,x20102))
% 25.54/25.43 [2011]~E(x20111,x20112)+E(f457(x20111,x20113),f457(x20112,x20113))
% 25.54/25.43 [2012]~E(x20121,x20122)+E(f457(x20123,x20121),f457(x20123,x20122))
% 25.54/25.43 [2013]~E(x20131,x20132)+E(f769(x20131,x20133,x20134),f769(x20132,x20133,x20134))
% 25.54/25.43 [2014]~E(x20141,x20142)+E(f769(x20143,x20141,x20144),f769(x20143,x20142,x20144))
% 25.54/25.43 [2015]~E(x20151,x20152)+E(f769(x20153,x20154,x20151),f769(x20153,x20154,x20152))
% 25.54/25.43 [2016]~E(x20161,x20162)+E(f37(x20161),f37(x20162))
% 25.54/25.43 [2017]~E(x20171,x20172)+E(f884(x20171,x20173,x20174,x20175,x20176),f884(x20172,x20173,x20174,x20175,x20176))
% 25.54/25.43 [2018]~E(x20181,x20182)+E(f884(x20183,x20181,x20184,x20185,x20186),f884(x20183,x20182,x20184,x20185,x20186))
% 25.54/25.43 [2019]~E(x20191,x20192)+E(f884(x20193,x20194,x20191,x20195,x20196),f884(x20193,x20194,x20192,x20195,x20196))
% 25.54/25.43 [2020]~E(x20201,x20202)+E(f884(x20203,x20204,x20205,x20201,x20206),f884(x20203,x20204,x20205,x20202,x20206))
% 25.54/25.43 [2021]~E(x20211,x20212)+E(f884(x20213,x20214,x20215,x20216,x20211),f884(x20213,x20214,x20215,x20216,x20212))
% 25.54/25.43 [2022]~E(x20221,x20222)+E(f495(x20221,x20223,x20224),f495(x20222,x20223,x20224))
% 25.54/25.43 [2023]~E(x20231,x20232)+E(f495(x20233,x20231,x20234),f495(x20233,x20232,x20234))
% 25.54/25.43 [2024]~E(x20241,x20242)+E(f495(x20243,x20244,x20241),f495(x20243,x20244,x20242))
% 25.54/25.43 [2025]~E(x20251,x20252)+E(f820(x20251,x20253,x20254,x20255,x20256,x20257),f820(x20252,x20253,x20254,x20255,x20256,x20257))
% 25.54/25.43 [2026]~E(x20261,x20262)+E(f820(x20263,x20261,x20264,x20265,x20266,x20267),f820(x20263,x20262,x20264,x20265,x20266,x20267))
% 25.54/25.43 [2027]~E(x20271,x20272)+E(f820(x20273,x20274,x20271,x20275,x20276,x20277),f820(x20273,x20274,x20272,x20275,x20276,x20277))
% 25.54/25.43 [2028]~E(x20281,x20282)+E(f820(x20283,x20284,x20285,x20281,x20286,x20287),f820(x20283,x20284,x20285,x20282,x20286,x20287))
% 25.54/25.43 [2029]~E(x20291,x20292)+E(f820(x20293,x20294,x20295,x20296,x20291,x20297),f820(x20293,x20294,x20295,x20296,x20292,x20297))
% 25.54/25.43 [2030]~E(x20301,x20302)+E(f820(x20303,x20304,x20305,x20306,x20307,x20301),f820(x20303,x20304,x20305,x20306,x20307,x20302))
% 25.54/25.43 [2031]~E(x20311,x20312)+E(f898(x20311,x20313,x20314,x20315),f898(x20312,x20313,x20314,x20315))
% 25.54/25.43 [2032]~E(x20321,x20322)+E(f898(x20323,x20321,x20324,x20325),f898(x20323,x20322,x20324,x20325))
% 25.54/25.43 [2033]~E(x20331,x20332)+E(f898(x20333,x20334,x20331,x20335),f898(x20333,x20334,x20332,x20335))
% 25.54/25.43 [2034]~E(x20341,x20342)+E(f898(x20343,x20344,x20345,x20341),f898(x20343,x20344,x20345,x20342))
% 25.54/25.43 [2035]~E(x20351,x20352)+E(f388(x20351,x20353),f388(x20352,x20353))
% 25.54/25.43 [2036]~E(x20361,x20362)+E(f388(x20363,x20361),f388(x20363,x20362))
% 25.54/25.43 [2037]~E(x20371,x20372)+E(f740(x20371,x20373),f740(x20372,x20373))
% 25.54/25.43 [2038]~E(x20381,x20382)+E(f740(x20383,x20381),f740(x20383,x20382))
% 25.54/25.43 [2039]~E(x20391,x20392)+E(f895(x20391,x20393,x20394),f895(x20392,x20393,x20394))
% 25.54/25.43 [2040]~E(x20401,x20402)+E(f895(x20403,x20401,x20404),f895(x20403,x20402,x20404))
% 25.54/25.43 [2041]~E(x20411,x20412)+E(f895(x20413,x20414,x20411),f895(x20413,x20414,x20412))
% 25.54/25.43 [2042]~E(x20421,x20422)+E(f752(x20421,x20423,x20424,x20425,x20426),f752(x20422,x20423,x20424,x20425,x20426))
% 25.54/25.43 [2043]~E(x20431,x20432)+E(f752(x20433,x20431,x20434,x20435,x20436),f752(x20433,x20432,x20434,x20435,x20436))
% 25.54/25.43 [2044]~E(x20441,x20442)+E(f752(x20443,x20444,x20441,x20445,x20446),f752(x20443,x20444,x20442,x20445,x20446))
% 25.54/25.43 [2045]~E(x20451,x20452)+E(f752(x20453,x20454,x20455,x20451,x20456),f752(x20453,x20454,x20455,x20452,x20456))
% 25.54/25.43 [2046]~E(x20461,x20462)+E(f752(x20463,x20464,x20465,x20466,x20461),f752(x20463,x20464,x20465,x20466,x20462))
% 25.54/25.43 [2047]~E(x20471,x20472)+E(f858(x20471,x20473,x20474),f858(x20472,x20473,x20474))
% 25.54/25.43 [2048]~E(x20481,x20482)+E(f858(x20483,x20481,x20484),f858(x20483,x20482,x20484))
% 25.54/25.43 [2049]~E(x20491,x20492)+E(f858(x20493,x20494,x20491),f858(x20493,x20494,x20492))
% 25.54/25.43 [2050]~E(x20501,x20502)+E(f571(x20501,x20503,x20504,x20505),f571(x20502,x20503,x20504,x20505))
% 25.54/25.43 [2051]~E(x20511,x20512)+E(f571(x20513,x20511,x20514,x20515),f571(x20513,x20512,x20514,x20515))
% 25.54/25.43 [2052]~E(x20521,x20522)+E(f571(x20523,x20524,x20521,x20525),f571(x20523,x20524,x20522,x20525))
% 25.54/25.43 [2053]~E(x20531,x20532)+E(f571(x20533,x20534,x20535,x20531),f571(x20533,x20534,x20535,x20532))
% 25.54/25.43 [2054]~E(x20541,x20542)+E(f551(x20541,x20543,x20544,x20545,x20546),f551(x20542,x20543,x20544,x20545,x20546))
% 25.54/25.43 [2055]~E(x20551,x20552)+E(f551(x20553,x20551,x20554,x20555,x20556),f551(x20553,x20552,x20554,x20555,x20556))
% 25.54/25.43 [2056]~E(x20561,x20562)+E(f551(x20563,x20564,x20561,x20565,x20566),f551(x20563,x20564,x20562,x20565,x20566))
% 25.54/25.43 [2057]~E(x20571,x20572)+E(f551(x20573,x20574,x20575,x20571,x20576),f551(x20573,x20574,x20575,x20572,x20576))
% 25.54/25.43 [2058]~E(x20581,x20582)+E(f551(x20583,x20584,x20585,x20586,x20581),f551(x20583,x20584,x20585,x20586,x20582))
% 25.54/25.43 [2059]~E(x20591,x20592)+E(f673(x20591,x20593),f673(x20592,x20593))
% 25.54/25.43 [2060]~E(x20601,x20602)+E(f673(x20603,x20601),f673(x20603,x20602))
% 25.54/25.43 [2061]~E(x20611,x20612)+E(f465(x20611,x20613,x20614),f465(x20612,x20613,x20614))
% 25.54/25.43 [2062]~E(x20621,x20622)+E(f465(x20623,x20621,x20624),f465(x20623,x20622,x20624))
% 25.54/25.43 [2063]~E(x20631,x20632)+E(f465(x20633,x20634,x20631),f465(x20633,x20634,x20632))
% 25.54/25.43 [2064]~E(x20641,x20642)+E(f384(x20641,x20643,x20644,x20645,x20646,x20647),f384(x20642,x20643,x20644,x20645,x20646,x20647))
% 25.54/25.43 [2065]~E(x20651,x20652)+E(f384(x20653,x20651,x20654,x20655,x20656,x20657),f384(x20653,x20652,x20654,x20655,x20656,x20657))
% 25.54/25.43 [2066]~E(x20661,x20662)+E(f384(x20663,x20664,x20661,x20665,x20666,x20667),f384(x20663,x20664,x20662,x20665,x20666,x20667))
% 25.54/25.43 [2067]~E(x20671,x20672)+E(f384(x20673,x20674,x20675,x20671,x20676,x20677),f384(x20673,x20674,x20675,x20672,x20676,x20677))
% 25.54/25.43 [2068]~E(x20681,x20682)+E(f384(x20683,x20684,x20685,x20686,x20681,x20687),f384(x20683,x20684,x20685,x20686,x20682,x20687))
% 25.54/25.43 [2069]~E(x20691,x20692)+E(f384(x20693,x20694,x20695,x20696,x20697,x20691),f384(x20693,x20694,x20695,x20696,x20697,x20692))
% 25.54/25.43 [2070]~E(x20701,x20702)+E(f284(x20701,x20703,x20704),f284(x20702,x20703,x20704))
% 25.54/25.43 [2071]~E(x20711,x20712)+E(f284(x20713,x20711,x20714),f284(x20713,x20712,x20714))
% 25.54/25.43 [2072]~E(x20721,x20722)+E(f284(x20723,x20724,x20721),f284(x20723,x20724,x20722))
% 25.54/25.43 [2073]~E(x20731,x20732)+E(f849(x20731,x20733,x20734,x20735,x20736,x20737,x20738),f849(x20732,x20733,x20734,x20735,x20736,x20737,x20738))
% 25.54/25.43 [2074]~E(x20741,x20742)+E(f849(x20743,x20741,x20744,x20745,x20746,x20747,x20748),f849(x20743,x20742,x20744,x20745,x20746,x20747,x20748))
% 25.54/25.43 [2075]~E(x20751,x20752)+E(f849(x20753,x20754,x20751,x20755,x20756,x20757,x20758),f849(x20753,x20754,x20752,x20755,x20756,x20757,x20758))
% 25.54/25.43 [2076]~E(x20761,x20762)+E(f849(x20763,x20764,x20765,x20761,x20766,x20767,x20768),f849(x20763,x20764,x20765,x20762,x20766,x20767,x20768))
% 25.54/25.43 [2077]~E(x20771,x20772)+E(f849(x20773,x20774,x20775,x20776,x20771,x20777,x20778),f849(x20773,x20774,x20775,x20776,x20772,x20777,x20778))
% 25.54/25.43 [2078]~E(x20781,x20782)+E(f849(x20783,x20784,x20785,x20786,x20787,x20781,x20788),f849(x20783,x20784,x20785,x20786,x20787,x20782,x20788))
% 25.54/25.43 [2079]~E(x20791,x20792)+E(f849(x20793,x20794,x20795,x20796,x20797,x20798,x20791),f849(x20793,x20794,x20795,x20796,x20797,x20798,x20792))
% 25.54/25.43 [2080]~E(x20801,x20802)+E(f463(x20801,x20803,x20804,x20805),f463(x20802,x20803,x20804,x20805))
% 25.54/25.43 [2081]~E(x20811,x20812)+E(f463(x20813,x20811,x20814,x20815),f463(x20813,x20812,x20814,x20815))
% 25.54/25.43 [2082]~E(x20821,x20822)+E(f463(x20823,x20824,x20821,x20825),f463(x20823,x20824,x20822,x20825))
% 25.54/25.43 [2083]~E(x20831,x20832)+E(f463(x20833,x20834,x20835,x20831),f463(x20833,x20834,x20835,x20832))
% 25.54/25.43 [2084]~E(x20841,x20842)+E(f897(x20841,x20843,x20844),f897(x20842,x20843,x20844))
% 25.54/25.43 [2085]~E(x20851,x20852)+E(f897(x20853,x20851,x20854),f897(x20853,x20852,x20854))
% 25.54/25.43 [2086]~E(x20861,x20862)+E(f897(x20863,x20864,x20861),f897(x20863,x20864,x20862))
% 25.54/25.43 [2087]~E(x20871,x20872)+E(f373(x20871,x20873,x20874,x20875),f373(x20872,x20873,x20874,x20875))
% 25.54/25.43 [2088]~E(x20881,x20882)+E(f373(x20883,x20881,x20884,x20885),f373(x20883,x20882,x20884,x20885))
% 25.54/25.43 [2089]~E(x20891,x20892)+E(f373(x20893,x20894,x20891,x20895),f373(x20893,x20894,x20892,x20895))
% 25.54/25.43 [2090]~E(x20901,x20902)+E(f373(x20903,x20904,x20905,x20901),f373(x20903,x20904,x20905,x20902))
% 25.54/25.43 [2091]~E(x20911,x20912)+E(f201(x20911),f201(x20912))
% 25.54/25.43 [2092]~E(x20921,x20922)+E(f361(x20921,x20923,x20924,x20925,x20926),f361(x20922,x20923,x20924,x20925,x20926))
% 25.54/25.43 [2093]~E(x20931,x20932)+E(f361(x20933,x20931,x20934,x20935,x20936),f361(x20933,x20932,x20934,x20935,x20936))
% 25.54/25.43 [2094]~E(x20941,x20942)+E(f361(x20943,x20944,x20941,x20945,x20946),f361(x20943,x20944,x20942,x20945,x20946))
% 25.54/25.43 [2095]~E(x20951,x20952)+E(f361(x20953,x20954,x20955,x20951,x20956),f361(x20953,x20954,x20955,x20952,x20956))
% 25.54/25.43 [2096]~E(x20961,x20962)+E(f361(x20963,x20964,x20965,x20966,x20961),f361(x20963,x20964,x20965,x20966,x20962))
% 25.54/25.43 [2097]~E(x20971,x20972)+E(f574(x20971,x20973,x20974,x20975,x20976,x20977),f574(x20972,x20973,x20974,x20975,x20976,x20977))
% 25.54/25.43 [2098]~E(x20981,x20982)+E(f574(x20983,x20981,x20984,x20985,x20986,x20987),f574(x20983,x20982,x20984,x20985,x20986,x20987))
% 25.54/25.43 [2099]~E(x20991,x20992)+E(f574(x20993,x20994,x20991,x20995,x20996,x20997),f574(x20993,x20994,x20992,x20995,x20996,x20997))
% 25.54/25.43 [2100]~E(x21001,x21002)+E(f574(x21003,x21004,x21005,x21001,x21006,x21007),f574(x21003,x21004,x21005,x21002,x21006,x21007))
% 25.54/25.43 [2101]~E(x21011,x21012)+E(f574(x21013,x21014,x21015,x21016,x21011,x21017),f574(x21013,x21014,x21015,x21016,x21012,x21017))
% 25.54/25.43 [2102]~E(x21021,x21022)+E(f574(x21023,x21024,x21025,x21026,x21027,x21021),f574(x21023,x21024,x21025,x21026,x21027,x21022))
% 25.54/25.43 [2103]~E(x21031,x21032)+E(f327(x21031,x21033,x21034),f327(x21032,x21033,x21034))
% 25.54/25.43 [2104]~E(x21041,x21042)+E(f327(x21043,x21041,x21044),f327(x21043,x21042,x21044))
% 25.54/25.43 [2105]~E(x21051,x21052)+E(f327(x21053,x21054,x21051),f327(x21053,x21054,x21052))
% 25.54/25.43 [2106]~E(x21061,x21062)+E(f650(x21061,x21063,x21064,x21065),f650(x21062,x21063,x21064,x21065))
% 25.54/25.43 [2107]~E(x21071,x21072)+E(f650(x21073,x21071,x21074,x21075),f650(x21073,x21072,x21074,x21075))
% 25.54/25.43 [2108]~E(x21081,x21082)+E(f650(x21083,x21084,x21081,x21085),f650(x21083,x21084,x21082,x21085))
% 25.54/25.43 [2109]~E(x21091,x21092)+E(f650(x21093,x21094,x21095,x21091),f650(x21093,x21094,x21095,x21092))
% 25.54/25.43 [2110]~E(x21101,x21102)+E(f504(x21101,x21103,x21104),f504(x21102,x21103,x21104))
% 25.54/25.43 [2111]~E(x21111,x21112)+E(f504(x21113,x21111,x21114),f504(x21113,x21112,x21114))
% 25.54/25.43 [2112]~E(x21121,x21122)+E(f504(x21123,x21124,x21121),f504(x21123,x21124,x21122))
% 25.54/25.43 [2113]~E(x21131,x21132)+E(f550(x21131,x21133,x21134,x21135),f550(x21132,x21133,x21134,x21135))
% 25.54/25.43 [2114]~E(x21141,x21142)+E(f550(x21143,x21141,x21144,x21145),f550(x21143,x21142,x21144,x21145))
% 25.54/25.43 [2115]~E(x21151,x21152)+E(f550(x21153,x21154,x21151,x21155),f550(x21153,x21154,x21152,x21155))
% 25.54/25.43 [2116]~E(x21161,x21162)+E(f550(x21163,x21164,x21165,x21161),f550(x21163,x21164,x21165,x21162))
% 25.54/25.43 [2117]~E(x21171,x21172)+E(f289(x21171,x21173,x21174),f289(x21172,x21173,x21174))
% 25.54/25.43 [2118]~E(x21181,x21182)+E(f289(x21183,x21181,x21184),f289(x21183,x21182,x21184))
% 25.54/25.43 [2119]~E(x21191,x21192)+E(f289(x21193,x21194,x21191),f289(x21193,x21194,x21192))
% 25.54/25.43 [2120]~E(x21201,x21202)+E(f723(x21201,x21203,x21204),f723(x21202,x21203,x21204))
% 25.54/25.43 [2121]~E(x21211,x21212)+E(f723(x21213,x21211,x21214),f723(x21213,x21212,x21214))
% 25.54/25.43 [2122]~E(x21221,x21222)+E(f723(x21223,x21224,x21221),f723(x21223,x21224,x21222))
% 25.54/25.43 [2123]~E(x21231,x21232)+E(f363(x21231,x21233,x21234),f363(x21232,x21233,x21234))
% 25.54/25.43 [2124]~E(x21241,x21242)+E(f363(x21243,x21241,x21244),f363(x21243,x21242,x21244))
% 25.54/25.43 [2125]~E(x21251,x21252)+E(f363(x21253,x21254,x21251),f363(x21253,x21254,x21252))
% 25.54/25.43 [2126]~E(x21261,x21262)+E(f777(x21261,x21263,x21264,x21265),f777(x21262,x21263,x21264,x21265))
% 25.54/25.43 [2127]~E(x21271,x21272)+E(f777(x21273,x21271,x21274,x21275),f777(x21273,x21272,x21274,x21275))
% 25.54/25.43 [2128]~E(x21281,x21282)+E(f777(x21283,x21284,x21281,x21285),f777(x21283,x21284,x21282,x21285))
% 25.54/25.43 [2129]~E(x21291,x21292)+E(f777(x21293,x21294,x21295,x21291),f777(x21293,x21294,x21295,x21292))
% 25.54/25.43 [2130]~E(x21301,x21302)+E(f918(x21301,x21303,x21304,x21305,x21306),f918(x21302,x21303,x21304,x21305,x21306))
% 25.54/25.43 [2131]~E(x21311,x21312)+E(f918(x21313,x21311,x21314,x21315,x21316),f918(x21313,x21312,x21314,x21315,x21316))
% 25.54/25.43 [2132]~E(x21321,x21322)+E(f918(x21323,x21324,x21321,x21325,x21326),f918(x21323,x21324,x21322,x21325,x21326))
% 25.54/25.43 [2133]~E(x21331,x21332)+E(f918(x21333,x21334,x21335,x21331,x21336),f918(x21333,x21334,x21335,x21332,x21336))
% 25.54/25.43 [2134]~E(x21341,x21342)+E(f918(x21343,x21344,x21345,x21346,x21341),f918(x21343,x21344,x21345,x21346,x21342))
% 25.54/25.43 [2135]~E(x21351,x21352)+E(f548(x21351,x21353),f548(x21352,x21353))
% 25.54/25.43 [2136]~E(x21361,x21362)+E(f548(x21363,x21361),f548(x21363,x21362))
% 25.54/25.43 [2137]~E(x21371,x21372)+E(f638(x21371,x21373,x21374,x21375,x21376),f638(x21372,x21373,x21374,x21375,x21376))
% 25.54/25.43 [2138]~E(x21381,x21382)+E(f638(x21383,x21381,x21384,x21385,x21386),f638(x21383,x21382,x21384,x21385,x21386))
% 25.54/25.43 [2139]~E(x21391,x21392)+E(f638(x21393,x21394,x21391,x21395,x21396),f638(x21393,x21394,x21392,x21395,x21396))
% 25.54/25.43 [2140]~E(x21401,x21402)+E(f638(x21403,x21404,x21405,x21401,x21406),f638(x21403,x21404,x21405,x21402,x21406))
% 25.54/25.43 [2141]~E(x21411,x21412)+E(f638(x21413,x21414,x21415,x21416,x21411),f638(x21413,x21414,x21415,x21416,x21412))
% 25.54/25.43 [2142]~E(x21421,x21422)+E(f418(x21421,x21423,x21424),f418(x21422,x21423,x21424))
% 25.54/25.43 [2143]~E(x21431,x21432)+E(f418(x21433,x21431,x21434),f418(x21433,x21432,x21434))
% 25.54/25.43 [2144]~E(x21441,x21442)+E(f418(x21443,x21444,x21441),f418(x21443,x21444,x21442))
% 25.54/25.43 [2145]~E(x21451,x21452)+E(f366(x21451,x21453,x21454,x21455,x21456),f366(x21452,x21453,x21454,x21455,x21456))
% 25.54/25.43 [2146]~E(x21461,x21462)+E(f366(x21463,x21461,x21464,x21465,x21466),f366(x21463,x21462,x21464,x21465,x21466))
% 25.54/25.43 [2147]~E(x21471,x21472)+E(f366(x21473,x21474,x21471,x21475,x21476),f366(x21473,x21474,x21472,x21475,x21476))
% 25.54/25.43 [2148]~E(x21481,x21482)+E(f366(x21483,x21484,x21485,x21481,x21486),f366(x21483,x21484,x21485,x21482,x21486))
% 25.54/25.43 [2149]~E(x21491,x21492)+E(f366(x21493,x21494,x21495,x21496,x21491),f366(x21493,x21494,x21495,x21496,x21492))
% 25.54/25.43 [2150]~E(x21501,x21502)+E(f524(x21501),f524(x21502))
% 25.54/25.43 [2151]~E(x21511,x21512)+E(f508(x21511,x21513,x21514),f508(x21512,x21513,x21514))
% 25.54/25.43 [2152]~E(x21521,x21522)+E(f508(x21523,x21521,x21524),f508(x21523,x21522,x21524))
% 25.54/25.43 [2153]~E(x21531,x21532)+E(f508(x21533,x21534,x21531),f508(x21533,x21534,x21532))
% 25.54/25.43 [2154]~E(x21541,x21542)+E(f881(x21541,x21543,x21544,x21545),f881(x21542,x21543,x21544,x21545))
% 25.54/25.43 [2155]~E(x21551,x21552)+E(f881(x21553,x21551,x21554,x21555),f881(x21553,x21552,x21554,x21555))
% 25.54/25.43 [2156]~E(x21561,x21562)+E(f881(x21563,x21564,x21561,x21565),f881(x21563,x21564,x21562,x21565))
% 25.54/25.43 [2157]~E(x21571,x21572)+E(f881(x21573,x21574,x21575,x21571),f881(x21573,x21574,x21575,x21572))
% 25.54/25.43 [2158]~E(x21581,x21582)+E(f461(x21581,x21583,x21584),f461(x21582,x21583,x21584))
% 25.54/25.43 [2159]~E(x21591,x21592)+E(f461(x21593,x21591,x21594),f461(x21593,x21592,x21594))
% 25.54/25.43 [2160]~E(x21601,x21602)+E(f461(x21603,x21604,x21601),f461(x21603,x21604,x21602))
% 25.54/25.43 [2161]~E(x21611,x21612)+E(f491(x21611,x21613,x21614,x21615,x21616),f491(x21612,x21613,x21614,x21615,x21616))
% 25.54/25.43 [2162]~E(x21621,x21622)+E(f491(x21623,x21621,x21624,x21625,x21626),f491(x21623,x21622,x21624,x21625,x21626))
% 25.54/25.43 [2163]~E(x21631,x21632)+E(f491(x21633,x21634,x21631,x21635,x21636),f491(x21633,x21634,x21632,x21635,x21636))
% 25.54/25.43 [2164]~E(x21641,x21642)+E(f491(x21643,x21644,x21645,x21641,x21646),f491(x21643,x21644,x21645,x21642,x21646))
% 25.54/25.43 [2165]~E(x21651,x21652)+E(f491(x21653,x21654,x21655,x21656,x21651),f491(x21653,x21654,x21655,x21656,x21652))
% 25.54/25.43 [2166]~E(x21661,x21662)+E(f462(x21661,x21663,x21664),f462(x21662,x21663,x21664))
% 25.54/25.43 [2167]~E(x21671,x21672)+E(f462(x21673,x21671,x21674),f462(x21673,x21672,x21674))
% 25.54/25.43 [2168]~E(x21681,x21682)+E(f462(x21683,x21684,x21681),f462(x21683,x21684,x21682))
% 25.54/25.43 [2169]~E(x21691,x21692)+E(f333(x21691,x21693,x21694),f333(x21692,x21693,x21694))
% 25.54/25.43 [2170]~E(x21701,x21702)+E(f333(x21703,x21701,x21704),f333(x21703,x21702,x21704))
% 25.54/25.43 [2171]~E(x21711,x21712)+E(f333(x21713,x21714,x21711),f333(x21713,x21714,x21712))
% 25.54/25.43 [2172]~E(x21721,x21722)+E(f679(x21721,x21723,x21724),f679(x21722,x21723,x21724))
% 25.54/25.43 [2173]~E(x21731,x21732)+E(f679(x21733,x21731,x21734),f679(x21733,x21732,x21734))
% 25.54/25.43 [2174]~E(x21741,x21742)+E(f679(x21743,x21744,x21741),f679(x21743,x21744,x21742))
% 25.54/25.43 [2175]~E(x21751,x21752)+E(f478(x21751,x21753,x21754,x21755,x21756),f478(x21752,x21753,x21754,x21755,x21756))
% 25.54/25.43 [2176]~E(x21761,x21762)+E(f478(x21763,x21761,x21764,x21765,x21766),f478(x21763,x21762,x21764,x21765,x21766))
% 25.54/25.43 [2177]~E(x21771,x21772)+E(f478(x21773,x21774,x21771,x21775,x21776),f478(x21773,x21774,x21772,x21775,x21776))
% 25.54/25.43 [2178]~E(x21781,x21782)+E(f478(x21783,x21784,x21785,x21781,x21786),f478(x21783,x21784,x21785,x21782,x21786))
% 25.54/25.43 [2179]~E(x21791,x21792)+E(f478(x21793,x21794,x21795,x21796,x21791),f478(x21793,x21794,x21795,x21796,x21792))
% 25.54/25.43 [2180]~E(x21801,x21802)+E(f891(x21801,x21803),f891(x21802,x21803))
% 25.54/25.43 [2181]~E(x21811,x21812)+E(f891(x21813,x21811),f891(x21813,x21812))
% 25.54/25.43 [2182]~E(x21821,x21822)+E(f843(x21821,x21823,x21824,x21825,x21826,x21827,x21828,x21829),f843(x21822,x21823,x21824,x21825,x21826,x21827,x21828,x21829))
% 25.54/25.43 [2183]~E(x21831,x21832)+E(f843(x21833,x21831,x21834,x21835,x21836,x21837,x21838,x21839),f843(x21833,x21832,x21834,x21835,x21836,x21837,x21838,x21839))
% 25.54/25.43 [2184]~E(x21841,x21842)+E(f843(x21843,x21844,x21841,x21845,x21846,x21847,x21848,x21849),f843(x21843,x21844,x21842,x21845,x21846,x21847,x21848,x21849))
% 25.54/25.43 [2185]~E(x21851,x21852)+E(f843(x21853,x21854,x21855,x21851,x21856,x21857,x21858,x21859),f843(x21853,x21854,x21855,x21852,x21856,x21857,x21858,x21859))
% 25.54/25.43 [2186]~E(x21861,x21862)+E(f843(x21863,x21864,x21865,x21866,x21861,x21867,x21868,x21869),f843(x21863,x21864,x21865,x21866,x21862,x21867,x21868,x21869))
% 25.54/25.43 [2187]~E(x21871,x21872)+E(f843(x21873,x21874,x21875,x21876,x21877,x21871,x21878,x21879),f843(x21873,x21874,x21875,x21876,x21877,x21872,x21878,x21879))
% 25.54/25.43 [2188]~E(x21881,x21882)+E(f843(x21883,x21884,x21885,x21886,x21887,x21888,x21881,x21889),f843(x21883,x21884,x21885,x21886,x21887,x21888,x21882,x21889))
% 25.54/25.43 [2189]~E(x21891,x21892)+E(f843(x21893,x21894,x21895,x21896,x21897,x21898,x21899,x21891),f843(x21893,x21894,x21895,x21896,x21897,x21898,x21899,x21892))
% 25.54/25.43 [2190]~E(x21901,x21902)+E(f497(x21901,x21903,x21904),f497(x21902,x21903,x21904))
% 25.54/25.43 [2191]~E(x21911,x21912)+E(f497(x21913,x21911,x21914),f497(x21913,x21912,x21914))
% 25.54/25.43 [2192]~E(x21921,x21922)+E(f497(x21923,x21924,x21921),f497(x21923,x21924,x21922))
% 25.54/25.43 [2193]~E(x21931,x21932)+E(f471(x21931,x21933),f471(x21932,x21933))
% 25.54/25.43 [2194]~E(x21941,x21942)+E(f471(x21943,x21941),f471(x21943,x21942))
% 25.54/25.43 [2195]~E(x21951,x21952)+E(f765(x21951,x21953,x21954),f765(x21952,x21953,x21954))
% 25.54/25.43 [2196]~E(x21961,x21962)+E(f765(x21963,x21961,x21964),f765(x21963,x21962,x21964))
% 25.54/25.43 [2197]~E(x21971,x21972)+E(f765(x21973,x21974,x21971),f765(x21973,x21974,x21972))
% 25.54/25.43 [2198]~E(x21981,x21982)+E(f493(x21981,x21983),f493(x21982,x21983))
% 25.54/25.43 [2199]~E(x21991,x21992)+E(f493(x21993,x21991),f493(x21993,x21992))
% 25.54/25.43 [2200]~E(x22001,x22002)+E(f403(x22001,x22003,x22004,x22005),f403(x22002,x22003,x22004,x22005))
% 25.54/25.43 [2201]~E(x22011,x22012)+E(f403(x22013,x22011,x22014,x22015),f403(x22013,x22012,x22014,x22015))
% 25.54/25.43 [2202]~E(x22021,x22022)+E(f403(x22023,x22024,x22021,x22025),f403(x22023,x22024,x22022,x22025))
% 25.54/25.43 [2203]~E(x22031,x22032)+E(f403(x22033,x22034,x22035,x22031),f403(x22033,x22034,x22035,x22032))
% 25.54/25.43 [2204]~E(x22041,x22042)+E(f448(x22041,x22043,x22044),f448(x22042,x22043,x22044))
% 25.54/25.43 [2205]~E(x22051,x22052)+E(f448(x22053,x22051,x22054),f448(x22053,x22052,x22054))
% 25.54/25.43 [2206]~E(x22061,x22062)+E(f448(x22063,x22064,x22061),f448(x22063,x22064,x22062))
% 25.54/25.43 [2207]~E(x22071,x22072)+E(f553(x22071,x22073),f553(x22072,x22073))
% 25.54/25.43 [2208]~E(x22081,x22082)+E(f553(x22083,x22081),f553(x22083,x22082))
% 25.54/25.43 [2209]~E(x22091,x22092)+E(f200(x22091,x22093,x22094,x22095,x22096,x22097,x22098),f200(x22092,x22093,x22094,x22095,x22096,x22097,x22098))
% 25.54/25.43 [2210]~E(x22101,x22102)+E(f200(x22103,x22101,x22104,x22105,x22106,x22107,x22108),f200(x22103,x22102,x22104,x22105,x22106,x22107,x22108))
% 25.54/25.43 [2211]~E(x22111,x22112)+E(f200(x22113,x22114,x22111,x22115,x22116,x22117,x22118),f200(x22113,x22114,x22112,x22115,x22116,x22117,x22118))
% 25.54/25.43 [2212]~E(x22121,x22122)+E(f200(x22123,x22124,x22125,x22121,x22126,x22127,x22128),f200(x22123,x22124,x22125,x22122,x22126,x22127,x22128))
% 25.54/25.43 [2213]~E(x22131,x22132)+E(f200(x22133,x22134,x22135,x22136,x22131,x22137,x22138),f200(x22133,x22134,x22135,x22136,x22132,x22137,x22138))
% 25.54/25.43 [2214]~E(x22141,x22142)+E(f200(x22143,x22144,x22145,x22146,x22147,x22141,x22148),f200(x22143,x22144,x22145,x22146,x22147,x22142,x22148))
% 25.54/25.43 [2215]~E(x22151,x22152)+E(f200(x22153,x22154,x22155,x22156,x22157,x22158,x22151),f200(x22153,x22154,x22155,x22156,x22157,x22158,x22152))
% 25.54/25.43 [2216]~E(x22161,x22162)+E(f267(x22161,x22163),f267(x22162,x22163))
% 25.54/25.43 [2217]~E(x22171,x22172)+E(f267(x22173,x22171),f267(x22173,x22172))
% 25.54/25.43 [2218]~E(x22181,x22182)+E(f604(x22181,x22183,x22184,x22185,x22186,x22187),f604(x22182,x22183,x22184,x22185,x22186,x22187))
% 25.54/25.43 [2219]~E(x22191,x22192)+E(f604(x22193,x22191,x22194,x22195,x22196,x22197),f604(x22193,x22192,x22194,x22195,x22196,x22197))
% 25.54/25.43 [2220]~E(x22201,x22202)+E(f604(x22203,x22204,x22201,x22205,x22206,x22207),f604(x22203,x22204,x22202,x22205,x22206,x22207))
% 25.54/25.43 [2221]~E(x22211,x22212)+E(f604(x22213,x22214,x22215,x22211,x22216,x22217),f604(x22213,x22214,x22215,x22212,x22216,x22217))
% 25.54/25.43 [2222]~E(x22221,x22222)+E(f604(x22223,x22224,x22225,x22226,x22221,x22227),f604(x22223,x22224,x22225,x22226,x22222,x22227))
% 25.54/25.43 [2223]~E(x22231,x22232)+E(f604(x22233,x22234,x22235,x22236,x22237,x22231),f604(x22233,x22234,x22235,x22236,x22237,x22232))
% 25.54/25.43 [2224]~E(x22241,x22242)+E(f822(x22241,x22243,x22244,x22245,x22246),f822(x22242,x22243,x22244,x22245,x22246))
% 25.54/25.43 [2225]~E(x22251,x22252)+E(f822(x22253,x22251,x22254,x22255,x22256),f822(x22253,x22252,x22254,x22255,x22256))
% 25.54/25.43 [2226]~E(x22261,x22262)+E(f822(x22263,x22264,x22261,x22265,x22266),f822(x22263,x22264,x22262,x22265,x22266))
% 25.54/25.43 [2227]~E(x22271,x22272)+E(f822(x22273,x22274,x22275,x22271,x22276),f822(x22273,x22274,x22275,x22272,x22276))
% 25.54/25.43 [2228]~E(x22281,x22282)+E(f822(x22283,x22284,x22285,x22286,x22281),f822(x22283,x22284,x22285,x22286,x22282))
% 25.54/25.43 [2229]~E(x22291,x22292)+E(f684(x22291,x22293,x22294,x22295),f684(x22292,x22293,x22294,x22295))
% 25.54/25.43 [2230]~E(x22301,x22302)+E(f684(x22303,x22301,x22304,x22305),f684(x22303,x22302,x22304,x22305))
% 25.54/25.43 [2231]~E(x22311,x22312)+E(f684(x22313,x22314,x22311,x22315),f684(x22313,x22314,x22312,x22315))
% 25.54/25.43 [2232]~E(x22321,x22322)+E(f684(x22323,x22324,x22325,x22321),f684(x22323,x22324,x22325,x22322))
% 25.54/25.43 [2233]~E(x22331,x22332)+E(f864(x22331,x22333),f864(x22332,x22333))
% 25.54/25.43 [2234]~E(x22341,x22342)+E(f864(x22343,x22341),f864(x22343,x22342))
% 25.54/25.43 [2235]~E(x22351,x22352)+E(f395(x22351,x22353),f395(x22352,x22353))
% 25.54/25.43 [2236]~E(x22361,x22362)+E(f395(x22363,x22361),f395(x22363,x22362))
% 25.54/25.43 [2237]~E(x22371,x22372)+E(f269(x22371,x22373,x22374,x22375),f269(x22372,x22373,x22374,x22375))
% 25.54/25.43 [2238]~E(x22381,x22382)+E(f269(x22383,x22381,x22384,x22385),f269(x22383,x22382,x22384,x22385))
% 25.54/25.43 [2239]~E(x22391,x22392)+E(f269(x22393,x22394,x22391,x22395),f269(x22393,x22394,x22392,x22395))
% 25.54/25.43 [2240]~E(x22401,x22402)+E(f269(x22403,x22404,x22405,x22401),f269(x22403,x22404,x22405,x22402))
% 25.54/25.43 [2241]~E(x22411,x22412)+E(f358(x22411),f358(x22412))
% 25.54/25.43 [2242]~E(x22421,x22422)+E(f913(x22421),f913(x22422))
% 25.54/25.43 [2243]~E(x22431,x22432)+E(f451(x22431,x22433,x22434),f451(x22432,x22433,x22434))
% 25.54/25.43 [2244]~E(x22441,x22442)+E(f451(x22443,x22441,x22444),f451(x22443,x22442,x22444))
% 25.54/25.43 [2245]~E(x22451,x22452)+E(f451(x22453,x22454,x22451),f451(x22453,x22454,x22452))
% 25.54/25.43 [2246]~E(x22461,x22462)+E(f687(x22461,x22463,x22464,x22465,x22466),f687(x22462,x22463,x22464,x22465,x22466))
% 25.54/25.43 [2247]~E(x22471,x22472)+E(f687(x22473,x22471,x22474,x22475,x22476),f687(x22473,x22472,x22474,x22475,x22476))
% 25.54/25.43 [2248]~E(x22481,x22482)+E(f687(x22483,x22484,x22481,x22485,x22486),f687(x22483,x22484,x22482,x22485,x22486))
% 25.54/25.43 [2249]~E(x22491,x22492)+E(f687(x22493,x22494,x22495,x22491,x22496),f687(x22493,x22494,x22495,x22492,x22496))
% 25.54/25.43 [2250]~E(x22501,x22502)+E(f687(x22503,x22504,x22505,x22506,x22501),f687(x22503,x22504,x22505,x22506,x22502))
% 25.54/25.43 [2251]~E(x22511,x22512)+E(f634(x22511,x22513,x22514,x22515,x22516),f634(x22512,x22513,x22514,x22515,x22516))
% 25.54/25.43 [2252]~E(x22521,x22522)+E(f634(x22523,x22521,x22524,x22525,x22526),f634(x22523,x22522,x22524,x22525,x22526))
% 25.54/25.43 [2253]~E(x22531,x22532)+E(f634(x22533,x22534,x22531,x22535,x22536),f634(x22533,x22534,x22532,x22535,x22536))
% 25.54/25.43 [2254]~E(x22541,x22542)+E(f634(x22543,x22544,x22545,x22541,x22546),f634(x22543,x22544,x22545,x22542,x22546))
% 25.54/25.43 [2255]~E(x22551,x22552)+E(f634(x22553,x22554,x22555,x22556,x22551),f634(x22553,x22554,x22555,x22556,x22552))
% 25.54/25.43 [2256]~E(x22561,x22562)+E(f406(x22561),f406(x22562))
% 25.54/25.43 [2257]~E(x22571,x22572)+E(f569(x22571,x22573),f569(x22572,x22573))
% 25.54/25.43 [2258]~E(x22581,x22582)+E(f569(x22583,x22581),f569(x22583,x22582))
% 25.54/25.43 [2259]~E(x22591,x22592)+E(f914(x22591,x22593,x22594),f914(x22592,x22593,x22594))
% 25.54/25.43 [2260]~E(x22601,x22602)+E(f914(x22603,x22601,x22604),f914(x22603,x22602,x22604))
% 25.54/25.43 [2261]~E(x22611,x22612)+E(f914(x22613,x22614,x22611),f914(x22613,x22614,x22612))
% 25.54/25.43 [2262]~E(x22621,x22622)+E(f204(x22621,x22623,x22624,x22625,x22626,x22627,x22628),f204(x22622,x22623,x22624,x22625,x22626,x22627,x22628))
% 25.54/25.43 [2263]~E(x22631,x22632)+E(f204(x22633,x22631,x22634,x22635,x22636,x22637,x22638),f204(x22633,x22632,x22634,x22635,x22636,x22637,x22638))
% 25.54/25.43 [2264]~E(x22641,x22642)+E(f204(x22643,x22644,x22641,x22645,x22646,x22647,x22648),f204(x22643,x22644,x22642,x22645,x22646,x22647,x22648))
% 25.54/25.43 [2265]~E(x22651,x22652)+E(f204(x22653,x22654,x22655,x22651,x22656,x22657,x22658),f204(x22653,x22654,x22655,x22652,x22656,x22657,x22658))
% 25.54/25.43 [2266]~E(x22661,x22662)+E(f204(x22663,x22664,x22665,x22666,x22661,x22667,x22668),f204(x22663,x22664,x22665,x22666,x22662,x22667,x22668))
% 25.54/25.43 [2267]~E(x22671,x22672)+E(f204(x22673,x22674,x22675,x22676,x22677,x22671,x22678),f204(x22673,x22674,x22675,x22676,x22677,x22672,x22678))
% 25.54/25.43 [2268]~E(x22681,x22682)+E(f204(x22683,x22684,x22685,x22686,x22687,x22688,x22681),f204(x22683,x22684,x22685,x22686,x22687,x22688,x22682))
% 25.54/25.43 [2269]~E(x22691,x22692)+E(f392(x22691,x22693),f392(x22692,x22693))
% 25.54/25.43 [2270]~E(x22701,x22702)+E(f392(x22703,x22701),f392(x22703,x22702))
% 25.54/25.43 [2271]~E(x22711,x22712)+E(f517(x22711,x22713,x22714),f517(x22712,x22713,x22714))
% 25.54/25.43 [2272]~E(x22721,x22722)+E(f517(x22723,x22721,x22724),f517(x22723,x22722,x22724))
% 25.54/25.43 [2273]~E(x22731,x22732)+E(f517(x22733,x22734,x22731),f517(x22733,x22734,x22732))
% 25.54/25.43 [2274]~E(x22741,x22742)+E(f414(x22741),f414(x22742))
% 25.54/25.43 [2275]~E(x22751,x22752)+E(f567(x22751),f567(x22752))
% 25.54/25.43 [2276]~E(x22761,x22762)+E(f259(x22761),f259(x22762))
% 25.54/25.43 [2277]~E(x22771,x22772)+E(f81(x22771),f81(x22772))
% 25.54/25.43 [2278]~E(x22781,x22782)+E(f811(x22781),f811(x22782))
% 25.54/25.43 [2279]~E(x22791,x22792)+E(f876(x22791,x22793,x22794),f876(x22792,x22793,x22794))
% 25.54/25.43 [2280]~E(x22801,x22802)+E(f876(x22803,x22801,x22804),f876(x22803,x22802,x22804))
% 25.54/25.43 [2281]~E(x22811,x22812)+E(f876(x22813,x22814,x22811),f876(x22813,x22814,x22812))
% 25.54/25.43 [2282]~E(x22821,x22822)+E(f642(x22821,x22823,x22824,x22825,x22826),f642(x22822,x22823,x22824,x22825,x22826))
% 25.54/25.43 [2283]~E(x22831,x22832)+E(f642(x22833,x22831,x22834,x22835,x22836),f642(x22833,x22832,x22834,x22835,x22836))
% 25.54/25.43 [2284]~E(x22841,x22842)+E(f642(x22843,x22844,x22841,x22845,x22846),f642(x22843,x22844,x22842,x22845,x22846))
% 25.54/25.43 [2285]~E(x22851,x22852)+E(f642(x22853,x22854,x22855,x22851,x22856),f642(x22853,x22854,x22855,x22852,x22856))
% 25.54/25.43 [2286]~E(x22861,x22862)+E(f642(x22863,x22864,x22865,x22866,x22861),f642(x22863,x22864,x22865,x22866,x22862))
% 25.54/25.43 [2287]~E(x22871,x22872)+E(f707(x22871,x22873,x22874,x22875,x22876),f707(x22872,x22873,x22874,x22875,x22876))
% 25.54/25.43 [2288]~E(x22881,x22882)+E(f707(x22883,x22881,x22884,x22885,x22886),f707(x22883,x22882,x22884,x22885,x22886))
% 25.54/25.43 [2289]~E(x22891,x22892)+E(f707(x22893,x22894,x22891,x22895,x22896),f707(x22893,x22894,x22892,x22895,x22896))
% 25.54/25.43 [2290]~E(x22901,x22902)+E(f707(x22903,x22904,x22905,x22901,x22906),f707(x22903,x22904,x22905,x22902,x22906))
% 25.54/25.43 [2291]~E(x22911,x22912)+E(f707(x22913,x22914,x22915,x22916,x22911),f707(x22913,x22914,x22915,x22916,x22912))
% 25.54/25.43 [2292]~E(x22921,x22922)+E(f657(x22921,x22923,x22924),f657(x22922,x22923,x22924))
% 25.54/25.43 [2293]~E(x22931,x22932)+E(f657(x22933,x22931,x22934),f657(x22933,x22932,x22934))
% 25.54/25.43 [2294]~E(x22941,x22942)+E(f657(x22943,x22944,x22941),f657(x22943,x22944,x22942))
% 25.54/25.43 [2295]~E(x22951,x22952)+E(f623(x22951,x22953,x22954),f623(x22952,x22953,x22954))
% 25.54/25.43 [2296]~E(x22961,x22962)+E(f623(x22963,x22961,x22964),f623(x22963,x22962,x22964))
% 25.54/25.43 [2297]~E(x22971,x22972)+E(f623(x22973,x22974,x22971),f623(x22973,x22974,x22972))
% 25.54/25.43 [2298]~E(x22981,x22982)+E(f817(x22981,x22983),f817(x22982,x22983))
% 25.54/25.43 [2299]~E(x22991,x22992)+E(f817(x22993,x22991),f817(x22993,x22992))
% 25.54/25.43 [2300]~E(x23001,x23002)+E(f219(x23001,x23003,x23004,x23005,x23006),f219(x23002,x23003,x23004,x23005,x23006))
% 25.54/25.43 [2301]~E(x23011,x23012)+E(f219(x23013,x23011,x23014,x23015,x23016),f219(x23013,x23012,x23014,x23015,x23016))
% 25.54/25.43 [2302]~E(x23021,x23022)+E(f219(x23023,x23024,x23021,x23025,x23026),f219(x23023,x23024,x23022,x23025,x23026))
% 25.54/25.43 [2303]~E(x23031,x23032)+E(f219(x23033,x23034,x23035,x23031,x23036),f219(x23033,x23034,x23035,x23032,x23036))
% 25.54/25.43 [2304]~E(x23041,x23042)+E(f219(x23043,x23044,x23045,x23046,x23041),f219(x23043,x23044,x23045,x23046,x23042))
% 25.54/25.43 [2305]~E(x23051,x23052)+E(f239(x23051,x23053,x23054),f239(x23052,x23053,x23054))
% 25.54/25.43 [2306]~E(x23061,x23062)+E(f239(x23063,x23061,x23064),f239(x23063,x23062,x23064))
% 25.54/25.43 [2307]~E(x23071,x23072)+E(f239(x23073,x23074,x23071),f239(x23073,x23074,x23072))
% 25.54/25.43 [2308]~E(x23081,x23082)+E(f393(x23081,x23083,x23084),f393(x23082,x23083,x23084))
% 25.54/25.43 [2309]~E(x23091,x23092)+E(f393(x23093,x23091,x23094),f393(x23093,x23092,x23094))
% 25.54/25.43 [2310]~E(x23101,x23102)+E(f393(x23103,x23104,x23101),f393(x23103,x23104,x23102))
% 25.54/25.43 [2311]~E(x23111,x23112)+E(f915(x23111,x23113,x23114,x23115,x23116),f915(x23112,x23113,x23114,x23115,x23116))
% 25.54/25.43 [2312]~E(x23121,x23122)+E(f915(x23123,x23121,x23124,x23125,x23126),f915(x23123,x23122,x23124,x23125,x23126))
% 25.54/25.43 [2313]~E(x23131,x23132)+E(f915(x23133,x23134,x23131,x23135,x23136),f915(x23133,x23134,x23132,x23135,x23136))
% 25.54/25.43 [2314]~E(x23141,x23142)+E(f915(x23143,x23144,x23145,x23141,x23146),f915(x23143,x23144,x23145,x23142,x23146))
% 25.54/25.43 [2315]~E(x23151,x23152)+E(f915(x23153,x23154,x23155,x23156,x23151),f915(x23153,x23154,x23155,x23156,x23152))
% 25.54/25.43 [2316]~E(x23161,x23162)+E(f282(x23161,x23163),f282(x23162,x23163))
% 25.54/25.43 [2317]~E(x23171,x23172)+E(f282(x23173,x23171),f282(x23173,x23172))
% 25.54/25.43 [2318]~E(x23181,x23182)+E(f906(x23181,x23183,x23184,x23185),f906(x23182,x23183,x23184,x23185))
% 25.54/25.43 [2319]~E(x23191,x23192)+E(f906(x23193,x23191,x23194,x23195),f906(x23193,x23192,x23194,x23195))
% 25.54/25.43 [2320]~E(x23201,x23202)+E(f906(x23203,x23204,x23201,x23205),f906(x23203,x23204,x23202,x23205))
% 25.54/25.43 [2321]~E(x23211,x23212)+E(f906(x23213,x23214,x23215,x23211),f906(x23213,x23214,x23215,x23212))
% 25.54/25.43 [2322]~E(x23221,x23222)+E(f641(x23221,x23223,x23224,x23225,x23226),f641(x23222,x23223,x23224,x23225,x23226))
% 25.54/25.43 [2323]~E(x23231,x23232)+E(f641(x23233,x23231,x23234,x23235,x23236),f641(x23233,x23232,x23234,x23235,x23236))
% 25.54/25.43 [2324]~E(x23241,x23242)+E(f641(x23243,x23244,x23241,x23245,x23246),f641(x23243,x23244,x23242,x23245,x23246))
% 25.54/25.43 [2325]~E(x23251,x23252)+E(f641(x23253,x23254,x23255,x23251,x23256),f641(x23253,x23254,x23255,x23252,x23256))
% 25.54/25.43 [2326]~E(x23261,x23262)+E(f641(x23263,x23264,x23265,x23266,x23261),f641(x23263,x23264,x23265,x23266,x23262))
% 25.54/25.43 [2327]~E(x23271,x23272)+E(f808(x23271,x23273),f808(x23272,x23273))
% 25.54/25.43 [2328]~E(x23281,x23282)+E(f808(x23283,x23281),f808(x23283,x23282))
% 25.54/25.43 [2329]~E(x23291,x23292)+E(f693(x23291,x23293,x23294,x23295),f693(x23292,x23293,x23294,x23295))
% 25.54/25.43 [2330]~E(x23301,x23302)+E(f693(x23303,x23301,x23304,x23305),f693(x23303,x23302,x23304,x23305))
% 25.54/25.43 [2331]~E(x23311,x23312)+E(f693(x23313,x23314,x23311,x23315),f693(x23313,x23314,x23312,x23315))
% 25.54/25.43 [2332]~E(x23321,x23322)+E(f693(x23323,x23324,x23325,x23321),f693(x23323,x23324,x23325,x23322))
% 25.54/25.43 [2333]~E(x23331,x23332)+E(f653(x23331,x23333,x23334,x23335,x23336,x23337),f653(x23332,x23333,x23334,x23335,x23336,x23337))
% 25.54/25.43 [2334]~E(x23341,x23342)+E(f653(x23343,x23341,x23344,x23345,x23346,x23347),f653(x23343,x23342,x23344,x23345,x23346,x23347))
% 25.54/25.43 [2335]~E(x23351,x23352)+E(f653(x23353,x23354,x23351,x23355,x23356,x23357),f653(x23353,x23354,x23352,x23355,x23356,x23357))
% 25.54/25.43 [2336]~E(x23361,x23362)+E(f653(x23363,x23364,x23365,x23361,x23366,x23367),f653(x23363,x23364,x23365,x23362,x23366,x23367))
% 25.54/25.43 [2337]~E(x23371,x23372)+E(f653(x23373,x23374,x23375,x23376,x23371,x23377),f653(x23373,x23374,x23375,x23376,x23372,x23377))
% 25.54/25.43 [2338]~E(x23381,x23382)+E(f653(x23383,x23384,x23385,x23386,x23387,x23381),f653(x23383,x23384,x23385,x23386,x23387,x23382))
% 25.54/25.43 [2339]~E(x23391,x23392)+E(f877(x23391,x23393,x23394),f877(x23392,x23393,x23394))
% 25.54/25.43 [2340]~E(x23401,x23402)+E(f877(x23403,x23401,x23404),f877(x23403,x23402,x23404))
% 25.54/25.43 [2341]~E(x23411,x23412)+E(f877(x23413,x23414,x23411),f877(x23413,x23414,x23412))
% 25.54/25.43 [2342]~E(x23421,x23422)+E(f304(x23421,x23423),f304(x23422,x23423))
% 25.54/25.43 [2343]~E(x23431,x23432)+E(f304(x23433,x23431),f304(x23433,x23432))
% 25.54/25.43 [2344]~E(x23441,x23442)+E(f750(x23441,x23443,x23444,x23445,x23446),f750(x23442,x23443,x23444,x23445,x23446))
% 25.54/25.43 [2345]~E(x23451,x23452)+E(f750(x23453,x23451,x23454,x23455,x23456),f750(x23453,x23452,x23454,x23455,x23456))
% 25.54/25.43 [2346]~E(x23461,x23462)+E(f750(x23463,x23464,x23461,x23465,x23466),f750(x23463,x23464,x23462,x23465,x23466))
% 25.54/25.43 [2347]~E(x23471,x23472)+E(f750(x23473,x23474,x23475,x23471,x23476),f750(x23473,x23474,x23475,x23472,x23476))
% 25.54/25.43 [2348]~E(x23481,x23482)+E(f750(x23483,x23484,x23485,x23486,x23481),f750(x23483,x23484,x23485,x23486,x23482))
% 25.54/25.43 [2349]~E(x23491,x23492)+E(f663(x23491,x23493,x23494,x23495,x23496),f663(x23492,x23493,x23494,x23495,x23496))
% 25.54/25.43 [2350]~E(x23501,x23502)+E(f663(x23503,x23501,x23504,x23505,x23506),f663(x23503,x23502,x23504,x23505,x23506))
% 25.54/25.43 [2351]~E(x23511,x23512)+E(f663(x23513,x23514,x23511,x23515,x23516),f663(x23513,x23514,x23512,x23515,x23516))
% 25.54/25.43 [2352]~E(x23521,x23522)+E(f663(x23523,x23524,x23525,x23521,x23526),f663(x23523,x23524,x23525,x23522,x23526))
% 25.54/25.43 [2353]~E(x23531,x23532)+E(f663(x23533,x23534,x23535,x23536,x23531),f663(x23533,x23534,x23535,x23536,x23532))
% 25.54/25.43 [2354]~E(x23541,x23542)+E(f528(x23541,x23543),f528(x23542,x23543))
% 25.54/25.43 [2355]~E(x23551,x23552)+E(f528(x23553,x23551),f528(x23553,x23552))
% 25.54/25.43 [2356]~E(x23561,x23562)+E(f328(x23561),f328(x23562))
% 25.54/25.43 [2357]~E(x23571,x23572)+E(f759(x23571,x23573,x23574,x23575),f759(x23572,x23573,x23574,x23575))
% 25.54/25.43 [2358]~E(x23581,x23582)+E(f759(x23583,x23581,x23584,x23585),f759(x23583,x23582,x23584,x23585))
% 25.54/25.43 [2359]~E(x23591,x23592)+E(f759(x23593,x23594,x23591,x23595),f759(x23593,x23594,x23592,x23595))
% 25.54/25.43 [2360]~E(x23601,x23602)+E(f759(x23603,x23604,x23605,x23601),f759(x23603,x23604,x23605,x23602))
% 25.54/25.43 [2361]~E(x23611,x23612)+E(f381(x23611,x23613,x23614,x23615),f381(x23612,x23613,x23614,x23615))
% 25.54/25.43 [2362]~E(x23621,x23622)+E(f381(x23623,x23621,x23624,x23625),f381(x23623,x23622,x23624,x23625))
% 25.54/25.43 [2363]~E(x23631,x23632)+E(f381(x23633,x23634,x23631,x23635),f381(x23633,x23634,x23632,x23635))
% 25.54/25.43 [2364]~E(x23641,x23642)+E(f381(x23643,x23644,x23645,x23641),f381(x23643,x23644,x23645,x23642))
% 25.54/25.43 [2365]~E(x23651,x23652)+E(f865(x23651,x23653),f865(x23652,x23653))
% 25.54/25.43 [2366]~E(x23661,x23662)+E(f865(x23663,x23661),f865(x23663,x23662))
% 25.54/25.43 [2367]~E(x23671,x23672)+E(f665(x23671,x23673,x23674),f665(x23672,x23673,x23674))
% 25.54/25.43 [2368]~E(x23681,x23682)+E(f665(x23683,x23681,x23684),f665(x23683,x23682,x23684))
% 25.54/25.43 [2369]~E(x23691,x23692)+E(f665(x23693,x23694,x23691),f665(x23693,x23694,x23692))
% 25.54/25.43 [2370]~E(x23701,x23702)+E(f633(x23701,x23703,x23704,x23705,x23706),f633(x23702,x23703,x23704,x23705,x23706))
% 25.54/25.43 [2371]~E(x23711,x23712)+E(f633(x23713,x23711,x23714,x23715,x23716),f633(x23713,x23712,x23714,x23715,x23716))
% 25.54/25.43 [2372]~E(x23721,x23722)+E(f633(x23723,x23724,x23721,x23725,x23726),f633(x23723,x23724,x23722,x23725,x23726))
% 25.54/25.43 [2373]~E(x23731,x23732)+E(f633(x23733,x23734,x23735,x23731,x23736),f633(x23733,x23734,x23735,x23732,x23736))
% 25.54/25.43 [2374]~E(x23741,x23742)+E(f633(x23743,x23744,x23745,x23746,x23741),f633(x23743,x23744,x23745,x23746,x23742))
% 25.54/25.43 [2375]~E(x23751,x23752)+E(f526(x23751,x23753,x23754,x23755,x23756),f526(x23752,x23753,x23754,x23755,x23756))
% 25.54/25.43 [2376]~E(x23761,x23762)+E(f526(x23763,x23761,x23764,x23765,x23766),f526(x23763,x23762,x23764,x23765,x23766))
% 25.54/25.43 [2377]~E(x23771,x23772)+E(f526(x23773,x23774,x23771,x23775,x23776),f526(x23773,x23774,x23772,x23775,x23776))
% 25.54/25.43 [2378]~E(x23781,x23782)+E(f526(x23783,x23784,x23785,x23781,x23786),f526(x23783,x23784,x23785,x23782,x23786))
% 25.54/25.43 [2379]~E(x23791,x23792)+E(f526(x23793,x23794,x23795,x23796,x23791),f526(x23793,x23794,x23795,x23796,x23792))
% 25.54/25.43 [2380]~E(x23801,x23802)+E(f268(x23801,x23803,x23804,x23805),f268(x23802,x23803,x23804,x23805))
% 25.54/25.43 [2381]~E(x23811,x23812)+E(f268(x23813,x23811,x23814,x23815),f268(x23813,x23812,x23814,x23815))
% 25.54/25.43 [2382]~E(x23821,x23822)+E(f268(x23823,x23824,x23821,x23825),f268(x23823,x23824,x23822,x23825))
% 25.54/25.43 [2383]~E(x23831,x23832)+E(f268(x23833,x23834,x23835,x23831),f268(x23833,x23834,x23835,x23832))
% 25.54/25.43 [2384]~E(x23841,x23842)+E(f496(x23841,x23843,x23844),f496(x23842,x23843,x23844))
% 25.54/25.43 [2385]~E(x23851,x23852)+E(f496(x23853,x23851,x23854),f496(x23853,x23852,x23854))
% 25.54/25.43 [2386]~E(x23861,x23862)+E(f496(x23863,x23864,x23861),f496(x23863,x23864,x23862))
% 25.54/25.43 [2387]~E(x23871,x23872)+E(f449(x23871,x23873,x23874),f449(x23872,x23873,x23874))
% 25.54/25.43 [2388]~E(x23881,x23882)+E(f449(x23883,x23881,x23884),f449(x23883,x23882,x23884))
% 25.54/25.43 [2389]~E(x23891,x23892)+E(f449(x23893,x23894,x23891),f449(x23893,x23894,x23892))
% 25.54/25.43 [2390]~E(x23901,x23902)+E(f853(x23901,x23903,x23904,x23905,x23906),f853(x23902,x23903,x23904,x23905,x23906))
% 25.54/25.43 [2391]~E(x23911,x23912)+E(f853(x23913,x23911,x23914,x23915,x23916),f853(x23913,x23912,x23914,x23915,x23916))
% 25.54/25.43 [2392]~E(x23921,x23922)+E(f853(x23923,x23924,x23921,x23925,x23926),f853(x23923,x23924,x23922,x23925,x23926))
% 25.54/25.43 [2393]~E(x23931,x23932)+E(f853(x23933,x23934,x23935,x23931,x23936),f853(x23933,x23934,x23935,x23932,x23936))
% 25.54/25.43 [2394]~E(x23941,x23942)+E(f853(x23943,x23944,x23945,x23946,x23941),f853(x23943,x23944,x23945,x23946,x23942))
% 25.54/25.43 [2395]~E(x23951,x23952)+E(f354(x23951,x23953,x23954,x23955,x23956),f354(x23952,x23953,x23954,x23955,x23956))
% 25.54/25.43 [2396]~E(x23961,x23962)+E(f354(x23963,x23961,x23964,x23965,x23966),f354(x23963,x23962,x23964,x23965,x23966))
% 25.54/25.43 [2397]~E(x23971,x23972)+E(f354(x23973,x23974,x23971,x23975,x23976),f354(x23973,x23974,x23972,x23975,x23976))
% 25.54/25.43 [2398]~E(x23981,x23982)+E(f354(x23983,x23984,x23985,x23981,x23986),f354(x23983,x23984,x23985,x23982,x23986))
% 25.54/25.43 [2399]~E(x23991,x23992)+E(f354(x23993,x23994,x23995,x23996,x23991),f354(x23993,x23994,x23995,x23996,x23992))
% 25.54/25.43 [2400]~E(x24001,x24002)+E(f850(x24001,x24003,x24004,x24005,x24006,x24007,x24008),f850(x24002,x24003,x24004,x24005,x24006,x24007,x24008))
% 25.54/25.43 [2401]~E(x24011,x24012)+E(f850(x24013,x24011,x24014,x24015,x24016,x24017,x24018),f850(x24013,x24012,x24014,x24015,x24016,x24017,x24018))
% 25.54/25.43 [2402]~E(x24021,x24022)+E(f850(x24023,x24024,x24021,x24025,x24026,x24027,x24028),f850(x24023,x24024,x24022,x24025,x24026,x24027,x24028))
% 25.54/25.43 [2403]~E(x24031,x24032)+E(f850(x24033,x24034,x24035,x24031,x24036,x24037,x24038),f850(x24033,x24034,x24035,x24032,x24036,x24037,x24038))
% 25.54/25.43 [2404]~E(x24041,x24042)+E(f850(x24043,x24044,x24045,x24046,x24041,x24047,x24048),f850(x24043,x24044,x24045,x24046,x24042,x24047,x24048))
% 25.54/25.43 [2405]~E(x24051,x24052)+E(f850(x24053,x24054,x24055,x24056,x24057,x24051,x24058),f850(x24053,x24054,x24055,x24056,x24057,x24052,x24058))
% 25.54/25.43 [2406]~E(x24061,x24062)+E(f850(x24063,x24064,x24065,x24066,x24067,x24068,x24061),f850(x24063,x24064,x24065,x24066,x24067,x24068,x24062))
% 25.54/25.43 [2407]~E(x24071,x24072)+E(f795(x24071,x24073,x24074,x24075,x24076,x24077,x24078),f795(x24072,x24073,x24074,x24075,x24076,x24077,x24078))
% 25.54/25.43 [2408]~E(x24081,x24082)+E(f795(x24083,x24081,x24084,x24085,x24086,x24087,x24088),f795(x24083,x24082,x24084,x24085,x24086,x24087,x24088))
% 25.54/25.43 [2409]~E(x24091,x24092)+E(f795(x24093,x24094,x24091,x24095,x24096,x24097,x24098),f795(x24093,x24094,x24092,x24095,x24096,x24097,x24098))
% 25.54/25.43 [2410]~E(x24101,x24102)+E(f795(x24103,x24104,x24105,x24101,x24106,x24107,x24108),f795(x24103,x24104,x24105,x24102,x24106,x24107,x24108))
% 25.54/25.43 [2411]~E(x24111,x24112)+E(f795(x24113,x24114,x24115,x24116,x24111,x24117,x24118),f795(x24113,x24114,x24115,x24116,x24112,x24117,x24118))
% 25.54/25.43 [2412]~E(x24121,x24122)+E(f795(x24123,x24124,x24125,x24126,x24127,x24121,x24128),f795(x24123,x24124,x24125,x24126,x24127,x24122,x24128))
% 25.54/25.43 [2413]~E(x24131,x24132)+E(f795(x24133,x24134,x24135,x24136,x24137,x24138,x24131),f795(x24133,x24134,x24135,x24136,x24137,x24138,x24132))
% 25.54/25.43 [2414]~E(x24141,x24142)+E(f427(x24141,x24143),f427(x24142,x24143))
% 25.54/25.43 [2415]~E(x24151,x24152)+E(f427(x24153,x24151),f427(x24153,x24152))
% 25.54/25.43 [2416]~E(x24161,x24162)+E(f512(x24161,x24163,x24164,x24165,x24166,x24167),f512(x24162,x24163,x24164,x24165,x24166,x24167))
% 25.54/25.43 [2417]~E(x24171,x24172)+E(f512(x24173,x24171,x24174,x24175,x24176,x24177),f512(x24173,x24172,x24174,x24175,x24176,x24177))
% 25.54/25.43 [2418]~E(x24181,x24182)+E(f512(x24183,x24184,x24181,x24185,x24186,x24187),f512(x24183,x24184,x24182,x24185,x24186,x24187))
% 25.54/25.43 [2419]~E(x24191,x24192)+E(f512(x24193,x24194,x24195,x24191,x24196,x24197),f512(x24193,x24194,x24195,x24192,x24196,x24197))
% 25.54/25.43 [2420]~E(x24201,x24202)+E(f512(x24203,x24204,x24205,x24206,x24201,x24207),f512(x24203,x24204,x24205,x24206,x24202,x24207))
% 25.54/25.43 [2421]~E(x24211,x24212)+E(f512(x24213,x24214,x24215,x24216,x24217,x24211),f512(x24213,x24214,x24215,x24216,x24217,x24212))
% 25.54/25.43 [2422]~E(x24221,x24222)+E(f501(x24221,x24223,x24224),f501(x24222,x24223,x24224))
% 25.54/25.43 [2423]~E(x24231,x24232)+E(f501(x24233,x24231,x24234),f501(x24233,x24232,x24234))
% 25.54/25.43 [2424]~E(x24241,x24242)+E(f501(x24243,x24244,x24241),f501(x24243,x24244,x24242))
% 25.54/25.43 [2425]~E(x24251,x24252)+E(f383(x24251,x24253,x24254,x24255),f383(x24252,x24253,x24254,x24255))
% 25.54/25.43 [2426]~E(x24261,x24262)+E(f383(x24263,x24261,x24264,x24265),f383(x24263,x24262,x24264,x24265))
% 25.54/25.43 [2427]~E(x24271,x24272)+E(f383(x24273,x24274,x24271,x24275),f383(x24273,x24274,x24272,x24275))
% 25.54/25.43 [2428]~E(x24281,x24282)+E(f383(x24283,x24284,x24285,x24281),f383(x24283,x24284,x24285,x24282))
% 25.54/25.43 [2429]~E(x24291,x24292)+E(f525(x24291,x24293,x24294,x24295),f525(x24292,x24293,x24294,x24295))
% 25.54/25.43 [2430]~E(x24301,x24302)+E(f525(x24303,x24301,x24304,x24305),f525(x24303,x24302,x24304,x24305))
% 25.54/25.43 [2431]~E(x24311,x24312)+E(f525(x24313,x24314,x24311,x24315),f525(x24313,x24314,x24312,x24315))
% 25.54/25.43 [2432]~E(x24321,x24322)+E(f525(x24323,x24324,x24325,x24321),f525(x24323,x24324,x24325,x24322))
% 25.54/25.43 [2433]~E(x24331,x24332)+E(f535(x24331,x24333,x24334,x24335),f535(x24332,x24333,x24334,x24335))
% 25.54/25.43 [2434]~E(x24341,x24342)+E(f535(x24343,x24341,x24344,x24345),f535(x24343,x24342,x24344,x24345))
% 25.54/25.43 [2435]~E(x24351,x24352)+E(f535(x24353,x24354,x24351,x24355),f535(x24353,x24354,x24352,x24355))
% 25.54/25.43 [2436]~E(x24361,x24362)+E(f535(x24363,x24364,x24365,x24361),f535(x24363,x24364,x24365,x24362))
% 25.54/25.43 [2437]~E(x24371,x24372)+E(f706(x24371,x24373,x24374,x24375,x24376),f706(x24372,x24373,x24374,x24375,x24376))
% 25.54/25.43 [2438]~E(x24381,x24382)+E(f706(x24383,x24381,x24384,x24385,x24386),f706(x24383,x24382,x24384,x24385,x24386))
% 25.54/25.43 [2439]~E(x24391,x24392)+E(f706(x24393,x24394,x24391,x24395,x24396),f706(x24393,x24394,x24392,x24395,x24396))
% 25.54/25.43 [2440]~E(x24401,x24402)+E(f706(x24403,x24404,x24405,x24401,x24406),f706(x24403,x24404,x24405,x24402,x24406))
% 25.54/25.43 [2441]~E(x24411,x24412)+E(f706(x24413,x24414,x24415,x24416,x24411),f706(x24413,x24414,x24415,x24416,x24412))
% 25.54/25.43 [2442]~E(x24421,x24422)+E(f719(x24421,x24423,x24424),f719(x24422,x24423,x24424))
% 25.54/25.43 [2443]~E(x24431,x24432)+E(f719(x24433,x24431,x24434),f719(x24433,x24432,x24434))
% 25.54/25.43 [2444]~E(x24441,x24442)+E(f719(x24443,x24444,x24441),f719(x24443,x24444,x24442))
% 25.54/25.43 [2445]~E(x24451,x24452)+E(f346(x24451,x24453),f346(x24452,x24453))
% 25.54/25.43 [2446]~E(x24461,x24462)+E(f346(x24463,x24461),f346(x24463,x24462))
% 25.54/25.43 [2447]~E(x24471,x24472)+E(f410(x24471),f410(x24472))
% 25.54/25.43 [2448]~E(x24481,x24482)+E(f556(x24481,x24483,x24484,x24485),f556(x24482,x24483,x24484,x24485))
% 25.54/25.43 [2449]~E(x24491,x24492)+E(f556(x24493,x24491,x24494,x24495),f556(x24493,x24492,x24494,x24495))
% 25.54/25.43 [2450]~E(x24501,x24502)+E(f556(x24503,x24504,x24501,x24505),f556(x24503,x24504,x24502,x24505))
% 25.54/25.43 [2451]~E(x24511,x24512)+E(f556(x24513,x24514,x24515,x24511),f556(x24513,x24514,x24515,x24512))
% 25.54/25.43 [2452]~E(x24521,x24522)+E(f677(x24521,x24523),f677(x24522,x24523))
% 25.54/25.43 [2453]~E(x24531,x24532)+E(f677(x24533,x24531),f677(x24533,x24532))
% 25.54/25.43 [2454]~E(x24541,x24542)+E(f577(x24541,x24543,x24544,x24545,x24546),f577(x24542,x24543,x24544,x24545,x24546))
% 25.54/25.43 [2455]~E(x24551,x24552)+E(f577(x24553,x24551,x24554,x24555,x24556),f577(x24553,x24552,x24554,x24555,x24556))
% 25.54/25.43 [2456]~E(x24561,x24562)+E(f577(x24563,x24564,x24561,x24565,x24566),f577(x24563,x24564,x24562,x24565,x24566))
% 25.54/25.43 [2457]~E(x24571,x24572)+E(f577(x24573,x24574,x24575,x24571,x24576),f577(x24573,x24574,x24575,x24572,x24576))
% 25.54/25.43 [2458]~E(x24581,x24582)+E(f577(x24583,x24584,x24585,x24586,x24581),f577(x24583,x24584,x24585,x24586,x24582))
% 25.54/25.43 [2459]~E(x24591,x24592)+E(f652(x24591,x24593,x24594,x24595,x24596,x24597),f652(x24592,x24593,x24594,x24595,x24596,x24597))
% 25.54/25.43 [2460]~E(x24601,x24602)+E(f652(x24603,x24601,x24604,x24605,x24606,x24607),f652(x24603,x24602,x24604,x24605,x24606,x24607))
% 25.54/25.43 [2461]~E(x24611,x24612)+E(f652(x24613,x24614,x24611,x24615,x24616,x24617),f652(x24613,x24614,x24612,x24615,x24616,x24617))
% 25.54/25.43 [2462]~E(x24621,x24622)+E(f652(x24623,x24624,x24625,x24621,x24626,x24627),f652(x24623,x24624,x24625,x24622,x24626,x24627))
% 25.54/25.43 [2463]~E(x24631,x24632)+E(f652(x24633,x24634,x24635,x24636,x24631,x24637),f652(x24633,x24634,x24635,x24636,x24632,x24637))
% 25.54/25.43 [2464]~E(x24641,x24642)+E(f652(x24643,x24644,x24645,x24646,x24647,x24641),f652(x24643,x24644,x24645,x24646,x24647,x24642))
% 25.54/25.43 [2465]~E(x24651,x24652)+E(f364(x24651,x24653,x24654,x24655),f364(x24652,x24653,x24654,x24655))
% 25.54/25.43 [2466]~E(x24661,x24662)+E(f364(x24663,x24661,x24664,x24665),f364(x24663,x24662,x24664,x24665))
% 25.54/25.43 [2467]~E(x24671,x24672)+E(f364(x24673,x24674,x24671,x24675),f364(x24673,x24674,x24672,x24675))
% 25.54/25.43 [2468]~E(x24681,x24682)+E(f364(x24683,x24684,x24685,x24681),f364(x24683,x24684,x24685,x24682))
% 25.54/25.43 [2469]~E(x24691,x24692)+E(f257(x24691,x24693,x24694),f257(x24692,x24693,x24694))
% 25.54/25.43 [2470]~E(x24701,x24702)+E(f257(x24703,x24701,x24704),f257(x24703,x24702,x24704))
% 25.54/25.43 [2471]~E(x24711,x24712)+E(f257(x24713,x24714,x24711),f257(x24713,x24714,x24712))
% 25.54/25.43 [2472]~E(x24721,x24722)+E(f547(x24721,x24723,x24724),f547(x24722,x24723,x24724))
% 25.54/25.43 [2473]~E(x24731,x24732)+E(f547(x24733,x24731,x24734),f547(x24733,x24732,x24734))
% 25.54/25.43 [2474]~E(x24741,x24742)+E(f547(x24743,x24744,x24741),f547(x24743,x24744,x24742))
% 25.54/25.43 [2475]~E(x24751,x24752)+E(f237(x24751,x24753,x24754),f237(x24752,x24753,x24754))
% 25.54/25.43 [2476]~E(x24761,x24762)+E(f237(x24763,x24761,x24764),f237(x24763,x24762,x24764))
% 25.54/25.43 [2477]~E(x24771,x24772)+E(f237(x24773,x24774,x24771),f237(x24773,x24774,x24772))
% 25.54/25.43 [2478]~E(x24781,x24782)+E(f382(x24781,x24783,x24784,x24785),f382(x24782,x24783,x24784,x24785))
% 25.54/25.43 [2479]~E(x24791,x24792)+E(f382(x24793,x24791,x24794,x24795),f382(x24793,x24792,x24794,x24795))
% 25.54/25.43 [2480]~E(x24801,x24802)+E(f382(x24803,x24804,x24801,x24805),f382(x24803,x24804,x24802,x24805))
% 25.54/25.43 [2481]~E(x24811,x24812)+E(f382(x24813,x24814,x24815,x24811),f382(x24813,x24814,x24815,x24812))
% 25.54/25.43 [2482]~E(x24821,x24822)+E(f840(x24821,x24823,x24824),f840(x24822,x24823,x24824))
% 25.54/25.43 [2483]~E(x24831,x24832)+E(f840(x24833,x24831,x24834),f840(x24833,x24832,x24834))
% 25.54/25.43 [2484]~E(x24841,x24842)+E(f840(x24843,x24844,x24841),f840(x24843,x24844,x24842))
% 25.54/25.43 [2485]~E(x24851,x24852)+E(f792(x24851),f792(x24852))
% 25.54/25.43 [2486]~E(x24861,x24862)+E(f823(x24861,x24863),f823(x24862,x24863))
% 25.54/25.43 [2487]~E(x24871,x24872)+E(f823(x24873,x24871),f823(x24873,x24872))
% 25.54/25.43 [2488]~E(x24881,x24882)+E(f404(x24881,x24883,x24884,x24885),f404(x24882,x24883,x24884,x24885))
% 25.54/25.43 [2489]~E(x24891,x24892)+E(f404(x24893,x24891,x24894,x24895),f404(x24893,x24892,x24894,x24895))
% 25.54/25.43 [2490]~E(x24901,x24902)+E(f404(x24903,x24904,x24901,x24905),f404(x24903,x24904,x24902,x24905))
% 25.54/25.43 [2491]~E(x24911,x24912)+E(f404(x24913,x24914,x24915,x24911),f404(x24913,x24914,x24915,x24912))
% 25.54/25.43 [2492]~E(x24921,x24922)+E(f617(x24921,x24923,x24924,x24925),f617(x24922,x24923,x24924,x24925))
% 25.54/25.43 [2493]~E(x24931,x24932)+E(f617(x24933,x24931,x24934,x24935),f617(x24933,x24932,x24934,x24935))
% 25.54/25.43 [2494]~E(x24941,x24942)+E(f617(x24943,x24944,x24941,x24945),f617(x24943,x24944,x24942,x24945))
% 25.54/25.43 [2495]~E(x24951,x24952)+E(f617(x24953,x24954,x24955,x24951),f617(x24953,x24954,x24955,x24952))
% 25.54/25.43 [2496]~E(x24961,x24962)+E(f19(x24961,x24963,x24964,x24965),f19(x24962,x24963,x24964,x24965))
% 25.54/25.43 [2497]~E(x24971,x24972)+E(f19(x24973,x24971,x24974,x24975),f19(x24973,x24972,x24974,x24975))
% 25.54/25.43 [2498]~E(x24981,x24982)+E(f19(x24983,x24984,x24981,x24985),f19(x24983,x24984,x24982,x24985))
% 25.54/25.43 [2499]~E(x24991,x24992)+E(f19(x24993,x24994,x24995,x24991),f19(x24993,x24994,x24995,x24992))
% 25.54/25.43 [2500]~E(x25001,x25002)+E(f768(x25001,x25003,x25004),f768(x25002,x25003,x25004))
% 25.54/25.43 [2501]~E(x25011,x25012)+E(f768(x25013,x25011,x25014),f768(x25013,x25012,x25014))
% 25.54/25.43 [2502]~E(x25021,x25022)+E(f768(x25023,x25024,x25021),f768(x25023,x25024,x25022))
% 25.54/25.43 [2503]~E(x25031,x25032)+E(f826(x25031,x25033),f826(x25032,x25033))
% 25.54/25.43 [2504]~E(x25041,x25042)+E(f826(x25043,x25041),f826(x25043,x25042))
% 25.54/25.43 [2505]~E(x25051,x25052)+E(f356(x25051,x25053,x25054,x25055,x25056),f356(x25052,x25053,x25054,x25055,x25056))
% 25.54/25.43 [2506]~E(x25061,x25062)+E(f356(x25063,x25061,x25064,x25065,x25066),f356(x25063,x25062,x25064,x25065,x25066))
% 25.54/25.43 [2507]~E(x25071,x25072)+E(f356(x25073,x25074,x25071,x25075,x25076),f356(x25073,x25074,x25072,x25075,x25076))
% 25.54/25.43 [2508]~E(x25081,x25082)+E(f356(x25083,x25084,x25085,x25081,x25086),f356(x25083,x25084,x25085,x25082,x25086))
% 25.54/25.43 [2509]~E(x25091,x25092)+E(f356(x25093,x25094,x25095,x25096,x25091),f356(x25093,x25094,x25095,x25096,x25092))
% 25.54/25.43 [2510]~E(x25101,x25102)+E(f745(x25101,x25103),f745(x25102,x25103))
% 25.54/25.43 [2511]~E(x25111,x25112)+E(f745(x25113,x25111),f745(x25113,x25112))
% 25.54/25.43 [2512]~E(x25121,x25122)+E(f807(x25121,x25123),f807(x25122,x25123))
% 25.54/25.43 [2513]~E(x25131,x25132)+E(f807(x25133,x25131),f807(x25133,x25132))
% 25.54/25.43 [2514]~E(x25141,x25142)+E(f566(x25141,x25143,x25144,x25145),f566(x25142,x25143,x25144,x25145))
% 25.54/25.43 [2515]~E(x25151,x25152)+E(f566(x25153,x25151,x25154,x25155),f566(x25153,x25152,x25154,x25155))
% 25.54/25.43 [2516]~E(x25161,x25162)+E(f566(x25163,x25164,x25161,x25165),f566(x25163,x25164,x25162,x25165))
% 25.54/25.43 [2517]~E(x25171,x25172)+E(f566(x25173,x25174,x25175,x25171),f566(x25173,x25174,x25175,x25172))
% 25.54/25.43 [2518]~E(x25181,x25182)+E(f385(x25181,x25183,x25184),f385(x25182,x25183,x25184))
% 25.54/25.43 [2519]~E(x25191,x25192)+E(f385(x25193,x25191,x25194),f385(x25193,x25192,x25194))
% 25.54/25.43 [2520]~E(x25201,x25202)+E(f385(x25203,x25204,x25201),f385(x25203,x25204,x25202))
% 25.54/25.43 [2521]~E(x25211,x25212)+E(f485(x25211,x25213,x25214,x25215,x25216),f485(x25212,x25213,x25214,x25215,x25216))
% 25.54/25.43 [2522]~E(x25221,x25222)+E(f485(x25223,x25221,x25224,x25225,x25226),f485(x25223,x25222,x25224,x25225,x25226))
% 25.54/25.43 [2523]~E(x25231,x25232)+E(f485(x25233,x25234,x25231,x25235,x25236),f485(x25233,x25234,x25232,x25235,x25236))
% 25.54/25.43 [2524]~E(x25241,x25242)+E(f485(x25243,x25244,x25245,x25241,x25246),f485(x25243,x25244,x25245,x25242,x25246))
% 25.54/25.43 [2525]~E(x25251,x25252)+E(f485(x25253,x25254,x25255,x25256,x25251),f485(x25253,x25254,x25255,x25256,x25252))
% 25.54/25.43 [2526]~E(x25261,x25262)+E(f460(x25261,x25263,x25264),f460(x25262,x25263,x25264))
% 25.54/25.43 [2527]~E(x25271,x25272)+E(f460(x25273,x25271,x25274),f460(x25273,x25272,x25274))
% 25.54/25.43 [2528]~E(x25281,x25282)+E(f460(x25283,x25284,x25281),f460(x25283,x25284,x25282))
% 25.54/25.43 [2529]~E(x25291,x25292)+E(f189(x25291,x25293,x25294,x25295),f189(x25292,x25293,x25294,x25295))
% 25.54/25.43 [2530]~E(x25301,x25302)+E(f189(x25303,x25301,x25304,x25305),f189(x25303,x25302,x25304,x25305))
% 25.54/25.43 [2531]~E(x25311,x25312)+E(f189(x25313,x25314,x25311,x25315),f189(x25313,x25314,x25312,x25315))
% 25.54/25.43 [2532]~E(x25321,x25322)+E(f189(x25323,x25324,x25325,x25321),f189(x25323,x25324,x25325,x25322))
% 25.54/25.43 [2533]~E(x25331,x25332)+E(f477(x25331,x25333,x25334,x25335),f477(x25332,x25333,x25334,x25335))
% 25.54/25.43 [2534]~E(x25341,x25342)+E(f477(x25343,x25341,x25344,x25345),f477(x25343,x25342,x25344,x25345))
% 25.54/25.43 [2535]~E(x25351,x25352)+E(f477(x25353,x25354,x25351,x25355),f477(x25353,x25354,x25352,x25355))
% 25.54/25.43 [2536]~E(x25361,x25362)+E(f477(x25363,x25364,x25365,x25361),f477(x25363,x25364,x25365,x25362))
% 25.54/25.43 [2537]~E(x25371,x25372)+E(f658(x25371,x25373,x25374),f658(x25372,x25373,x25374))
% 25.54/25.43 [2538]~E(x25381,x25382)+E(f658(x25383,x25381,x25384),f658(x25383,x25382,x25384))
% 25.54/25.43 [2539]~E(x25391,x25392)+E(f658(x25393,x25394,x25391),f658(x25393,x25394,x25392))
% 25.54/25.43 [2540]~E(x25401,x25402)+E(f616(x25401,x25403,x25404,x25405,x25406),f616(x25402,x25403,x25404,x25405,x25406))
% 25.54/25.43 [2541]~E(x25411,x25412)+E(f616(x25413,x25411,x25414,x25415,x25416),f616(x25413,x25412,x25414,x25415,x25416))
% 25.54/25.43 [2542]~E(x25421,x25422)+E(f616(x25423,x25424,x25421,x25425,x25426),f616(x25423,x25424,x25422,x25425,x25426))
% 25.54/25.43 [2543]~E(x25431,x25432)+E(f616(x25433,x25434,x25435,x25431,x25436),f616(x25433,x25434,x25435,x25432,x25436))
% 25.54/25.43 [2544]~E(x25441,x25442)+E(f616(x25443,x25444,x25445,x25446,x25441),f616(x25443,x25444,x25445,x25446,x25442))
% 25.54/25.43 [2545]~E(x25451,x25452)+E(f543(x25451,x25453,x25454,x25455),f543(x25452,x25453,x25454,x25455))
% 25.54/25.43 [2546]~E(x25461,x25462)+E(f543(x25463,x25461,x25464,x25465),f543(x25463,x25462,x25464,x25465))
% 25.54/25.43 [2547]~E(x25471,x25472)+E(f543(x25473,x25474,x25471,x25475),f543(x25473,x25474,x25472,x25475))
% 25.54/25.43 [2548]~E(x25481,x25482)+E(f543(x25483,x25484,x25485,x25481),f543(x25483,x25484,x25485,x25482))
% 25.54/25.43 [2549]~E(x25491,x25492)+E(f711(x25491,x25493,x25494),f711(x25492,x25493,x25494))
% 25.54/25.43 [2550]~E(x25501,x25502)+E(f711(x25503,x25501,x25504),f711(x25503,x25502,x25504))
% 25.54/25.43 [2551]~E(x25511,x25512)+E(f711(x25513,x25514,x25511),f711(x25513,x25514,x25512))
% 25.54/25.43 [2552]~E(x25521,x25522)+E(f390(x25521,x25523,x25524,x25525),f390(x25522,x25523,x25524,x25525))
% 25.54/25.43 [2553]~E(x25531,x25532)+E(f390(x25533,x25531,x25534,x25535),f390(x25533,x25532,x25534,x25535))
% 25.54/25.43 [2554]~E(x25541,x25542)+E(f390(x25543,x25544,x25541,x25545),f390(x25543,x25544,x25542,x25545))
% 25.54/25.43 [2555]~E(x25551,x25552)+E(f390(x25553,x25554,x25555,x25551),f390(x25553,x25554,x25555,x25552))
% 25.54/25.43 [2556]~E(x25561,x25562)+E(f648(x25561,x25563,x25564,x25565),f648(x25562,x25563,x25564,x25565))
% 25.54/25.43 [2557]~E(x25571,x25572)+E(f648(x25573,x25571,x25574,x25575),f648(x25573,x25572,x25574,x25575))
% 25.54/25.43 [2558]~E(x25581,x25582)+E(f648(x25583,x25584,x25581,x25585),f648(x25583,x25584,x25582,x25585))
% 25.54/25.43 [2559]~E(x25591,x25592)+E(f648(x25593,x25594,x25595,x25591),f648(x25593,x25594,x25595,x25592))
% 25.54/25.43 [2560]~E(x25601,x25602)+E(f545(x25601,x25603),f545(x25602,x25603))
% 25.54/25.43 [2561]~E(x25611,x25612)+E(f545(x25613,x25611),f545(x25613,x25612))
% 25.54/25.43 [2562]~E(x25621,x25622)+E(f522(x25621),f522(x25622))
% 25.54/25.43 [2563]~E(x25631,x25632)+E(f481(x25631,x25633,x25634,x25635,x25636),f481(x25632,x25633,x25634,x25635,x25636))
% 25.54/25.43 [2564]~E(x25641,x25642)+E(f481(x25643,x25641,x25644,x25645,x25646),f481(x25643,x25642,x25644,x25645,x25646))
% 25.54/25.43 [2565]~E(x25651,x25652)+E(f481(x25653,x25654,x25651,x25655,x25656),f481(x25653,x25654,x25652,x25655,x25656))
% 25.54/25.43 [2566]~E(x25661,x25662)+E(f481(x25663,x25664,x25665,x25661,x25666),f481(x25663,x25664,x25665,x25662,x25666))
% 25.54/25.43 [2567]~E(x25671,x25672)+E(f481(x25673,x25674,x25675,x25676,x25671),f481(x25673,x25674,x25675,x25676,x25672))
% 25.54/25.43 [2568]~E(x25681,x25682)+E(f893(x25681,x25683,x25684,x25685),f893(x25682,x25683,x25684,x25685))
% 25.54/25.43 [2569]~E(x25691,x25692)+E(f893(x25693,x25691,x25694,x25695),f893(x25693,x25692,x25694,x25695))
% 25.54/25.43 [2570]~E(x25701,x25702)+E(f893(x25703,x25704,x25701,x25705),f893(x25703,x25704,x25702,x25705))
% 25.54/25.43 [2571]~E(x25711,x25712)+E(f893(x25713,x25714,x25715,x25711),f893(x25713,x25714,x25715,x25712))
% 25.54/25.43 [2572]~E(x25721,x25722)+E(f743(x25721,x25723),f743(x25722,x25723))
% 25.54/25.43 [2573]~E(x25731,x25732)+E(f743(x25733,x25731),f743(x25733,x25732))
% 25.54/25.43 [2574]~E(x25741,x25742)+E(f805(x25741,x25743,x25744,x25745,x25746),f805(x25742,x25743,x25744,x25745,x25746))
% 25.54/25.43 [2575]~E(x25751,x25752)+E(f805(x25753,x25751,x25754,x25755,x25756),f805(x25753,x25752,x25754,x25755,x25756))
% 25.54/25.43 [2576]~E(x25761,x25762)+E(f805(x25763,x25764,x25761,x25765,x25766),f805(x25763,x25764,x25762,x25765,x25766))
% 25.54/25.43 [2577]~E(x25771,x25772)+E(f805(x25773,x25774,x25775,x25771,x25776),f805(x25773,x25774,x25775,x25772,x25776))
% 25.54/25.43 [2578]~E(x25781,x25782)+E(f805(x25783,x25784,x25785,x25786,x25781),f805(x25783,x25784,x25785,x25786,x25782))
% 25.54/25.43 [2579]~E(x25791,x25792)+E(f608(x25791,x25793,x25794),f608(x25792,x25793,x25794))
% 25.54/25.43 [2580]~E(x25801,x25802)+E(f608(x25803,x25801,x25804),f608(x25803,x25802,x25804))
% 25.54/25.43 [2581]~E(x25811,x25812)+E(f608(x25813,x25814,x25811),f608(x25813,x25814,x25812))
% 25.54/25.43 [2582]~E(x25821,x25822)+E(f203(x25821,x25823,x25824,x25825),f203(x25822,x25823,x25824,x25825))
% 25.54/25.43 [2583]~E(x25831,x25832)+E(f203(x25833,x25831,x25834,x25835),f203(x25833,x25832,x25834,x25835))
% 25.54/25.43 [2584]~E(x25841,x25842)+E(f203(x25843,x25844,x25841,x25845),f203(x25843,x25844,x25842,x25845))
% 25.54/25.43 [2585]~E(x25851,x25852)+E(f203(x25853,x25854,x25855,x25851),f203(x25853,x25854,x25855,x25852))
% 25.54/25.43 [2586]~E(x25861,x25862)+E(f450(x25861,x25863,x25864),f450(x25862,x25863,x25864))
% 25.54/25.43 [2587]~E(x25871,x25872)+E(f450(x25873,x25871,x25874),f450(x25873,x25872,x25874))
% 25.54/25.43 [2588]~E(x25881,x25882)+E(f450(x25883,x25884,x25881),f450(x25883,x25884,x25882))
% 25.54/25.43 [2589]~E(x25891,x25892)+E(f829(x25891,x25893,x25894,x25895),f829(x25892,x25893,x25894,x25895))
% 25.54/25.43 [2590]~E(x25901,x25902)+E(f829(x25903,x25901,x25904,x25905),f829(x25903,x25902,x25904,x25905))
% 25.54/25.43 [2591]~E(x25911,x25912)+E(f829(x25913,x25914,x25911,x25915),f829(x25913,x25914,x25912,x25915))
% 25.54/25.43 [2592]~E(x25921,x25922)+E(f829(x25923,x25924,x25925,x25921),f829(x25923,x25924,x25925,x25922))
% 25.54/25.43 [2593]~E(x25931,x25932)+E(f436(x25931,x25933,x25934),f436(x25932,x25933,x25934))
% 25.54/25.43 [2594]~E(x25941,x25942)+E(f436(x25943,x25941,x25944),f436(x25943,x25942,x25944))
% 25.54/25.43 [2595]~E(x25951,x25952)+E(f436(x25953,x25954,x25951),f436(x25953,x25954,x25952))
% 25.54/25.43 [2596]~E(x25961,x25962)+E(f590(x25961,x25963,x25964),f590(x25962,x25963,x25964))
% 25.54/25.43 [2597]~E(x25971,x25972)+E(f590(x25973,x25971,x25974),f590(x25973,x25972,x25974))
% 25.54/25.43 [2598]~E(x25981,x25982)+E(f590(x25983,x25984,x25981),f590(x25983,x25984,x25982))
% 25.54/25.43 [2599]~E(x25991,x25992)+E(f438(x25991,x25993,x25994),f438(x25992,x25993,x25994))
% 25.54/25.43 [2600]~E(x26001,x26002)+E(f438(x26003,x26001,x26004),f438(x26003,x26002,x26004))
% 25.54/25.43 [2601]~E(x26011,x26012)+E(f438(x26013,x26014,x26011),f438(x26013,x26014,x26012))
% 25.54/25.43 [2602]~E(x26021,x26022)+E(f609(x26021,x26023),f609(x26022,x26023))
% 25.54/25.43 [2603]~E(x26031,x26032)+E(f609(x26033,x26031),f609(x26033,x26032))
% 25.54/25.43 [2604]~E(x26041,x26042)+E(f909(x26041,x26043,x26044,x26045),f909(x26042,x26043,x26044,x26045))
% 25.54/25.43 [2605]~E(x26051,x26052)+E(f909(x26053,x26051,x26054,x26055),f909(x26053,x26052,x26054,x26055))
% 25.54/25.43 [2606]~E(x26061,x26062)+E(f909(x26063,x26064,x26061,x26065),f909(x26063,x26064,x26062,x26065))
% 25.54/25.43 [2607]~E(x26071,x26072)+E(f909(x26073,x26074,x26075,x26071),f909(x26073,x26074,x26075,x26072))
% 25.54/25.43 [2608]~E(x26081,x26082)+E(f376(x26081,x26083,x26084,x26085),f376(x26082,x26083,x26084,x26085))
% 25.54/25.43 [2609]~E(x26091,x26092)+E(f376(x26093,x26091,x26094,x26095),f376(x26093,x26092,x26094,x26095))
% 25.54/25.43 [2610]~E(x26101,x26102)+E(f376(x26103,x26104,x26101,x26105),f376(x26103,x26104,x26102,x26105))
% 25.54/25.43 [2611]~E(x26111,x26112)+E(f376(x26113,x26114,x26115,x26111),f376(x26113,x26114,x26115,x26112))
% 25.54/25.43 [2612]~E(x26121,x26122)+E(f557(x26121,x26123),f557(x26122,x26123))
% 25.54/25.43 [2613]~E(x26131,x26132)+E(f557(x26133,x26131),f557(x26133,x26132))
% 25.54/25.43 [2614]~E(x26141,x26142)+E(f809(x26141,x26143),f809(x26142,x26143))
% 25.54/25.43 [2615]~E(x26151,x26152)+E(f809(x26153,x26151),f809(x26153,x26152))
% 25.54/25.43 [2616]~E(x26161,x26162)+E(f732(x26161,x26163),f732(x26162,x26163))
% 25.54/25.43 [2617]~E(x26171,x26172)+E(f732(x26173,x26171),f732(x26173,x26172))
% 25.54/25.43 [2618]~E(x26181,x26182)+E(f696(x26181,x26183,x26184),f696(x26182,x26183,x26184))
% 25.54/25.43 [2619]~E(x26191,x26192)+E(f696(x26193,x26191,x26194),f696(x26193,x26192,x26194))
% 25.54/25.43 [2620]~E(x26201,x26202)+E(f696(x26203,x26204,x26201),f696(x26203,x26204,x26202))
% 25.54/25.43 [2621]~E(x26211,x26212)+E(f261(x26211,x26213),f261(x26212,x26213))
% 25.54/25.43 [2622]~E(x26221,x26222)+E(f261(x26223,x26221),f261(x26223,x26222))
% 25.54/25.43 [2623]~E(x26231,x26232)+E(f654(x26231,x26233,x26234,x26235,x26236,x26237),f654(x26232,x26233,x26234,x26235,x26236,x26237))
% 25.54/25.43 [2624]~E(x26241,x26242)+E(f654(x26243,x26241,x26244,x26245,x26246,x26247),f654(x26243,x26242,x26244,x26245,x26246,x26247))
% 25.54/25.43 [2625]~E(x26251,x26252)+E(f654(x26253,x26254,x26251,x26255,x26256,x26257),f654(x26253,x26254,x26252,x26255,x26256,x26257))
% 25.54/25.43 [2626]~E(x26261,x26262)+E(f654(x26263,x26264,x26265,x26261,x26266,x26267),f654(x26263,x26264,x26265,x26262,x26266,x26267))
% 25.54/25.43 [2627]~E(x26271,x26272)+E(f654(x26273,x26274,x26275,x26276,x26271,x26277),f654(x26273,x26274,x26275,x26276,x26272,x26277))
% 25.54/25.43 [2628]~E(x26281,x26282)+E(f654(x26283,x26284,x26285,x26286,x26287,x26281),f654(x26283,x26284,x26285,x26286,x26287,x26282))
% 25.54/25.43 [2629]~E(x26291,x26292)+E(f620(x26291,x26293,x26294),f620(x26292,x26293,x26294))
% 25.54/25.43 [2630]~E(x26301,x26302)+E(f620(x26303,x26301,x26304),f620(x26303,x26302,x26304))
% 25.54/25.43 [2631]~E(x26311,x26312)+E(f620(x26313,x26314,x26311),f620(x26313,x26314,x26312))
% 25.54/25.43 [2632]~E(x26321,x26322)+E(f447(x26321,x26323,x26324),f447(x26322,x26323,x26324))
% 25.54/25.43 [2633]~E(x26331,x26332)+E(f447(x26333,x26331,x26334),f447(x26333,x26332,x26334))
% 25.54/25.43 [2634]~E(x26341,x26342)+E(f447(x26343,x26344,x26341),f447(x26343,x26344,x26342))
% 25.54/25.43 [2635]~E(x26351,x26352)+E(f426(x26351),f426(x26352))
% 25.54/25.43 [2636]~E(x26361,x26362)+E(f336(x26361,x26363,x26364),f336(x26362,x26363,x26364))
% 25.54/25.43 [2637]~E(x26371,x26372)+E(f336(x26373,x26371,x26374),f336(x26373,x26372,x26374))
% 25.54/25.43 [2638]~E(x26381,x26382)+E(f336(x26383,x26384,x26381),f336(x26383,x26384,x26382))
% 25.54/25.43 [2639]~E(x26391,x26392)+E(f717(x26391,x26393,x26394),f717(x26392,x26393,x26394))
% 25.54/25.43 [2640]~E(x26401,x26402)+E(f717(x26403,x26401,x26404),f717(x26403,x26402,x26404))
% 25.54/25.43 [2641]~E(x26411,x26412)+E(f717(x26413,x26414,x26411),f717(x26413,x26414,x26412))
% 25.54/25.43 [2642]~E(x26421,x26422)+E(f412(x26421,x26423,x26424),f412(x26422,x26423,x26424))
% 25.54/25.43 [2643]~E(x26431,x26432)+E(f412(x26433,x26431,x26434),f412(x26433,x26432,x26434))
% 25.54/25.43 [2644]~E(x26441,x26442)+E(f412(x26443,x26444,x26441),f412(x26443,x26444,x26442))
% 25.54/25.43 [2645]~E(x26451,x26452)+E(f424(x26451),f424(x26452))
% 25.54/25.43 [2646]~E(x26461,x26462)+E(f624(x26461,x26463,x26464,x26465,x26466),f624(x26462,x26463,x26464,x26465,x26466))
% 25.54/25.43 [2647]~E(x26471,x26472)+E(f624(x26473,x26471,x26474,x26475,x26476),f624(x26473,x26472,x26474,x26475,x26476))
% 25.54/25.43 [2648]~E(x26481,x26482)+E(f624(x26483,x26484,x26481,x26485,x26486),f624(x26483,x26484,x26482,x26485,x26486))
% 25.54/25.43 [2649]~E(x26491,x26492)+E(f624(x26493,x26494,x26495,x26491,x26496),f624(x26493,x26494,x26495,x26492,x26496))
% 25.54/25.43 [2650]~E(x26501,x26502)+E(f624(x26503,x26504,x26505,x26506,x26501),f624(x26503,x26504,x26505,x26506,x26502))
% 25.54/25.43 [2651]~E(x26511,x26512)+E(f621(x26511,x26513),f621(x26512,x26513))
% 25.54/25.43 [2652]~E(x26521,x26522)+E(f621(x26523,x26521),f621(x26523,x26522))
% 25.54/25.43 [2653]~E(x26531,x26532)+E(f399(x26531,x26533,x26534,x26535),f399(x26532,x26533,x26534,x26535))
% 25.54/25.43 [2654]~E(x26541,x26542)+E(f399(x26543,x26541,x26544,x26545),f399(x26543,x26542,x26544,x26545))
% 25.54/25.43 [2655]~E(x26551,x26552)+E(f399(x26553,x26554,x26551,x26555),f399(x26553,x26554,x26552,x26555))
% 25.54/25.43 [2656]~E(x26561,x26562)+E(f399(x26563,x26564,x26565,x26561),f399(x26563,x26564,x26565,x26562))
% 25.54/25.43 [2657]~E(x26571,x26572)+E(f860(x26571,x26573,x26574),f860(x26572,x26573,x26574))
% 25.54/25.43 [2658]~E(x26581,x26582)+E(f860(x26583,x26581,x26584),f860(x26583,x26582,x26584))
% 25.54/25.43 [2659]~E(x26591,x26592)+E(f860(x26593,x26594,x26591),f860(x26593,x26594,x26592))
% 25.54/25.43 [2660]~E(x26601,x26602)+E(f563(x26601,x26603,x26604,x26605),f563(x26602,x26603,x26604,x26605))
% 25.54/25.43 [2661]~E(x26611,x26612)+E(f563(x26613,x26611,x26614,x26615),f563(x26613,x26612,x26614,x26615))
% 25.54/25.43 [2662]~E(x26621,x26622)+E(f563(x26623,x26624,x26621,x26625),f563(x26623,x26624,x26622,x26625))
% 25.54/25.43 [2663]~E(x26631,x26632)+E(f563(x26633,x26634,x26635,x26631),f563(x26633,x26634,x26635,x26632))
% 25.54/25.43 [2664]~E(x26641,x26642)+E(f733(x26641,x26643),f733(x26642,x26643))
% 25.54/25.43 [2665]~E(x26651,x26652)+E(f733(x26653,x26651),f733(x26653,x26652))
% 25.54/25.43 [2666]~E(x26661,x26662)+E(f606(x26661,x26663),f606(x26662,x26663))
% 25.54/25.43 [2667]~E(x26671,x26672)+E(f606(x26673,x26671),f606(x26673,x26672))
% 25.54/25.43 [2668]~E(x26681,x26682)+E(f271(x26681,x26683,x26684,x26685),f271(x26682,x26683,x26684,x26685))
% 25.54/25.43 [2669]~E(x26691,x26692)+E(f271(x26693,x26691,x26694,x26695),f271(x26693,x26692,x26694,x26695))
% 25.54/25.43 [2670]~E(x26701,x26702)+E(f271(x26703,x26704,x26701,x26705),f271(x26703,x26704,x26702,x26705))
% 25.54/25.43 [2671]~E(x26711,x26712)+E(f271(x26713,x26714,x26715,x26711),f271(x26713,x26714,x26715,x26712))
% 25.54/25.43 [2672]~E(x26721,x26722)+E(f265(x26721,x26723,x26724,x26725),f265(x26722,x26723,x26724,x26725))
% 25.54/25.43 [2673]~E(x26731,x26732)+E(f265(x26733,x26731,x26734,x26735),f265(x26733,x26732,x26734,x26735))
% 25.54/25.43 [2674]~E(x26741,x26742)+E(f265(x26743,x26744,x26741,x26745),f265(x26743,x26744,x26742,x26745))
% 25.54/25.43 [2675]~E(x26751,x26752)+E(f265(x26753,x26754,x26755,x26751),f265(x26753,x26754,x26755,x26752))
% 25.54/25.43 [2676]~E(x26761,x26762)+E(f614(x26761,x26763,x26764),f614(x26762,x26763,x26764))
% 25.54/25.43 [2677]~E(x26771,x26772)+E(f614(x26773,x26771,x26774),f614(x26773,x26772,x26774))
% 25.54/25.43 [2678]~E(x26781,x26782)+E(f614(x26783,x26784,x26781),f614(x26783,x26784,x26782))
% 25.54/25.43 [2679]~E(x26791,x26792)+E(f115(x26791,x26793,x26794,x26795),f115(x26792,x26793,x26794,x26795))
% 25.54/25.43 [2680]~E(x26801,x26802)+E(f115(x26803,x26801,x26804,x26805),f115(x26803,x26802,x26804,x26805))
% 25.54/25.43 [2681]~E(x26811,x26812)+E(f115(x26813,x26814,x26811,x26815),f115(x26813,x26814,x26812,x26815))
% 25.54/25.43 [2682]~E(x26821,x26822)+E(f115(x26823,x26824,x26825,x26821),f115(x26823,x26824,x26825,x26822))
% 25.54/25.43 [2683]~E(x26831,x26832)+E(f828(x26831,x26833),f828(x26832,x26833))
% 25.54/25.43 [2684]~E(x26841,x26842)+E(f828(x26843,x26841),f828(x26843,x26842))
% 25.54/25.43 [2685]~E(x26851,x26852)+E(f486(x26851,x26853,x26854,x26855),f486(x26852,x26853,x26854,x26855))
% 25.54/25.43 [2686]~E(x26861,x26862)+E(f486(x26863,x26861,x26864,x26865),f486(x26863,x26862,x26864,x26865))
% 25.54/25.43 [2687]~E(x26871,x26872)+E(f486(x26873,x26874,x26871,x26875),f486(x26873,x26874,x26872,x26875))
% 25.54/25.43 [2688]~E(x26881,x26882)+E(f486(x26883,x26884,x26885,x26881),f486(x26883,x26884,x26885,x26882))
% 25.54/25.43 [2689]~E(x26891,x26892)+E(f611(x26891,x26893,x26894),f611(x26892,x26893,x26894))
% 25.54/25.43 [2690]~E(x26901,x26902)+E(f611(x26903,x26901,x26904),f611(x26903,x26902,x26904))
% 25.54/25.43 [2691]~E(x26911,x26912)+E(f611(x26913,x26914,x26911),f611(x26913,x26914,x26912))
% 25.54/25.43 [2692]~E(x26921,x26922)+E(f902(x26921,x26923,x26924),f902(x26922,x26923,x26924))
% 25.54/25.43 [2693]~E(x26931,x26932)+E(f902(x26933,x26931,x26934),f902(x26933,x26932,x26934))
% 25.54/25.43 [2694]~E(x26941,x26942)+E(f902(x26943,x26944,x26941),f902(x26943,x26944,x26942))
% 25.54/25.43 [2695]~E(x26951,x26952)+E(f595(x26951,x26953,x26954),f595(x26952,x26953,x26954))
% 25.54/25.43 [2696]~E(x26961,x26962)+E(f595(x26963,x26961,x26964),f595(x26963,x26962,x26964))
% 25.54/25.43 [2697]~E(x26971,x26972)+E(f595(x26973,x26974,x26971),f595(x26973,x26974,x26972))
% 25.54/25.43 [2698]~E(x26981,x26982)+E(f763(x26981,x26983,x26984),f763(x26982,x26983,x26984))
% 25.54/25.43 [2699]~E(x26991,x26992)+E(f763(x26993,x26991,x26994),f763(x26993,x26992,x26994))
% 25.54/25.43 [2700]~E(x27001,x27002)+E(f763(x27003,x27004,x27001),f763(x27003,x27004,x27002))
% 25.54/25.43 [2701]~E(x27011,x27012)+E(f695(x27011,x27013,x27014,x27015,x27016),f695(x27012,x27013,x27014,x27015,x27016))
% 25.54/25.43 [2702]~E(x27021,x27022)+E(f695(x27023,x27021,x27024,x27025,x27026),f695(x27023,x27022,x27024,x27025,x27026))
% 25.54/25.43 [2703]~E(x27031,x27032)+E(f695(x27033,x27034,x27031,x27035,x27036),f695(x27033,x27034,x27032,x27035,x27036))
% 25.54/25.43 [2704]~E(x27041,x27042)+E(f695(x27043,x27044,x27045,x27041,x27046),f695(x27043,x27044,x27045,x27042,x27046))
% 25.54/25.43 [2705]~E(x27051,x27052)+E(f695(x27053,x27054,x27055,x27056,x27051),f695(x27053,x27054,x27055,x27056,x27052))
% 25.54/25.43 [2706]~E(x27061,x27062)+E(f409(x27061,x27063),f409(x27062,x27063))
% 25.54/25.43 [2707]~E(x27071,x27072)+E(f409(x27073,x27071),f409(x27073,x27072))
% 25.54/25.43 [2708]~E(x27081,x27082)+E(f467(x27081,x27083,x27084),f467(x27082,x27083,x27084))
% 25.54/25.43 [2709]~E(x27091,x27092)+E(f467(x27093,x27091,x27094),f467(x27093,x27092,x27094))
% 25.54/25.43 [2710]~E(x27101,x27102)+E(f467(x27103,x27104,x27101),f467(x27103,x27104,x27102))
% 25.54/25.43 [2711]~E(x27111,x27112)+E(f252(x27111,x27113,x27114,x27115,x27116),f252(x27112,x27113,x27114,x27115,x27116))
% 25.54/25.43 [2712]~E(x27121,x27122)+E(f252(x27123,x27121,x27124,x27125,x27126),f252(x27123,x27122,x27124,x27125,x27126))
% 25.54/25.43 [2713]~E(x27131,x27132)+E(f252(x27133,x27134,x27131,x27135,x27136),f252(x27133,x27134,x27132,x27135,x27136))
% 25.54/25.43 [2714]~E(x27141,x27142)+E(f252(x27143,x27144,x27145,x27141,x27146),f252(x27143,x27144,x27145,x27142,x27146))
% 25.54/25.43 [2715]~E(x27151,x27152)+E(f252(x27153,x27154,x27155,x27156,x27151),f252(x27153,x27154,x27155,x27156,x27152))
% 25.54/25.43 [2716]~E(x27161,x27162)+E(f789(x27161,x27163),f789(x27162,x27163))
% 25.54/25.43 [2717]~E(x27171,x27172)+E(f789(x27173,x27171),f789(x27173,x27172))
% 25.54/25.43 [2718]~E(x27181,x27182)+E(f221(x27181,x27183,x27184),f221(x27182,x27183,x27184))
% 25.54/25.43 [2719]~E(x27191,x27192)+E(f221(x27193,x27191,x27194),f221(x27193,x27192,x27194))
% 25.54/25.43 [2720]~E(x27201,x27202)+E(f221(x27203,x27204,x27201),f221(x27203,x27204,x27202))
% 25.54/25.43 [2721]~E(x27211,x27212)+E(f325(x27211),f325(x27212))
% 25.54/25.43 [2722]~E(x27221,x27222)+E(f883(x27221,x27223),f883(x27222,x27223))
% 25.54/25.43 [2723]~E(x27231,x27232)+E(f883(x27233,x27231),f883(x27233,x27232))
% 25.54/25.43 [2724]~E(x27241,x27242)+E(f825(x27241,x27243,x27244),f825(x27242,x27243,x27244))
% 25.54/25.43 [2725]~E(x27251,x27252)+E(f825(x27253,x27251,x27254),f825(x27253,x27252,x27254))
% 25.54/25.43 [2726]~E(x27261,x27262)+E(f825(x27263,x27264,x27261),f825(x27263,x27264,x27262))
% 25.54/25.43 [2727]~E(x27271,x27272)+E(f343(x27271,x27273),f343(x27272,x27273))
% 25.54/25.43 [2728]~E(x27281,x27282)+E(f343(x27283,x27281),f343(x27283,x27282))
% 25.54/25.43 [2729]~E(x27291,x27292)+E(f749(x27291,x27293,x27294,x27295,x27296),f749(x27292,x27293,x27294,x27295,x27296))
% 25.54/25.43 [2730]~E(x27301,x27302)+E(f749(x27303,x27301,x27304,x27305,x27306),f749(x27303,x27302,x27304,x27305,x27306))
% 25.54/25.43 [2731]~E(x27311,x27312)+E(f749(x27313,x27314,x27311,x27315,x27316),f749(x27313,x27314,x27312,x27315,x27316))
% 25.54/25.43 [2732]~E(x27321,x27322)+E(f749(x27323,x27324,x27325,x27321,x27326),f749(x27323,x27324,x27325,x27322,x27326))
% 25.54/25.43 [2733]~E(x27331,x27332)+E(f749(x27333,x27334,x27335,x27336,x27331),f749(x27333,x27334,x27335,x27336,x27332))
% 25.54/25.43 [2734]~E(x27341,x27342)+E(f562(x27341,x27343),f562(x27342,x27343))
% 25.54/25.43 [2735]~E(x27351,x27352)+E(f562(x27353,x27351),f562(x27353,x27352))
% 25.54/25.43 [2736]~E(x27361,x27362)+E(f570(x27361,x27363),f570(x27362,x27363))
% 25.54/25.43 [2737]~E(x27371,x27372)+E(f570(x27373,x27371),f570(x27373,x27372))
% 25.54/25.43 [2738]~E(x27381,x27382)+E(f830(x27381,x27383,x27384,x27385,x27386,x27387),f830(x27382,x27383,x27384,x27385,x27386,x27387))
% 25.54/25.43 [2739]~E(x27391,x27392)+E(f830(x27393,x27391,x27394,x27395,x27396,x27397),f830(x27393,x27392,x27394,x27395,x27396,x27397))
% 25.54/25.43 [2740]~E(x27401,x27402)+E(f830(x27403,x27404,x27401,x27405,x27406,x27407),f830(x27403,x27404,x27402,x27405,x27406,x27407))
% 25.54/25.43 [2741]~E(x27411,x27412)+E(f830(x27413,x27414,x27415,x27411,x27416,x27417),f830(x27413,x27414,x27415,x27412,x27416,x27417))
% 25.54/25.43 [2742]~E(x27421,x27422)+E(f830(x27423,x27424,x27425,x27426,x27421,x27427),f830(x27423,x27424,x27425,x27426,x27422,x27427))
% 25.54/25.43 [2743]~E(x27431,x27432)+E(f830(x27433,x27434,x27435,x27436,x27437,x27431),f830(x27433,x27434,x27435,x27436,x27437,x27432))
% 25.54/25.43 [2744]~E(x27441,x27442)+E(f334(x27441,x27443,x27444,x27445),f334(x27442,x27443,x27444,x27445))
% 25.54/25.43 [2745]~E(x27451,x27452)+E(f334(x27453,x27451,x27454,x27455),f334(x27453,x27452,x27454,x27455))
% 25.54/25.43 [2746]~E(x27461,x27462)+E(f334(x27463,x27464,x27461,x27465),f334(x27463,x27464,x27462,x27465))
% 25.54/25.43 [2747]~E(x27471,x27472)+E(f334(x27473,x27474,x27475,x27471),f334(x27473,x27474,x27475,x27472))
% 25.54/25.43 [2748]~E(x27481,x27482)+E(f341(x27481,x27483,x27484,x27485),f341(x27482,x27483,x27484,x27485))
% 25.54/25.43 [2749]~E(x27491,x27492)+E(f341(x27493,x27491,x27494,x27495),f341(x27493,x27492,x27494,x27495))
% 25.54/25.43 [2750]~E(x27501,x27502)+E(f341(x27503,x27504,x27501,x27505),f341(x27503,x27504,x27502,x27505))
% 25.54/25.43 [2751]~E(x27511,x27512)+E(f341(x27513,x27514,x27515,x27511),f341(x27513,x27514,x27515,x27512))
% 25.54/25.43 [2752]~E(x27521,x27522)+E(f489(x27521,x27523,x27524,x27525),f489(x27522,x27523,x27524,x27525))
% 25.54/25.43 [2753]~E(x27531,x27532)+E(f489(x27533,x27531,x27534,x27535),f489(x27533,x27532,x27534,x27535))
% 25.54/25.43 [2754]~E(x27541,x27542)+E(f489(x27543,x27544,x27541,x27545),f489(x27543,x27544,x27542,x27545))
% 25.54/25.43 [2755]~E(x27551,x27552)+E(f489(x27553,x27554,x27555,x27551),f489(x27553,x27554,x27555,x27552))
% 25.54/25.43 [2756]~E(x27561,x27562)+E(f411(x27561,x27563),f411(x27562,x27563))
% 25.54/25.43 [2757]~E(x27571,x27572)+E(f411(x27573,x27571),f411(x27573,x27572))
% 25.54/25.43 [2758]~E(x27581,x27582)+E(f818(x27581,x27583,x27584,x27585,x27586),f818(x27582,x27583,x27584,x27585,x27586))
% 25.54/25.43 [2759]~E(x27591,x27592)+E(f818(x27593,x27591,x27594,x27595,x27596),f818(x27593,x27592,x27594,x27595,x27596))
% 25.54/25.43 [2760]~E(x27601,x27602)+E(f818(x27603,x27604,x27601,x27605,x27606),f818(x27603,x27604,x27602,x27605,x27606))
% 25.54/25.43 [2761]~E(x27611,x27612)+E(f818(x27613,x27614,x27615,x27611,x27616),f818(x27613,x27614,x27615,x27612,x27616))
% 25.54/25.43 [2762]~E(x27621,x27622)+E(f818(x27623,x27624,x27625,x27626,x27621),f818(x27623,x27624,x27625,x27626,x27622))
% 25.54/25.43 [2763]~E(x27631,x27632)+E(f756(x27631,x27633),f756(x27632,x27633))
% 25.54/25.43 [2764]~E(x27641,x27642)+E(f756(x27643,x27641),f756(x27643,x27642))
% 25.54/25.43 [2765]~E(x27651,x27652)+E(f544(x27651,x27653,x27654,x27655,x27656,x27657,x27658,x27659),f544(x27652,x27653,x27654,x27655,x27656,x27657,x27658,x27659))
% 25.54/25.43 [2766]~E(x27661,x27662)+E(f544(x27663,x27661,x27664,x27665,x27666,x27667,x27668,x27669),f544(x27663,x27662,x27664,x27665,x27666,x27667,x27668,x27669))
% 25.54/25.43 [2767]~E(x27671,x27672)+E(f544(x27673,x27674,x27671,x27675,x27676,x27677,x27678,x27679),f544(x27673,x27674,x27672,x27675,x27676,x27677,x27678,x27679))
% 25.54/25.43 [2768]~E(x27681,x27682)+E(f544(x27683,x27684,x27685,x27681,x27686,x27687,x27688,x27689),f544(x27683,x27684,x27685,x27682,x27686,x27687,x27688,x27689))
% 25.54/25.43 [2769]~E(x27691,x27692)+E(f544(x27693,x27694,x27695,x27696,x27691,x27697,x27698,x27699),f544(x27693,x27694,x27695,x27696,x27692,x27697,x27698,x27699))
% 25.54/25.43 [2770]~E(x27701,x27702)+E(f544(x27703,x27704,x27705,x27706,x27707,x27701,x27708,x27709),f544(x27703,x27704,x27705,x27706,x27707,x27702,x27708,x27709))
% 25.54/25.43 [2771]~E(x27711,x27712)+E(f544(x27713,x27714,x27715,x27716,x27717,x27718,x27711,x27719),f544(x27713,x27714,x27715,x27716,x27717,x27718,x27712,x27719))
% 25.54/25.43 [2772]~E(x27721,x27722)+E(f544(x27723,x27724,x27725,x27726,x27727,x27728,x27729,x27721),f544(x27723,x27724,x27725,x27726,x27727,x27728,x27729,x27722))
% 25.54/25.43 [2773]~E(x27731,x27732)+E(f369(x27731,x27733,x27734),f369(x27732,x27733,x27734))
% 25.54/25.43 [2774]~E(x27741,x27742)+E(f369(x27743,x27741,x27744),f369(x27743,x27742,x27744))
% 25.54/25.43 [2775]~E(x27751,x27752)+E(f369(x27753,x27754,x27751),f369(x27753,x27754,x27752))
% 25.54/25.43 [2776]~E(x27761,x27762)+E(f222(x27761,x27763,x27764,x27765),f222(x27762,x27763,x27764,x27765))
% 25.54/25.43 [2777]~E(x27771,x27772)+E(f222(x27773,x27771,x27774,x27775),f222(x27773,x27772,x27774,x27775))
% 25.54/25.43 [2778]~E(x27781,x27782)+E(f222(x27783,x27784,x27781,x27785),f222(x27783,x27784,x27782,x27785))
% 25.54/25.43 [2779]~E(x27791,x27792)+E(f222(x27793,x27794,x27795,x27791),f222(x27793,x27794,x27795,x27792))
% 25.54/25.43 [2780]~E(x27801,x27802)+E(f698(x27801,x27803,x27804),f698(x27802,x27803,x27804))
% 25.54/25.43 [2781]~E(x27811,x27812)+E(f698(x27813,x27811,x27814),f698(x27813,x27812,x27814))
% 25.54/25.43 [2782]~E(x27821,x27822)+E(f698(x27823,x27824,x27821),f698(x27823,x27824,x27822))
% 25.54/25.43 [2783]~E(x27831,x27832)+E(f720(x27831,x27833,x27834),f720(x27832,x27833,x27834))
% 25.54/25.43 [2784]~E(x27841,x27842)+E(f720(x27843,x27841,x27844),f720(x27843,x27842,x27844))
% 25.54/25.43 [2785]~E(x27851,x27852)+E(f720(x27853,x27854,x27851),f720(x27853,x27854,x27852))
% 25.54/25.43 [2786]~E(x27861,x27862)+E(f197(x27861),f197(x27862))
% 25.54/25.43 [2787]~E(x27871,x27872)+E(f401(x27871,x27873,x27874,x27875),f401(x27872,x27873,x27874,x27875))
% 25.54/25.43 [2788]~E(x27881,x27882)+E(f401(x27883,x27881,x27884,x27885),f401(x27883,x27882,x27884,x27885))
% 25.54/25.43 [2789]~E(x27891,x27892)+E(f401(x27893,x27894,x27891,x27895),f401(x27893,x27894,x27892,x27895))
% 25.54/25.43 [2790]~E(x27901,x27902)+E(f401(x27903,x27904,x27905,x27901),f401(x27903,x27904,x27905,x27902))
% 25.54/25.43 [2791]~E(x27911,x27912)+E(f629(x27911,x27913,x27914),f629(x27912,x27913,x27914))
% 25.54/25.43 [2792]~E(x27921,x27922)+E(f629(x27923,x27921,x27924),f629(x27923,x27922,x27924))
% 25.54/25.43 [2793]~E(x27931,x27932)+E(f629(x27933,x27934,x27931),f629(x27933,x27934,x27932))
% 25.54/25.43 [2794]~E(x27941,x27942)+E(f762(x27941,x27943,x27944),f762(x27942,x27943,x27944))
% 25.54/25.43 [2795]~E(x27951,x27952)+E(f762(x27953,x27951,x27954),f762(x27953,x27952,x27954))
% 25.54/25.43 [2796]~E(x27961,x27962)+E(f762(x27963,x27964,x27961),f762(x27963,x27964,x27962))
% 25.54/25.43 [2797]~E(x27971,x27972)+E(f266(x27971,x27973,x27974),f266(x27972,x27973,x27974))
% 25.54/25.43 [2798]~E(x27981,x27982)+E(f266(x27983,x27981,x27984),f266(x27983,x27982,x27984))
% 25.54/25.43 [2799]~E(x27991,x27992)+E(f266(x27993,x27994,x27991),f266(x27993,x27994,x27992))
% 25.54/25.43 [2800]~E(x28001,x28002)+E(f596(x28001,x28003,x28004),f596(x28002,x28003,x28004))
% 25.54/25.43 [2801]~E(x28011,x28012)+E(f596(x28013,x28011,x28014),f596(x28013,x28012,x28014))
% 25.54/25.43 [2802]~E(x28021,x28022)+E(f596(x28023,x28024,x28021),f596(x28023,x28024,x28022))
% 25.54/25.43 [2803]~E(x28031,x28032)+E(f815(x28031,x28033),f815(x28032,x28033))
% 25.54/25.43 [2804]~E(x28041,x28042)+E(f815(x28043,x28041),f815(x28043,x28042))
% 25.54/25.43 [2805]~E(x28051,x28052)+E(f788(x28051,x28053),f788(x28052,x28053))
% 25.54/25.43 [2806]~E(x28061,x28062)+E(f788(x28063,x28061),f788(x28063,x28062))
% 25.54/25.43 [2807]~E(x28071,x28072)+E(f767(x28071,x28073,x28074),f767(x28072,x28073,x28074))
% 25.54/25.43 [2808]~E(x28081,x28082)+E(f767(x28083,x28081,x28084),f767(x28083,x28082,x28084))
% 25.54/25.43 [2809]~E(x28091,x28092)+E(f767(x28093,x28094,x28091),f767(x28093,x28094,x28092))
% 25.54/25.43 [2810]~E(x28101,x28102)+E(f773(x28101,x28103,x28104),f773(x28102,x28103,x28104))
% 25.54/25.43 [2811]~E(x28111,x28112)+E(f773(x28113,x28111,x28114),f773(x28113,x28112,x28114))
% 25.54/25.43 [2812]~E(x28121,x28122)+E(f773(x28123,x28124,x28121),f773(x28123,x28124,x28122))
% 25.54/25.43 [2813]~E(x28131,x28132)+E(f581(x28131,x28133,x28134,x28135),f581(x28132,x28133,x28134,x28135))
% 25.54/25.43 [2814]~E(x28141,x28142)+E(f581(x28143,x28141,x28144,x28145),f581(x28143,x28142,x28144,x28145))
% 25.54/25.43 [2815]~E(x28151,x28152)+E(f581(x28153,x28154,x28151,x28155),f581(x28153,x28154,x28152,x28155))
% 25.54/25.43 [2816]~E(x28161,x28162)+E(f581(x28163,x28164,x28165,x28161),f581(x28163,x28164,x28165,x28162))
% 25.54/25.43 [2817]~E(x28171,x28172)+E(f814(x28171),f814(x28172))
% 25.54/25.43 [2818]~E(x28181,x28182)+E(f215(x28181,x28183,x28184),f215(x28182,x28183,x28184))
% 25.54/25.43 [2819]~E(x28191,x28192)+E(f215(x28193,x28191,x28194),f215(x28193,x28192,x28194))
% 25.54/25.43 [2820]~E(x28201,x28202)+E(f215(x28203,x28204,x28201),f215(x28203,x28204,x28202))
% 25.54/25.43 [2821]~E(x28211,x28212)+E(f196(x28211,x28213,x28214),f196(x28212,x28213,x28214))
% 25.54/25.43 [2822]~E(x28221,x28222)+E(f196(x28223,x28221,x28224),f196(x28223,x28222,x28224))
% 25.54/25.43 [2823]~E(x28231,x28232)+E(f196(x28233,x28234,x28231),f196(x28233,x28234,x28232))
% 25.54/25.43 [2824]~E(x28241,x28242)+E(f218(x28241,x28243,x28244,x28245,x28246),f218(x28242,x28243,x28244,x28245,x28246))
% 25.54/25.43 [2825]~E(x28251,x28252)+E(f218(x28253,x28251,x28254,x28255,x28256),f218(x28253,x28252,x28254,x28255,x28256))
% 25.54/25.43 [2826]~E(x28261,x28262)+E(f218(x28263,x28264,x28261,x28265,x28266),f218(x28263,x28264,x28262,x28265,x28266))
% 25.54/25.43 [2827]~E(x28271,x28272)+E(f218(x28273,x28274,x28275,x28271,x28276),f218(x28273,x28274,x28275,x28272,x28276))
% 25.54/25.43 [2828]~E(x28281,x28282)+E(f218(x28283,x28284,x28285,x28286,x28281),f218(x28283,x28284,x28285,x28286,x28282))
% 25.54/25.43 [2829]~E(x28291,x28292)+E(f482(x28291,x28293,x28294,x28295,x28296),f482(x28292,x28293,x28294,x28295,x28296))
% 25.54/25.43 [2830]~E(x28301,x28302)+E(f482(x28303,x28301,x28304,x28305,x28306),f482(x28303,x28302,x28304,x28305,x28306))
% 25.54/25.43 [2831]~E(x28311,x28312)+E(f482(x28313,x28314,x28311,x28315,x28316),f482(x28313,x28314,x28312,x28315,x28316))
% 25.54/25.43 [2832]~E(x28321,x28322)+E(f482(x28323,x28324,x28325,x28321,x28326),f482(x28323,x28324,x28325,x28322,x28326))
% 25.54/25.43 [2833]~E(x28331,x28332)+E(f482(x28333,x28334,x28335,x28336,x28331),f482(x28333,x28334,x28335,x28336,x28332))
% 25.54/25.43 [2834]~E(x28341,x28342)+E(f352(x28341,x28343,x28344),f352(x28342,x28343,x28344))
% 25.54/25.43 [2835]~E(x28351,x28352)+E(f352(x28353,x28351,x28354),f352(x28353,x28352,x28354))
% 25.54/25.43 [2836]~E(x28361,x28362)+E(f352(x28363,x28364,x28361),f352(x28363,x28364,x28362))
% 25.54/25.43 [2837]~E(x28371,x28372)+E(f561(x28371,x28373),f561(x28372,x28373))
% 25.54/25.43 [2838]~E(x28381,x28382)+E(f561(x28383,x28381),f561(x28383,x28382))
% 25.54/25.43 [2839]~P1(x28391)+P1(x28392)+~E(x28391,x28392)
% 25.54/25.43 [2840]~P2(x28401)+P2(x28402)+~E(x28401,x28402)
% 25.54/25.43 [2841]~P104(x28411)+P104(x28412)+~E(x28411,x28412)
% 25.54/25.43 [2842]~P109(x28421)+P109(x28422)+~E(x28421,x28422)
% 25.54/25.43 [2843]P49(x28432,x28433)+~E(x28431,x28432)+~P49(x28431,x28433)
% 25.54/25.43 [2844]P49(x28443,x28442)+~E(x28441,x28442)+~P49(x28443,x28441)
% 25.54/25.43 [2845]~P86(x28451)+P86(x28452)+~E(x28451,x28452)
% 25.54/25.43 [2846]~P61(x28461)+P61(x28462)+~E(x28461,x28462)
% 25.54/25.43 [2847]P35(x28472,x28473)+~E(x28471,x28472)+~P35(x28471,x28473)
% 25.54/25.43 [2848]P35(x28483,x28482)+~E(x28481,x28482)+~P35(x28483,x28481)
% 25.54/25.43 [2849]~P127(x28491)+P127(x28492)+~E(x28491,x28492)
% 25.54/25.43 [2850]~P3(x28501)+P3(x28502)+~E(x28501,x28502)
% 25.54/25.43 [2851]~P91(x28511)+P91(x28512)+~E(x28511,x28512)
% 25.54/25.43 [2852]P149(x28522,x28523,x28524)+~E(x28521,x28522)+~P149(x28521,x28523,x28524)
% 25.54/25.43 [2853]P149(x28533,x28532,x28534)+~E(x28531,x28532)+~P149(x28533,x28531,x28534)
% 25.54/25.43 [2854]P149(x28543,x28544,x28542)+~E(x28541,x28542)+~P149(x28543,x28544,x28541)
% 25.54/25.43 [2855]~P66(x28551)+P66(x28552)+~E(x28551,x28552)
% 25.54/25.43 [2856]~P99(x28561)+P99(x28562)+~E(x28561,x28562)
% 25.54/25.43 [2857]~P111(x28571)+P111(x28572)+~E(x28571,x28572)
% 25.54/25.43 [2858]~P92(x28581)+P92(x28582)+~E(x28581,x28582)
% 25.54/25.43 [2859]~P62(x28591)+P62(x28592)+~E(x28591,x28592)
% 25.54/25.43 [2860]~P108(x28601)+P108(x28602)+~E(x28601,x28602)
% 25.54/25.43 [2861]~P71(x28611)+P71(x28612)+~E(x28611,x28612)
% 25.54/25.43 [2862]~P59(x28621)+P59(x28622)+~E(x28621,x28622)
% 25.54/25.43 [2863]P36(x28632,x28633)+~E(x28631,x28632)+~P36(x28631,x28633)
% 25.54/25.43 [2864]P36(x28643,x28642)+~E(x28641,x28642)+~P36(x28643,x28641)
% 25.54/25.43 [2865]~P135(x28651)+P135(x28652)+~E(x28651,x28652)
% 25.54/25.43 [2866]~P72(x28661)+P72(x28662)+~E(x28661,x28662)
% 25.54/25.43 [2867]P16(x28672,x28673,x28674)+~E(x28671,x28672)+~P16(x28671,x28673,x28674)
% 25.54/25.43 [2868]P16(x28683,x28682,x28684)+~E(x28681,x28682)+~P16(x28683,x28681,x28684)
% 25.54/25.43 [2869]P16(x28693,x28694,x28692)+~E(x28691,x28692)+~P16(x28693,x28694,x28691)
% 25.54/25.43 [2870]~P110(x28701)+P110(x28702)+~E(x28701,x28702)
% 25.54/25.43 [2871]P5(x28712,x28713)+~E(x28711,x28712)+~P5(x28711,x28713)
% 25.54/25.43 [2872]P5(x28723,x28722)+~E(x28721,x28722)+~P5(x28723,x28721)
% 25.54/25.43 [2873]P11(x28732,x28733)+~E(x28731,x28732)+~P11(x28731,x28733)
% 25.54/25.43 [2874]P11(x28743,x28742)+~E(x28741,x28742)+~P11(x28743,x28741)
% 25.54/25.43 [2875]~P87(x28751)+P87(x28752)+~E(x28751,x28752)
% 25.54/25.43 [2876]~P93(x28761)+P93(x28762)+~E(x28761,x28762)
% 25.54/25.43 [2877]~P38(x28771)+P38(x28772)+~E(x28771,x28772)
% 25.54/25.43 [2878]P18(x28782,x28783,x28784,x28785)+~E(x28781,x28782)+~P18(x28781,x28783,x28784,x28785)
% 25.54/25.43 [2879]P18(x28793,x28792,x28794,x28795)+~E(x28791,x28792)+~P18(x28793,x28791,x28794,x28795)
% 25.54/25.43 [2880]P18(x28803,x28804,x28802,x28805)+~E(x28801,x28802)+~P18(x28803,x28804,x28801,x28805)
% 25.54/25.43 [2881]P18(x28813,x28814,x28815,x28812)+~E(x28811,x28812)+~P18(x28813,x28814,x28815,x28811)
% 25.54/25.43 [2882]~P58(x28821)+P58(x28822)+~E(x28821,x28822)
% 25.54/25.43 [2883]P22(x28832,x28833,x28834,x28835)+~E(x28831,x28832)+~P22(x28831,x28833,x28834,x28835)
% 25.54/25.43 [2884]P22(x28843,x28842,x28844,x28845)+~E(x28841,x28842)+~P22(x28843,x28841,x28844,x28845)
% 25.54/25.43 [2885]P22(x28853,x28854,x28852,x28855)+~E(x28851,x28852)+~P22(x28853,x28854,x28851,x28855)
% 25.54/25.43 [2886]P22(x28863,x28864,x28865,x28862)+~E(x28861,x28862)+~P22(x28863,x28864,x28865,x28861)
% 25.54/25.43 [2887]P24(x28872,x28873)+~E(x28871,x28872)+~P24(x28871,x28873)
% 25.54/25.43 [2888]P24(x28883,x28882)+~E(x28881,x28882)+~P24(x28883,x28881)
% 25.54/25.43 [2889]~P98(x28891)+P98(x28892)+~E(x28891,x28892)
% 25.54/25.43 [2890]~P94(x28901)+P94(x28902)+~E(x28901,x28902)
% 25.54/25.43 [2891]~P103(x28911)+P103(x28912)+~E(x28911,x28912)
% 25.54/25.43 [2892]P148(x28922,x28923,x28924)+~E(x28921,x28922)+~P148(x28921,x28923,x28924)
% 25.54/25.43 [2893]P148(x28933,x28932,x28934)+~E(x28931,x28932)+~P148(x28933,x28931,x28934)
% 25.54/25.43 [2894]P148(x28943,x28944,x28942)+~E(x28941,x28942)+~P148(x28943,x28944,x28941)
% 25.54/25.43 [2895]~P120(x28951)+P120(x28952)+~E(x28951,x28952)
% 25.54/25.43 [2896]P6(x28962,x28963,x28964)+~E(x28961,x28962)+~P6(x28961,x28963,x28964)
% 25.54/25.43 [2897]P6(x28973,x28972,x28974)+~E(x28971,x28972)+~P6(x28973,x28971,x28974)
% 25.54/25.43 [2898]P6(x28983,x28984,x28982)+~E(x28981,x28982)+~P6(x28983,x28984,x28981)
% 25.54/25.43 [2899]~P112(x28991)+P112(x28992)+~E(x28991,x28992)
% 25.54/25.43 [2900]~P102(x29001)+P102(x29002)+~E(x29001,x29002)
% 25.54/25.43 [2901]~P95(x29011)+P95(x29012)+~E(x29011,x29012)
% 25.54/25.43 [2902]~P67(x29021)+P67(x29022)+~E(x29021,x29022)
% 25.54/25.43 [2903]P50(x29032,x29033,x29034)+~E(x29031,x29032)+~P50(x29031,x29033,x29034)
% 25.54/25.43 [2904]P50(x29043,x29042,x29044)+~E(x29041,x29042)+~P50(x29043,x29041,x29044)
% 25.54/25.43 [2905]P50(x29053,x29054,x29052)+~E(x29051,x29052)+~P50(x29053,x29054,x29051)
% 25.54/25.43 [2906]~P139(x29061)+P139(x29062)+~E(x29061,x29062)
% 25.54/25.43 [2907]~P78(x29071)+P78(x29072)+~E(x29071,x29072)
% 25.54/25.43 [2908]P26(x29082,x29083)+~E(x29081,x29082)+~P26(x29081,x29083)
% 25.54/25.43 [2909]P26(x29093,x29092)+~E(x29091,x29092)+~P26(x29093,x29091)
% 25.54/25.43 [2910]~P96(x29101)+P96(x29102)+~E(x29101,x29102)
% 25.54/25.43 [2911]~P68(x29111)+P68(x29112)+~E(x29111,x29112)
% 25.54/25.43 [2912]~P82(x29121)+P82(x29122)+~E(x29121,x29122)
% 25.54/25.43 [2913]P13(x29132,x29133)+~E(x29131,x29132)+~P13(x29131,x29133)
% 25.54/25.43 [2914]P13(x29143,x29142)+~E(x29141,x29142)+~P13(x29143,x29141)
% 25.54/25.43 [2915]~P69(x29151)+P69(x29152)+~E(x29151,x29152)
% 25.54/25.43 [2916]P23(x29162,x29163,x29164,x29165,x29166)+~E(x29161,x29162)+~P23(x29161,x29163,x29164,x29165,x29166)
% 25.54/25.43 [2917]P23(x29173,x29172,x29174,x29175,x29176)+~E(x29171,x29172)+~P23(x29173,x29171,x29174,x29175,x29176)
% 25.54/25.43 [2918]P23(x29183,x29184,x29182,x29185,x29186)+~E(x29181,x29182)+~P23(x29183,x29184,x29181,x29185,x29186)
% 25.54/25.43 [2919]P23(x29193,x29194,x29195,x29192,x29196)+~E(x29191,x29192)+~P23(x29193,x29194,x29195,x29191,x29196)
% 25.54/25.43 [2920]P23(x29203,x29204,x29205,x29206,x29202)+~E(x29201,x29202)+~P23(x29203,x29204,x29205,x29206,x29201)
% 25.54/25.43 [2921]~P65(x29211)+P65(x29212)+~E(x29211,x29212)
% 25.54/25.43 [2922]P15(x29222,x29223,x29224)+~E(x29221,x29222)+~P15(x29221,x29223,x29224)
% 25.54/25.43 [2923]P15(x29233,x29232,x29234)+~E(x29231,x29232)+~P15(x29233,x29231,x29234)
% 25.54/25.43 [2924]P15(x29243,x29244,x29242)+~E(x29241,x29242)+~P15(x29243,x29244,x29241)
% 25.54/25.43 [2925]~P125(x29251)+P125(x29252)+~E(x29251,x29252)
% 25.54/25.43 [2926]~P113(x29261)+P113(x29262)+~E(x29261,x29262)
% 25.54/25.43 [2927]~P60(x29271)+P60(x29272)+~E(x29271,x29272)
% 25.54/25.43 [2928]~P126(x29281)+P126(x29282)+~E(x29281,x29282)
% 25.54/25.43 [2929]~P119(x29291)+P119(x29292)+~E(x29291,x29292)
% 25.54/25.43 [2930]~P64(x29301)+P64(x29302)+~E(x29301,x29302)
% 25.54/25.43 [2931]P52(x29312,x29313,x29314)+~E(x29311,x29312)+~P52(x29311,x29313,x29314)
% 25.54/25.43 [2932]P52(x29323,x29322,x29324)+~E(x29321,x29322)+~P52(x29323,x29321,x29324)
% 25.54/25.43 [2933]P52(x29333,x29334,x29332)+~E(x29331,x29332)+~P52(x29333,x29334,x29331)
% 25.54/25.43 [2934]P57(x29342,x29343)+~E(x29341,x29342)+~P57(x29341,x29343)
% 25.54/25.43 [2935]P57(x29353,x29352)+~E(x29351,x29352)+~P57(x29353,x29351)
% 25.54/25.43 [2936]~P121(x29361)+P121(x29362)+~E(x29361,x29362)
% 25.54/25.43 [2937]~P128(x29371)+P128(x29372)+~E(x29371,x29372)
% 25.54/25.43 [2938]~P83(x29381)+P83(x29382)+~E(x29381,x29382)
% 25.54/25.43 [2939]P32(x29392,x29393,x29394,x29395,x29396)+~E(x29391,x29392)+~P32(x29391,x29393,x29394,x29395,x29396)
% 25.54/25.43 [2940]P32(x29403,x29402,x29404,x29405,x29406)+~E(x29401,x29402)+~P32(x29403,x29401,x29404,x29405,x29406)
% 25.54/25.43 [2941]P32(x29413,x29414,x29412,x29415,x29416)+~E(x29411,x29412)+~P32(x29413,x29414,x29411,x29415,x29416)
% 25.54/25.43 [2942]P32(x29423,x29424,x29425,x29422,x29426)+~E(x29421,x29422)+~P32(x29423,x29424,x29425,x29421,x29426)
% 25.54/25.43 [2943]P32(x29433,x29434,x29435,x29436,x29432)+~E(x29431,x29432)+~P32(x29433,x29434,x29435,x29436,x29431)
% 25.54/25.43 [2944]~P80(x29441)+P80(x29442)+~E(x29441,x29442)
% 25.54/25.43 [2945]~P70(x29451)+P70(x29452)+~E(x29451,x29452)
% 25.54/25.43 [2946]P31(x29462,x29463,x29464)+~E(x29461,x29462)+~P31(x29461,x29463,x29464)
% 25.54/25.43 [2947]P31(x29473,x29472,x29474)+~E(x29471,x29472)+~P31(x29473,x29471,x29474)
% 25.54/25.43 [2948]P31(x29483,x29484,x29482)+~E(x29481,x29482)+~P31(x29483,x29484,x29481)
% 25.54/25.43 [2949]P33(x29492,x29493,x29494)+~E(x29491,x29492)+~P33(x29491,x29493,x29494)
% 25.54/25.43 [2950]P33(x29503,x29502,x29504)+~E(x29501,x29502)+~P33(x29503,x29501,x29504)
% 25.54/25.43 [2951]P33(x29513,x29514,x29512)+~E(x29511,x29512)+~P33(x29513,x29514,x29511)
% 25.54/25.43 [2952]~P73(x29521)+P73(x29522)+~E(x29521,x29522)
% 25.54/25.43 [2953]~P145(x29531)+P145(x29532)+~E(x29531,x29532)
% 25.54/25.43 [2954]~P134(x29541)+P134(x29542)+~E(x29541,x29542)
% 25.54/25.43 [2955]~P74(x29551)+P74(x29552)+~E(x29551,x29552)
% 25.54/25.43 [2956]~P75(x29561)+P75(x29562)+~E(x29561,x29562)
% 25.54/25.43 [2957]~P84(x29571)+P84(x29572)+~E(x29571,x29572)
% 25.54/25.43 [2958]P14(x29582,x29583,x29584)+~E(x29581,x29582)+~P14(x29581,x29583,x29584)
% 25.54/25.43 [2959]P14(x29593,x29592,x29594)+~E(x29591,x29592)+~P14(x29593,x29591,x29594)
% 25.54/25.43 [2960]P14(x29603,x29604,x29602)+~E(x29601,x29602)+~P14(x29603,x29604,x29601)
% 25.54/25.43 [2961]~P147(x29611)+P147(x29612)+~E(x29611,x29612)
% 25.54/25.43 [2962]~P76(x29621)+P76(x29622)+~E(x29621,x29622)
% 25.54/25.43 [2963]~P85(x29631)+P85(x29632)+~E(x29631,x29632)
% 25.54/25.43 [2964]~P100(x29641)+P100(x29642)+~E(x29641,x29642)
% 25.54/25.43 [2965]P53(x29652,x29653,x29654)+~E(x29651,x29652)+~P53(x29651,x29653,x29654)
% 25.54/25.43 [2966]P53(x29663,x29662,x29664)+~E(x29661,x29662)+~P53(x29663,x29661,x29664)
% 25.54/25.43 [2967]P53(x29673,x29674,x29672)+~E(x29671,x29672)+~P53(x29673,x29674,x29671)
% 25.54/25.43 [2968]~P140(x29681)+P140(x29682)+~E(x29681,x29682)
% 25.54/25.43 [2969]~P116(x29691)+P116(x29692)+~E(x29691,x29692)
% 25.54/25.43 [2970]~P81(x29701)+P81(x29702)+~E(x29701,x29702)
% 25.54/25.43 [2971]~P114(x29711)+P114(x29712)+~E(x29711,x29712)
% 25.54/25.43 [2972]P29(x29722,x29723,x29724)+~E(x29721,x29722)+~P29(x29721,x29723,x29724)
% 25.54/25.43 [2973]P29(x29733,x29732,x29734)+~E(x29731,x29732)+~P29(x29733,x29731,x29734)
% 25.54/25.43 [2974]P29(x29743,x29744,x29742)+~E(x29741,x29742)+~P29(x29743,x29744,x29741)
% 25.54/25.43 [2975]~P34(x29751)+P34(x29752)+~E(x29751,x29752)
% 25.54/25.43 [2976]P55(x29762,x29763)+~E(x29761,x29762)+~P55(x29761,x29763)
% 25.54/25.43 [2977]P55(x29773,x29772)+~E(x29771,x29772)+~P55(x29773,x29771)
% 25.54/25.43 [2978]~P115(x29781)+P115(x29782)+~E(x29781,x29782)
% 25.54/25.43 [2979]P21(x29792,x29793,x29794,x29795,x29796,x29797)+~E(x29791,x29792)+~P21(x29791,x29793,x29794,x29795,x29796,x29797)
% 25.54/25.43 [2980]P21(x29803,x29802,x29804,x29805,x29806,x29807)+~E(x29801,x29802)+~P21(x29803,x29801,x29804,x29805,x29806,x29807)
% 25.54/25.43 [2981]P21(x29813,x29814,x29812,x29815,x29816,x29817)+~E(x29811,x29812)+~P21(x29813,x29814,x29811,x29815,x29816,x29817)
% 25.54/25.43 [2982]P21(x29823,x29824,x29825,x29822,x29826,x29827)+~E(x29821,x29822)+~P21(x29823,x29824,x29825,x29821,x29826,x29827)
% 25.54/25.43 [2983]P21(x29833,x29834,x29835,x29836,x29832,x29837)+~E(x29831,x29832)+~P21(x29833,x29834,x29835,x29836,x29831,x29837)
% 25.54/25.43 [2984]P21(x29843,x29844,x29845,x29846,x29847,x29842)+~E(x29841,x29842)+~P21(x29843,x29844,x29845,x29846,x29847,x29841)
% 25.54/25.43 [2985]~P133(x29851)+P133(x29852)+~E(x29851,x29852)
% 25.54/25.43 [2986]~P63(x29861)+P63(x29862)+~E(x29861,x29862)
% 25.54/25.43 [2987]~P144(x29871)+P144(x29872)+~E(x29871,x29872)
% 25.54/25.43 [2988]~P146(x29881)+P146(x29882)+~E(x29881,x29882)
% 25.54/25.43 [2989]~P79(x29891)+P79(x29892)+~E(x29891,x29892)
% 25.54/25.43 [2990]P10(x29902,x29903,x29904,x29905,x29906,x29907)+~E(x29901,x29902)+~P10(x29901,x29903,x29904,x29905,x29906,x29907)
% 25.54/25.43 [2991]P10(x29913,x29912,x29914,x29915,x29916,x29917)+~E(x29911,x29912)+~P10(x29913,x29911,x29914,x29915,x29916,x29917)
% 25.54/25.43 [2992]P10(x29923,x29924,x29922,x29925,x29926,x29927)+~E(x29921,x29922)+~P10(x29923,x29924,x29921,x29925,x29926,x29927)
% 25.54/25.43 [2993]P10(x29933,x29934,x29935,x29932,x29936,x29937)+~E(x29931,x29932)+~P10(x29933,x29934,x29935,x29931,x29936,x29937)
% 25.54/25.43 [2994]P10(x29943,x29944,x29945,x29946,x29942,x29947)+~E(x29941,x29942)+~P10(x29943,x29944,x29945,x29946,x29941,x29947)
% 25.54/25.43 [2995]P10(x29953,x29954,x29955,x29956,x29957,x29952)+~E(x29951,x29952)+~P10(x29953,x29954,x29955,x29956,x29957,x29951)
% 25.54/25.43 [2996]~P4(x29961)+P4(x29962)+~E(x29961,x29962)
% 25.54/25.43 [2997]P152(x29972,x29973)+~E(x29971,x29972)+~P152(x29971,x29973)
% 25.54/25.43 [2998]P152(x29983,x29982)+~E(x29981,x29982)+~P152(x29983,x29981)
% 25.54/25.43 [2999]~P142(x29991)+P142(x29992)+~E(x29991,x29992)
% 25.54/25.43 [3000]P56(x30002,x30003,x30004,x30005)+~E(x30001,x30002)+~P56(x30001,x30003,x30004,x30005)
% 25.54/25.43 [3001]P56(x30013,x30012,x30014,x30015)+~E(x30011,x30012)+~P56(x30013,x30011,x30014,x30015)
% 25.54/25.43 [3002]P56(x30023,x30024,x30022,x30025)+~E(x30021,x30022)+~P56(x30023,x30024,x30021,x30025)
% 25.54/25.43 [3003]P56(x30033,x30034,x30035,x30032)+~E(x30031,x30032)+~P56(x30033,x30034,x30035,x30031)
% 25.54/25.43 [3004]P27(x30042,x30043,x30044)+~E(x30041,x30042)+~P27(x30041,x30043,x30044)
% 25.54/25.43 [3005]P27(x30053,x30052,x30054)+~E(x30051,x30052)+~P27(x30053,x30051,x30054)
% 25.54/25.43 [3006]P27(x30063,x30064,x30062)+~E(x30061,x30062)+~P27(x30063,x30064,x30061)
% 25.54/25.43 [3007]P28(x30072,x30073,x30074)+~E(x30071,x30072)+~P28(x30071,x30073,x30074)
% 25.54/25.43 [3008]P28(x30083,x30082,x30084)+~E(x30081,x30082)+~P28(x30083,x30081,x30084)
% 25.54/25.43 [3009]P28(x30093,x30094,x30092)+~E(x30091,x30092)+~P28(x30093,x30094,x30091)
% 25.54/25.43 [3010]P47(x30102,x30103)+~E(x30101,x30102)+~P47(x30101,x30103)
% 25.54/25.43 [3011]P47(x30113,x30112)+~E(x30111,x30112)+~P47(x30113,x30111)
% 25.54/25.43 [3012]~P141(x30121)+P141(x30122)+~E(x30121,x30122)
% 25.54/25.43 [3013]~P130(x30131)+P130(x30132)+~E(x30131,x30132)
% 25.54/25.43 [3014]~P90(x30141)+P90(x30142)+~E(x30141,x30142)
% 25.54/25.43 [3015]P150(x30152,x30153)+~E(x30151,x30152)+~P150(x30151,x30153)
% 25.54/25.43 [3016]P150(x30163,x30162)+~E(x30161,x30162)+~P150(x30163,x30161)
% 25.54/25.43 [3017]~P118(x30171)+P118(x30172)+~E(x30171,x30172)
% 25.54/25.43 [3018]P48(x30182,x30183)+~E(x30181,x30182)+~P48(x30181,x30183)
% 25.54/25.43 [3019]P48(x30193,x30192)+~E(x30191,x30192)+~P48(x30193,x30191)
% 25.54/25.43 [3020]P9(x30202,x30203,x30204,x30205)+~E(x30201,x30202)+~P9(x30201,x30203,x30204,x30205)
% 25.54/25.43 [3021]P9(x30213,x30212,x30214,x30215)+~E(x30211,x30212)+~P9(x30213,x30211,x30214,x30215)
% 25.54/25.43 [3022]P9(x30223,x30224,x30222,x30225)+~E(x30221,x30222)+~P9(x30223,x30224,x30221,x30225)
% 25.54/25.43 [3023]P9(x30233,x30234,x30235,x30232)+~E(x30231,x30232)+~P9(x30233,x30234,x30235,x30231)
% 25.54/25.43 [3024]~P105(x30241)+P105(x30242)+~E(x30241,x30242)
% 25.54/25.43 [3025]P12(x30252,x30253,x30254)+~E(x30251,x30252)+~P12(x30251,x30253,x30254)
% 25.54/25.43 [3026]P12(x30263,x30262,x30264)+~E(x30261,x30262)+~P12(x30263,x30261,x30264)
% 25.54/25.43 [3027]P12(x30273,x30274,x30272)+~E(x30271,x30272)+~P12(x30273,x30274,x30271)
% 25.54/25.43 [3028]~P88(x30281)+P88(x30282)+~E(x30281,x30282)
% 25.54/25.43 [3029]P40(x30292,x30293,x30294,x30295,x30296,x30297)+~E(x30291,x30292)+~P40(x30291,x30293,x30294,x30295,x30296,x30297)
% 25.54/25.43 [3030]P40(x30303,x30302,x30304,x30305,x30306,x30307)+~E(x30301,x30302)+~P40(x30303,x30301,x30304,x30305,x30306,x30307)
% 25.54/25.43 [3031]P40(x30313,x30314,x30312,x30315,x30316,x30317)+~E(x30311,x30312)+~P40(x30313,x30314,x30311,x30315,x30316,x30317)
% 25.54/25.43 [3032]P40(x30323,x30324,x30325,x30322,x30326,x30327)+~E(x30321,x30322)+~P40(x30323,x30324,x30325,x30321,x30326,x30327)
% 25.54/25.43 [3033]P40(x30333,x30334,x30335,x30336,x30332,x30337)+~E(x30331,x30332)+~P40(x30333,x30334,x30335,x30336,x30331,x30337)
% 25.54/25.43 [3034]P40(x30343,x30344,x30345,x30346,x30347,x30342)+~E(x30341,x30342)+~P40(x30343,x30344,x30345,x30346,x30347,x30341)
% 25.54/25.43 [3035]P37(x30352,x30353)+~E(x30351,x30352)+~P37(x30351,x30353)
% 25.54/25.43 [3036]P37(x30363,x30362)+~E(x30361,x30362)+~P37(x30363,x30361)
% 25.54/25.43 [3037]~P143(x30371)+P143(x30372)+~E(x30371,x30372)
% 25.54/25.43 [3038]P45(x30382,x30383,x30384)+~E(x30381,x30382)+~P45(x30381,x30383,x30384)
% 25.54/25.43 [3039]P45(x30393,x30392,x30394)+~E(x30391,x30392)+~P45(x30393,x30391,x30394)
% 25.54/25.43 [3040]P45(x30403,x30404,x30402)+~E(x30401,x30402)+~P45(x30403,x30404,x30401)
% 25.54/25.43 [3041]~P97(x30411)+P97(x30412)+~E(x30411,x30412)
% 25.54/25.43 [3042]~P106(x30421)+P106(x30422)+~E(x30421,x30422)
% 25.54/25.43 [3043]~P42(x30431)+P42(x30432)+~E(x30431,x30432)
% 25.54/25.43 [3044]~P122(x30441)+P122(x30442)+~E(x30441,x30442)
% 25.54/25.43 [3045]P19(x30452,x30453,x30454,x30455,x30456)+~E(x30451,x30452)+~P19(x30451,x30453,x30454,x30455,x30456)
% 25.54/25.43 [3046]P19(x30463,x30462,x30464,x30465,x30466)+~E(x30461,x30462)+~P19(x30463,x30461,x30464,x30465,x30466)
% 25.54/25.43 [3047]P19(x30473,x30474,x30472,x30475,x30476)+~E(x30471,x30472)+~P19(x30473,x30474,x30471,x30475,x30476)
% 25.54/25.43 [3048]P19(x30483,x30484,x30485,x30482,x30486)+~E(x30481,x30482)+~P19(x30483,x30484,x30485,x30481,x30486)
% 25.54/25.43 [3049]P19(x30493,x30494,x30495,x30496,x30492)+~E(x30491,x30492)+~P19(x30493,x30494,x30495,x30496,x30491)
% 25.54/25.43 [3050]P54(x30502,x30503,x30504,x30505,x30506)+~E(x30501,x30502)+~P54(x30501,x30503,x30504,x30505,x30506)
% 25.54/25.43 [3051]P54(x30513,x30512,x30514,x30515,x30516)+~E(x30511,x30512)+~P54(x30513,x30511,x30514,x30515,x30516)
% 25.54/25.43 [3052]P54(x30523,x30524,x30522,x30525,x30526)+~E(x30521,x30522)+~P54(x30523,x30524,x30521,x30525,x30526)
% 25.54/25.43 [3053]P54(x30533,x30534,x30535,x30532,x30536)+~E(x30531,x30532)+~P54(x30533,x30534,x30535,x30531,x30536)
% 25.54/25.43 [3054]P54(x30543,x30544,x30545,x30546,x30542)+~E(x30541,x30542)+~P54(x30543,x30544,x30545,x30546,x30541)
% 25.54/25.43 [3055]~P138(x30551)+P138(x30552)+~E(x30551,x30552)
% 25.54/25.43 [3056]~P136(x30561)+P136(x30562)+~E(x30561,x30562)
% 25.54/25.43 [3057]~P101(x30571)+P101(x30572)+~E(x30571,x30572)
% 25.54/25.43 [3058]P30(x30582,x30583,x30584,x30585)+~E(x30581,x30582)+~P30(x30581,x30583,x30584,x30585)
% 25.54/25.43 [3059]P30(x30593,x30592,x30594,x30595)+~E(x30591,x30592)+~P30(x30593,x30591,x30594,x30595)
% 25.54/25.43 [3060]P30(x30603,x30604,x30602,x30605)+~E(x30601,x30602)+~P30(x30603,x30604,x30601,x30605)
% 25.54/25.43 [3061]P30(x30613,x30614,x30615,x30612)+~E(x30611,x30612)+~P30(x30613,x30614,x30615,x30611)
% 25.54/25.43 [3062]P17(x30622,x30623,x30624,x30625)+~E(x30621,x30622)+~P17(x30621,x30623,x30624,x30625)
% 25.54/25.43 [3063]P17(x30633,x30632,x30634,x30635)+~E(x30631,x30632)+~P17(x30633,x30631,x30634,x30635)
% 25.54/25.43 [3064]P17(x30643,x30644,x30642,x30645)+~E(x30641,x30642)+~P17(x30643,x30644,x30641,x30645)
% 25.54/25.43 [3065]P17(x30653,x30654,x30655,x30652)+~E(x30651,x30652)+~P17(x30653,x30654,x30655,x30651)
% 25.54/25.43 [3066]P39(x30662,x30663,x30664,x30665)+~E(x30661,x30662)+~P39(x30661,x30663,x30664,x30665)
% 25.54/25.43 [3067]P39(x30673,x30672,x30674,x30675)+~E(x30671,x30672)+~P39(x30673,x30671,x30674,x30675)
% 25.54/25.43 [3068]P39(x30683,x30684,x30682,x30685)+~E(x30681,x30682)+~P39(x30683,x30684,x30681,x30685)
% 25.54/25.43 [3069]P39(x30693,x30694,x30695,x30692)+~E(x30691,x30692)+~P39(x30693,x30694,x30695,x30691)
% 25.54/25.43 [3070]~P107(x30701)+P107(x30702)+~E(x30701,x30702)
% 25.54/25.43 [3071]P151(x30712,x30713)+~E(x30711,x30712)+~P151(x30711,x30713)
% 25.54/25.43 [3072]P151(x30723,x30722)+~E(x30721,x30722)+~P151(x30723,x30721)
% 25.54/25.43 [3073]~P137(x30731)+P137(x30732)+~E(x30731,x30732)
% 25.54/25.43 [3074]~P124(x30741)+P124(x30742)+~E(x30741,x30742)
% 25.54/25.43 [3075]P51(x30752,x30753)+~E(x30751,x30752)+~P51(x30751,x30753)
% 25.54/25.43 [3076]P51(x30763,x30762)+~E(x30761,x30762)+~P51(x30763,x30761)
% 25.54/25.43 [3077]~P25(x30771)+P25(x30772)+~E(x30771,x30772)
% 25.54/25.43 [3078]~P129(x30781)+P129(x30782)+~E(x30781,x30782)
% 25.54/25.43 [3079]~P123(x30791)+P123(x30792)+~E(x30791,x30792)
% 25.54/25.43 [3080]P44(x30802,x30803,x30804)+~E(x30801,x30802)+~P44(x30801,x30803,x30804)
% 25.54/25.43 [3081]P44(x30813,x30812,x30814)+~E(x30811,x30812)+~P44(x30813,x30811,x30814)
% 25.54/25.43 [3082]P44(x30823,x30824,x30822)+~E(x30821,x30822)+~P44(x30823,x30824,x30821)
% 25.54/25.43 [3083]P43(x30832,x30833)+~E(x30831,x30832)+~P43(x30831,x30833)
% 25.54/25.43 [3084]P43(x30843,x30842)+~E(x30841,x30842)+~P43(x30843,x30841)
% 25.54/25.43 [3085]~P117(x30851)+P117(x30852)+~E(x30851,x30852)
% 25.54/25.43 [3086]P46(x30862,x30863)+~E(x30861,x30862)+~P46(x30861,x30863)
% 25.54/25.43 [3087]P46(x30873,x30872)+~E(x30871,x30872)+~P46(x30873,x30871)
% 25.54/25.43 [3088]P20(x30882,x30883,x30884,x30885,x30886,x30887)+~E(x30881,x30882)+~P20(x30881,x30883,x30884,x30885,x30886,x30887)
% 25.54/25.43 [3089]P20(x30893,x30892,x30894,x30895,x30896,x30897)+~E(x30891,x30892)+~P20(x30893,x30891,x30894,x30895,x30896,x30897)
% 25.54/25.43 [3090]P20(x30903,x30904,x30902,x30905,x30906,x30907)+~E(x30901,x30902)+~P20(x30903,x30904,x30901,x30905,x30906,x30907)
% 25.54/25.43 [3091]P20(x30913,x30914,x30915,x30912,x30916,x30917)+~E(x30911,x30912)+~P20(x30913,x30914,x30915,x30911,x30916,x30917)
% 25.54/25.43 [3092]P20(x30923,x30924,x30925,x30926,x30922,x30927)+~E(x30921,x30922)+~P20(x30923,x30924,x30925,x30926,x30921,x30927)
% 25.54/25.43 [3093]P20(x30933,x30934,x30935,x30936,x30937,x30932)+~E(x30931,x30932)+~P20(x30933,x30934,x30935,x30936,x30937,x30931)
% 25.54/25.43 [3094]~P131(x30941)+P131(x30942)+~E(x30941,x30942)
% 25.54/25.43 [3095]~P77(x30951)+P77(x30952)+~E(x30951,x30952)
% 25.54/25.43 [3096]~P89(x30961)+P89(x30962)+~E(x30961,x30962)
% 25.54/25.43 [3097]~P132(x30971)+P132(x30972)+~E(x30971,x30972)
% 25.54/25.43 [3098]P8(x30982,x30983,x30984,x30985,x30986)+~E(x30981,x30982)+~P8(x30981,x30983,x30984,x30985,x30986)
% 25.54/25.43 [3099]P8(x30993,x30992,x30994,x30995,x30996)+~E(x30991,x30992)+~P8(x30993,x30991,x30994,x30995,x30996)
% 25.54/25.43 [3100]P8(x31003,x31004,x31002,x31005,x31006)+~E(x31001,x31002)+~P8(x31003,x31004,x31001,x31005,x31006)
% 25.54/25.43 [3101]P8(x31013,x31014,x31015,x31012,x31016)+~E(x31011,x31012)+~P8(x31013,x31014,x31015,x31011,x31016)
% 25.54/25.43 [3102]P8(x31023,x31024,x31025,x31026,x31022)+~E(x31021,x31022)+~P8(x31023,x31024,x31025,x31026,x31021)
% 25.54/25.43 [3103]P41(x31032,x31033)+~E(x31031,x31032)+~P41(x31031,x31033)
% 25.54/25.43 [3104]P41(x31043,x31042)+~E(x31041,x31042)+~P41(x31043,x31041)
% 25.54/25.43 [3105]P7(x31052,x31053,x31054)+~E(x31051,x31052)+~P7(x31051,x31053,x31054)
% 25.54/25.43 [3106]P7(x31063,x31062,x31064)+~E(x31061,x31062)+~P7(x31063,x31061,x31064)
% 25.54/25.43 [3107]P7(x31073,x31074,x31072)+~E(x31071,x31072)+~P7(x31073,x31074,x31071)
% 25.54/25.43
% 25.54/25.43 %-------------------------------------------
% 25.54/25.43 cnf(10484,plain,
% 25.54/25.43 ($false),
% 25.54/25.43 inference(scs_inference,[],[3330,4667,3108,2,4799,4773]),
% 25.54/25.43 ['proof']).
% 25.54/25.43 % SZS output end Proof
% 25.54/25.43 % Total time :19.900000s
%------------------------------------------------------------------------------