TSTP Solution File: SWW368+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW368+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:08:35 EDT 2024
% Result : Theorem 94.68s 94.43s
% Output : CNFRefutation 94.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW368+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jun 19 09:00:39 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.53/0.59 start to proof:theBenchmark
% 94.19/94.26 %-------------------------------------------
% 94.19/94.26 % File :CSE---1.7
% 94.19/94.26 % Problem :theBenchmark
% 94.19/94.26 % Transform :cnf
% 94.19/94.26 % Format :tptp:raw
% 94.19/94.26 % Command :java -jar mcs_scs.jar %d %s
% 94.19/94.26
% 94.19/94.26 % Result :Theorem 80.130000s
% 94.19/94.26 % Output :CNFRefutation 80.130000s
% 94.19/94.26 %-------------------------------------------
% 94.19/94.27 %------------------------------------------------------------------------------
% 94.19/94.27 % File : SWW368+1 : TPTP v8.2.0. Released v5.2.0.
% 94.19/94.27 % Domain : Software Verification
% 94.19/94.27 % Problem : Hoare's Logic with Procedures 435456, 5000 axioms selected
% 94.19/94.27 % Version : Especial.
% 94.19/94.27 % English :
% 94.19/94.27
% 94.19/94.27 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 94.19/94.27 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 94.19/94.27 % Source : [Bla11]
% 94.19/94.27 % Names : hoare_435456.5000.p [Bla11]
% 94.19/94.27
% 94.19/94.27 % Status : ContradictoryAxioms
% 94.19/94.27 % Rating : 0.58 v8.2.0, 0.61 v8.1.0, 0.64 v7.5.0, 0.72 v7.4.0, 0.83 v7.3.0, 0.72 v7.1.0, 0.74 v7.0.0, 0.77 v6.4.0, 0.73 v6.3.0, 0.75 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.83 v5.5.0, 0.85 v5.4.0, 0.89 v5.3.0, 0.96 v5.2.0
% 94.19/94.27 % Syntax : Number of formulae : 5230 (1640 unt; 0 def)
% 94.19/94.27 % Number of atoms : 12832 (4422 equ)
% 94.19/94.27 % Maximal formula atoms : 13 ( 2 avg)
% 94.19/94.27 % Number of connectives : 8610 (1008 ~; 154 |; 737 &)
% 94.19/94.27 % ( 911 <=>;5800 =>; 0 <=; 0 <~>)
% 94.19/94.27 % Maximal formula depth : 22 ( 6 avg)
% 94.19/94.27 % Maximal term depth : 19 ( 2 avg)
% 94.19/94.27 % Number of predicates : 150 ( 149 usr; 0 prp; 1-6 aty)
% 94.19/94.27 % Number of functors : 378 ( 378 usr; 51 con; 0-7 aty)
% 94.19/94.27 % Number of variables : 16544 (16392 !; 152 ?)
% 94.19/94.27 % SPC : FOF_CAX_RFO_SEQ
% 94.19/94.27
% 94.19/94.27 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 94.19/94.27 % 2011-03-01 12:41:01
% 94.19/94.27 %------------------------------------------------------------------------------
% 94.19/94.27 %----Relevant facts (4983)
% 94.19/94.27 fof(fact_ext,axiom,
% 94.19/94.27 ! [V_g_2,V_f_2] :
% 94.19/94.27 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 94.19/94.27 => V_f_2 = V_g_2 ) ).
% 94.19/94.27
% 94.19/94.27 fof(fact_assms_I1_J,axiom,
% 94.19/94.27 ! [V_G_2,V_ts_2] :
% 94.19/94.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),V_ts_2),V_G_2))
% 94.19/94.27 => v_P(V_G_2,V_ts_2) ) ).
% 94.19/94.27
% 94.19/94.27 fof(fact_finite__imageI,axiom,
% 94.19/94.27 ! [V_h_2,T_c,V_F_2,T_b] :
% 94.19/94.27 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.19/94.27 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_card__insert__if,axiom,
% 94.19/94.28 ! [V_x_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.28 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => 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) )
% 94.19/94.28 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => 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)) ) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_card__insert__disjoint,axiom,
% 94.19/94.28 ! [V_x_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => 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)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_finite_OinsertI,axiom,
% 94.19/94.28 ! [V_a_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_image__eqI,axiom,
% 94.19/94.28 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 94.19/94.28 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_subsetD,axiom,
% 94.19/94.28 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insertE,axiom,
% 94.19/94.28 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 94.19/94.28 => ( V_a_2 != V_b_2
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insertCI,axiom,
% 94.19/94.28 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 94.19/94.28 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 94.19/94.28 => V_a_2 = V_b_2 )
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_card__image__le,axiom,
% 94.19/94.28 ! [V_f_2,T_c,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.28 => 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))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_card__mono,axiom,
% 94.19/94.28 ! [V_A_2,V_B_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => 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))) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_card__seteq,axiom,
% 94.19/94.28 ! [V_A_2,V_B_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( 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)))
% 94.19/94.28 => V_A_2 = V_B_2 ) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_equalityCE,axiom,
% 94.19/94.28 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.19/94.28 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 94.19/94.28 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_equalityI,axiom,
% 94.19/94.28 ! [V_B_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.19/94.28 => V_A_2 = V_B_2 ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_eq__mem__trans,axiom,
% 94.19/94.28 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 94.19/94.28 ( V_a_2 = V_b_2
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_eqelem__imp__iff,axiom,
% 94.19/94.28 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 94.19/94.28 ( V_x_2 = V_y_2
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_eqset__imp__iff,axiom,
% 94.19/94.28 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_mem__def,axiom,
% 94.19/94.28 ! [V_A_2,V_x_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_finite__code,axiom,
% 94.19/94.28 ! [V_A_2,T_b] :
% 94.19/94.28 ( class_Finite__Set_Ofinite(T_b)
% 94.19/94.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_finite,axiom,
% 94.19/94.28 ! [V_A_2,T_b] :
% 94.19/94.28 ( class_Finite__Set_Ofinite(T_b)
% 94.19/94.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__code,axiom,
% 94.19/94.28 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 94.19/94.28 <=> ( V_y_2 = V_x_2
% 94.19/94.28 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__commute,axiom,
% 94.19/94.28 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__absorb2,axiom,
% 94.19/94.28 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_equalityE,axiom,
% 94.19/94.28 ! [T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_subset__trans,axiom,
% 94.19/94.28 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_equalityD2,axiom,
% 94.19/94.28 ! [T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_equalityD1,axiom,
% 94.19/94.28 ! [T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_set__eq__subset,axiom,
% 94.19/94.28 ! [T_b,V_B_2,V_A_2] :
% 94.19/94.28 ( V_A_2 = V_B_2
% 94.19/94.28 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_subset__refl,axiom,
% 94.19/94.28 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_image__image,axiom,
% 94.19/94.28 ! [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) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__absorb,axiom,
% 94.19/94.28 ! [V_A_2,V_a_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.19/94.28 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insertI2,axiom,
% 94.19/94.28 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__ident,axiom,
% 94.19/94.28 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 94.19/94.28 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.19/94.28 => ( 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)
% 94.19/94.28 <=> V_A_2 = V_B_2 ) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insert__iff,axiom,
% 94.19/94.28 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 94.19/94.28 <=> ( V_a_2 = V_b_2
% 94.19/94.28 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_insertI1,axiom,
% 94.19/94.28 ! [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))) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_set__mp,axiom,
% 94.19/94.28 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_set__rev__mp,axiom,
% 94.19/94.28 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_in__mono,axiom,
% 94.19/94.28 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_rev__image__eqI,axiom,
% 94.19/94.28 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 94.19/94.28 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_imageI,axiom,
% 94.19/94.28 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.28 => 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))) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_image__iff,axiom,
% 94.19/94.28 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 94.19/94.28 <=> ? [B_x] :
% 94.19/94.28 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.19/94.28 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 94.19/94.28
% 94.19/94.28 fof(fact_finite__insert,axiom,
% 94.19/94.28 ! [V_A_2,V_a_2,T_b] :
% 94.19/94.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 94.19/94.29 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_finite__subset,axiom,
% 94.19/94.29 ! [V_B_2,V_A_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.29 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.19/94.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_rev__finite__subset,axiom,
% 94.19/94.29 ! [V_A_2,V_B_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.19/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_insert__mono,axiom,
% 94.19/94.29 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 94.19/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_subset__insertI2,axiom,
% 94.19/94.29 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_subset__insertI,axiom,
% 94.19/94.29 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_image__insert,axiom,
% 94.19/94.29 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_image__mono,axiom,
% 94.19/94.29 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.19/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_subset__image__iff,axiom,
% 94.19/94.29 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 94.19/94.29 <=> ? [B_AA] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 94.19/94.29 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_subset__insert,axiom,
% 94.19/94.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 94.19/94.29 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 94.19/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_insert__subset,axiom,
% 94.19/94.29 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 94.19/94.29 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.19/94.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_insert__image,axiom,
% 94.19/94.29 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.19/94.29 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_finite__surj,axiom,
% 94.19/94.29 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.19/94.29 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_card__insert__le,axiom,
% 94.19/94.29 ! [V_x_2,V_A_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.19/94.29 => 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)))) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_Suc__diff__le,axiom,
% 94.19/94.29 ! [V_m,V_n] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.19/94.29 => 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)) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_order__refl,axiom,
% 94.19/94.29 ! [V_x,T_a] :
% 94.19/94.29 ( class_Orderings_Opreorder(T_a)
% 94.19/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_pred__subset__eq,axiom,
% 94.19/94.29 ! [V_S_2,V_R_2,T_b] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 94.19/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_le__diff__iff,axiom,
% 94.19/94.29 ! [V_na_2,V_m_2,V_k_2] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 94.19/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2))
% 94.19/94.29 => ( 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_na_2),V_k_2)))
% 94.19/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_Nat_Odiff__diff__eq,axiom,
% 94.19/94.29 ! [V_n,V_m,V_k] :
% 94.19/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 94.19/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 94.19/94.29 => 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) ) ) ).
% 94.19/94.29
% 94.19/94.29 fof(fact_eq__diff__iff,axiom,
% 94.19/94.29 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2))
% 94.26/94.29 => ( 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_na_2),V_k_2)
% 94.26/94.29 <=> V_m_2 = V_na_2 ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__diff__cancel,axiom,
% 94.26/94.29 ! [V_n,V_i] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 94.26/94.29 => 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 ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__le__mono,axiom,
% 94.26/94.29 ! [V_l,V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 => 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))) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__le__mono2,axiom,
% 94.26/94.29 ! [V_l,V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 => 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))) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__le__self,axiom,
% 94.26/94.29 ! [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)) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__diff__diff,axiom,
% 94.26/94.29 ! [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) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_linorder__linear,axiom,
% 94.26/94.29 ! [V_y,V_x,T_a] :
% 94.26/94.29 ( class_Orderings_Olinorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_order__eq__iff,axiom,
% 94.26/94.29 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.29 ( class_Orderings_Oorder(T_b)
% 94.26/94.29 => ( V_x_2 = V_y_2
% 94.26/94.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.29 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_order__eq__refl,axiom,
% 94.26/94.29 ! [V_y,V_x,T_a] :
% 94.26/94.29 ( class_Orderings_Opreorder(T_a)
% 94.26/94.29 => ( V_x = V_y
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_order__antisym__conv,axiom,
% 94.26/94.29 ! [V_x_2,V_y_2,T_b] :
% 94.26/94.29 ( class_Orderings_Oorder(T_b)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.29 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_ord__eq__le__trans,axiom,
% 94.26/94.29 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.29 ( class_Orderings_Oord(T_a)
% 94.26/94.29 => ( V_a = V_b
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_xt1_I3_J,axiom,
% 94.26/94.29 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.29 ( class_Orderings_Oorder(T_a)
% 94.26/94.29 => ( V_a = V_b
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_ord__le__eq__trans,axiom,
% 94.26/94.29 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.29 ( class_Orderings_Oord(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.29 => ( V_b = V_c
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_xt1_I4_J,axiom,
% 94.26/94.29 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.29 ( class_Orderings_Oorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.29 => ( V_b = V_c
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_order__antisym,axiom,
% 94.26/94.29 ! [V_y,V_x,T_a] :
% 94.26/94.29 ( class_Orderings_Oorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.29 => V_x = V_y ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_order__trans,axiom,
% 94.26/94.29 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.29 ( class_Orderings_Opreorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_xt1_I5_J,axiom,
% 94.26/94.29 ! [V_x,V_y,T_a] :
% 94.26/94.29 ( class_Orderings_Oorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.29 => V_x = V_y ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_xt1_I6_J,axiom,
% 94.26/94.29 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.29 ( class_Orderings_Oorder(T_a)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_linorder__le__cases,axiom,
% 94.26/94.29 ! [V_y,V_x,T_a] :
% 94.26/94.29 ( class_Orderings_Olinorder(T_a)
% 94.26/94.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_eq__mem,axiom,
% 94.26/94.29 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 94.26/94.29 <=> V_x_2 = V_y_2 ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_n__not__Suc__n,axiom,
% 94.26/94.29 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__n__not__n,axiom,
% 94.26/94.29 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 94.26/94.29
% 94.26/94.29 fof(fact_nat_Oinject,axiom,
% 94.26/94.29 ! [V_nat_H_2,V_nat_2] :
% 94.26/94.29 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 94.26/94.29 <=> V_nat_2 = V_nat_H_2 ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__inject,axiom,
% 94.26/94.29 ! [V_y,V_x] :
% 94.26/94.29 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 94.26/94.29 => V_x = V_y ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_rev__predicate1D,axiom,
% 94.26/94.29 ! [V_Q_2,T_b,V_x_2,V_Pa_2] :
% 94.26/94.29 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 94.26/94.29 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_predicate1D,axiom,
% 94.26/94.29 ! [V_x_2,V_Q_2,V_Pa_2,T_b] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Q_2))
% 94.26/94.29 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.26/94.29 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__refl,axiom,
% 94.26/94.29 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_nat__le__linear,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_eq__imp__le,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( V_m = V_n
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__trans,axiom,
% 94.26/94.29 ! [V_k,V_j,V_i] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__antisym,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.29 => V_m = V_n ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__commute,axiom,
% 94.26/94.29 ! [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) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_pred__equals__eq,axiom,
% 94.26/94.29 ! [V_S_2,V_R_2,T_b] :
% 94.26/94.29 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 94.26/94.29 <=> V_R_2 = V_S_2 ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__fun__def,axiom,
% 94.26/94.29 ! [V_g_2,V_f_2,T_b,T_c] :
% 94.26/94.29 ( class_Orderings_Oord(T_c)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.26/94.29 <=> ! [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))) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__funD,axiom,
% 94.26/94.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 94.26/94.29 ( class_Orderings_Oord(T_c)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.26/94.29 => 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))) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__funE,axiom,
% 94.26/94.29 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 94.26/94.29 ( class_Orderings_Oord(T_c)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.26/94.29 => 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))) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__n__not__le__n,axiom,
% 94.26/94.29 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_not__less__eq__eq,axiom,
% 94.26/94.29 ! [V_na_2,V_m_2] :
% 94.26/94.29 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__Suc__eq,axiom,
% 94.26/94.29 ! [V_na_2,V_m_2] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 94.26/94.29 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.29 | V_m_2 = hAPP(c_Nat_OSuc,V_na_2) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__le__mono,axiom,
% 94.26/94.29 ! [V_m_2,V_na_2] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2)))
% 94.26/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__SucI,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_le__SucE,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 94.26/94.29 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.29 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_Suc__leD,axiom,
% 94.26/94.29 ! [V_n,V_m] :
% 94.26/94.29 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 94.26/94.29 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__Suc__Suc,axiom,
% 94.26/94.29 ! [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) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_diff__eq__diff__less__eq,axiom,
% 94.26/94.29 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.29 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.29 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 94.26/94.29 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 94.26/94.29 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 94.26/94.29
% 94.26/94.29 fof(fact_folding__image__simple_Oinsert,axiom,
% 94.26/94.29 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 94.26/94.30 => 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)) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 94.26/94.30 ! [V_na_2,V_m_2] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 94.26/94.30 <=> 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_na_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_assms_I3_J,axiom,
% 94.26/94.30 ! [V_G_2,V_c_2] :
% 94.26/94.30 ( v_wt(V_c_2)
% 94.26/94.30 => ( ! [B_x] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_U))
% 94.26/94.30 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,B_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) )
% 94.26/94.30 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.30 => 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) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => 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)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 94.26/94.30 => 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) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__ident,axiom,
% 94.26/94.30 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 94.26/94.30
% 94.26/94.30 fof(fact_fun__diff__def,axiom,
% 94.26/94.30 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.30 ( class_Groups_Ominus(T_b)
% 94.26/94.30 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__inj__on__le,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => ( 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))
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one__idem_Oin__idem,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_assms_I4_J,axiom,
% 94.26/94.30 ! [V_pn_2] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),v_U))
% 94.26/94.30 => v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(V_pn_2))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_DiffE,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.30 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_DiffI,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.30 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite__Diff,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => 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))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_emptyE,axiom,
% 94.26/94.30 ! [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)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite_OemptyI,axiom,
% 94.26/94.30 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_empty__subsetI,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__empty,axiom,
% 94.26/94.30 ! [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))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_assms_I2_J,axiom,
% 94.26/94.30 ! [V_G_2,V_pn_2] :
% 94.26/94.30 ( v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,V_pn_2)),V_G_2),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(V_pn_2)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
% 94.26/94.30 => v_P(V_G_2,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,V_pn_2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_bot__apply,axiom,
% 94.26/94.30 ! [V_x_2,T_c,T_b] :
% 94.26/94.30 ( class_Orderings_Obot(T_b)
% 94.26/94.30 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_bot__fun__def,axiom,
% 94.26/94.30 ! [V_x_2,T_c,T_b] :
% 94.26/94.30 ( class_Orderings_Obot(T_b)
% 94.26/94.30 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__id2,axiom,
% 94.26/94.30 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__def,axiom,
% 94.26/94.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 <=> ! [B_x] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.30 => ! [B_xa] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 94.26/94.30 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 94.26/94.30 => B_x = B_xa ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__diff,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => 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)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple_Oempty,axiom,
% 94.26/94.30 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__cancel,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__empty,axiom,
% 94.26/94.30 ! [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 ).
% 94.26/94.30
% 94.26/94.30 fof(fact_empty__Diff,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__onD,axiom,
% 94.26/94.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.26/94.30 => V_x_2 = V_y_2 ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__iff,axiom,
% 94.26/94.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.26/94.30 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 94.26/94.30 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__contraD,axiom,
% 94.26/94.30 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => ( V_x_2 != V_y_2
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.26/94.30 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__insert,axiom,
% 94.26/94.30 ! [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)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__insert2,axiom,
% 94.26/94.30 ! [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) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_insert__Diff__single,axiom,
% 94.26/94.30 ! [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) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_subset__inj__on,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.30 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one__idem_Oidem,axiom,
% 94.26/94.30 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.30 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__image__set__diff,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.30 => 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)) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 94.26/94.30 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__insert,axiom,
% 94.26/94.30 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 94.26/94.30 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 & ~ 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))))))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => 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)))))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_insert__Diff,axiom,
% 94.26/94.30 ! [V_A_2,V_a_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.30 => 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 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__insert__absorb,axiom,
% 94.26/94.30 ! [V_A_2,V_x_2,T_b] :
% 94.26/94.30 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => 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 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__Suc,axiom,
% 94.26/94.30 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__image__simple_Oremove,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 94.26/94.30 => 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)))))) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_DiffD2,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.30 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_DiffD1,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__iff,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.30 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.30 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite__Diff2,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.30 => ( 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)))
% 94.26/94.30 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_double__diff,axiom,
% 94.26/94.30 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.30 => 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 ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__mono,axiom,
% 94.26/94.30 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 94.26/94.30 => 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))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_Diff__subset,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_equals0D,axiom,
% 94.26/94.30 ! [V_a_2,T_b,V_A_2] :
% 94.26/94.30 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_empty__iff,axiom,
% 94.26/94.30 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_ex__in__conv,axiom,
% 94.26/94.30 ! [V_A_2,T_b] :
% 94.26/94.30 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.30 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_all__not__in__conv,axiom,
% 94.26/94.30 ! [V_A_2,T_b] :
% 94.26/94.30 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite_Oequations_I1_J,axiom,
% 94.26/94.30 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_singleton__inject,axiom,
% 94.26/94.30 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.30 ( 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)))
% 94.26/94.30 => V_a_2 = V_b_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_doubleton__eq__iff,axiom,
% 94.26/94.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.30 ( 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_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 94.26/94.30 <=> ( ( V_a_2 = V_c_2
% 94.26/94.30 & V_b_2 = V_d_2 )
% 94.26/94.30 | ( V_a_2 = V_d_2
% 94.26/94.30 & V_b_2 = V_c_2 ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_insert__not__empty,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_empty__not__insert,axiom,
% 94.26/94.30 ! [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) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_subset__empty,axiom,
% 94.26/94.30 ! [V_A_2,T_b] :
% 94.26/94.30 ( 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))))
% 94.26/94.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__is__empty,axiom,
% 94.26/94.30 ! [V_A_2,V_f_2,T_b,T_c] :
% 94.26/94.30 ( 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))
% 94.26/94.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__empty,axiom,
% 94.26/94.30 ! [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)) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_empty__is__image,axiom,
% 94.26/94.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( 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)
% 94.26/94.30 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => 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)) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.30 => 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) ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_diff__single__insert,axiom,
% 94.26/94.30 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( 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))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => 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))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_subset__insert__iff,axiom,
% 94.26/94.30 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( 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)))
% 94.26/94.30 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => 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)) )
% 94.26/94.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_bot__empty__eq,axiom,
% 94.26/94.30 ! [V_x_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 94.26/94.30 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_bot__least,axiom,
% 94.26/94.30 ! [V_x,T_a] :
% 94.26/94.30 ( class_Orderings_Obot(T_a)
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite__imageD,axiom,
% 94.26/94.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 94.26/94.30 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 94.26/94.30 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__image,axiom,
% 94.26/94.30 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => 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) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__insert,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__Diff1__le,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_insert__Diff1,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.26/94.30 => 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) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_insert__Diff__if,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 94.26/94.30 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.26/94.30 => 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) )
% 94.26/94.30 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.26/94.30 => 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)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite__Diff__insert,axiom,
% 94.26/94.30 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 94.26/94.30 ( 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))))
% 94.26/94.30 <=> 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))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__diff__subset,axiom,
% 94.26/94.30 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(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)))) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_singletonE,axiom,
% 94.26/94.30 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.30 ( 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)))))
% 94.26/94.30 => V_b_2 = V_a_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_singleton__iff,axiom,
% 94.26/94.30 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.30 ( 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)))))
% 94.26/94.30 <=> V_b_2 = V_a_2 ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_subset__singletonD,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( 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)))))
% 94.26/94.30 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 | 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))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__Suc__Diff1,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_nat__case__Suc,axiom,
% 94.26/94.30 ! [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) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__constant__conv,axiom,
% 94.26/94.30 ! [V_c_2,T_c,T_b,V_A_2] :
% 94.26/94.30 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 94.26/94.30 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_endo__inj__surj,axiom,
% 94.26/94.30 ! [V_f_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( 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))
% 94.26/94.30 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 94.26/94.30 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_finite__surj__inj,axiom,
% 94.26/94.30 ! [V_f_2,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( 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)))
% 94.26/94.30 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_eq__card__imp__inj__on,axiom,
% 94.26/94.30 ! [V_f_2,T_c,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( 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)
% 94.26/94.30 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__iff__eq__card,axiom,
% 94.26/94.30 ! [V_f_2,T_c,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 <=> 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) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_diff__eq__diff__eq,axiom,
% 94.26/94.30 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.30 ( class_Groups_Oab__group__add(T_b)
% 94.26/94.30 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 94.26/94.30 => ( V_a_2 = V_b_2
% 94.26/94.30 <=> V_c_2 = V_d_2 ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_minus__apply,axiom,
% 94.26/94.30 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.30 ( class_Groups_Ominus(T_b)
% 94.26/94.30 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_image__constant,axiom,
% 94.26/94.30 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__bij__eq,axiom,
% 94.26/94.30 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.30 => ( 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))
% 94.26/94.30 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 94.26/94.30 => ( 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))
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.30 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_card__Diff__subset,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.30 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_diff__card__le__card__Diff,axiom,
% 94.26/94.30 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.30 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__iff__card__le,axiom,
% 94.26/94.30 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.26/94.30 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.30 => ( ? [B_f] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 94.26/94.30 & 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)) )
% 94.26/94.30 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_inj__on__iff__surj,axiom,
% 94.26/94.30 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 94.26/94.30 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => ( ? [B_f] :
% 94.26/94.30 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 94.26/94.30 & 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)) )
% 94.26/94.30 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_the__elem__eq,axiom,
% 94.26/94.30 ! [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 ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one_Oremove,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.30 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.30 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.30 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.30 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 94.26/94.30 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.30 => 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)))))) ) ) ) ) ) ).
% 94.26/94.30
% 94.26/94.30 fof(fact_folding__one_Oinsert,axiom,
% 94.26/94.30 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.31 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_the__inv__into__into,axiom,
% 94.26/94.31 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Diff__singleton,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Diff__singleton__if,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)) )
% 94.26/94.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_finite__subset__induct,axiom,
% 94.26/94.31 ! [V_Pa_2,V_A_2,V_F_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 94.26/94.31 => ( ! [B_a,B_F] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 94.26/94.31 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 94.26/94.31 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 94.26/94.31 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.31 => ( ! [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))
% 94.26/94.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.26/94.31 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.31 => 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)) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_folding__one_Oinsert__remove,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.31 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 94.26/94.31 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.31 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_one__reorient,axiom,
% 94.26/94.31 ! [V_x_2,T_b] :
% 94.26/94.31 ( class_Groups_Oone(T_b)
% 94.26/94.31 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 94.26/94.31 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_Diff__idemp,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__Suc__1,axiom,
% 94.26/94.31 ! [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 ).
% 94.26/94.31
% 94.26/94.31 fof(fact_the__inv__into__f__f,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_the__inv__into__f__eq,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 94.26/94.31 ! [V_N_2] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 94.26/94.31 <=> ? [B_m] :
% 94.26/94.31 ! [B_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_inj__on__the__inv__into,axiom,
% 94.26/94.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_the__inv__into__onto,axiom,
% 94.26/94.31 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_folding__one_Osingleton,axiom,
% 94.26/94.31 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.31 => 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 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_f__the__inv__into__f,axiom,
% 94.26/94.31 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.26/94.31 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Diff__insert,axiom,
% 94.26/94.31 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 94.26/94.31 => 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)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OatMost__iff,axiom,
% 94.26/94.31 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OatLeast__iff,axiom,
% 94.26/94.31 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OlessThan__iff,axiom,
% 94.26/94.31 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OgreaterThan__iff,axiom,
% 94.26/94.31 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 94.26/94.31 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 94.26/94.31 ( 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)))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 94.26/94.31 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 94.26/94.31 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 94.26/94.31 ( 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)))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 94.26/94.31 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 94.26/94.31 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 94.26/94.31 ( 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)))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 94.26/94.31 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 94.26/94.31 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 94.26/94.31 ( 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)))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 94.26/94.31 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card_Oremove,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)))))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_folding__one_Oclosed,axiom,
% 94.26/94.31 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.31 => ( ! [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))))))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__image,axiom,
% 94.26/94.31 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 94.26/94.31 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)))))) )
% 94.26/94.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__triv,axiom,
% 94.26/94.31 ! [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 ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__right__cancel,axiom,
% 94.26/94.31 ! [V_na_2,V_k_2,V_m_2] :
% 94.26/94.31 ( 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_na_2),V_k_2)
% 94.26/94.31 <=> V_m_2 = V_na_2 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__left__cancel,axiom,
% 94.26/94.31 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.31 ( 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_na_2)
% 94.26/94.31 <=> V_m_2 = V_na_2 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__assoc,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__left__commute,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__commute,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__right__imp__eq,axiom,
% 94.26/94.31 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.31 ( class_Groups_Ocancel__semigroup__add(T_a)
% 94.26/94.31 => ( 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)
% 94.26/94.31 => V_b = V_c ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__imp__eq,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 94.26/94.31 => ( 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)
% 94.26/94.31 => V_b = V_c ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__left__imp__eq,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Ocancel__semigroup__add(T_a)
% 94.26/94.31 => ( 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)
% 94.26/94.31 => V_b = V_c ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__idem,axiom,
% 94.26/94.31 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 94.26/94.31 ( hAPP(V_f_2,V_x_2) = V_y_2
% 94.26/94.31 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__other,axiom,
% 94.26/94.31 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 94.26/94.31 ( V_z_2 != V_x_2
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__twist,axiom,
% 94.26/94.31 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 94.26/94.31 ( V_a_2 != V_c_2
% 94.26/94.31 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__apply,axiom,
% 94.26/94.31 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 94.26/94.31 ( ( V_z_2 = V_x_2
% 94.26/94.31 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 94.26/94.31 & ( V_z_2 != V_x_2
% 94.26/94.31 => 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) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__same,axiom,
% 94.26/94.31 ! [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 ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__upd,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__idem__iff,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 94.26/94.31 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__right__cancel,axiom,
% 94.26/94.31 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 94.26/94.31 ( class_Groups_Ocancel__semigroup__add(T_b)
% 94.26/94.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
% 94.26/94.31 <=> V_b_2 = V_c_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__left__cancel,axiom,
% 94.26/94.31 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.31 ( class_Groups_Ocancel__semigroup__add(T_b)
% 94.26/94.31 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
% 94.26/94.31 <=> V_b_2 = V_c_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oab__semigroup__add(T_a)
% 94.26/94.31 => 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)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__upd__def,axiom,
% 94.26/94.31 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 94.26/94.31 ( ( V_x_2 = V_a_2
% 94.26/94.31 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 94.26/94.31 & ( V_x_2 != V_a_2
% 94.26/94.31 => 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) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__imp__le__left,axiom,
% 94.26/94.31 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.31 => ( 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)))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__imp__le__right,axiom,
% 94.26/94.31 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.31 => ( 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)))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__mono,axiom,
% 94.26/94.31 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 94.26/94.31 => 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))) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__left__mono,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__right__mono,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__cancel__left,axiom,
% 94.26/94.31 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__cancel__right,axiom,
% 94.26/94.31 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__diff__cancel,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.31 => 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 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__add__cancel,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.31 => 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 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__Suc__shift,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__Suc,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__Suc__right,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__leE,axiom,
% 94.26/94.31 ! [V_n,V_k,V_m] :
% 94.26/94.31 ( 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))
% 94.26/94.31 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__leD1,axiom,
% 94.26/94.31 ! [V_n,V_k,V_m] :
% 94.26/94.31 ( 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))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__leD2,axiom,
% 94.26/94.31 ! [V_n,V_k,V_m] :
% 94.26/94.31 ( 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))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__mono,axiom,
% 94.26/94.31 ! [V_l,V_k,V_j,V_i] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__le__mono1,axiom,
% 94.26/94.31 ! [V_k,V_j,V_i] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_trans__le__add2,axiom,
% 94.26/94.31 ! [V_m,V_j,V_i] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_trans__le__add1,axiom,
% 94.26/94.31 ! [V_m,V_j,V_i] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__add__left__cancel__le,axiom,
% 94.26/94.31 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.31 ( 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_na_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__iff__add,axiom,
% 94.26/94.31 ! [V_na_2,V_m_2] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.31 <=> ? [B_k] : V_na_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__add1,axiom,
% 94.26/94.31 ! [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))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__add2,axiom,
% 94.26/94.31 ! [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))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__cancel2,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__cancel,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__diff__left,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__add__inverse,axiom,
% 94.26/94.31 ! [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 ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__add__inverse2,axiom,
% 94.26/94.31 ! [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 ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__add__assoc2,axiom,
% 94.26/94.31 ! [V_i,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__diff__assoc2,axiom,
% 94.26/94.31 ! [V_i,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__add__assoc,axiom,
% 94.26/94.31 ! [V_i,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__imp__diff__is__add,axiom,
% 94.26/94.31 ! [V_k_2,V_j_2,V_i_2] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 94.26/94.31 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 94.26/94.31 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__add__diff__inverse2,axiom,
% 94.26/94.31 ! [V_m,V_n] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.31 => 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 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__diff__conv2,axiom,
% 94.26/94.31 ! [V_i_2,V_j_2,V_k_2] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 94.26/94.31 => ( 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)))
% 94.26/94.31 <=> 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)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__diff__assoc,axiom,
% 94.26/94.31 ! [V_i,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__add__diff__inverse,axiom,
% 94.26/94.31 ! [V_m,V_n] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.31 => 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 ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__add__diff,axiom,
% 94.26/94.31 ! [V_m,V_n,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_le__diff__conv,axiom,
% 94.26/94.31 ! [V_i_2,V_k_2,V_j_2] :
% 94.26/94.31 ( 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))
% 94.26/94.31 <=> 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__diff__right,axiom,
% 94.26/94.31 ! [V_i,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_Suc__eq__plus1__left,axiom,
% 94.26/94.31 ! [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) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_Suc__eq__plus1,axiom,
% 94.26/94.31 ! [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)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_inj__on__add__nat,axiom,
% 94.26/94.31 ! [V_N_2,V_k_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2),V_N_2) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__Suc__diff__eq2,axiom,
% 94.26/94.31 ! [V_m,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__Suc__diff__eq1,axiom,
% 94.26/94.31 ! [V_m,V_j,V_k] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 94.26/94.31 => 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)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_inj__on__fun__updI,axiom,
% 94.26/94.31 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.26/94.31 => 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) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card_Oinsert,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card_Oinsert__remove,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => 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)))))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_termination__basic__simps_I4_J,axiom,
% 94.26/94.31 ! [V_y,V_z,V_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_termination__basic__simps_I3_J,axiom,
% 94.26/94.31 ! [V_z,V_y,V_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Diff2__less,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.26/94.31 => 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))) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Diff1__less,axiom,
% 94.26/94.31 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_finite__empty__induct,axiom,
% 94.26/94.31 ! [V_Pa_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,V_A_2))
% 94.26/94.31 => ( ! [B_a,B_A] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,B_A))
% 94.26/94.31 => 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)))))) ) ) )
% 94.26/94.31 => hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_the__elem__def,axiom,
% 94.26/94.31 ! [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))))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__left__comm__idem__remove,axiom,
% 94.26/94.31 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_inj__on__diff__nat,axiom,
% 94.26/94.31 ! [V_k_2,V_N_2] :
% 94.26/94.31 ( ! [B_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_card__Plus,axiom,
% 94.26/94.31 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.31 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.31 => 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)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__insert__iff,axiom,
% 94.26/94.31 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 94.26/94.31 ( 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)))
% 94.26/94.31 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 94.26/94.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 94.26/94.31 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => 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)) )
% 94.26/94.31 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_finite__induct,axiom,
% 94.26/94.31 ! [V_Pa_2,V_F_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 94.26/94.31 => ( ! [B_x,B_F] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 94.26/94.31 => ( hBOOL(hAPP(V_Pa_2,B_F))
% 94.26/94.31 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 94.26/94.31 => hBOOL(hAPP(V_Pa_2,V_F_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_lessI,axiom,
% 94.26/94.31 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_Suc__mono,axiom,
% 94.26/94.31 ! [V_n,V_m] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__trans,axiom,
% 94.26/94.31 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__not__refl,axiom,
% 94.26/94.31 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__irrefl,axiom,
% 94.26/94.31 ! [V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__neq__iff,axiom,
% 94.26/94.31 ! [V_na_2,V_m_2] :
% 94.26/94.31 ( V_m_2 != V_na_2
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__neq__iff,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( V_x_2 != V_y_2
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_not__less__iff__gr__or__eq,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 94.26/94.31 | V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__less__linear,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 | V_x = V_y
% 94.26/94.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__antisym__conv3,axiom,
% 94.26/94.31 ! [V_x_2,V_y_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__neqE,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( V_x != V_y
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__neqE__nat,axiom,
% 94.26/94.31 ! [V_y,V_x] :
% 94.26/94.31 ( V_x != V_y
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__irrefl__nat,axiom,
% 94.26/94.31 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__not__refl2,axiom,
% 94.26/94.31 ! [V_m,V_n] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 94.26/94.31 => V_m != V_n ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__not__refl3,axiom,
% 94.26/94.31 ! [V_t,V_s] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 94.26/94.31 => V_s != V_t ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__imp__neq,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => V_x != V_y ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__not__sym,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__imp__not__less,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__imp__not__eq,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => V_x != V_y ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__imp__not__eq2,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => V_y != V_x ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__asym_H,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I9_J,axiom,
% 94.26/94.31 ! [V_a,V_b,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord__eq__less__trans,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oord(T_a)
% 94.26/94.31 => ( V_a = V_b
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I1_J,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( V_a = V_b
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_ord__less__eq__trans,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oord(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.31 => ( V_b = V_c
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I2_J,axiom,
% 94.26/94.31 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.31 => ( V_b = V_c
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__trans,axiom,
% 94.26/94.31 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I10_J,axiom,
% 94.26/94.31 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__asym,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__cases,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ( V_x != V_y
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_nat__less__cases,axiom,
% 94.26/94.31 ! [V_Pa_2,V_na_2,V_m_2] :
% 94.26/94.31 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 94.26/94.31 => ( ( V_m_2 = V_na_2
% 94.26/94.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 94.26/94.31 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) )
% 94.26/94.31 => hBOOL(hAPP(hAPP(V_Pa_2,V_na_2),V_m_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 94.26/94.31 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.26/94.31 => 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) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_termination__basic__simps_I2_J,axiom,
% 94.26/94.31 ! [V_y,V_z,V_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_termination__basic__simps_I1_J,axiom,
% 94.26/94.31 ! [V_z,V_y,V_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 94.26/94.31 => 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))) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_termination__basic__simps_I5_J,axiom,
% 94.26/94.31 ! [V_y,V_x] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__card__mono,axiom,
% 94.26/94.31 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 94.26/94.31 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.26/94.31 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.26/94.31 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__fun__def,axiom,
% 94.26/94.31 ! [V_g_2,V_f_2,T_b,T_c] :
% 94.26/94.31 ( class_Orderings_Oord(T_c)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.26/94.31 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__not__less,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__not__le,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__le__less__linear,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.31 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__le,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Oorder(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 & V_x_2 != V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_less__le__not__le,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__le__less,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Oorder(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 | V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_leI,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_not__leE,axiom,
% 94.26/94.31 ! [V_x,V_y,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__antisym__conv1,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__neq__le__trans,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( V_a != V_b
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I12_J,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( V_a != V_b
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_leD,axiom,
% 94.26/94.31 ! [V_x,V_y,T_a] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.31 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__imp__le,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_linorder__antisym__conv2,axiom,
% 94.26/94.31 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.31 ( class_Orderings_Olinorder(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.31 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 94.26/94.31 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__le__imp__less__or__eq,axiom,
% 94.26/94.31 ! [V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 | V_x = V_y ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__le__neq__trans,axiom,
% 94.26/94.31 ! [V_b,V_a,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.31 => ( V_a != V_b
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I11_J,axiom,
% 94.26/94.31 ! [V_a,V_b,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.31 => ( V_a != V_b
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__less__le__trans,axiom,
% 94.26/94.31 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I7_J,axiom,
% 94.26/94.31 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_order__le__less__trans,axiom,
% 94.26/94.31 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.31 ( class_Orderings_Opreorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_xt1_I8_J,axiom,
% 94.26/94.31 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.31 ( class_Orderings_Oorder(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubsetD,axiom,
% 94.26/94.31 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__less__cancel__right,axiom,
% 94.26/94.31 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__less__cancel__left,axiom,
% 94.26/94.31 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__strict__right__mono,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__strict__left__mono,axiom,
% 94.26/94.31 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.31 => 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))) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__strict__mono,axiom,
% 94.26/94.31 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 94.26/94.31 => 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))) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__less__imp__less__right,axiom,
% 94.26/94.31 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.31 => ( 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)))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_add__less__imp__less__left,axiom,
% 94.26/94.31 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.31 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.31 => ( 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)))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_not__psubset__empty,axiom,
% 94.26/94.31 ! [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)))) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_diff__eq__diff__less,axiom,
% 94.26/94.31 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.31 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.31 => ( 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_c_2),V_d_2)
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.26/94.31 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__eq,axiom,
% 94.26/94.31 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 & V_A_2 != V_B_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_subset__iff__psubset__eq,axiom,
% 94.26/94.31 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 | V_A_2 = V_B_2 ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__imp__subset,axiom,
% 94.26/94.31 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_psubset__subset__trans,axiom,
% 94.26/94.31 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_subset__psubset__trans,axiom,
% 94.26/94.31 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.26/94.31 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.31 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.31 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 94.26/94.31
% 94.26/94.31 fof(fact_not__less__eq,axiom,
% 94.26/94.31 ! [V_na_2,V_m_2] :
% 94.26/94.31 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__Suc__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 94.26/94.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 | V_m_2 = V_na_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__less__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__less__less__Suc__eq,axiom,
% 94.26/94.32 ! [V_m_2,V_na_2] :
% 94.26/94.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 94.26/94.32 <=> V_na_2 = V_m_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__antisym,axiom,
% 94.26/94.32 ! [V_m,V_n] :
% 94.26/94.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 94.26/94.32 => V_m = V_n ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__SucI,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__lessI,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__trans__Suc,axiom,
% 94.26/94.32 ! [V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__SucE,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 94.26/94.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => V_m = V_n ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__lessD,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__less__SucD,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__add__less1,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__add__less2,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__add__left__cancel__less,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.32 ( 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_na_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_trans__less__add1,axiom,
% 94.26/94.32 ! [V_m,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_trans__less__add2,axiom,
% 94.26/94.32 ! [V_m,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__less__mono1,axiom,
% 94.26/94.32 ! [V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__less__mono,axiom,
% 94.26/94.32 ! [V_l,V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__add__eq__less,axiom,
% 94.26/94.32 ! [V_n,V_m,V_l,V_k] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 94.26/94.32 => ( 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)
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__lessD1,axiom,
% 94.26/94.32 ! [V_k,V_j,V_i] :
% 94.26/94.32 ( 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))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__less__le,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 & V_m_2 != V_na_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__eq__less__or__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 | V_m_2 = V_na_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__imp__le__nat,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__neq__implies__less,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => ( V_m != V_n
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__or__eq__imp__le,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 | V_m = V_n )
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__imp__diff__less,axiom,
% 94.26/94.32 ! [V_n,V_k,V_j] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__less__mono2,axiom,
% 94.26/94.32 ! [V_l,V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_finite__nat__set__iff__bounded,axiom,
% 94.26/94.32 ! [V_N_2] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 94.26/94.32 <=> ? [B_m] :
% 94.26/94.32 ! [B_x] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__psubset,axiom,
% 94.26/94.32 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.32 => ( 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)))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fun__left__comm__idem__insert,axiom,
% 94.26/94.32 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_finite__Plus__iff,axiom,
% 94.26/94.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_finite__Plus,axiom,
% 94.26/94.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_finite__PlusD_I1_J,axiom,
% 94.26/94.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_finite__PlusD_I2_J,axiom,
% 94.26/94.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__le__less__mono,axiom,
% 94.26/94.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__less__le__mono,axiom,
% 94.26/94.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__iff__Suc__add,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 <=> ? [B_k] : V_na_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__add__Suc2,axiom,
% 94.26/94.32 ! [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)))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__add__Suc1,axiom,
% 94.26/94.32 ! [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)))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_inj__on__strict__subset,axiom,
% 94.26/94.32 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__eq__Suc__le,axiom,
% 94.26/94.32 ! [V_m_2,V_na_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__Suc__eq__le,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__le__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__imp__less__Suc,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__leI,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__less__Suc__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
% 94.26/94.32 <=> V_na_2 = V_m_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__le__lessD,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__less__Suc,axiom,
% 94.26/94.32 ! [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))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__diff__inverse,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => 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 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__diff__conv,axiom,
% 94.26/94.32 ! [V_k_2,V_j_2,V_i_2] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 <=> 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__less__mono,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__diff__iff,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_2))
% 94.26/94.32 => ( 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_na_2),V_k_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__eq__Suc__le__raw,axiom,
% 94.26/94.32 ! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_pigeonhole,axiom,
% 94.26/94.32 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_the__inv__into__def,axiom,
% 94.26/94.32 ! [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))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__add__one,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => 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)))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_flat__lub__def,axiom,
% 94.26/94.32 ! [V_b_2,V_A_2,T_b] :
% 94.26/94.32 ( ( 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)))))
% 94.26/94.32 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 94.26/94.32 & ( ~ 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)))))
% 94.26/94.32 => 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)))))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Plus__eq__empty__conv,axiom,
% 94.26/94.32 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.32 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__Plus__conv__if,axiom,
% 94.26/94.32 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.26/94.32 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 94.26/94.32 => 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)) )
% 94.26/94.32 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 94.26/94.32 => 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) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_the__eq__trivial,axiom,
% 94.26/94.32 ! [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 ).
% 94.26/94.32
% 94.26/94.32 fof(fact_the__sym__eq__trivial,axiom,
% 94.26/94.32 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 94.26/94.32 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.32 => ( 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)
% 94.26/94.32 => 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)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Diff1__fold__graph,axiom,
% 94.26/94.32 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__eq__if,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 94.26/94.32 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => 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)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__pred_H,axiom,
% 94.26/94.32 ! [V_n] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__zeroE,axiom,
% 94.26/94.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le0,axiom,
% 94.26/94.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__less__Suc,axiom,
% 94.26/94.32 ! [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))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_bot__nat__def,axiom,
% 94.26/94.32 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__reorient,axiom,
% 94.26/94.32 ! [V_x_2,T_b] :
% 94.26/94.32 ( class_Groups_Ozero(T_b)
% 94.26/94.32 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 94.26/94.32 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_one__neq__zero,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Ozero__neq__one(T_a)
% 94.26/94.32 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__neq__one,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Ozero__neq__one(T_a)
% 94.26/94.32 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add_Ocomm__neutral,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ocomm__monoid__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__0__right,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Omonoid__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_double__zero__sym,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 94.26/94.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__0,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ocomm__monoid__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__0__left,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Omonoid__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_right__minus__eq,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 <=> V_a_2 = V_b_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_eq__iff__diff__eq__0,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Oab__group__add(T_b)
% 94.26/94.32 => ( V_a_2 = V_b_2
% 94.26/94.32 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__self,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__0__right,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__neq__Zero,axiom,
% 94.26/94.32 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Zero__neq__Suc,axiom,
% 94.26/94.32 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat_Osimps_I3_J,axiom,
% 94.26/94.32 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__not__Zero,axiom,
% 94.26/94.32 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat_Osimps_I2_J,axiom,
% 94.26/94.32 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Zero__not__Suc,axiom,
% 94.26/94.32 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_gr0I,axiom,
% 94.26/94.32 ! [V_n] :
% 94.26/94.32 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_gr__implies__not0,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__nat__zero__code,axiom,
% 94.26/94.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_neq0__conv,axiom,
% 94.26/94.32 ! [V_na_2] :
% 94.26/94.32 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__less0,axiom,
% 94.26/94.32 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__eq__self__zero,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 94.26/94.32 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__is__0,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Nat_Oadd__0__right,axiom,
% 94.26/94.32 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 94.26/94.32
% 94.26/94.32 fof(fact_plus__nat_Oadd__0,axiom,
% 94.26/94.32 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__0__eq,axiom,
% 94.26/94.32 ! [V_na_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 94.26/94.32 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 94.26/94.32 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diffs0__imp__equal,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => V_m = V_n ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__self__eq__0,axiom,
% 94.26/94.32 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_minus__nat_Odiff__0,axiom,
% 94.26/94.32 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__0__eq__0,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_pos__add__strict,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_empty__fold__graphE,axiom,
% 94.26/94.32 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 => V_x_2 = V_z_2 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_OemptyI,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph__imp__finite,axiom,
% 94.26/94.32 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 94.26/94.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__le__one,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__one__le__zero,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => ~ 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_not__one__less__zero,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__less__one,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__case__0,axiom,
% 94.26/94.32 ! [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 ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__less__two,axiom,
% 94.26/94.32 ! [T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.32 => 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)))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__nonneg__nonneg,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__nonneg__eq__0__iff,axiom,
% 94.26/94.32 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__increasing,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__increasing2,axiom,
% 94.26/94.32 ! [V_a,V_b,V_c,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__nonpos__nonpos,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__neg__neg,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__pos__pos,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__iff__diff__le__0,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 94.26/94.32 <=> 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__iff__diff__less__0,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.26/94.32 <=> 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_gr0__conv__Suc,axiom,
% 94.26/94.32 ! [V_na_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 94.26/94.32 <=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__Suc0,axiom,
% 94.26/94.32 ! [V_na_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 94.26/94.32 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__Suc__eq__0__disj,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 94.26/94.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 | ? [B_j] :
% 94.26/94.32 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 94.26/94.32 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_one__is__add,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( 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_na_2)
% 94.26/94.32 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.26/94.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.32 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__is__1,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.26/94.32 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.26/94.32 & V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.32 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__gr__0,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( 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_na_2)))
% 94.26/94.32 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 94.26/94.32 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card_Oempty,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__infinite,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_zero__less__diff,axiom,
% 94.26/94.32 ! [V_m_2,V_na_2] :
% 94.26/94.32 ( 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_na_2),V_m_2)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__less,axiom,
% 94.26/94.32 ! [V_m,V_n] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 94.26/94.32 => 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)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__add__0,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__is__0__eq_H,axiom,
% 94.26/94.32 ! [V_n,V_m] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.32 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__is__0__eq,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_One__nat__def,axiom,
% 94.26/94.32 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_OinsertI,axiom,
% 94.26/94.32 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 94.26/94.32 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__Suc,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__nonpos__neg,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__neg__nonpos,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__strict__increasing2,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__strict__increasing,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__nonneg__pos,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__pos__nonneg,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_linorder__neqE__linordered__idom,axiom,
% 94.26/94.32 ! [V_y,V_x,T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.32 => ( V_x != V_y
% 94.26/94.32 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__eq__0__iff,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.32 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__ge__0__finite,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 94.26/94.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__Suc__less,axiom,
% 94.26/94.32 ! [V_i,V_n] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__pred,axiom,
% 94.26/94.32 ! [V_n] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.32 => 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 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__diff__split,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,V_Pa_2] :
% 94.26/94.32 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 94.26/94.32 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.32 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 94.26/94.32 & ! [B_d] :
% 94.26/94.32 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 94.26/94.32 => hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__diff__split__asm,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,V_Pa_2] :
% 94.26/94.32 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 94.26/94.32 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.32 & ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 94.26/94.32 | ? [B_d] :
% 94.26/94.32 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 94.26/94.32 & ~ hBOOL(hAPP(V_Pa_2,B_d)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__gt__0__iff,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 94.26/94.32 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__diff__1,axiom,
% 94.26/94.32 ! [V_n] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.32 => 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 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_even__less__0__iff,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold1Set_Ointros,axiom,
% 94.26/94.32 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 94.26/94.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.32 => 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)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__Suc__eq,axiom,
% 94.26/94.32 ! [V_k_2,V_A_2,T_b] :
% 94.26/94.32 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 94.26/94.32 <=> ? [B_b,B_B] :
% 94.26/94.32 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 94.26/94.32 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 94.26/94.32 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 94.26/94.32 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 94.26/94.32 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.32 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 94.26/94.32 | ? [B_x,B_y] :
% 94.26/94.32 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 94.26/94.32 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 94.26/94.32 & 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) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__0__iff,axiom,
% 94.26/94.32 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.32 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 94.26/94.32 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 94.26/94.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_double__eq__0__iff,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_ex__least__nat__less,axiom,
% 94.26/94.32 ! [V_na_2,V_Pa_2] :
% 94.26/94.32 ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 94.26/94.32 => ( hBOOL(hAPP(V_Pa_2,V_na_2))
% 94.26/94.32 => ? [B_k] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2))
% 94.26/94.32 & ! [B_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 94.26/94.32 => ~ hBOOL(hAPP(V_Pa_2,B_i)) )
% 94.26/94.32 & 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)))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card_Oeq__fold__g,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__image__empty,axiom,
% 94.26/94.32 ! [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 ).
% 94.26/94.32
% 94.26/94.32 fof(fact_empty__fold1SetE,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold1Set__nonempty,axiom,
% 94.26/94.32 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 94.26/94.32 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 94.26/94.32 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.32 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.32 => 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) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 94.26/94.32 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 94.26/94.32 ! [V_d,V_c,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 94.26/94.32 ! [V_d,V_c,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 94.26/94.32 ! [V_c,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold1Set__sing,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 <=> V_a_2 = V_b_2 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card__def,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => 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) )
% 94.26/94.32 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Ints__odd__less__0,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold1Set_Oequations,axiom,
% 94.26/94.32 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 <=> ? [B_a,B_A] :
% 94.26/94.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 94.26/94.32 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 94.26/94.32 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_insert__fold1SetE,axiom,
% 94.26/94.32 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 94.26/94.32 ( 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))
% 94.26/94.32 => ~ ! [B_a,B_A] :
% 94.26/94.32 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 94.26/94.32 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 94.26/94.32 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Ints__odd__nonzero,axiom,
% 94.26/94.32 ! [V_a_2,T_b] :
% 94.26/94.32 ( class_Int_Oring__char__0(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.32 => 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) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fold__graph__permute__diff,axiom,
% 94.26/94.32 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 94.26/94.32 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.26/94.32 => ( 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))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.32 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 94.26/94.32 => 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)) ) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_card_Oneutral,axiom,
% 94.26/94.32 ! [V_A_2,T_b] :
% 94.26/94.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.32 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.32 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.32 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_expand__Suc,axiom,
% 94.26/94.32 ! [V_v] :
% 94.26/94.32 ( 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)))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_convex__bound__lt,axiom,
% 94.26/94.32 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 94.26/94.32 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 94.26/94.32 => 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)) ) ) ) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_pair__box_Osize_I1_J,axiom,
% 94.26/94.32 ! [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))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Ints__number__of,axiom,
% 94.26/94.32 ! [V_w_2,T_b] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_b)
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 94.26/94.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 94.26/94.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 94.26/94.32 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 94.26/94.32 ! [V_rx,V_ly,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 94.26/94.32 ! [V_rx,V_ly,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__number__of__left,axiom,
% 94.26/94.32 ! [V_z,V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_eq__number__of,axiom,
% 94.26/94.32 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.32 & class_Int_Oring__char__0(T_b) )
% 94.26/94.32 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 94.26/94.32 <=> V_x_2 = V_y_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_arith__simps_I32_J,axiom,
% 94.26/94.32 ! [V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_number__of__reorient,axiom,
% 94.26/94.32 ! [V_x_2,V_w_2,T_b] :
% 94.26/94.32 ( class_Int_Onumber(T_b)
% 94.26/94.32 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 94.26/94.32 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 94.26/94.32 ! [V_ry,V_rx,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 94.26/94.32 ! [V_ry,V_rx,V_lx,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_number__of__mult,axiom,
% 94.26/94.32 ! [V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_left__diff__distrib__number__of,axiom,
% 94.26/94.32 ! [V_v,V_b,V_a,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber(T_b)
% 94.26/94.32 & class_Rings_Oring(T_b) )
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_right__diff__distrib__number__of,axiom,
% 94.26/94.32 ! [V_c,V_b,V_v,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber(T_b)
% 94.26/94.32 & class_Rings_Oring(T_b) )
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_left__distrib__number__of,axiom,
% 94.26/94.32 ! [V_v,V_b,V_a,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber(T_b)
% 94.26/94.32 & class_Rings_Osemiring(T_b) )
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_right__distrib__number__of,axiom,
% 94.26/94.32 ! [V_c,V_b,V_v,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber(T_b)
% 94.26/94.32 & class_Rings_Osemiring(T_b) )
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Groups_Oab__semigroup__mult(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__left__idem,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__idem,axiom,
% 94.26/94.32 ! [V_x,T_a] :
% 94.26/94.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_times_Oidem,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_pair__box_Oinject,axiom,
% 94.26/94.32 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 94.26/94.32 ( 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)
% 94.26/94.32 <=> ( V_a_2 = V_a_H_2
% 94.26/94.32 & V_b_2 = V_b_H_2 ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Ints__mult,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Rings_Oring__1(T_b)
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.32 => 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))) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__number__of,axiom,
% 94.26/94.32 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.32 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_less__number__of,axiom,
% 94.26/94.32 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.32 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.32 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.32 => ( 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)))
% 94.26/94.32 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_number__of__add,axiom,
% 94.26/94.32 ! [V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__number__of__eq,axiom,
% 94.26/94.32 ! [V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__number__of__left,axiom,
% 94.26/94.32 ! [V_z,V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_number__of__diff,axiom,
% 94.26/94.32 ! [V_w,V_v,T_a] :
% 94.26/94.32 ( class_Int_Onumber__ring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__zero__left,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Omult__zero(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__zero__right,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Omult__zero(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__eq__0__iff,axiom,
% 94.26/94.32 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Rings_Oring__no__zero__divisors(T_b)
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.32 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_no__zero__divisors,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ono__zero__divisors(T_a)
% 94.26/94.32 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.32 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_divisors__zero,axiom,
% 94.26/94.32 ! [V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ono__zero__divisors(T_a)
% 94.26/94.32 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.32 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.32 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__class_Odistrib,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_combine__common__factor,axiom,
% 94.26/94.32 ! [V_c,V_b,V_e,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Osemiring(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 94.26/94.32 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_crossproduct__noteq,axiom,
% 94.26/94.32 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.32 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 94.26/94.32 => ( ( V_a_2 != V_b_2
% 94.26/94.32 & V_c_2 != V_d_2 )
% 94.26/94.32 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 94.26/94.32 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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)) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 94.26/94.32 ! [V_b,V_m,V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => 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) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_crossproduct__eq,axiom,
% 94.26/94.32 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 94.26/94.32 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 94.26/94.32 => ( 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))
% 94.26/94.32 <=> ( V_w_2 = V_x_2
% 94.26/94.32 | V_y_2 = V_z_2 ) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult_Ocomm__neutral,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ocomm__monoid__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__1__right,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__1,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Ocomm__monoid__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__1__left,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 94.26/94.32 ! [V_a,T_a] :
% 94.26/94.32 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.32 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__cancel2,axiom,
% 94.26/94.32 ! [V_na_2,V_k_2,V_m_2] :
% 94.26/94.32 ( 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_na_2),V_k_2)
% 94.26/94.32 <=> ( V_m_2 = V_na_2
% 94.26/94.32 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__cancel1,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.32 ( 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_na_2)
% 94.26/94.32 <=> ( V_m_2 = V_na_2
% 94.26/94.32 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__is__0,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.32 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__0__right,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__0,axiom,
% 94.26/94.32 ! [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) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_Suc__mult__cancel1,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.32 ( 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_na_2)
% 94.26/94.32 <=> V_m_2 = V_na_2 ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__mult__distrib,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_add__mult__distrib2,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__le__mono,axiom,
% 94.26/94.32 ! [V_l,V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 94.26/94.32 => 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))) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__le__mono2,axiom,
% 94.26/94.32 ! [V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_mult__le__mono1,axiom,
% 94.26/94.32 ! [V_k,V_j,V_i] :
% 94.26/94.32 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.32 => 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))) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__cube,axiom,
% 94.26/94.32 ! [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)))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_le__square,axiom,
% 94.26/94.32 ! [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))) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__mult__distrib,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_diff__mult__distrib2,axiom,
% 94.26/94.32 ! [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)) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__mult__eq__1__iff,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 94.26/94.32 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 94.26/94.32 & V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__mult__1__right,axiom,
% 94.26/94.32 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__1__eq__mult__iff,axiom,
% 94.26/94.32 ! [V_na_2,V_m_2] :
% 94.26/94.32 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)
% 94.26/94.32 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 94.26/94.32 & V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 94.26/94.32
% 94.26/94.32 fof(fact_nat__mult__1,axiom,
% 94.26/94.32 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 94.26/94.32
% 94.26/94.32 fof(fact_fun__left__comm__idem,axiom,
% 94.26/94.32 ! [T_b] :
% 94.26/94.32 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.26/94.32 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 94.26/94.32
% 94.26/94.33 fof(fact_le__number__of__eq__not__less,axiom,
% 94.26/94.33 ! [V_w_2,V_v_2,T_b] :
% 94.26/94.33 ( ( class_Int_Onumber(T_b)
% 94.26/94.33 & class_Orderings_Olinorder(T_b) )
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> ~ 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__number__of__diff1,axiom,
% 94.26/94.33 ! [V_c,V_w,V_v,T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_split__mult__neg__le,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__cancel__semiring(T_a)
% 94.26/94.33 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_split__mult__pos__le,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_a)
% 94.26/94.33 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__mono,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__mono_H,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__left__mono__neg,axiom,
% 94.26/94.33 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__right__mono__neg,axiom,
% 94.26/94.33 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_comm__mult__left__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__comm__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__left__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__right__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nonpos__nonpos,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nonpos__nonneg,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__cancel__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nonneg__nonpos2,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__cancel__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nonneg__nonpos,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__cancel__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nonneg__nonneg,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Oordered__cancel__semiring(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__0__iff,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__le__mult__iff,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__le__square,axiom,
% 94.26/94.33 ! [V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring(T_a)
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__left__mono__neg,axiom,
% 94.26/94.33 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__right__mono__neg,axiom,
% 94.26/94.33 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_comm__mult__strict__left__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__left__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__right__mono,axiom,
% 94.26/94.33 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__neg__neg,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__neg__pos,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel__left__neg,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__less__mult__pos2,axiom,
% 94.26/94.33 ! [V_a,V_b,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__less__mult__pos,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__pos__neg2,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__pos__neg,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__pos__pos,axiom,
% 94.26/94.33 ! [V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel__left__pos,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel__left__disj,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel__right__disj,axiom,
% 94.26/94.33 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 94.26/94.33 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__square__less__zero,axiom,
% 94.26/94.33 ! [V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring(T_a)
% 94.26/94.33 => ~ 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_sum__squares__eq__zero__iff,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( 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)
% 94.26/94.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__scale__eq__noteq,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 94.26/94.33 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 94.26/94.33 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.33 => ( ( V_a = V_b
% 94.26/94.33 & V_c != V_d )
% 94.26/94.33 => 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)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__1__mult,axiom,
% 94.26/94.33 ! [V_n,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_eq__add__iff2,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oring(T_b)
% 94.26/94.33 => ( 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_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 94.26/94.33 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_eq__add__iff1,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oring(T_b)
% 94.26/94.33 => ( 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_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 94.26/94.33 <=> 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_c_2) = V_d_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 94.26/94.33 ! [V_m,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 94.26/94.33 ! [V_a,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 94.26/94.33 ! [V_m,T_a] :
% 94.26/94.33 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__eq__1__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.26/94.33 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.26/94.33 & V_na_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__mono2,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__mono1,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel2,axiom,
% 94.26/94.33 ! [V_na_2,V_k_2,V_m_2] :
% 94.26/94.33 ( 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_na_2),V_k_2)))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__0__less__mult__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Suc__mult__less__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__Suc__right,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__Suc,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Suc__mult__le__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__eq__self__implies__10,axiom,
% 94.26/94.33 ! [V_n,V_m] :
% 94.26/94.33 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 94.26/94.33 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 94.26/94.33 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__0,axiom,
% 94.26/94.33 ! [T_b] :
% 94.26/94.33 ( class_Rings_Oring__1(T_b)
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__add,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oring__1(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__diff,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oring__1(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__left__le__imp__le,axiom,
% 94.26/94.33 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__right__le__imp__le,axiom,
% 94.26/94.33 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__imp__less__left,axiom,
% 94.26/94.33 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__left__less__imp__less,axiom,
% 94.26/94.33 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__imp__less__right,axiom,
% 94.26/94.33 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__right__less__imp__less,axiom,
% 94.26/94.33 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__less__imp__less,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__less__le__imp__less,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__mono_H,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__strict__mono,axiom,
% 94.26/94.33 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__strict(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.33 => 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))) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__cancel__left__neg,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__cancel__left__pos,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__1,axiom,
% 94.26/94.33 ! [T_b] :
% 94.26/94.33 ( class_Rings_Oring__1(T_b)
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_sum__squares__le__zero__iff,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( 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_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)))
% 94.26/94.33 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.33 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_sum__squares__ge__zero,axiom,
% 94.26/94.33 ! [V_y,V_x,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring(T_a)
% 94.26/94.33 => 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)))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__sum__squares__lt__zero,axiom,
% 94.26/94.33 ! [V_y,V_x,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__ring(T_a)
% 94.26/94.33 => ~ 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_sum__squares__gt__zero__iff,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__ring__strict(T_b)
% 94.26/94.33 => ( 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))))
% 94.26/94.33 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.33 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__left__le__one__le,axiom,
% 94.26/94.33 ! [V_y,V_x,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.33 => 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)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__right__le__one__le,axiom,
% 94.26/94.33 ! [V_y,V_x,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.33 => 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)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__add__iff1,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_b)
% 94.26/94.33 => ( 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_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 94.26/94.33 <=> 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_c_2)),V_d_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__add__iff2,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_b)
% 94.26/94.33 => ( 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_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__add__iff2,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_b)
% 94.26/94.33 => ( 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_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__add__iff1,axiom,
% 94.26/94.33 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Oordered__ring(T_b)
% 94.26/94.33 => ( 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_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 94.26/94.33 <=> 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_c_2)),V_d_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_one__less__mult,axiom,
% 94.26/94.33 ! [V_m,V_n] :
% 94.26/94.33 ( 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))
% 94.26/94.33 => ( 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))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_n__less__n__mult__m,axiom,
% 94.26/94.33 ! [V_m,V_n] :
% 94.26/94.33 ( 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))
% 94.26/94.33 => ( 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))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_n__less__m__mult__n,axiom,
% 94.26/94.33 ! [V_m,V_n] :
% 94.26/94.33 ( 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))
% 94.26/94.33 => ( 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))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_one__le__mult__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> ( 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))
% 94.26/94.33 & 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_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__cancel2,axiom,
% 94.26/94.33 ! [V_na_2,V_k_2,V_m_2] :
% 94.26/94.33 ( 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_na_2),V_k_2)))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__le__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_na_2)))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold__graph__insert__swap,axiom,
% 94.26/94.33 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 94.26/94.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.26/94.33 => ( 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))
% 94.26/94.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold__image__distrib,axiom,
% 94.26/94.33 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_convex__bound__le,axiom,
% 94.26/94.33 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semiring__1(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 94.26/94.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 94.26/94.33 => 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)) ) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold__image__insert,axiom,
% 94.26/94.33 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 94.26/94.33 ( class_Groups_Oab__semigroup__mult(T_c)
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.33 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),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)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__eq__if,axiom,
% 94.26/94.33 ! [V_n,V_m] :
% 94.26/94.33 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.33 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.33 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__double__eq__0__iff,axiom,
% 94.26/94.33 ! [V_a_2,T_b] :
% 94.26/94.33 ( class_Int_Oring__char__0(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.33 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.33 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__less__add__iff2,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> 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_na_2))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__less__add__iff1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> 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_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__le__add__iff1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> 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_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__diff__add__eq1,axiom,
% 94.26/94.33 ! [V_n,V_m,V_u,V_i,V_j] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__eq__add__iff1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 94.26/94.33 => ( 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_na_2)
% 94.26/94.33 <=> 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_na_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__le__add__iff2,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> 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_na_2))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__diff__add__eq2,axiom,
% 94.26/94.33 ! [V_n,V_m,V_u,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__eq__add__iff2,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 94.26/94.33 => ( 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_na_2)
% 94.26/94.33 <=> 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_na_2) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__le__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_pos__zmult__eq__1__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 94.26/94.33 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.33 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.33 & V_na_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__zless__mono2,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__number__of__int__code,axiom,
% 94.26/94.33 ! [V_l_2,V_k_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__1__right,axiom,
% 94.26/94.33 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__1,axiom,
% 94.26/94.33 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__eq__number__of__int__code,axiom,
% 94.26/94.33 ! [V_l_2,V_k_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__assoc,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_times__numeral__code_I5_J,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__commute,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiff__zmult__distrib,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiff__zmult__distrib2,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__zmult__distrib,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_plus__numeral__code_I9_J,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__zmult__distrib2,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__assoc,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__commute,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__commute,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__left__commute,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__assoc,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__left__mono,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__antisym,axiom,
% 94.26/94.33 ! [V_w,V_z] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 94.26/94.33 => V_z = V_w ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__trans,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__linear,axiom,
% 94.26/94.33 ! [V_w,V_z] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 94.26/94.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__refl,axiom,
% 94.26/94.33 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__bin__lemma,axiom,
% 94.26/94.33 ! [V_l_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 94.26/94.33 <=> 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__linear,axiom,
% 94.26/94.33 ! [V_y,V_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 94.26/94.33 | V_x = V_y
% 94.26/94.33 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__le,axiom,
% 94.26/94.33 ! [V_w_2,V_z_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 94.26/94.33 & V_z_2 != V_w_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__zless__mono,axiom,
% 94.26/94.33 ! [V_z,V_z_H,V_w,V_w_H] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__strict__right__mono,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__0__right,axiom,
% 94.26/94.33 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__0,axiom,
% 94.26/94.33 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 94.26/94.33
% 94.26/94.33 fof(fact_odd__nonzero,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__0__less__1,axiom,
% 94.26/94.33 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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__add1__eq,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( 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))))
% 94.26/94.33 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 94.26/94.33 | V_w_2 = V_z_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_odd__less__0,axiom,
% 94.26/94.33 ! [V_z_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__imp__add1__zle,axiom,
% 94.26/94.33 ! [V_z,V_w] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__imp__0__less,axiom,
% 94.26/94.33 ! [V_z] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add1__zle__eq,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( 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))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__diff1__eq,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( 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))))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__add1__eq__le,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( 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))))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__one__le__iff__zero__less,axiom,
% 94.26/94.33 ! [V_z_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( 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_na_2)
% 94.26/94.33 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.33 | V_m_2 = V_na_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_left__add__mult__distrib,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__eq__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 => ( 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_na_2)
% 94.26/94.33 <=> V_m_2 = V_na_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__mult__less__cancel1,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_self__quotient__aux2,axiom,
% 94.26/94.33 ! [V_q,V_r,V_a] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.33 => ( 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))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_self__quotient__aux1,axiom,
% 94.26/94.33 ! [V_q,V_r,V_a] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.33 => ( 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))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 94.26/94.33 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 94.26/94.33 ( 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)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_unique__quotient__lemma__neg,axiom,
% 94.26/94.33 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiv__mono2__lemma,axiom,
% 94.26/94.33 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 94.26/94.33 ( 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)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_unique__quotient__lemma,axiom,
% 94.26/94.33 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_q__neg__lemma,axiom,
% 94.26/94.33 ! [V_r_H,V_q_H,V_b_H] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_q__pos__lemma,axiom,
% 94.26/94.33 ! [V_r_H,V_q_H,V_b_H] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_number__of__is__id,axiom,
% 94.26/94.33 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__0__neq__1,axiom,
% 94.26/94.33 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 94.26/94.33 ! [V_y,V_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 94.26/94.33 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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 94.26/94.33 ! [V_y,V_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_pair__box_Osize_I2_J,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_pair__box_Osimps_I2_J,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_pair__box_Orecs,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 94.26/94.33 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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__number__of__lemma,axiom,
% 94.26/94.33 ! [V_v,T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__eq__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,T_b] :
% 94.26/94.33 ( class_Nat_Osemiring__char__0(T_b)
% 94.26/94.33 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)
% 94.26/94.33 <=> V_m_2 = V_na_2 ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 94.26/94.33 ! [V_A_2] :
% 94.26/94.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 94.26/94.33 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 94.26/94.33 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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 94.26/94.33 ! [V_Pa_2] :
% 94.26/94.33 ( ! [B_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.26/94.33 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.33 <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 94.26/94.33 ! [V_Pa_2] :
% 94.26/94.33 ( ? [B_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.26/94.33 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.33 <=> ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 94.26/94.33 ! [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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 94.26/94.33 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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__0,axiom,
% 94.26/94.33 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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__eq__0__conv,axiom,
% 94.26/94.33 ! [V_na_2] :
% 94.26/94.33 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.33 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__zle__int,axiom,
% 94.26/94.33 ! [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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__less__0__conv,axiom,
% 94.26/94.33 ! [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))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__int,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__int,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__int,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zadd__int__left,axiom,
% 94.26/94.33 ! [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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zle__iff__zadd,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 94.26/94.33 <=> ? [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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__le__imp__of__nat,axiom,
% 94.26/94.33 ! [V_m,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__0__le__iff,axiom,
% 94.26/94.33 ! [V_n,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__less__0__iff,axiom,
% 94.26/94.33 ! [V_m,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => ~ 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__int,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__mult,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__0,axiom,
% 94.26/94.33 ! [T_a] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__less__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__imp__of__nat__less,axiom,
% 94.26/94.33 ! [V_n,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__less__imp__less,axiom,
% 94.26/94.33 ! [V_n,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.33 => ( 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)))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__1,axiom,
% 94.26/94.33 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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__le__iff,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__add,axiom,
% 94.26/94.33 ! [V_n,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__mult,axiom,
% 94.26/94.33 ! [V_n,V_m,T_a] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__1,axiom,
% 94.26/94.33 ! [T_a] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.33 => 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) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Ints__of__nat,axiom,
% 94.26/94.33 ! [V_na_2,T_b] :
% 94.26/94.33 ( class_Rings_Oring__1(T_b)
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__le__0__conv,axiom,
% 94.26/94.33 ! [V_na_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.33 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__Suc0__eq__1,axiom,
% 94.26/94.33 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) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zless__iff__Suc__zadd,axiom,
% 94.26/94.33 ! [V_z_2,V_w_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 94.26/94.33 <=> ? [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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__Suc,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiff__int,axiom,
% 94.26/94.33 ! [V_m,V_n] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__Suc,axiom,
% 94.26/94.33 ! [V_m,T_a] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.33 => 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)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__diff,axiom,
% 94.26/94.33 ! [V_m,V_n,T_a] :
% 94.26/94.33 ( class_Rings_Oring__1(T_a)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__less__int__conv,axiom,
% 94.26/94.33 ! [V_na_2] :
% 94.26/94.33 ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zmult__zless__mono2__lemma,axiom,
% 94.26/94.33 ! [V_k,V_j,V_i] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__0__less__iff,axiom,
% 94.26/94.33 ! [V_na_2,T_b] :
% 94.26/94.33 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.33 => ( 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_na_2)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zdiff__int__split,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2,V_Pa_2] :
% 94.26/94.33 ( 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))))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 94.26/94.33 => 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)))) )
% 94.26/94.33 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 94.26/94.33 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 94.26/94.33 ! [V_na_2,T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_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_na_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_tsub__def,axiom,
% 94.26/94.33 ! [V_x,V_y] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 94.26/94.33 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 94.26/94.33 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__number__of__eq,axiom,
% 94.26/94.33 ! [V_v,T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__insert,axiom,
% 94.26/94.33 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.26/94.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.33 => 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)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__number__of__mult__left,axiom,
% 94.26/94.33 ! [V_k,V_v_H,V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__nat__number__of,axiom,
% 94.26/94.33 ! [V_v_H,V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold__image__1,axiom,
% 94.26/94.33 ! [V_f_2,V_S_2,T_b,T_c] :
% 94.26/94.33 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.33 => ( ! [B_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.26/94.33 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.26/94.33 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 94.26/94.33 ! [V_A_2,V_x_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 94.26/94.33 ! [V_B_2,V_A_2] :
% 94.26/94.33 ( V_A_2 = V_B_2
% 94.26/94.33 <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 94.26/94.33 ! [V_y_2,V_x_2] :
% 94.26/94.33 ( 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)
% 94.26/94.33 <=> V_x_2 = V_y_2 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__neg__int,axiom,
% 94.26/94.33 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 94.26/94.33 ! [V_A_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__int__eq,axiom,
% 94.26/94.33 ! [V_na_2,V_m_2] :
% 94.26/94.33 ( 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_na_2)
% 94.26/94.33 <=> V_m_2 = V_na_2 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 94.26/94.33 c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 94.26/94.33 ! [V_B_2,V_A_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 94.26/94.33 ! [V_B_2,V_A_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_B_2))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__neg__number__of__Pls,axiom,
% 94.26/94.33 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Pls__def,axiom,
% 94.26/94.33 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_rel__simps_I19_J,axiom,
% 94.26/94.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_rel__simps_I2_J,axiom,
% 94.26/94.33 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__Pls__right,axiom,
% 94.26/94.33 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__Pls,axiom,
% 94.26/94.33 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 94.26/94.33
% 94.26/94.33 fof(fact_mult__Pls,axiom,
% 94.26/94.33 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 94.26/94.33
% 94.26/94.33 fof(fact_diff__bin__simps_I1_J,axiom,
% 94.26/94.33 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__neg__0,axiom,
% 94.26/94.33 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__neg__1,axiom,
% 94.26/94.33 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_semiring__norm_I112_J,axiom,
% 94.26/94.33 ! [T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_number__of__Pls,axiom,
% 94.26/94.33 ! [T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__numeral__0,axiom,
% 94.26/94.33 ! [V_a,T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => 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 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__numeral__0__right,axiom,
% 94.26/94.33 ! [V_a,T_a] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_a)
% 94.26/94.33 => 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 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_number__of2,axiom,
% 94.26/94.33 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_bin__less__0__simps_I1_J,axiom,
% 94.26/94.33 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__number__of__Pls,axiom,
% 94.26/94.33 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_semiring__norm_I113_J,axiom,
% 94.26/94.33 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_zero__is__num__zero,axiom,
% 94.26/94.33 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__singleton,axiom,
% 94.26/94.33 ! [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 ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__singleton__def,axiom,
% 94.26/94.33 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 94.26/94.33 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 94.26/94.33 => 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 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_not__neg__eq__ge__0,axiom,
% 94.26/94.33 ! [V_x_2] :
% 94.26/94.33 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_neg__def,axiom,
% 94.26/94.33 ! [V_Z_2] :
% 94.26/94.33 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_folding__one_Oeq__fold,axiom,
% 94.26/94.33 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.33 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 94.26/94.33 ! [V_i_2,V_inc_2,T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => 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 ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 94.26/94.33 ! [V_i_2,V_na_2,V_inc_2,T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_na_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_na_2,hAPP(V_inc_2,V_i_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_eq__number__of__0,axiom,
% 94.26/94.33 ! [V_v_2] :
% 94.26/94.33 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_eq__0__number__of,axiom,
% 94.26/94.33 ! [V_v_2] :
% 94.26/94.33 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__nat__number__of,axiom,
% 94.26/94.33 ! [V_v_H_2,V_v_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 94.26/94.33 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__nat__number__of,axiom,
% 94.26/94.33 ! [V_v_H_2,V_v_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__def,axiom,
% 94.26/94.33 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_neg__imp__number__of__eq__0,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_int__nat__number__of,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__special_I3_J,axiom,
% 94.26/94.33 ! [V_x_2,T_b] :
% 94.26/94.33 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.33 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__special_I1_J,axiom,
% 94.26/94.33 ! [V_y_2,T_b] :
% 94.26/94.33 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.33 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__special_I3_J,axiom,
% 94.26/94.33 ! [V_x_2,T_b] :
% 94.26/94.33 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.33 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__special_I1_J,axiom,
% 94.26/94.33 ! [V_y_2,T_b] :
% 94.26/94.33 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.33 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.33 => ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_less__0__number__of,axiom,
% 94.26/94.33 ! [V_v_2] :
% 94.26/94.33 ( 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)))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_add__nat__number__of,axiom,
% 94.26/94.33 ! [V_v_H,V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 94.26/94.33 => 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)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__insert__idem,axiom,
% 94.26/94.33 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.33 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.26/94.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => 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)) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_eq__nat__number__of,axiom,
% 94.26/94.33 ! [V_v_H_2,V_v_2] :
% 94.26/94.33 ( 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)
% 94.26/94.33 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 94.26/94.33 => 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))) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 94.26/94.33 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 94.26/94.33 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 94.26/94.33 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__number__of__add__left,axiom,
% 94.26/94.33 ! [V_k,V_v_H,V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.33 => 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) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 94.26/94.33 ! [V_y,V_x] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_tsub__eq,axiom,
% 94.26/94.33 ! [V_x,V_y] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 94.26/94.33 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Suc__nat__number__of__add,axiom,
% 94.26/94.33 ! [V_n,V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Suc__nat__number__of,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__1__add__number__of,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__number__of__add__1,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_nat__number__of__diff__1,axiom,
% 94.26/94.33 ! [V_v] :
% 94.26/94.33 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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) )
% 94.26/94.33 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 94.26/94.33 => 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)) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_fold1__in,axiom,
% 94.26/94.33 ! [V_A_2,T_b] :
% 94.26/94.33 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.33 => ( ! [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))))))
% 94.26/94.33 => 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)) ) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nats__number__of,axiom,
% 94.26/94.33 ! [V_w_2,T_b] :
% 94.26/94.33 ( class_Int_Onumber__ring(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 94.26/94.33 => 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))) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Suc__diff__number__of,axiom,
% 94.26/94.33 ! [V_m,V_v] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 94.26/94.33 => 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))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_succ__pred,axiom,
% 94.26/94.33 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 94.26/94.33
% 94.26/94.33 fof(fact_le__iff__pred__less,axiom,
% 94.26/94.33 ! [V_l_2,V_k_2] :
% 94.26/94.33 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 94.26/94.33 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_pred__def,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_succ__def,axiom,
% 94.26/94.33 ! [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)) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nats__0,axiom,
% 94.26/94.33 ! [T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nats__add,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 94.26/94.33 => 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))) ) ) ) ).
% 94.26/94.33
% 94.26/94.33 fof(fact_Nats__mult,axiom,
% 94.26/94.33 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.33 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 94.26/94.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 94.26/94.34 => 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))) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nats__1,axiom,
% 94.26/94.34 ! [T_b] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_of__nat__in__Nats,axiom,
% 94.26/94.34 ! [V_na_2,T_b] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of__succ,axiom,
% 94.26/94.34 ! [V_k,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__number__of__pred__iff__0,axiom,
% 94.26/94.34 ! [V_v_2] :
% 94.26/94.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 94.26/94.34 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__case__add__eq__if,axiom,
% 94.26/94.34 ! [V_na_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_na_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_na_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_na_2)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__Suc__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_na_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 94.26/94.34 <=> 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_na_2)),c_Int_Onat))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__number__of__Suc,axiom,
% 94.26/94.34 ! [V_na_2,V_v_2] :
% 94.26/94.34 ( 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_na_2)))
% 94.26/94.34 <=> 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_na_2)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__Suc__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_na_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
% 94.26/94.34 <=> 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_na_2)),c_Int_Onat))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__number__of__Suc,axiom,
% 94.26/94.34 ! [V_na_2,V_v_2] :
% 94.26/94.34 ( 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_na_2)))
% 94.26/94.34 <=> 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_na_2)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_decr__mult__lemma,axiom,
% 94.26/94.34 ! [V_k_2,V_Pa_2,V_d_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 94.26/94.34 => ( ! [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.26/94.34 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.26/94.34 => ! [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.26/94.34 => 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)))) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__number__of__Bit1,axiom,
% 94.26/94.34 ! [V_w_2] :
% 94.26/94.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 94.26/94.34 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 94.26/94.34 => 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)))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_hom__fold1__commute,axiom,
% 94.26/94.34 ! [V_N_2,V_h_2,T_b] :
% 94.26/94.34 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.26/94.34 => ( ! [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))
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.26/94.34 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => 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)) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I51_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 94.26/94.34 <=> V_k_2 = V_l_2 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I34_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__eq__int__code_I16_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__int__code_I16_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I17_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__int,axiom,
% 94.26/94.34 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I46_J,axiom,
% 94.26/94.34 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I39_J,axiom,
% 94.26/94.34 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 94.26/94.34 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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__0,axiom,
% 94.26/94.34 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 94.26/94.34 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_eq__nat__nat__iff,axiom,
% 94.26/94.34 ! [V_z_H_2,V_z_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 94.26/94.34 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 94.26/94.34 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ex__nat,axiom,
% 94.26/94.34 ! [V_Pa_2] :
% 94.26/94.34 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.26/94.34 <=> ? [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.26/94.34 & hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_all__nat,axiom,
% 94.26/94.34 ! [V_Pa_2] :
% 94.26/94.34 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.26/94.34 <=> ! [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.26/94.34 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 94.26/94.34 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 94.26/94.34 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_bin__less__0__simps_I4_J,axiom,
% 94.26/94.34 ! [V_w_2] :
% 94.26/94.34 ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__number__of__def,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__number__of,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I22_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I12_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 94.26/94.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Bit1__def,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__nat,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 94.26/94.34 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_not__neg__nat,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 94.26/94.34 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__number__of__Bit1,axiom,
% 94.26/94.34 ! [V_w_2] :
% 94.26/94.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 94.26/94.34 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 94.26/94.34 ! [V_A_2] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) = V_A_2 ).
% 94.26/94.34
% 94.26/94.34 fof(fact_succ__Pls,axiom,
% 94.26/94.34 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 94.26/94.34 c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__0__iff,axiom,
% 94.26/94.34 ! [V_i_2] :
% 94.26/94.34 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__le__0,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.34 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zless__nat__conj,axiom,
% 94.26/94.34 ! [V_z_2,V_w_2] :
% 94.26/94.34 ( 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)))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__mono__iff,axiom,
% 94.26/94.34 ! [V_w_2,V_z_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of__Bit1,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__1,axiom,
% 94.26/94.34 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__numeral__1,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__numeral__1__right,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_int__nat__eq,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 94.26/94.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => 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) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_int__eq__iff,axiom,
% 94.26/94.34 ! [V_z_2,V_m_2] :
% 94.26/94.34 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 94.26/94.34 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__0__le,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zless__nat__eq__int__zless,axiom,
% 94.26/94.34 ! [V_z_2,V_m_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 94.26/94.34 <=> 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_numeral__1__eq__1,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_semiring__norm_I110_J,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I5_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I29_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_one__is__num__one,axiom,
% 94.26/94.34 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__numeral__1__eq__1,axiom,
% 94.26/94.34 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Numeral1__eq1__nat,axiom,
% 94.26/94.34 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__less__nat__eq,axiom,
% 94.26/94.34 ! [V_z_2] :
% 94.26/94.34 ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__less__eq__zless,axiom,
% 94.26/94.34 ! [V_z_2,V_w_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__eq__iff,axiom,
% 94.26/94.34 ! [V_m_2,V_w_2] :
% 94.26/94.34 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 94.26/94.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__eq__iff2,axiom,
% 94.26/94.34 ! [V_w_2,V_m_2] :
% 94.26/94.34 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 94.26/94.34 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__le__eq__zle,axiom,
% 94.26/94.34 ! [V_z_2,V_w_2] :
% 94.26/94.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_split__nat,axiom,
% 94.26/94.34 ! [V_i_2,V_Pa_2] :
% 94.26/94.34 ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
% 94.26/94.34 <=> ( ! [B_n] :
% 94.26/94.34 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 94.26/94.34 => hBOOL(hAPP(V_Pa_2,B_n)) )
% 94.26/94.34 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.34 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__add__distrib,axiom,
% 94.26/94.34 ! [V_z_H,V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 94.26/94.34 ! [V_y,V_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_int__eq__iff__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_m_2] :
% 94.26/94.34 ( 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)
% 94.26/94.34 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 94.26/94.34 & 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__mult__distrib,axiom,
% 94.26/94.34 ! [V_z_H,V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 94.26/94.34 ! [V_y,V_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__diff__distrib,axiom,
% 94.26/94.34 ! [V_z,V_z_H] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_numeral__3__eq__3,axiom,
% 94.26/94.34 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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_numeral__1__eq__Suc__0,axiom,
% 94.26/94.34 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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 94.26/94.34 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))))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Suc3__eq__add__3,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 94.26/94.34 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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 94.26/94.34 ! [V_y,V_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__nat__eq__if,axiom,
% 94.26/94.34 ! [V_z_2,V_z_H_2] :
% 94.26/94.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 94.26/94.34 => 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) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_one__less__nat__eq,axiom,
% 94.26/94.34 ! [V_z_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Int_Onat,V_z_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__less__iff,axiom,
% 94.26/94.34 ! [V_m_2,V_w_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 94.26/94.34 <=> 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__special_I2_J,axiom,
% 94.26/94.34 ! [V_y_2,T_b] :
% 94.26/94.34 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__special_I4_J,axiom,
% 94.26/94.34 ! [V_x_2,T_b] :
% 94.26/94.34 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 94.26/94.34 ! [V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__special_I4_J,axiom,
% 94.26/94.34 ! [V_x_2,T_b] :
% 94.26/94.34 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__special_I2_J,axiom,
% 94.26/94.34 ! [V_y_2,T_b] :
% 94.26/94.34 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 & class_Rings_Olinordered__idom(T_b) )
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__special_I3_J,axiom,
% 94.26/94.34 ! [V_v,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__special_I2_J,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 94.26/94.34 ! [V_m,V_n] :
% 94.26/94.34 ( 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))
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Suc__eq__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_na_2] :
% 94.26/94.34 ( hAPP(c_Nat_OSuc,V_na_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 94.26/94.34 <=> 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_na_2))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_eq__number__of__Suc,axiom,
% 94.26/94.34 ! [V_na_2,V_v_2] :
% 94.26/94.34 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_na_2)
% 94.26/94.34 <=> 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_na_2))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__case__number__of,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__aux__def,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__rec__add__eq__if,axiom,
% 94.26/94.34 ! [V_na_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_na_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_na_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_na_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_na_2))))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__rec__number__of,axiom,
% 94.26/94.34 ! [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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__morphism__nat__int,axiom,
% 94.26/94.34 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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__nat__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_v_H_2] :
% 94.26/94.34 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 94.26/94.34 => 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) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_of__nat__double,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__number__of__odd__number__of,axiom,
% 94.26/94.34 ! [V_v_2,V_w_2,T_b] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 => ( ( 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)))
% 94.26/94.34 => 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))) )
% 94.26/94.34 & ( ~ 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)))
% 94.26/94.34 => 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) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__Suc__number__of,axiom,
% 94.26/94.34 ! [V_na_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_na_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_na_2)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_inj__uminus,axiom,
% 94.26/94.34 ! [V_A_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_negative__zle,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_negative__zless,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_int__power,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zpower__int,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of__minus,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_arith__simps_I30_J,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_fun__Compl__def,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.26/94.34 ( class_Groups_Ouminus(T_b)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__minus,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_double__compl,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Lattices_Oboolean__algebra(T_a)
% 94.26/94.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf_Oidem,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_uminus__apply,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.26/94.34 ( class_Groups_Ouminus(T_b)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf_Ocommute,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__commute,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_equation__minus__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 94.26/94.34 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__left__idem,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 94.26/94.34 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__left__commute,axiom,
% 94.26/94.34 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__equation__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 94.26/94.34 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__equal__iff__equal,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 94.26/94.34 <=> V_a_2 = V_b_2 ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_compl__eq__compl__iff,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Lattices_Oboolean__algebra(T_b)
% 94.26/94.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 94.26/94.34 <=> V_x_2 = V_y_2 ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf_Oassoc,axiom,
% 94.26/94.34 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__assoc,axiom,
% 94.26/94.34 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zminus__zminus,axiom,
% 94.26/94.34 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__Bit0,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I48_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 94.26/94.34 <=> V_k_2 = V_l_2 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__minus,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring__1(T_a)
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__number__of__mult,axiom,
% 94.26/94.34 ! [V_z,V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__minus__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__le__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__le__iff__le,axiom,
% 94.26/94.34 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_compl__le__compl__iff,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Lattices_Oboolean__algebra(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__imp__neg__le,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_compl__mono,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Lattices_Oboolean__algebra(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__le__iff__disj,axiom,
% 94.26/94.34 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 94.26/94.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__le1,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__le2,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__iff__inf,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.34 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__inf__iff,axiom,
% 94.26/94.34 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__infI1,axiom,
% 94.26/94.34 ! [V_b,V_x,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__infI2,axiom,
% 94.26/94.34 ! [V_a,V_x,V_b,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__absorb1,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__absorb2,axiom,
% 94.26/94.34 ! [V_x,V_y,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__infI,axiom,
% 94.26/94.34 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 94.26/94.34 => 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))) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__greatest,axiom,
% 94.26/94.34 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 94.26/94.34 => 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))) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oinf__mono,axiom,
% 94.26/94.34 ! [V_d,V_b,V_c,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 94.26/94.34 => 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))) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ole__infE,axiom,
% 94.26/94.34 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.26/94.34 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__zero,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__0__equal__iff__equal,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 94.26/94.34 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_equal__neg__zero,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.34 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 94.26/94.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__equal__0__iff__equal,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__equal__zero,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.34 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 94.26/94.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__minus__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__less__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__less__iff__less,axiom,
% 94.26/94.34 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oless__infI1,axiom,
% 94.26/94.34 ! [V_b,V_x,V_a,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Oless__infI2,axiom,
% 94.26/94.34 ! [V_a,V_x,V_b,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__less__iff__conj,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__less__iff__disj,axiom,
% 94.26/94.34 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 94.26/94.34 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__add__distrib,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Oab__group__add(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__add,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__minus__cancel,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__add__cancel,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__mult__right,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__mult__left,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__mult__commute,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__mult__minus,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_square__eq__iff,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Oidom(T_b)
% 94.26/94.34 => ( 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)
% 94.26/94.34 <=> ( V_a_2 = V_b_2
% 94.26/94.34 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__add__distrib__left,axiom,
% 94.26/94.34 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 94.26/94.34 ! [V_q,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__diff__eq,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Oab__group__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__diff__distrib__left,axiom,
% 94.26/94.34 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__0L,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__0R,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__Suc__Suc,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__number__of__even,axiom,
% 94.26/94.34 ! [V_w_2,V_z_2,T_b] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__eq__int__code_I13_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I31_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I14_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__int__code_I13_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zminus__0,axiom,
% 94.26/94.34 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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Bit0__Pls,axiom,
% 94.26/94.34 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I38_J,axiom,
% 94.26/94.34 ! [V_l_2] :
% 94.26/94.34 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 94.26/94.34 <=> c_Int_OPls = V_l_2 ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I44_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 94.26/94.34 <=> V_k_2 = c_Int_OPls ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I49_J,axiom,
% 94.26/94.34 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I50_J,axiom,
% 94.26/94.34 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Bit0__def,axiom,
% 94.26/94.34 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__Bit0__Bit0,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 94.26/94.34 ! [V_q,V_p,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__diff,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zpower__zpower,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zpower__number__of__even,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__Bit0,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__Pls,axiom,
% 94.26/94.34 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zminus__zadd__distrib,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__numeral__code_I5_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__bin__simps_I7_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zmult__zminus,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__eq__1__iff,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 94.26/94.34 => ( 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)
% 94.26/94.34 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 94.26/94.34 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__minus__even,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 94.26/94.34 ! [T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 94.26/94.34 ! [V_n,V_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__power__eq,axiom,
% 94.26/94.34 ! [V_n,V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__minus1__even,axiom,
% 94.26/94.34 ! [V_n,T_a] :
% 94.26/94.34 ( class_Rings_Oring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__number__of__even__number__of,axiom,
% 94.26/94.34 ! [V_w_2,V_v_2,T_b] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__minus1__odd,axiom,
% 94.26/94.34 ! [V_n,T_a] :
% 94.26/94.34 ( class_Rings_Oring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__eq__power2,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 94.26/94.34 => ( 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)
% 94.26/94.34 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__power2,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__eq__square,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_one__power2,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__even__eq,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__0__le__iff__le,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_le__minus__self__iff,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__le__0__iff__le,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__le__self__iff,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__minus__self__iff,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__less__nonneg,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__less__0__iff__less,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__0__less__iff__less,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_right__minus,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 94.26/94.34 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_b)
% 94.26/94.34 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 94.26/94.34 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_left__minus,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ab__left__minus,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Oab__group__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__unique,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.34 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__0,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__number__of,axiom,
% 94.26/94.34 ! [V_v,V_u,T_b] :
% 94.26/94.34 ( ( class_Int_Onumber(T_b)
% 94.26/94.34 & class_Orderings_Oord(T_b) )
% 94.26/94.34 => ( ( 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)))
% 94.26/94.34 => 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) )
% 94.26/94.34 & ( ~ 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)))
% 94.26/94.34 => 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) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__ring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__minus__eq__add,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ab__diff__minus,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Oab__group__add(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__def,axiom,
% 94.26/94.34 ! [V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ogroup__add(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_square__eq__1__iff,axiom,
% 94.26/94.34 ! [V_x_2,T_b] :
% 94.26/94.34 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 94.26/94.34 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 94.26/94.34 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 94.26/94.34 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__ring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 94.26/94.34 ! [V_q,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 94.26/94.34 ! [V_q,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 94.26/94.34 ! [V_q,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 94.26/94.34 ! [V_q,V_p,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_bin__less__0__simps_I3_J,axiom,
% 94.26/94.34 ! [V_w_2] :
% 94.26/94.34 ( 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)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 94.26/94.34 ! [V_n,V_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__rec__0,axiom,
% 94.26/94.34 ! [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 ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__rec__Suc,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I21_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I27_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__eq__int__code_I14_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I32_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I10_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I4_J,axiom,
% 94.26/94.34 ! [V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I16_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__int__code_I15_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__Bit1__Bit0,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__Bit0__Bit1,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zpower__zadd__distrib,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zadd__zminus__inverse2,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_negative__eq__positive,axiom,
% 94.26/94.34 ! [V_m_2,V_na_2] :
% 94.26/94.34 ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)
% 94.26/94.34 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__bin__simps_I3_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__bin__simps_I10_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__bin__simps_I9_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_not__int__zless__negative,axiom,
% 94.26/94.34 ! [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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__int__def,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__int__def__symmetric,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Ints__minus,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Oring__1(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Ints__power,axiom,
% 94.26/94.34 ! [V_na_2,V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Oring__1(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__number__of__Bit0,axiom,
% 94.26/94.34 ! [V_w_2] :
% 94.26/94.34 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 94.26/94.34 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_pred__Bit0,axiom,
% 94.26/94.34 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_pred__Bit1,axiom,
% 94.26/94.34 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__Bit1,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__le__power2,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => 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)))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__le__imp__le,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.34 => ( 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))))))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__eq__imp__eq,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.34 => ( 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))))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.34 => V_x = V_y ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__less__power2,axiom,
% 94.26/94.34 ! [V_a_2,T_b] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.34 => ( 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))))))
% 94.26/94.34 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__less__0,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => ~ 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_sum__power2__eq__zero__iff,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.34 => ( 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)
% 94.26/94.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__eq__square__number__of,axiom,
% 94.26/94.34 ! [V_w,T_b] :
% 94.26/94.34 ( ( class_Groups_Omonoid__mult(T_b)
% 94.26/94.34 & class_Int_Onumber(T_b) )
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_succ__Bit1,axiom,
% 94.26/94.34 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_succ__Bit0,axiom,
% 94.26/94.34 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 94.26/94.34 ! [V_n,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__number__of__Bit0,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__nat__number__of__number__of,axiom,
% 94.26/94.34 ! [V_w,V_v] :
% 94.26/94.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.34 => 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)) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__nat__number__of,axiom,
% 94.26/94.34 ! [V_n,V_v] :
% 94.26/94.34 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.34 => 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) )
% 94.26/94.34 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.34 => 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)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__less__imp__less,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.34 => ( 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))))))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_sum__power2__ge__zero,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => 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_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))))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_sum__power2__le__zero__iff,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.34 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_not__sum__power2__lt__zero,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => ~ 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_sum__power2__gt__zero__iff,axiom,
% 94.26/94.34 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.34 => ( 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_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)))))))
% 94.26/94.34 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.34 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__sum,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zero__le__even__power_H,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__odd__eq,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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))))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 94.26/94.34 ! [V_n,V_x,T_a] :
% 94.26/94.34 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of__Bit0,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__eq__int__code_I15_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I33_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__int__code_I14_J,axiom,
% 94.26/94.34 ! [V_k2_2,V_k1_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_rel__simps_I15_J,axiom,
% 94.26/94.34 ! [V_l_2,V_k_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__number__of__eq,axiom,
% 94.26/94.34 ! [V_w,V_v,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__Bit1,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_int__zle__neg,axiom,
% 94.26/94.34 ! [V_m_2,V_na_2] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))))
% 94.26/94.34 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_negative__zle__0,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__zminus__int,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_minus__numeral__code_I6_J,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_neg__zminus__int,axiom,
% 94.26/94.34 ! [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))))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__bin__simps_I8_J,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power2__diff,axiom,
% 94.26/94.34 ! [V_y,V_x,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => ( 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)))))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_odd__power__less__zero,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__idom(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.34 => 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))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__Bit1__Bit1,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_double__number__of__Bit0,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__Suc1,axiom,
% 94.26/94.34 ! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__Suc2,axiom,
% 94.26/94.34 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power3__eq__cube,axiom,
% 94.26/94.34 ! [V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__number__of__diff2,axiom,
% 94.26/94.34 ! [V_w,V_c,V_v,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of1,axiom,
% 94.26/94.34 ! [V_n] :
% 94.26/94.34 ( 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)))
% 94.26/94.34 => ( 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))))
% 94.26/94.34 & 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)))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_number__of__pred,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_not__zle__0__negative,axiom,
% 94.26/94.34 ! [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))))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_negative__zless__0,axiom,
% 94.26/94.34 ! [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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__eq__if,axiom,
% 94.26/94.34 ! [V_p,V_m] :
% 94.26/94.34 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 94.26/94.34 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 => 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)))) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__2__right,axiom,
% 94.26/94.34 ! [V_z,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_mult__2,axiom,
% 94.26/94.34 ! [V_z,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_one__add__one__is__two,axiom,
% 94.26/94.34 ! [T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_semiring__norm_I115_J,axiom,
% 94.26/94.34 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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_numeral__2__eq__2,axiom,
% 94.26/94.34 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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 94.26/94.34 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))))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__2__eq__Suc_H,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_add__2__eq__Suc,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__mult__2__right,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__mult__2,axiom,
% 94.26/94.34 ! [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) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 94.26/94.34 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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 94.26/94.34 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)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__1__add__1,axiom,
% 94.26/94.34 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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__mult__distrib__neg,axiom,
% 94.26/94.34 ! [V_z_H,V_z] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_less__2__cases,axiom,
% 94.26/94.34 ! [V_n] :
% 94.26/94.34 ( 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)))))
% 94.26/94.34 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__2,axiom,
% 94.26/94.34 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))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__special_I1_J,axiom,
% 94.26/94.34 ! [V_w,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_diff__special_I2_J,axiom,
% 94.26/94.34 ! [V_v,T_a] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_a)
% 94.26/94.34 => 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)))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__number__of__odd,axiom,
% 94.26/94.34 ! [V_z_2,V_w_2,T_b] :
% 94.26/94.34 ( class_Int_Onumber__ring(T_b)
% 94.26/94.34 => ( ( 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)))
% 94.26/94.34 => 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))) )
% 94.26/94.34 & ( ~ 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)))
% 94.26/94.34 => 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) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_zpower__number__of__odd,axiom,
% 94.26/94.34 ! [V_z_2,V_w_2] :
% 94.26/94.34 ( ( 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)))
% 94.26/94.34 => 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))) )
% 94.26/94.34 & ( ~ 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)))
% 94.26/94.34 => 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) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__number__of__Suc,axiom,
% 94.26/94.34 ! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat)))) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_fold1__antimono,axiom,
% 94.26/94.34 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.34 => 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))) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__strict__mono,axiom,
% 94.26/94.34 ! [V_n,V_b,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.34 => 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))) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_strict__below__fold1__iff,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> ! [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_fold1__strict__below__iff,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> ? [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 <=> ! [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_fold1__below__iff,axiom,
% 94.26/94.34 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.34 => ( 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))
% 94.26/94.34 <=> ? [B_x] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.34 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_min__max_Ofold1__belowI,axiom,
% 94.26/94.34 ! [V_a_2,V_A_2,T_b] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_b)
% 94.26/94.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.34 => 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)) ) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ComplI,axiom,
% 94.26/94.34 ! [V_A_2,V_c_2,T_b] :
% 94.26/94.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ComplE,axiom,
% 94.26/94.34 ! [V_A_2,V_c_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 94.26/94.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_ComplD,axiom,
% 94.26/94.34 ! [V_A_2,V_c_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 94.26/94.34 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Compl__iff,axiom,
% 94.26/94.34 ! [V_A_2,V_c_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 94.26/94.34 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Compl__anti__mono,axiom,
% 94.26/94.34 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Compl__subset__Compl__iff,axiom,
% 94.26/94.34 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
% 94.26/94.34 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_subset__Compl__self__eq,axiom,
% 94.26/94.34 ! [V_A_2,T_b] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 94.26/94.34 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_Min_Oidem,axiom,
% 94.26/94.34 ! [V_x,T_a] :
% 94.26/94.34 ( class_Orderings_Olinorder(T_a)
% 94.26/94.34 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_field__power__not__zero,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 94.26/94.34 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.34 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__Suc__0,axiom,
% 94.26/94.34 ! [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)) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 94.26/94.34 ! [V_m_2,V_x_2] :
% 94.26/94.34 ( 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))
% 94.26/94.34 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.34 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__power__less__imp__less,axiom,
% 94.26/94.34 ! [V_n,V_m,V_i] :
% 94.26/94.34 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 94.26/94.34 => ( 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)))
% 94.26/94.34 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_nat__zero__less__power__iff,axiom,
% 94.26/94.34 ! [V_na_2,V_x_2] :
% 94.26/94.34 ( 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_na_2)))
% 94.26/94.34 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 94.26/94.34 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__commutes,axiom,
% 94.26/94.34 ! [V_n,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__mult__distrib,axiom,
% 94.26/94.34 ! [V_n,V_b,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Ocomm__monoid__mult(T_a)
% 94.26/94.34 => 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)) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__one,axiom,
% 94.26/94.34 ! [V_n,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_of__nat__power,axiom,
% 94.26/94.34 ! [V_n,V_m,T_a] :
% 94.26/94.34 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.34 => 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) ) ).
% 94.26/94.34
% 94.26/94.34 fof(fact_power__mult,axiom,
% 94.26/94.34 ! [V_n,V_m,V_a,T_a] :
% 94.26/94.34 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__one__right,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.35 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__mono,axiom,
% 94.26/94.35 ! [V_n,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zero__le__power,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zero__less__power,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__eq__0__iff,axiom,
% 94.26/94.35 ! [V_na_2,V_a_2,T_b] :
% 94.26/94.35 ( ( class_Power_Opower(T_b)
% 94.26/94.35 & class_Rings_Omult__zero(T_b)
% 94.26/94.35 & class_Rings_Ono__zero__divisors(T_b)
% 94.26/94.35 & class_Rings_Ozero__neq__one(T_b) )
% 94.26/94.35 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.35 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.35 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_one__le__power,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__0__Suc,axiom,
% 94.26/94.35 ! [V_n,T_a] :
% 94.26/94.35 ( ( class_Power_Opower(T_a)
% 94.26/94.35 & class_Rings_Osemiring__0(T_a) )
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__inject__exp,axiom,
% 94.26/94.35 ! [V_na_2,V_m_2,V_a_2,T_b] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 94.26/94.35 => ( 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_na_2)
% 94.26/94.35 <=> V_m_2 = V_na_2 ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__Suc,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Power_Opower(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__Suc2,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__one__le__power,axiom,
% 94.26/94.35 ! [V_n,V_i] :
% 94.26/94.35 ( 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))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__0,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Power_Opower(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__add,axiom,
% 94.26/94.35 ! [V_n,V_m,V_a,T_a] :
% 94.26/94.35 ( class_Groups_Omonoid__mult(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__less__imp__less__base,axiom,
% 94.26/94.35 ! [V_b,V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( 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)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__inject__base,axiom,
% 94.26/94.35 ! [V_b,V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( 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))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.35 => V_a = V_b ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__le__imp__le__base,axiom,
% 94.26/94.35 ! [V_b,V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( 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))))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__gt1__lemma,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__less__power__Suc,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__0__left,axiom,
% 94.26/94.35 ! [V_n,T_a] :
% 94.26/94.35 ( ( class_Power_Opower(T_a)
% 94.26/94.35 & class_Rings_Osemiring__0(T_a) )
% 94.26/94.35 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__gt1,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__strict__increasing__iff,axiom,
% 94.26/94.35 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__less__imp__less__exp,axiom,
% 94.26/94.35 ! [V_n,V_m,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__strict__increasing,axiom,
% 94.26/94.35 ! [V_a,V_N,V_n,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__increasing,axiom,
% 94.26/94.35 ! [V_a,V_N,V_n,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__minus,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__Suc__less,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__eq__imp__eq__base,axiom,
% 94.26/94.35 ! [V_b,V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( 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)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => V_a = V_b ) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__Suc__less__one,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__strict__decreasing,axiom,
% 94.26/94.35 ! [V_a,V_N,V_n,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.35 => 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))) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__decreasing,axiom,
% 94.26/94.35 ! [V_a,V_N,V_n,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 94.26/94.35 => 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))) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__increasing__iff,axiom,
% 94.26/94.35 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__le__imp__le__exp,axiom,
% 94.26/94.35 ! [V_n,V_m,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_one__less__power,axiom,
% 94.26/94.35 ! [V_n,V_a,T_a] :
% 94.26/94.35 ( class_Rings_Olinordered__semidom(T_a)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_semilattice__big_OF__eq,axiom,
% 94.26/94.35 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.35 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 94.26/94.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.35 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__special_I4_J,axiom,
% 94.26/94.35 ! [V_x_2,T_b] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 94.26/94.35 <=> 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))))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__special_I2_J,axiom,
% 94.26/94.35 ! [V_y_2,T_b] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 94.26/94.35 <=> 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__zmod__mult__2,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__number__of__Bit1,axiom,
% 94.26/94.35 ! [V_v,V_w] :
% 94.26/94.35 ( ( 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_w)))
% 94.26/94.35 => 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)) )
% 94.26/94.35 & ( ~ 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_w)))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_dual__max,axiom,
% 94.26/94.35 ! [T_b] :
% 94.26/94.35 ( class_Orderings_Olinorder(T_b)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__zmod__mult__2,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_double__complement,axiom,
% 94.26/94.35 ! [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 ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Compl__eq__Compl__iff,axiom,
% 94.26/94.35 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.35 ( 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)
% 94.26/94.35 <=> V_A_2 = V_B_2 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mod__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__self,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__by__0,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__0,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__cong,axiom,
% 94.26/94.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 94.26/94.35 => 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__simps_I1_J,axiom,
% 94.26/94.35 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__simps_I2_J,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__left__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__right__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__self1,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__add__self2,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__cong,axiom,
% 94.26/94.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 94.26/94.35 => 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__simps_I4_J,axiom,
% 94.26/94.35 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__mult2,axiom,
% 94.26/94.35 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__mult1,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__left__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__right__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__diff__right__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__diff__left__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__diff__eq,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__diff__cong,axiom,
% 94.26/94.35 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 94.26/94.35 => 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__minus__eq,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__minus__cong,axiom,
% 94.26/94.35 ! [V_a_H,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Oring__div(T_a)
% 94.26/94.35 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__self,axiom,
% 94.26/94.35 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zero,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__simps_I3_J,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zmult1__eq,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiff__zmod__right,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiff__zmod__left,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus2,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus__zminus,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zminus__zmod,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zpower__zmod,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self1__is__0,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self2__is__0,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self1,axiom,
% 94.26/94.35 ! [V_b,V_c,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self2,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__by__1,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_iszero__def,axiom,
% 94.26/94.35 ! [V_z_2,T_b] :
% 94.26/94.35 ( class_Rings_Osemiring__1(T_b)
% 94.26/94.35 => ( c_Int_Oiszero(T_b,V_z_2)
% 94.26/94.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_iszero__0,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.35 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_not__iszero__1,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Rings_Osemiring__1(T_a)
% 94.26/94.35 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__le__nonneg__dividend,axiom,
% 94.26/94.35 ! [V_k,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__mod__bound,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__mod__bound,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__eq__0__iff,axiom,
% 94.26/94.35 ! [V_d_2,V_m_2] :
% 94.26/94.35 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus2__not__zero,axiom,
% 94.26/94.35 ! [V_l,V_k] :
% 94.26/94.35 ( 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)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus1__not__zero,axiom,
% 94.26/94.35 ! [V_l,V_k] :
% 94.26/94.35 ( 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)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__neg__neg__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__mod__conj,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 & 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__mod__sign,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__pos__pos__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__mod__conj,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 & 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__mod__sign,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus2__eq__if,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zminus1__eq__if,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_iszero__Numeral0,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_iszero__number__of__Bit1,axiom,
% 94.26/94.35 ! [V_w,T_a] :
% 94.26/94.35 ( ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 & class_Int_Oring__char__0(T_a) )
% 94.26/94.35 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_iszero__number__of__Bit0,axiom,
% 94.26/94.35 ! [V_w_2,T_b] :
% 94.26/94.35 ( ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 & class_Int_Oring__char__0(T_b) )
% 94.26/94.35 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 94.26/94.35 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__pos__neg__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_divmod__int__rel__mod__eq,axiom,
% 94.26/94.35 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 94.26/94.35 ( 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)
% 94.26/94.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 94.26/94.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult2__lemma__aux2,axiom,
% 94.26/94.35 ! [V_q,V_r,V_b,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult2__lemma__aux1,axiom,
% 94.26/94.35 ! [V_q,V_r,V_b,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult2__lemma__aux4,axiom,
% 94.26/94.35 ! [V_q,V_b,V_r,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult2__lemma__aux3,axiom,
% 94.26/94.35 ! [V_q,V_b,V_r,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__zmod,axiom,
% 94.26/94.35 ! [V_k_2,V_na_2,V_Pa_2] :
% 94.26/94.35 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
% 94.26/94.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,V_na_2)) )
% 94.26/94.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.26/94.35 => ! [B_i,B_j] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) )
% 94.26/94.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ! [B_i,B_j] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__number__of__Bit0,axiom,
% 94.26/94.35 ! [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))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_not__iszero__Numeral1,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__number__of__eq,axiom,
% 94.26/94.35 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 94.26/94.35 <=> 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__special_I3_J,axiom,
% 94.26/94.35 ! [V_x_2,T_b] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.35 <=> 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__special_I1_J,axiom,
% 94.26/94.35 ! [V_y_2,T_b] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_b)
% 94.26/94.35 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 94.26/94.35 <=> 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_z3mod__def,axiom,
% 94.26/94.35 ! [V_k,V_l] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.35 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_comm__monoid__big_OF__eq,axiom,
% 94.26/94.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.35 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.26/94.35 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__zdiv__mult__2,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__zdiv__mult__2,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_min__ord__min,axiom,
% 94.26/94.35 ! [T_b] :
% 94.26/94.35 ( class_Orderings_Oord(T_b)
% 94.26/94.35 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__power__power,axiom,
% 94.26/94.35 ! [T_b] :
% 94.26/94.35 ( class_Power_Opower(T_b)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zero,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__less,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__less__eq__dividend,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__distrib2,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__distrib,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zminus__zminus,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zminus2,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__by__0,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__0,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__by__1,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__1,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__Suc,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.35 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__less__divisor,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 94.26/94.35 ! [V_a_2,V_b_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 94.26/94.35 ! [V_a_2,V_b_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__neg__pos__less0,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__self,axiom,
% 94.26/94.35 ! [V_a] :
% 94.26/94.35 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__eq__0__iff,axiom,
% 94.26/94.35 ! [V_d_2,V_m_2] :
% 94.26/94.35 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__if,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__geq,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__number__of__Bit0,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zdiv__trivial,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_DIVISION__BY__ZERO,axiom,
% 94.26/94.35 ! [V_a] :
% 94.26/94.35 ( 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)
% 94.26/94.35 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self3,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_le__mod__geq,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zadd1__eq,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__int,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__mult1__if,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self2__is__id,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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 ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self1__is__id,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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 ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__mult2,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__mult1,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__self,axiom,
% 94.26/94.35 ! [V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__div__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__eq__0__iff,axiom,
% 94.26/94.35 ! [V_k_2,V_i_2] :
% 94.26/94.35 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 94.26/94.35 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 94.26/94.35 ! [V_a_2,V_b_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 94.26/94.35 ! [V_i_2,V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 94.26/94.35 ! [V_b_2,V_a_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__mono2,axiom,
% 94.26/94.35 ! [V_b,V_b_H,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__nonneg__neg__le0,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__pos__pos__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 94.26/94.35 ! [V_a_2,V_b_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__nonpos__pos__le0,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__mono2__neg,axiom,
% 94.26/94.35 ! [V_b,V_b_H,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 94.26/94.35 => 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__neg__neg__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__mono1,axiom,
% 94.26/94.35 ! [V_b,V_a_H,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__mono1__neg,axiom,
% 94.26/94.35 ! [V_b,V_a_H,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__le__divisor,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_int__div__less__self,axiom,
% 94.26/94.35 ! [V_k,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zmult2__eq,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult__self4,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zmod__equality2,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zmod__equality,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zmult1__eq,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zdiv__equality,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult__div__cancel,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zdiv__equality_H,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power_Opower_Opower__0,axiom,
% 94.26/94.35 ! [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 ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power_Opower_Opower__Suc,axiom,
% 94.26/94.35 ! [V_na_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_na_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_na_2)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self2,axiom,
% 94.26/94.35 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self1,axiom,
% 94.26/94.35 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__add__self1,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__add__self2,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__div__equality2,axiom,
% 94.26/94.35 ! [V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__div__equality,axiom,
% 94.26/94.35 ! [V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mod__equality2,axiom,
% 94.26/94.35 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mod__equality,axiom,
% 94.26/94.35 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.35 ( class_Divides_Osemiring__div(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__mod,axiom,
% 94.26/94.35 ! [V_k_2,V_na_2,V_Pa_2] :
% 94.26/94.35 ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_na_2,V_k_2)))
% 94.26/94.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,V_na_2)) )
% 94.26/94.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => ! [B_i,B_j] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 94.26/94.35 => ( V_na_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)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_j)) ) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__lemma,axiom,
% 94.26/94.35 ! [V_q,V_b,V_r,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__times__mod__eq,axiom,
% 94.26/94.35 ! [V_m,V_k] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__mod__distrib,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 94.26/94.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.35 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.26/94.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__zdiv,axiom,
% 94.26/94.35 ! [V_k_2,V_na_2,V_Pa_2] :
% 94.26/94.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)))
% 94.26/94.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.26/94.35 => ! [B_i] :
% 94.26/94.35 ( ? [B_j] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) )
% 94.26/94.35 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ! [B_i] :
% 94.26/94.35 ( ? [B_j] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_divmod__int__rel__div__eq,axiom,
% 94.26/94.35 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 94.26/94.35 ( 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)
% 94.26/94.35 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 94.26/94.35 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__zmult2__eq,axiom,
% 94.26/94.35 ! [V_b,V_a,V_c] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod2__Suc__Suc,axiom,
% 94.26/94.35 ! [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)))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zminus2__eq__if,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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)) )
% 94.26/94.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__zminus1__eq__if,axiom,
% 94.26/94.35 ! [V_a,V_b] :
% 94.26/94.35 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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)) )
% 94.26/94.35 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.35 => 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)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__pos__lemma,axiom,
% 94.26/94.35 ! [V_na_2,V_Pa_2,V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
% 94.26/94.35 <=> ! [B_i,B_j] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__neg__lemma,axiom,
% 94.26/94.35 ! [V_na_2,V_Pa_2,V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
% 94.26/94.35 <=> ! [B_i,B_j] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 94.26/94.35 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 & V_na_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) )
% 94.26/94.35 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__nat__number__of,axiom,
% 94.26/94.35 ! [V_v_H,V_v] :
% 94.26/94.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.35 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.35 => 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))) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__number__of__Bit1,axiom,
% 94.26/94.35 ! [V_v,V_w] :
% 94.26/94.35 ( ( 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_w)))
% 94.26/94.35 => 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)) )
% 94.26/94.35 & ( ~ 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_w)))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_int__power__div__base,axiom,
% 94.26/94.35 ! [V_k,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 94.26/94.35 => 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)))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod2__gr__0,axiom,
% 94.26/94.35 ! [V_m_2] :
% 94.26/94.35 ( 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))))))
% 94.26/94.35 <=> 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_one__mod__nat__number__of,axiom,
% 94.26/94.35 ! [V_v_H] :
% 94.26/94.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.35 => 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)) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_z3div__def,axiom,
% 94.26/94.35 ! [V_k,V_l] :
% 94.26/94.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.35 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__m1__odd,axiom,
% 94.26/94.35 ! [V_n,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_power__m1__even,axiom,
% 94.26/94.35 ! [V_n,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 94.26/94.35 ! [V_B_2,V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.35 <=> 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 94.26/94.35 ! [V_B_2,V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.35 <=> 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))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 94.26/94.35 ! [V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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)))))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__add1__eq,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__le__dividend,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__le__mono,axiom,
% 94.26/94.35 ! [V_k,V_n,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult2__eq,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I24_J,axiom,
% 94.26/94.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I7_J,axiom,
% 94.26/94.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I40_J,axiom,
% 94.26/94.35 c_Int_OMin != c_Int_OPls ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I37_J,axiom,
% 94.26/94.35 c_Int_OPls != c_Int_OMin ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Bit1__Min,axiom,
% 94.26/94.35 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I43_J,axiom,
% 94.26/94.35 ! [V_l_2] :
% 94.26/94.35 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 94.26/94.35 <=> c_Int_OMin = V_l_2 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I47_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 94.26/94.35 <=> V_k_2 = c_Int_OMin ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I42_J,axiom,
% 94.26/94.35 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I45_J,axiom,
% 94.26/94.35 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__1,axiom,
% 94.26/94.35 ! [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 ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__less,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__mult__div__cancel__disj,axiom,
% 94.26/94.35 ! [V_n,V_m,V_k] :
% 94.26/94.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mod__mult2__eq,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult1__eq,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Omod__div__equality_H,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mult__div__cancel,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mod__equality_H,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__int,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_bin__less__0__simps_I2_J,axiom,
% 94.26/94.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I23_J,axiom,
% 94.26/94.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I20_J,axiom,
% 94.26/94.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I30_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I26_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I3_J,axiom,
% 94.26/94.35 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I6_J,axiom,
% 94.26/94.35 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I9_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I13_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I28_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I8_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_eq__number__of__Pls__Min,axiom,
% 94.26/94.35 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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Int_OMin__def,axiom,
% 94.26/94.35 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mult__Min,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_neg__number__of__Min,axiom,
% 94.26/94.35 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pred__Pls,axiom,
% 94.26/94.35 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 94.26/94.35
% 94.26/94.35 fof(fact_add__Min__right,axiom,
% 94.26/94.35 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_add__Min,axiom,
% 94.26/94.35 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pred__Min,axiom,
% 94.26/94.35 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 94.26/94.35 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nonzero__number__of__Min,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_succ__Min,axiom,
% 94.26/94.35 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 94.26/94.35
% 94.26/94.35 fof(fact_diff__bin__simps_I2_J,axiom,
% 94.26/94.35 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__set__def,axiom,
% 94.26/94.35 ! [V_S_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_S_2)
% 94.26/94.35 <=> ! [B_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__le__mono2,axiom,
% 94.26/94.35 ! [V_k,V_n,V_m] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__mult__div__cancel1,axiom,
% 94.26/94.35 ! [V_n,V_m,V_k] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self__is__m,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__mult__self1__is__m,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__less__dividend,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mult__minus1__right,axiom,
% 94.26/94.35 ! [V_z,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_mult__minus1,axiom,
% 94.26/94.35 ! [V_z,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_arith__simps_I31_J,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_number__of__Min,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 94.26/94.35 ! [V_B_2,V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.26/94.35 => ( V_A_2 = V_B_2
% 94.26/94.35 <=> 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) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I11_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_rel__simps_I25_J,axiom,
% 94.26/94.35 ! [V_k_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__minus1__right,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_diff__bin__simps_I4_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_minus__Min,axiom,
% 94.26/94.35 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 94.26/94.35 ! [V_n,V_m] :
% 94.26/94.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.35 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.35 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmult__eq__1__iff,axiom,
% 94.26/94.35 ! [V_na_2,V_m_2] :
% 94.26/94.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.35 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 94.26/94.35 & V_na_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 94.26/94.35 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 94.26/94.35 & V_na_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_diff__bin__simps_I6_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_diff__bin__simps_I5_J,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zdiv__minus1__right,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__geq,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__if,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.35 => 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)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__div,axiom,
% 94.26/94.35 ! [V_k_2,V_na_2,V_Pa_2] :
% 94.26/94.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_na_2),V_k_2)))
% 94.26/94.35 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 94.26/94.35 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 => ! [B_i,B_j] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 94.26/94.35 => ( V_na_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)
% 94.26/94.35 => hBOOL(hAPP(V_Pa_2,B_i)) ) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_nat__div__distrib,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__eq__minus1,axiom,
% 94.26/94.35 ! [V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 94.26/94.35 ! [V_x_2,V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_le__div__geq,axiom,
% 94.26/94.35 ! [V_m,V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__div_H,axiom,
% 94.26/94.35 ! [V_na_2,V_m_2,V_Pa_2] :
% 94.26/94.35 ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2)))
% 94.26/94.35 <=> ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.35 & hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 94.26/94.35 | ? [B_q] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q)),V_m_2))
% 94.26/94.35 & 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_na_2),hAPP(c_Nat_OSuc,B_q))))
% 94.26/94.35 & hBOOL(hAPP(V_Pa_2,B_q)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_split__div__lemma,axiom,
% 94.26/94.35 ! [V_m_2,V_q_2,V_na_2] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 94.26/94.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_q_2)),V_m_2))
% 94.26/94.35 & 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_na_2),hAPP(c_Nat_OSuc,V_q_2)))) )
% 94.26/94.35 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Suc__div__eq__add3__div,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__Suc__eq__div__add3,axiom,
% 94.26/94.35 ! [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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div2__Suc__Suc,axiom,
% 94.26/94.35 ! [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))))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_add__self__div__2,axiom,
% 94.26/94.35 ! [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 ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 94.26/94.35 ! [V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => 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 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__nat__number__of,axiom,
% 94.26/94.35 ! [V_v_H,V_v] :
% 94.26/94.35 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.35 => 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) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 94.26/94.35 => 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))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__pos__neg__trivial,axiom,
% 94.26/94.35 ! [V_b,V_a] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.35 => ( 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)))
% 94.26/94.35 => 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) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zmod__minus1,axiom,
% 94.26/94.35 ! [V_b] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 94.26/94.35 ! [V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 94.26/94.35 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 94.26/94.35 ! [V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_div__2__gt__zero,axiom,
% 94.26/94.35 ! [V_n] :
% 94.26/94.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 94.26/94.35 => 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)))))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_one__div__nat__number__of,axiom,
% 94.26/94.35 ! [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))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_int__of__code,axiom,
% 94.26/94.35 ! [V_k] :
% 94.26/94.35 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.26/94.35 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.35 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.26/94.35 => ( ( 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)
% 94.26/94.35 => 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)))))) )
% 94.26/94.35 & ( 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)
% 94.26/94.35 => 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)) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 94.26/94.35 ! [V_A_2,V_x_2] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 94.26/94.35 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_card__greaterThanLessThan__int,axiom,
% 94.26/94.35 ! [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)))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_one__code__numeral__code,axiom,
% 94.26/94.35 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)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Min_Oremove,axiom,
% 94.26/94.35 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.35 ( class_Orderings_Olinorder(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.35 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.35 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 94.26/94.35 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.35 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__of__nat,axiom,
% 94.26/94.35 ! [V_k,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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)))) )
% 94.26/94.35 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.35 => 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)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_finite__greaterThanLessThan__int,axiom,
% 94.26/94.35 ! [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))) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__eq__iff,axiom,
% 94.26/94.35 ! [V_z_2,V_w_2,T_b] :
% 94.26/94.35 ( class_Int_Oring__char__0(T_b)
% 94.26/94.35 => ( 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)
% 94.26/94.35 <=> V_w_2 = V_z_2 ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_code__numeral__zero__minus__one,axiom,
% 94.26/94.35 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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_number__of__eq,axiom,
% 94.26/94.35 ! [V_k,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_int__number__of__def,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__int__eq,axiom,
% 94.26/94.35 ! [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) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 94.26/94.35 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 94.26/94.35 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 94.26/94.35 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 94.26/94.35 ! [V_n,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 94.26/94.35 ! [V_y,V_x] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x)
% 94.26/94.35 => ( c_Nat__Transfer_Ois__nat(V_y)
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__0,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__0__eq__iff,axiom,
% 94.26/94.35 ! [V_z_2,T_b] :
% 94.26/94.35 ( class_Int_Oring__char__0(T_b)
% 94.26/94.35 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 94.26/94.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__eq__0__iff,axiom,
% 94.26/94.35 ! [V_z_2,T_b] :
% 94.26/94.35 ( class_Int_Oring__char__0(T_b)
% 94.26/94.35 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.35 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__le__iff,axiom,
% 94.26/94.35 ! [V_z_2,V_w_2,T_b] :
% 94.26/94.35 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__less__iff,axiom,
% 94.26/94.35 ! [V_z_2,V_w_2,T_b] :
% 94.26/94.35 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.35 => ( 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)))
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__add,axiom,
% 94.26/94.35 ! [V_z,V_w,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__number__of__eq,axiom,
% 94.26/94.35 ! [V_v,T_a] :
% 94.26/94.35 ( class_Int_Onumber__ring(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__mult,axiom,
% 94.26/94.35 ! [V_z,V_w,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__1,axiom,
% 94.26/94.35 ! [T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__diff,axiom,
% 94.26/94.35 ! [V_z,V_w,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Min_Osingleton,axiom,
% 94.26/94.35 ! [V_x_2,T_b] :
% 94.26/94.35 ( class_Orderings_Olinorder(T_b)
% 94.26/94.35 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__of__nat__eq,axiom,
% 94.26/94.35 ! [V_n,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__minus,axiom,
% 94.26/94.35 ! [V_z,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Ints__of__int,axiom,
% 94.26/94.35 ! [V_z_2,T_b] :
% 94.26/94.35 ( class_Rings_Oring__1(T_b)
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_of__int__power,axiom,
% 94.26/94.35 ! [V_n,V_z,T_a] :
% 94.26/94.35 ( class_Rings_Oring__1(T_a)
% 94.26/94.35 => 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) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_is__nat__def,axiom,
% 94.26/94.35 ! [V_x_2] :
% 94.26/94.35 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 94.26/94.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_greaterThanLessThan__empty,axiom,
% 94.26/94.35 ! [V_k_2,V_l_2,T_b] :
% 94.26/94.35 ( class_Orderings_Oorder(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 94.26/94.35 => 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)) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 94.26/94.35 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.35 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.26/94.35 => 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)) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Min__le,axiom,
% 94.26/94.35 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.35 ( class_Orderings_Olinorder(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 94.26/94.35 ! [V_x_2,V_A_2] :
% 94.26/94.35 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.35 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 94.26/94.35 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_Min__in,axiom,
% 94.26/94.35 ! [V_A_2,T_b] :
% 94.26/94.35 ( class_Orderings_Olinorder(T_b)
% 94.26/94.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.35 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 94.26/94.35
% 94.26/94.35 fof(fact_zero__code__numeral__code,axiom,
% 94.26/94.36 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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_Oin__idem,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => 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) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__m1,axiom,
% 94.26/94.36 ! [T_a] :
% 94.26/94.36 ( class_Int_Onumber__ring(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_OF__eq,axiom,
% 94.26/94.36 ! [V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 94.26/94.36 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__le__0__iff,axiom,
% 94.26/94.36 ! [V_z_2,T_b] :
% 94.26/94.36 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__0__le__iff,axiom,
% 94.26/94.36 ! [V_z_2,T_b] :
% 94.26/94.36 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__less__0__iff,axiom,
% 94.26/94.36 ! [V_z_2,T_b] :
% 94.26/94.36 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__0__less__iff,axiom,
% 94.26/94.36 ! [V_z_2,T_b] :
% 94.26/94.36 ( class_Rings_Olinordered__idom(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min__antimono,axiom,
% 94.26/94.36 ! [V_N_2,V_M_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 94.26/94.36 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__nat__nat,axiom,
% 94.26/94.36 ! [V_z,T_a] :
% 94.26/94.36 ( class_Rings_Oring__1(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min__insert,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_Osubset__idem,axiom,
% 94.26/94.36 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.36 => 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) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 94.26/94.36 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_Oinsert,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => 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)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_Oinsert__remove,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ( 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))
% 94.26/94.36 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 94.26/94.36 & ( 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))
% 94.26/94.36 => 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)))))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nat__of__aux__code,axiom,
% 94.26/94.36 ! [V_n,V_i] :
% 94.26/94.36 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.26/94.36 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 94.26/94.36 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__num,axiom,
% 94.26/94.36 ! [V_k_2,T_b] :
% 94.26/94.36 ( class_Rings_Oring__1(T_b)
% 94.26/94.36 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 94.26/94.36 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => 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))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => 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))))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Min_Oclosed,axiom,
% 94.26/94.36 ! [V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => ( ! [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))))))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osize_I1_J,axiom,
% 94.26/94.36 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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => ( ( 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))
% 94.26/94.36 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 94.26/94.36 & ( 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))
% 94.26/94.36 => 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)))))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__gen__delta,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_finite__greaterThanLessThan,axiom,
% 94.26/94.36 ! [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))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__int__setprod,axiom,
% 94.26/94.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.36 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 & class_Rings_Oring__1(T_b) )
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_of__nat__setprod,axiom,
% 94.26/94.36 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.36 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 & class_Rings_Osemiring__1(T_b) )
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_int__setprod,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__timesf,axiom,
% 94.26/94.36 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__1,axiom,
% 94.26/94.36 ! [V_A_2,T_c,T_b] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 94.26/94.36 ! [V_A_2,V_f_2,T_b] :
% 94.26/94.36 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.26/94.36 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__zero,axiom,
% 94.26/94.36 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Rings_Ocomm__semiring__1(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ? [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.36 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 94.26/94.36 => 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) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__zero__iff,axiom,
% 94.26/94.36 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 94.26/94.36 & class_Rings_Ono__zero__divisors(T_c) )
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( 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)
% 94.26/94.36 <=> ? [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.36 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__empty,axiom,
% 94.26/94.36 ! [V_f_2,T_c,T_b] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oempty,axiom,
% 94.26/94.36 ! [V_g_2,T_c,T_b] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__infinite,axiom,
% 94.26/94.36 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oinfinite,axiom,
% 94.26/94.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__eq__1__iff,axiom,
% 94.26/94.36 ! [V_f_2,V_F_2,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.26/94.36 => ( 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)
% 94.26/94.36 <=> ! [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 94.26/94.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 94.26/94.36 ! [V_f_2,V_A_2,T_b] :
% 94.26/94.36 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.26/94.36 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.26/94.36 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Odistrib,axiom,
% 94.26/94.36 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__pos__nat__iff,axiom,
% 94.26/94.36 ! [V_f_2,V_S_2,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> ! [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__delta_H,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => 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) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => 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) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__delta,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => 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) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.26/94.36 => 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) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__constant,axiom,
% 94.26/94.36 ! [V_y_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => 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) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 94.26/94.36 ! [V_x_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => 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 ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__insert,axiom,
% 94.26/94.36 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oinsert,axiom,
% 94.26/94.36 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 94.26/94.36 ! [V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oeq__fold,axiom,
% 94.26/94.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_OF__eq,axiom,
% 94.26/94.36 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oinsert__remove,axiom,
% 94.26/94.36 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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)))))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_card__greaterThanLessThan,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 94.26/94.36 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.36 => 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) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod_Oremove,axiom,
% 94.26/94.36 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => 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)))))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => 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)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 94.26/94.36 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( ( 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))
% 94.26/94.36 => 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 )
% 94.26/94.36 & ( 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))
% 94.26/94.36 => 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)))))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osize_I2_J,axiom,
% 94.26/94.36 ! [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))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 94.26/94.36 ! [V_A_2,T_b] :
% 94.26/94.36 ( class_Orderings_Olinorder(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.36 => ( ! [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))))))
% 94.26/94.36 => 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)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__def,axiom,
% 94.26/94.36 ! [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))))))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Nitpick_OFrac__def,axiom,
% 94.26/94.36 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)))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__diff1,axiom,
% 94.26/94.36 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Fields_Ofield(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.36 => 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) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_adjust__def,axiom,
% 94.26/94.36 ! [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))))))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__zero,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__zero__left,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pred__equals__eq2,axiom,
% 94.26/94.36 ! [V_S_2,V_R_2,T_c,T_b] :
% 94.26/94.36 ( 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)
% 94.26/94.36 <=> V_R_2 = V_S_2 ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_bot__empty__eq2,axiom,
% 94.26/94.36 ! [V_y_2,V_x_2,T_c,T_b] :
% 94.26/94.36 ( 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))
% 94.26/94.36 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pred__subset__eq2,axiom,
% 94.26/94.36 ! [V_S_2,V_R_2,T_c,T_b] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 <=> 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__0,axiom,
% 94.26/94.36 ! [V_b] :
% 94.26/94.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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)))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_self__remainder,axiom,
% 94.26/94.36 ! [V_r,V_q,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_unique__quotient,axiom,
% 94.26/94.36 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => V_q = V_q_H ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_unique__remainder,axiom,
% 94.26/94.36 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => V_r = V_r_H ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Oinject,axiom,
% 94.26/94.36 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 94.26/94.36 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 94.26/94.36 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_add__divide__distrib,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_times__divide__eq__right,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_diff__divide__distrib,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__1,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_minus__divide__left,axiom,
% 94.26/94.36 ! [V_b,V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_power__divide,axiom,
% 94.26/94.36 ! [V_n,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_self__quotient,axiom,
% 94.26/94.36 ! [V_r,V_q,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__mod,axiom,
% 94.26/94.36 ! [V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__div,axiom,
% 94.26/94.36 ! [V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__div__mod,axiom,
% 94.26/94.36 ! [V_a,V_b] :
% 94.26/94.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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)))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nonzero__eq__divide__eq,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_b)
% 94.26/94.36 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 94.26/94.36 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nonzero__divide__eq__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_b)
% 94.26/94.36 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 94.26/94.36 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__eq__imp,axiom,
% 94.26/94.36 ! [V_a,V_b,V_c,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 94.26/94.36 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_eq__divide__imp,axiom,
% 94.26/94.36 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 94.26/94.36 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__self__if,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 94.26/94.36 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 94.26/94.36 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__self,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_right__inverse__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,T_b] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_b)
% 94.26/94.36 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 94.26/94.36 <=> V_a_2 = V_b_2 ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nonzero__minus__divide__divide,axiom,
% 94.26/94.36 ! [V_a,V_b,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nonzero__minus__divide__right,axiom,
% 94.26/94.36 ! [V_a,V_b,T_a] :
% 94.26/94.36 ( class_Rings_Odivision__ring(T_a)
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_nonzero__power__divide,axiom,
% 94.26/94.36 ! [V_n,V_a,V_b,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_power__one__over,axiom,
% 94.26/94.36 ! [V_n,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 94.26/94.36 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zadd1__lemma,axiom,
% 94.26/94.36 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zminus1__lemma,axiom,
% 94.26/94.36 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => 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))))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_setprod__dividef,axiom,
% 94.26/94.36 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_c)
% 94.26/94.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__relI,axiom,
% 94.26/94.36 ! [V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)
% 94.26/94.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 94.26/94.36 => 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))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_eq__divide__eq__number__of1,axiom,
% 94.26/94.36 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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))
% 94.26/94.36 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => 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 )
% 94.26/94.36 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_eq__divide__eq__number__of,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 94.26/94.36 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 94.26/94.36 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__eq__eq__number__of,axiom,
% 94.26/94.36 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 94.26/94.36 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) )
% 94.26/94.36 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__eq__eq__number__of1,axiom,
% 94.26/94.36 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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
% 94.26/94.36 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zmult1__lemma,axiom,
% 94.26/94.36 ! [V_a,V_r,V_q,V_c,V_b] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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)))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__Numeral0,axiom,
% 94.26/94.36 ! [V_x,T_a] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__numeral__1,axiom,
% 94.26/94.36 ! [V_a,T_a] :
% 94.26/94.36 ( ( class_Fields_Ofield(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => 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 ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__Numeral1,axiom,
% 94.26/94.36 ! [V_x,T_a] :
% 94.26/94.36 ( ( class_Fields_Ofield(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => 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 ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__minus1,axiom,
% 94.26/94.36 ! [V_x,T_a] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__correct,axiom,
% 94.26/94.36 ! [V_a,V_b] :
% 94.26/94.36 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zmult2__lemma,axiom,
% 94.26/94.36 ! [V_c,V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__mod__div,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__less__eq__number__of1,axiom,
% 94.26/94.36 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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))
% 94.26/94.36 <=> ( ( 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_w_2)))
% 94.26/94.36 => 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)))) )
% 94.26/94.36 & ( ~ 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_w_2)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__less__eq__number__of,axiom,
% 94.26/94.36 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => 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_w_2))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_less__divide__eq__number__of,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => 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))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_less__divide__eq__number__of1,axiom,
% 94.26/94.36 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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))))
% 94.26/94.36 <=> ( ( 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_w_2)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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_w_2)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)))) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_power__diff,axiom,
% 94.26/94.36 ! [V_m,V_n,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_minus1__divide,axiom,
% 94.26/94.36 ! [V_x,T_a] :
% 94.26/94.36 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Suc__code__numeral__minus__one,axiom,
% 94.26/94.36 ! [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 ).
% 94.26/94.36
% 94.26/94.36 fof(fact_le__divide__eq__number__of1,axiom,
% 94.26/94.36 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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))))
% 94.26/94.36 <=> ( ( 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_w_2)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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_w_2)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)))) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_le__divide__eq__number__of,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => 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))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__le__eq__number__of,axiom,
% 94.26/94.36 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => 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_w_2))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__le__eq__number__of1,axiom,
% 94.26/94.36 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber(T_b) )
% 94.26/94.36 => ( 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))
% 94.26/94.36 <=> ( ( 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_w_2)))
% 94.26/94.36 => 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)))) )
% 94.26/94.36 & ( ~ 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_w_2)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_half__gt__zero,axiom,
% 94.26/94.36 ! [V_r,T_a] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.26/94.36 & class_Int_Onumber__ring(T_a) )
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 94.26/94.36 => 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)))))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_half__gt__zero__iff,axiom,
% 94.26/94.36 ! [V_r_2,T_b] :
% 94.26/94.36 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 & class_Int_Onumber__ring(T_b) )
% 94.26/94.36 => ( 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))))))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_adjust__eq,axiom,
% 94.26/94.36 ! [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))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pair__imageI,axiom,
% 94.26/94.36 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 94.26/94.36 ( 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))
% 94.26/94.36 => 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))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_norm__frac_Osimps,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2] :
% 94.26/94.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 94.26/94.36 ! [V_w] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( 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))))
% 94.26/94.36 => 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))) )
% 94.26/94.36 & ( ~ 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))))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_prod__caseI,axiom,
% 94.26/94.36 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 94.26/94.36 => 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))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_splitI,axiom,
% 94.26/94.36 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 94.26/94.36 => 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))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mem__splitI,axiom,
% 94.26/94.36 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_bot2E,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_splitD_H,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_predicate2D,axiom,
% 94.26/94.36 ! [V_y_2,V_x_2,V_Q_2,V_Pa_2,T_c,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_rev__predicate2D,axiom,
% 94.26/94.36 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_Pa_2),V_Q_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_less__by__empty,axiom,
% 94.26/94.36 ! [V_B_2,T_b,V_A_2] :
% 94.26/94.36 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Pair__inject,axiom,
% 94.26/94.36 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 94.26/94.36 ( 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)
% 94.26/94.36 => ~ ( V_a = V_a_H
% 94.26/94.36 => V_b != V_b_H ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Pair__eq,axiom,
% 94.26/94.36 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 94.26/94.36 ( 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)
% 94.26/94.36 <=> ( V_a_2 = V_a_H_2
% 94.26/94.36 & V_b_2 = V_b_H_2 ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__paired__All,axiom,
% 94.26/94.36 ! [T_c,T_b,V_Pa_2] :
% 94.26/94.36 ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.26/94.36 <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__weak__cong,axiom,
% 94.26/94.36 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 94.26/94.36 ( V_p_2 = V_q_2
% 94.26/94.36 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__correct,axiom,
% 94.26/94.36 ! [V_b,V_a] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__conv,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_prod_Osimps_I2_J,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_splitD,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__div__mod,axiom,
% 94.26/94.36 ! [V_l,V_k] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__minus1,axiom,
% 94.26/94.36 ! [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))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__eta,axiom,
% 94.26/94.36 ! [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 ).
% 94.26/94.36
% 94.26/94.36 fof(fact_The__split__eq,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__paired__The,axiom,
% 94.26/94.36 ! [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)))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_swap__inj__on,axiom,
% 94.26/94.36 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_split__twice,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg_Osimps,axiom,
% 94.26/94.36 ! [V_b,V_a] :
% 94.26/94.36 ( ( ( 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),V_a),V_b)))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ ( 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),V_a),V_b)))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__eqn,axiom,
% 94.26/94.36 ! [V_a,V_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => ( ( 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),V_a),V_b)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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),V_a),V_b)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg__eqn__number__of,axiom,
% 94.26/94.36 ! [V_w,V_v] :
% 94.26/94.36 ( 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_v)))
% 94.26/94.36 => ( ( 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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 94.26/94.36 => 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))) )
% 94.26/94.36 & ( ~ 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),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_in__rel__def,axiom,
% 94.26/94.36 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 94.26/94.36 <=> 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)),V_R_2)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_div__mod__code__numeral__def,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__left__mono__neg,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__left__mono,axiom,
% 94.26/94.36 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_neg__divide__le__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_times__divide__times__eq,axiom,
% 94.26/94.36 ! [V_w,V_z,V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_minus__divide__divide,axiom,
% 94.26/94.36 ! [V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_minus__divide__right,axiom,
% 94.26/94.36 ! [V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__right__mono__neg,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__right__mono,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__le__0__iff,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 94.26/94.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zero__le__divide__iff,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 94.26/94.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__strict__right__mono__neg,axiom,
% 94.26/94.36 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__strict__right__mono,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__neg__neg,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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_x),V_y))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__neg__pos,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__pos__neg,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__pos__pos,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => 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_x),V_y))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__less__0__iff,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( 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)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 94.26/94.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_zero__less__divide__iff,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( 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_a_2),V_b_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 94.26/94.36 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_eq__divide__eq,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 94.26/94.36 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 94.26/94.36 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__eq__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_b)
% 94.26/94.36 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 94.26/94.36 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 94.26/94.36 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__divide__mult__cancel__right,axiom,
% 94.26/94.36 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__divide__mult__cancel__left,axiom,
% 94.26/94.36 ! [V_b,V_a,V_c,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_frac__eq__eq,axiom,
% 94.26/94.36 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 94.26/94.36 ( class_Fields_Ofield(T_b)
% 94.26/94.36 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.26/94.36 => ( 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)
% 94.26/94.36 <=> 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) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__nonpos__neg,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__nonpos__pos,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_frac__le,axiom,
% 94.26/94.36 ! [V_z,V_w,V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 94.26/94.36 => 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))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_frac__less,axiom,
% 94.26/94.36 ! [V_z,V_w,V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 94.26/94.36 => 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))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_frac__less2,axiom,
% 94.26/94.36 ! [V_z,V_w,V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 94.26/94.36 => 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))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__nonneg__neg,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__nonneg__pos,axiom,
% 94.26/94.36 ! [V_y,V_x,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__strict__left__mono__neg,axiom,
% 94.26/94.36 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__strict__left__mono,axiom,
% 94.26/94.36 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_neg__divide__less__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_neg__less__divide__eq,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__imp__less__div__pos,axiom,
% 94.26/94.36 ! [V_x,V_z,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => ( 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))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__imp__div__pos__less,axiom,
% 94.26/94.36 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pos__divide__less__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pos__less__divide__eq,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__less__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_less__divide__eq,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_add__num__frac,axiom,
% 94.26/94.36 ! [V_x,V_z,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_add__divide__eq__iff,axiom,
% 94.26/94.36 ! [V_y,V_x,V_z,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_add__frac__num,axiom,
% 94.26/94.36 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Ofield__inverse__zero(T_a)
% 94.26/94.36 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__add__eq__iff,axiom,
% 94.26/94.36 ! [V_y,V_x,V_z,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_add__frac__eq,axiom,
% 94.26/94.36 ! [V_w,V_x,V_z,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_diff__divide__eq__iff,axiom,
% 94.26/94.36 ! [V_y,V_x,V_z,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__diff__eq__iff,axiom,
% 94.26/94.36 ! [V_y,V_x,V_z,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_diff__frac__eq,axiom,
% 94.26/94.36 ! [V_w,V_x,V_z,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Ofield(T_a)
% 94.26/94.36 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_gt__half__sum,axiom,
% 94.26/94.36 ! [V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_less__half__sum,axiom,
% 94.26/94.36 ! [V_b,V_a,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 94.26/94.36 => 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))))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_le__divide__eq,axiom,
% 94.26/94.36 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divide__le__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pos__le__divide__eq,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_pos__divide__le__eq,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__imp__div__pos__le,axiom,
% 94.26/94.36 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => ( 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)))
% 94.26/94.36 => 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)) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mult__imp__le__div__pos,axiom,
% 94.26/94.36 ! [V_x,V_z,V_y,T_a] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_a)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.26/94.36 => ( 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))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_neg__le__divide__eq,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.26/94.36 ( class_Fields_Olinordered__field(T_b)
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 94.26/94.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_Nitpick_Orefl_H__def,axiom,
% 94.26/94.36 ! [V_r_2,T_b] :
% 94.26/94.36 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 94.26/94.36 <=> ! [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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 94.26/94.36 ! [V_w] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg_Osimps,axiom,
% 94.26/94.36 ! [V_b,V_a] :
% 94.26/94.36 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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) )
% 94.26/94.36 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__eqn,axiom,
% 94.26/94.36 ! [V_a,V_b] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.36 => 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) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__eqn__number__of,axiom,
% 94.26/94.36 ! [V_w,V_v] :
% 94.26/94.36 ( 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_v)))
% 94.26/94.36 => ( ( 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)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ 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)))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__0,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__correct,axiom,
% 94.26/94.36 ! [V_b,V_a] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg__div__mod,axiom,
% 94.26/94.36 ! [V_l,V_k] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__def,axiom,
% 94.26/94.36 ! [V_b,V_a] :
% 94.26/94.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 => 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))) ) ) ) ) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.36 => 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))) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__step,axiom,
% 94.26/94.36 ! [V_m,V_n] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.26/94.36 => 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)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osize_I4_J,axiom,
% 94.26/94.36 ! [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))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg_Opsimps,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( ( 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),V_a_2),V_b_2)))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ ( 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),V_a_2),V_b_2)))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 94.26/94.36 ! [V_f_2,V_A_2,T_b] :
% 94.26/94.36 ( ! [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.36 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 94.26/94.36 => 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)) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__zero,axiom,
% 94.26/94.36 ! [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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__base,axiom,
% 94.26/94.36 ! [V_n,V_m] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.26/94.36 => 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) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negateSnd__eq,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__div__mod,axiom,
% 94.26/94.36 ! [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)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__int__rel__neg,axiom,
% 94.26/94.36 ! [V_qr,V_b,V_a] :
% 94.26/94.36 ( 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))
% 94.26/94.36 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_code__numeral_Osize_I3_J,axiom,
% 94.26/94.36 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) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__if,axiom,
% 94.26/94.36 ! [V_m_2,V_na_2] :
% 94.26/94.36 ( ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
% 94.26/94.36 => c_Divides_Odivmod__nat(V_m_2,V_na_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
% 94.26/94.36 & ( ~ ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
% 94.26/94.36 => c_Divides_Odivmod__nat(V_m_2,V_na_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_na_2),V_na_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_posDivAlg_Opsimps,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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) )
% 94.26/94.36 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_norm__frac_Opsimps,axiom,
% 94.26/94.36 ! [V_b_2,V_a_2] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.36 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.36 => 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)) )
% 94.26/94.36 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.26/94.36 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.26/94.36 => 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))) ) ) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_negDivAlg_Opinduct,axiom,
% 94.26/94.36 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ! [B_a,B_b] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( ( ~ ( 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),B_a),B_b)))
% 94.26/94.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.36 => 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))) )
% 94.26/94.36 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 94.26/94.36 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_accp__subset,axiom,
% 94.26/94.36 ! [V_R2_2,V_R1_2,T_b] :
% 94.26/94.36 ( 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))
% 94.26/94.36 => 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))) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 94.26/94.36 ! [V_c,V_r,V_q,V_b,V_a] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 94.26/94.36 => 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)))) ) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__rel__unique,axiom,
% 94.26/94.36 ! [V_qr_H,V_qr,V_n,V_m] :
% 94.26/94.36 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 94.26/94.36 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 94.26/94.36 => V_qr = V_qr_H ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 94.26/94.36 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__eq,axiom,
% 94.26/94.36 ! [V_qr,V_n,V_m] :
% 94.26/94.36 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 94.26/94.36 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_divmod__nat__def,axiom,
% 94.26/94.36 ! [V_na_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_na_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_na_2)) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_mod__eq,axiom,
% 94.26/94.36 ! [V_r,V_q,V_n,V_m] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_div__eq,axiom,
% 94.26/94.36 ! [V_r,V_q,V_n,V_m] :
% 94.26/94.36 ( 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)))
% 94.26/94.36 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_accp__downward,axiom,
% 94.26/94.36 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 94.26/94.36 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 94.26/94.36 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_accp_Oequations,axiom,
% 94.26/94.36 ! [V_a_2,V_r_2,T_b] :
% 94.26/94.36 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 94.26/94.36 <=> ! [B_x] :
% 94.26/94.36 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 94.26/94.36 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 94.26/94.36
% 94.26/94.36 fof(fact_accp_Osimps,axiom,
% 94.26/94.36 ! [V_a_2,V_r_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 94.26/94.37 <=> ! [B_x] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 94.26/94.37 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_divmod__nat__rel,axiom,
% 94.26/94.37 ! [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)))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 94.26/94.37 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( 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)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 94.26/94.37 => 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)))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 94.26/94.37 ! [V_a,V_r,V_q,V_c,V_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 94.26/94.37 => 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)))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_posDivAlg_Opinduct,axiom,
% 94.26/94.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( ! [B_a,B_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 94.26/94.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 94.26/94.37 => 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))) )
% 94.26/94.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 94.26/94.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat_Osize_I2_J,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__pos__neg__1__number__of,axiom,
% 94.26/94.37 ! [V_w] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => 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))))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_in__measure,axiom,
% 94.26/94.37 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 <=> 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_norm__frac_Opinduct,axiom,
% 94.26/94.37 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( ! [B_a,B_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => 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))) )
% 94.26/94.37 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) )
% 94.26/94.37 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_snd__eqD,axiom,
% 94.26/94.37 ! [V_a,V_y,V_x,T_a,T_b] :
% 94.26/94.37 ( 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
% 94.26/94.37 => V_y = V_a ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_snd__conv,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_snd__def,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__int__def,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat_Osize_I1_J,axiom,
% 94.26/94.37 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__neg__pos,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__pos__pos,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__pos__pos__1__number__of,axiom,
% 94.26/94.37 ! [V_w] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__pos__neg,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => 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)))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__neg__neg,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => 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)))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__pos__neg__1__number__of,axiom,
% 94.26/94.37 ! [V_w] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => 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))))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mlex__leq,axiom,
% 94.26/94.37 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mlex__less,axiom,
% 94.26/94.37 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__neg__neg,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => 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)))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat_Osize_I4_J,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat__size,axiom,
% 94.26/94.37 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 94.26/94.37
% 94.26/94.37 fof(fact_fst__conv,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_fst__eqD,axiom,
% 94.26/94.37 ! [V_a,V_y,V_x,T_b,T_a] :
% 94.26/94.37 ( 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
% 94.26/94.37 => V_x = V_a ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Pair__fst__snd__eq,axiom,
% 94.26/94.37 ! [T_c,T_b,V_t_2,V_s_2] :
% 94.26/94.37 ( V_s_2 = V_t_2
% 94.26/94.37 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 94.26/94.37 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_prod__eqI,axiom,
% 94.26/94.37 ! [V_q,V_p,T_b,T_a] :
% 94.26/94.37 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 94.26/94.37 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 94.26/94.37 => V_p = V_q ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_fst__def,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__collapse,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_surjective__pairing,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_prod__case__beta,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__int__def,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mod__nat__def,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_split__comp__eq,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_split__beta,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat_Osize_I3_J,axiom,
% 94.26/94.37 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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_split__def,axiom,
% 94.26/94.37 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_The__split,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__neg__pos,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__pos__pos,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__pos__pos__1__number__of,axiom,
% 94.26/94.37 ! [V_w] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__pos__neg,axiom,
% 94.26/94.37 ! [V_b,V_a] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.26/94.37 => 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)))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_prod__size__simp,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_exI__realizer,axiom,
% 94.26/94.37 ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
% 94.26/94.37 => 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)))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_conjI__realizer,axiom,
% 94.26/94.37 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_Pa_2] :
% 94.26/94.37 ( hBOOL(hAPP(V_Pa_2,V_p_2))
% 94.26/94.37 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 94.26/94.37 => ( 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))))
% 94.26/94.37 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_prod_Orecs,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_in__lex__prod,axiom,
% 94.26/94.37 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 <=> ( 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))
% 94.26/94.37 | ( V_a_2 = V_a_H_2
% 94.26/94.37 & 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_div__nat__def,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_divmod__nat__rel__def,axiom,
% 94.26/94.37 ! [V_qr_2,V_na_2,V_m_2] :
% 94.26/94.37 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_na_2),V_qr_2))
% 94.26/94.37 <=> ( 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_na_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))
% 94.26/94.37 & ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.37 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.26/94.37 & ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.26/94.37 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 94.26/94.37 => ( 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)))
% 94.26/94.37 & 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_na_2)) ) )
% 94.26/94.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)))
% 94.26/94.37 & 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))) ) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_same__fstI,axiom,
% 94.26/94.37 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
% 94.26/94.37 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.26/94.37 => ( 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)))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_in__finite__psubset,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__Suc__number__of,axiom,
% 94.26/94.37 ! [V_na_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_na_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_na_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_na_2)))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__number__of__Suc,axiom,
% 94.26/94.37 ! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__lessI2,axiom,
% 94.26/94.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__Suc__Suc,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__less__iff__conj,axiom,
% 94.26/94.37 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( 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))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 94.26/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_less__max__iff__disj,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( 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)))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 94.26/94.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oless__supI2,axiom,
% 94.26/94.37 ! [V_a,V_b,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oless__supI1,axiom,
% 94.26/94.37 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oidem,axiom,
% 94.26/94.37 ! [V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup_Oidem,axiom,
% 94.26/94.37 ! [V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup_Ocommute,axiom,
% 94.26/94.37 ! [V_b,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__commute,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 94.26/94.37 ! [V_b,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__left__idem,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 94.26/94.37 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__left__commute,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup_Oassoc,axiom,
% 94.26/94.37 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__assoc,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__0R,axiom,
% 94.26/94.37 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__0L,axiom,
% 94.26/94.37 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__diff__distrib__left,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Groups_Oordered__ab__group__add(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__add__distrib__left,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__max__iff__disj,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( 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)))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 94.26/94.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__maxI1,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__maxI2,axiom,
% 94.26/94.37 ! [V_x,V_y,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__iff__sup,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.37 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__sup__iff,axiom,
% 94.26/94.37 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( 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))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 94.26/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__supI1,axiom,
% 94.26/94.37 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__supI2,axiom,
% 94.26/94.37 ! [V_a,V_b,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__absorb2,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__absorb1,axiom,
% 94.26/94.37 ! [V_x,V_y,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.37 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__supI,axiom,
% 94.26/94.37 ! [V_b,V_x,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__least,axiom,
% 94.26/94.37 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__mono,axiom,
% 94.26/94.37 ! [V_d,V_b,V_c,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 94.26/94.37 => 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))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ole__supE,axiom,
% 94.26/94.37 ! [V_x,V_b,V_a,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.26/94.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 94.26/94.37 ! [V_x,V_z,V_y,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 94.26/94.37 ! [V_x,V_z,V_y,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__inf__absorb,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 94.26/94.37 ! [T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__number__of,axiom,
% 94.26/94.37 ! [V_v,V_u,T_b] :
% 94.26/94.37 ( ( class_Int_Onumber(T_b)
% 94.26/94.37 & class_Orderings_Oord(T_b) )
% 94.26/94.37 => ( ( 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)))
% 94.26/94.37 => 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) )
% 94.26/94.37 & ( ~ 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)))
% 94.26/94.37 => 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) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Odistrib__sup__le,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Odistrib__inf__le,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_a)
% 94.26/94.37 => 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)))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_minus__max__eq__min,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Groups_Olinordered__ab__group__add(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_minus__min__eq__max,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Groups_Olinordered__ab__group__add(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_nat__minus__add__max,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__Suc2,axiom,
% 94.26/94.37 ! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__Suc1,axiom,
% 94.26/94.37 ! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__ord__max,axiom,
% 94.26/94.37 ! [T_b] :
% 94.26/94.37 ( class_Orderings_Oord(T_b)
% 94.26/94.37 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_dual__min,axiom,
% 94.26/94.37 ! [T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 94.26/94.37 ! [V_a_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.37 => 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 ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__lessI1,axiom,
% 94.26/94.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__leqI2,axiom,
% 94.26/94.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_smax__insertI,axiom,
% 94.26/94.37 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_smin__insertI,axiom,
% 94.26/94.37 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__leqI1,axiom,
% 94.26/94.37 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oremove,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 94.26/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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)))))) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_smax__emptyI,axiom,
% 94.26/94.37 ! [V_Y_2] :
% 94.26/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 94.26/94.37 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_smin__emptyI,axiom,
% 94.26/94.37 ! [V_X_2] :
% 94.26/94.37 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Osingleton,axiom,
% 94.26/94.37 ! [V_x_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max__ge,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => 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))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max__in,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oin__idem,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_OF__eq,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max__mono,axiom,
% 94.26/94.37 ! [V_N_2,V_M_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 94.26/94.37 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.26/94.37 => 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))) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max__insert,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Osubset__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oinsert,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oinsert__remove,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 94.26/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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)))))) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_minus__Min__eq__Max,axiom,
% 94.26/94.37 ! [V_S_2,T_b] :
% 94.26/94.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.37 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_minus__Max__eq__Min,axiom,
% 94.26/94.37 ! [V_S_2,T_b] :
% 94.26/94.37 ( class_Groups_Olinordered__ab__group__add(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.26/94.37 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_wmin__insertI,axiom,
% 94.26/94.37 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_wmax__insertI,axiom,
% 94.26/94.37 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ( 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))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max_Oclosed,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( ! [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))))))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_wmax__emptyI,axiom,
% 94.26/94.37 ! [V_X_2] :
% 94.26/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_wmin__emptyI,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__rpair__set,axiom,
% 94.26/94.37 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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__rpair__set,axiom,
% 94.26/94.37 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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__strict__def,axiom,
% 94.26/94.37 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_less__than__iff,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_intrel__iff,axiom,
% 94.26/94.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_pair__less__def,axiom,
% 94.26/94.37 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_mlex__prod__def,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__weak__def,axiom,
% 94.26/94.37 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)))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OInf__le__Sup,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 94.26/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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)))))) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_rp__inv__image__rp,axiom,
% 94.26/94.37 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 94.26/94.37 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 94.26/94.37 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup1E,axiom,
% 94.26/94.37 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 94.26/94.37 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup1CI,axiom,
% 94.26/94.37 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 94.26/94.37 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 94.26/94.37 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_UnE,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_UnCI,axiom,
% 94.26/94.37 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 94.26/94.37 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__iff,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.37 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_UnI1,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_UnI2,axiom,
% 94.26/94.37 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 94.26/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__max,axiom,
% 94.26/94.37 ! [T_b] :
% 94.26/94.37 ( ( class_Lattices_Osemilattice__sup(T_b)
% 94.26/94.37 & class_Orderings_Olinorder(T_b) )
% 94.26/94.37 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__insert__right,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__insert__left,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__fun__def,axiom,
% 94.26/94.37 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__Diff__cancel,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__Diff__cancel2,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__Diff,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_less__supI2,axiom,
% 94.26/94.37 ! [V_a,V_b,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_less__supI1,axiom,
% 94.26/94.37 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Oidem,axiom,
% 94.26/94.37 ! [V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup_Oidem,axiom,
% 94.26/94.37 ! [V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__idem,axiom,
% 94.26/94.37 ! [V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup_Ocommute,axiom,
% 94.26/94.37 ! [V_b,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__aci_I5_J,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__commute,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup_Oleft__idem,axiom,
% 94.26/94.37 ! [V_b,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__aci_I8_J,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__left__idem,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup_Oleft__commute,axiom,
% 94.26/94.37 ! [V_c,V_a,V_b,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__aci_I7_J,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__left__commute,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup_Oassoc,axiom,
% 94.26/94.37 ! [V_c,V_b,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__aci_I6_J,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__assoc,axiom,
% 94.26/94.37 ! [V_z,V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__apply,axiom,
% 94.26/94.37 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__absorb,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__commute,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__left__absorb,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__left__commute,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__assoc,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_bex__Un,axiom,
% 94.26/94.37 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( ? [B_x] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.37 <=> ( ? [B_x] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.37 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.37 | ? [B_x] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 94.26/94.37 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_ball__Un,axiom,
% 94.26/94.37 ! [V_Pa_2,V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( ! [B_x] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.37 <=> ( ! [B_x] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.26/94.37 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.26/94.37 & ! [B_x] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 94.26/94.37 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup1I1,axiom,
% 94.26/94.37 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 94.26/94.37 ( hBOOL(hAPP(V_A_2,V_x_2))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup1I2,axiom,
% 94.26/94.37 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 94.26/94.37 ( hBOOL(hAPP(V_B_2,V_x_2))
% 94.26/94.37 => 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__ord_I3_J,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__ge1,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inf__sup__ord_I4_J,axiom,
% 94.26/94.37 ! [V_x,V_y,T_a] :
% 94.26/94.37 ( class_Lattices_Olattice(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__ge2,axiom,
% 94.26/94.37 ! [V_x,V_y,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__iff__sup,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.26/94.37 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__sup__iff,axiom,
% 94.26/94.37 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_b)
% 94.26/94.37 => ( 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))
% 94.26/94.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 94.26/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__supI1,axiom,
% 94.26/94.37 ! [V_b,V_a,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__supI2,axiom,
% 94.26/94.37 ! [V_a,V_b,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__absorb2,axiom,
% 94.26/94.37 ! [V_y,V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__absorb1,axiom,
% 94.26/94.37 ! [V_x,V_y,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__supI,axiom,
% 94.26/94.37 ! [V_b,V_x,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__least,axiom,
% 94.26/94.37 ! [V_z,V_x,V_y,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__mono,axiom,
% 94.26/94.37 ! [V_d,V_b,V_c,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 94.26/94.37 => 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))) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_le__supE,axiom,
% 94.26/94.37 ! [V_x,V_b,V_a,T_a] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_a)
% 94.26/94.37 => ( 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))
% 94.26/94.37 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.26/94.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_image__Un,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__mono,axiom,
% 94.26/94.37 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__least,axiom,
% 94.26/94.37 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__absorb2,axiom,
% 94.26/94.37 ! [V_A_2,V_B_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__absorb1,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_subset__Un__eq,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.37 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__upper2,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__upper1,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__empty__left,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__empty__right,axiom,
% 94.26/94.37 ! [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 ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Un__empty,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_finite__Un,axiom,
% 94.26/94.37 ! [V_G_2,V_F_2,T_b] :
% 94.26/94.37 ( 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_G_2)))
% 94.26/94.37 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.26/94.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_finite__UnI,axiom,
% 94.26/94.37 ! [V_G_2,V_F_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 94.26/94.37 => 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_G_2))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__bot__left,axiom,
% 94.26/94.37 ! [V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Obounded__lattice__bot(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__bot__right,axiom,
% 94.26/94.37 ! [V_x,T_a] :
% 94.26/94.37 ( class_Lattices_Obounded__lattice__bot(T_a)
% 94.26/94.37 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__eq__bot__iff,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( class_Lattices_Obounded__lattice__bot(T_b)
% 94.26/94.37 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 94.26/94.37 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 94.26/94.37 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_fun__left__comm__idem__sup,axiom,
% 94.26/94.37 ! [T_b] :
% 94.26/94.37 ( class_Lattices_Osemilattice__sup(T_b)
% 94.26/94.37 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__Un__eq,axiom,
% 94.26/94.37 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_insert__is__Un,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Diff__partition,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Diff__subset__conv,axiom,
% 94.26/94.37 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> 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))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 => ( 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)
% 94.26/94.37 <=> V_A_2 = V_B_2 ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Compl__Diff__eq,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_rp__inv__image__def,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.26/94.37 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.26/94.37 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 94.26/94.37 ! [V_x_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.26/94.37 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_fold1__Un2,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Min__Un,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Max__Un,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_image__eq__fold__image,axiom,
% 94.26/94.37 ! [V_f_2,T_c,V_A_2,T_b] :
% 94.26/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => 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) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 94.26/94.37 ! [V_a_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.26/94.37 => 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 ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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 )
% 94.26/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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)))))) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_max__weak__def,axiom,
% 94.26/94.37 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)))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_in__inv__image,axiom,
% 94.26/94.37 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 94.26/94.37 ( 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)))
% 94.26/94.37 <=> 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)) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( ! [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))))))
% 94.26/94.37 => 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)) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_ivl__disj__un_I4_J,axiom,
% 94.26/94.37 ! [V_u_2,V_l_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 94.26/94.37 => 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) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Oremove,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 94.26/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.26/94.37 => 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)))))) ) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_finite__greaterThanAtMost,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_finite__greaterThanAtMost__int,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__nat__def,axiom,
% 94.26/94.37 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2] :
% 94.26/94.37 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.37 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 94.26/94.37 ! [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))) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Osingleton,axiom,
% 94.26/94.37 ! [V_x_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => 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 ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2] :
% 94.26/94.37 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.26/94.37 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.26/94.37 => 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))) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_greaterThanAtMost__empty,axiom,
% 94.26/94.37 ! [V_k_2,V_l_2,T_b] :
% 94.26/94.37 ( class_Orderings_Oorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 94.26/94.37 => 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)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 94.26/94.37 ! [V_l_2,V_k_2,T_b] :
% 94.26/94.37 ( class_Orderings_Oorder(T_b)
% 94.26/94.37 => ( 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))
% 94.26/94.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 94.26/94.37 ! [V_l_2,V_k_2,T_b] :
% 94.26/94.37 ( class_Orderings_Oorder(T_b)
% 94.26/94.37 => ( 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)
% 94.26/94.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_ivl__disj__un_I20_J,axiom,
% 94.26/94.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.26/94.37 ( class_Orderings_Olinorder(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.26/94.37 => 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) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_card__greaterThanAtMost,axiom,
% 94.26/94.37 ! [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) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_sup__Un__eq2,axiom,
% 94.26/94.37 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 94.26/94.37 ( 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))
% 94.26/94.37 <=> 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__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Oin__idem,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_OF__eq,axiom,
% 94.26/94.37 ! [V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 94.26/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => 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)) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Osubset__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.26/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.26/94.37 => 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) ) ) ) ) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_card__greaterThanAtMost__int,axiom,
% 94.26/94.37 ! [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)) ).
% 94.26/94.37
% 94.26/94.37 fof(fact_Sup__fin_Ounion__idem,axiom,
% 94.26/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.26/94.37 ( class_Lattices_Olattice(T_b)
% 94.26/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.26/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.37 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_max__strict__def,axiom,
% 94.59/94.37 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_ivl__disj__un_I16_J,axiom,
% 94.59/94.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 94.59/94.37 => 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) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_measure__def,axiom,
% 94.59/94.37 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Sup__fin_Oinsert,axiom,
% 94.59/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.37 ( class_Lattices_Olattice(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.37 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 94.59/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.37 ( class_Lattices_Olattice(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.37 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.37 => 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 )
% 94.59/94.37 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.37 => 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)))))) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_max__ext__additive,axiom,
% 94.59/94.37 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ( 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)))
% 94.59/94.37 => 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))) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_max__extp__max__ext__eq,axiom,
% 94.59/94.37 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 94.59/94.37 ( 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)
% 94.59/94.37 <=> 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_irrefl__def,axiom,
% 94.59/94.37 ! [V_r_2,T_b] :
% 94.59/94.37 ( c_Relation_Oirrefl(T_b,V_r_2)
% 94.59/94.37 <=> ! [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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Field__insert,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Sup__fin_Oclosed,axiom,
% 94.59/94.37 ! [V_A_2,T_b] :
% 94.59/94.37 ( class_Lattices_Olattice(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.37 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => ( ! [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))))))
% 94.59/94.37 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 94.59/94.37 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( ! [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))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_sup2E,axiom,
% 94.59/94.37 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.37 ( 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))
% 94.59/94.37 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 94.59/94.37 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_sup2CI,axiom,
% 94.59/94.37 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 94.59/94.37 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 94.59/94.37 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_sup2I1,axiom,
% 94.59/94.37 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_sup2I2,axiom,
% 94.59/94.37 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Field__empty,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_mono__Field,axiom,
% 94.59/94.37 ! [V_s_2,V_r_2,T_b] :
% 94.59/94.37 ( 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))
% 94.59/94.37 => 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Field__Un,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_finite__Field,axiom,
% 94.59/94.37 ! [V_r_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 94.59/94.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 94.59/94.37 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( ! [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))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Max_Ohom__commute,axiom,
% 94.59/94.37 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( ! [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))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Min_Ohom__commute,axiom,
% 94.59/94.37 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( ! [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))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Sup__fin_Ohom__commute,axiom,
% 94.59/94.37 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.37 ( class_Lattices_Olattice(T_b)
% 94.59/94.37 => ( ! [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))
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.37 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_negD,axiom,
% 94.59/94.37 ! [V_x] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.59/94.37 => ? [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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_incr__mult__lemma,axiom,
% 94.59/94.37 ! [V_k_2,V_Pa_2,V_d_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 94.59/94.37 => ( ! [B_x] :
% 94.59/94.37 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.59/94.37 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.59/94.37 => 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)))) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_setprod__mono__one__left,axiom,
% 94.59/94.37 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 94.59/94.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 94.59/94.37 => ( ! [B_x] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.59/94.37 => 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) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_setprod__mono__one__right,axiom,
% 94.59/94.37 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 94.59/94.37 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 94.59/94.37 => ( ! [B_x] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.59/94.37 => 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) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_zero__less__imp__eq__int,axiom,
% 94.59/94.37 ! [V_k] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 94.59/94.37 => ? [B_n] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 94.59/94.37 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_card__Pow,axiom,
% 94.59/94.37 ! [V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_ivl__disj__un_I19_J,axiom,
% 94.59/94.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.59/94.37 => 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) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_equiv__intrel__iff,axiom,
% 94.59/94.37 ! [V_y_2,V_x_2] :
% 94.59/94.37 ( 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))))
% 94.59/94.37 <=> 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_finite__atLeastAtMost,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_finite__atLeastAtMost__int,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_PowI,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.37 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Image__Un,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__not__empty,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_image__Suc__atLeastAtMost,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Cantors__paradox,axiom,
% 94.59/94.37 ! [V_A_2,T_b] :
% 94.59/94.37 ~ ? [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) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__top,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Image__empty,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__empty,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__bottom,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_finite__Pow__iff,axiom,
% 94.59/94.37 ! [V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 94.59/94.37 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__insert,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__iff,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 94.59/94.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_PowD,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 94.59/94.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Pow__mono,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.37 => 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_image__Pow__surj,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 94.59/94.37 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 94.59/94.37 => 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) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Un__Pow__subset,axiom,
% 94.59/94.37 ! [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)))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_image__add__atLeastAtMost,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 94.59/94.37 ! [V_na_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_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_na_2))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 94.59/94.37 ! [V_na_2,V_m_2] :
% 94.59/94.37 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 94.59/94.37 => ( c_Nat__Transfer_Ois__nat(V_na_2)
% 94.59/94.37 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_na_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_na_2))) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastAtMostSuc__conv,axiom,
% 94.59/94.37 ! [V_na_2,V_m_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
% 94.59/94.37 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Image__mono,axiom,
% 94.59/94.37 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 94.59/94.37 ( 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))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 94.59/94.37 => 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))) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Un__Image,axiom,
% 94.59/94.37 ! [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)) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 94.59/94.37 ! [V_y_2,V_x_2] :
% 94.59/94.37 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 94.59/94.37 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastatMost__empty__iff2,axiom,
% 94.59/94.37 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( 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)
% 94.59/94.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastatMost__empty__iff,axiom,
% 94.59/94.37 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( 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))
% 94.59/94.37 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastatMost__empty,axiom,
% 94.59/94.37 ! [V_a_2,V_b_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 94.59/94.37 => 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)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastatMost__subset__iff,axiom,
% 94.59/94.37 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 94.59/94.37 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 94.59/94.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 94.59/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastAtMost__singleton_H,axiom,
% 94.59/94.37 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( V_a_2 = V_b_2
% 94.59/94.37 => 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))) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 94.59/94.37 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.37 <=> ( V_a_2 = V_b_2
% 94.59/94.37 & V_b_2 = V_c_2 ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastAtMost__singleton,axiom,
% 94.59/94.37 ! [V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_image__uminus__atLeastAtMost,axiom,
% 94.59/94.37 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.37 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_image__Pow__mono,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.37 ( 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_f_2),V_A_2)),V_B_2))
% 94.59/94.37 => 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 94.59/94.37 ! [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) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 94.59/94.37 ! [V_y_2,V_x_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 94.59/94.37 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Image__iff,axiom,
% 94.59/94.37 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 94.59/94.37 <=> ? [B_x] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.37 & 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)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_rev__ImageI,axiom,
% 94.59/94.37 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.37 => ( 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))
% 94.59/94.37 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_card__atLeastAtMost,axiom,
% 94.59/94.37 ! [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) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 94.59/94.37 ! [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) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_atLeastatMost__psubset__iff,axiom,
% 94.59/94.37 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.37 ( class_Orderings_Oorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 94.59/94.37 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 94.59/94.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 94.59/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 94.59/94.37 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 94.59/94.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 94.59/94.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_ivl__disj__un_I22_J,axiom,
% 94.59/94.37 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.59/94.37 => 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) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_simp__from__to,axiom,
% 94.59/94.37 ! [V_i_2,V_j_2] :
% 94.59/94.37 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 94.59/94.37 => 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)) )
% 94.59/94.37 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 94.59/94.37 => 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)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Image__singleton__iff,axiom,
% 94.59/94.37 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 94.59/94.37 ( 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))))))
% 94.59/94.37 <=> 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_card__atLeastAtMost__int,axiom,
% 94.59/94.37 ! [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))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_ivl__disj__un_I5_J,axiom,
% 94.59/94.37 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.37 ( class_Orderings_Olinorder(T_b)
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.37 => 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) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_of__int,axiom,
% 94.59/94.37 ! [V_j_2,V_i_2,T_b] :
% 94.59/94.37 ( class_Rings_Oring__1(T_b)
% 94.59/94.37 => 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)) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_One__int__def,axiom,
% 94.59/94.37 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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_mult,axiom,
% 94.59/94.37 ! [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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_le,axiom,
% 94.59/94.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 94.59/94.37 ( 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)))))))
% 94.59/94.37 <=> 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_minus,axiom,
% 94.59/94.37 ! [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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Zero__int__def,axiom,
% 94.59/94.37 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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_int__def,axiom,
% 94.59/94.37 ! [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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_add,axiom,
% 94.59/94.37 ! [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))))) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_nat,axiom,
% 94.59/94.37 ! [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) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_less,axiom,
% 94.59/94.37 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 94.59/94.37 ( 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)))))))
% 94.59/94.37 <=> 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_ex__nat__less,axiom,
% 94.59/94.37 ! [V_Pa_2,V_na_2] :
% 94.59/94.37 ( ? [B_m] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2))
% 94.59/94.37 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 94.59/94.37 <=> ? [B_x] :
% 94.59/94.37 ( 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_na_2)))
% 94.59/94.37 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_all__nat__less,axiom,
% 94.59/94.37 ! [V_Pa_2,V_na_2] :
% 94.59/94.37 ( ! [B_m] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2))
% 94.59/94.37 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 94.59/94.37 <=> ! [B_x] :
% 94.59/94.37 ( 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_na_2)))
% 94.59/94.37 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_aset_I6_J,axiom,
% 94.59/94.37 ! [V_A_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( 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))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( ! [B_xa] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xb] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 94.59/94.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_bset_I8_J,axiom,
% 94.59/94.37 ! [V_B_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( 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))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( ! [B_xa] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xb] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 94.59/94.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 94.59/94.37 => 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))) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Powp__Pow__eq,axiom,
% 94.59/94.37 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.37 ( 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))
% 94.59/94.37 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_bset_I3_J,axiom,
% 94.59/94.37 ! [V_B_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( 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))
% 94.59/94.37 => ( ! [B_x] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xa] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 94.59/94.37 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 94.59/94.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_aset_I3_J,axiom,
% 94.59/94.37 ! [V_A_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( 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))
% 94.59/94.37 => ( ! [B_x] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xa] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 94.59/94.37 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 94.59/94.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_aset_I5_J,axiom,
% 94.59/94.37 ! [V_A_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( ! [B_xa] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xb] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 94.59/94.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 94.59/94.37 => 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)) ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_Powp__mono,axiom,
% 94.59/94.37 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.37 => 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))) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_aset_I4_J,axiom,
% 94.59/94.37 ! [V_A_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( ! [B_xa] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xb] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 94.59/94.37 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.37 => ( B_x != V_t_2
% 94.59/94.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 94.59/94.37
% 94.59/94.37 fof(fact_bset_I4_J,axiom,
% 94.59/94.37 ! [V_B_2,V_t_2,V_D_2] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.37 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 94.59/94.37 => ! [B_x] :
% 94.59/94.37 ( ! [B_xa] :
% 94.59/94.37 ( 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)))
% 94.59/94.37 => ! [B_xb] :
% 94.59/94.37 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 94.59/94.37 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.37 => ( B_x != V_t_2
% 94.59/94.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_bset_I7_J,axiom,
% 94.59/94.38 ! [V_B_2,V_t_2,V_D_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 94.59/94.38 => ! [B_x] :
% 94.59/94.38 ( ! [B_xa] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => ! [B_xb] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 94.59/94.38 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 94.59/94.38 => 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))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_bset_I6_J,axiom,
% 94.59/94.38 ! [V_t_2,V_B_2,V_D_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.38 => ! [B_x] :
% 94.59/94.38 ( ! [B_xa] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => ! [B_xb] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 94.59/94.38 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_aset_I8_J,axiom,
% 94.59/94.38 ! [V_t_2,V_A_2,V_D_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.38 => ! [B_x] :
% 94.59/94.38 ( ! [B_xa] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => ! [B_xb] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 94.59/94.38 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_eq__Abs__Integ,axiom,
% 94.59/94.38 ! [V_z_2] :
% 94.59/94.38 ~ ! [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))))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_periodic__finite__ex,axiom,
% 94.59/94.38 ! [V_Pa_2,V_d_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 94.59/94.38 => ( ! [B_x,B_k] :
% 94.59/94.38 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.59/94.38 <=> 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)))) )
% 94.59/94.38 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.59/94.38 <=> ? [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_aset_I7_J,axiom,
% 94.59/94.38 ! [V_t_2,V_A_2,V_D_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.38 => ! [B_x] :
% 94.59/94.38 ( ! [B_xa] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => ! [B_xb] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 94.59/94.38 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_bset_I5_J,axiom,
% 94.59/94.38 ! [V_t_2,V_B_2,V_D_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 94.59/94.38 => ! [B_x] :
% 94.59/94.38 ( ! [B_xa] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => ! [B_xb] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 94.59/94.38 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 94.59/94.38 ! [V_x_2,V_y_2,V_c_2] :
% 94.59/94.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 94.59/94.38 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 94.59/94.38 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 94.59/94.38 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 94.59/94.38 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_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_na_2))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ImageE,axiom,
% 94.59/94.38 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 94.59/94.38 => ~ ! [B_x] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__atLeastLessThan,axiom,
% 94.59/94.38 ! [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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__atMost,axiom,
% 94.59/94.38 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__eq__iff,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 94.59/94.38 <=> ( V_a_2 = V_c_2
% 94.59/94.38 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 94.59/94.38 => V_a_2 = V_c_2 ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 94.59/94.38 => V_b_2 = V_d_2 ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__eq__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 94.59/94.38 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ex__nat__less__eq,axiom,
% 94.59/94.38 ! [V_Pa_2,V_na_2] :
% 94.59/94.38 ( ? [B_m] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2))
% 94.59/94.38 & hBOOL(hAPP(V_Pa_2,B_m)) )
% 94.59/94.38 <=> ? [B_x] :
% 94.59/94.38 ( 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_na_2)))
% 94.59/94.38 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_all__nat__less__eq,axiom,
% 94.59/94.38 ! [V_Pa_2,V_na_2] :
% 94.59/94.38 ( ! [B_m] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2))
% 94.59/94.38 => hBOOL(hAPP(V_Pa_2,B_m)) )
% 94.59/94.38 <=> ! [B_x] :
% 94.59/94.38 ( 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_na_2)))
% 94.59/94.38 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan0,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__atLeastLessThan,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__Suc__atLeastLessThan,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__empty,axiom,
% 94.59/94.38 ! [V_a_2,V_b_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__empty__iff,axiom,
% 94.59/94.38 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => ( 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))
% 94.59/94.38 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 94.59/94.38 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => ( 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)
% 94.59/94.38 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__subset__iff,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 94.59/94.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 94.59/94.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I17_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__diff,axiom,
% 94.59/94.38 ! [V_m_2,V_na_2,V_i_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_na_2))
% 94.59/94.38 => 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_na_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_na_2),V_m_2) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast0AtMost,axiom,
% 94.59/94.38 ! [V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__add__atLeastLessThan,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__atMost,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__Suc,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__iff,axiom,
% 94.59/94.38 ! [V_k_2,V_i_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oord(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__subset__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__singleton,axiom,
% 94.59/94.38 ! [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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I21_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThan__add__Un,axiom,
% 94.59/94.38 ! [V_k_2,V_j_2,V_i_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 94.59/94.38 => 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_subset__card__intvl__is__intvl,axiom,
% 94.59/94.38 ! [V_k_2,V_A_2] :
% 94.59/94.38 ( 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)))))
% 94.59/94.38 => 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__atLeastLessThan,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThanSuc,axiom,
% 94.59/94.38 ! [V_na_2,V_m_2] :
% 94.59/94.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_na_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__0,axiom,
% 94.59/94.38 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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I9_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I15_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I6_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I3_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I18_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I7_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I10_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I2_J,axiom,
% 94.59/94.38 ! [V_u_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fold__Un__disjoint,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf1I,axiom,
% 94.59/94.38 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 94.59/94.38 ( hBOOL(hAPP(V_A_2,V_x_2))
% 94.59/94.38 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf1E,axiom,
% 94.59/94.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 94.59/94.38 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__lessThan,axiom,
% 94.59/94.38 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__atLeastLessThan__int,axiom,
% 94.59/94.38 ! [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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_IntE,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.59/94.38 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.38 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_IntI,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__Int,axiom,
% 94.59/94.38 ! [V_G_2,V_F_2,T_b] :
% 94.59/94.38 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.59/94.38 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 94.59/94.38 => 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_G_2))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I2_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Pow__Int__eq,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2] :
% 94.59/94.38 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.59/94.38 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inj__on__Int,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.38 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__fun__def,axiom,
% 94.59/94.38 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Int__distrib,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__Diff,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Int__distrib2,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Int2,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__min,axiom,
% 94.59/94.38 ! [T_b] :
% 94.59/94.38 ( ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 & class_Orderings_Olinorder(T_b) )
% 94.59/94.38 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_less__infI2,axiom,
% 94.59/94.38 ! [V_a,V_x,V_b,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_less__infI1,axiom,
% 94.59/94.38 ! [V_b,V_x,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oidem,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf_Oidem,axiom,
% 94.59/94.38 ! [V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__idem,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf_Ocommute,axiom,
% 94.59/94.38 ! [V_b,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__aci_I1_J,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__commute,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf_Oleft__idem,axiom,
% 94.59/94.38 ! [V_b,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__aci_I4_J,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__left__idem,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf_Oleft__commute,axiom,
% 94.59/94.38 ! [V_c,V_a,V_b,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__aci_I3_J,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__left__commute,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf_Oassoc,axiom,
% 94.59/94.38 ! [V_c,V_b,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__aci_I2_J,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__assoc,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__apply,axiom,
% 94.59/94.38 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__absorb,axiom,
% 94.59/94.38 ! [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 ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__commute,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__left__absorb,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__left__commute,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__assoc,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf1D1,axiom,
% 94.59/94.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf1D2,axiom,
% 94.59/94.38 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__eq__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 94.59/94.38 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__absorb,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sup__inf__absorb,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__distrib1,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Odistrib__lattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sup__inf__distrib1,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Odistrib__lattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__distrib2,axiom,
% 94.59/94.38 ! [V_x,V_z,V_y,T_a] :
% 94.59/94.38 ( class_Lattices_Odistrib__lattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sup__inf__distrib2,axiom,
% 94.59/94.38 ! [V_x,V_z,V_y,T_a] :
% 94.59/94.38 ( class_Lattices_Odistrib__lattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__Un__distrib,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Un__Int__distrib,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__Un__distrib2,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Un__Int__distrib2,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Un__Int__crazy,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_insert__inter__insert,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__empty__left,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__empty__right,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_disjoint__iff__not__equal,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 <=> ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 => ! [B_xa] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 94.59/94.38 => B_x != B_xa ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__bot__left,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__bot__right,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Obounded__lattice__bot(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__lower1,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__lower2,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__absorb2,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__absorb1,axiom,
% 94.59/94.38 ! [V_A_2,V_B_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__greatest,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 94.59/94.38 => 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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__mono,axiom,
% 94.59/94.38 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__infE,axiom,
% 94.59/94.38 ! [V_b,V_a,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.59/94.38 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__mono,axiom,
% 94.59/94.38 ! [V_d,V_b,V_c,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__greatest,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__infI,axiom,
% 94.59/94.38 ! [V_b,V_a,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__absorb2,axiom,
% 94.59/94.38 ! [V_x,V_y,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__absorb1,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__infI2,axiom,
% 94.59/94.38 ! [V_a,V_x,V_b,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__infI1,axiom,
% 94.59/94.38 ! [V_b,V_x,V_a,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__inf__iff,axiom,
% 94.59/94.38 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.59/94.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_le__iff__inf,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.59/94.38 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__le2,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__ord_I2_J,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__le1,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__sup__ord_I1_J,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_IntD2,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_IntD1,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__iff,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 94.59/94.38 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.38 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I4_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fun__left__comm__idem__inf,axiom,
% 94.59/94.38 ! [T_b] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__Int__eq,axiom,
% 94.59/94.38 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 <=> 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__lessThan,axiom,
% 94.59/94.38 ! [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 ).
% 94.59/94.38
% 94.59/94.38 fof(fact_distrib__inf__le,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_distrib__sup__le,axiom,
% 94.59/94.38 ! [V_z,V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Olattice(T_a)
% 94.59/94.38 => 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)))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_compl__inf__bot,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__compl__bot,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_diff__eq,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_compl__sup,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_compl__inf,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__right,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 94.59/94.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__left,axiom,
% 94.59/94.38 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 94.59/94.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 94.59/94.38 => 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)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__right__if0,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 94.59/94.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__left__if0,axiom,
% 94.59/94.38 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 94.59/94.38 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__right__if1,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__insert__left__if1,axiom,
% 94.59/94.38 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__Int__subset,axiom,
% 94.59/94.38 ! [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)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__triv,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Un__Int__assoc__eq,axiom,
% 94.59/94.38 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Int,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Un,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Un__Diff__Int,axiom,
% 94.59/94.38 ! [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 ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I11_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 94.59/94.38 ! [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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__disjoint2,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__disjoint,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Image__Int__subset,axiom,
% 94.59/94.38 ! [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)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__Un,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__Int,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__eq,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Diff__Compl,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I14_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast0LessThan,axiom,
% 94.59/94.38 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__0,axiom,
% 94.59/94.38 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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2] :
% 94.59/94.38 ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.59/94.38 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.59/94.38 => 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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__Suc,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__Suc__atMost,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 94.59/94.38 ! [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))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 94.59/94.38 ! [V_u_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 94.59/94.38 => 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__iff,axiom,
% 94.59/94.38 ! [V_k_2,V_i_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oord(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__Sup__absorb,axiom,
% 94.59/94.38 ! [V_a_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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 ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__subset__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inj__on__image__Int,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_disjoint__eq__subset__Compl,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 <=> 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I15_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastAtMost,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastLessThan,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__strict__subset__iff,axiom,
% 94.59/94.38 ! [V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( 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_na_2)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_na_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I16_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I13_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I12_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__greaterThanAtMost,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I9_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__greaterThanLessThan,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastAtMostR1,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastAtMostL1,axiom,
% 94.59/94.38 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I3_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I10_J,axiom,
% 94.59/94.38 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I1_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fold1__belowI,axiom,
% 94.59/94.38 ! [V_a_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__add__int__atLeastLessThan,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_below__fold1__iff,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Osemilattice__inf(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__atLeastLessThan__int,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod__Un__Int,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod_Ounion__inter,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__Un__Int,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__Diff__subset__Int,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_folding__one_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.59/94.38 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_folding__one_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.59/94.38 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_single__Diff__lessThan,axiom,
% 94.59/94.38 ! [V_k_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I8_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod__Un__disjoint,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__Un__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inj__on__Un,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( 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)),V_A_2),V_B_2))
% 94.59/94.38 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.38 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.38 & 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fold__image__Un__Int,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fold1__Un,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Sup__fin_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Min_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Min_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Max_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Max_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 94.59/94.38 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_arith__series__int,axiom,
% 94.59/94.38 ! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card_Ounion__inter__neutral,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( ( ? [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)))
% 94.59/94.38 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod__Un,axiom,
% 94.59/94.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Fields_Ofield(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 94.59/94.38 => 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))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_fold__image__Un__one,axiom,
% 94.59/94.38 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__nat__def,axiom,
% 94.59/94.38 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__negf,axiom,
% 94.59/94.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__0,axiom,
% 94.59/94.38 ! [V_A_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__addf,axiom,
% 94.59/94.38 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__product,axiom,
% 94.59/94.38 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Rings_Osemiring__0(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__left__distrib,axiom,
% 94.59/94.38 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Rings_Osemiring__0(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__right__distrib,axiom,
% 94.59/94.38 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 94.59/94.38 ( class_Rings_Osemiring__0(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__commute,axiom,
% 94.59/94.38 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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(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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_of__nat__setsum,axiom,
% 94.59/94.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Rings_Osemiring__1(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_of__int__setsum,axiom,
% 94.59/94.38 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Rings_Oring__1(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__subtractf,axiom,
% 94.59/94.38 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__divide__distrib,axiom,
% 94.59/94.38 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Fields_Ofield(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__empty,axiom,
% 94.59/94.38 ! [V_f_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oempty,axiom,
% 94.59/94.38 ! [V_g_2,T_c,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__infinite,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oinfinite,axiom,
% 94.59/94.38 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf__Int__eq2,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 <=> 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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Odistrib,axiom,
% 94.59/94.38 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__lessThan__Suc,axiom,
% 94.59/94.38 ! [V_na_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2))),hAPP(V_f_2,V_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 94.59/94.38 ! [V_na_2,V_m_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 94.59/94.38 ! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 94.59/94.38 ! [V_na_2,V_m_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 94.59/94.38 ! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__add__nat__ivl,axiom,
% 94.59/94.38 ! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
% 94.59/94.38 => 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_na_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_na_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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff__nat__ivl,axiom,
% 94.59/94.38 ! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
% 94.59/94.38 => 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_na_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_na_2),V_p_2)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__delta,axiom,
% 94.59/94.38 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.59/94.38 => 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) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__delta_H,axiom,
% 94.59/94.38 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.59/94.38 => 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) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__constant,axiom,
% 94.59/94.38 ! [V_A_2,V_y_2,T_c,T_b] :
% 94.59/94.38 ( class_Rings_Osemiring__1(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__atMost__Suc,axiom,
% 94.59/94.38 ! [V_na_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => 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_na_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_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__insert,axiom,
% 94.59/94.38 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.59/94.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oinsert,axiom,
% 94.59/94.38 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__Un__Int,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff,axiom,
% 94.59/94.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oeq__fold,axiom,
% 94.59/94.38 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_OF__eq,axiom,
% 94.59/94.38 ! [V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 94.59/94.38 ! [V_k_2,V_f_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__head__upt__Suc,axiom,
% 94.59/94.38 ! [V_f_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => 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_na_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_na_2))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__head__Suc,axiom,
% 94.59/94.38 ! [V_f_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => 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_na_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_na_2))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__restrict__set,axiom,
% 94.59/94.38 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oinsert__remove,axiom,
% 94.59/94.38 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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)))))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__Un__disjoint,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__Un,axiom,
% 94.59/94.38 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__op__ivl__Suc,axiom,
% 94.59/94.38 ! [V_f_2,V_m_2,V_na_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 94.59/94.38 => 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_na_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
% 94.59/94.38 => 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_na_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_na_2))),hAPP(V_f_2,V_na_2)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__cl__ivl__Suc,axiom,
% 94.59/94.38 ! [V_f_2,V_m_2,V_na_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
% 94.59/94.38 => 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_na_2))) = c_Groups_Ozero__class_Ozero(T_b) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
% 94.59/94.38 => 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_na_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_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__head,axiom,
% 94.59/94.38 ! [V_Pa_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => 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_na_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_na_2))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__ub__add__nat,axiom,
% 94.59/94.38 ! [V_p_2,V_f_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 => ( 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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
% 94.59/94.38 => 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_na_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_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_p_2)))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Oremove,axiom,
% 94.59/94.38 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.38 => 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)))))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff1_H,axiom,
% 94.59/94.38 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)))))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff1__ring,axiom,
% 94.59/94.38 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Rings_Oring(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff1,axiom,
% 94.59/94.38 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_arith__series__general,axiom,
% 94.59/94.38 ! [V_na_2,V_d_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Ocomm__semiring__1(T_b)
% 94.59/94.38 => 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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_geometric__sum,axiom,
% 94.59/94.38 ! [V_na_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Fields_Ofield(T_b)
% 94.59/94.38 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 94.59/94.38 => 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_na_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_na_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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_gauss__sum,axiom,
% 94.59/94.38 ! [V_na_2,T_b] :
% 94.59/94.38 ( class_Rings_Ocomm__semiring__1(T_b)
% 94.59/94.38 => 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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__natinterval__difff,axiom,
% 94.59/94.38 ! [V_f_2,V_na_2,V_m_2,T_b] :
% 94.59/94.38 ( class_Groups_Oab__group__add(T_b)
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => 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_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.38 => 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_na_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__mono2,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.38 => ( ! [B_b] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 94.59/94.38 => 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))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setprod__Un__one,axiom,
% 94.59/94.38 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__bounded,axiom,
% 94.59/94.38 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 94.59/94.38 & class_Rings_Osemiring__1(T_c) )
% 94.59/94.38 => ( ! [B_i] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 94.59/94.38 => 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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf2I,axiom,
% 94.59/94.38 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf2E,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 94.59/94.38 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf2D1,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_inf2D2,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.38 ( 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))
% 94.59/94.38 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__eq__0__iff,axiom,
% 94.59/94.38 ! [V_f_2,V_F_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.59/94.38 => ( 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)
% 94.59/94.38 <=> ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_card__eq__setsum,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_int__setsum,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__eq__Suc0__iff,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 <=> ? [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.59/94.38 & ! [B_xa] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 94.59/94.38 => ( B_x != B_xa
% 94.59/94.38 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__eq__1__iff,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( 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)
% 94.59/94.38 <=> ? [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 94.59/94.38 & ! [B_xa] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 94.59/94.38 => ( B_x != B_xa
% 94.59/94.38 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 94.59/94.38 ! [V_k_2,V_f_2] :
% 94.59/94.38 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 94.59/94.38 ! [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)) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff__nat,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 94.59/94.38 ! [V_A_2,V_f_2,T_b] :
% 94.59/94.38 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__diff1__nat,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 94.59/94.38 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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)) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__Un__nat,axiom,
% 94.59/94.38 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => 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))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,T_b] :
% 94.59/94.38 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.59/94.38 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 94.59/94.38 => 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)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_arith__series__nat,axiom,
% 94.59/94.38 ! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,T_b] :
% 94.59/94.38 ( ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 94.59/94.38 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__Un__zero,axiom,
% 94.59/94.38 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__mono3,axiom,
% 94.59/94.38 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 94.59/94.38 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 94.59/94.38 => 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))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oremove,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.38 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.38 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 94.59/94.38 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.38 => 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)))))) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__nonneg__leq__bound,axiom,
% 94.59/94.38 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 94.59/94.38 => ( ! [B_i] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 94.59/94.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__nonneg__0,axiom,
% 94.59/94.38 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 94.59/94.38 => ( ! [B_i] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 94.59/94.38 => ( 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)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 94.59/94.38 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sum__diff__distrib,axiom,
% 94.59/94.38 ! [V_na_2,V_Pa_2,V_Q_2] :
% 94.59/94.38 ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_Pa_2,B_x)))
% 94.59/94.38 => 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_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_Pa_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Osingleton,axiom,
% 94.59/94.38 ! [V_x_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => 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 ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sup__Inf__absorb,axiom,
% 94.59/94.38 ! [V_a_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.38 => 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 ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oin__idem,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.38 => 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) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_OF__eq,axiom,
% 94.59/94.38 ! [V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Osubset__idem,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Ounion__idem,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => 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)) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__le__Sup,axiom,
% 94.59/94.38 ! [V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => 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))) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oinsert,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 94.59/94.38 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.38 => 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 )
% 94.59/94.38 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_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))
% 94.59/94.38 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_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)))))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Ounion__inter,axiom,
% 94.59/94.38 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.38 => ( 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))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Oclosed,axiom,
% 94.59/94.38 ! [V_A_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( ! [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))))))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Inf__fin_Ohom__commute,axiom,
% 94.59/94.38 ! [V_N_2,V_h_2,T_b] :
% 94.59/94.38 ( class_Lattices_Olattice(T_b)
% 94.59/94.38 => ( ! [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))
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.38 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__mono__zero__right,axiom,
% 94.59/94.38 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__mono__zero__left,axiom,
% 94.59/94.38 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 94.59/94.38 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( 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)))
% 94.59/94.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_setsum__strict__mono,axiom,
% 94.59/94.38 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 94.59/94.38 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.38 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 94.59/94.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.38 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 94.59/94.38 => 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))) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atMost__Int__atLeast,axiom,
% 94.59/94.38 ! [V_na_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_na_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_na_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_na_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_field__le__mult__one__interval,axiom,
% 94.59/94.38 ! [V_y,V_x,T_a] :
% 94.59/94.38 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.59/94.38 => ( ! [B_z] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 94.59/94.38 => 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)) ) )
% 94.59/94.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 94.59/94.38 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 94.59/94.38 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.38 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.59/94.38 => ( V_A_2 = V_B_2
% 94.59/94.38 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.59/94.38 => ( ! [B_x] :
% 94.59/94.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.59/94.38 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 94.59/94.38 => 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) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast__eq__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 94.59/94.38 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast__iff,axiom,
% 94.59/94.38 ! [V_k_2,V_i_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oord(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast__subset__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__lessThan,axiom,
% 94.59/94.38 ! [V_k_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__atLeast,axiom,
% 94.59/94.38 ! [V_k_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I14_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I8_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastAtMostR2,axiom,
% 94.59/94.38 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Int__atLeastAtMostL2,axiom,
% 94.59/94.38 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I6_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__atMost,axiom,
% 94.59/94.38 ! [V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__atLeast,axiom,
% 94.59/94.38 ! [V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast__Suc,axiom,
% 94.59/94.38 ! [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)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I12_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I13_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I1_J,axiom,
% 94.59/94.38 ! [V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__if,axiom,
% 94.59/94.38 ! [V_x,T_a] :
% 94.59/94.38 ( class_Groups_Osgn__if(T_a)
% 94.59/94.38 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 94.59/94.38 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_greaterThan__eq__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 94.59/94.38 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__sgn,axiom,
% 94.59/94.38 ! [V_a,T_a] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_atLeast__Suc__greaterThan,axiom,
% 94.59/94.38 ! [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) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__0__0,axiom,
% 94.59/94.38 ! [V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.38 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.59/94.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn0,axiom,
% 94.59/94.38 ! [T_a] :
% 94.59/94.38 ( class_Groups_Osgn__if(T_a)
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__times,axiom,
% 94.59/94.38 ! [V_b,V_a,T_a] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__less,axiom,
% 94.59/94.38 ! [V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__greater,axiom,
% 94.59/94.38 ! [V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_greaterThan__iff,axiom,
% 94.59/94.38 ! [V_k_2,V_i_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oord(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_greaterThan__subset__iff,axiom,
% 94.59/94.38 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( 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)))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__atMost,axiom,
% 94.59/94.38 ! [V_k_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_Compl__greaterThan,axiom,
% 94.59/94.38 ! [V_k_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => 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) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__1__pos,axiom,
% 94.59/94.38 ! [V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.38 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__pos,axiom,
% 94.59/94.38 ! [V_a,T_a] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I7_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__un_I11_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Olinorder(T_b)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 94.59/94.38 => 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) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__greaterThan,axiom,
% 94.59/94.38 ! [V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_image__uminus__lessThan,axiom,
% 94.59/94.38 ! [V_x_2,T_b] :
% 94.59/94.38 ( class_Groups_Oordered__ab__group__add(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_ivl__disj__int_I5_J,axiom,
% 94.59/94.38 ! [V_u_2,V_l_2,T_b] :
% 94.59/94.38 ( class_Orderings_Oorder(T_b)
% 94.59/94.38 => 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)) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_greaterThan__Suc,axiom,
% 94.59/94.38 ! [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)))) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_zsgn__def,axiom,
% 94.59/94.38 ! [V_i] :
% 94.59/94.38 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 94.59/94.38 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 94.59/94.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 94.59/94.38 => 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)) ) ) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__neg,axiom,
% 94.59/94.38 ! [V_a,T_a] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.59/94.38 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_sgn__1__neg,axiom,
% 94.59/94.38 ! [V_a_2,T_b] :
% 94.59/94.38 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.38 => ( 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))
% 94.59/94.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 94.59/94.38
% 94.59/94.38 fof(fact_equiv__class__nondisjoint,axiom,
% 94.59/94.38 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.38 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.38 => ( 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)))))))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_subset__equiv__class,axiom,
% 94.59/94.39 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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))))))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_decr__lemma,axiom,
% 94.59/94.39 ! [V_z,V_x,V_d] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__abs,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__abs__ge__zero,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__minus__commute,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__setsum__abs,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__setprod,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( class_Fields_Olinordered__field(T_b)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__divide,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__one,axiom,
% 94.59/94.39 ! [T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__minus__cancel,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__eq__0,axiom,
% 94.59/94.39 ! [V_a_2,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 94.59/94.39 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__zero,axiom,
% 94.59/94.39 ! [T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__idempotent,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__mult__self,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__mult,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__add__abs,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_power__abs,axiom,
% 94.59/94.39 ! [V_n,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__of__nat,axiom,
% 94.59/94.39 ! [V_n,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__int__eq,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__le__D1,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__ge__self,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__ge__zero,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__le__zero__iff,axiom,
% 94.59/94.39 ! [V_a_2,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__of__nonneg,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__of__pos,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zero__less__abs__iff,axiom,
% 94.59/94.39 ! [V_a_2,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__not__less__zero,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ~ 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__triangle__ineq,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__mult__less,axiom,
% 94.59/94.39 ! [V_d,V_b,V_c,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 94.59/94.39 => 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))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__triangle__ineq3,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__triangle__ineq2,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__triangle__ineq2__sym,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__ge__minus__self,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__le__iff,axiom,
% 94.59/94.39 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.59/94.39 => ( 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))
% 94.59/94.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 94.59/94.39 & 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__leI,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__le__D2,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__less__iff,axiom,
% 94.59/94.39 ! [V_b_2,V_a_2,T_b] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 94.59/94.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nonzero__abs__divide,axiom,
% 94.59/94.39 ! [V_a,V_b,T_a] :
% 94.59/94.39 ( class_Fields_Olinordered__field(T_a)
% 94.59/94.39 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__power__minus,axiom,
% 94.59/94.39 ! [V_n,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__zmult__eq__1,axiom,
% 94.59/94.39 ! [V_n,V_m] :
% 94.59/94.39 ( 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)
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__sgn,axiom,
% 94.59/94.39 ! [V_k,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_mult__sgn__abs,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__mult__pos,axiom,
% 94.59/94.39 ! [V_y,V_x,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__eq__mult,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Oordered__ring__abs(T_a)
% 94.59/94.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.59/94.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 94.59/94.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 94.59/94.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__triangle__ineq4,axiom,
% 94.59/94.39 ! [V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__diff__triangle__ineq,axiom,
% 94.59/94.39 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__minus__le__zero,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__of__nonpos,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__of__neg,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__if,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Groups_Oabs__if(T_a)
% 94.59/94.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zero__le__power__abs,axiom,
% 94.59/94.39 ! [V_n,V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__div__pos,axiom,
% 94.59/94.39 ! [V_x,V_y,T_a] :
% 94.59/94.39 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__minus__one,axiom,
% 94.59/94.39 ! [T_a] :
% 94.59/94.39 ( ( class_Int_Onumber__ring(T_a)
% 94.59/94.39 & class_Rings_Olinordered__idom(T_a) )
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zabs__less__one__iff,axiom,
% 94.59/94.39 ! [V_z_2] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zabs__def,axiom,
% 94.59/94.39 ! [V_i] :
% 94.59/94.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 94.59/94.39 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__abs__mult__distrib,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zero__le__zpower__abs,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__class__self,axiom,
% 94.59/94.39 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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)))))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__number__of,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( ( class_Int_Onumber__ring(T_a)
% 94.59/94.39 & class_Rings_Olinordered__idom(T_a) )
% 94.59/94.39 => ( ( 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)))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( ~ 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)))
% 94.59/94.39 => 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) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__power__minus__one,axiom,
% 94.59/94.39 ! [V_n,T_a] :
% 94.59/94.39 ( ( class_Int_Onumber__ring(T_a)
% 94.59/94.39 & class_Rings_Olinordered__idom(T_a) )
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_zero__less__zpower__abs__iff,axiom,
% 94.59/94.39 ! [V_na_2,V_x_2] :
% 94.59/94.39 ( 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_na_2)))
% 94.59/94.39 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__class__eq,axiom,
% 94.59/94.39 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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))
% 94.59/94.39 => 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)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_abs__power2,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_power2__abs,axiom,
% 94.59/94.39 ! [V_a,T_a] :
% 94.59/94.39 ( class_Rings_Olinordered__idom(T_a)
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__class__eq__iff,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 94.59/94.39 <=> ( 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))))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_eq__equiv__class,axiom,
% 94.59/94.39 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_eq__equiv__class__iff,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.59/94.39 => ( 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))))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__class__subset,axiom,
% 94.59/94.39 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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))
% 94.59/94.39 => 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)))))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_incr__lemma,axiom,
% 94.59/94.39 ! [V_x,V_z,V_d] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_divmod__int__pdivmod,axiom,
% 94.59/94.39 ! [V_l_2,V_k_2] :
% 94.59/94.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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) )
% 94.59/94.39 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)))) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_divmod__int__code,axiom,
% 94.59/94.39 ! [V_l_2,V_k_2] :
% 94.59/94.39 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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) )
% 94.59/94.39 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)))) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_pdivmod__posDivAlg,axiom,
% 94.59/94.39 ! [V_k,V_l] :
% 94.59/94.39 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__conv,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_fst__apsnd,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__eq__conv,axiom,
% 94.59/94.39 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 94.59/94.39 ( 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)
% 94.59/94.39 <=> 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_snd__apsnd,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_negateSnd__def,axiom,
% 94.59/94.39 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__gcd_Osimps,axiom,
% 94.59/94.39 ! [V_x,V_y] :
% 94.59/94.39 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.39 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 94.59/94.39 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_pdivmod__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__gcd_Opsimps,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.39 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 94.59/94.39 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__quotient__disjoint,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( 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)
% 94.59/94.39 => 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) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_eq__equiv__class__iff2,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 94.59/94.39 => ( 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)
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__is__empty,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__is__empty2,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( 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)
% 94.59/94.39 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__empty,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__disj,axiom,
% 94.59/94.39 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( V_X_2 = V_Y_2
% 94.59/94.39 | 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)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__diff1,axiom,
% 94.59/94.39 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 94.59/94.39 ( 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)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotientI,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__eqI,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 94.59/94.39 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__eq__iff,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 94.59/94.39 => ( V_X_2 = V_Y_2
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_singleton__quotient,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__gcd_Opinduct,axiom,
% 94.59/94.39 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => ( ! [B_x,B_y] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotientE,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => ~ ! [B_x] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_quotient__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP1__I,axiom,
% 94.59/94.39 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__UN,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP1__iff,axiom,
% 94.59/94.39 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> ? [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Image__UN,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Image__eq__UN,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__I,axiom,
% 94.59/94.39 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__Pow__subset,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__eq__UN,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__equiv__class2,axiom,
% 94.59/94.39 ! [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] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 94.59/94.39 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 94.59/94.39 => 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) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_ball__UN,axiom,
% 94.59/94.39 ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( ! [B_x] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 => ! [B_xa] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 94.59/94.39 => hBOOL(hAPP(V_Pa_2,B_xa)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__le__add__shift,axiom,
% 94.59/94.39 ! [V_k_2,V_M_2,V_na_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_na_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_na_2),V_k_2))),V_M_2) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__commute,axiom,
% 94.59/94.39 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I9_J,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I9_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__UN__flatten,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_congruent2D,axiom,
% 94.59/94.39 ! [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] :
% 94.59/94.39 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 94.59/94.39 => ( 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))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__le__eq__Un0,axiom,
% 94.59/94.39 ! [V_M_2,V_na_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_na_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_na_2)),V_M_2)),hAPP(V_M_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__le__iff,axiom,
% 94.59/94.39 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.59/94.39 => ( 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))
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_less__SUP__iff,axiom,
% 94.59/94.39 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 94.59/94.39 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.59/94.39 & class_Orderings_Olinorder(T_b) )
% 94.59/94.39 => ( 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)))
% 94.59/94.39 <=> ? [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__iff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 <=> ? [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__const,axiom,
% 94.59/94.39 ! [V_M_2,T_b,V_A_2,T_c] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNION__empty__conv_I2_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__constant,axiom,
% 94.59/94.39 ! [V_c_2,T_c,T_b,V_A_2] :
% 94.59/94.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 94.59/94.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__empty2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNION__empty__conv_I1_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( 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)
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.59/94.39 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__subset__iff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I10_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__UN,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I10_J,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__Un__distrib,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__Un,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__UN__distrib2,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I4_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__UN__distrib,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I5_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I4_J,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I5_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUPR__apply,axiom,
% 94.59/94.39 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I6_J,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I6_J,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__subset,axiom,
% 94.59/94.39 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_le__SUPI,axiom,
% 94.59/94.39 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 94.59/94.39 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__insert__distrib,axiom,
% 94.59/94.39 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__upper,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__absorb,axiom,
% 94.59/94.39 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I1_J,axiom,
% 94.59/94.39 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__singleton,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I1_J,axiom,
% 94.59/94.39 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))) )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I3_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__simps_I2_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I3_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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 )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__extend__simps_I2_J,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.59/94.39 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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 )
% 94.59/94.39 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__insert,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_congruent2__implies__congruent__UN,axiom,
% 94.59/94.39 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 94.59/94.39 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 94.59/94.39 => 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)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_minus__int__def,axiom,
% 94.59/94.39 ! [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))))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__equiv__class,axiom,
% 94.59/94.39 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP2__I,axiom,
% 94.59/94.39 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 94.59/94.39 => 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_c_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Rep__Integ__inject,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2] :
% 94.59/94.39 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 94.59/94.39 <=> V_x_2 = V_y_2 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Rep__Integ__inverse,axiom,
% 94.59/94.39 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_congruentD,axiom,
% 94.59/94.39 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 94.59/94.39 => ( 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))
% 94.59/94.39 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__def,axiom,
% 94.59/94.39 ! [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)))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_congruent2__implies__congruent,axiom,
% 94.59/94.39 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__equiv__class__inject,axiom,
% 94.59/94.39 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 94.59/94.39 => ( 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)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => ! [B_y] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 94.59/94.39 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 94.59/94.39 => 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)) ) ) )
% 94.59/94.39 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__equiv__class__type2,axiom,
% 94.59/94.39 ! [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] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 94.59/94.39 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( ! [B_x1] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 94.59/94.39 => ! [B_x2] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 94.59/94.39 => 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)) ) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__equiv__class__type,axiom,
% 94.59/94.39 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 94.59/94.39 => 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)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP2__iff,axiom,
% 94.59/94.39 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 94.59/94.39 ( 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_c_2))
% 94.59/94.39 <=> ? [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apfst__apsnd,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__apfst,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apfst__conv,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apfst__eq__conv,axiom,
% 94.59/94.39 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.39 ( 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)
% 94.59/94.39 <=> 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_fst__apfst,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_snd__apfst,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__apfst__commute,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__def_H,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__empty,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Image__Id__on,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__iff,axiom,
% 94.59/94.39 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 94.59/94.39 ( 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_Relation_OId__on(T_b,V_A_2)))
% 94.59/94.39 <=> ( V_x_2 = V_y_2
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__eqI,axiom,
% 94.59/94.39 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 94.59/94.39 ( V_a_2 = V_b_2
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__onE,axiom,
% 94.59/94.39 ! [V_A_2,V_c_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 94.59/94.39 => ~ ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_compl__unique,axiom,
% 94.59/94.39 ! [V_y,V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.39 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 94.59/94.39 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 94.59/94.39 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 94.59/94.39 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.39 & class_Groups_Ocomm__monoid__mult(T_b) )
% 94.59/94.39 => ( V_A_2 = V_B_2
% 94.59/94.39 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.59/94.39 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 94.59/94.39 => 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) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNIV__I,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_top__greatest,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Orderings_Otop(T_a)
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_infinite__UNIV__nat,axiom,
% 94.59/94.39 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Pow__UNIV,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__UNIV__unit,axiom,
% 94.59/94.39 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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNIV__Plus__UNIV,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_top__apply,axiom,
% 94.59/94.39 ! [V_x_2,T_c,T_b] :
% 94.59/94.39 ( class_Orderings_Otop(T_b)
% 94.59/94.39 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Un__UNIV__left,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Un__UNIV__right,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNIV__not__empty,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_subset__UNIV,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__fun__UNIVD2,axiom,
% 94.59/94.39 ! [T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__option__UNIV,axiom,
% 94.59/94.39 ! [T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Prod__UNIV,axiom,
% 94.59/94.39 ! [T_c,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 94.59/94.39 => 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)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__UNIV,axiom,
% 94.59/94.39 ! [T_b] :
% 94.59/94.39 ( class_Finite__Set_Ofinite(T_b)
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Plus__UNIV__iff,axiom,
% 94.59/94.39 ! [T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__UNIV__right,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__UNIV__left,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_range__composition,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__intrel,axiom,
% 94.59/94.39 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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_infinite__UNIV__int,axiom,
% 94.59/94.39 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__int,axiom,
% 94.59/94.39 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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_injD,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 94.59/94.39 => V_x_2 = V_y_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__eq,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 94.59/94.39 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_sup__top__left,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_sup__top__right,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inf__top__left,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 94.59/94.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inf__top__right,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Obounded__lattice__top(T_a)
% 94.59/94.39 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inf__eq__top__iff,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,T_b] :
% 94.59/94.39 ( class_Lattices_Obounded__lattice__top(T_b)
% 94.59/94.39 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 94.59/94.39 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 94.59/94.39 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__lessThan__UNIV,axiom,
% 94.59/94.39 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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__atMost__UNIV,axiom,
% 94.59/94.39 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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_rangeI,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_range__eqI,axiom,
% 94.59/94.39 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 94.59/94.39 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__atLeast__UNIV,axiom,
% 94.59/94.39 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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Diff__UNIV,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 94.59/94.39 ! [V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__image__eq__iff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( 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)
% 94.59/94.39 <=> V_A_2 = V_B_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__empty__eq,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__UNIV__eq,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__compl,axiom,
% 94.59/94.39 ! [V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 94.59/94.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__partition2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__partition,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__UN__eq,axiom,
% 94.59/94.39 ! [V_x_2,V_r_2,T_c,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__range__imageI,axiom,
% 94.59/94.39 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 94.59/94.39 ( 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)))))
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_the__inv__f__f,axiom,
% 94.59/94.39 ! [V_x_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__fun__UNIVD1,axiom,
% 94.59/94.39 ! [T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__of__nat,axiom,
% 94.59/94.39 ! [T_b] :
% 94.59/94.39 ( class_Nat_Osemiring__char__0(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_atLeast__0,axiom,
% 94.59/94.39 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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__fun,axiom,
% 94.59/94.39 ! [T_d,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_compl__top__eq,axiom,
% 94.59/94.39 ! [T_a] :
% 94.59/94.39 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.39 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_compl__bot__eq,axiom,
% 94.59/94.39 ! [T_a] :
% 94.59/94.39 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.39 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_compl__sup__top,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_sup__compl__top,axiom,
% 94.59/94.39 ! [V_x,T_a] :
% 94.59/94.39 ( class_Lattices_Oboolean__algebra(T_a)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_range__ex1__eq,axiom,
% 94.59/94.39 ! [V_b_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( 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)))))
% 94.59/94.39 <=> ? [B_x] :
% 94.59/94.39 ( V_b_2 = hAPP(V_f_2,B_x)
% 94.59/94.39 & ! [B_y] :
% 94.59/94.39 ( V_b_2 = hAPP(V_f_2,B_y)
% 94.59/94.39 => B_y = B_x ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__image__mem__iff,axiom,
% 94.59/94.39 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__UNIV__inj__surj,axiom,
% 94.59/94.39 ! [V_f_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__UNIV__surj__inj,axiom,
% 94.59/94.39 ! [V_f_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__image__subset__iff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( 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)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__Int,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__set__diff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_surj__Compl__image__subset,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_b,T_c] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__UN__finite__eq,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__singleton,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__UNIV__card__ge__0,axiom,
% 94.59/94.39 ! [T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__UNIV__bool,axiom,
% 94.59/94.39 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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__image__Compl__subset,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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),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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_greaterThan__0,axiom,
% 94.59/94.39 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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SUP__UN__eq2,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 94.59/94.39 ( 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))),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))
% 94.59/94.39 <=> 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__finite2__subset,axiom,
% 94.59/94.39 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 94.59/94.39 ( ! [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)))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__finite2__eq,axiom,
% 94.59/94.39 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 94.59/94.39 ( ! [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)
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__finite__subset,axiom,
% 94.59/94.39 ! [V_C_2,V_A_2,T_b] :
% 94.59/94.39 ( ! [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))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_top1I,axiom,
% 94.59/94.39 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Integ__def,axiom,
% 94.59/94.39 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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_iso__tuple__UNIV__I,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equivp__equiv,axiom,
% 94.59/94.39 ! [V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 94.59/94.39 <=> 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_identity__equivp,axiom,
% 94.59/94.39 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equivp__def,axiom,
% 94.59/94.39 ! [V_R_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.59/94.39 <=> ! [B_x,B_y] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 94.59/94.39 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equivp__reflp,axiom,
% 94.59/94.39 ! [V_x_2,V_R_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equivp__symp,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equivp__transp,axiom,
% 94.59/94.39 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Rep__Integ,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition__Integ,axiom,
% 94.59/94.39 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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__vimage__singleton,axiom,
% 94.59/94.39 ! [V_a_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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),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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_accp__acc__eq,axiom,
% 94.59/94.39 ! [V_x_2,V_r_2,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimageI,axiom,
% 94.59/94.39 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 94.59/94.39 ( hAPP(V_f_2,V_a_2) = V_b_2
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__Int,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__eq,axiom,
% 94.59/94.39 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimageD,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimageI2,axiom,
% 94.59/94.39 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__mono,axiom,
% 94.59/94.39 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__empty,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__Un,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__code,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 94.59/94.39 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__ident,axiom,
% 94.59/94.39 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__Compl,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__Diff,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__UN,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__UNIV,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__vimage__subset,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_surj__image__vimage__eq,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_b,T_c] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => 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 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_acc__subset,axiom,
% 94.59/94.39 ! [V_R2_2,V_R1_2,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__singleton__eq,axiom,
% 94.59/94.39 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 94.59/94.39 ( 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))))))
% 94.59/94.39 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__insert,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__vimageD,axiom,
% 94.59/94.39 ! [V_F_2,V_h_2,T_c,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__subsetD,axiom,
% 94.59/94.39 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__vimage__eq,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__vimageI,axiom,
% 94.59/94.39 ! [V_h_2,T_c,V_F_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 94.59/94.39 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__vimage__image__eq,axiom,
% 94.59/94.39 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => 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 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__const,axiom,
% 94.59/94.39 ! [T_c,V_A_2,V_c_2,T_b] :
% 94.59/94.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__eq__UN,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_acc_Osimps,axiom,
% 94.59/94.39 ! [V_r_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 94.59/94.39 <=> ! [B_x] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_acc__downward,axiom,
% 94.59/94.39 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__subsetI,axiom,
% 94.59/94.39 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__if,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 94.59/94.39 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.39 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 94.59/94.39 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 94.59/94.39 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_OAbs__image,axiom,
% 94.59/94.39 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_ORep__range,axiom,
% 94.59/94.39 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => 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 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_OAbs__inject,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 94.59/94.39 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 94.59/94.39 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_ORep__inject,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 94.59/94.39 <=> V_x_2 = V_y_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_ORep__inverse,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_ORep,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_type__definition_OAbs__inverse,axiom,
% 94.59/94.39 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 94.59/94.39 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 94.59/94.39 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_max__extp_Oequations,axiom,
% 94.59/94.39 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 94.59/94.39 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 94.59/94.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 94.59/94.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 94.59/94.39 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 & ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 94.59/94.39 => ? [B_xa] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_max__ext_Ointros,axiom,
% 94.59/94.39 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 94.59/94.39 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 94.59/94.39 => ? [B_xa] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 94.59/94.39 => 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))) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Oone__frac__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Ofrac__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__split__eq__Sigma,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_int__val__lemma,axiom,
% 94.59/94.39 ! [V_k_2,V_f_2,V_na_2] :
% 94.59/94.39 ( ! [B_i] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2))
% 94.59/94.39 => 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))) )
% 94.59/94.39 => ( 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))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2)))
% 94.59/94.39 => ? [B_i] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2))
% 94.59/94.39 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat0__intermed__int__val,axiom,
% 94.59/94.39 ! [V_k_2,V_f_2,V_na_2] :
% 94.59/94.39 ( ! [B_i] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2))
% 94.59/94.39 => 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))) )
% 94.59/94.39 => ( 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))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2)))
% 94.59/94.39 => ? [B_i] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2))
% 94.59/94.39 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SigmaI,axiom,
% 94.59/94.39 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Diff__distrib2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__Diff__distrib1,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Diff__distrib1,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__eq__cancel2,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 94.59/94.39 => ( 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))
% 94.59/94.39 <=> V_A_2 = V_B_2 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__empty1,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__cartesian__product,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__cartesian__product,axiom,
% 94.59/94.39 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__empty,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__empty2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__Times__UNIV1,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__Times__UNIV2,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setprod__cartesian__product,axiom,
% 94.59/94.39 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__mult(T_b)
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Un__distrib2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__Un__distrib1,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Un__distrib1,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_swap__product,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__cartesian__product,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.59/94.39 => 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)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_equiv__type,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Int__distrib2,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__Int__distrib1,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__Int__distrib1,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Id__on__subset__Times,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNIV__Times__UNIV,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_mem__Sigma__iff,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SigmaD1,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SigmaD2,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SigmaE2,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__cartesian__product__singleton,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Times__subset__cancel2,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 94.59/94.39 => ( 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))))
% 94.59/94.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Image__subset,axiom,
% 94.59/94.39 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => 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)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__cartesian__productD1,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__cartesian__productD2,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_fst__image__times,axiom,
% 94.59/94.39 ! [V_A_2,T_c,T_b,V_B_2] :
% 94.59/94.39 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_snd__image__times,axiom,
% 94.59/94.39 ! [V_B_2,T_c,T_b,V_A_2] :
% 94.59/94.39 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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)) )
% 94.59/94.39 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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 ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_insert__times__insert,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__equiv__class,axiom,
% 94.59/94.39 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UN__Times__distrib,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Sigma__def,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__quotient,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 94.59/94.39 ! [V_A_2,V_I_2,T_c,T_b] :
% 94.59/94.39 ? [B_f] :
% 94.59/94.39 ( 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))
% 94.59/94.39 & 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_fold__image__Sigma,axiom,
% 94.59/94.39 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__SigmaI,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( ! [B_a] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setprod__Sigma,axiom,
% 94.59/94.39 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__Sigma,axiom,
% 94.59/94.39 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_d)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__SigmaI,axiom,
% 94.59/94.39 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 94.59/94.39 => 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) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SigmaE,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 94.59/94.39 => ~ ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => ! [B_y] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 94.59/94.39 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__surj,axiom,
% 94.59/94.39 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => ( 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))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__inj__on,axiom,
% 94.59/94.39 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.39 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__imageI,axiom,
% 94.59/94.39 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.39 ( 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))
% 94.59/94.39 => 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_fst__map__pair,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__simp,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__ident,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_snd__prod__fun,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair__surj__on,axiom,
% 94.59/94.39 ! [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] :
% 94.59/94.39 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 94.59/94.39 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_prod__fun__imageE,axiom,
% 94.59/94.39 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 94.59/94.39 => ~ ! [B_x,B_y] :
% 94.59/94.39 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 94.59/94.39 => ~ 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__on__def,axiom,
% 94.59/94.39 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 94.59/94.39 & ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setprod__pos__nat,axiom,
% 94.59/94.39 ! [V_f_2,V_S_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.59/94.39 => 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))) )
% 94.59/94.39 => 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))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__on__Id__on,axiom,
% 94.59/94.39 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__on__empty,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__on__Un,axiom,
% 94.59/94.39 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__on__Int,axiom,
% 94.59/94.39 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__onD,axiom,
% 94.59/94.39 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.59/94.39 => 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_a_2)),V_r_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__onD1,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__onD2,axiom,
% 94.59/94.39 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 94.59/94.39 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.39 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_refl__onI,axiom,
% 94.59/94.39 ! [V_A_2,V_r_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 94.59/94.39 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Rep__Integ__cases,axiom,
% 94.59/94.39 ! [V_y_2] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 94.59/94.39 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Rep__Integ__induct,axiom,
% 94.59/94.39 ! [V_Pa_2,V_y_2] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 94.59/94.39 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
% 94.59/94.39 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.39 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( 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)))
% 94.59/94.39 => hAPP(V_g_2,B_x) = V_z_2 )
% 94.59/94.39 => 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)) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__less__Suc,axiom,
% 94.59/94.39 ! [V_i_2,V_M_2] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__less,axiom,
% 94.59/94.39 ! [V_i_2,V_M_2] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 94.59/94.39 => 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) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_CollectI,axiom,
% 94.59/94.39 ! [T_b,V_a_2,V_Pa_2] :
% 94.59/94.39 ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.59/94.39 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__conjI,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_b] :
% 94.59/94.39 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__less__nat,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__le__nat,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_SetCompr__Sigma__eq,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__split,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__neg__eq,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__conj__eq,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_empty__Collect__eq,axiom,
% 94.59/94.39 ! [V_Pa_2,T_b] :
% 94.59/94.39 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
% 94.59/94.39 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__empty__eq,axiom,
% 94.59/94.39 ! [V_Pa_2,T_b] :
% 94.59/94.39 ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__def,axiom,
% 94.59/94.39 ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__disj__eq,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_insert__Collect,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_empty__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__disjI,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_Pa_2)),V_Q_2))))
% 94.59/94.39 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_UNIV__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__Collect__eq,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_CollectE,axiom,
% 94.59/94.39 ! [V_Pa_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_CollectD,axiom,
% 94.59/94.39 ! [V_Pa_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 => hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_mem__Collect__eq,axiom,
% 94.59/94.39 ! [V_Pa_2,V_a_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__mem__eq,axiom,
% 94.59/94.39 ! [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 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_insert__compr__raw,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_insert__compr,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Un__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__Collect,axiom,
% 94.59/94.39 ! [V_Pa_2,V_A_2,V_x_2,T_b] :
% 94.59/94.39 ( 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))))
% 94.59/94.39 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.39 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Int__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__conv__if,axiom,
% 94.59/94.39 ! [T_b,V_a_2,V_Pa_2] :
% 94.59/94.39 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.59/94.39 => 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))) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__conv__if2,axiom,
% 94.59/94.39 ! [T_b,V_a_2,V_Pa_2] :
% 94.59/94.39 ( ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.59/94.39 => 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))) )
% 94.59/94.39 & ( ~ hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_singleton__conv,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_singleton__conv2,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_set__diff__eq,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__not,axiom,
% 94.59/94.39 ! [V_Pa_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 => ( 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))))
% 94.59/94.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_insert__def,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Compl__eq,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Collect__imp__eq,axiom,
% 94.59/94.39 ! [V_Q_2,V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_Pa_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__M__bounded__by__nat,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__setsum__restrict,axiom,
% 94.59/94.39 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_d)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 94.59/94.39 => 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) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_if__image__distrib,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_nat__seg__image__imp__finite,axiom,
% 94.59/94.39 ! [V_na_2,V_f_2,T_b,V_A_2] :
% 94.59/94.39 ( 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_na_2)))
% 94.59/94.39 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__restrict__set_H,axiom,
% 94.59/94.39 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => 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) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__image__gen,axiom,
% 94.59/94.39 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.39 => 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)) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Image__singleton,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__cases,axiom,
% 94.59/94.39 ! [V_g_2,V_f_2,V_Pa_2,V_A_2,T_b,T_c] :
% 94.59/94.39 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => 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))))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_card__less__Suc2,axiom,
% 94.59/94.39 ! [V_i_2,V_M_2] :
% 94.59/94.39 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 94.59/94.39 => 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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__multicount,axiom,
% 94.59/94.39 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 94.59/94.39 => 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 )
% 94.59/94.39 => 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)) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Orderings_Olinorder(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Orderings_Olinorder(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))))) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__subsets,axiom,
% 94.59/94.39 ! [V_A_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => 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)))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Pow__Compl,axiom,
% 94.59/94.39 ! [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))))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Pow__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__Collect__bounded__ex,axiom,
% 94.59/94.39 ! [V_Q_2,T_c,V_Pa_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 => ( 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),V_Pa_2))),V_Q_2)))))
% 94.59/94.39 <=> ! [B_y] :
% 94.59/94.39 ( hBOOL(hAPP(V_Pa_2,B_y))
% 94.59/94.39 => 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_Q_2),B_y)))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__image__set,axiom,
% 94.59/94.39 ! [V_f_2,T_c,V_Pa_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
% 94.59/94.39 => 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_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))))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__graph,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_finite__psubset__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inv__image__def,axiom,
% 94.59/94.39 ! [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))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_add__Min__commute,axiom,
% 94.59/94.39 ! [V_k_2,V_N_2,T_b] :
% 94.59/94.39 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.39 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_add__Max__commute,axiom,
% 94.59/94.39 ! [V_k_2,V_N_2,T_b] :
% 94.59/94.39 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 94.59/94.39 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_sup__Inf1__distrib,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Lattices_Odistrib__lattice(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_sup__Inf2__distrib,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Lattices_Odistrib__lattice(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))))) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inf__Sup2__distrib,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Lattices_Odistrib__lattice(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))))) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inf__Sup1__distrib,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Lattices_Odistrib__lattice(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Orderings_Olinorder(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.39 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))))) ) ) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 94.59/94.39 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.39 ( class_Orderings_Olinorder(T_b)
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.39 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.39 => 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))))) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_Nitpick_Oprod__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_int__ge__less__than__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_int__ge__less__than2__def,axiom,
% 94.59/94.39 ! [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)))) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_reflp__def,axiom,
% 94.59/94.39 ! [V_r_2,T_b] :
% 94.59/94.39 ( c_Predicate_Oreflp(T_b,V_r_2)
% 94.59/94.39 <=> 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))) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 94.59/94.39 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.39 ( class_Rings_Osemiring__0(T_d)
% 94.59/94.39 => ( 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)))
% 94.59/94.39 => 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))))))) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_setsum__multicount__gen,axiom,
% 94.59/94.39 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 94.59/94.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 94.59/94.39 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 94.59/94.39 => ( ! [B_x] :
% 94.59/94.39 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 94.59/94.39 => 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) )
% 94.59/94.39 => 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) ) ) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_inj__on__id,axiom,
% 94.59/94.39 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_vimage__id,axiom,
% 94.59/94.39 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apfst__id,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_id__def,axiom,
% 94.59/94.39 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_id__apply,axiom,
% 94.59/94.39 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 94.59/94.39
% 94.59/94.39 fof(fact_reflpE,axiom,
% 94.59/94.39 ! [V_x_2,V_r_2,T_b] :
% 94.59/94.39 ( c_Predicate_Oreflp(T_b,V_r_2)
% 94.59/94.39 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__id,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair_Oid,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_map__pair_Oidentity,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_image__id,axiom,
% 94.59/94.39 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 94.59/94.39
% 94.59/94.39 fof(fact_of__int__eq__id,axiom,
% 94.59/94.39 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_surj__id,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apfst__def,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_apsnd__def,axiom,
% 94.59/94.39 ! [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) ).
% 94.59/94.39
% 94.59/94.39 fof(fact_split__Pair,axiom,
% 94.59/94.39 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__reindex__id,axiom,
% 94.59/94.40 ! [V_B_2,V_f_2,T_b,T_c] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setprod__reindex__id,axiom,
% 94.59/94.40 ! [V_B_2,V_f_2,T_b,T_c] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__conv__nat__seg__image,axiom,
% 94.59/94.40 ! [V_A_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 <=> ? [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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__def,axiom,
% 94.59/94.40 ! [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))))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__Collect__split,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__compI,axiom,
% 94.59/94.40 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_RangeI,axiom,
% 94.59/94.40 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__UNION__distrib2,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__UNION__distrib,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__mono,axiom,
% 94.59/94.40 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__empty1,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__empty2,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__distrib,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__distrib2,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_O__assoc,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__Id__on,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_union__comp__emptyR,axiom,
% 94.59/94.40 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_union__comp__emptyL,axiom,
% 94.59/94.40 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__empty,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__empty__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_b,T_c] :
% 94.59/94.40 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.40 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rel__comp__subset__Sigma,axiom,
% 94.59/94.40 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( 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))))
% 94.59/94.40 => ( 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))))
% 94.59/94.40 => 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)))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__Un__eq,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__Range,axiom,
% 94.59/94.40 ! [V_r_2,T_c,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 94.59/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_snd__eq__Range,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_c,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 94.59/94.40 <=> ? [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__insert,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__Int__subset,axiom,
% 94.59/94.40 ! [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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Range__Diff__subset,axiom,
% 94.59/94.40 ! [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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_max__ext__compat,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_min__ext__compat,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_RangeP__Range__eq,axiom,
% 94.59/94.40 ! [V_x_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_RangeE,axiom,
% 94.59/94.40 ! [V_r_2,T_c,V_b_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 94.59/94.40 => ~ ! [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_pred__comp__rel__comp__eq,axiom,
% 94.59/94.40 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_pred__comp_Ointros,axiom,
% 94.59/94.40 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_RangeP_Ointros,axiom,
% 94.59/94.40 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 94.59/94.40 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_pred__comp_Oequations,axiom,
% 94.59/94.40 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> ? [B_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 94.59/94.40 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_RangeP_Oequations,axiom,
% 94.59/94.40 ! [V_a2_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 94.59/94.40 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_reduction__pairI,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__Collect__split,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_pigeonhole__infinite,axiom,
% 94.59/94.40 ! [V_f_2,T_c,V_A_2,T_b] :
% 94.59/94.40 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.59/94.40 => ? [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 & ~ 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)))))) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__less__than,axiom,
% 94.59/94.40 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__empty,axiom,
% 94.59/94.40 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__inv__image,axiom,
% 94.59/94.40 ! [V_f_2,T_c,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__lex__prod,axiom,
% 94.59/94.40 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 94.59/94.40 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__measure,axiom,
% 94.59/94.40 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_DomainI,axiom,
% 94.59/94.40 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__comp__self,axiom,
% 94.59/94.40 ! [V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_min__ext__wf,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__subset,axiom,
% 94.59/94.40 ! [V_p_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__finite__psubset,axiom,
% 94.59/94.40 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__Int1,axiom,
% 94.59/94.40 ! [V_r_H_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__Int2,axiom,
% 94.59/94.40 ! [V_r_H_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_max__ext__wf,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__pair__less,axiom,
% 94.59/94.40 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__Id__on,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__mlex,axiom,
% 94.59/94.40 ! [V_f_2,V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__less,axiom,
% 94.59/94.40 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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__irrefl,axiom,
% 94.59/94.40 ! [V_a_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ~ hBOOL(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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__asym,axiom,
% 94.59/94.40 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ( hBOOL(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))
% 94.59/94.40 => ~ hBOOL(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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__not__sym,axiom,
% 94.59/94.40 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ( hBOOL(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))
% 94.59/94.40 => ~ hBOOL(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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__not__refl,axiom,
% 94.59/94.40 ! [V_a_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ~ hBOOL(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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__int__ge__less__than2,axiom,
% 94.59/94.40 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__int__ge__less__than,axiom,
% 94.59/94.40 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__Un,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__acc__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_acc__wfD,axiom,
% 94.59/94.40 ! [V_x_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__no__loop,axiom,
% 94.59/94.40 ! [V_R_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__union__merge,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__empty,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__empty__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_c,T_b] :
% 94.59/94.40 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.40 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__mono,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__Un__eq,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__Domain,axiom,
% 94.59/94.40 ! [V_r_2,T_c,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 94.59/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fst__eq__Domain,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 <=> ~ ? [B_f] :
% 94.59/94.40 ! [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfE__pf,axiom,
% 94.59/94.40 ! [V_A_2,V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 => ( 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)))
% 94.59/94.40 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__union__compatible,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_c,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 94.59/94.40 <=> ? [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf,axiom,
% 94.59/94.40 ! [T_b] :
% 94.59/94.40 ( class_Orderings_Owellorder(T_b)
% 94.59/94.40 => 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)))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__insert,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_reduction__pair__def,axiom,
% 94.59/94.40 ! [V_Pa_2,T_b] :
% 94.59/94.40 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 94.59/94.40 <=> ( 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))
% 94.59/94.40 & 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_reduction__pair__lemma,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,V_Pa_2,T_b] :
% 94.59/94.40 ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
% 94.59/94.40 => ( 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)))
% 94.59/94.40 => ( 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)))
% 94.59/94.40 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 94.59/94.40 => 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)) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__Int__subset,axiom,
% 94.59/94.40 ! [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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Domain__Diff__subset,axiom,
% 94.59/94.40 ! [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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Field__def,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__map__pair__image,axiom,
% 94.59/94.40 ! [V_f_2,T_c,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_DomainP__Domain__eq,axiom,
% 94.59/94.40 ! [V_x_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__lenlex,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_DomainE,axiom,
% 94.59/94.40 ! [V_r_2,T_c,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 94.59/94.40 => ~ ! [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_DomainP_Ointros,axiom,
% 94.59/94.40 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 94.59/94.40 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_DomainP_Oequations,axiom,
% 94.59/94.40 ! [V_a1_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 94.59/94.40 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_pred__nat__def,axiom,
% 94.59/94.40 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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__lex,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__lexn,axiom,
% 94.59/94.40 ! [V_na_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_lex__def,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_lexn_Osimps_I1_J,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__pred__nat,axiom,
% 94.59/94.40 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__same__fst,axiom,
% 94.59/94.40 ! [T_b,V_R_2,T_c,V_Pa_2] :
% 94.59/94.40 ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.59/94.40 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 94.59/94.40 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__if__measure,axiom,
% 94.59/94.40 ! [T_b,V_g_2,V_f_2,V_Pa_2] :
% 94.59/94.40 ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.59/94.40 => 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))) )
% 94.59/94.40 => 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))))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__def,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 94.59/94.40 <=> 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__empty,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_accp__wfPD,axiom,
% 94.59/94.40 ! [V_x_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 94.59/94.40 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__accp__iff,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 94.59/94.40 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__subset,axiom,
% 94.59/94.40 ! [V_p_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__in__rel,axiom,
% 94.59/94.40 ! [V_R_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_R_2)
% 94.59/94.40 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__wf__eq,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__acyclicP,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_refl__on__def_H,axiom,
% 94.59/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.59/94.40 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.59/94.40 <=> ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 94.59/94.40 => 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)) )
% 94.59/94.40 & ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Abs__Integ__induct,axiom,
% 94.59/94.40 ! [V_x_2,V_Pa_2] :
% 94.59/94.40 ( ! [B_y] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_ball__empty,axiom,
% 94.59/94.40 ! [V_Pa_2,T_b,B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__acyclic,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_acyclic__subset,axiom,
% 94.59/94.40 ! [V_r_2,V_s_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Powp__def,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 94.59/94.40 <=> ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 94.59/94.40 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_congruent__def,axiom,
% 94.59/94.40 ! [V_f_2,V_r_2,T_c,T_b] :
% 94.59/94.40 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 94.59/94.40 <=> ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__acyclic__wf,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 94.59/94.40 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 94.59/94.40 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Nitpick_Owf_H__def,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 94.59/94.40 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.59/94.40 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 94.59/94.40 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Abs__Integ__cases,axiom,
% 94.59/94.40 ! [V_x_2] :
% 94.59/94.40 ~ ! [B_y] :
% 94.59/94.40 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 94.59/94.40 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__UN__I,axiom,
% 94.59/94.40 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( ! [B_a] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 94.59/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 94.59/94.40 => 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfP__SUP,axiom,
% 94.59/94.40 ! [T_b,V_r_2,T_c] :
% 94.59/94.40 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 94.59/94.40 => ( ! [B_i,B_j] :
% 94.59/94.40 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 94.59/94.40 => 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)) )
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_mem__splitE,axiom,
% 94.59/94.40 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
% 94.59/94.40 => ~ ! [B_x,B_y] :
% 94.59/94.40 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 94.59/94.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_mem__splitI2,axiom,
% 94.59/94.40 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 94.59/94.40 ( ! [B_a,B_b] :
% 94.59/94.40 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_vimage__Times,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__SucD,axiom,
% 94.59/94.40 ! [V_na_2,V_A_2,V_f_2,T_b] :
% 94.59/94.40 ( 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_na_2)
% 94.59/94.40 => ? [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 & 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Eps__split,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_id__o,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__id,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__eq__id__dest,axiom,
% 94.59/94.40 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 94.59/94.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
% 94.59/94.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_exE__some,axiom,
% 94.59/94.40 ! [T_b,V_c_2,V_Pa_2] :
% 94.59/94.40 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.59/94.40 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_vimage__compose,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_apfst__compose,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 94.59/94.40 ! [V_x_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.59/94.40 => 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) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__def,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_someI__ex,axiom,
% 94.59/94.40 ! [T_b,V_Pa_2] :
% 94.59/94.40 ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_some__eq__ex,axiom,
% 94.59/94.40 ! [T_b,V_Pa_2] :
% 94.59/94.40 ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
% 94.59/94.40 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_some__eq__trivial,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_some__sym__eq__trivial,axiom,
% 94.59/94.40 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__assoc,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__apply,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__eq__dest,axiom,
% 94.59/94.40 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 94.59/94.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 94.59/94.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__eq__elim,axiom,
% 94.59/94.40 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 94.59/94.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 94.59/94.40 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_tfl__some,axiom,
% 94.59/94.40 ! [T_b,B_P] :
% 94.59/94.40 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 94.59/94.40 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_someI,axiom,
% 94.59/94.40 ! [T_b,V_x_2,V_Pa_2] :
% 94.59/94.40 ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_comp__cong,axiom,
% 94.59/94.40 ! [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] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fun__upd__comp,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_apsnd__compose,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_o__eq__dest__lhs,axiom,
% 94.59/94.40 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 94.59/94.40 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 94.59/94.40 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_K__record__comp,axiom,
% 94.59/94.40 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_map__pair_Ocompositionality,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_map__pair__compose,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_map__pair_Ocomp,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_image__compose,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_inj__on__imageI2,axiom,
% 94.59/94.40 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 94.59/94.40 ( 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)
% 94.59/94.40 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_inj__on__imageI,axiom,
% 94.59/94.40 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 94.59/94.40 ( 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)
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_comp__inj__on,axiom,
% 94.59/94.40 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_comp__inj__on__iff,axiom,
% 94.59/94.40 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.40 => ( 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))
% 94.59/94.40 <=> 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_inj__comp,axiom,
% 94.59/94.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 94.59/94.40 => 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_comp__surj,axiom,
% 94.59/94.40 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__reindex,axiom,
% 94.59/94.40 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__add(T_d)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.40 => 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setprod__reindex,axiom,
% 94.59/94.40 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 94.59/94.40 => 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setprod__reindex__cong,axiom,
% 94.59/94.40 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.40 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 94.59/94.40 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 94.59/94.40 => 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) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Eps__split__eq,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_split__paired__Eps,axiom,
% 94.59/94.40 ! [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)))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum_Oreindex,axiom,
% 94.59/94.40 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setprod_Oreindex,axiom,
% 94.59/94.40 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_the__inv__into__comp,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 94.59/94.40 => ( 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))))
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fold__image__reindex,axiom,
% 94.59/94.40 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Oab__semigroup__mult(T_d)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Oremove,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__image_Oreindex,axiom,
% 94.59/94.40 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.40 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ounion,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 94.59/94.40 ! [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] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 94.59/94.40 => 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) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__comp,axiom,
% 94.59/94.40 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__left__comp,axiom,
% 94.59/94.40 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_UN__o,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fst__comp__map__pair,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_snd__comp__map__pair,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__image_Odistrib,axiom,
% 94.59/94.40 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_split__comp,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__comp_H,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 94.59/94.40 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 94.59/94.40 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Oempty,axiom,
% 94.59/94.40 ! [V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__image_Oeq__fold,axiom,
% 94.59/94.40 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.59/94.40 => 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Oinsert,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Ounion__inter,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding_Oinsert__remove,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__reindex__nonzero,axiom,
% 94.59/94.40 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__add(T_d)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 94.59/94.40 => ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.59/94.40 => ! [B_y] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 94.59/94.40 => ( B_x != B_y
% 94.59/94.40 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 94.59/94.40 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Ounion__idem,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.59/94.40 => 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)) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 94.59/94.40 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Oidem__comp,axiom,
% 94.59/94.40 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => 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) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 94.59/94.40 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => 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) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_folding__idem_Oinsert__idem,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.59/94.40 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_strong__setprod__reindex__cong,axiom,
% 94.59/94.40 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.40 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 94.59/94.40 => ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 => 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) )
% 94.59/94.40 => 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) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_nat__mod__eq__lemma,axiom,
% 94.59/94.40 ! [V_y,V_n,V_x] :
% 94.59/94.40 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 94.59/94.40 => ? [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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wfI__pf,axiom,
% 94.59/94.40 ! [V_R_2,T_b] :
% 94.59/94.40 ( ! [B_A] :
% 94.59/94.40 ( 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)))
% 94.59/94.40 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 94.59/94.40 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Sigma__mono,axiom,
% 94.59/94.40 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 94.59/94.40 => ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 => 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))) )
% 94.59/94.40 => 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_not__acc__down,axiom,
% 94.59/94.40 ! [V_R_2,V_x_2,T_b] :
% 94.59/94.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 94.59/94.40 => ~ ! [B_z] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_acc_OaccI,axiom,
% 94.59/94.40 ! [V_r_2,V_x_2,T_b] :
% 94.59/94.40 ( ! [B_y] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_max__ext_Osimps,axiom,
% 94.59/94.40 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 94.59/94.40 ( 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)))
% 94.59/94.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 94.59/94.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 94.59/94.40 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.59/94.40 & ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 94.59/94.40 => ? [B_xa] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 94.59/94.40 & 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)) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_mod__induct__0,axiom,
% 94.59/94.40 ! [V_i_2,V_Pa_2,V_p_2] :
% 94.59/94.40 ( ! [B_i] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 94.59/94.40 => ( hBOOL(hAPP(V_Pa_2,B_i))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 94.59/94.40 => ( hBOOL(hAPP(V_Pa_2,V_i_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 94.59/94.40 => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_fold__image__cong,axiom,
% 94.59/94.40 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 94.59/94.40 ( class_Groups_Oab__semigroup__mult(T_c)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.59/94.40 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 94.59/94.40 => 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) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Max__eqI,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.40 ( class_Orderings_Olinorder(T_b)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( ! [B_y] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.40 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Min__eqI,axiom,
% 94.59/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.59/94.40 ( class_Orderings_Olinorder(T_b)
% 94.59/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.59/94.40 => ( ! [B_y] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.59/94.40 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__no__infinite__down__chainE,axiom,
% 94.59/94.40 ! [V_f_2,V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => ~ ! [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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__reindex__cong,axiom,
% 94.59/94.40 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 94.59/94.40 ( class_Groups_Ocomm__monoid__add(T_d)
% 94.59/94.40 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.59/94.40 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 94.59/94.40 => ( ! [B_a] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 94.59/94.40 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 94.59/94.40 => 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) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_scomp__unfold,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_setsum__ivl__cong,axiom,
% 94.59/94.40 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 94.59/94.40 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 94.59/94.40 & class_Orderings_Oord(T_b) )
% 94.59/94.40 => ( V_a_2 = V_c_2
% 94.59/94.40 => ( V_b_2 = V_d_2
% 94.59/94.40 => ( ! [B_x] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 94.59/94.40 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 94.59/94.40 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Pair__scomp,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_scomp__Pair,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_scomp__scomp,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_scomp__apply,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_scomp__def,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_iterate_Osimps,axiom,
% 94.59/94.40 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 94.59/94.40 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.59/94.40 => 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) )
% 94.59/94.40 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_less__eq,axiom,
% 94.59/94.40 ! [V_na_2,V_m_2] :
% 94.59/94.40 ( 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_na_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 94.59/94.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_nat__intermed__int__val,axiom,
% 94.59/94.40 ! [V_k_2,V_f_2,V_na_2,V_m_2] :
% 94.59/94.40 ( ! [B_i] :
% 94.59/94.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 94.59/94.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2)) )
% 94.59/94.40 => 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))) )
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2)))
% 94.59/94.40 => ? [B_i] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 94.59/94.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2))
% 94.59/94.40 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_wf__trancl,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.59/94.40 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_less__than__def,axiom,
% 94.59/94.40 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_acyclic__def,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.59/94.40 <=> ! [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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl_Or__into__trancl,axiom,
% 94.59/94.40 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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))
% 94.59/94.40 => hBOOL(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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__subset__Field2,axiom,
% 94.59/94.40 ! [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))))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__Int__subset,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_r__into__trancl_H,axiom,
% 94.59/94.40 ! [V_r_2,V_p_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__empty,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__domain,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__range,axiom,
% 94.59/94.40 ! [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) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_finite__trancl,axiom,
% 94.59/94.40 ! [V_r_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 94.59/94.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_r__r__into__trancl,axiom,
% 94.59/94.40 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__into__trancl2,axiom,
% 94.59/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 94.59/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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)))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__trans,axiom,
% 94.59/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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)))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__mono,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__unfold,axiom,
% 94.59/94.40 ! [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)) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__subset__Sigma,axiom,
% 94.59/94.40 ! [V_A_2,V_r_2,T_b] :
% 94.59/94.40 ( 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))))
% 94.59/94.40 => 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)))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_log_Osimps,axiom,
% 94.59/94.40 ! [V_i,V_b] :
% 94.59/94.40 ( ( ( 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)))
% 94.59/94.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 94.59/94.40 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 94.59/94.40 & ( ~ ( 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)))
% 94.59/94.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 94.59/94.40 => 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))) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_minus__shift__def,axiom,
% 94.59/94.40 ! [V_r,V_l,V_k] :
% 94.59/94.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 94.59/94.40 => 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) )
% 94.59/94.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 94.59/94.40 => 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) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_inc__shift__def,axiom,
% 94.59/94.40 ! [V_k,V_v] :
% 94.59/94.40 ( ( V_v = V_k
% 94.59/94.40 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 94.59/94.40 & ( V_v != V_k
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_range,axiom,
% 94.59/94.40 ! [V_s,V_k] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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)) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__insert,axiom,
% 94.59/94.40 ! [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)))))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_reflcl__set__eq,axiom,
% 94.59/94.40 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 <=> hBOOL(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)))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_r__into__rtrancl,axiom,
% 94.59/94.40 ! [V_r_2,V_p_2,T_b] :
% 94.59/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 94.59/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_IdI,axiom,
% 94.59/94.40 ! [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))) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_trancl__into__rtrancl,axiom,
% 94.59/94.40 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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)))
% 94.59/94.40 => hBOOL(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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl__Int__subset,axiom,
% 94.59/94.40 ! [V_r_2,V_s_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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))
% 94.59/94.40 => 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)) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Image__closed__trancl,axiom,
% 94.59/94.40 ! [V_X_2,V_r_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl__mono,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl__subset,axiom,
% 94.59/94.40 ! [V_S_2,V_R_2,T_b] :
% 94.59/94.40 ( 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))
% 94.59/94.40 => ( 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)))
% 94.59/94.40 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl__subset__rtrancl,axiom,
% 94.59/94.40 ! [V_s_2,V_r_2,T_b] :
% 94.59/94.40 ( 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)))
% 94.59/94.40 => 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))) ) ).
% 94.59/94.40
% 94.59/94.40 fof(fact_R__O__Id,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Id__O__R,axiom,
% 94.59/94.40 ! [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 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_Image__Id,axiom,
% 94.59/94.40 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 94.59/94.40
% 94.59/94.40 fof(fact_rtrancl__trans,axiom,
% 94.59/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.59/94.40 ( hBOOL(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)))
% 94.59/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 94.64/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 94.64/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__idemp,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__r__diff__Id,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__reflcl,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__Un__rtrancl,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__reflcl__absorb,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__idemp__self__comp,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_r__comp__rtrancl__eq,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__unfold,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__empty,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_reflcl__trancl,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__reflcl,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__trancl__absorb,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__rtrancl__absorb,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_in__rtrancl__UnI,axiom,
% 94.64/94.40 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 94.64/94.40 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 94.64/94.40 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 94.64/94.40 => 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)))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Domain__rtrancl,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Range__rtrancl,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_refl__rtrancl,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__unfold__right,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__unfold__left,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__Un__subset,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_pair__in__Id__conv,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 <=> V_a_2 = V_b_2 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__trancl__trancl,axiom,
% 94.64/94.40 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( 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)))
% 94.64/94.40 => hBOOL(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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__rtrancl__trancl,axiom,
% 94.64/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__into__trancl1,axiom,
% 94.64/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtranclD,axiom,
% 94.64/94.40 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( V_a_2 = V_b_2
% 94.64/94.40 | ( V_a_2 != V_b_2
% 94.64/94.40 & hBOOL(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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__into__trancl2,axiom,
% 94.64/94.40 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__eq__or__trancl,axiom,
% 94.64/94.40 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 <=> ( V_x_2 = V_y_2
% 94.64/94.40 | ( V_x_2 != V_y_2
% 94.64/94.40 & hBOOL(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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Domain__Id,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Range__Id,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_refl__Id,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_pair__leq__def,axiom,
% 94.64/94.40 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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Not__Domain__rtrancl,axiom,
% 94.64/94.40 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 94.64/94.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 94.64/94.40 => ( hBOOL(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)))
% 94.64/94.40 <=> V_x_2 = V_y_2 ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_acc__downwards,axiom,
% 94.64/94.40 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 94.64/94.40 => ( 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)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_acc__downwards__aux,axiom,
% 94.64/94.40 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_wf__insert,axiom,
% 94.64/94.40 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.64/94.40 & ~ hBOOL(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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_acyclic__insert,axiom,
% 94.64/94.40 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.64/94.40 & ~ hBOOL(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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_refl__reflcl,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Id__def,axiom,
% 94.64/94.40 ! [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))))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_irrefl__diff__Id,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_pred__nat__trancl__eq__le,axiom,
% 94.64/94.40 ! [V_na_2,V_m_2] :
% 94.64/94.40 ( 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_na_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
% 94.64/94.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__subset__Sigma__aux,axiom,
% 94.64/94.40 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ( 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))))
% 94.64/94.40 => ( V_a_2 = V_b_2
% 94.64/94.40 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_irrefl__tranclI,axiom,
% 94.64/94.40 ! [V_x_2,V_r_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ~ hBOOL(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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_sequence__trans,axiom,
% 94.64/94.40 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 94.64/94.40 ( ! [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)))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_total__on__diff__Id,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__Id,axiom,
% 94.64/94.40 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__converse,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__converse,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_acyclic__converse,axiom,
% 94.64/94.40 ! [V_r_2,T_b] :
% 94.64/94.40 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.40 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_refl__on__converse,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.40 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__converse,axiom,
% 94.64/94.40 ! [V_r_2,T_c,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 94.64/94.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__Id__on,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Field__converse,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__converse,axiom,
% 94.64/94.40 ! [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 ).
% 94.64/94.40
% 94.64/94.40 fof(fact_total__on__converse,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.40 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__inv__image,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__Int,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__Un,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__rel__comp,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__UNION,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__iff,axiom,
% 94.64/94.40 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 <=> 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converseI,axiom,
% 94.64/94.40 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converseD,axiom,
% 94.64/94.40 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_wf__converse__trancl,axiom,
% 94.64/94.40 ! [V_r_2,T_b] :
% 94.64/94.40 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.40 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_equiv__comp__eq,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.64/94.40 => 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 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Range__def,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Domain__converse,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Range__converse,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_total__on__empty,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__converseI,axiom,
% 94.64/94.40 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => hBOOL(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)))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__converseD,axiom,
% 94.64/94.40 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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))))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__converseD,axiom,
% 94.64/94.40 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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))))
% 94.64/94.40 => hBOOL(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)))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__converseI,axiom,
% 94.64/94.40 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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))))
% 94.64/94.40 => hBOOL(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)))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Image__subset__eq,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> 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))))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_refl__on__comp__subset,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_comp__equivI,axiom,
% 94.64/94.40 ! [V_A_2,V_r_2,T_b] :
% 94.64/94.40 ( 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
% 94.64/94.40 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 94.64/94.40 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__acyclic__wf__converse,axiom,
% 94.64/94.40 ! [V_r_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 94.64/94.40 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.64/94.40 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_total__on__def,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.40 => ! [B_xa] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 94.64/94.40 => ( B_x != B_xa
% 94.64/94.40 => ( 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))
% 94.64/94.40 | 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)) ) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__def,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 94.64/94.40 ! [V_R_2,V_p_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 94.64/94.40 => 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)))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_acyclicI,axiom,
% 94.64/94.40 ! [V_r_2,T_b] :
% 94.64/94.40 ( ! [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)))
% 94.64/94.40 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Image__Int__eq,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__subset,axiom,
% 94.64/94.40 ! [V_s_2,V_r_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 94.64/94.40 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_comp__funpow,axiom,
% 94.64/94.40 ! [V_f_2,V_na_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_na_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_na_2),V_f_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_wf__exp,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,T_b] :
% 94.64/94.40 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))
% 94.64/94.40 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow__mult,axiom,
% 94.64/94.40 ! [V_f_2,V_m_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_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_na_2)),V_f_2) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow__swap1,axiom,
% 94.64/94.40 ! [V_x_2,V_na_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__1,axiom,
% 94.64/94.40 ! [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 ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__rel__pow,axiom,
% 94.64/94.40 ! [V_na_2,V_R_2,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 94.64/94.40 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__commute,axiom,
% 94.64/94.40 ! [V_na_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_na_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_na_2),V_R_2)),V_R_2) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__rel__comp,axiom,
% 94.64/94.40 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 94.64/94.40 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__Id,axiom,
% 94.64/94.40 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__imp__rtrancl,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_p_2,T_b] :
% 94.64/94.40 ( 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_na_2),V_R_2)))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__power,axiom,
% 94.64/94.40 ! [V_R_2,V_p_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 94.64/94.40 <=> ? [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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__Id__on,axiom,
% 94.64/94.40 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_relpow_Osimps_I2_J,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_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_na_2),V_R_2)),V_R_2) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__add,axiom,
% 94.64/94.40 ! [V_R_2,V_na_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_na_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_na_2),V_R_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_relpow_Osimps_I1_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__0__I,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__0__E,axiom,
% 94.64/94.40 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => V_x_2 = V_y_2 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__Suc__I2,axiom,
% 94.64/94.40 ! [V_na_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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))
% 94.64/94.40 => ( 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_na_2),V_R_2)))
% 94.64/94.40 => hBOOL(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_na_2)),V_R_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__Suc__I,axiom,
% 94.64/94.40 ! [V_z_2,V_R_2,V_na_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2),V_R_2)))
% 94.64/94.40 => ( 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))
% 94.64/94.40 => hBOOL(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_na_2)),V_R_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow_Osimps_I2_J,axiom,
% 94.64/94.40 ! [V_f_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_na_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_na_2),V_f_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow__add,axiom,
% 94.64/94.40 ! [V_f_2,V_na_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_na_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_na_2),V_f_2)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valuedD,axiom,
% 94.64/94.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 94.64/94.40 => ( 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))
% 94.64/94.40 => ( 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))
% 94.64/94.40 => V_y_2 = V_z_2 ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__def,axiom,
% 94.64/94.40 ! [V_r_2,T_c,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 94.64/94.40 <=> ! [B_x,B_y] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ! [B_z] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => B_y = B_z ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow_Osimps_I1_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_trancl__power,axiom,
% 94.64/94.40 ! [V_R_2,V_p_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 94.64/94.40 <=> ? [B_n] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 94.64/94.40 & 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_single__valued__confluent,axiom,
% 94.64/94.40 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 94.64/94.40 => ( hBOOL(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)))
% 94.64/94.40 => ( hBOOL(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)))
% 94.64/94.40 => ( 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)))
% 94.64/94.40 | 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))) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_funpow__code__def,axiom,
% 94.64/94.40 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__E2,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2),V_R_2)))
% 94.64/94.40 => ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.40 => V_x_2 != V_z_2 )
% 94.64/94.40 => ~ ! [B_y,B_m] :
% 94.64/94.40 ( V_na_2 = hAPP(c_Nat_OSuc,B_m)
% 94.64/94.40 => ( 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))
% 94.64/94.40 => ~ 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))) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__E,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2),V_R_2)))
% 94.64/94.40 => ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.40 => V_x_2 != V_z_2 )
% 94.64/94.40 => ~ ! [B_y,B_m] :
% 94.64/94.40 ( V_na_2 = hAPP(c_Nat_OSuc,B_m)
% 94.64/94.40 => ( 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)))
% 94.64/94.40 => ~ 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)) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__Un__separatorE,axiom,
% 94.64/94.40 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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_Q_2))))
% 94.64/94.40 => ( ! [B_x] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ! [B_y] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
% 94.64/94.40 => B_x = B_y ) )
% 94.64/94.40 => hBOOL(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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 94.64/94.40 ! [V_Q_2,V_Pa_2,V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(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_Q_2))))
% 94.64/94.40 => ( ! [B_x] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ! [B_y] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
% 94.64/94.40 => B_y = B_x ) )
% 94.64/94.40 => hBOOL(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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__Suc__D2,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2)),V_R_2)))
% 94.64/94.40 => ? [B_y] :
% 94.64/94.40 ( 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))
% 94.64/94.40 & 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_na_2),V_R_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__Suc__E,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2)),V_R_2)))
% 94.64/94.40 => ~ ! [B_y] :
% 94.64/94.40 ( 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_na_2),V_R_2)))
% 94.64/94.40 => ~ 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_rel__pow__Suc__E2,axiom,
% 94.64/94.40 ! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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_na_2)),V_R_2)))
% 94.64/94.40 => ~ ! [B_y] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ~ 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_na_2),V_R_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_tranclD,axiom,
% 94.64/94.40 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ? [B_z] :
% 94.64/94.40 ( 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))
% 94.64/94.40 & 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_tranclD2,axiom,
% 94.64/94.40 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 94.64/94.40 ( hBOOL(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)))
% 94.64/94.40 => ? [B_z] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 & 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_IdE,axiom,
% 94.64/94.40 ! [V_p_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 94.64/94.40 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__empty,axiom,
% 94.64/94.40 ! [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 ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__image__def,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_folding_Oeq__fold,axiom,
% 94.64/94.40 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__def,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_union__fold__insert,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__sup__insert,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Osemilattice__sup(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__inf__insert,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Osemilattice__inf(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_Ofold__inf__insert,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_Ofold__sup__insert,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 94.64/94.40 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 94.64/94.40 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_sup__SUPR__fold__sup,axiom,
% 94.64/94.40 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_sup__le__fold__sup,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Osemilattice__sup(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold__inf__le__inf,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Osemilattice__inf(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold1__eq__fold__idem,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Olattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Olattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_minus__fold__remove,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_folding__one_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_SUPR__fold__sup,axiom,
% 94.64/94.40 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fold1__eq__fold,axiom,
% 94.64/94.40 ! [V_a_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Olattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Lattices_Olattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Min_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Max_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 94.64/94.40 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Orderings_Olinorder(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 94.64/94.40 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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)))))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 94.64/94.40 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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)))))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INFI__fold__inf,axiom,
% 94.64/94.40 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__D,axiom,
% 94.64/94.40 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__E,axiom,
% 94.64/94.40 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 94.64/94.40 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF1__D,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF1__E,axiom,
% 94.64/94.40 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 94.64/94.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF2__D,axiom,
% 94.64/94.40 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF2__E,axiom,
% 94.64/94.40 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 94.64/94.40 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__INT,axiom,
% 94.64/94.40 ! [V_A_2,T_c,V_I_2,T_b] :
% 94.64/94.40 ( ? [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 94.64/94.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__empty,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__constant,axiom,
% 94.64/94.40 ! [V_c_2,T_c,T_b,V_A_2] :
% 94.64/94.40 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 94.64/94.40 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I9_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I9_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_le__INF__iff,axiom,
% 94.64/94.40 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( 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)))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__less__iff,axiom,
% 94.64/94.40 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 94.64/94.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 & class_Orderings_Olinorder(T_b) )
% 94.64/94.40 => ( 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))
% 94.64/94.40 <=> ? [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.64/94.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__insert__distrib,axiom,
% 94.64/94.40 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm,axiom,
% 94.64/94.40 ! [T_b] :
% 94.64/94.40 ( class_Groups_Oab__semigroup__mult(T_b)
% 94.64/94.40 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__iff,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__INT__eq2,axiom,
% 94.64/94.40 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.64/94.40 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b] :
% 94.64/94.40 ( 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)
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.64/94.40 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 94.64/94.40 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 94.64/94.40 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__Int__distrib,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INFI__apply,axiom,
% 94.64/94.40 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__commute,axiom,
% 94.64/94.40 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Pow__INT__eq,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I10_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I10_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I5_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I5_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INFI__bool__eq,axiom,
% 94.64/94.40 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_vimage__INT,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 94.64/94.40 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__subset__iff,axiom,
% 94.64/94.40 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 94.64/94.40 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 94.64/94.40 => V_y_2 = V_x_2 ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Un__INT__distrib2,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I6_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Un__INT__distrib,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I7_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I6_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I7_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_converse__INTER,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__const,axiom,
% 94.64/94.40 ! [V_M_2,T_b,V_A_2,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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 ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__absorb,axiom,
% 94.64/94.40 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__INT__eq,axiom,
% 94.64/94.40 ! [V_x_2,V_r_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__lower,axiom,
% 94.64/94.40 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I1_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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 )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I2_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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 )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__insert,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Collect__ball__eq,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__Un,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UN__simps_I7_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UN__extend__simps_I7_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Image__INT__subset,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Compl__INT,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Compl__UN,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__subset,axiom,
% 94.64/94.40 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INTER__def,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I1_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I2_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I3_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I3_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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) )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I4_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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 )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 94.64/94.40 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF__leI,axiom,
% 94.64/94.40 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 94.64/94.40 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 94.64/94.40 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__greaterThan__UNIV,axiom,
% 94.64/94.40 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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I4_J,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 94.64/94.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) )
% 94.64/94.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Image__INT__eq,axiom,
% 94.64/94.40 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 94.64/94.40 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 94.64/94.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_inf__INFI__fold__inf,axiom,
% 94.64/94.40 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 94.64/94.40 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 94.64/94.40 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 94.64/94.40 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 94.64/94.40 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.40 => ? [B_y_H] :
% 94.64/94.40 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 94.64/94.40 & 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)) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__fold__inf,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__fold__sup,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__Inter,axiom,
% 94.64/94.40 ! [V_M_2,T_b] :
% 94.64/94.40 ( ? [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 94.64/94.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 94.64/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UnionI,axiom,
% 94.64/94.40 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_InterD,axiom,
% 94.64/94.40 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_InterE,axiom,
% 94.64/94.40 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF2__iff,axiom,
% 94.64/94.40 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INF1__iff,axiom,
% 94.64/94.40 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__simps_I8_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INT__extend__simps_I8_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__image__eq,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_INTER__eq__Inter__image,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Un__Inter,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__disjoint,axiom,
% 94.64/94.40 ! [V_A_2,V_C_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__upper,axiom,
% 94.64/94.40 ! [V_A_2,V_B_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_less__Sup__iff,axiom,
% 94.64/94.40 ! [V_S_2,V_a_2,T_b] :
% 94.64/94.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 & class_Orderings_Olinorder(T_b) )
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 94.64/94.40 <=> ? [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.64/94.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__less__iff,axiom,
% 94.64/94.40 ! [V_a_2,V_S_2,T_b] :
% 94.64/94.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 & class_Orderings_Olinorder(T_b) )
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 94.64/94.40 <=> ? [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.64/94.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_le__Inf__iff,axiom,
% 94.64/94.40 ! [V_A_2,V_b_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( 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)))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__le__iff,axiom,
% 94.64/94.40 ! [V_b_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( 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))
% 94.64/94.40 <=> ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Field__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__Pow__eq,axiom,
% 94.64/94.40 ! [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 ).
% 94.64/94.40
% 94.64/94.40 fof(fact_image__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sigma__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UN__extend__simps_I8_J,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UN__simps_I8_J,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Int__Union2,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Int__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Range__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Domain__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_vimage__Union,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__Sup,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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))))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__Inf,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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)))))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__lower,axiom,
% 94.64/94.40 ! [V_A_2,V_B_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__empty,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__mono,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__quotient,axiom,
% 94.64/94.40 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.40 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.64/94.40 => 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 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__insert,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__UnionD,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 94.64/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_subset__Pow__Union,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__anti__mono,axiom,
% 94.64/94.40 ! [V_A_2,V_B_2,T_b] :
% 94.64/94.40 ( 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))
% 94.64/94.40 => 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))) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__empty,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__eq,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__UNIV,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__Un__distrib,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__insert,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_UNION__eq__Union__image,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__image__eq,axiom,
% 94.64/94.40 ! [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) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__upper,axiom,
% 94.64/94.40 ! [V_A_2,V_x_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__UNIV,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__lower,axiom,
% 94.64/94.40 ! [V_A_2,V_x_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__empty,axiom,
% 94.64/94.40 ! [T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__Un__distrib,axiom,
% 94.64/94.40 ! [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)) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__singleton,axiom,
% 94.64/94.40 ! [V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__insert,axiom,
% 94.64/94.40 ! [V_A_2,V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Int__Inter__image,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__singleton,axiom,
% 94.64/94.40 ! [V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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 ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__UNIV,axiom,
% 94.64/94.40 ! [T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__empty,axiom,
% 94.64/94.40 ! [T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__UNIV,axiom,
% 94.64/94.40 ! [T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__insert,axiom,
% 94.64/94.40 ! [V_A_2,V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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)) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Un__eq__Union,axiom,
% 94.64/94.40 ! [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))))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Un__Union__image,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__Int__subset,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Int__eq__Inter,axiom,
% 94.64/94.40 ! [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))))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__Un__subset,axiom,
% 94.64/94.40 ! [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)))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__binary,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__binary,axiom,
% 94.64/94.40 ! [V_b_2,V_a_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => 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) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_sup__Sup__fold__sup,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Sup__fin__Sup,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_inf__Inf__fold__inf,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => 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) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inf__fin__Inf,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.40 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_image__INT,axiom,
% 94.64/94.40 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 94.64/94.40 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 94.64/94.40 => ( ! [B_x] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 94.64/94.40 => 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)) )
% 94.64/94.40 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 94.64/94.40 => 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)) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_card__partition,axiom,
% 94.64/94.40 ! [V_k_2,V_C_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 94.64/94.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 94.64/94.40 => ( ! [B_c] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 94.64/94.40 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 94.64/94.40 => ( ! [B_c1] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 94.64/94.40 => ! [B_c2] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 94.64/94.40 => ( B_c1 != B_c2
% 94.64/94.40 => 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)) ) ) )
% 94.64/94.40 => 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)) ) ) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__def,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Union__def,axiom,
% 94.64/94.40 ! [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))) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_finite__Union,axiom,
% 94.64/94.40 ! [V_A_2,T_b] :
% 94.64/94.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 94.64/94.40 => ( ! [B_M] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 94.64/94.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_insert__partition,axiom,
% 94.64/94.40 ! [V_F_2,V_x_2,T_b] :
% 94.64/94.40 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 94.64/94.40 => ( ! [B_x] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ! [B_xa] :
% 94.64/94.40 ( 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)))
% 94.64/94.40 => ( B_x != B_xa
% 94.64/94.40 => 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)) ) ) )
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_inj__on__Inter,axiom,
% 94.64/94.40 ! [V_f_2,T_c,T_b,V_S_2] :
% 94.64/94.40 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 94.64/94.40 => ( ! [B_A] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 94.64/94.40 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 94.64/94.40 => 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)) ) ) ).
% 94.64/94.40
% 94.64/94.40 fof(fact_Inter__subset,axiom,
% 94.64/94.40 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.40 ( ! [B_X] :
% 94.64/94.40 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 94.64/94.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 94.64/94.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__on__INTER,axiom,
% 94.64/94.41 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 94.64/94.41 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.41 => ( ! [B_i] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 94.64/94.41 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 94.64/94.41 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.41 => ( 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))
% 94.64/94.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.41 => ~ ! [B_y] :
% 94.64/94.41 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 94.64/94.41 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 94.64/94.41 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 94.64/94.41 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_InterI,axiom,
% 94.64/94.41 ! [V_A_2,V_C_2,T_b] :
% 94.64/94.41 ( ! [B_X] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inf__le__fold__inf,axiom,
% 94.64/94.41 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Lattices_Osemilattice__inf(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fold__sup__le__sup,axiom,
% 94.64/94.41 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Lattices_Osemilattice__sup(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_mod__div__decomp,axiom,
% 94.64/94.41 ! [V_b,V_a,T_a] :
% 94.64/94.41 ( class_Divides_Osemiring__div(T_a)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_wf__eq__minimal,axiom,
% 94.64/94.41 ! [V_r_2,T_b] :
% 94.64/94.41 ( c_Wellfounded_Owf(T_b,V_r_2)
% 94.64/94.41 <=> ! [B_Q] :
% 94.64/94.41 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 94.64/94.41 => ? [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 94.64/94.41 & ! [B_y] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_transfer__nat__int__set__cong,axiom,
% 94.64/94.41 ! [V_P_H_2,V_Pa_2] :
% 94.64/94.41 ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 94.64/94.41 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.41 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Int__Collect__mono,axiom,
% 94.64/94.41 ! [V_Q_2,V_Pa_2,V_B_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.41 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_UnionE,axiom,
% 94.64/94.41 ! [V_C_2,V_A_2,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ~ ! [B_X] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_converseE,axiom,
% 94.64/94.41 ! [V_r_2,V_yx_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ~ ! [B_x,B_y] :
% 94.64/94.41 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 94.64/94.41 => ~ 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rel__compE,axiom,
% 94.64/94.41 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ~ ! [B_x,B_y,B_z] :
% 94.64/94.41 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 94.64/94.41 => ( 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))
% 94.64/94.41 => ~ 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_setprod__pos,axiom,
% 94.64/94.41 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.64/94.41 ( class_Rings_Olinordered__semidom(T_c)
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Oof__frac__def,axiom,
% 94.64/94.41 ! [V_q,T_a,T_b] :
% 94.64/94.41 ( ( class_Rings_Oinverse(T_b)
% 94.64/94.41 & class_Rings_Oring__1(T_b) )
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Oless__frac__def,axiom,
% 94.64/94.41 ! [V_r_2,V_q_2,T_b] :
% 94.64/94.41 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 94.64/94.41 <=> 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 94.64/94.41 ! [V_r_2,V_q_2,T_b] :
% 94.64/94.41 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 94.64/94.41 <=> 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Odenom__def,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Onum__def,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_internal__split__def,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_setprod__nonneg,axiom,
% 94.64/94.41 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.64/94.41 ( class_Rings_Olinordered__semidom(T_c)
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_internal__split__conv,axiom,
% 94.64/94.41 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_bool_Osize_I1_J,axiom,
% 94.64/94.41 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_bool_Osize_I2_J,axiom,
% 94.64/94.41 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_finite__less__ub,axiom,
% 94.64/94.41 ! [V_u_2,V_f_2] :
% 94.64/94.41 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lenlex__def,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_neq__if__length__neq,axiom,
% 94.64/94.41 ! [V_ys,V_xs,T_a] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => V_xs != V_ys ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexn__length,axiom,
% 94.64/94.41 ! [V_na_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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_na_2)))
% 94.64/94.41 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_na_2
% 94.64/94.41 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lenlex__conv,axiom,
% 94.64/94.41 ! [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)))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__sublist,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexn_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_na_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_na_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_na_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_na_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_na_2)))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_impossible__Cons,axiom,
% 94.64/94.41 ! [V_x,V_ys,V_xs,T_a] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_not__Cons__self,axiom,
% 94.64/94.41 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_not__Cons__self2,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Oinject,axiom,
% 94.64/94.41 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ( V_a_2 = V_a_H_2
% 94.64/94.41 & V_list_2 = V_list_H_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osize_I4_J,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__in__lex,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( ( hBOOL(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))
% 94.64/94.41 & 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) )
% 94.64/94.41 | ( V_x_2 = V_y_2
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__Cons__def,axiom,
% 94.64/94.41 ! [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)))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_pick_Osimps,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_i] :
% 94.64/94.41 ( ( 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)))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select__weight__cons__zero,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__cons__cons,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( hBOOL(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))
% 94.64/94.41 | ( V_a_2 = V_b_2
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__lex,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 & 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(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)))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osize_I2_J,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__acc__listrel1I,axiom,
% 94.64/94.41 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 94.64/94.41 => ( 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))))
% 94.64/94.41 => 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)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__converse,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__mono,axiom,
% 94.64/94.41 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1I2,axiom,
% 94.64/94.41 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 94.64/94.41 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__eq__len,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__listrel1__converse,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__listrel1__Cons,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( ( hBOOL(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))
% 94.64/94.41 & V_xs_2 = V_ys_2 )
% 94.64/94.41 | ( V_x_2 = V_y_2
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1I1,axiom,
% 94.64/94.41 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(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))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Cons,axiom,
% 94.64/94.41 ! [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))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__linear,axiom,
% 94.64/94.41 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 94.64/94.41 ( ! [B_a,B_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 | B_a = B_b
% 94.64/94.41 | 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)) )
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 | V_x_2 = V_y_2
% 94.64/94.41 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__rtrancl__refl,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__mono,axiom,
% 94.64/94.41 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__eq__len,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__rtrancl__trans,axiom,
% 94.64/94.41 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__subset__listrel,axiom,
% 94.64/94.41 ! [V_r_H_2,V_r_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel_OCons,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(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))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrelp__listrel__eq,axiom,
% 94.64/94.41 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Cons1,axiom,
% 94.64/94.41 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => ~ ! [B_y,B_ys] :
% 94.64/94.41 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 94.64/94.41 => ( 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))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrelp_OCons,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 94.64/94.41 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrelp_Oequations_I2_J,axiom,
% 94.64/94.41 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 94.64/94.41 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Cons2,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => ~ ! [B_x,B_xs] :
% 94.64/94.41 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 94.64/94.41 => ( 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))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__subset,axiom,
% 94.64/94.41 ! [V_A_2,V_r_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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))))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__UNIV,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__mono,axiom,
% 94.64/94.41 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_equiv__listrel,axiom,
% 94.64/94.41 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.41 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__refl__on,axiom,
% 94.64/94.41 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.41 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__in__lists__iff,axiom,
% 94.64/94.41 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__accD,axiom,
% 94.64/94.41 ! [V_r_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__accI,axiom,
% 94.64/94.41 ! [V_r_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__iff__nth,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__irreflexive,axiom,
% 94.64/94.41 ! [V_y_2,V_r_2,T_b] :
% 94.64/94.41 ( ! [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))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_infinite__UNIV__listI,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__eq__iff__nth__eq,axiom,
% 94.64/94.41 ! [T_b,V_ys_2,V_xs_2] :
% 94.64/94.41 ( V_xs_2 = V_ys_2
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__Cons__0,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__Cons__Suc,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth_Osimps,axiom,
% 94.64/94.41 ! [V_na_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_na_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_na_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__Cons_H,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_n] :
% 94.64/94.41 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 94.64/94.41 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__Cons__number__of,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_v] :
% 94.64/94.41 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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 )
% 94.64/94.41 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__take__index__conv,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( ( 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)))
% 94.64/94.41 & 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 )
% 94.64/94.41 | ? [B_i] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 94.64/94.41 & 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__sublist,axiom,
% 94.64/94.41 ! [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))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_finite__set,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__subset__Cons,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__all,axiom,
% 94.64/94.41 ! [V_n,V_xs,T_a] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__take__subset__set__take,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_na_2,V_m_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.64/94.41 => 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_na_2),V_xs_2)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__take__subset,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_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_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__sublist__subset,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__take,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n,V_i] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_notin__set__sublistI,axiom,
% 94.64/94.41 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => ~ 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__takeD,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__sublistD,axiom,
% 94.64/94.41 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__ConsD,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => ( V_y_2 = V_x_2
% 94.64/94.41 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Suc__Cons,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__take,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__take,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__upt__eq__take,axiom,
% 94.64/94.41 ! [V_na_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2)) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_l_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_card__length,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_all__set__conv__all__nth,axiom,
% 94.64/94.41 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.41 ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.41 <=> ! [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__size__estimation,axiom,
% 94.64/94.41 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__size__estimation_H,axiom,
% 94.64/94.41 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__lists__conv__set,axiom,
% 94.64/94.41 ! [V_A_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 94.64/94.41 <=> ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__pos__if__in__set,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__conv__nth,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 <=> ? [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__mem,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__eq__set,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__conv__nth,axiom,
% 94.64/94.41 ! [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))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_finite__lists__length__eq,axiom,
% 94.64/94.41 ! [V_na_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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_na_2))))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_finite__lists__length__le,axiom,
% 94.64/94.41 ! [V_na_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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_na_2))))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__iff__zip,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_x] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__zip,axiom,
% 94.64/94.41 ! [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)))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__zip,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__zip,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__Cons__Cons,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__eq__iff__zip__eq,axiom,
% 94.64/94.41 ! [T_b,V_ys_2,V_xs_2] :
% 94.64/94.41 ( V_xs_2 = V_ys_2
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_x] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__zipE,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__zip__rightD,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__zip__leftD,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__same,axiom,
% 94.64/94.41 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 94.64/94.41 ( hBOOL(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))))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 & V_a_2 = V_b_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__zip,axiom,
% 94.64/94.41 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_greaterThanLessThan__upto,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__setsum__nth,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__upto,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_atLeastAtMost__upto,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 94.64/94.41 ! [V_ns_2] :
% 94.64/94.41 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 <=> ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 94.64/94.41 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_elem__le__listsum__nat,axiom,
% 94.64/94.41 ! [V_ns,V_k] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__simps_I2_J,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_a)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_atLeastLessThan__upto,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_greaterThanAtMost__upto,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__list__def,axiom,
% 94.64/94.41 ! [V_l_2] :
% 94.64/94.41 ( c_List_Onat__list(V_l_2)
% 94.64/94.41 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__size__pointwise,axiom,
% 94.64/94.41 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 94.64/94.41 ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__update__nat,axiom,
% 94.64/94.41 ! [V_n,V_ns,V_k] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__take,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__beyond,axiom,
% 94.64/94.41 ! [V_x,V_i,V_xs,T_a] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__list__update__neq,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a,V_j,V_i] :
% 94.64/94.41 ( V_i != V_j
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__id,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__list__update,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a,V_k] :
% 94.64/94.41 ( ( 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))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( 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))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__list__update,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__update,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_update__zip,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__overwrite,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__swap,axiom,
% 94.64/94.41 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 94.64/94.41 ( V_i != V_i_H
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__code_I2_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__code_I3_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__butlastD,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__update__subsetI,axiom,
% 94.64/94.41 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__update__subset__insert,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__list__update,axiom,
% 94.64/94.41 ! [V_x,V_j,V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( ( V_i = V_j
% 94.64/94.41 => 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 )
% 94.64/94.41 & ( V_i != V_j
% 94.64/94.41 => 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) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__same__conv,axiom,
% 94.64/94.41 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 94.64/94.41 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__list__update__eq,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__butlast,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__butlast,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__update__memI,axiom,
% 94.64/94.41 ! [V_x_2,V_xs_2,T_b,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.41 => 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_na_2),V_x_2)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__conv__take,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1__iff__update,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ? [B_y,B_n] :
% 94.64/94.41 ( 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))
% 94.64/94.41 & 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)))
% 94.64/94.41 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__list__update,axiom,
% 94.64/94.41 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => ( ~ 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))))))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__upto,axiom,
% 94.64/94.41 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__take,axiom,
% 94.64/94.41 ! [V_i,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__sublistI,axiom,
% 94.64/94.41 ! [V_I_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__zipI1,axiom,
% 94.64/94.41 ! [V_ys,T_b,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__zipI2,axiom,
% 94.64/94.41 ! [V_xs,T_b,V_ys,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 94.64/94.41 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_card__distinct,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__card,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__conv__nth,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 <=> ! [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ! [B_j] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( B_i != B_j
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__eq__iff__index__eq,axiom,
% 94.64/94.41 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => ( 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)
% 94.64/94.41 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Ocard_H__def,axiom,
% 94.64/94.41 ! [V_A_2,T_b] :
% 94.64/94.41 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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)))) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__take__lemma,axiom,
% 94.64/94.41 ! [V_ys,V_xs,T_a,V_k] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => ( ! [B_i] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 94.64/94.41 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__remove1__eq,axiom,
% 94.64/94.41 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Cons__number__of,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_v] :
% 94.64/94.41 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists_ONil,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Nil2,axiom,
% 94.64/94.41 ! [V_r_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Nil1,axiom,
% 94.64/94.41 ! [V_r_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__butlast,axiom,
% 94.64/94.41 ! [T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__remove1,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct_Osimps_I1_J,axiom,
% 94.64/94.41 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast_Osimps_I1_J,axiom,
% 94.64/94.41 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_x,T_a,V_xs] :
% 94.64/94.41 ( ( V_xs = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 94.64/94.41 & ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osimps_I3_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_y,V_x] :
% 94.64/94.41 ( ( V_x = V_y
% 94.64/94.41 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 94.64/94.41 & ( V_x != V_y
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upto__empty,axiom,
% 94.64/94.41 ! [V_i,V_j] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 94.64/94.41 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__eq__Nil,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__0,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Nil,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__nil,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1__commute,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1_Osimps_I1_J,axiom,
% 94.64/94.41 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrelp_Oequations_I1_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrelp_ONil,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__Nil,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__simps_I1_J,axiom,
% 94.64/94.41 ! [T_a] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_a)
% 94.64/94.41 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__0__conv,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osize_I3_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__empty,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__empty2,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__code_I1_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__nonempty,axiom,
% 94.64/94.41 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osize_I1_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1__idem,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_notin__set__remove1,axiom,
% 94.64/94.41 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => ~ 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__remove1,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 94.64/94.41 ( V_a_2 != V_b_2
% 94.64/94.41 => ( 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))))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__empty,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__remove1__subset,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__greater__0__conv,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__1__Cons,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_not__listrel1__Nil,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_not__Nil__listrel1,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel_ONil,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__Nil__right,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nil2__notin__lex,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nil__notin__lex,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Cons,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_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_na_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upto_Osimps,axiom,
% 94.64/94.41 ! [V_j,V_i] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 94.64/94.41 => 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)) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 94.64/94.41 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__singleton,axiom,
% 94.64/94.41 ! [V_x_2,T_b,V_A_2] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 94.64/94.41 => 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)) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__empty,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Cons_H,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_n] :
% 94.64/94.41 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upto__rec__number__of,axiom,
% 94.64/94.41 ! [V_n,V_m] :
% 94.64/94.41 ( ( 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)))
% 94.64/94.41 => 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))) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel__Nil,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__Cons__sing__Nil,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__remove1,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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)) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upto_Opsimps,axiom,
% 94.64/94.41 ! [V_j_2,V_i_2] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 94.64/94.41 => 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)) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 94.64/94.41 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select,axiom,
% 94.64/94.41 ! [V_s_2,T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listset_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__Cons,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osimps_I5_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list_Osimps_I4_J,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listset_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__Cons1,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sorted__list__of__set__remove,axiom,
% 94.64/94.41 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upto_Opinduct,axiom,
% 94.64/94.41 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( ! [B_i,B_j] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 94.64/94.41 => 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)) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j)) ) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sorted__list__of__set__empty,axiom,
% 94.64/94.41 ! [T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_anamorph_Osimps,axiom,
% 94.64/94.41 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 94.64/94.41 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__Cons,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__eq__Cons__conv,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 94.64/94.41 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 94.64/94.41 | ? [B_ys_H] :
% 94.64/94.41 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 94.64/94.41 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__eq__append__conv,axiom,
% 94.64/94.41 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 94.64/94.41 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 94.64/94.41 | ? [B_ys_H] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 94.64/94.41 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append1__eq__conv,axiom,
% 94.64/94.41 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 <=> ( V_xs_2 = V_ys_2
% 94.64/94.41 & V_x_2 = V_y_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__Cons,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Cons__eq__appendI,axiom,
% 94.64/94.41 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 94.64/94.41 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 94.64/94.41 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__in__lists__conv,axiom,
% 94.64/94.41 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__eq__appendI,axiom,
% 94.64/94.41 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 94.64/94.41 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 94.64/94.41 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__same__eq,axiom,
% 94.64/94.41 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> V_ys_2 = V_zs_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_same__append__eq,axiom,
% 94.64/94.41 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> V_ys_2 = V_zs_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__eq__append__conv2,axiom,
% 94.64/94.41 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ? [B_us] :
% 94.64/94.41 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 94.64/94.41 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_ts_2 )
% 94.64/94.41 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 94.64/94.41 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_2) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__assoc,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__append,axiom,
% 94.64/94.41 ! [V_ys,V_xs,T_a] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_a)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__append,axiom,
% 94.64/94.41 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( 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)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__Nil,axiom,
% 94.64/94.41 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nil__is__append__conv,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 94.64/94.41 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 94.64/94.41 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__Nil2,axiom,
% 94.64/94.41 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 94.64/94.41
% 94.64/94.41 fof(fact_self__append__conv,axiom,
% 94.64/94.41 ! [V_ys_2,T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 94.64/94.41 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_self__append__conv2,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_ys_2] :
% 94.64/94.41 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__is__Nil__conv,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 94.64/94.41 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__self__conv,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 94.64/94.41 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__self__conv2,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_eq__Nil__appendI,axiom,
% 94.64/94.41 ! [T_a,V_ys,V_xs] :
% 94.64/94.41 ( V_xs = V_ys
% 94.64/94.41 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__append,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_ys] :
% 94.64/94.41 ( ( V_ys = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 94.64/94.41 & ( V_ys != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__append__length,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__append__length__plus,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__append1,axiom,
% 94.64/94.41 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__length,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1__append,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__butlast__appendI,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 94.64/94.41 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 94.64/94.41 => 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))))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__snoc,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__listrel1I,axiom,
% 94.64/94.41 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 & V_us_2 = V_vs_2 )
% 94.64/94.41 | ( V_xs_2 = V_ys_2
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) )
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__append__leftI,axiom,
% 94.64/94.41 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__append,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 94.64/94.41 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 94.64/94.41 & 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__append,axiom,
% 94.64/94.41 ! [V_ys,V_xs,T_a,V_n] :
% 94.64/94.41 ( ( 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)))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__update__append,axiom,
% 94.64/94.41 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 94.64/94.41 ( ( 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)))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublist__append,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1I,axiom,
% 94.64/94.41 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(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))
% 94.64/94.41 => ( 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))
% 94.64/94.41 => ( 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))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__append__left__rightI,axiom,
% 94.64/94.41 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 94.64/94.41 ( hBOOL(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))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Suc__conv__app__nth,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 & V_x_2 = V_y_2 )
% 94.64/94.41 | ( V_xs_2 = V_ys_2
% 94.64/94.41 & hBOOL(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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listrel1E,axiom,
% 94.64/94.41 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => ~ ! [B_x,B_y] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => ! [B_us,B_vs] :
% 94.64/94.41 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 94.64/94.41 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__append__leftD,axiom,
% 94.64/94.41 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 => ( ! [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))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate1__def,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_upd__conv__take__nth__drop,axiom,
% 94.64/94.41 ! [V_a,V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__take__drop__id,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Suc__Cons,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__1__Cons,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__via__drop,axiom,
% 94.64/94.41 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__drop,axiom,
% 94.64/94.41 ! [V_i,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct1__rotate,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 94.64/94.41 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_butlast__drop,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__butlast,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__drop,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__take,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__drop,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__0,axiom,
% 94.64/94.41 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__zip,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__rotate1,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__drop,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__rotate1,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__set__dropD,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,V_x_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__drop__subset,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_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_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Nil,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate1__is__Nil__conv,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__drop__subset__set__drop,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_m_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2))
% 94.64/94.41 => 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_na_2),V_xs_2)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__eq__Nil,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> 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_na_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__all,axiom,
% 94.64/94.41 ! [V_n,V_xs,T_a] :
% 94.64/94.41 ( 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))
% 94.64/94.41 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__eq__conv__conj,axiom,
% 94.64/94.41 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Cons,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_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_na_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Cons_H,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_n] :
% 94.64/94.41 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__drop,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_i,V_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__eq__append__conv__if,axiom,
% 94.64/94.41 ! [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] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ( ( 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)))
% 94.64/94.41 => ( 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)
% 94.64/94.41 & 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) ) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => ( 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
% 94.64/94.41 & 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 ) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__drop_H,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__simps,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_b,T_a] :
% 94.64/94.41 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 94.64/94.41 & 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Cons__number__of,axiom,
% 94.64/94.41 ! [V_xs,V_x,T_a,V_v] :
% 94.64/94.41 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__add,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_j,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate1__length01,axiom,
% 94.64/94.41 ! [V_xs,T_a] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__append1,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__append2,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_id__take__nth__drop,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__hd__drop,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__drop__conv__nth,axiom,
% 94.64/94.41 ! [V_n,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd_Osimps,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__append2,axiom,
% 94.64/94.41 ! [V_ys,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__append,axiom,
% 94.64/94.41 ! [V_ys,T_a,V_xs] :
% 94.64/94.41 ( ( V_xs = c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__in__set,axiom,
% 94.64/94.41 ! [T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__conv__nth,axiom,
% 94.64/94.41 ! [T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate1__hd__tl,axiom,
% 94.64/94.41 ! [T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__rotate__conv__nth,axiom,
% 94.64/94.41 ! [V_n,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__tl,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl__drop,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__tl,axiom,
% 94.64/94.41 ! [V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__rotate,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2)))
% 94.64/94.41 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__add,axiom,
% 94.64/94.41 ! [V_na_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_na_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_na_2)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__rotate,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate0,axiom,
% 94.64/94.41 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__rotate,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__rotate,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl_Osimps_I1_J,axiom,
% 94.64/94.41 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__is__Nil__conv,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] :
% 94.64/94.41 ( hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate1__rotate__swap,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__def,axiom,
% 94.64/94.41 ! [V_na_2,T_b] : c_List_Orotate(T_b,V_na_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_na_2),c_List_Orotate1(T_b)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl__append2,axiom,
% 94.64/94.41 ! [V_ys,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__tl,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__conv__mod,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__Suc,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__Suc,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl__append,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__id,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__length01,axiom,
% 94.64/94.41 ! [V_n,V_xs,T_a] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__tl,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_tl__take,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__Suc,axiom,
% 94.64/94.41 ! [V_n,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__drop__take,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fold1__set,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 94.64/94.41 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__append__rightI,axiom,
% 94.64/94.41 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 94.64/94.41 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__Nil,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_start__le__sum,axiom,
% 94.64/94.41 ! [V_ns_2,V_na_2,V_m_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
% 94.64/94.41 => 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_na_2),V_ns_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__absorb0,axiom,
% 94.64/94.41 ! [V_zs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__assoc,axiom,
% 94.64/94.41 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Groups_Osemigroup__add(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__Cons,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__append,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__foldl,axiom,
% 94.64/94.41 ! [T_b] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sum__eq__0__conv,axiom,
% 94.64/94.41 ! [V_ns_2,V_m_2] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 & ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 94.64/94.41 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 94.64/94.41 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Sup__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Inf__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Sup__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Lattices_Olattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Inf__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Lattices_Olattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Min__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Max__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_SUPR__set__fold,axiom,
% 94.64/94.41 ! [V_f_2,V_xs_2,T_c,T_b] :
% 94.64/94.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_INFI__set__fold,axiom,
% 94.64/94.41 ! [V_f_2,V_xs_2,T_c,T_b] :
% 94.64/94.41 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_elem__le__sum,axiom,
% 94.64/94.41 ! [V_ns_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_na_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sorted__list__of__set__insert,axiom,
% 94.64/94.41 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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)))))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lexord__Nil__left,axiom,
% 94.64/94.41 ! [V_r_2,V_y_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.41 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__key_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( ( 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)))
% 94.64/94.41 => 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)) )
% 94.64/94.41 & ( ~ 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)))
% 94.64/94.41 => 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__key_Osimps_I1_J,axiom,
% 94.64/94.41 ! [V_x_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__insort,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__insort,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fun__left__comm__insort,axiom,
% 94.64/94.41 ! [T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__left__comm,axiom,
% 94.64/94.41 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__key__left__comm,axiom,
% 94.64/94.41 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1__insort,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__not__Nil,axiom,
% 94.64/94.41 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__insort,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => ( 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)))
% 94.64/94.41 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__insert__insort__key,axiom,
% 94.64/94.41 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( ~ 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))))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__insert__insort,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__insort__insert,axiom,
% 94.64/94.41 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_c)
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__insert__triv,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__insort__insert,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_insort__insert__key__triv,axiom,
% 94.64/94.41 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Orderings_Olinorder(T_b)
% 94.64/94.41 => ( 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))))
% 94.64/94.41 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__list__update,axiom,
% 94.64/94.41 ! [V_x,V_k,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => ( ( 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))
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 94.64/94.41 & ( 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))
% 94.64/94.41 => 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) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__conv__nth,axiom,
% 94.64/94.41 ! [T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last_Osimps,axiom,
% 94.64/94.41 ! [V_x,T_a,V_xs] :
% 94.64/94.41 ( ( V_xs = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 94.64/94.41 & ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__ConsR,axiom,
% 94.64/94.41 ! [V_x,T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__ConsL,axiom,
% 94.64/94.41 ! [V_x,T_a,V_xs] :
% 94.64/94.41 ( V_xs = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__append,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_ys] :
% 94.64/94.41 ( ( V_ys = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 94.64/94.41 & ( V_ys != c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__appendR,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_ys] :
% 94.64/94.41 ( V_ys != c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__appendL,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_ys] :
% 94.64/94.41 ( V_ys = c_List_Olist_ONil(T_a)
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__in__set,axiom,
% 94.64/94.41 ! [T_b,V_as_2] :
% 94.64/94.41 ( V_as_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__snoc,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__drop,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_n] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__butlast__last__id,axiom,
% 94.64/94.41 ! [T_a,V_xs] :
% 94.64/94.41 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.41 => 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 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_snoc__eq__iff__butlast,axiom,
% 94.64/94.41 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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
% 94.64/94.41 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 94.64/94.41 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists_Osimps,axiom,
% 94.64/94.41 ! [V_A_2,V_a_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 94.64/94.41 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 94.64/94.41 | ? [B_a,B_l] :
% 94.64/94.41 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 94.64/94.41 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select__weigth__select,axiom,
% 94.64/94.41 ! [T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__mapI,axiom,
% 94.64/94.41 ! [V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_last__map,axiom,
% 94.64/94.41 ! [V_f_2,T_c,T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_foldl__map,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_rotate__map,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(c_List_Orotate(T_b,V_na_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_na_2),V_xs_2)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__tl,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__map2,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__zip__map2,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__zip__map,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__map1,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__map__map,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__same__conv__map,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__is__Nil__conv,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nil__is__map__conv,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__update,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__eq__conv,axiom,
% 94.64/94.41 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 94.64/94.41 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__map,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__eq__imp__length__eq,axiom,
% 94.64/94.41 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__0,axiom,
% 94.64/94.41 ! [V_xs_2,T_c,T_b] :
% 94.64/94.41 ( class_Groups_Omonoid__add(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__mult__const,axiom,
% 94.64/94.41 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( class_Rings_Osemiring__0(T_b)
% 94.64/94.41 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__const__mult,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 94.64/94.41 ( class_Rings_Osemiring__0(T_b)
% 94.64/94.41 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__subtractf,axiom,
% 94.64/94.41 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( class_Groups_Oab__group__add(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__addf,axiom,
% 94.64/94.41 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__injective,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 94.64/94.41 => V_xs_2 = V_ys_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__map__eq__map,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.41 => ( 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)
% 94.64/94.41 <=> V_xs_2 = V_ys_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__ident,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_take__map,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_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_na_2),V_xs_2)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__butlast,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__map,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_hd__map,axiom,
% 94.64/94.41 ! [V_f_2,T_c,T_b,V_xs_2] :
% 94.64/94.41 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_drop__map,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_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_na_2),V_xs_2)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Omap_Ocomp,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__comp__map,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Omap_Ocompositionality,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__map,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Omap_Oidentity,axiom,
% 94.64/94.41 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__size__map,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_List_Omap_Oid,axiom,
% 94.64/94.41 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__on__map__eq__map,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( 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)
% 94.64/94.41 <=> V_xs_2 = V_ys_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__inj__on,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => V_xs_2 = V_ys_2 ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nth__map,axiom,
% 94.64/94.41 ! [V_f_2,T_c,V_xs_2,T_b,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.41 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_na_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__fun__upd,axiom,
% 94.64/94.41 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 94.64/94.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__map,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 94.64/94.41 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 94.64/94.41 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__abs,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_uminus__listsum__map,axiom,
% 94.64/94.41 ! [V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( class_Groups_Oab__group__add(T_b)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__on__mapI,axiom,
% 94.64/94.41 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__map,axiom,
% 94.64/94.41 ! [V_f_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_inj__mapD,axiom,
% 94.64/94.41 ! [V_f_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 94.64/94.41 ! [V_f_2,V_xs_2,T_b,T_c] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__triv,axiom,
% 94.64/94.41 ! [V_xs_2,V_r_2,T_c,T_b] :
% 94.64/94.41 ( class_Rings_Osemiring__1(T_b)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__map__remove1,axiom,
% 94.64/94.41 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 94.64/94.41 ! [V_f_2,V_A_2,T_b,T_c] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.64/94.41 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => 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))))) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.41 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_pick__same,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_l_2] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zero__code__numeral__def,axiom,
% 94.64/94.41 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_times__code__numeral__code,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 94.64/94.41 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 94.64/94.41 ! [V_m_2,V_na_2] :
% 94.64/94.41 ( hAPP(c_Code__Numeral_Oof__nat,V_na_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 94.64/94.41 <=> V_na_2 = V_m_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_one__code__numeral__def,axiom,
% 94.64/94.41 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_less__code__numeral__code,axiom,
% 94.64/94.41 ! [V_m_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 94.64/94.41 ! [V_y_2,V_x_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.41 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 94.64/94.41 <=> V_x_2 = V_y_2 ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__fst__zip,axiom,
% 94.64/94.41 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => 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 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__snd__zip,axiom,
% 94.64/94.41 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => 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 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_number__of__code__numeral__def,axiom,
% 94.64/94.41 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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__map__fst__snd,axiom,
% 94.64/94.41 ! [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 ).
% 94.64/94.41
% 94.64/94.41 fof(fact_plus__code__numeral__code,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_less__eq__code__numeral__code,axiom,
% 94.64/94.41 ! [V_m_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_pick__member,axiom,
% 94.64/94.41 ! [V_xs_2,T_b,V_i_2] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_zip__eq__conv,axiom,
% 94.64/94.41 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 94.64/94.41 <=> ( 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
% 94.64/94.41 & 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 ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__size__conv__listsum,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_code__numeral__not__eq__zero,axiom,
% 94.64/94.41 ! [V_i_2] :
% 94.64/94.41 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.64/94.41 <=> 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 94.64/94.41 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 94.64/94.41 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 94.64/94.41 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select__weight__member,axiom,
% 94.64/94.41 ! [V_s_2,V_xs_2,T_b] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select__weight__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_select__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_subtract__code__numeral__code,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of__inverse,axiom,
% 94.64/94.41 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 94.64/94.41
% 94.64/94.41 fof(fact_of__nat__nat__of,axiom,
% 94.64/94.41 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of__of__nat,axiom,
% 94.64/94.41 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 94.64/94.41 ! [V_l_2,V_k_2] :
% 94.64/94.41 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 94.64/94.41 <=> V_k_2 = V_l_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_code__numeral_Onat__of__inject,axiom,
% 94.64/94.41 ! [V_y_2,V_x_2] :
% 94.64/94.41 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 94.64/94.41 <=> V_x_2 = V_y_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_times__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_type__definition__code__numeral,axiom,
% 94.64/94.41 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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_less__code__numeral__def,axiom,
% 94.64/94.41 ! [V_m_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of,axiom,
% 94.64/94.41 ! [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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of__number,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_int__of__def,axiom,
% 94.64/94.41 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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_less__eq__code__numeral__def,axiom,
% 94.64/94.41 ! [V_m_2,V_na_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of__code,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_nat__of__aux__def,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_Suc__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_minus__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_of__nat__inverse,axiom,
% 94.64/94.41 ! [V_y_2] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.41 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_plus__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_div__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_minus__code__numeral__code,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_subtract__code__numeral__def,axiom,
% 94.64/94.41 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_mod__code__numeral__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_code__numeral__decr,axiom,
% 94.64/94.41 ! [V_k] :
% 94.64/94.41 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsum__mono,axiom,
% 94.64/94.41 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 94.64/94.41 ( ( class_Groups_Omonoid__add(T_c)
% 94.64/94.41 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 94.64/94.41 => 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)))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_partition__set,axiom,
% 94.64/94.41 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__Int__eq,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp_ONil,axiom,
% 94.64/94.41 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp_Oequations_I1_J,axiom,
% 94.64/94.41 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_in__listsp__conv__set,axiom,
% 94.64/94.41 ! [V_xs_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 94.64/94.41 <=> ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp__conj__eq,axiom,
% 94.64/94.41 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 94.64/94.41 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp__inf__eq,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp__infI,axiom,
% 94.64/94.41 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp_Oequations_I2_J,axiom,
% 94.64/94.41 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 94.64/94.41 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 94.64/94.41 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_append__in__listsp__conv,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 94.64/94.41 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 94.64/94.41 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp__mono,axiom,
% 94.64/94.41 ! [V_B_2,V_A_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.64/94.41 => 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))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_partition__P,axiom,
% 94.64/94.41 ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 94.64/94.41 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.41 & ! [B_x] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 94.64/94.41 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_partition_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_listsp__lists__eq,axiom,
% 94.64/94.41 ! [V_x_2,V_A_2,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_partition_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_lists__IntI,axiom,
% 94.64/94.41 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_product_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__def,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_x] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__map1,axiom,
% 94.64/94.41 ! [V_bs_2,V_as_2,V_f_2,T_d,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__map2,axiom,
% 94.64/94.41 ! [V_bs_2,V_f_2,T_d,V_as_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 <=> 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__dropI,axiom,
% 94.64/94.41 ! [V_na_2,V_bs_2,V_as_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_as_2,V_bs_2)
% 94.64/94.41 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_na_2),V_bs_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__appendI,axiom,
% 94.64/94.41 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2)
% 94.64/94.41 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_c_2,V_d_2)
% 94.64/94.41 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__append,axiom,
% 94.64/94.41 ! [V_vs_2,V_us_2,V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 => ( 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))
% 94.64/94.41 <=> ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_us_2,V_vs_2) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__Cons,axiom,
% 94.64/94.41 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( 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))
% 94.64/94.41 <=> ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 94.64/94.41 & c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__takeI,axiom,
% 94.64/94.41 ! [V_na_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_na_2),V_ys_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__eq,axiom,
% 94.64/94.41 ! [T_b,V_ys_2,V_xs_2] :
% 94.64/94.41 ( V_xs_2 = V_ys_2
% 94.64/94.41 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__lengthD,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => 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) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__Nil,axiom,
% 94.64/94.41 ! [V_ys_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,c_List_Olist_ONil(T_b),V_ys_2)
% 94.64/94.41 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__Nil2,axiom,
% 94.64/94.41 ! [V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,c_List_Olist_ONil(T_c))
% 94.64/94.41 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_product_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__conv__all__nth,axiom,
% 94.64/94.41 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 <=> ( 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)
% 94.64/94.41 & ! [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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))) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__nthD,axiom,
% 94.64/94.41 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__nthD2,axiom,
% 94.64/94.41 ! [V_p_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => 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))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__update__cong,axiom,
% 94.64/94.41 ! [V_y_2,V_x_2,V_ys_2,V_Pa_2,T_c,V_xs_2,T_b,V_i_2] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 94.64/94.41 => 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2__update__cong2,axiom,
% 94.64/94.41 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.41 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2)
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
% 94.64/94.41 => ( 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)))
% 94.64/94.41 => 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)) ) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__product,axiom,
% 94.64/94.41 ! [V_ys,T_b,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_product__list__set,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublists__powset,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__sublists,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublists_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_sublists_Osimps_I2_J,axiom,
% 94.64/94.41 ! [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))))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__set__sublists,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.41 => 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)))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__n__lists,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_na_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_na_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)))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_enum__the__def,axiom,
% 94.64/94.41 ! [V_Pa_2,T_b] : c_Enum_Oenum__the(T_b,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__n__lists,axiom,
% 94.64/94.41 ! [V_n,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_n__lists__Nil,axiom,
% 94.64/94.41 ! [T_a,V_n] :
% 94.64/94.41 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => 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))) )
% 94.64/94.41 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.41 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_n__lists_Osimps_I1_J,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__n__lists,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__n__lists__elem,axiom,
% 94.64/94.41 ! [V_xs_2,V_na_2,V_ys_2,T_b] :
% 94.64/94.41 ( 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_na_2,V_xs_2))))
% 94.64/94.41 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_list__all2I,axiom,
% 94.64/94.41 ! [V_Pa_2,V_b_2,V_a_2,T_c,T_b] :
% 94.64/94.41 ( ! [B_x] :
% 94.64/94.41 ( 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))))
% 94.64/94.41 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_Pa_2),B_x)) )
% 94.64/94.41 => ( 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)
% 94.64/94.41 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_all__nth__imp__all__set,axiom,
% 94.64/94.41 ! [V_x_2,V_Pa_2,V_xs_2,T_b] :
% 94.64/94.41 ( ! [B_i] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 94.64/94.41 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 94.64/94.41 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_map__removeAll__inj__on,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.41 ( 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)))
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__remdups,axiom,
% 94.64/94.41 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__remdups__leq,axiom,
% 94.64/94.41 ! [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))) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__remdups__id,axiom,
% 94.64/94.41 ! [V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__removeAll,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups__id__iff__distinct,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 94.64/94.41 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_set__remdups,axiom,
% 94.64/94.41 ! [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) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__remdups__eq,axiom,
% 94.64/94.41 ! [V_xs_2,T_b] :
% 94.64/94.41 ( 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)
% 94.64/94.41 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups__remdups,axiom,
% 94.64/94.41 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups__eq__nil__iff,axiom,
% 94.64/94.41 ! [V_x_2,T_b] :
% 94.64/94.41 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 94.64/94.41 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_removeAll_Osimps_I1_J,axiom,
% 94.64/94.41 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups__eq__nil__right__iff,axiom,
% 94.64/94.41 ! [V_x_2,T_b] :
% 94.64/94.41 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 94.64/94.41 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups_Osimps_I1_J,axiom,
% 94.64/94.41 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_removeAll_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_xs,T_a,V_y,V_x] :
% 94.64/94.41 ( ( V_x = V_y
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( V_x != V_y
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_removeAll__append,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups__map__remdups,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remove1__remdups,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => 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)) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_removeAll__id,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_distinct__remove1__removeAll,axiom,
% 94.64/94.41 ! [V_x,V_xs,T_a] :
% 94.64/94.41 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.41 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_remdups_Osimps_I2_J,axiom,
% 94.64/94.41 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.41 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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) )
% 94.64/94.41 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.41 => 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)) ) ) ).
% 94.64/94.41
% 94.64/94.41 fof(fact_length__remdups__card__conv,axiom,
% 94.64/94.41 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__removeAll__inj,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__removeAll,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__remdups__concat,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__conv__foldl,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sort__key__simps_I1_J,axiom,
% 94.64/94.42 ! [V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldl__conv__concat,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__sort,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__sort,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__sort,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 94.64/94.42 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat_Osimps_I1_J,axiom,
% 94.64/94.42 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__eq__Nil__conv,axiom,
% 94.64/94.42 ! [V_xss_2,T_b] :
% 94.64/94.42 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 94.64/94.42 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Nil__eq__concat__conv,axiom,
% 94.64/94.42 ! [V_xss_2,T_b] :
% 94.64/94.42 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 94.64/94.42 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__concat,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__concat,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__concat,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sort__key__simps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__append,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sort__foldl__insort,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__eq__concat__iff,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => 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)) )
% 94.64/94.42 => ( 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)
% 94.64/94.42 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 94.64/94.42 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__injective,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 94.64/94.42 => ( 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)
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => 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)) )
% 94.64/94.42 => V_xs_2 = V_ys_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__map__singleton,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_n__lists_Osimps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,V_na_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_na_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_na_2,V_xs_2))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Osimps_I3_J,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__aux__filter__head,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__concat,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__sort,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,V_Pa_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__filter,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sum__length__filter__compl,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__is__subset,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__id__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__filter__le,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_partition__filter__conv,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_partition__filter2,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_partition__filter1,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__filter,axiom,
% 94.64/94.42 ! [V_xs_2,V_Q_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_Pa_2)),V_xs_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__remove1,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_remove1__filter__not,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__insort__triv,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter_Osimps_I1_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Osimps_I1_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter_Osimps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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)) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__append,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__empty__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__filter__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_remdups__filter,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_removeAll__filter__not,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_removeAll__filter__not__eq,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__transpose,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_i_2] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__map__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__filter,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__filter__less,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__minus__filter__out,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__in__sublist,axiom,
% 94.64/94.42 ! [V_s_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__empty,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__filter__conv__card,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__aux__filter__tail,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Opsimps_I3_J,axiom,
% 94.64/94.42 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Opsimps_I2_J,axiom,
% 94.64/94.42 ! [V_xss_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sublist__shift__lemma__Suc,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_select__weigth__drop__zero,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pick__drop__zero,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose_Opsimps_I1_J,axiom,
% 94.64/94.42 ! [T_b] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__max__length,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__aux__max,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr_Osimps_I1_J,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr__append,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr__conv__foldl,axiom,
% 94.64/94.42 ! [V_a_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Groups_Oab__semigroup__add(T_b)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr__map,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldl__foldr1,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( class_Groups_Omonoid__add(T_b)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldl__foldr1__lemma,axiom,
% 94.64/94.42 ! [V_xs_2,V_a_2,T_b] :
% 94.64/94.42 ( class_Groups_Omonoid__add(T_b)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__transpose,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sublist__def,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sublist__shift__lemma,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_atLeastLessThan__upt,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__upt,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__Suc__append,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__Suc,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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))) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__add__eq__append,axiom,
% 94.64/94.42 ! [V_k,V_j,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__rec,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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)) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__conv__Cons,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__conv__Nil,axiom,
% 94.64/94.42 ! [V_i,V_j] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 94.64/94.42 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__eq__Nil__conv,axiom,
% 94.64/94.42 ! [V_j_2,V_i_2] :
% 94.64/94.42 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 94.64/94.42 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__0,axiom,
% 94.64/94.42 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_take__upt,axiom,
% 94.64/94.42 ! [V_n,V_m,V_i] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__list__of__set__range,axiom,
% 94.64/94.42 ! [V_na_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_na_2)) = c_List_Oupt(V_m_2,V_na_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_hd__upt,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_drop__upt,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__upt,axiom,
% 94.64/94.42 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__upt,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__rec__number__of,axiom,
% 94.64/94.42 ! [V_n,V_m] :
% 94.64/94.42 ( ( 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)))
% 94.64/94.42 => 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))) )
% 94.64/94.42 & ( ~ 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)))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_upt__eq__Cons__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 94.64/94.42 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 94.64/94.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 94.64/94.42 & V_i_2 = V_x_2
% 94.64/94.42 & 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 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_last__upt,axiom,
% 94.64/94.42 ! [V_j,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__Suc__upt,axiom,
% 94.64/94.42 ! [V_na_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_na_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_atLeastAtMost__upt,axiom,
% 94.64/94.42 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_na_2,hAPP(c_Nat_OSuc,V_m_2))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_atLeast__upt,axiom,
% 94.64/94.42 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__upt,axiom,
% 94.64/94.42 ! [V_j,V_k,V_i] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_greaterThanAtMost__upt,axiom,
% 94.64/94.42 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_greaterThanLessThan__upt,axiom,
% 94.64/94.42 ! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),V_m_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_atMost__upto,axiom,
% 94.64/94.42 ! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__nth,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 94.64/94.42 ! [V_na_2,V_m_2,V_f_2,T_b] :
% 94.64/94.42 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.42 => 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_na_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_na_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 94.64/94.42 ! [V_na_2,V_m_2,V_f_2,T_b] :
% 94.64/94.42 ( class_Groups_Ocomm__monoid__add(T_b)
% 94.64/94.42 => 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_na_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_na_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__map__upt,axiom,
% 94.64/94.42 ! [V_f_2,T_b,V_m_2,V_na_2,V_i_2] :
% 94.64/94.42 ( 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_na_2),V_m_2)))
% 94.64/94.42 => 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_na_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__rectangle,axiom,
% 94.64/94.42 ! [V_na_2,T_b,V_xs_2] :
% 94.64/94.42 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 94.64/94.42 => V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 94.64/94.42 => ( ! [B_i] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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_na_2 )
% 94.64/94.42 => 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_na_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_insort__key__remove1,axiom,
% 94.64/94.42 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 94.64/94.42 => ( 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
% 94.64/94.42 => 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 ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted_ONil,axiom,
% 94.64/94.42 ! [T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__single,axiom,
% 94.64/94.42 ! [V_x,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__upt,axiom,
% 94.64/94.42 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__sort,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__insort__insert,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__drop,axiom,
% 94.64/94.42 ! [V_n,V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__upto,axiom,
% 94.64/94.42 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__take,axiom,
% 94.64/94.42 ! [V_n,V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__remove1,axiom,
% 94.64/94.42 ! [V_a,V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__tl,axiom,
% 94.64/94.42 ! [V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__insort,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( 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))
% 94.64/94.42 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__butlast,axiom,
% 94.64/94.42 ! [V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted_Oequations_I1_J,axiom,
% 94.64/94.42 ! [T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__many__eq,axiom,
% 94.64/94.42 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( 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)))
% 94.64/94.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__many,axiom,
% 94.64/94.42 ! [V_zs,V_y,V_x,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 94.64/94.42 => 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))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__remdups,axiom,
% 94.64/94.42 ! [V_l,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__distinct__set__unique,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 94.64/94.42 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 94.64/94.42 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__sort__key,axiom,
% 94.64/94.42 ! [V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__insort__insert__key,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__map__remove1,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__insort__key,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( 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)))
% 94.64/94.42 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__filter,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__map__same,axiom,
% 94.64/94.42 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__same,axiom,
% 94.64/94.42 ! [V_xs_2,V_g_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__Cons,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 94.64/94.42 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 & ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__append,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 94.64/94.42 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 94.64/94.42 & ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ! [B_xa] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__insort,axiom,
% 94.64/94.42 ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 94.64/94.42 => ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted_Oequations_I2_J,axiom,
% 94.64/94.42 ! [V_a1_2,V_a2_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 94.64/94.42 <=> ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__list__of__set,axiom,
% 94.64/94.42 ! [V_A_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.42 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 94.64/94.42 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_insort__remove1,axiom,
% 94.64/94.42 ! [V_xs_2,V_a_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => 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 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__nth__mono,axiom,
% 94.64/94.42 ! [V_j,V_i,V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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))) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__equals__nth__mono,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 <=> ! [B_j] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ! [B_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 94.64/94.42 => 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))) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__sorted__distinct__set__unique,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 94.64/94.42 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 94.64/94.42 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__column,axiom,
% 94.64/94.42 ! [V_i_2,V_xs_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__nth__transpose__sorted,axiom,
% 94.64/94.42 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( 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))))
% 94.64/94.42 => ( 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))))
% 94.64/94.42 => 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) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inj__on__rev,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__rev,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 94.64/94.42 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__is__Nil__conv,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.42 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Nil__is__rev__conv,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 94.64/94.42 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev_Osimps_I1_J,axiom,
% 94.64/94.42 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_singleton__rev__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__singleton__conv,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__append,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__concat,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__filter,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_zip__rev,axiom,
% 94.64/94.42 ! [V_ys,T_b,V_xs,T_a] :
% 94.64/94.42 ( 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)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__rev,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all2__rev,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,V_ys_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all2__rev1,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] :
% 94.64/94.42 ( c_List_Olist__all2(T_b,T_c,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 94.64/94.42 <=> c_List_Olist__all2(T_b,T_c,V_Pa_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__rev__ident,axiom,
% 94.64/94.42 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__swap,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 94.64/94.42 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__is__rev__conv,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 94.64/94.42 <=> V_xs_2 = V_ys_2 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_listsum__rev,axiom,
% 94.64/94.42 ! [V_xs,T_a] :
% 94.64/94.42 ( class_Groups_Ocomm__monoid__add(T_a)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__rev,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldl__foldr,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr__foldl,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__eq__Cons__iff,axiom,
% 94.64/94.42 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 94.64/94.42 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 94.64/94.42 <=> 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_hd__rev,axiom,
% 94.64/94.42 ! [T_a,V_xs] :
% 94.64/94.42 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.42 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_last__rev,axiom,
% 94.64/94.42 ! [T_a,V_xs] :
% 94.64/94.42 ( V_xs != c_List_Olist_ONil(T_a)
% 94.64/94.42 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__transpose,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__foldl__cons,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__drop,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__take,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rotate__rev,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__nth,axiom,
% 94.64/94.42 ! [V_xs,T_a,V_n] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__update,axiom,
% 94.64/94.42 ! [V_y,V_xs,T_a,V_k] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__rev__nth__mono,axiom,
% 94.64/94.42 ! [V_j,V_i,V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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))) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldr__max__sorted,axiom,
% 94.64/94.42 ! [V_y_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 94.64/94.42 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 94.64/94.42 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 94.64/94.42 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.42 => 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) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__transpose__sorted,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 94.64/94.42 => 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) )
% 94.64/94.42 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 94.64/94.42 => 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))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__column__length,axiom,
% 94.64/94.42 ! [V_i_2,V_xs_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpose__transpose,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 94.64/94.42 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__takeWhile,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__takeWhile__le,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__eq__all__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__takeWhileD,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_zip__takeWhile__snd,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_zip__takeWhile__fst,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__tail,axiom,
% 94.64/94.42 ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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)) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__eq__take,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__takeWhile,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_return__list__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__append1,axiom,
% 94.64/94.42 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__nth,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__length__takeWhile,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ~ 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))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__not__last,axiom,
% 94.64/94.42 ! [T_b,V_xs_2] :
% 94.64/94.42 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 94.64/94.42 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 94.64/94.42 ! [V_l] :
% 94.64/94.42 ( c_List_Onat__list(V_l)
% 94.64/94.42 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_embed__list__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__neq__rev,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__neq__rev,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__dropWhile__id,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__dropWhile,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__dropWhile__le,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__dropWhile,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_hd__dropWhile,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__map,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__append1,axiom,
% 94.64/94.42 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 94.64/94.42 ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 <=> ( 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))
% 94.64/94.42 & ~ hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__eq__drop,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__nth,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => 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)))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_listsum__map__filter,axiom,
% 94.64/94.42 ! [V_f_2,V_Pa_2,V_xs_2,T_b,T_c] :
% 94.64/94.42 ( class_Groups_Omonoid__add(T_c)
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => ( ~ hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.42 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted__nth__monoI,axiom,
% 94.64/94.42 ! [V_xs,T_a] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_a)
% 94.64/94.42 => ( ! [B_i,B_j] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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))) ) )
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__eq__filter,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b,V_na_2] :
% 94.64/94.42 ( ! [B_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 94.64/94.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) )
% 94.64/94.42 => c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__takeWhile__less__P__nth,axiom,
% 94.64/94.42 ! [V_xs_2,T_b,V_Pa_2,V_j_2] :
% 94.64/94.42 ( ! [B_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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)))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted_Osimps,axiom,
% 94.64/94.42 ! [V_a_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 94.64/94.42 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 94.64/94.42 | ? [B_xs,B_x] :
% 94.64/94.42 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 94.64/94.42 & ! [B_xa] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_List_Oinsert__def,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_not__in__set__insert,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_insert__remdups,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__insert,axiom,
% 94.64/94.42 ! [V_x,V_xs,T_a] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__insert,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_List_Oset__insert,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_insert__Nil,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_maps__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__map__maps,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_maps__simps_I2_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_maps__simps_I1_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_distinct__concat,axiom,
% 94.64/94.42 ! [V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 94.64/94.42 => ( ! [B_ys] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 94.64/94.42 => ( ! [B_ys] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => ! [B_zs] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => ( B_ys != B_zs
% 94.64/94.42 => 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)) ) ) )
% 94.64/94.42 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measures__lesseq,axiom,
% 94.64/94.42 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( hBOOL(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)))
% 94.64/94.42 => hBOOL(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)))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_wf__measures,axiom,
% 94.64/94.42 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__measures_I1_J,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measures__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__measures_I2_J,axiom,
% 94.64/94.42 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(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))))
% 94.64/94.42 <=> ( 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)))
% 94.64/94.42 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 94.64/94.42 & hBOOL(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))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measures__less,axiom,
% 94.64/94.42 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => hBOOL(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)))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_foldl__apply,axiom,
% 94.64/94.42 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => 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)) )
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_order__fun_I2_J,axiom,
% 94.64/94.42 ! [V_g_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( ( class_Orderings_Oorder(T_c)
% 94.64/94.42 & class_Enum_Oenum(T_b) )
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.64/94.42 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.64/94.42 & 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)))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_enum__ex__prod__def,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b,T_c] :
% 94.64/94.42 ( ( class_Enum_Oenum(T_c)
% 94.64/94.42 & class_Enum_Oenum(T_b) )
% 94.64/94.42 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_Pa_2))
% 94.64/94.42 <=> 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))))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_enum__ex,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ( class_Enum_Oenum(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2))
% 94.64/94.42 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_exists__code,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ( class_Enum_Oenum(T_b)
% 94.64/94.42 => ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.64/94.42 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_Pa_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_zip__obtain__same__length,axiom,
% 94.64/94.42 ! [V_Pa_2,V_ys_2,T_c,V_xs_2,T_b] :
% 94.64/94.42 ( ( 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))
% 94.64/94.42 => 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)))) )
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__not__random__dseq__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_dropWhile__append2,axiom,
% 94.64/94.42 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all2__all__nthI,axiom,
% 94.64/94.42 ! [V_Pa_2,V_b_2,T_c,V_a_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 => ( ! [B_n] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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))) )
% 94.64/94.42 => c_List_Olist__all2(T_b,T_c,V_Pa_2,V_a_2,V_b_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_finite__sorted__distinct__unique,axiom,
% 94.64/94.42 ! [V_A_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.42 => ? [B_x] :
% 94.64/94.42 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 94.64/94.42 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 94.64/94.42 & ! [B_y] :
% 94.64/94.42 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 94.64/94.42 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 94.64/94.42 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 94.64/94.42 => B_y = B_x ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_takeWhile__append2,axiom,
% 94.64/94.42 ! [V_ys_2,V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_insort__is__Cons,axiom,
% 94.64/94.42 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_c)
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Cons__eq__filter__iff,axiom,
% 94.64/94.42 ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 <=> ? [B_us,B_vs] :
% 94.64/94.42 ( 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))
% 94.64/94.42 & ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__eq__Cons__iff,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_ys_2,V_Pa_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 <=> ? [B_us,B_vs] :
% 94.64/94.42 ( 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))
% 94.64/94.42 & ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 94.64/94.42 => ~ hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_Pa_2),B_vs) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_order__fun_I1_J,axiom,
% 94.64/94.42 ! [V_g_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( ( class_Orderings_Oorder(T_c)
% 94.64/94.42 & class_Enum_Oenum(T_b) )
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 94.64/94.42 <=> 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_all__code,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ( class_Enum_Oenum(T_b)
% 94.64/94.42 => ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
% 94.64/94.42 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_enum__all,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ( class_Enum_Oenum(T_b)
% 94.64/94.42 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_Pa_2))
% 94.64/94.42 <=> ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_enum__all__prod__def,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b,T_c] :
% 94.64/94.42 ( ( class_Enum_Oenum(T_c)
% 94.64/94.42 & class_Enum_Oenum(T_b) )
% 94.64/94.42 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_Pa_2))
% 94.64/94.42 <=> 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))))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ball__nth,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b,V_na_2] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sorted_OCons,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( class_Orderings_Olinorder(T_b)
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 94.64/94.42 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 94.64/94.42 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__length,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ? [B_n] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__conv__decomp,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 <=> ? [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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__simps_I2_J,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__append,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 94.64/94.42 <=> ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 | c_List_Olist__ex(T_b,V_Pa_2,V_ys_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__iff,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__rev,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 94.64/94.42 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__simps_I1_J,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 94.64/94.42 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 | c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__conv__decomp__first,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 <=> ? [B_ys] :
% 94.64/94.42 ( ? [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))
% 94.64/94.42 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__conv__decomp__last,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 <=> ? [B_ys,B_zs] :
% 94.64/94.42 ( 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))
% 94.64/94.42 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__length,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ! [B_n] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measure__function__int,axiom,
% 94.64/94.42 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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__simps_I2_J,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] : c_List_Olist__all(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__append,axiom,
% 94.64/94.42 ! [V_ys_2,V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 94.64/94.42 <=> ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 & c_List_Olist__all(T_b,V_Pa_2,V_ys_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measure__size,axiom,
% 94.64/94.42 ! [T_b] :
% 94.64/94.42 ( class_Nat_Osize(T_b)
% 94.64/94.42 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_is__measure_Osimps,axiom,
% 94.64/94.42 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_is__measure_Oequations,axiom,
% 94.64/94.42 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_is__measure_Ointros,axiom,
% 94.64/94.42 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__iff,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measure__fst,axiom,
% 94.64/94.42 ! [T_c,V_f_2,T_b] :
% 94.64/94.42 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_measure__snd,axiom,
% 94.64/94.42 ! [T_c,V_f_2,T_b] :
% 94.64/94.42 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__rev,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 94.64/94.42 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__simps_I1_J,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 94.64/94.42 <=> ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 & c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Ball__set__list__all,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 <=> c_List_Olist__all(T_b,V_Pa_2,V_xs_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__iff__raw,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__all(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex1__simps_I2_J,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex1(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 94.64/94.42 <=> ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => 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) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transfer__morphism__int__nat,axiom,
% 94.64/94.42 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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex1__simps_I1_J,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] : ~ c_List_Olist__ex1(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bool_Osize_I4_J,axiom,
% 94.64/94.42 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bool_Osize_I3_J,axiom,
% 94.64/94.42 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex1__iff,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.42 & ! [B_y] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 94.64/94.42 => B_y = B_x ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 94.64/94.42 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 94.64/94.42 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.42 => 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) )
% 94.64/94.42 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 94.64/94.42 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 94.64/94.42 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.42 => 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) )
% 94.64/94.42 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 94.64/94.42 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__empty__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_neg__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_neg__map__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_neg__single__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__bind__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__map__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__single__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__splice,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_splice_Osimps_I3_J,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_splice_Osimps_I1_J,axiom,
% 94.64/94.42 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 94.64/94.42
% 94.64/94.42 fof(fact_splice__Nil2,axiom,
% 94.64/94.42 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 94.64/94.42
% 94.64/94.42 fof(fact_splice_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Opos__single__def,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_acyclicP__converse,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( 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))))
% 94.64/94.42 <=> 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_converse__meet,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_converse__join,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_converse__pred__comp,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversepD,axiom,
% 94.64/94.42 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep_Ointros,axiom,
% 94.64/94.42 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep_Oequations,axiom,
% 94.64/94.42 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 94.64/94.42 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep__iff,axiom,
% 94.64/94.42 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 94.64/94.42 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep__conversep,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep__eq,axiom,
% 94.64/94.42 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep__noteq,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> V_x_2 != V_y_2 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_conversep__converse__eq,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_tl__replicate,axiom,
% 94.64/94.42 ! [V_x,T_a,V_n] :
% 94.64/94.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__length__filter,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_length__replicate,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__replicate__const,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__app__Cons__same,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__Suc,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_rev__replicate,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_drop__replicate,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_hd__replicate,axiom,
% 94.64/94.42 ! [V_x,T_a,V_n] :
% 94.64/94.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_last__replicate,axiom,
% 94.64/94.42 ! [V_x,T_a,V_n] :
% 94.64/94.42 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_take__replicate,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_zip__replicate,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Bex__set__replicate,axiom,
% 94.64/94.42 ! [V_Pa_2,V_a_2,V_na_2,T_b] :
% 94.64/94.42 ( ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2))))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.64/94.42 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Ball__set__replicate,axiom,
% 94.64/94.42 ! [V_Pa_2,V_a_2,V_na_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2))))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 <=> ( hBOOL(hAPP(V_Pa_2,V_a_2))
% 94.64/94.42 | V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__eq__replicate,axiom,
% 94.64/94.42 ! [V_y_2,V_na_2,V_x_2,V_m_2,T_b] :
% 94.64/94.42 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_na_2,V_y_2)
% 94.64/94.42 <=> ( V_m_2 = V_na_2
% 94.64/94.42 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => V_x_2 = V_y_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nth__replicate,axiom,
% 94.64/94.42 ! [V_x,T_a,V_n,V_i] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 94.64/94.42 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__add,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_append__replicate__commute,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_filter__replicate,axiom,
% 94.64/94.42 ! [V_na_2,T_b,V_x_2,V_Pa_2] :
% 94.64/94.42 ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,V_x_2) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
% 94.64/94.42 => hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_concat__replicate__trivial,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__0,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_empty__replicate,axiom,
% 94.64/94.42 ! [V_x_2,V_na_2,T_b] :
% 94.64/94.42 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_na_2,V_x_2)
% 94.64/94.42 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__empty,axiom,
% 94.64/94.42 ! [V_x_2,V_na_2,T_b] :
% 94.64/94.42 ( c_List_Oreplicate(T_b,V_na_2,V_x_2) = c_List_Olist_ONil(T_b)
% 94.64/94.42 <=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__replicate,axiom,
% 94.64/94.42 ! [V_x_2,V_na_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_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,hAPP(V_f_2,V_x_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__replicate,axiom,
% 94.64/94.42 ! [V_y_2,V_na_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_y_2))))
% 94.64/94.42 <=> ( V_x_2 = V_y_2
% 94.64/94.42 & V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_replicate__append__same,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_map__replicate__trivial,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__replicate,axiom,
% 94.64/94.42 ! [V_x_2,T_b,V_na_2] :
% 94.64/94.42 ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__replicate__conv__if,axiom,
% 94.64/94.42 ! [V_x_2,T_b,V_na_2] :
% 94.64/94.42 ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 94.64/94.42 & ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.64/94.42 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_set__replicate__Suc,axiom,
% 94.64/94.42 ! [V_x_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_na_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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy__list_Osimps,axiom,
% 94.64/94.42 ! [V_d_2,T_b] :
% 94.64/94.42 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 94.64/94.42 => 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)))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_eq__comp__r,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy__prod__def,axiom,
% 94.64/94.42 ! [V_d,T_b,T_a] :
% 94.64/94.42 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 94.64/94.42 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_New__DSequence_Opos__union__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_field__le__epsilon,axiom,
% 94.64/94.42 ! [V_y,V_x,T_a] :
% 94.64/94.42 ( class_Fields_Olinordered__field(T_a)
% 94.64/94.42 => ( ! [B_e] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 94.64/94.42 => 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))) )
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_pos__union__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy_H_Osimps,axiom,
% 94.64/94.42 ! [V_i,V_d] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 94.64/94.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 94.64/94.42 => 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)))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy__int__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy_H_Opsimps,axiom,
% 94.64/94.42 ! [V_i_2,V_d_2] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 94.64/94.42 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 94.64/94.42 => 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)))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact__01,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Oinject,axiom,
% 94.64/94.42 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 <=> ( V_a_2 = V_a_H_2
% 94.64/94.42 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_small__lazy_H_Opinduct,axiom,
% 94.64/94.42 ! [V_Pa_2,V_a1_2,V_a0_2] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( ! [B_d,B_i] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 94.64/94.42 => 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)))) )
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_Pa_2,B_d),B_i)) ) )
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_size__code,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence__size__code,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_seq__case,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_yieldn__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_refl__on__INTER,axiom,
% 94.64/94.42 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.64/94.42 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_in__set__member,axiom,
% 94.64/94.42 ! [V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_member__rec_I1_J,axiom,
% 94.64/94.42 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> ( V_x_2 = V_y_2
% 94.64/94.42 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_member__set,axiom,
% 94.64/94.42 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_member__rec_I2_J,axiom,
% 94.64/94.42 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_List_Omember__def,axiom,
% 94.64/94.42 ! [V_x_2,V_xs_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 94.64/94.42 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex1__iff__raw,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex1(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.42 & ! [B_y] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_y)) )
% 94.64/94.42 => B_y = B_x ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_setsum__UNION__zero,axiom,
% 94.64/94.42 ! [V_f_2,V_S_2,T_b,T_c] :
% 94.64/94.42 ( class_Groups_Ocomm__monoid__add(T_c)
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 94.64/94.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 94.64/94.42 => ( ! [B_T1] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 94.64/94.42 => ! [B_T2] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 94.64/94.42 => ( B_T1 != B_T2
% 94.64/94.42 => ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 94.64/94.42 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 94.64/94.42 => 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) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_THE__default__def,axiom,
% 94.64/94.42 ! [V_d_2,T_b,V_Pa_2] :
% 94.64/94.42 ( ( ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.42 & ! [B_y] :
% 94.64/94.42 ( hBOOL(hAPP(V_Pa_2,B_y))
% 94.64/94.42 => B_y = B_x ) )
% 94.64/94.42 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = c_HOL_OThe(T_b,V_Pa_2) )
% 94.64/94.42 & ( ~ ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(V_Pa_2,B_x))
% 94.64/94.42 & ! [B_y] :
% 94.64/94.42 ( hBOOL(hAPP(V_Pa_2,B_y))
% 94.64/94.42 => B_y = B_x ) )
% 94.64/94.42 => c_FunDef_OTHE__default(T_b,V_d_2,V_Pa_2) = V_d_2 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_INF2__I,axiom,
% 94.64/94.42 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 94.64/94.42 ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 94.64/94.42 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_SUP2__E,axiom,
% 94.64/94.42 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 94.64/94.42 => ~ ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.42 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_finite__maxlen,axiom,
% 94.64/94.42 ! [V_M_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 94.64/94.42 => ? [B_n] :
% 94.64/94.42 ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact__02,axiom,
% 94.64/94.42 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 94.64/94.42 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.64/94.42 ( c_List_Olist__ex(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 94.64/94.42 <=> ~ 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__all__iff__all__interval__int,axiom,
% 94.64/94.42 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.64/94.42 ( c_List_Olist__all(tc_Int_Oint,V_Pa_2,c_List_Oupto(V_i_2,V_j_2))
% 94.64/94.42 <=> c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_all__interval__int__def,axiom,
% 94.64/94.42 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.64/94.42 ( c_List_Oall__interval__int(V_Pa_2,V_i_2,V_j_2)
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Random_Osimps,axiom,
% 94.64/94.42 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 94.64/94.42 ( ( 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)))
% 94.64/94.42 => 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)) )
% 94.64/94.42 & ( ~ 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)))
% 94.64/94.42 => 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))))))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Random__Sequence_Oempty__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Random__Sequence_Osingle__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Random__Sequence_Omap__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_exE__realizer,axiom,
% 94.64/94.42 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_Pa_2] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( ! [B_x,B_y] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x))
% 94.64/94.42 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 94.64/94.42 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Image__Collect__split,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lexord__trans,axiom,
% 94.64/94.42 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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)))
% 94.64/94.42 => ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_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))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__less__than,axiom,
% 94.64/94.42 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__lex__prod,axiom,
% 94.64/94.42 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_R1_2)
% 94.64/94.42 => ( c_Relation_Otrans(T_c,V_R2_2)
% 94.64/94.42 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__def,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 <=> ! [B_x,B_y] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => ! [B_z] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transD,axiom,
% 94.64/94.42 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => ( hBOOL(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))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Union__eq,axiom,
% 94.64/94.42 ! [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)))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__reflclI,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__inv__image,axiom,
% 94.64/94.42 ! [V_f_2,T_c,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__O__subset,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_SUPR__bool__eq,axiom,
% 94.64/94.42 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__Int,axiom,
% 94.64/94.42 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Otrans(T_b,V_s_2)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bex__UNIV,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ( ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_finite__Collect__bex,axiom,
% 94.64/94.42 ! [V_Q_2,T_c,V_A_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
% 94.64/94.42 <=> ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.64/94.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_listrel__trans,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bex__empty,axiom,
% 94.64/94.42 ! [V_Pa_2,T_b] :
% 94.64/94.42 ~ ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__converse,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.42 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lexord__transI,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__finite__psubset,axiom,
% 94.64/94.42 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__Id,axiom,
% 94.64/94.42 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__Id__on,axiom,
% 94.64/94.42 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__trancl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trancl__id,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__rtrancl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_list__ex__iff__raw,axiom,
% 94.64/94.42 ! [V_xs_2,V_Pa_2,T_b] :
% 94.64/94.42 ( c_List_Olist__ex(T_b,V_Pa_2,V_xs_2)
% 94.64/94.42 <=> ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Bex__set__list__ex,axiom,
% 94.64/94.42 ! [V_Pa_2,V_xs_2,T_b] :
% 94.64/94.42 ( ? [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 94.64/94.42 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.64/94.42 <=> c_List_Olist__ex(T_b,V_Pa_2,V_xs_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_UN__eq,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_INT__eq,axiom,
% 94.64/94.42 ! [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))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Sup__fun__def,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.64/94.42 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.42 => 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)))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Sup__apply,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.64/94.42 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.42 => 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)))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Inf__fun__def,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.64/94.42 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.42 => 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)))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_Inf__apply,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,T_c,T_b] :
% 94.64/94.42 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 94.64/94.42 => 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)))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_max__extp_Ointros,axiom,
% 94.64/94.42 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 94.64/94.42 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 94.64/94.42 => ? [B_xa] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 94.64/94.42 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 94.64/94.42 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transp__def,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Predicate_Otransp(T_b,V_r_2)
% 94.64/94.42 <=> 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_transpE,axiom,
% 94.64/94.42 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Predicate_Otransp(T_b,V_r_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivp__reflp__symp__transp,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.64/94.42 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 94.64/94.42 & c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivpI,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Predicate_Oreflp(T_b,V_R_2)
% 94.64/94.42 => ( c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 => ( c_Predicate_Otransp(T_b,V_R_2)
% 94.64/94.42 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sympE,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Predicate_Osymp(T_b,V_r_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivpE,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.64/94.42 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 94.64/94.42 => ( c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_max__extp_Osimps,axiom,
% 94.64/94.42 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 94.64/94.42 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 94.64/94.42 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 94.64/94.42 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 94.64/94.42 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 94.64/94.42 & ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 94.64/94.42 => ? [B_xa] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 94.64/94.42 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_trans__diff__Id,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Oantisym(T_b,V_r_2)
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__Id__on,axiom,
% 94.64/94.42 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__subset,axiom,
% 94.64/94.42 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => ( c_Relation_Oantisym(T_b,V_s_2)
% 94.64/94.42 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__Id,axiom,
% 94.64/94.42 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__empty,axiom,
% 94.64/94.42 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__converse,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.42 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__def,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Oantisym(T_b,V_r_2)
% 94.64/94.42 <=> ! [B_x,B_y] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => ( 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))
% 94.64/94.42 => B_x = B_y ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisymD,axiom,
% 94.64/94.42 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Oantisym(T_b,V_r_2)
% 94.64/94.42 => ( hBOOL(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))
% 94.64/94.42 => ( 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))
% 94.64/94.42 => V_a_2 = V_b_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_antisym__reflcl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_fun__lub__def,axiom,
% 94.64/94.42 ! [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)))))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__trans__comp__subset,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__def,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 <=> ! [B_x,B_y] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_symD,axiom,
% 94.64/94.42 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ( hBOOL(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))
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__inv__image,axiom,
% 94.64/94.42 ! [V_f_2,T_c,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Un__converse,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Int,axiom,
% 94.64/94.42 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Osym(T_b,V_s_2)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_listrel__sym,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__converse,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 94.64/94.42 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__conv__converse__eq,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Id,axiom,
% 94.64/94.42 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Un,axiom,
% 94.64/94.42 ! [V_s_2,V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Osym(T_b,V_s_2)
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Id__on,axiom,
% 94.64/94.42 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__trancl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__rtrancl,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_sym__Int__converse,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equiv__def,axiom,
% 94.64/94.42 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.64/94.42 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.64/94.42 & c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivI,axiom,
% 94.64/94.42 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.42 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.64/94.42 => ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ( c_Relation_Otrans(T_b,V_r_2)
% 94.64/94.42 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivE,axiom,
% 94.64/94.42 ! [V_r_2,V_A_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.64/94.42 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 94.64/94.42 => ( c_Relation_Osym(T_b,V_r_2)
% 94.64/94.42 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_symp__def,axiom,
% 94.64/94.42 ! [V_r_2,T_b] :
% 94.64/94.42 ( c_Predicate_Osymp(T_b,V_r_2)
% 94.64/94.42 <=> 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivp__refl__symp__transp,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 94.64/94.42 & c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivpI,axiom,
% 94.64/94.42 ! [T_b,V_R_2] :
% 94.64/94.42 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 94.64/94.42 => ( c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 => ( c_Predicate_Otransp(T_b,V_R_2)
% 94.64/94.42 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_equivp__implies__part__equivp,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.64/94.42 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivp__def,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 94.64/94.42 & ! [B_x,B_y] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 94.64/94.42 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 94.64/94.42 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 94.64/94.42 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivp__symp,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivp__transp,axiom,
% 94.64/94.42 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 94.64/94.42 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivpE,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 94.64/94.42 => ( c_Predicate_Osymp(T_b,V_R_2)
% 94.64/94.42 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_part__equivp__typedef,axiom,
% 94.64/94.42 ! [V_R_2,T_b] :
% 94.64/94.42 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 94.64/94.42 => ? [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))))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inj__iff,axiom,
% 94.64/94.42 ! [V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 <=> 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__o__cancel,axiom,
% 94.64/94.42 ! [V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inj__on__inv__into,axiom,
% 94.64/94.42 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__image__cancel,axiom,
% 94.64/94.42 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 94.64/94.42 => 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 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_surj__imp__inj__inv,axiom,
% 94.64/94.42 ! [V_f_2,T_b,T_c] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__image__comp,axiom,
% 94.64/94.42 ! [V_X_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_image__inv__f__f,axiom,
% 94.64/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inj__imp__surj__inv,axiom,
% 94.64/94.42 ! [V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_image__inv__into__cancel,axiom,
% 94.64/94.42 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 94.64/94.42 => 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 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_surj__iff__all,axiom,
% 94.64/94.42 ! [V_f_2,T_b,T_c] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> ! [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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_surj__f__inv__f,axiom,
% 94.64/94.42 ! [V_y_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_image__surj__f__inv__f,axiom,
% 94.64/94.42 ! [V_A_2,V_f_2,T_b,T_c] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_f__inv__into__f,axiom,
% 94.64/94.42 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__into,axiom,
% 94.64/94.42 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 94.64/94.42 => 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)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__injective,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 94.64/94.42 ( 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)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 94.64/94.42 => V_x_2 = V_y_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__f__f,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.42 => 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 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__f__eq,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 94.64/94.42 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 94.64/94.42 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__f__eq,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 94.64/94.42 => 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 ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__f__f,axiom,
% 94.64/94.42 ! [V_x_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__id,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__def,axiom,
% 94.64/94.42 ! [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))) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__def,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_o__inv__o__cancel,axiom,
% 94.64/94.42 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__comp,axiom,
% 94.64/94.42 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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))
% 94.64/94.42 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 94.64/94.42 => ( 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))))
% 94.64/94.42 => 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) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_surj__iff,axiom,
% 94.64/94.42 ! [V_f_2,T_b,T_c] :
% 94.64/94.42 ( 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))
% 94.64/94.42 <=> 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inj__transfer,axiom,
% 94.64/94.42 ! [V_x_2,V_Pa_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.64/94.42 => ( ! [B_y] :
% 94.64/94.42 ( 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)))))
% 94.64/94.42 => 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))) )
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_fold__image__UN__disjoint,axiom,
% 94.64/94.42 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 94.64/94.42 ( class_Groups_Ocomm__monoid__mult(T_d)
% 94.64/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 94.64/94.42 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 94.64/94.42 => ( ! [B_x] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 94.64/94.42 => ! [B_xa] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 94.64/94.42 => ( B_x != B_xa
% 94.64/94.42 => 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)) ) ) )
% 94.64/94.42 => 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) ) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nat__of__induct,axiom,
% 94.64/94.42 ! [V_Pa_2,V_y_2] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.42 => ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,V_y_2)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_nat__of__cases,axiom,
% 94.64/94.42 ! [V_y_2] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.42 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_of__nat__induct,axiom,
% 94.64/94.42 ! [V_x_2,V_Pa_2] :
% 94.64/94.42 ( ! [B_y] :
% 94.64/94.42 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 94.64/94.42 => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_of__nat__cases,axiom,
% 94.64/94.42 ! [V_x_2] :
% 94.64/94.42 ~ ! [B_y] :
% 94.64/94.42 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 94.64/94.42 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 94.64/94.42 ! [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 ).
% 94.64/94.42
% 94.64/94.42 fof(fact_beyond__def,axiom,
% 94.64/94.42 ! [V_l,V_k] :
% 94.64/94.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 94.64/94.42 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 94.64/94.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 94.64/94.42 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_beyond__zero,axiom,
% 94.64/94.42 ! [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) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 94.64/94.42 ! [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)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__image__Collect__eq,axiom,
% 94.64/94.42 ! [V_Pa_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_curry__def,axiom,
% 94.64/94.42 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_curryI,axiom,
% 94.64/94.42 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 94.64/94.42 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 94.64/94.42 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__betw__id,axiom,
% 94.64/94.42 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__imp__bij__inv,axiom,
% 94.64/94.42 ! [V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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))) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__inv__eq,axiom,
% 94.64/94.42 ! [V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => 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 ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_inv__into__inv__into__eq,axiom,
% 94.64/94.42 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 94.64/94.42 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 94.64/94.42 => 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) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__betw__inv__into,axiom,
% 94.64/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.64/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.64/94.42 => 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) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_o__inv__distrib,axiom,
% 94.64/94.42 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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)) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__betw__comp__iff2,axiom,
% 94.64/94.42 ! [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] :
% 94.64/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 94.64/94.42 => ( 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))
% 94.64/94.42 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 94.64/94.42 <=> 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) ) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__comp,axiom,
% 94.64/94.42 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 94.64/94.42 ( 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)))
% 94.64/94.42 => ( 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)))
% 94.64/94.42 => 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))) ) ) ).
% 94.64/94.42
% 94.64/94.42 fof(fact_bij__betw__comp__iff,axiom,
% 94.64/94.42 ! [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] :
% 94.64/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 94.68/94.42 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 94.68/94.42 <=> 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) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__trans,axiom,
% 94.68/94.42 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 94.68/94.42 => 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) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_curryD,axiom,
% 94.68/94.42 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 94.68/94.42 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_curryE,axiom,
% 94.68/94.42 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 94.68/94.42 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_curry__conv,axiom,
% 94.68/94.42 ! [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)) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__image__Compl__eq,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => 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)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_finite__vimage__iff,axiom,
% 94.68/94.42 ! [V_F_2,V_h_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 94.68/94.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__Disj__Un,axiom,
% 94.68/94.42 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 94.68/94.42 ( 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))
% 94.68/94.42 => ( 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))
% 94.68/94.42 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 94.68/94.42 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 94.68/94.42 => 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)) ) ) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__combine,axiom,
% 94.68/94.42 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 94.68/94.42 => ( 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))
% 94.68/94.42 => 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)) ) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__id,axiom,
% 94.68/94.42 ! [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))) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__id__iff,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 94.68/94.42 <=> V_A_2 = V_B_2 ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__finite,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.68/94.42 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_BIJ,axiom,
% 94.68/94.42 ! [V_B_2,T_c,V_A_2,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.68/94.42 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 94.68/94.42 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 94.68/94.42 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__empty2,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__empty1,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)
% 94.68/94.42 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__same__card,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__the__inv__into,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => 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) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__is__inj,axiom,
% 94.68/94.42 ! [V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__imp__inj__on,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__def,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 94.68/94.42 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.68/94.42 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_inj__on__imp__bij__betw,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.68/94.42 => 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)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__is__surj,axiom,
% 94.68/94.42 ! [V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => 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)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__imp__surj,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => 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)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__betw__subset,axiom,
% 94.68/94.42 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 94.68/94.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.68/94.42 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 94.68/94.42 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__def,axiom,
% 94.68/94.42 ! [V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.68/94.42 & 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)) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bijI,axiom,
% 94.68/94.42 ! [V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 94.68/94.42 => ( 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))
% 94.68/94.42 => 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))) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_curry__split,axiom,
% 94.68/94.42 ! [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 ).
% 94.68/94.42
% 94.68/94.42 fof(fact_split__curry,axiom,
% 94.68/94.42 ! [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 ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__image__INT,axiom,
% 94.68/94.42 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => 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)) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_vimage__subset__eq,axiom,
% 94.68/94.42 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => ( 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))
% 94.68/94.42 <=> 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))) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_bij__vimage__eq__inv__image,axiom,
% 94.68/94.42 ! [V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( 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)))
% 94.68/94.42 => 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) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 94.68/94.42 ! [V_M_2,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 94.68/94.42 => ? [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) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_Cantor__Bernstein,axiom,
% 94.68/94.42 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 94.68/94.42 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 94.68/94.42 => ( 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))
% 94.68/94.42 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 94.68/94.42 => ( 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))
% 94.68/94.42 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_ex__bij__betw__nat__finite,axiom,
% 94.68/94.42 ! [V_M_2,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 94.68/94.42 => ? [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) ) ).
% 94.68/94.42
% 94.68/94.42 fof(fact_ex__bij__betw__finite__nat,axiom,
% 94.68/94.42 ! [V_M_2,T_b] :
% 94.68/94.42 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 94.68/94.42 => ? [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))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_refl__on__UNION,axiom,
% 94.68/94.43 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 94.68/94.43 ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 94.68/94.43 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 94.68/94.43 => 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)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_bex__reg__eqv,axiom,
% 94.68/94.43 ! [V_Pa_2,V_R_2,T_b] :
% 94.68/94.43 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.68/94.43 => ( ? [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 94.68/94.43 & hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.68/94.43 <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_Respects__def,axiom,
% 94.68/94.43 ! [V_x_2,V_R_2,T_b] :
% 94.68/94.43 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_in__respects,axiom,
% 94.68/94.43 ! [V_R_2,V_x_2,T_b] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_bex__reg__right,axiom,
% 94.68/94.43 ! [V_Pa_2,V_Q_2,V_R_2,T_b] :
% 94.68/94.43 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.68/94.43 => ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(V_Q_2,B_x))
% 94.68/94.43 => hBOOL(hAPP(V_Pa_2,B_x)) )
% 94.68/94.43 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 94.68/94.43 => ? [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 94.68/94.43 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_babs__reg__eqv,axiom,
% 94.68/94.43 ! [V_Pa_2,T_c,V_R_2,T_b] :
% 94.68/94.43 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 94.68/94.43 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_Pa_2) = V_Pa_2 ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_Babs__def,axiom,
% 94.68/94.43 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 94.68/94.43 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_wf__weak__decr__stable,axiom,
% 94.68/94.43 ! [V_r_2,V_f_2,T_b] :
% 94.68/94.43 ( ! [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)))
% 94.68/94.43 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 94.68/94.43 => ? [B_i] :
% 94.68/94.43 ! [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) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_INT__anti__mono,axiom,
% 94.68/94.43 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 94.68/94.43 => ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.68/94.43 => 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))) )
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_INT__greatest,axiom,
% 94.68/94.43 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 94.68/94.43 ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 94.68/94.43 => 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))) )
% 94.68/94.43 => 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))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_rtrancl__induct2,axiom,
% 94.68/94.43 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2))
% 94.68/94.43 => ( ! [B_a,B_b] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ! [B_aa,B_ba] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
% 94.68/94.43 => hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba)) ) ) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_converse__rtranclE2,axiom,
% 94.68/94.43 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( 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)
% 94.68/94.43 => ~ ! [B_a,B_b] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => ~ 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_converse__rtrancl__induct2,axiom,
% 94.68/94.43 ! [V_Pa_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,V_bx_2),V_by_2))
% 94.68/94.43 => ( ! [B_a,B_b,B_aa,B_ba] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(V_Pa_2,B_aa),B_ba))
% 94.68/94.43 => hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b)) ) ) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(V_Pa_2,V_ax_2),V_ay_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_congruent2I_H,axiom,
% 94.68/94.43 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 94.68/94.43 ( ! [B_y1,B_z1] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => ! [B_y2,B_z2] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 94.68/94.43 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_congruentI,axiom,
% 94.68/94.43 ! [T_c,V_f_2,V_r_2,T_b] :
% 94.68/94.43 ( ! [B_y,B_z] :
% 94.68/94.43 ( 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))
% 94.68/94.43 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 94.68/94.43 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact__03,axiom,
% 94.68/94.43 ! [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)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_list__all__iff__all__interval__nat,axiom,
% 94.68/94.43 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.68/94.43 ( c_List_Olist__all(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 94.68/94.43 <=> c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact__04,axiom,
% 94.68/94.43 ! [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) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_all__interval__nat__def,axiom,
% 94.68/94.43 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.68/94.43 ( c_List_Oall__interval__nat(V_Pa_2,V_i_2,V_j_2)
% 94.68/94.43 <=> ! [B_x] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 94.68/94.43 ! [V_j_2,V_i_2,V_Pa_2] :
% 94.68/94.43 ( c_List_Olist__ex(tc_Nat_Onat,V_Pa_2,c_List_Oupt(V_i_2,V_j_2))
% 94.68/94.43 <=> ~ 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) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact__05,axiom,
% 94.68/94.43 ! [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)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_folding__image_Ocong,axiom,
% 94.68/94.43 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 94.68/94.43 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 94.68/94.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 94.68/94.43 => ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 94.68/94.43 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 94.68/94.43 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact__06,axiom,
% 94.68/94.43 ! [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)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact__07,axiom,
% 94.68/94.43 ! [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) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_New__DSequence_Opos__map__def,axiom,
% 94.68/94.43 ! [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)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_power__dvd__imp__le,axiom,
% 94.68/94.43 ! [V_n,V_m,V_i] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oorder__refl,axiom,
% 94.68/94.43 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__0__right,axiom,
% 94.68/94.43 ! [V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__1__left,axiom,
% 94.68/94.43 ! [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)) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__imp__le,axiom,
% 94.68/94.43 ! [V_n,V_k] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__cancel,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_nat__mult__dvd__cancel1,axiom,
% 94.68/94.43 ! [V_na_2,V_m_2,V_k_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 94.68/94.43 => ( 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_na_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_setprod__dvd__setprod__subset,axiom,
% 94.68/94.43 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 94.68/94.43 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 94.68/94.43 & class_Rings_Odvd(T_c) )
% 94.68/94.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 94.68/94.43 => 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2,T_b] :
% 94.68/94.43 ( ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 & class_Int_Onumber(T_b) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 94.68/94.43 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__div__div__eq__mult,axiom,
% 94.68/94.43 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.68/94.43 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 94.68/94.43 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 94.68/94.43 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__div__eq__mult,axiom,
% 94.68/94.43 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 94.68/94.43 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 94.68/94.43 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__diffD,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__diffD1,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_le__imp__power__dvd,axiom,
% 94.68/94.43 ! [V_a,V_n,V_m,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__power__le,axiom,
% 94.68/94.43 ! [V_m,V_n,V_y,V_x,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 94.68/94.43 => 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_power__le__dvd,axiom,
% 94.68/94.43 ! [V_m,V_b,V_n,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( 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))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 94.68/94.43 => 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)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 94.68/94.43 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 94.68/94.43 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 94.68/94.43 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 94.68/94.43 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeast__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_i_2] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatMost__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_i_2] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OlessThan__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_i_2] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OgreaterThan__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_i_2] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_div__power,axiom,
% 94.68/94.43 ! [V_n,V_x,V_y,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 94.68/94.43 => 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)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__abs__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_m_2,T_b] :
% 94.68/94.43 ( class_Rings_Olinordered__idom(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_abs__dvd__iff,axiom,
% 94.68/94.43 ! [V_k_2,V_m_2,T_b] :
% 94.68/94.43 ( class_Rings_Olinordered__idom(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__if__abs__eq,axiom,
% 94.68/94.43 ! [V_k,V_l,T_a] :
% 94.68/94.43 ( class_Rings_Olinordered__idom(T_a)
% 94.68/94.43 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_nat__dvd__1__iff__1,axiom,
% 94.68/94.43 ! [V_m_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 94.68/94.43 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_one__dvd,axiom,
% 94.68/94.43 ! [V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__0__left,axiom,
% 94.68/94.43 ! [V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 94.68/94.43 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__refl,axiom,
% 94.68/94.43 ! [V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__trans,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oeq__iff,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2] :
% 94.68/94.43 ( V_x_2 = V_y_2
% 94.68/94.43 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Ole__less,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 94.68/94.43 | V_x_2 = V_y_2 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__le,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 94.68/94.43 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 & V_x_2 != V_y_2 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oneq__le__trans,axiom,
% 94.68/94.43 ! [V_b,V_a] :
% 94.68/94.43 ( V_a != V_b
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oeq__refl,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( V_x = V_y
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oantisym__conv,axiom,
% 94.68/94.43 ! [V_x_2,V_y_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 <=> V_x_2 = V_y_2 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 | V_x = V_y ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Ole__neq__trans,axiom,
% 94.68/94.43 ! [V_b,V_a] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 => ( V_a != V_b
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a] :
% 94.68/94.43 ( V_a = V_b
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 => ( V_b = V_c
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__antisym,axiom,
% 94.68/94.43 ! [V_n,V_m] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 94.68/94.43 => V_m = V_n ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oantisym,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 94.68/94.43 => V_x = V_y ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oorder__trans,axiom,
% 94.68/94.43 ! [V_z,V_y,V_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a] :
% 94.68/94.43 ( V_a = V_b
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Ole__less__trans,axiom,
% 94.68/94.43 ! [V_z,V_y,V_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__imp__neq,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => V_x != V_y ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__not__sym,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__imp__le,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__imp__not__less,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => V_x != V_y ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => V_y != V_x ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 94.68/94.43 => ( V_b = V_c
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__le__trans,axiom,
% 94.68/94.43 ! [V_z,V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__asym_H,axiom,
% 94.68/94.43 ! [V_b,V_a] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 94.68/94.43 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__trans,axiom,
% 94.68/94.43 ! [V_z,V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Oless__asym,axiom,
% 94.68/94.43 ! [V_y,V_x] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 94.68/94.43 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_div__dvd__div,axiom,
% 94.68/94.43 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__power__same,axiom,
% 94.68/94.43 ! [V_n,V_y,V_x,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mod__imp__dvd,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mod,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_mod__mod__cancel,axiom,
% 94.68/94.43 ! [V_a,V_b,V_c,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 94.68/94.43 => 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) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mod__iff,axiom,
% 94.68/94.43 ! [V_m_2,V_na_2,V_k_2,T_b] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_na_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_na_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__minus__iff,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2,T_b] :
% 94.68/94.43 ( class_Rings_Ocomm__ring__1(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_minus__dvd__iff,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2,T_b] :
% 94.68/94.43 ( class_Rings_Ocomm__ring__1(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__diff__nat,axiom,
% 94.68/94.43 ! [V_n,V_m,V_k] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__diff,axiom,
% 94.68/94.43 ! [V_z,V_y,V_x,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__ring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__imp__mod__0,axiom,
% 94.68/94.43 ! [V_b,V_a,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__eq__mod__eq__0,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2,T_b] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 94.68/94.43 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__div__neg,axiom,
% 94.68/94.43 ! [V_x,V_y,T_a] :
% 94.68/94.43 ( class_Divides_Oring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 94.68/94.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__neg__div,axiom,
% 94.68/94.43 ! [V_x,V_y,T_a] :
% 94.68/94.43 ( class_Divides_Oring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 94.68/94.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_nat__dvd__not__less,axiom,
% 94.68/94.43 ! [V_n,V_m] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 94.68/94.43 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__1__iff__1,axiom,
% 94.68/94.43 ! [V_m_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 94.68/94.43 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
% 94.68/94.43 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 94.68/94.43 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 94.68/94.43 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 94.68/94.43 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 94.68/94.43 & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2)) )
% 94.68/94.43 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2)) ) ) ) )
% 94.68/94.43 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_div__add,axiom,
% 94.68/94.43 ! [V_y,V_x,V_z,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 94.68/94.43 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__reduce,axiom,
% 94.68/94.43 ! [V_na_2,V_k_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2)))
% 94.68/94.43 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_na_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__add,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2] :
% 94.68/94.43 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 94.68/94.43 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 94.68/94.43 ! [V_l_2,V_k_2] :
% 94.68/94.43 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 94.68/94.43 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2] :
% 94.68/94.43 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 94.68/94.43 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 94.68/94.43 ! [V_l_2,V_k_2] :
% 94.68/94.43 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 94.68/94.43 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 94.68/94.43 ! [V_k_2,V_l_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 94.68/94.43 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 94.68/94.43 ! [V_a_2,V_b_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 94.68/94.43 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 94.68/94.43 ! [V_k_2,V_l_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 94.68/94.43 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2] :
% 94.68/94.43 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 94.68/94.43 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2] :
% 94.68/94.43 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 94.68/94.43 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 94.68/94.43 ! [V_a_2,V_b_2] :
% 94.68/94.43 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 94.68/94.43 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 94.68/94.43 ! [V_c_2,V_b_2,V_a_2] :
% 94.68/94.43 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 94.68/94.43 <=> ( V_a_2 = V_b_2
% 94.68/94.43 & V_b_2 = V_c_2 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 94.68/94.43 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2] :
% 94.68/94.43 ( V_a_2 = V_b_2
% 94.68/94.43 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_inf__period_I4_J,axiom,
% 94.68/94.43 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 94.68/94.43 ( ( class_Rings_Ocomm__ring(T_b)
% 94.68/94.43 & class_Rings_Odvd(T_b) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 94.68/94.43 => ! [B_x,B_k] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_inf__period_I3_J,axiom,
% 94.68/94.43 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 94.68/94.43 ( ( class_Rings_Ocomm__ring(T_b)
% 94.68/94.43 & class_Rings_Odvd(T_b) )
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 94.68/94.43 => ! [B_x,B_k] :
% 94.68/94.43 ( 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)))
% 94.68/94.43 <=> 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 94.68/94.43 ! [V_na_2,V_m_2,V_k_2] :
% 94.68/94.43 ( 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_na_2)))
% 94.68/94.43 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__div__cancel,axiom,
% 94.68/94.43 ! [V_b,V_a,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => 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 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_div__mult__swap,axiom,
% 94.68/94.43 ! [V_a,V_b,V_c,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 94.68/94.43 => 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) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__div__mult__self,axiom,
% 94.68/94.43 ! [V_b,V_a,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => 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 ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__div__mult,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => 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) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_div__mult__div__if__dvd,axiom,
% 94.68/94.43 ! [V_w,V_z,V_x,V_y,T_a] :
% 94.68/94.43 ( class_Divides_Osemiring__div(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 94.68/94.43 => 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)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__triv__left,axiom,
% 94.68/94.43 ! [V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => 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))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__triv__right,axiom,
% 94.68/94.43 ! [V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => 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))) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult2,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult,axiom,
% 94.68/94.43 ! [V_b,V_c,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 94.68/94.43 => 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))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_mult__dvd__mono,axiom,
% 94.68/94.43 ! [V_d,V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 94.68/94.43 => 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))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvdI,axiom,
% 94.68/94.43 ! [V_k,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Odvd(T_a)
% 94.68/94.43 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__left,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( 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))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__right,axiom,
% 94.68/94.43 ! [V_c,V_b,V_a,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( 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))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__cancel__left,axiom,
% 94.68/94.43 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 94.68/94.43 ( class_Rings_Oidom(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 94.68/94.43 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__cancel__right,axiom,
% 94.68/94.43 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 94.68/94.43 ( class_Rings_Oidom(T_b)
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 94.68/94.43 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_unity__coeff__ex,axiom,
% 94.68/94.43 ! [V_l_2,V_Pa_2,T_b] :
% 94.68/94.43 ( ( class_Rings_Odvd(T_b)
% 94.68/94.43 & class_Rings_Osemiring__0(T_b) )
% 94.68/94.43 => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 94.68/94.43 <=> ? [B_x] :
% 94.68/94.43 ( 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))))
% 94.68/94.43 & hBOOL(hAPP(V_Pa_2,B_x)) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__setprod,axiom,
% 94.68/94.43 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_c)
% 94.68/94.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__power,axiom,
% 94.68/94.43 ! [V_x,V_n,T_a] :
% 94.68/94.43 ( class_Rings_Ocomm__semiring__1(T_a)
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 94.68/94.43 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__cancel1,axiom,
% 94.68/94.43 ! [V_na_2,V_m_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_m_2))
% 94.68/94.43 <=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd__mult__cancel2,axiom,
% 94.68/94.43 ! [V_na_2,V_m_2] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_m_2)),V_m_2))
% 94.68/94.43 <=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_dvd_Ostrict__monoD,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2,V_f_2,T_b] :
% 94.68/94.43 ( class_Orderings_Oorder(T_b)
% 94.68/94.43 => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
% 94.68/94.43 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
% 94.68/94.43 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_equiv__imp__dvd__card,axiom,
% 94.68/94.43 ! [V_k_2,V_r_2,V_A_2,T_b] :
% 94.68/94.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 94.68/94.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 94.68/94.43 => ( ! [B_x] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_zdvd__imp__le,axiom,
% 94.68/94.43 ! [V_n,V_z] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 94.68/94.43 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ) ).
% 94.68/94.43
% 94.68/94.43 fof(fact_zdvd__antisym__nonneg,axiom,
% 94.68/94.43 ! [V_n,V_m] :
% 94.68/94.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
% 94.68/94.43 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
% 94.68/94.43 => V_m = V_n ) ) ) ) ).
% 94.68/94.43
% 94.68/94.43 %----Arity declarations (220)
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 94.68/94.43 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Obounded__lattice(T_1)
% 94.68/94.43 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 94.68/94.43 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Obounded__lattice(T_1)
% 94.68/94.43 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Obounded__lattice(T_1)
% 94.68/94.43 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Olattice(T_1)
% 94.68/94.43 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Olattice(T_1)
% 94.68/94.43 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Odistrib__lattice(T_1)
% 94.68/94.43 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Oboolean__algebra(T_1)
% 94.68/94.43 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Orderings_Opreorder,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Orderings_Opreorder(T_1)
% 94.68/94.43 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Finite__Set_Ofinite(T_2)
% 94.68/94.43 & class_Finite__Set_Ofinite(T_1) )
% 94.68/94.43 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Lattices_Olattice,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Lattices_Olattice(T_1)
% 94.68/94.43 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Orderings_Oorder,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Orderings_Oorder(T_1)
% 94.68/94.43 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Orderings_Otop,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Orderings_Otop(T_1)
% 94.68/94.43 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Orderings_Oord,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Orderings_Oord(T_1)
% 94.68/94.43 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Orderings_Obot,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Orderings_Obot(T_1)
% 94.68/94.43 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Groups_Ouminus,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Groups_Ouminus(T_1)
% 94.68/94.43 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Groups_Ominus,axiom,
% 94.68/94.43 ! [T_2,T_1] :
% 94.68/94.43 ( class_Groups_Ominus(T_1)
% 94.68/94.43 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_fun__Enum_Oenum,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Enum_Oenum(T_2)
% 94.68/94.43 & class_Enum_Oenum(T_1) )
% 94.68/94.43 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Com__Ocom__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_Com_Ocom) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 94.68/94.43 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 94.68/94.43 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 94.68/94.43 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 94.68/94.43 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 94.68/94.43 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 94.68/94.43 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 94.68/94.43 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 94.68/94.43 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 94.68/94.43 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 94.68/94.43 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 94.68/94.43 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 94.68/94.43 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 94.68/94.43 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 94.68/94.43 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 94.68/94.43 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 94.68/94.43 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 94.68/94.43 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 94.68/94.43 class_Orderings_Opreorder(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 94.68/94.43 class_Orderings_Olinorder(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 94.68/94.43 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 94.68/94.43 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 94.68/94.43 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 94.68/94.43 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 94.68/94.43 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 94.68/94.43 class_Lattices_Olattice(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 94.68/94.43 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 94.68/94.43 class_Divides_Oring__div(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 94.68/94.43 class_Rings_Omult__zero(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 94.68/94.43 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 94.68/94.43 class_Orderings_Oorder(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 94.68/94.43 class_Int_Oring__char__0(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 94.68/94.43 class_Int_Onumber__ring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 94.68/94.43 class_Rings_Osemiring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 94.68/94.43 class_Orderings_Oord(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 94.68/94.43 class_Groups_Ouminus(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 94.68/94.43 class_Groups_Osgn__if(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 94.68/94.43 class_Groups_Oabs__if(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 94.68/94.43 class_Rings_Oring__1(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 94.68/94.43 class_Groups_Ominus(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Power_Opower,axiom,
% 94.68/94.43 class_Power_Opower(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 94.68/94.43 class_Groups_Ozero(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oring,axiom,
% 94.68/94.43 class_Rings_Oring(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 94.68/94.43 class_Rings_Oidom(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Int_Onumber,axiom,
% 94.68/94.43 class_Int_Onumber(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Groups_Oone,axiom,
% 94.68/94.43 class_Groups_Oone(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 94.68/94.43 class_Rings_Odvd(tc_Int_Oint) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 94.68/94.43 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 94.68/94.43 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 94.68/94.43 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 94.68/94.43 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 94.68/94.43 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 94.68/94.43 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 94.68/94.43 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 94.68/94.43 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 94.68/94.43 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 94.68/94.43 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 94.68/94.43 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 94.68/94.43 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 94.68/94.43 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 94.68/94.43 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 94.68/94.43 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 94.68/94.43 class_Lattices_Olattice(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 94.68/94.43 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 94.68/94.43 class_Orderings_Oorder(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 94.68/94.43 class_Rings_Osemiring(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 94.68/94.43 class_Orderings_Oord(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 94.68/94.43 class_Orderings_Obot(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 94.68/94.43 class_Groups_Ominus(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Power_Opower,axiom,
% 94.68/94.43 class_Power_Opower(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 94.68/94.43 class_Groups_Ozero(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 94.68/94.43 class_Int_Onumber(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 94.68/94.43 class_Groups_Oone(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 94.68/94.43 class_Rings_Odvd(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_Nat_Onat) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 94.68/94.43 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 94.68/94.43 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 94.68/94.43 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 94.68/94.43 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 94.68/94.43 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 94.68/94.43 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 94.68/94.43 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 94.68/94.43 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 94.68/94.43 class_Lattices_Olattice(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 94.68/94.43 class_Orderings_Oorder(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 94.68/94.43 class_Orderings_Otop(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 94.68/94.43 class_Orderings_Oord(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 94.68/94.43 class_Orderings_Obot(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 94.68/94.43 class_Groups_Ouminus(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 94.68/94.43 class_Groups_Ominus(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 94.68/94.43 class_Enum_Oenum(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_HOL_Obool) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 94.68/94.43 ! [T_1] :
% 94.68/94.43 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 94.68/94.43 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_List__Olist__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Finite__Set_Ofinite(T_2)
% 94.68/94.43 & class_Finite__Set_Ofinite(T_1) )
% 94.68/94.43 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_sum__Enum_Oenum,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Enum_Oenum(T_2)
% 94.68/94.43 & class_Enum_Oenum(T_1) )
% 94.68/94.43 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_sum__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 94.68/94.43 ! [T_1] :
% 94.68/94.43 ( class_Finite__Set_Ofinite(T_1)
% 94.68/94.43 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 94.68/94.43 ! [T_1] :
% 94.68/94.43 ( class_Enum_Oenum(T_1)
% 94.68/94.43 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 94.68/94.43 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 94.68/94.43 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Finite__Set_Ofinite(T_2)
% 94.68/94.43 & class_Finite__Set_Ofinite(T_1) )
% 94.68/94.43 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_prod__Enum_Oenum,axiom,
% 94.68/94.43 ! [T_1,T_2] :
% 94.68/94.43 ( ( class_Enum_Oenum(T_2)
% 94.68/94.43 & class_Enum_Oenum(T_1) )
% 94.68/94.43 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_prod__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 94.68/94.43 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 94.68/94.43 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 94.68/94.43 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 94.68/94.43 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 94.68/94.43 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 94.68/94.43 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 94.68/94.43 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 94.68/94.43 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 94.68/94.43 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 94.68/94.43 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 94.68/94.43 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 94.68/94.43 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 94.68/94.43 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 94.68/94.43 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 94.68/94.43 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 94.68/94.43 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 94.68/94.43 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 94.68/94.43 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 94.68/94.43 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 94.68/94.43 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 94.68/94.43 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 94.68/94.43 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 94.68/94.43 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 94.68/94.43 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 94.68/94.43 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 94.68/94.43 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 94.68/94.43 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 94.68/94.43 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 94.68/94.43 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 94.68/94.43 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 94.68/94.43 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 94.68/94.43
% 94.68/94.43 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 94.68/94.43 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 94.68/94.43
% 94.68/94.43 %----Helper facts (20)
% 94.68/94.43 fof(help_c__COMBI__1,axiom,
% 94.68/94.43 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__COMBK__1,axiom,
% 94.68/94.43 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__COMBB__1,axiom,
% 94.68/94.43 ! [V_R_2,V_Q_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Q_2,V_R_2)) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__COMBC__1,axiom,
% 94.68/94.43 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Q_2) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__COMBS__1,axiom,
% 94.68/94.43 ! [V_R_2,V_Q_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fequal__1,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 94.68/94.43 | V_x_2 = V_y_2 ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fequal__2,axiom,
% 94.68/94.43 ! [V_y_2,V_x_2] :
% 94.68/94.43 ( V_x_2 != V_y_2
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fFalse__1,axiom,
% 94.68/94.43 ~ hBOOL(c_fFalse) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fTrue__1,axiom,
% 94.68/94.43 hBOOL(c_fTrue) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fNot__1,axiom,
% 94.68/94.43 ! [V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(c_fNot,V_Pa_2))
% 94.68/94.43 | ~ hBOOL(V_Pa_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fNot__2,axiom,
% 94.68/94.43 ! [V_Pa_2] :
% 94.68/94.43 ( ~ ~ hBOOL(V_Pa_2)
% 94.68/94.43 | hBOOL(hAPP(c_fNot,V_Pa_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fconj__1,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(V_Pa_2)
% 94.68/94.43 | ~ hBOOL(V_Q_2)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fconj__2,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 94.68/94.43 | hBOOL(V_Pa_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fconj__3,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Q_2))
% 94.68/94.43 | hBOOL(V_Q_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fdisj__1,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(V_Pa_2)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fdisj__2,axiom,
% 94.68/94.43 ! [V_Pa_2,V_Q_2] :
% 94.68/94.43 ( ~ hBOOL(V_Q_2)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fdisj__3,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Q_2))
% 94.68/94.43 | hBOOL(V_Pa_2)
% 94.68/94.43 | hBOOL(V_Q_2) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fimplies__1,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( hBOOL(V_Pa_2)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fimplies__2,axiom,
% 94.68/94.43 ! [V_Pa_2,V_Q_2] :
% 94.68/94.43 ( ~ hBOOL(V_Q_2)
% 94.68/94.43 | hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2)) ) ).
% 94.68/94.43
% 94.68/94.43 fof(help_c__fimplies__3,axiom,
% 94.68/94.43 ! [V_Q_2,V_Pa_2] :
% 94.68/94.43 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Q_2))
% 94.68/94.43 | ~ hBOOL(V_Pa_2)
% 94.68/94.43 | hBOOL(V_Q_2) ) ).
% 94.68/94.43
% 94.68/94.43 %----Conjectures (7)
% 94.68/94.43 fof(conj_0,hypothesis,
% 94.68/94.43 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_1,hypothesis,
% 94.68/94.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_2,hypothesis,
% 94.68/94.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_3,hypothesis,
% 94.68/94.43 hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_4,hypothesis,
% 94.68/94.43 hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_5,hypothesis,
% 94.68/94.43 ~ hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)) ).
% 94.68/94.43
% 94.68/94.43 fof(conj_6,conjecture,
% 94.68/94.43 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),v_G)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ).
% 94.68/94.43
% 94.68/94.43 %------------------------------------------------------------------------------
% 94.68/94.43 %-------------------------------------------
% 94.68/94.43 % Proof found
% 94.68/94.43 % SZS status Theorem for theBenchmark
% 94.68/94.43 % SZS output start Proof
% 94.68/94.43 %ClaNum:10392(EqnAxiom:3032)
% 94.68/94.43 %VarNum:70764(SingletonVarNum:20400)
% 94.68/94.43 %MaxLitNum:8
% 94.68/94.43 %MaxfuncDepth:13
% 94.68/94.43 %SharedTerms:1028
% 94.68/94.43 %goalClause: 4632
% 94.68/94.43 %singleGoalClaCount:1
% 94.68/94.43 [3036]P1(a177)
% 94.68/94.43 [3037]P2(a893)
% 94.68/94.43 [3038]P2(a896)
% 94.68/94.43 [3039]P65(a893)
% 94.68/94.43 [3040]P65(a897)
% 94.68/94.43 [3041]P65(a1)
% 94.68/94.43 [3042]P65(a89)
% 94.68/94.43 [3043]P66(a897)
% 94.68/94.43 [3044]P66(a1)
% 94.68/94.43 [3045]P66(a89)
% 94.68/94.43 [3046]P108(a893)
% 94.68/94.43 [3047]P108(a897)
% 94.68/94.43 [3048]P108(a1)
% 94.68/94.43 [3049]P108(a89)
% 94.68/94.43 [3050]P109(a893)
% 94.68/94.43 [3051]P109(a897)
% 94.68/94.43 [3052]P109(a1)
% 94.68/94.43 [3053]P109(a89)
% 94.68/94.43 [3054]P67(a1)
% 94.68/94.43 [3055]P68(a893)
% 94.68/94.43 [3056]P68(a897)
% 94.68/94.43 [3057]P68(a1)
% 94.68/94.43 [3058]P68(a89)
% 94.68/94.43 [3059]P83(a893)
% 94.68/94.43 [3060]P83(a897)
% 94.68/94.43 [3061]P69(a1)
% 94.68/94.43 [3062]P80(a897)
% 94.68/94.43 [3063]P80(a1)
% 94.68/94.43 [3064]P80(a89)
% 94.68/94.43 [3065]P70(a897)
% 94.68/94.43 [3066]P70(a1)
% 94.68/94.43 [3067]P70(a89)
% 94.68/94.43 [3068]P71(a897)
% 94.68/94.43 [3069]P71(a1)
% 94.68/94.43 [3070]P71(a89)
% 94.68/94.43 [3071]P72(a897)
% 94.68/94.43 [3072]P72(a1)
% 94.68/94.43 [3073]P72(a89)
% 94.68/94.43 [3074]P84(a897)
% 94.68/94.43 [3075]P84(a1)
% 94.68/94.43 [3076]P84(a89)
% 94.68/94.43 [3077]P85(a897)
% 94.68/94.43 [3078]P85(a1)
% 94.68/94.43 [3079]P85(a89)
% 94.68/94.43 [3080]P75(a1)
% 94.68/94.43 [3081]P87(a897)
% 94.68/94.43 [3082]P87(a1)
% 94.68/94.43 [3083]P87(a89)
% 94.68/94.43 [3084]P110(a897)
% 94.68/94.43 [3085]P110(a1)
% 94.68/94.43 [3086]P110(a89)
% 94.68/94.43 [3087]P88(a897)
% 94.68/94.43 [3088]P88(a1)
% 94.68/94.43 [3089]P88(a89)
% 94.68/94.43 [3090]P127(a897)
% 94.68/94.43 [3091]P127(a1)
% 94.68/94.43 [3092]P127(a89)
% 94.68/94.43 [3093]P76(a897)
% 94.68/94.43 [3094]P76(a1)
% 94.68/94.43 [3095]P76(a89)
% 94.68/94.43 [3096]P81(a897)
% 94.68/94.43 [3097]P81(a1)
% 94.68/94.43 [3098]P81(a89)
% 94.68/94.43 [3099]P78(a1)
% 94.68/94.43 [3100]P89(a897)
% 94.68/94.43 [3101]P89(a1)
% 94.68/94.43 [3102]P89(a89)
% 94.68/94.43 [3103]P111(a1)
% 94.68/94.43 [3104]P112(a897)
% 94.68/94.43 [3105]P112(a1)
% 94.68/94.43 [3106]P112(a89)
% 94.68/94.43 [3107]P146(a897)
% 94.68/94.43 [3108]P146(a1)
% 94.68/94.43 [3109]P93(a1)
% 94.68/94.43 [3110]P73(a897)
% 94.68/94.43 [3111]P73(a1)
% 94.68/94.43 [3112]P73(a89)
% 94.68/94.43 [3113]P128(a1)
% 94.68/94.43 [3114]P94(a1)
% 94.68/94.43 [3115]P95(a897)
% 94.68/94.43 [3116]P95(a1)
% 94.68/94.43 [3117]P95(a89)
% 94.68/94.43 [3118]P131(a1)
% 94.68/94.43 [3119]P140(a897)
% 94.68/94.43 [3120]P140(a1)
% 94.68/94.43 [3121]P140(a89)
% 94.68/94.43 [3122]P141(a1)
% 94.68/94.43 [3123]P132(a897)
% 94.68/94.43 [3124]P132(a1)
% 94.68/94.43 [3125]P132(a89)
% 94.68/94.43 [3126]P142(a1)
% 94.68/94.43 [3127]P134(a897)
% 94.68/94.43 [3128]P134(a1)
% 94.68/94.43 [3129]P134(a89)
% 94.68/94.43 [3130]P113(a897)
% 94.68/94.43 [3131]P113(a1)
% 94.68/94.43 [3132]P113(a89)
% 94.68/94.43 [3133]P77(a897)
% 94.68/94.43 [3134]P77(a1)
% 94.68/94.43 [3135]P77(a89)
% 94.68/94.43 [3136]P82(a897)
% 94.68/94.43 [3137]P82(a1)
% 94.68/94.43 [3138]P82(a89)
% 94.68/94.43 [3139]P135(a897)
% 94.68/94.43 [3140]P135(a1)
% 94.68/94.43 [3141]P135(a89)
% 94.68/94.43 [3142]P136(a1)
% 94.68/94.43 [3143]P138(a897)
% 94.68/94.43 [3144]P138(a1)
% 94.68/94.43 [3145]P138(a89)
% 94.68/94.43 [3146]P137(a897)
% 94.68/94.43 [3147]P137(a1)
% 94.68/94.43 [3148]P137(a89)
% 94.68/94.43 [3149]P125(a1)
% 94.68/94.43 [3150]P126(a1)
% 94.68/94.43 [3151]P119(a897)
% 94.68/94.43 [3152]P119(a1)
% 94.68/94.43 [3153]P119(a89)
% 94.68/94.43 [3154]P133(a897)
% 94.68/94.43 [3155]P133(a1)
% 94.68/94.43 [3156]P133(a89)
% 94.68/94.43 [3157]P129(a897)
% 94.68/94.43 [3158]P129(a1)
% 94.68/94.43 [3159]P129(a89)
% 94.68/94.43 [3160]P130(a1)
% 94.68/94.43 [3161]P96(a897)
% 94.68/94.43 [3162]P96(a1)
% 94.68/94.43 [3163]P96(a89)
% 94.68/94.43 [3164]P144(a897)
% 94.68/94.43 [3165]P144(a1)
% 94.68/94.43 [3166]P144(a89)
% 94.68/94.43 [3167]P90(a893)
% 94.68/94.43 [3168]P90(a1)
% 94.68/94.43 [3169]P97(a893)
% 94.68/94.43 [3170]P120(a1)
% 94.68/94.43 [3171]P143(a1)
% 94.68/94.43 [3172]P114(a1)
% 94.68/94.43 [3173]P115(a897)
% 94.68/94.43 [3174]P115(a1)
% 94.68/94.43 [3175]P115(a89)
% 94.68/94.43 [3176]P145(a897)
% 94.68/94.43 [3177]P145(a1)
% 94.68/94.43 [3178]P145(a89)
% 94.68/94.43 [3179]P3(a897)
% 94.68/94.43 [3180]P3(a1)
% 94.68/94.43 [3181]P3(a89)
% 94.68/94.43 [3182]P4(a1)
% 94.68/94.43 [3183]P99(a893)
% 94.68/94.43 [3184]P99(a897)
% 94.68/94.43 [3185]P99(a1)
% 94.68/94.43 [3186]P100(a893)
% 94.68/94.43 [3187]P100(a897)
% 94.68/94.43 [3188]P100(a1)
% 94.68/94.43 [3189]P101(a893)
% 94.68/94.43 [3190]P105(a893)
% 94.68/94.43 [3191]P105(a897)
% 94.68/94.43 [3192]P105(a1)
% 94.68/94.43 [3193]P103(a893)
% 94.68/94.43 [3194]P103(a897)
% 94.68/94.43 [3195]P103(a1)
% 94.68/94.43 [3196]P91(a1)
% 94.68/94.43 [3197]P86(a1)
% 94.68/94.43 [3198]P139(a1)
% 94.68/94.43 [3199]P74(a1)
% 94.68/94.43 [3200]P5(a893)
% 94.68/94.43 [3201]P116(a893)
% 94.68/94.43 [3202]P104(a893)
% 94.68/94.43 [3203]P79(a897)
% 94.68/94.43 [3204]P79(a1)
% 94.68/94.43 [3205]P79(a89)
% 94.68/94.43 [3206]P117(a897)
% 94.68/94.43 [3207]P92(a897)
% 94.68/94.43 [3208]P92(a1)
% 94.68/94.43 [3209]P92(a89)
% 94.68/94.43 [3210]P60(a893)
% 94.68/94.43 [3211]P60(a896)
% 94.68/94.43 [3212]P107(a893)
% 94.68/94.43 [3213]P107(a897)
% 94.68/94.43 [3214]P107(a894)
% 94.68/94.43 [3215]P107(a89)
% 94.68/94.43 [3216]P107(a896)
% 94.68/94.43 [3217]P107(a313)
% 94.68/94.43 [3218]P106(a1)
% 94.68/94.43 [3219]P106(a896)
% 94.68/94.43 [3220]P121(a897)
% 94.68/94.43 [3221]P121(a1)
% 94.68/94.43 [3222]P121(a89)
% 94.68/94.43 [3223]P118(a1)
% 94.68/94.43 [3224]P102(a893)
% 94.68/94.43 [3238]P36(a897,a230)
% 94.68/94.43 [3239]P36(a897,a307)
% 94.68/94.43 [3240]P37(a897,a230)
% 94.68/94.43 [4567]~E(a87,a77)
% 94.68/94.43 [4568]~P1(a229)
% 94.68/94.43 [3033]E(f2(a1),a77)
% 94.68/94.43 [3034]E(f90(a89),a3)
% 94.68/94.43 [3035]E(f23(a89),a24)
% 94.68/94.43 [3225]E(f178(a897),f2(a897))
% 94.68/94.43 [3226]E(f223(a897),f91(a897))
% 94.68/94.43 [3227]E(f228(a897),f92(a897))
% 94.68/94.43 [3228]E(f93(a1),f25(a1))
% 94.68/94.43 [3229]E(f78(a229),f2(a897))
% 94.68/94.43 [3230]E(f78(a177),f2(a897))
% 94.68/94.43 [3231]P6(f72(a1))
% 94.68/94.43 [3232]P6(f2(a1))
% 94.68/94.43 [3286]P36(f903(a897,a897),a26)
% 94.68/94.43 [3628]E(f309(a897,a897,a230,a230),a26)
% 94.68/94.43 [4569]~E(f72(a1),f2(a1))
% 94.68/94.43 [3233]E(f4(f2(a89)),f2(a897))
% 94.68/94.43 [3234]E(f101(f2(a897)),f2(a897))
% 94.68/94.43 [3242]E(f317(f73(a1),a77),a77)
% 94.68/94.43 [3245]E(f317(a102,f2(a897)),f72(a897))
% 94.68/94.43 [3246]E(f317(a95,f72(a1)),f72(a897))
% 94.68/94.43 [3247]E(f317(a3,f72(a897)),f72(a89))
% 94.68/94.43 [3249]E(f317(a3,f2(a897)),f2(a89))
% 94.68/94.43 [3251]E(f317(f94(a1),a77),f2(a1))
% 94.68/94.43 [3252]E(f317(f94(a89),a77),f2(a89))
% 94.68/94.43 [3253]E(f317(a95,f2(a1)),f2(a897))
% 94.68/94.43 [3254]E(f317(f94(a897),a77),f2(a897))
% 94.68/94.43 [3255]E(f317(f179(a893),a229),f2(a897))
% 94.68/94.43 [3256]E(f317(f179(a893),a177),f2(a897))
% 94.68/94.43 [3262]E(f317(f73(a1),f72(a1)),a87)
% 94.68/94.43 [3270]E(f317(f179(a89),f2(a89)),f2(a897))
% 94.68/94.43 [3271]E(f317(f90(a1),f72(a897)),f72(a1))
% 94.68/94.43 [3272]E(f317(f90(a1),f2(a897)),f2(a1))
% 94.68/94.43 [3273]E(f317(f73(a1),f2(a1)),f2(a1))
% 94.68/94.43 [3283]E(f317(a95,f72(a1)),f317(a102,f2(a897)))
% 94.68/94.43 [3284]E(f308(f903(a897,a897),a26),a27)
% 94.68/94.43 [3285]E(f310(f903(a897,a897),a26),a63)
% 94.68/94.43 [3287]P1(f317(f28(a895),a905))
% 94.68/94.43 [3313]E(f317(f272(a897),f2(a897)),f178(f904(a897,a893)))
% 94.68/94.43 [3314]E(f317(f273(a897),f2(a897)),f232(f904(a897,a893)))
% 94.68/94.43 [3322]P39(f178(f904(a1,a893)))
% 94.68/94.43 [3356]E(f317(f317(f23(a89),f2(a89)),f72(a89)),f2(a89))
% 94.68/94.43 [3432]P1(f317(f317(f225(a1),a87),f2(a1)))
% 94.68/94.43 [3456]P1(f317(f317(f224(a1),f2(a1)),f72(a1)))
% 94.68/94.43 [3458]P1(f317(f317(f225(a1),f2(a1)),f72(a1)))
% 94.68/94.43 [3659]E(f317(f317(f279(a897,a897,a897),a307),f297(a897,a307)),a230)
% 94.68/94.43 [3696]P40(a1,a897,a95,f317(f224(a1),f2(a1)))
% 94.68/94.43 [3700]E(f317(f317(f34(a897,f904(a897,a893)),f232(f904(a897,a893))),f291(a897)),f232(f904(a897,a893)))
% 94.68/94.43 [3701]E(f317(f317(f34(a897,f904(a897,a893)),f232(f904(a897,a893))),f272(a897)),f232(f904(a897,a893)))
% 94.68/94.43 [3702]E(f317(f317(f34(a897,f904(a897,a893)),f232(f904(a897,a893))),f273(a897)),f232(f904(a897,a893)))
% 94.68/94.43 [3703]E(f317(f317(f35(a897,f904(a897,a893)),f232(f904(a897,a893))),f294(a897)),f178(f904(a897,a893)))
% 94.68/94.43 [3718]P24(a897,a1,f90(a1),f232(f904(a897,a893)))
% 94.68/94.43 [3732]P40(a897,a1,f90(a1),f317(f16(a893,a897),a177))
% 94.68/94.43 [3867]E(f317(f67(a897,a89,a1,a3),a95),f94(a89))
% 94.68/94.43 [4040]E(f317(f317(f23(a897),f317(f29(a892),f317(f300(a895,a892,a908),a905))),f317(a102,a910)),f317(f29(a892),a906))
% 94.68/94.43 [4089]P56(a89,a897,a20,a3,f232(f904(a897,a893)))
% 94.68/94.43 [4093]P56(a1,f904(f903(a897,a897),a893),a97,a83,a88)
% 94.68/94.43 [4347]E(f248(a1,a1,a1,a1,f25(a1),f73(a1)),a46)
% 94.68/94.43 [4578]~E(f317(f94(a1),a87),f317(f94(a1),a77))
% 94.68/94.43 [4579]~P1(f317(a183,f72(a1)))
% 94.68/94.43 [4580]~P1(f317(a183,f2(a1)))
% 94.68/94.43 [4605]~P1(f317(f317(f225(a1),a77),f2(a1)))
% 94.68/94.43 [3305]E(f317(f317(f23(a1),a87),a87),a77)
% 94.68/94.43 [3320]E(f317(f90(a1),f317(a102,f2(a897))),f72(a1))
% 94.68/94.43 [3385]E(f317(f29(a896),f232(f904(a896,a893))),f72(a897))
% 94.68/94.43 [3405]P1(f317(a183,f317(f94(a1),a87)))
% 94.68/94.43 [3407]P1(f317(f317(f224(a1),a87),a77))
% 94.68/94.43 [3409]P1(f317(f317(f319(a895),a907),a905))
% 94.68/94.43 [3410]P1(f317(f317(f225(a1),a87),a77))
% 94.68/94.43 [3466]E(f317(f317(f299(a897),f2(a897)),f178(f904(a897,a893))),f317(f291(a897),f2(a897)))
% 94.68/94.43 [3519]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),a77)))
% 94.68/94.43 [3531]E(f317(f300(a897,a897,a102),f232(f904(a897,a893))),f317(f294(a897),f2(a897)))
% 94.68/94.43 [3566]P8(f903(a897,a897),f232(f904(f903(a897,a897),a893)),a99)
% 94.68/94.43 [3874]E(f317(f67(a897,a1,a89,f90(a1)),a20),a22)
% 94.68/94.43 [3933]P36(a897,f317(f252(f903(a897,a897)),f317(f247(a897,a897,a893),f225(a897))))
% 94.68/94.43 [3971]P1(f317(f317(f224(f904(a892,a893)),a906),f317(f300(a895,a892,a908),a905)))
% 94.68/94.43 [4596]~P1(f317(a183,f317(f94(a1),a77)))
% 94.68/94.43 [4597]~P1(f317(f317(f224(a1),a77),a87))
% 94.68/94.43 [4598]~P1(f317(f317(f225(a1),a77),a77))
% 94.68/94.43 [4599]~P1(f317(f317(f225(a1),a77),a87))
% 94.68/94.43 [4600]~P1(f317(f317(f225(a1),a87),a87))
% 94.68/94.43 [4609]~P1(f317(f28(a897),f232(f904(a897,a893))))
% 94.68/94.43 [4610]~P1(f317(f28(a1),f232(f904(a1,a893))))
% 94.68/94.43 [4612]~P1(f317(f317(f319(a892),f317(a908,a907)),a906))
% 94.68/94.43 [4632]~P1(f317(f317(f224(f904(a892,a893)),f317(f317(f299(a892),f317(a908,a907)),a906)),f317(f300(a895,a892,a908),a905)))
% 94.68/94.43 [4058]P1(f317(f317(f224(a897),f317(a102,a910)),f317(f29(a892),f317(f300(a895,a892,a908),a905))))
% 94.68/94.43 [4513]E(f317(f247(a1,a1,a893),f317(f317(f8(f904(a1,a893),f904(a1,a893),a1),f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f225(a1),f2(a1))))),f317(f317(f7(a1,a1,f904(a1,a893)),f317(f317(f8(f904(a1,f904(a1,a893)),f904(a1,f904(a1,a893)),a1),f7(a1,a1,a893)),f317(f317(f8(f904(a1,a1),f904(a1,f904(a1,a893)),a1),f317(f8(a1,f904(a1,a893),a1),a314)),a207))),f72(a1)))),a203)
% 94.68/94.43 [3603]E(f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87),f317(f73(a1),a87))
% 94.68/94.43 [3641]E(f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87),f317(f317(f23(a1),a77),a87))
% 94.68/94.43 [3801]E(f317(f317(f55(f903(a897,a897)),f232(f904(f903(a897,a897),a893))),a99),a88)
% 94.68/94.43 [3830]E(f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a1))
% 94.68/94.43 [3831]E(f317(f94(a89),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a89))
% 94.68/94.43 [3832]E(f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(a897))
% 94.68/94.43 [3835]E(f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(a102,f2(a897)))
% 94.68/94.43 [4215]E(f317(f317(f91(f904(f903(f903(a897,a897),f903(a897,a897)),a893)),a26),f297(f903(a897,a897),f178(f904(f903(f903(a897,a897),f903(a897,a897)),a893)))),a65)
% 94.68/94.43 [4281]E(f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),f72(a897)),f2(a897))),f178(f904(f903(a897,a897),a893))))),f72(a1))
% 94.68/94.43 [4282]E(f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),f2(a897)),f2(a897))),f178(f904(f903(a897,a897),a893))))),f2(a1))
% 94.68/94.43 [4295]E(f317(f252(f903(a897,a897)),f317(f247(a897,a897,a893),f317(f317(f8(a897,f904(a897,a893),a897),f317(f7(a897,a897,a893),a314)),a102))),a307)
% 94.68/94.43 [4267]E(f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(a102,f317(a102,f2(a897))))
% 94.68/94.43 [4270]E(f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(f317(f74(a897),f72(a897)),f72(a897)))
% 94.68/94.43 [4271]E(f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),f317(f29(a893),f232(f904(a893,a893))))
% 94.68/94.43 [4334]P6(f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))
% 94.68/94.43 [4403]P26(f904(f903(a897,a897),a893),f317(f317(f242(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893),f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)),a27),a64))
% 94.68/94.43 [4404]P26(f904(f903(a897,a897),a893),f317(f317(f242(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893),f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)),a63),a66))
% 94.68/94.43 [4444]E(f317(f317(f91(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)),f310(f903(a897,a897),a65)),f317(f317(f299(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f178(f904(f903(a897,a897),a893))),f178(f904(f903(a897,a897),a893)))),f178(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)))),a66)
% 94.68/94.43 [4445]E(f317(f317(f91(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)),f308(f903(a897,a897),a65)),f317(f317(f299(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f178(f904(f903(a897,a897),a893))),f178(f904(f903(a897,a897),a893)))),f178(f904(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a893)))),a64)
% 94.68/94.43 [4336]E(f317(a95,f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(a102,f2(a897))))
% 94.68/94.43 [4381]E(f317(f90(a1),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))
% 94.68/94.43 [4414]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.43 [4415]E(f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87)),f317(a102,f317(a102,f317(a102,f2(a897)))))
% 94.68/94.43 [4459]P6(f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87)))
% 94.68/94.43 [4485]E(f317(f90(a1),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87)))
% 94.68/94.43 [4498]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))))
% 94.68/94.43 [3241]P7(x32411,a314)
% 94.68/94.43 [3629]P24(a897,a897,a102,x36291)
% 94.68/94.43 [3235]P107(f900(x32351))
% 94.68/94.43 [3236]P107(f898(x32361))
% 94.68/94.43 [3237]P107(f899(x32371))
% 94.68/94.43 [3257]P36(a1,f96(x32571))
% 94.68/94.43 [3258]P36(a1,f98(x32581))
% 94.68/94.43 [3309]P36(f904(x33091,a893),f304(x33091))
% 94.68/94.43 [3310]P37(f904(x33101,a893),f304(x33101))
% 94.68/94.43 [3334]E(f233(x33341,x33341,a314),a314)
% 94.68/94.43 [3349]E(f40(a1,x33491,x33491),f2(a1))
% 94.68/94.43 [3402]P14(x34021,f904(x34021,a893),f299(x34021))
% 94.68/94.43 [4571]~E(f317(a102,x45711),x45711)
% 94.68/94.43 [4577]~E(f317(a102,x45771),f2(a897))
% 94.68/94.43 [3243]E(f317(f94(a1),x32431),x32431)
% 94.68/94.43 [3244]E(f317(f179(a897),x32441),x32441)
% 94.68/94.43 [3259]E(f317(a83,f318(x32591)),x32591)
% 94.68/94.43 [3260]E(f317(a3,f514(x32601)),x32601)
% 94.68/94.43 [3261]E(f231(x32611,f2(a89)),f2(a89))
% 94.68/94.43 [3274]E(f104(x32741,f103(x32741)),f103(x32741))
% 94.68/94.43 [3275]E(f142(x32751,f103(x32751)),f103(x32751))
% 94.68/94.43 [3280]E(f317(f157(x32801),f103(x32801)),f103(x32801))
% 94.68/94.43 [3281]E(f317(f161(x32811),f103(x32811)),f103(x32811))
% 94.68/94.43 [3282]E(f317(f158(x32821),f103(x32821)),f103(x32821))
% 94.68/94.43 [3288]E(f317(f94(a1),x32881),f317(f93(a1),x32881))
% 94.68/94.43 [3289]E(f317(a83,f317(a97,x32891)),x32891)
% 94.68/94.43 [3291]E(f317(a3,f317(a20,x32911)),x32911)
% 94.68/94.43 [3292]E(f317(a20,f317(a3,x32921)),x32921)
% 94.68/94.43 [3294]P6(f317(f90(a1),x32941))
% 94.68/94.43 [3303]E(f317(f179(f898(x33031)),f103(x33031)),f2(a897))
% 94.68/94.43 [3304]E(f317(f179(f899(x33041)),f109(x33041)),f2(a897))
% 94.68/94.43 [3325]E(f317(f317(f23(a897),x33251),f2(a897)),x33251)
% 94.68/94.43 [3326]E(f317(f317(f74(a897),x33261),f2(a897)),x33261)
% 94.68/94.43 [3327]E(f317(f317(f74(a1),x33271),f2(a1)),x33271)
% 94.68/94.43 [3328]E(f317(f317(f75(a897),x33281),f72(a897)),x33281)
% 94.68/94.43 [3329]E(f317(f317(f75(a1),x33291),f72(a1)),x33291)
% 94.68/94.43 [3330]E(f317(f317(f223(a897),x33301),f2(a897)),x33301)
% 94.68/94.43 [3331]E(f317(f317(f75(a897),x33311),f2(a897)),f2(a897))
% 94.68/94.43 [3332]E(f317(f317(f228(a897),x33321),f2(a897)),f2(a897))
% 94.68/94.43 [3333]E(f317(f317(f30(a1),x33331),f2(a1)),f2(a1))
% 94.68/94.43 [3340]E(f317(f162(x33401),f103(x33401)),f178(f904(x33401,a893)))
% 94.68/94.43 [3344]P1(f317(f127(x33441),f103(x33441)))
% 94.68/94.43 [3350]E(f317(f144(x33501,x33501),f5(x33501)),f25(f898(x33501)))
% 94.68/94.43 [3351]E(f317(f144(x33511,x33511),f25(x33511)),f25(f898(x33511)))
% 94.68/94.43 [3352]E(f40(a1,x33521,f2(a1)),x33521)
% 94.68/94.43 [3353]E(f317(f224(a897),f317(a102,x33531)),f317(f225(a897),x33531))
% 94.68/94.43 [3354]E(f317(f272(a897),f317(a102,x33541)),f317(f291(a897),x33541))
% 94.68/94.43 [3355]E(f317(f273(a897),f317(a102,x33551)),f317(f294(a897),x33551))
% 94.68/94.43 [3357]E(f40(a1,f2(a1),x33571),f2(a1))
% 94.68/94.43 [3370]E(f317(f317(f74(a897),x33701),f72(a897)),f317(a102,x33701))
% 94.68/94.43 [3379]E(f317(f292(a897,x33791),f2(a897)),f178(f904(a897,a893)))
% 94.68/94.43 [3391]E(f293(a897,f2(a897),x33911),f317(f291(a897),x33911))
% 94.68/94.43 [3435]E(f317(f317(f23(a897),f317(a102,x34351)),f72(a897)),x34351)
% 94.68/94.43 [3447]E(f42(f2(a1),x34471),f317(f317(f242(a1,a1),f2(a1)),f2(a1)))
% 94.68/94.43 [3494]P1(f317(f317(f225(a897),x34941),f317(a102,x34941)))
% 94.68/94.43 [3506]P1(f317(f317(f225(a897),f2(a897)),f317(a102,x35061)))
% 94.68/94.43 [3731]E(f85(x37311,x37311,f232(f904(x37311,a893)),f25(x37311)),f25(x37311))
% 94.68/94.43 [3788]E(f317(f317(f23(a89),f317(a3,f317(a102,f317(a20,x37881)))),f72(a89)),x37881)
% 94.68/94.43 [3858]P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x38581))),f2(a1)))
% 94.68/94.43 [4002]P1(f317(f317(f225(a1),f317(f73(a1),f317(f90(a1),f317(a102,x40021)))),f2(a1)))
% 94.68/94.43 [4585]~E(f232(f904(x45851,a893)),f178(f904(x45851,a893)))
% 94.68/94.43 [4608]~P1(f317(f317(f225(a897),x46081),f2(a897)))
% 94.68/94.43 [4620]~P1(f317(f317(f225(a1),f317(f90(a1),x46201)),f2(a1)))
% 94.68/94.43 [3293]E(f110(x32931,f109(f899(x32931))),f109(x32931))
% 94.68/94.43 [3308]E(f169(x33081,f103(f898(x33081))),f103(f898(x33081)))
% 94.68/94.43 [3311]E(f317(f317(f75(a1),a77),x33111),a77)
% 94.68/94.43 [3312]E(f317(f317(f74(a1),a77),x33121),x33121)
% 94.68/94.43 [3315]E(f317(a95,f317(f90(a1),x33151)),x33151)
% 94.68/94.43 [3316]E(f317(f317(f23(a1),x33161),a77),x33161)
% 94.68/94.43 [3317]E(f317(f317(f74(a1),x33171),a77),x33171)
% 94.68/94.43 [3319]E(f317(f317(f23(a897),x33191),x33191),f2(a897))
% 94.68/94.43 [3323]E(f317(f29(a897),f317(f272(a897),x33231)),x33231)
% 94.68/94.43 [3324]E(f317(f73(a1),f317(f73(a1),x33241)),x33241)
% 94.68/94.43 [3335]E(f317(f317(f74(a897),f2(a897)),x33351),x33351)
% 94.68/94.43 [3336]E(f317(f317(f74(a1),f2(a1)),x33361),x33361)
% 94.68/94.43 [3337]E(f317(f317(f75(a897),f72(a897)),x33371),x33371)
% 94.68/94.43 [3338]E(f317(f317(f75(a1),f72(a1)),x33381),x33381)
% 94.68/94.43 [3339]E(f317(f317(f223(a897),f2(a897)),x33391),x33391)
% 94.68/94.43 [3345]E(f317(f317(f23(a897),f2(a897)),x33451),f2(a897))
% 94.68/94.43 [3346]E(f317(f317(f75(a897),f2(a897)),x33461),f2(a897))
% 94.68/94.43 [3347]E(f317(f317(f228(a897),f2(a897)),x33471),f2(a897))
% 94.68/94.43 [3348]E(f317(f317(f30(a1),f2(a1)),x33481),f2(a1))
% 94.68/94.43 [3358]E(f118(x33581,f317(f73(a1),x33581)),f122(a1,x33581))
% 94.68/94.43 [3363]E(f317(f292(a897,f2(a897)),x33631),f317(f272(a897),x33631))
% 94.68/94.43 [3364]E(f317(f317(f75(a1),a87),x33641),f317(f73(a1),x33641))
% 94.68/94.43 [3372]E(f317(a95,f317(f94(a1),x33721)),f317(f94(a897),x33721))
% 94.68/94.43 [3373]E(f317(a20,f317(f94(a89),x33731)),f317(f94(a897),x33731))
% 94.68/94.43 [3374]E(f317(f29(a897),f317(f291(a897),x33741)),f317(a102,x33741))
% 94.68/94.43 [3383]E(f317(f317(f74(a897),f72(a897)),x33831),f317(a102,x33831))
% 94.68/94.43 [3387]E(f317(f93(a1),f317(f90(a1),x33871)),f317(f90(a1),x33871))
% 94.68/94.43 [3388]E(f317(f70(a1),f317(f90(a1),x33881)),f317(f90(a1),x33881))
% 94.68/94.43 [3392]E(f317(f29(x33921),f178(f904(x33921,a893))),f2(a897))
% 94.68/94.43 [3394]E(f317(f317(f30(a897),x33941),f317(a102,f2(a897))),x33941)
% 94.68/94.43 [3403]E(f40(a897,x34031,f317(a102,f2(a897))),f2(a897))
% 94.68/94.43 [3404]E(f40(a1,x34041,f317(f94(a1),a87)),f2(a1))
% 94.68/94.43 [3419]E(f317(f317(f30(a1),x34191),f317(f94(a1),a87)),f317(f73(a1),x34191))
% 94.68/94.43 [3423]E(f129(a897,f317(f292(a897,x34231),f2(a897))),f103(a897))
% 94.68/94.43 [3424]E(f317(f317(f74(a1),x34241),f72(a1)),f317(f317(f23(a1),x34241),a87))
% 94.68/94.43 [3425]E(f317(f317(f23(a1),x34251),f72(a1)),f317(f317(f74(a1),x34251),a87))
% 94.68/94.43 [3429]P1(f317(f317(f224(a897),x34291),x34291))
% 94.68/94.43 [3430]P1(f317(f317(f224(a1),x34301),x34301))
% 94.68/94.43 [3431]P1(f317(f317(f277(a897),x34311),x34311))
% 94.68/94.43 [3436]E(f317(f73(a1),f317(f94(a1),x34361)),f317(f94(a1),f317(f73(a1),x34361)))
% 94.68/94.43 [3437]P1(f317(f28(a897),f317(f291(a897),x34371)))
% 94.68/94.43 [3438]P1(f317(f28(a897),f317(f272(a897),x34381)))
% 94.68/94.43 [3445]E(f151(x34451,f232(f904(x34451,a893))),f232(f904(f898(x34451),a893)))
% 94.68/94.43 [3450]P1(f317(f317(f224(a897),f2(a897)),x34501))
% 94.68/94.43 [3460]E(f317(f317(f74(a897),f101(x34601)),f317(a102,f2(a897))),f101(f317(a102,x34601)))
% 94.68/94.43 [3461]E(f317(f252(x34611),f317(f16(a893,x34611),a229)),f178(f904(x34611,a893)))
% 94.68/94.43 [3462]E(f317(f252(x34621),f317(f16(a893,x34621),a177)),f232(f904(x34621,a893)))
% 94.68/94.43 [3465]E(f317(f317(f299(a897),x34651),f317(f272(a897),x34651)),f317(f272(a897),f317(a102,x34651)))
% 94.68/94.43 [3477]E(f317(f317(f74(a1),f72(a1)),f317(f90(a1),x34771)),f317(f90(a1),f317(a102,x34771)))
% 94.68/94.43 [3479]E(f317(f317(f141(f898(x34791)),f103(x34791)),f103(f898(x34791))),f49(x34791,f103(x34791)))
% 94.68/94.43 [3497]E(f178(f904(f903(x34971,x34971),a893)),f253(x34971,f178(f904(x34971,a893))))
% 94.68/94.43 [3498]E(f317(f298(x34981),f232(f904(x34981,a893))),f232(f904(f904(x34981,a893),a893)))
% 94.68/94.43 [3499]E(f317(f73(f904(x34991,a893)),f178(f904(x34991,a893))),f232(f904(x34991,a893)))
% 94.68/94.43 [3500]E(f317(f73(f904(x35001,a893)),f232(f904(x35001,a893))),f178(f904(x35001,a893)))
% 94.68/94.43 [3502]P1(f317(f28(x35021),f178(f904(x35021,a893))))
% 94.68/94.43 [3504]E(f317(f292(a897,x35041),f317(a102,x35041)),f317(f317(f299(a897),x35041),f178(f904(a897,a893))))
% 94.68/94.43 [3505]E(f79(f903(a897,a897),f43(x35051,f2(a897))),f317(f317(f242(a897,a897),f2(a897)),x35051))
% 94.68/94.43 [3518]E(f317(f317(f299(a897),f317(a102,x35181)),f317(f291(a897),x35181)),f317(f291(a897),f317(a102,x35181)))
% 94.68/94.43 [3522]P36(x35221,f178(f904(f903(x35221,x35221),a893)))
% 94.68/94.43 [3523]P38(x35231,f178(f904(f903(x35231,x35231),a893)))
% 94.68/94.43 [3526]P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x35261)))
% 94.68/94.43 [3533]E(f317(f317(f74(a897),f317(f179(a897),x35331)),f317(a102,f2(a897))),f317(f179(a897),f317(a102,x35331)))
% 94.68/94.43 [3636]P39(f317(f300(a897,a1,f90(a1)),x36361))
% 94.68/94.43 [3674]P52(x36741,f178(f904(x36741,a893)),f178(f904(f903(x36741,x36741),a893)))
% 94.68/94.43 [3692]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f23(a1),x36921),f72(a1))),f45(f317(f94(a1),a87),x36921))
% 94.68/94.43 [3744]P59(x37441,f317(f16(f904(x37441,a893),x37441),f317(f16(a893,x37441),a229)))
% 94.68/94.43 [3756]E(f280(a897,f277(a897),x37561,x37561),f317(f317(f299(a897),x37561),f178(f904(a897,a893))))
% 94.68/94.43 [3945]P1(f317(f317(f319(f904(f903(a897,a897),a893)),f318(x39451)),a88))
% 94.68/94.43 [3970]P1(f317(f317(f319(f904(f903(a897,a897),a893)),f317(a97,x39701)),a88))
% 94.68/94.43 [4102]P24(x41021,f904(x41021,a893),f317(f317(f7(x41021,f904(x41021,a893),f904(x41021,a893)),f299(x41021)),f178(f904(x41021,a893))),f232(f904(x41021,a893)))
% 94.68/94.43 [4582]~E(f317(f317(f74(a1),x45821),x45821),a87)
% 94.68/94.43 [4595]~E(f317(a3,f317(a102,f317(a20,x45951))),f2(a89))
% 94.68/94.43 [4601]~P1(f317(a183,f317(f90(a1),x46011)))
% 94.68/94.43 [4604]~P1(f317(f317(f225(a897),x46041),x46041))
% 94.68/94.43 [4613]~P1(f317(f317(f224(a897),f317(a102,x46131)),x46131))
% 94.68/94.43 [3452]E(f317(a95,f317(f73(a1),f317(f90(a1),x34521))),f2(a897))
% 94.68/94.43 [3455]E(f317(f317(f74(a1),f317(f73(a1),x34551)),x34551),f2(a1))
% 94.68/94.43 [3459]E(f317(f29(a1),f317(f292(a1,f2(a1)),x34591)),f317(a95,x34591))
% 94.68/94.43 [3470]E(f317(f317(f234(a897),f317(a102,f2(a897))),x34701),f317(a102,f2(a897)))
% 94.68/94.43 [3563]E(f317(f271(x35631),f178(f904(f903(x35631,x35631),a893))),f178(f904(x35631,a893)))
% 94.68/94.43 [3571]E(f32(f904(x35711,a893),f178(f904(f904(x35711,a893),a893))),f232(f904(x35711,a893)))
% 94.68/94.43 [3572]E(f32(f904(x35721,a893),f232(f904(f904(x35721,a893),a893))),f178(f904(x35721,a893)))
% 94.68/94.43 [3573]E(f31(f904(x35731,a893),f178(f904(f904(x35731,a893),a893))),f178(f904(x35731,a893)))
% 94.68/94.43 [3574]E(f31(f904(x35741,a893),f232(f904(f904(x35741,a893),a893))),f232(f904(x35741,a893)))
% 94.68/94.43 [3578]P1(f317(f317(f277(a897),f317(a102,f2(a897))),x35781))
% 94.68/94.43 [3619]E(f317(f317(f299(f898(x36191)),f103(x36191)),f178(f904(f898(x36191),a893))),f151(x36191,f178(f904(x36191,a893))))
% 94.68/94.43 [3620]E(f317(f317(f299(f898(x36201)),f103(x36201)),f178(f904(f898(x36201),a893))),f152(x36201,f103(f904(x36201,a893))))
% 94.68/94.43 [3658]E(f317(f317(f74(a897),f4(x36581)),f317(a102,f2(a897))),f4(f317(a3,f317(a102,f317(a20,x36581)))))
% 94.68/94.43 [3683]E(f317(f29(a1),f317(f300(a897,a1,f90(a1)),x36831)),f317(f29(a897),x36831))
% 94.68/94.43 [3686]P1(f317(f317(f224(a897),x36861),f317(f317(f75(a897),x36861),x36861)))
% 94.68/94.43 [3722]E(f317(f300(a1,a897,a95),f293(a1,f2(a1),f317(f90(a1),x37221))),f317(f291(a897),x37221))
% 94.68/94.43 [3739]E(f317(f317(f30(a897),f317(a102,f2(a897))),f317(f94(a897),x37391)),f317(a95,f317(f317(f30(a1),f72(a1)),f317(f94(a1),x37391))))
% 94.68/94.43 [3741]E(f317(f162(a897),f129(a897,f317(f292(a897,f2(a897)),f317(a102,x37411)))),f317(f291(a897),x37411))
% 94.68/94.43 [3742]E(f317(f317(f74(a897),f317(f179(a89),x37421)),f317(a102,f2(a897))),f317(f179(a89),f317(a3,f317(a102,f317(a20,x37421)))))
% 94.68/94.43 [3762]P38(x37621,f297(x37621,f178(f904(f903(x37621,x37621),a893))))
% 94.68/94.43 [3763]P51(x37631,f297(x37631,f178(f904(f903(x37631,x37631),a893))))
% 94.68/94.43 [3764]E(f317(f300(a1,a897,a95),f317(f300(a897,a1,f90(a1)),x37641)),x37641)
% 94.68/94.43 [3794]E(f317(f317(f299(a897),f2(a897)),f317(f300(a897,a897,a102),f317(f272(a897),x37941))),f317(f272(a897),f317(a102,x37941)))
% 94.68/94.43 [3800]P54(x38001,x38001,f297(x38001,f178(f904(f903(x38001,x38001),a893))))
% 94.68/94.43 [3806]P1(f317(a183,f317(f73(a1),f317(f90(a1),f317(a102,x38061)))))
% 94.68/94.43 [3816]E(f317(f317(f23(f904(a897,a893)),f317(f273(a897),x38161)),f317(f317(f299(a897),x38161),f178(f904(a897,a893)))),f317(f273(a897),f317(a102,x38161)))
% 94.68/94.43 [3833]E(f317(f317(f74(a1),f317(f317(f23(a1),a77),x38331)),f317(f317(f23(a1),a77),x38331)),f317(f317(f23(a1),a77),f317(f317(f74(a1),x38331),x38331)))
% 94.68/94.43 [3847]E(f317(f317(f299(f904(x38471,a893)),f178(f904(x38471,a893))),f178(f904(f904(x38471,a893),a893))),f317(f298(x38471),f178(f904(x38471,a893))))
% 94.68/94.43 [3875]E(f317(f317(f23(f904(a897,a893)),f317(f294(a897),x38751)),f317(f317(f299(a897),f317(a102,x38751)),f178(f904(a897,a893)))),f317(f294(a897),f317(a102,x38751)))
% 94.68/94.43 [3983]E(f317(f94(a897),f317(f317(f74(a1),x39831),x39831)),f317(f317(f80(a897,a897),f317(f94(a897),x39831)),f317(f317(f18(a897,a897,a897),f74(a897)),f5(a897))))
% 94.68/94.43 [4356]P14(x43561,f904(x43561,a893),f317(f317(f8(f904(x43561,a893),f904(f904(x43561,a893),f904(x43561,a893)),x43561),f317(f7(f904(x43561,a893),f904(x43561,a893),f904(x43561,a893)),f23(f904(x43561,a893)))),f317(f317(f7(x43561,f904(x43561,a893),f904(x43561,a893)),f299(x43561)),f178(f904(x43561,a893)))))
% 94.68/94.43 [4443]E(f317(f252(f903(a1,a1)),f317(f247(a1,a1,a893),f317(f317(f8(f904(a1,a893),f904(a1,a893),a1),f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),x44431)))),f225(a1)))),f98(x44431))
% 94.68/94.43 [4476]E(f317(f252(f903(a1,a1)),f317(f247(a1,a1,a893),f317(f317(f18(a1,f904(a1,a893),f904(a1,a893)),f317(f317(f8(f904(a893,a893),f904(f904(a1,a893),f904(a1,a893)),a1),f8(a893,a893,a1)),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),x44761)))),f225(a1)))),f96(x44761))
% 94.68/94.43 [4529]E(f317(f252(f903(f904(x45291,a893),f904(x45291,a893))),f317(f247(f904(x45291,a893),f904(x45291,a893),a893),f317(f317(f7(f904(x45291,a893),f904(f904(x45291,a893),a893),f904(f904(x45291,a893),a893)),f317(f317(f8(f904(f904(x45291,a893),f904(a893,a893)),f904(f904(f904(x45291,a893),a893),f904(f904(x45291,a893),a893)),f904(x45291,a893)),f18(f904(x45291,a893),a893,a893)),f317(f317(f8(f904(f904(x45291,a893),a893),f904(f904(x45291,a893),f904(a893,a893)),f904(x45291,a893)),f317(f8(a893,f904(a893,a893),f904(x45291,a893)),a315)),f225(f904(x45291,a893))))),f28(x45291)))),f304(x45291))
% 94.68/94.43 [4617]~P1(f317(f28(f898(x46171)),f232(f904(f898(x46171),a893))))
% 94.68/94.43 [4629]~P1(f317(f317(f224(a1),f2(a1)),f317(f73(a1),f317(f90(a1),f317(a102,x46291)))))
% 94.68/94.43 [3598]E(f317(f317(f23(a1),f317(f317(f74(a1),x35981),a87)),a87),x35981)
% 94.68/94.43 [3612]E(f317(f162(a897),f129(a897,f317(f292(a897,f2(a897)),x36121))),f317(f272(a897),x36121))
% 94.68/94.43 [3854]E(f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x38541)),x38541),f317(f317(f23(a1),f317(f317(f74(a1),x38541),x38541)),a87))
% 94.68/94.43 [3902]E(f317(f276(x39021,x39021),f297(x39021,f178(f904(f903(x39021,x39021),a893)))),f297(x39021,f178(f904(f903(x39021,x39021),a893))))
% 94.68/94.43 [3948]P1(f317(f317(f224(a897),x39481),f317(f317(f75(a897),x39481),f317(f317(f75(a897),x39481),x39481))))
% 94.68/94.43 [4219]P1(f317(f28(a897),f317(f252(a897),f317(f317(f7(a897,a897,a893),f224(a897)),x42191))))
% 94.68/94.43 [4220]P1(f317(f28(a897),f317(f252(a897),f317(f317(f7(a897,a897,a893),f225(a897)),x42201))))
% 94.68/94.43 [4492]E(f317(f252(f903(x44921,x44921)),f317(f317(f8(f904(x44921,a893),a893,f903(x44921,x44921)),f81(x44921)),f317(f317(f7(f903(x44921,x44921),f904(x44921,f903(x44921,x44921)),f904(x44921,a893)),f317(f317(f8(f904(f903(x44921,x44921),a893),f904(f904(x44921,f903(x44921,x44921)),f904(x44921,a893)),f903(x44921,x44921)),f8(f903(x44921,x44921),a893,x44921)),a314)),f317(f317(f18(x44921,x44921,f903(x44921,x44921)),f242(x44921,x44921)),f5(x44921))))),f297(x44921,f178(f904(f903(x44921,x44921),a893))))
% 94.68/94.43 [4619]~E(f317(f317(f23(a1),f317(f317(f74(a1),x46191),x46191)),a87),a77)
% 94.68/94.43 [4621]~E(f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x46211)),x46211),f2(a1))
% 94.68/94.43 [3993]E(f317(f317(f74(a1),f317(f317(f23(a1),a87),x39931)),f317(f317(f23(a1),a87),x39931)),f317(f317(f23(a1),a87),f317(f317(f23(a1),f317(f317(f74(a1),x39931),x39931)),a87)))
% 94.68/94.43 [4110]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),a87),x41101)),f317(f317(f23(a1),a87),x41101))),a87),f317(f317(f23(a1),a87),f317(f317(f74(a1),x41101),x41101)))
% 94.68/94.43 [4142]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f74(a1),x41421),a87)),f317(f317(f74(a1),x41421),a87))),a87),f317(f317(f74(a1),f317(f317(f74(a1),x41421),x41421)),a87))
% 94.68/94.43 [4180]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),a87),x41801)),f317(f317(f23(a1),a87),x41801))),a87),f317(f317(f23(a1),a77),f317(f317(f23(a1),f317(f317(f74(a1),x41801),x41801)),a87)))
% 94.68/94.43 [4277]E(f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x42771),f2(a897))),f178(f904(f903(a897,a897),a893))))),f317(f90(a1),x42771))
% 94.68/94.43 [4287]E(f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),f322(x42871)),f378(x42871))),f178(f904(f903(a897,a897),a893))))),x42871)
% 94.68/94.43 [4320]E(f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x43201)),f317(f300(a897,a1,f90(a1)),f317(f252(a897),f317(f317(f8(a1,a893,a897),x43201),f90(a1)))))
% 94.68/94.43 [4364]P39(f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x43641)))
% 94.68/94.43 [4384]P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x43841),f178(f904(f903(a897,a897),a893)))),a66))
% 94.68/94.43 [4389]E(f317(f300(a1,a897,a95),f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),f317(f317(f8(a897,a893,a1),x43891),a95)))),f317(f252(a897),x43891))
% 94.68/94.43 [4544]E(f302(a897,f317(f317(f34(f903(a897,a897),f904(a897,a893)),f317(a97,x45441)),f317(f247(a897,a897,f904(a897,a893)),f317(f317(f7(a897,f904(a897,a893),f904(a897,f904(a897,a893))),f317(f317(f8(f904(a897,f904(f904(a897,a893),f904(a897,a893))),f904(f904(a897,a893),f904(a897,f904(a897,a893))),a897),f7(a897,f904(a897,a893),f904(a897,a893))),f317(f317(f8(f904(a897,a897),f904(a897,f904(f904(a897,a893),f904(a897,a893))),a897),f317(f8(a897,f904(f904(a897,a893),f904(a897,a893)),a897),f299(a897))),f23(a897)))),f178(f904(a897,a893)))))),f317(a95,x45441))
% 94.68/94.43 [4038]E(f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),x40381),x40381)),a87)),a87),f317(f317(f74(a1),x40381),x40381))
% 94.68/94.43 [4090]E(f317(f317(f23(a1),f317(f317(f23(a1),f317(f317(f74(a1),x40901),x40901)),a87)),a87),f317(f317(f74(a1),f317(f317(f23(a1),x40901),a87)),f317(f317(f23(a1),x40901),a87)))
% 94.68/94.43 [4293]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f74(a1),f317(f73(a1),x42931)),a87)),f317(f317(f74(a1),f317(f73(a1),x42931)),a87))),a87),f317(f73(a1),f317(f317(f23(a1),f317(f317(f74(a1),x42931),x42931)),a87)))
% 94.68/94.43 [4337]E(f317(f317(f74(a897),x43371),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(a102,x43371)))
% 94.68/94.43 [4338]E(f317(f317(f75(a897),x43381),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f74(a897),x43381),x43381))
% 94.68/94.43 [4339]E(f317(f317(f30(a897),f317(f317(f74(a897),x43391),x43391)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x43391)
% 94.68/94.43 [4417]E(f40(a897,f317(a102,f317(a102,x44171)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a897,x44171,f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.43 [4558]E(f317(a83,f317(f317(f34(f903(a897,a897),f904(f903(a897,a897),a893)),f317(a97,x45581)),f317(f247(a897,a897,f904(f903(a897,a897),a893)),f317(f317(f8(f904(a897,f904(f903(a897,a897),a893)),f904(a897,f904(f903(a897,a897),a893)),a897),f317(f8(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893),a897),f275(f903(a897,a897),f903(a897,a897),a99))),f317(f317(f7(a897,f904(f903(a897,a897),a893),f904(a897,f904(f903(a897,a897),a893))),f317(f317(f8(f904(a897,f904(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f904(f904(f903(a897,a897),a893),f904(a897,f904(f903(a897,a897),a893))),a897),f7(a897,f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f8(f904(a897,f903(a897,a897)),f904(a897,f904(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),a897),f317(f8(f903(a897,a897),f904(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),a897),f299(f903(a897,a897)))),f317(f7(a897,a897,f903(a897,a897)),f242(a897,a897))))),f178(f904(f903(a897,a897),a893))))))),f317(f73(a1),x45581))
% 94.68/94.43 [4412]E(f317(f317(f74(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x44121),f317(a102,f317(a102,x44121)))
% 94.68/94.43 [4413]E(f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x44131),f317(f317(f74(a897),x44131),x44131))
% 94.68/94.43 [4449]E(f317(f317(f30(a897),f317(a102,f317(a102,x44491))),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a102,f317(f317(f30(a897),x44491),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.43 [4499]E(f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x44991),f317(a102,f317(a102,f317(a102,x44991))))
% 94.68/94.43 [4565]E(f317(f247(a1,a1,f903(a1,a1)),f317(f317(f18(a1,f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f904(f903(a1,a1),f903(a1,a1))),f904(f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),a1),f18(a1,f903(a1,a1),f903(a1,a1))),f317(f317(f8(f904(a1,f903(a1,a1)),f904(a1,f904(f903(a1,a1),f903(a1,a1))),a1),f317(f18(a1,f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),f317(f317(f8(a893,f904(f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),a1),f86(f903(a1,a1))),f317(f317(f8(a1,a893,a1),f317(f224(a1),f2(a1))),f317(f317(f7(a1,a1,a1),f23(a1)),x45651))))),f317(f317(f7(a1,f904(a1,a1),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f903(a1,a1)),f904(f904(a1,a1),f904(a1,f903(a1,a1))),a1),f8(a1,f903(a1,a1),a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f904(a1,a1),a1),f74(a1)),f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f72(a1))))),f317(f317(f7(a1,a1,a1),f23(a1)),x45651))))),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))),f38(x45651))
% 94.68/94.43 [3277]P107(f902(x32771,x32772))
% 94.68/94.43 [3278]P107(f901(x32781,x32782))
% 94.68/94.43 [3279]P107(f903(x32791,x32792))
% 94.68/94.43 [3297]P13(a1,f168(x32971,x32972))
% 94.68/94.43 [3298]P36(x32981,f143(x32981,x32982))
% 94.68/94.43 [3299]P37(x32991,f253(x32991,x32992))
% 94.68/94.43 [3300]P37(x33001,f297(x33001,x33002))
% 94.68/94.43 [3301]P38(x33011,f253(x33011,x33012))
% 94.68/94.43 [3302]P51(x33021,f253(x33021,x33022))
% 94.68/94.43 [3365]P30(x33651,x33652,f103(x33651))
% 94.68/94.43 [3398]P52(x33981,x33982,f253(x33981,x33982))
% 94.68/94.43 [3399]P54(x33991,x33991,f253(x33991,x33992))
% 94.68/94.43 [3661]P24(x36611,x36611,f5(x36611),x36612)
% 94.68/94.43 [3662]P24(x36621,x36621,f25(x36621),x36622)
% 94.68/94.43 [3670]P31(x36701,x36702,f103(x36701),f103(x36701))
% 94.68/94.43 [3677]P24(f898(x36771),f898(x36771),f158(x36771),x36772)
% 94.68/94.43 [4080]P25(x40801,x40801,f25(x40801),x40802,x40802)
% 94.68/94.43 [4590]~P32(x45901,x45902,f103(x45901))
% 94.68/94.43 [4591]~P34(x45911,x45912,f103(x45911))
% 94.68/94.43 [3263]E(f317(f5(x32631),x32632),x32632)
% 94.68/94.43 [3264]E(f317(f252(x32641),x32642),x32642)
% 94.68/94.43 [3266]E(f317(f25(x32661),x32662),x32662)
% 94.68/94.43 [3276]E(f317(f181(x32761),x32762),f105(x32761))
% 94.68/94.43 [3295]E(f79(x32951,f317(a314,x32952)),x32952)
% 94.68/94.43 [3296]E(f84(x32961,f317(a314,x32962)),x32962)
% 94.68/94.43 [3318]E(f317(f115(x33181,x33182),f109(x33181)),f2(a897))
% 94.68/94.43 [3321]E(f317(f126(x33211,x33212),f103(x33211)),f103(x33211))
% 94.68/94.43 [3341]E(f297(x33411,f297(x33411,x33412)),f297(x33411,x33412))
% 94.68/94.43 [3342]E(f142(x33421,f142(x33421,x33422)),f142(x33421,x33422))
% 94.68/94.43 [3360]E(f317(f317(f124(x33601),x33602),f103(x33601)),x33602)
% 94.68/94.43 [3366]E(f163(x33661,x33662,f103(x33661)),x33662)
% 94.68/94.43 [3367]E(f163(x33671,f103(x33671),x33672),x33672)
% 94.68/94.43 [3368]E(f106(x33681,f109(x33681),x33682),x33682)
% 94.68/94.43 [3369]E(f159(x33691,f2(a897),x33692),f103(x33691))
% 94.68/94.43 [3375]E(f317(f317(f165(x33751),x33752),f103(x33751)),f103(x33751))
% 94.68/94.43 [3376]E(f317(f317(f128(x33761),x33762),f103(x33761)),f103(x33761))
% 94.68/94.43 [3378]E(f145(x33781,x33782,f103(x33781)),f2(a897))
% 94.68/94.43 [3380]E(f160(x33801,x33802,f103(x33801)),f103(x33801))
% 94.68/94.43 [3381]E(f167(x33811,x33812,f103(x33811)),f103(x33811))
% 94.68/94.43 [3382]E(f166(x33821,f103(x33821),x33822),f103(x33821))
% 94.68/94.43 [3386]E(f317(f162(x33861),f142(x33861,x33862)),f317(f162(x33861),x33862))
% 94.68/94.43 [3389]E(f317(f274(x33891,x33891),f253(x33891,x33892)),x33892)
% 94.68/94.43 [3390]E(f317(f254(x33901,x33901),f253(x33901,x33902)),x33902)
% 94.68/94.43 [3397]E(f317(f276(x33971,x33971),f253(x33971,x33972)),f253(x33971,x33972))
% 94.68/94.43 [3411]E(f297(f898(x34111),f147(x34111,x34112)),f148(x34111,f297(x34111,x34112)))
% 94.68/94.43 [3413]P1(f317(f127(a1),f168(x34131,x34132)))
% 94.68/94.43 [3421]E(f317(f274(x34211,x34211),f297(x34211,x34212)),f232(f904(x34211,a893)))
% 94.68/94.43 [3422]E(f317(f254(x34221,x34221),f297(x34221,x34222)),f232(f904(x34221,a893)))
% 94.68/94.43 [3426]P1(f317(f127(x34261),f142(x34261,x34262)))
% 94.68/94.43 [3428]P1(f317(f150(x34281,x34282),f103(x34281)))
% 94.68/94.43 [3434]E(f317(f162(a1),f168(x34341,x34342)),f293(a1,x34341,x34342))
% 94.68/94.43 [3448]P55(x34481,f178(f904(x34481,a893)),x34482)
% 94.68/94.43 [3453]E(f317(f246(a1,a1),f41(x34531,x34532)),f40(a1,x34531,x34532))
% 94.68/94.43 [3454]E(f317(f292(a897,x34541),f317(a102,x34542)),f293(a897,x34541,x34542))
% 94.68/94.43 [3469]E(f317(f317(f141(x34691),x34692),f103(x34691)),f130(x34691,x34692,f103(x34691)))
% 94.68/94.43 [3481]E(f293(a897,f317(a102,x34811),x34812),f295(a897,x34811,x34812))
% 94.68/94.43 [3482]P52(x34821,f232(f904(x34821,a893)),f297(x34821,x34822))
% 94.68/94.43 [3544]E(f317(f317(f23(a897),x35441),f317(a102,x35442)),f317(f29(a897),f296(a897,x35442,x35441)))
% 94.68/94.43 [3599]E(f156(x35991,x35992,f103(x35991)),f317(f317(f242(f898(x35991),f898(x35991)),f103(x35991)),f103(x35991)))
% 94.68/94.43 [3617]E(f317(f247(x36171,x36172,f903(x36171,x36172)),f242(x36171,x36172)),f25(f903(x36171,x36172)))
% 94.68/94.43 [3621]P1(f317(f317(f319(f898(x36211)),f103(x36211)),f151(x36211,x36212)))
% 94.68/94.43 [3622]E(f317(f179(f898(x36221)),f104(x36221,x36222)),f317(f317(f23(a897),f317(f179(f898(x36221)),x36222)),f72(a897)))
% 94.68/94.43 [3630]P1(f317(f28(a897),f296(a897,x36301,x36302)))
% 94.68/94.43 [3631]P1(f317(f28(a897),f295(a897,x36311,x36312)))
% 94.68/94.43 [3632]P1(f317(f28(a897),f293(a897,x36321,x36322)))
% 94.68/94.43 [3633]P1(f317(f28(a1),f296(a1,x36331,x36332)))
% 94.68/94.43 [3634]P1(f317(f28(a1),f295(a1,x36341,x36342)))
% 94.68/94.43 [3635]P1(f317(f28(a1),f293(a1,x36351,x36352)))
% 94.68/94.43 [3738]E(f317(f300(a897,a897,a102),f293(a897,x37381,x37382)),f293(a897,f317(a102,x37381),f317(a102,x37382)))
% 94.68/94.43 [3758]E(f317(f317(f279(x37581,x37581,x37581),f297(x37581,x37582)),f297(x37581,x37582)),f297(x37581,x37582))
% 94.68/94.43 [3792]E(f317(f317(f242(a1,a1),f317(f317(f30(a1),x37921),x37922)),f40(a1,x37921,x37922)),f41(x37921,x37922))
% 94.68/94.43 [3793]E(f317(f317(f242(a89,a89),f317(f317(f30(a89),x37931),x37932)),f40(a89,x37931,x37932)),f21(x37931,x37932))
% 94.68/94.43 [3820]E(f317(f317(f242(a897,a897),f317(f317(f30(a897),x38201),x38202)),f40(a897,x38201,x38202)),f79(f903(a897,a897),f43(x38201,x38202)))
% 94.68/94.43 [3871]P1(f317(f317(f225(a897),f317(f317(f23(a897),x38711),x38712)),f317(a102,x38711)))
% 94.68/94.43 [3919]P37(x39191,f317(f317(f279(x39191,x39191,x39191),x39192),f297(x39191,x39192)))
% 94.68/94.43 [3969]E(f317(f317(f74(a1),f317(f317(f75(a1),x39691),f317(f317(f30(a1),x39692),x39691))),f40(a1,x39692,x39691)),x39692)
% 94.68/94.43 [3974]E(f317(f317(f34(a897,f904(f903(f898(x39741),f898(x39741)),a893)),f232(f904(a897,a893))),f133(x39741,x39742)),f135(x39741,x39742))
% 94.68/94.43 [4196]P1(f317(f317(f319(f903(f898(x41961),f898(x41961))),f317(f317(f242(f898(x41961),f898(x41961)),f103(x41961)),f103(x41961))),f148(x41961,x41962)))
% 94.68/94.43 [4305]E(f243(x43051,x43051,x43051,a314,f243(x43051,x43051,x43051,x43052,a314)),x43052)
% 94.68/94.43 [4349]E(f248(x43491,x43491,x43492,x43492,f5(x43491),f5(x43492)),f25(f903(x43491,x43492)))
% 94.68/94.43 [4351]E(f248(x43511,x43511,x43512,x43512,f25(x43511),f25(x43512)),f25(f903(x43511,x43512)))
% 94.68/94.43 [3359]E(f317(f158(x33591),f317(f158(x33591),x33592)),x33592)
% 94.68/94.43 [3361]E(f317(f317(f128(x33611),f2(a897)),x33612),x33612)
% 94.68/94.43 [3377]E(f317(f317(f165(x33771),f2(a897)),x33772),f103(x33771))
% 94.68/94.43 [3384]E(f317(f317(f124(x33841),f103(x33841)),x33842),x33842)
% 94.68/94.43 [3393]E(f31(f904(x33931,a893),f317(f298(x33931),x33932)),x33932)
% 94.68/94.43 [3395]E(f317(f162(x33951),f317(f157(x33951),x33952)),f317(f162(x33951),x33952))
% 94.68/94.43 [3396]E(f317(f162(x33961),f317(f158(x33961),x33962)),f317(f162(x33961),x33962))
% 94.68/94.43 [3401]E(f317(f317(f23(a89),x34011),x34012),f317(f317(a24,x34011),x34012))
% 94.68/94.43 [3415]E(f317(f317(f74(a897),x34151),x34152),f317(f317(f74(a897),x34152),x34151))
% 94.68/94.43 [3416]E(f317(f317(f74(a1),x34161),x34162),f317(f317(f74(a1),x34162),x34161))
% 94.68/94.43 [3417]E(f317(f317(f75(a897),x34171),x34172),f317(f317(f75(a897),x34172),x34171))
% 94.68/94.43 [3418]E(f317(f317(f75(a1),x34181),x34182),f317(f317(f75(a1),x34182),x34181))
% 94.68/94.43 [3440]E(f317(f317(f173(x34401,x34401),f2(a897)),x34402),f25(x34401))
% 94.68/94.43 [3441]E(f317(f179(f898(x34411)),f317(f157(x34411),x34412)),f317(f179(f898(x34411)),x34412))
% 94.68/94.43 [3442]E(f317(f179(f898(x34421)),f317(f158(x34421),x34422)),f317(f179(f898(x34421)),x34422))
% 94.68/94.43 [3443]E(f166(x34431,x34432,f178(f904(a897,a893))),f103(x34431))
% 94.68/94.43 [3444]E(f317(f317(f144(x34441,x34441),f5(x34441)),x34442),x34442)
% 94.68/94.43 [3446]E(f317(f241(a1,a1),f41(x34461,x34462)),f317(f317(f30(a1),x34461),x34462))
% 94.68/94.43 [3463]E(f317(f179(f898(x34631)),f142(x34631,x34632)),f317(f29(x34631),f317(f162(x34631),x34632)))
% 94.68/94.43 [3464]E(f317(f271(x34641),f317(f276(x34641,x34641),x34642)),f317(f271(x34641),x34642))
% 94.68/94.43 [3468]P1(f317(f28(x34681),f317(f162(x34681),x34682)))
% 94.68/94.43 [3476]E(f317(f317(f74(a1),x34761),f317(f73(a1),x34762)),f317(f317(f23(a1),x34761),x34762))
% 94.68/94.43 [3483]E(f317(f300(x34831,x34831,f5(x34831)),x34832),x34832)
% 94.68/94.43 [3484]E(f317(f300(x34841,x34841,f25(x34841)),x34842),x34842)
% 94.68/94.43 [3485]E(f317(f301(x34851,x34851,f5(x34851)),x34852),x34852)
% 94.68/94.43 [3486]E(f317(f301(x34861,x34861,f25(x34861)),x34862),x34862)
% 94.68/94.43 [3487]P1(f317(f232(f904(x34871,a893)),x34872))
% 94.68/94.43 [3489]E(f317(f29(a897),f317(f292(a897,x34891),x34892)),f317(f317(f23(a897),x34892),x34891))
% 94.68/94.43 [3490]E(f317(f292(a897,f317(a102,x34901)),x34902),f296(a897,x34901,x34902))
% 94.68/94.43 [3503]E(f317(f317(f299(x35031),x35032),f178(f904(x35031,a893))),f317(f252(x35031),f317(a314,x35032)))
% 94.68/94.43 [3508]E(f297(x35081,f317(f276(x35081,x35081),x35082)),f317(f276(x35081,x35081),f297(x35081,x35082)))
% 94.68/94.43 [3513]E(f317(f317(f74(a897),f317(a102,x35131)),x35132),f317(f317(f74(a897),x35131),f317(a102,x35132)))
% 94.68/94.43 [3514]E(f317(f317(f23(a897),f317(a102,x35141)),f317(a102,x35142)),f317(f317(f23(a897),x35141),x35142))
% 94.68/94.43 [3520]E(f50(x35201,f2(a897),x35202),f317(f317(f141(f898(x35201)),f103(x35201)),f103(f898(x35201))))
% 94.68/94.43 [3521]E(f317(f29(a897),f295(a897,x35211,x35212)),f317(f317(f23(a897),x35212),x35211))
% 94.68/94.43 [3530]P36(x35301,f317(f317(f278(a897,x35301),a230),x35302))
% 94.68/94.43 [3532]P13(a897,f129(a897,f317(f292(a897,x35321),x35322)))
% 94.68/94.43 [3534]P1(f317(f28(a897),f317(f292(a897,x35341),x35342)))
% 94.68/94.43 [3535]P1(f317(f28(a1),f317(f292(a1,x35351),x35352)))
% 94.68/94.43 [3538]E(f317(f276(f898(x35381),f898(x35381)),f147(x35381,x35382)),f147(x35381,f317(f276(x35381,x35381),x35382)))
% 94.68/94.43 [3540]E(f317(f292(a1,x35401),f317(f317(f74(a1),x35402),f72(a1))),f293(a1,x35401,x35402))
% 94.68/94.43 [3543]E(f317(f317(f30(a1),f317(f73(a1),x35431)),f317(f73(a1),x35432)),f317(f317(f30(a1),x35431),x35432))
% 94.68/94.43 [3551]E(f317(f317(f173(f903(x35511,x35511),a893),f72(a897)),x35512),x35512)
% 94.68/94.43 [3553]E(f317(f317(f23(f904(x35531,a893)),x35532),f178(f904(x35531,a893))),x35532)
% 94.68/94.43 [3554]E(f317(f317(f91(f904(x35541,a893)),x35542),f178(f904(x35541,a893))),x35542)
% 94.68/94.43 [3555]E(f317(f317(f92(f904(x35551,a893)),x35552),f232(f904(x35551,a893))),x35552)
% 94.68/94.43 [3556]E(f317(f241(a897,a897),f79(f903(a897,a897),f43(x35561,x35562))),f317(f317(f30(a897),x35561),x35562))
% 94.68/94.43 [3562]E(f293(a1,f317(f317(f74(a1),x35621),f72(a1)),x35622),f295(a1,x35621,x35622))
% 94.68/94.43 [3567]E(f317(f246(a897,a897),f79(f903(a897,a897),f43(x35671,x35672))),f40(a897,x35671,x35672))
% 94.68/94.43 [3577]P1(f317(f317(f319(x35771),x35772),f232(f904(x35771,a893))))
% 94.68/94.43 [3582]E(f317(f317(f23(a897),f317(a102,x35821)),x35822),f317(f29(a897),f293(a897,x35822,x35821)))
% 94.68/94.43 [3608]E(f317(f317(f23(f904(x36081,a893)),x36082),f232(f904(x36081,a893))),f178(f904(x36081,a893)))
% 94.68/94.43 [3609]E(f317(f317(f91(f904(x36091,a893)),x36092),f232(f904(x36091,a893))),f232(f904(x36091,a893)))
% 94.68/94.43 [3610]E(f317(f317(f92(f904(x36101,a893)),x36102),f178(f904(x36101,a893))),f178(f904(x36101,a893)))
% 94.68/94.43 [3625]E(f40(a1,f317(f90(a1),x36251),f317(f90(a1),x36252)),f317(f90(a1),f40(a897,x36251,x36252)))
% 94.68/94.43 [3626]E(f40(a1,f317(f73(a1),x36261),f317(f73(a1),x36262)),f317(f73(a1),f40(a1,x36261,x36262)))
% 94.68/94.43 [3637]E(f317(f179(f898(x36371)),f317(f161(x36371),x36372)),f317(f317(f23(a897),f317(f179(f898(x36371)),x36372)),f72(a897)))
% 94.68/94.43 [3663]E(f317(f317(f30(a1),f40(a1,x36631,x36632)),x36632),f2(a1))
% 94.68/94.43 [3672]E(f317(a3,f40(a897,f317(a20,x36721),f317(a20,x36722))),f40(a89,x36721,x36722))
% 94.68/94.43 [3705]E(f317(a3,f317(f317(f23(a897),f317(a20,x37051)),f317(a20,x37052))),f317(f317(f23(a89),x37051),x37052))
% 94.68/94.43 [3706]E(f317(a3,f317(f317(f74(a897),f317(a20,x37061)),f317(a20,x37062))),f317(f317(f74(a89),x37061),x37062))
% 94.68/94.43 [3707]E(f317(a3,f317(f317(f75(a897),f317(a20,x37071)),f317(a20,x37072))),f317(f317(f75(a89),x37071),x37072))
% 94.68/94.43 [3708]E(f317(a3,f317(f317(f30(a897),f317(a20,x37081)),f317(a20,x37082))),f317(f317(f30(a89),x37081),x37082))
% 94.68/94.43 [3716]E(f317(f300(a897,a897,a102),f317(f292(a897,x37161),x37162)),f317(f292(a897,f317(a102,x37161)),f317(a102,x37162)))
% 94.68/94.43 [3743]P1(f317(f43(x37431,x37432),f79(f903(a897,a897),f43(x37431,x37432))))
% 94.68/94.43 [3767]E(f40(a897,f317(a102,f40(a897,x37671,x37672)),x37672),f40(a897,f317(a102,x37671),x37672))
% 94.68/94.43 [3779]E(f317(f317(f35(f904(x37791,a893),f904(x37791,a893)),x37792),f5(f904(x37791,a893))),f32(f904(x37791,a893),x37792))
% 94.68/94.43 [3780]E(f317(f317(f34(f904(x37801,a893),f904(x37801,a893)),x37802),f5(f904(x37801,a893))),f31(f904(x37801,a893),x37802))
% 94.68/94.43 [3781]E(f317(f300(f898(x37811),f904(x37811,a893),f162(x37811)),f317(f162(f898(x37811)),f49(x37811,x37812))),f317(f298(x37811),f317(f162(x37811),x37812)))
% 94.68/94.43 [3785]P1(f317(f317(f319(f904(x37851,a893)),x37852),f317(f298(x37851),x37852)))
% 94.68/94.43 [3791]E(f40(a1,f317(f73(a1),f40(a1,x37911,x37912)),x37912),f40(a1,f317(f73(a1),x37911),x37912))
% 94.68/94.43 [3802]P1(f317(f317(f224(f904(x38021,a893)),x38022),f232(f904(x38021,a893))))
% 94.68/94.43 [3804]E(f317(f317(f279(x38041,x38041,x38041),f297(x38041,x38042)),f297(x38041,f297(x38041,x38042))),f297(x38041,x38042))
% 94.68/94.43 [3805]E(f317(f317(f91(f904(x38051,a893)),f317(f254(x38051,x38051),x38052)),f317(f274(x38051,x38051),x38052)),f317(f271(x38051),x38052))
% 94.68/94.43 [3826]E(f303(x38261,x38262,f232(f904(x38261,a893)),f232(f904(x38262,a893))),f232(f904(f902(x38261,x38262),a893)))
% 94.68/94.43 [3876]P1(f317(f317(f224(a897),f40(a897,x38761,x38762)),x38761))
% 94.68/94.43 [3900]P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x39001))),f317(f90(a1),x39002)))
% 94.68/94.43 [3924]P1(f317(f317(f319(f904(x39241,a893)),f178(f904(x39241,a893))),f317(f298(x39241),x39242)))
% 94.68/94.43 [3929]E(f297(x39291,f317(f317(f279(x39291,x39291,x39291),x39292),f297(x39291,x39292))),f297(x39291,x39292))
% 94.68/94.43 [3932]E(f317(f317(f279(x39321,x39321,x39321),f297(x39321,x39322)),x39322),f317(f317(f279(x39321,x39321,x39321),x39322),f297(x39321,x39322)))
% 94.68/94.43 [3934]E(f317(a95,f317(f317(f74(a1),f317(f317(f23(a1),x39341),x39342)),f72(a1))),f317(f29(a1),f293(a1,x39342,x39341)))
% 94.68/94.43 [3949]E(f317(f274(x39491,x39491),f317(f317(f279(x39491,x39491,x39491),x39492),f297(x39491,x39492))),f317(f274(x39491,x39491),x39492))
% 94.68/94.43 [3950]E(f317(f254(x39501,x39501),f317(f317(f279(x39501,x39501,x39501),x39502),f297(x39501,x39502))),f317(f254(x39501,x39501),x39502))
% 94.68/94.43 [3968]E(f317(f132(f898(x39681),f898(x39681),f124(x39681),f103(x39681)),f159(f898(x39681),x39682,f103(x39681))),f103(x39681))
% 94.68/94.43 [3978]P24(a897,a897,f317(f317(f7(a897,a897,a897),f74(a897)),x39781),x39782)
% 94.68/94.43 [3980]P13(a897,f317(f158(a897),f317(f317(f144(f898(x39801),a897),f179(f898(x39801))),f169(x39801,x39802))))
% 94.68/94.43 [4010]P51(x40101,f317(f317(f91(f904(f903(x40101,x40101),a893)),x40102),f317(f276(x40101,x40101),x40102)))
% 94.68/94.43 [4011]P51(x40111,f317(f317(f92(f904(f903(x40111,x40111),a893)),x40112),f317(f276(x40111,x40111),x40112)))
% 94.68/94.43 [4022]P1(f317(f317(f225(a1),f317(f73(a1),f317(f90(a1),f317(a102,x40221)))),f317(f90(a1),x40222)))
% 94.68/94.43 [4069]E(f317(f132(f898(x40691),x40691,f317(f7(x40691,f898(x40691),f898(x40691)),f141(x40691)),f103(x40691)),x40692),f317(f158(x40691),x40692))
% 94.68/94.43 [4117]P1(f317(f317(f224(f904(f903(f898(x41171),f898(x41171)),a893)),f148(x41171,x41172)),f297(f898(x41171),f147(x41171,x41172))))
% 94.68/94.43 [4146]P1(f317(f43(x41461,x41462),f317(f317(f242(a897,a897),f317(f317(f30(a897),x41461),x41462)),f40(a897,x41461,x41462))))
% 94.68/94.43 [4158]P1(f317(f317(f224(f904(f903(f898(x41581),f898(x41581)),a893)),f147(x41581,f297(x41581,x41582))),f297(f898(x41581),f147(x41581,x41582))))
% 94.68/94.43 [4374]E(f317(f317(f249(f903(a89,a89),a89,f903(a89,a89),f903(x43741,f903(a89,a89))),f257(f317(f155(a89),f317(f317(f144(f903(a89,x43741),a89),f241(a89,x43741)),x43742)))),f317(f317(f8(x43741,f904(f903(a89,a89),f903(x43741,f903(a89,a89))),a89),f242(x43741,f903(a89,a89))),f258(x43741,x43742))),f256(x43741,x43742))
% 94.68/94.43 [4451]E(f213(a897,f903(x44511,f899(x44511)),f2(a897),f317(f247(x44511,f899(x44511),a897),f317(f16(f904(f899(x44511),a897),x44511),f317(f317(f7(f899(x44511),a897,a897),f317(f317(f8(a897,f904(a897,a897),f899(x44511)),f74(a897)),f179(f899(x44511)))),f72(a897)))),f317(f125(x44511),x44512)),f317(f179(f899(x44511)),x44512))
% 94.68/94.43 [4557]E(f317(f247(f904(f903(x45571,x45571),a893),f904(f903(x45571,x45571),a893),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f317(f317(f7(f904(f903(x45571,x45571),a893),f904(f904(f903(x45571,x45571),a893),f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893))),f904(f904(f903(x45571,x45571),a893),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893))))),f317(f317(f8(f904(f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893)),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f904(f904(f904(f903(x45571,x45571),a893),f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893))),f904(f904(f903(x45571,x45571),a893),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893))))),f904(f903(x45571,x45571),a893)),f8(f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893)),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893))),f904(f903(x45571,x45571),a893))),f317(f317(f8(f904(f904(x45572,x45571),f904(f904(f903(x45572,x45572),a893),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f904(f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893)),f904(f904(x45572,x45571),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f904(f903(x45571,x45571),a893)),f18(f904(x45572,x45571),f904(f903(x45572,x45572),a893),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f317(f317(f8(f904(f904(x45572,x45571),f904(f903(x45572,x45572),a893)),f904(f904(x45572,x45571),f904(f904(f903(x45572,x45572),a893),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f904(f903(x45571,x45571),a893)),f317(f8(f904(f903(x45572,x45572),a893),f904(f904(f903(x45572,x45572),a893),f903(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893))),f904(x45572,x45571)),f242(f904(f903(x45572,x45572),a893),f904(f903(x45572,x45572),a893)))),f278(x45571,x45572))))),f278(x45571,x45572))),f68(x45571,x45572))
% 94.68/94.43 [4602]~E(f317(f298(x46021),x46022),f178(f904(f904(x46021,a893),a893)))
% 94.68/94.43 [4611]~P1(f317(f317(f162(x46111),f103(x46111)),x46112))
% 94.68/94.43 [4616]~P1(f317(f317(f319(x46161),x46162),f178(f904(x46161,a893))))
% 94.68/94.43 [4624]~P1(f317(f317(f225(f904(x46241,a893)),x46242),f178(f904(x46241,a893))))
% 94.68/94.43 [3492]E(f317(f317(f23(a897),x34921),f317(f317(f74(a897),x34921),x34922)),f2(a897))
% 94.68/94.43 [3495]E(f317(f317(f91(f904(x34951,a893)),x34952),x34952),x34952)
% 94.68/94.43 [3496]E(f317(f317(f92(f904(x34961,a893)),x34962),x34962),x34962)
% 94.68/94.43 [3524]E(f317(f317(f23(f904(x35241,a893)),x35242),x35242),f178(f904(x35241,a893)))
% 94.68/94.43 [3527]E(f317(f133(x35271,x35272),f2(a897)),f178(f904(f903(f898(x35271),f898(x35271)),a893)))
% 94.68/94.43 [3528]E(f317(f317(f74(a897),x35281),f317(a102,x35282)),f317(a102,f317(f317(f74(a897),x35281),x35282)))
% 94.68/94.43 [3539]E(f184(f317(f90(a1),x35391),f317(f90(a1),x35392)),f317(f90(a1),f317(f317(f23(a897),x35391),x35392)))
% 94.68/94.43 [3542]E(f317(f317(f30(a1),f317(f73(a1),x35421)),x35422),f317(f317(f30(a1),x35421),f317(f73(a1),x35422)))
% 94.68/94.43 [3546]E(f317(f29(a1),f317(f292(a1,x35461),x35462)),f317(a95,f317(f317(f23(a1),x35462),x35461)))
% 94.68/94.43 [3549]E(f317(f317(f74(a897),f317(a102,x35491)),x35492),f317(a102,f317(f317(f74(a897),x35491),x35492)))
% 94.68/94.43 [3552]E(f317(f73(f904(x35521,a893)),f317(f73(f904(x35521,a893)),x35522)),x35522)
% 94.68/94.43 [3564]E(f169(x35641,f317(f317(f141(f898(x35641)),f103(x35641)),x35642)),f169(x35641,x35642))
% 94.68/94.43 [3568]E(f317(f317(f74(a897),x35681),f317(f317(f75(a897),x35681),x35682)),f317(f317(f75(a897),x35681),f317(a102,x35682)))
% 94.68/94.43 [3575]E(f317(f317(a24,f317(a3,x35751)),f317(a3,x35752)),f317(a3,f317(f317(f23(a897),x35751),x35752)))
% 94.68/94.43 [3590]E(f317(f317(f75(a1),f317(f73(a1),x35901)),x35902),f317(f73(a1),f317(f317(f75(a1),x35901),x35902)))
% 94.68/94.43 [3592]E(f317(f317(f234(a1),f317(f90(a1),x35921)),x35922),f317(f90(a1),f317(f317(f234(a897),x35921),x35922)))
% 94.68/94.43 [3593]E(f317(f317(f74(a89),f317(a3,x35931)),f317(a3,x35932)),f317(a3,f317(f317(f74(a897),x35931),x35932)))
% 94.68/94.43 [3594]E(f317(f317(f75(a89),f317(a3,x35941)),f317(a3,x35942)),f317(a3,f317(f317(f75(a897),x35941),x35942)))
% 94.68/94.43 [3595]E(f317(f317(f228(a897),f317(a102,x35951)),f317(a102,x35952)),f317(a102,f317(f317(f228(a897),x35951),x35952)))
% 94.68/94.43 [3596]E(f317(f317(f223(a897),f317(a102,x35961)),f317(a102,x35962)),f317(a102,f317(f317(f223(a897),x35961),x35962)))
% 94.68/94.43 [3601]E(f317(f162(a897),f129(a897,f317(f292(a897,x36011),x36012))),f317(f292(a897,x36011),x36012))
% 94.68/94.43 [3602]E(f302(x36021,f317(f317(f299(x36021),x36022),f178(f904(x36021,a893)))),x36022)
% 94.68/94.43 [3606]E(f317(f274(x36061,x36062),f178(f904(f903(x36061,x36062),a893))),f178(f904(x36062,a893)))
% 94.68/94.43 [3607]E(f317(f254(x36071,x36072),f178(f904(f903(x36071,x36072),a893))),f178(f904(x36071,a893)))
% 94.68/94.43 [3611]E(f317(a95,f317(f317(f23(a1),x36111),x36112)),f317(f29(a1),f295(a1,x36112,x36111)))
% 94.68/94.43 [3616]E(f317(f317(f74(a897),x36161),f317(f317(f75(a897),x36162),x36161)),f317(f317(f75(a897),f317(a102,x36162)),x36161))
% 94.68/94.43 [3618]E(f317(f317(f55(x36181),f178(f904(x36181,a893))),x36182),f178(f904(f904(x36181,a893),a893)))
% 94.68/94.43 [3627]E(f317(f179(f898(a897)),f129(a897,f317(f292(a897,x36271),x36272))),f317(f317(f23(a897),x36272),x36271))
% 94.68/94.43 [3642]E(f317(f317(f91(f904(x36421,a893)),f178(f904(x36421,a893))),x36422),x36422)
% 94.68/94.43 [3643]E(f317(f317(f92(f904(x36431,a893)),f232(f904(x36431,a893))),x36432),x36432)
% 94.68/94.43 [3646]E(f317(f317(f74(a1),f317(f73(a1),x36461)),f317(f73(a1),x36462)),f317(f73(a1),f317(f317(f74(a1),x36461),x36462)))
% 94.68/94.43 [3648]E(f317(f317(f74(a1),f317(f94(a1),x36481)),f317(f94(a1),x36482)),f317(f94(a1),f317(f317(f74(a1),x36481),x36482)))
% 94.68/94.43 [3650]E(f317(f317(f74(a1),f317(f90(a1),x36501)),f317(f90(a1),x36502)),f317(f90(a1),f317(f317(f74(a897),x36501),x36502)))
% 94.68/94.43 [3651]E(f317(f317(f75(a1),f317(f94(a1),x36511)),f317(f94(a1),x36512)),f317(f94(a1),f317(f317(f75(a1),x36511),x36512)))
% 94.68/94.43 [3653]E(f317(f317(f75(a1),f317(f90(a1),x36531)),f317(f90(a1),x36532)),f317(f90(a1),f317(f317(f75(a897),x36531),x36532)))
% 94.68/94.43 [3654]E(f317(f317(f30(a1),f317(f90(a1),x36541)),f317(f90(a1),x36542)),f317(f90(a1),f317(f317(f30(a897),x36541),x36542)))
% 94.68/94.43 [3673]E(f317(f317(f6(x36731,a897),f317(f16(a897,x36731),f72(a897))),x36732),f317(f29(x36731),x36732))
% 94.68/94.43 [3678]E(f317(f73(a1),f40(a1,f317(f73(a1),x36781),x36782)),f40(a1,x36781,f317(f73(a1),x36782)))
% 94.68/94.43 [3680]E(f317(f162(a1),f168(x36801,f317(f317(f23(a1),x36802),f72(a1)))),f317(f292(a1,x36801),x36802))
% 94.68/94.43 [3684]P1(f317(f317(f224(a897),x36841),f317(f317(f74(a897),x36842),x36841)))
% 94.68/94.43 [3685]P1(f317(f317(f224(a897),x36851),f317(f317(f74(a897),x36851),x36852)))
% 94.68/94.43 [3688]E(f317(f317(f23(f904(x36881,a893)),f178(f904(x36881,a893))),x36882),f178(f904(x36881,a893)))
% 94.68/94.43 [3689]E(f317(f317(f91(f904(x36891,a893)),f232(f904(x36891,a893))),x36892),f232(f904(x36891,a893)))
% 94.68/94.43 [3690]E(f317(f317(f92(f904(x36901,a893)),f178(f904(x36901,a893))),x36902),f178(f904(x36901,a893)))
% 94.68/94.43 [3697]E(f317(f317(f242(a1,a1),x36971),f317(f73(a1),x36972)),f317(a46,f317(f317(f242(a1,a1),x36971),x36972)))
% 94.68/94.43 [3698]E(f317(f292(a1,f317(f317(f74(a1),x36981),f72(a1))),x36982),f296(a1,x36981,x36982))
% 94.68/94.43 [3709]E(f317(f317(f75(a897),x37091),f317(f317(f30(a897),x37092),x37091)),f317(f317(f23(a897),x37092),f40(a897,x37092,x37091)))
% 94.68/94.43 [3710]E(f317(f317(f75(a1),x37101),f317(f317(f30(a1),x37102),x37101)),f317(f317(f23(a1),x37102),f40(a1,x37102,x37101)))
% 94.68/94.43 [3713]E(f317(f162(a1),f168(f317(f317(f74(a1),x37131),f72(a1)),x37132)),f295(a1,x37131,x37132))
% 94.68/94.43 [3717]P1(f317(f317(f224(f904(x37171,a893)),x37172),x37172))
% 94.68/94.43 [3720]E(f317(f317(f91(f904(x37201,a893)),x37202),f317(f73(f904(x37201,a893)),x37202)),f232(f904(x37201,a893)))
% 94.68/94.43 [3721]E(f317(f317(f92(f904(x37211,a893)),x37212),f317(f73(f904(x37211,a893)),x37212)),f178(f904(x37211,a893)))
% 94.68/94.43 [3729]E(f317(f317(f23(a897),f317(f317(f23(a897),x37291),f72(a897))),x37292),f317(f317(f23(a897),x37291),f317(a102,x37292)))
% 94.68/94.43 [3735]E(f317(f317(f23(f904(x37351,a893)),f232(f904(x37351,a893))),x37352),f317(f73(f904(x37351,a893)),x37352))
% 94.68/94.43 [3736]E(f317(f317(f23(a1),f317(f94(a1),x37361)),f317(f94(a1),x37362)),f317(f94(a1),f317(f317(f74(a1),x37361),f317(f73(a1),x37362))))
% 94.68/94.43 [3749]E(f317(f162(a897),f129(a897,f317(f292(a897,x37491),f317(a102,x37492)))),f293(a897,x37491,x37492))
% 94.68/94.43 [3765]E(f317(f179(f898(f898(x37651))),f49(x37651,x37652)),f317(f317(f234(a897),f317(a102,f317(a102,f2(a897)))),f317(f179(f898(x37651)),x37652)))
% 94.68/94.43 [3783]E(f317(f317(f173(f903(x37831,x37831),a893),f2(a897)),x37832),f297(x37831,f178(f904(f903(x37831,x37831),a893))))
% 94.68/94.43 [3787]P1(f317(f127(a897),f129(a897,f317(f292(a897,x37871),x37872))))
% 94.68/94.43 [3803]E(f317(f300(a1,a897,a95),f293(a1,f317(f90(a1),x38031),f317(f90(a1),x38032))),f293(a897,x38031,x38032))
% 94.68/94.43 [3812]E(f175(a897,f2(a897),f5(a897),f317(f317(f23(a897),x38121),x38122)),f317(f317(f23(a897),x38121),f317(a102,x38122)))
% 94.68/94.43 [3813]E(f317(a95,f317(f317(f23(a1),x38131),f317(f317(f74(a1),x38132),f72(a1)))),f317(f29(a1),f296(a1,x38132,x38131)))
% 94.68/94.43 [3848]E(f317(f317(f144(a897,a897),a102),f129(a897,f317(f292(a897,x38481),x38482))),f129(a897,f317(f292(a897,f317(a102,x38481)),f317(a102,x38482))))
% 94.68/94.43 [3856]E(f317(f162(a1),f168(f317(f317(f74(a1),x38561),f72(a1)),f317(f317(f23(a1),x38562),f72(a1)))),f296(a1,x38561,x38562))
% 94.68/94.43 [3868]P1(f317(f317(f224(f904(x38681,a893)),f178(f904(x38681,a893))),x38682))
% 94.68/94.43 [3872]E(f79(x38721,f317(f317(f7(x38721,x38721,a893),a314),x38722)),x38722)
% 94.68/94.43 [3873]E(f84(x38731,f317(f317(f7(x38731,x38731,a893),a314),x38732)),x38732)
% 94.68/94.43 [3877]E(f317(f162(a897),f129(a897,f317(f292(a897,f317(a102,x38771)),f317(a102,x38772)))),f295(a897,x38771,x38772))
% 94.68/94.43 [3903]E(f317(f317(f244(x39031,x39032),f232(f904(x39031,a893))),f317(f16(f904(x39032,a893),x39031),f232(f904(x39032,a893)))),f232(f904(f903(x39031,x39032),a893)))
% 94.68/94.43 [3936]E(f317(f252(x39361),f317(f317(f8(a893,a893,x39361),a312),x39362)),f317(f73(f904(x39361,a893)),f317(f252(x39361),x39362)))
% 94.68/94.43 [3939]E(f317(f252(x39391),f317(f317(f7(x39391,x39391,a893),a314),x39392)),f317(f317(f299(x39391),x39392),f178(f904(x39391,a893))))
% 94.68/94.43 [3946]E(f317(f317(f74(a1),f317(f317(f23(a1),x39461),x39462)),f317(f317(f23(a1),x39461),x39462)),f317(f317(f23(a1),f317(f317(f74(a1),x39461),x39461)),f317(f317(f74(a1),x39462),x39462)))
% 94.68/94.43 [3947]E(f317(f317(f74(a1),f317(f317(f74(a1),x39471),x39471)),f317(f317(f74(a1),x39472),x39472)),f317(f317(f74(a1),f317(f317(f74(a1),x39471),x39472)),f317(f317(f74(a1),x39471),x39472)))
% 94.68/94.43 [3963]P1(f317(f317(f224(a897),f317(f29(x39631),f317(f162(x39631),x39632))),f317(f179(f898(x39631)),x39632)))
% 94.68/94.43 [3964]P1(f317(f317(f224(a897),f317(f179(f898(x39641)),f142(x39641,x39642))),f317(f179(f898(x39641)),x39642)))
% 94.68/94.43 [3975]E(f317(f252(x39751),f317(f317(f7(x39751,f904(x39751,a893),a893),f319(x39751)),x39752)),x39752)
% 94.68/94.43 [3989]E(f317(f317(f165(x39891),f317(f317(f23(a897),f317(f179(f898(x39891)),x39892)),f72(a897))),x39892),f104(x39891,x39892))
% 94.68/94.43 [4009]E(f175(a897,f2(a897),f317(f317(f8(a897,a897,a897),a102),f317(f228(a897),x40091)),x40092),f317(f317(f228(a897),f317(a102,x40091)),x40092))
% 94.68/94.43 [4014]E(f31(f904(x40141,a893),f317(f300(f904(f903(x40141,x40141),a893),f904(x40141,a893),f271(x40141)),x40142)),f317(f271(x40141),f31(f904(f903(x40141,x40141),a893),x40142)))
% 94.68/94.43 [4015]E(f175(a897,f317(a102,x40151),f317(f317(f8(a897,a897,a897),a102),f317(f223(a897),x40151)),x40152),f317(f317(f223(a897),f317(a102,x40151)),x40152))
% 94.68/94.43 [4017]E(f317(f317(f242(a1,a1),f317(f317(f30(a1),f317(f70(a1),x40171)),f317(f70(a1),x40172))),f40(a1,f317(f70(a1),x40171),f317(f70(a1),x40172))),f48(x40171,x40172))
% 94.68/94.43 [4041]P1(f317(f317(f224(f904(f904(x40411,a893),a893)),x40412),f317(f298(x40411),f31(f904(x40411,a893),x40412))))
% 94.68/94.43 [4074]E(f317(f317(f34(x40741,f904(x40741,a893)),x40742),f317(f317(f7(x40741,f904(x40741,a893),f904(x40741,a893)),f299(x40741)),f178(f904(x40741,a893)))),x40742)
% 94.68/94.43 [4075]E(f317(f317(f279(x40751,x40751,x40751),f317(f276(x40751,x40751),x40752)),f297(x40751,f317(f276(x40751,x40751),x40752))),f317(f276(x40751,x40751),f317(f317(f279(x40751,x40751,x40751),x40752),f297(x40751,x40752))))
% 94.68/94.43 [4138]E(f317(f162(x41381),f317(f132(f898(x41381),f898(x41381),f124(x41381),f103(x41381)),x41382)),f317(f317(f34(f898(x41381),f904(x41381,a893)),f317(f162(f898(x41381)),x41382)),f162(x41381)))
% 94.68/94.43 [4169]E(f317(f317(f91(f904(f903(x41691,x41691),a893)),f297(x41691,f178(f904(f903(x41691,x41691),a893)))),f317(f317(f279(x41691,x41691,x41691),f297(x41691,x41692)),x41692)),f297(x41691,x41692))
% 94.68/94.43 [4205]E(f317(f317(f171(x42051,x42051),x42052),x42052),f317(f317(f144(x42051,f903(x42051,x42051)),f317(f317(f18(x42051,x42051,f903(x42051,x42051)),f242(x42051,x42051)),f5(x42051))),x42052))
% 94.68/94.43 [4316]E(f317(f132(a897,f898(x43161),f317(f7(f898(x43161),a897,a897),f317(f317(f8(a897,f904(a897,a897),f898(x43161)),f223(a897)),f179(f898(x43161)))),f2(a897)),f317(f158(f898(x43161)),x43162)),f317(f179(f898(f898(x43161))),f169(x43161,x43162)))
% 94.68/94.43 [4388]E(f317(f317(f278(f903(a897,f898(x43881)),f898(x43881)),f309(a897,f898(x43881),a230,f135(x43881,x43882))),f317(f317(f18(f898(x43881),f898(x43881),f903(a897,f898(x43881))),f317(f317(f8(a897,f904(f898(x43881),f903(a897,f898(x43881))),f898(x43881)),f242(a897,f898(x43881))),f179(f898(x43881)))),f5(f898(x43881)))),f136(x43881,x43882))
% 94.68/94.43 [4515]E(f317(f252(x45151),f317(f317(f8(f904(f904(x45151,a893),a893),a893,x45151),f82(f904(x45151,a893))),f317(f317(f8(f904(f904(x45151,a893),a893),f904(f904(x45151,a893),a893),x45151),f317(f18(f904(x45151,a893),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x45151,a893)),a320),f317(f317(f7(f904(x45151,a893),f904(f904(x45151,a893),a893),a893),f319(f904(x45151,a893))),x45152)))),f319(x45151)))),f32(f904(x45151,a893),x45152))
% 94.68/94.43 [4516]E(f317(f252(x45161),f317(f317(f8(f904(f904(x45161,a893),a893),a893,x45161),f81(f904(x45161,a893))),f317(f317(f8(f904(f904(x45161,a893),a893),f904(f904(x45161,a893),a893),x45161),f317(f18(f904(x45161,a893),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x45161,a893)),a315),f317(f317(f7(f904(x45161,a893),f904(f904(x45161,a893),a893),a893),f319(f904(x45161,a893))),x45162)))),f319(x45161)))),f31(f904(x45161,a893),x45162))
% 94.68/94.43 [4625]~P1(f317(f317(f225(a1),f317(f90(a1),x46251)),f317(f73(a1),f317(f90(a1),x46252))))
% 94.68/94.43 [3614]E(f317(f317(f23(a897),f317(f317(f74(a897),x36141),x36142)),x36142),x36141)
% 94.68/94.43 [3615]E(f317(f317(f23(a897),f317(f317(f74(a897),x36151),x36152)),x36151),x36152)
% 94.68/94.43 [3679]E(f317(f317(f74(a897),f317(f317(f23(a897),x36791),x36792)),x36792),f317(f317(f223(a897),x36791),x36792))
% 94.68/94.43 [3790]E(f317(f317(f75(a897),f317(f317(f30(a897),x37901),x37902)),x37902),f317(f317(f23(a897),x37901),f40(a897,x37901,x37902)))
% 94.68/94.43 [3817]E(f317(f162(a897),f129(a897,f317(f292(a897,f317(a102,x38171)),x38172))),f296(a897,x38171,x38172))
% 94.68/94.43 [3825]E(f317(f90(a1),f206(f317(a95,f317(f70(a1),x38251)),f317(a95,f317(f70(a1),x38252)))),f317(f317(a207,x38251),x38252))
% 94.68/94.43 [3827]E(f317(f317(f91(f904(x38271,a893)),f317(f73(f904(x38271,a893)),x38272)),x38272),f232(f904(x38271,a893)))
% 94.68/94.43 [3828]E(f317(f317(f92(f904(x38281,a893)),f317(f73(f904(x38281,a893)),x38282)),x38282),f178(f904(x38281,a893)))
% 94.68/94.43 [3844]P1(f317(f317(f224(a897),f317(f317(f23(a897),x38441),x38442)),x38441))
% 94.68/94.43 [3845]P1(f317(f317(f224(a897),f317(f317(f30(a897),x38451),x38452)),x38451))
% 94.68/94.43 [3869]P1(f317(f317(f225(a897),x38691),f317(a102,f317(f317(f74(a897),x38692),x38691))))
% 94.68/94.43 [3870]P1(f317(f317(f225(a897),x38701),f317(a102,f317(f317(f74(a897),x38701),x38702))))
% 94.68/94.43 [3887]E(f317(f317(f75(a897),f317(a95,f317(f70(a1),x38871))),f317(a95,f317(f70(a1),x38872))),f317(a95,f317(f70(a1),f317(f317(f75(a1),x38871),x38872))))
% 94.68/94.43 [3899]P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x38991)),x38992)))
% 94.68/94.43 [3967]E(f317(f275(f898(x39671),f898(x39671),f148(x39671,x39672)),f317(f317(f299(f898(x39671)),f103(x39671)),f178(f904(f898(x39671),a893)))),f317(f317(f299(f898(x39671)),f103(x39671)),f178(f904(f898(x39671),a893))))
% 94.68/94.43 [3987]E(f317(f317(f91(f904(f903(x39871,x39871),a893)),f297(x39871,x39872)),f297(x39871,f178(f904(f903(x39871,x39871),a893)))),f297(x39871,x39872))
% 94.68/94.43 [3999]E(f317(f317(f30(a1),f317(f94(a1),f317(f317(f74(a1),x39991),x39991))),f317(f94(a1),f317(f317(f74(a1),x39992),x39992))),f317(f317(f30(a1),f317(f94(a1),x39991)),f317(f94(a1),x39992)))
% 94.68/94.43 [4064]E(f317(f317(f234(a1),x40641),f317(f94(a897),f317(f317(f74(a1),x40642),x40642))),f317(f317(f80(a1,a1),f317(f317(f234(a1),x40641),f317(f94(a897),x40642))),f317(f317(f18(a1,a1,a1),f75(a1)),f5(a1))))
% 94.68/94.43 [4070]E(f317(f252(f904(x40701,a893)),f317(f317(f7(f904(x40701,a893),f904(x40701,a893),a893),f224(f904(x40701,a893))),x40702)),f317(f298(x40701),x40702))
% 94.68/94.43 [4086]E(f317(f317(f144(a1,a897),a95),f317(f317(f124(a1),f317(f317(f144(a897,a1),f90(a1)),x40861)),f317(f317(f144(a897,a1),f90(a1)),x40862))),f317(f317(f124(a897),x40861),x40862))
% 94.68/94.43 [4116]E(f317(f300(a1,a1,f317(f317(f7(a1,a1,a1),f74(a1)),x41161)),f317(f292(a1,f2(a1)),f317(f317(f23(a1),x41162),x41161))),f317(f292(a1,x41161),x41162))
% 94.68/94.43 [4118]P53(x41181,f317(f317(f23(f904(f903(x41181,x41181),a893)),x41182),f297(x41181,f178(f904(f903(x41181,x41181),a893)))))
% 94.68/94.43 [4136]E(f317(f179(f898(x41361)),f317(f132(f898(x41361),f898(x41361),f124(x41361),f103(x41361)),x41362)),f317(f155(a897),f317(f317(f144(f898(x41361),a897),f179(f898(x41361))),x41362)))
% 94.68/94.43 [4140]P52(x41401,f232(f904(x41401,a893)),f317(f317(f91(f904(f903(x41401,x41401),a893)),x41402),f297(x41401,f178(f904(f903(x41401,x41401),a893)))))
% 94.68/94.43 [4185]E(f175(a897,f2(a897),f317(f317(f8(a897,a897,a897),a102),f317(f317(f7(a897,a897,a897),f228(a897)),x41851)),x41852),f317(f317(f228(a897),x41852),f317(a102,x41851)))
% 94.68/94.43 [4188]E(f175(a897,f317(a102,x41881),f317(f317(f8(a897,a897,a897),a102),f317(f317(f7(a897,a897,a897),f223(a897)),x41881)),x41882),f317(f317(f223(a897),x41882),f317(a102,x41881)))
% 94.68/94.43 [4191]E(f317(f300(x41911,f898(x41911),f317(f317(f7(x41911,f898(x41911),f898(x41911)),f141(x41911)),f103(x41911))),x41912),f164(x41911,x41912,f317(f317(f299(f898(x41911)),f103(x41911)),f178(f904(f898(x41911),a893)))))
% 94.68/94.43 [4193]E(f317(f317(f91(f904(f903(x41931,x41931),a893)),f317(f317(f279(x41931,x41931,x41931),x41932),f297(x41931,x41932))),f297(x41931,f178(f904(f903(x41931,x41931),a893)))),f297(x41931,x41932))
% 94.68/94.43 [4200]P1(f317(f317(f224(f904(f903(x42001,x42001),a893)),f253(x42001,x42002)),f317(f317(f244(x42001,x42001),x42002),f317(f16(f904(x42001,a893),x42001),x42002))))
% 94.68/94.43 [4203]E(f317(f300(a1,a897,a95),f317(f317(f91(f904(a1,a893)),f317(f300(a897,a1,f90(a1)),x42031)),f317(f300(a897,a1,f90(a1)),x42032))),f317(f317(f91(f904(a897,a893)),x42031),x42032))
% 94.68/94.43 [4204]E(f317(f300(a1,a897,a95),f317(f317(f92(f904(a1,a893)),f317(f300(a897,a1,f90(a1)),x42041)),f317(f300(a897,a1,f90(a1)),x42042))),f317(f317(f92(f904(a897,a893)),x42041),x42042))
% 94.68/94.43 [4207]E(f317(f252(x42071),f317(f317(f8(a893,a893,x42071),a312),f317(f317(f7(x42071,f904(x42071,a893),a893),f319(x42071)),x42072))),f317(f73(f904(x42071,a893)),x42072))
% 94.68/94.43 [4234]E(f317(f132(f898(x42341),f898(x42341),f124(x42341),f103(x42341)),f317(f317(f144(f898(x42341),f898(x42341)),f158(x42341)),f317(f158(f898(x42341)),x42342))),f317(f158(x42341),f317(f132(f898(x42341),f898(x42341),f124(x42341),f103(x42341)),x42342)))
% 94.68/94.43 [4260]E(f317(f317(f34(a897,f904(f903(x42601,x42601),a893)),f232(f904(a897,a893))),f317(f317(f7(a897,f904(f903(x42601,x42601),a893),f904(f903(x42601,x42601),a893)),f173(f903(x42601,x42601),a893)),x42602)),f297(x42601,x42602))
% 94.68/94.43 [4278]E(f79(x42781,f317(f317(f8(f904(x42781,a893),a893,x42781),f317(a314,x42782)),f317(f317(f7(x42781,f904(x42781,a893),f904(x42781,a893)),f299(x42781)),f178(f904(x42781,a893))))),f302(x42781,x42782))
% 94.68/94.43 [4286]E(f317(f179(f898(x42861)),f142(x42861,f317(f132(f898(x42861),f898(x42861),f124(x42861),f103(x42861)),x42862))),f317(f29(x42861),f317(f317(f34(f898(x42861),f904(x42861,a893)),f317(f162(f898(x42861)),x42862)),f162(x42861))))
% 94.68/94.43 [4300]E(f317(f317(f91(f904(f903(x43001,x43001),a893)),x43002),f317(f317(f279(x43001,x43001,x43001),f317(f317(f279(x43001,x43001,x43001),x43002),f297(x43001,x43002))),x43002)),f317(f317(f279(x43001,x43001,x43001),x43002),f297(x43001,x43002)))
% 94.68/94.43 [4324]P1(f317(f317(f224(f904(f903(x43241,x43241),a893)),f317(f317(f279(x43241,x43241,x43241),x43242),f297(x43241,x43242))),f317(f317(f244(x43241,x43241),f317(f271(x43241),x43242)),f317(f16(f904(x43241,a893),x43241),f317(f271(x43241),x43242)))))
% 94.68/94.43 [4365]E(f317(f252(f898(x43651)),f317(f317(f7(f898(x43651),f904(x43651,a893),a893),f317(f317(f8(f904(x43651,a893),f904(f904(x43651,a893),a893),f898(x43651)),f224(f904(x43651,a893))),f162(x43651))),x43652)),f151(x43651,x43652))
% 94.68/94.43 [4376]E(f317(f146(f898(x43761),x43761,f103(x43761),f317(f317(f8(f898(x43761),f904(f898(x43761),f898(x43761)),x43761),f317(f7(f898(x43761),f898(x43761),f898(x43761)),f124(x43761))),f317(f317(f7(x43761,f898(x43761),f898(x43761)),f141(x43761)),f103(x43761)))),x43762),f317(f157(x43761),x43762))
% 94.68/94.43 [4416]P24(f904(x44161,x44162),f904(f903(x44161,x44162),a893),f317(f317(f8(f904(f903(x44161,x44162),a893),f904(f903(x44161,x44162),a893),f904(x44161,x44162)),f252(f903(x44161,x44162))),f317(f317(f8(f904(x44161,f904(x44162,a893)),f904(f903(x44161,x44162),a893),f904(x44161,x44162)),f247(x44161,x44162,a893)),f317(f8(x44162,f904(x44162,a893),x44161),f317(f7(x44162,x44162,a893),a314)))),f232(f904(f904(x44161,x44162),a893)))
% 94.68/94.43 [4421]E(f40(a1,f317(f94(a1),f317(f317(f74(a1),x44211),x44211)),f317(f94(a1),f317(f317(f74(a1),x44212),x44212))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a1,f317(f94(a1),x44211),f317(f94(a1),x44212))))
% 94.68/94.43 [4465]E(f317(f317(f34(x44651,f904(f903(x44651,x44651),a893)),x44652),f317(f317(f7(x44651,f904(f903(x44651,x44651),a893),f904(f903(x44651,x44651),a893)),f317(f317(f8(f903(x44651,x44651),f904(f904(f903(x44651,x44651),a893),f904(f903(x44651,x44651),a893)),x44651),f299(f903(x44651,x44651))),f317(f317(f18(x44651,x44651,f903(x44651,x44651)),f242(x44651,x44651)),f5(x44651)))),f178(f904(f903(x44651,x44651),a893)))),f253(x44651,x44652))
% 94.68/94.43 [4473]E(f192(x44731,f317(f317(f242(a1,a1),f317(f73(a1),f317(f317(f67(f903(a1,a1),a1,x44731,f241(a1,a1)),f202(x44731)),x44732))),f317(f317(f67(f903(a1,a1),a1,x44731,f246(a1,a1)),f202(x44731)),x44732))),f217(x44731,x44732))
% 94.68/94.43 [4554]E(f317(f252(f904(x45541,a893)),f317(f317(f8(f904(f904(x45541,a893),a893),a893,f904(x45541,a893)),f81(f904(x45541,a893))),f317(f317(f7(f904(x45541,a893),f904(f904(x45541,a893),a893),f904(f904(x45541,a893),a893)),f317(f317(f8(f904(f904(x45541,a893),f904(a893,a893)),f904(f904(f904(x45541,a893),a893),f904(f904(x45541,a893),a893)),f904(x45541,a893)),f18(f904(x45541,a893),a893,a893)),f317(f317(f8(f904(f904(x45541,a893),a893),f904(f904(x45541,a893),f904(a893,a893)),f904(x45541,a893)),f317(f8(a893,f904(a893,a893),f904(x45541,a893)),a315)),f317(f317(f7(f904(x45541,a893),f904(f904(x45541,a893),f904(x45541,a893)),f904(f904(x45541,a893),a893)),f317(f317(f8(f904(f904(x45541,a893),a893),f904(f904(f904(x45541,a893),f904(x45541,a893)),f904(f904(x45541,a893),a893)),f904(x45541,a893)),f8(f904(x45541,a893),a893,f904(x45541,a893))),a314)),f73(f904(x45541,a893)))))),f317(f317(f8(f904(f904(x45541,a893),a893),a893,f904(x45541,a893)),f317(f319(f904(x45541,a893)),x45542)),f298(x45541))))),f317(f298(x45541),f317(f73(f904(x45541,a893)),x45542)))
% 94.68/94.43 [4623]~E(f317(f317(f74(a1),x46231),x46231),f317(f317(f23(a1),f317(f317(f74(a1),x46232),x46232)),a87))
% 94.68/94.43 [4627]~P1(f317(f317(f225(a897),f317(f317(f74(a897),x46271),x46272)),x46272))
% 94.68/94.43 [4628]~P1(f317(f317(f225(a897),f317(f317(f74(a897),x46281),x46282)),x46281))
% 94.68/94.43 [3904]E(f317(f317(f23(a897),x39041),f317(f317(f75(a897),f317(f317(f30(a897),x39041),x39042)),x39042)),f40(a897,x39041,x39042))
% 94.68/94.43 [3905]E(f317(f317(f23(a1),x39051),f317(f317(f75(a1),f317(f317(f30(a1),x39051),x39052)),x39052)),f40(a1,x39051,x39052))
% 94.68/94.43 [3937]E(f317(f317(f144(a897,x39371),f317(f154(x39371),x39372)),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(x39371)),x39372)))),x39372)
% 94.68/94.43 [3995]E(f317(f275(x39951,x39951,f297(x39951,f178(f904(f903(x39951,x39951),a893)))),x39952),x39952)
% 94.68/94.43 [4121]E(f297(x41211,f317(f317(f23(f904(f903(x41211,x41211),a893)),x41212),f297(x41211,f178(f904(f903(x41211,x41211),a893))))),f297(x41211,x41212))
% 94.68/94.43 [4122]E(f297(x41221,f317(f317(f91(f904(f903(x41221,x41221),a893)),x41222),f297(x41221,f178(f904(f903(x41221,x41221),a893))))),f297(x41221,x41222))
% 94.68/94.43 [4172]E(f317(f317(f23(a1),f317(f317(f23(a1),f317(f317(f74(a1),x41721),x41721)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x41722),x41722)),a87)),f317(f317(f74(a1),f317(f317(f23(a1),x41721),x41722)),f317(f317(f23(a1),x41721),x41722)))
% 94.68/94.43 [4212]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f74(a1),x42121),x42122)),f317(f317(f74(a1),x42121),x42122))),a87),f317(f317(f74(a1),f317(f317(f74(a1),x42121),x42121)),f317(f317(f23(a1),f317(f317(f74(a1),x42122),x42122)),a87)))
% 94.68/94.43 [4237]E(f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),x42371),x42371)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x42372),x42372)),a87)),f317(f317(f74(a1),f317(f317(f74(a1),x42371),f317(f317(f23(a1),x42372),a87))),f317(f317(f74(a1),x42371),f317(f317(f23(a1),x42372),a87))))
% 94.68/94.43 [4248]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),x42481),x42482)),f317(f317(f23(a1),x42481),x42482))),a87),f317(f317(f23(a1),f317(f317(f23(a1),f317(f317(f74(a1),x42481),x42481)),a87)),f317(f317(f74(a1),x42482),x42482)))
% 94.68/94.43 [4249]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f74(a1),x42491),x42492)),f317(f317(f74(a1),x42491),x42492))),a87),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),x42491),x42491)),a87)),f317(f317(f74(a1),x42492),x42492)))
% 94.68/94.43 [4297]E(f317(f90(a1),f317(f317(f30(a897),f317(f317(f75(a897),f317(a95,f317(f70(a1),x42971))),f317(a95,f317(f70(a1),x42972)))),f206(f317(a95,f317(f70(a1),x42971)),f317(a95,f317(f70(a1),x42972))))),f208(x42971,x42972))
% 94.68/94.43 [4342]E(f317(f317(f249(f903(a89,a89),a89,f903(a89,a89),f903(x43421,f903(a89,a89))),f257(f317(a3,f317(f179(f898(x43421)),x43422)))),f317(f317(f8(x43421,f904(f903(a89,a89),f903(x43421,f903(a89,a89))),a89),f242(x43421,f903(a89,a89))),f317(f317(f8(a897,x43421,a89),f317(f154(x43421),x43422)),a20))),f265(x43421,x43422))
% 94.68/94.43 [4422]E(f317(f132(a897,f898(x44221),f317(f7(f898(x44221),a897,a897),f317(f317(f8(a897,f904(a897,a897),f898(x44221)),f223(a897)),f179(f898(x44221)))),f2(a897)),f317(f158(f898(x44221)),f169(x44221,x44222))),f317(f179(f898(f898(x44221))),f317(f126(f898(x44221),f317(f317(f8(a893,a893,f898(x44221)),a312),f317(f317(f7(f898(x44221),f898(x44221),a893),a314),f103(x44221)))),x44222)))
% 94.68/94.43 [4428]E(f317(f317(f34(a897,f904(x44281,a893)),f232(f904(a897,a893))),f317(f317(f7(a897,f904(a897,f904(x44281,a893)),f904(x44281,a893)),f317(f317(f8(f904(a897,a893),f904(f904(a897,f904(x44281,a893)),f904(x44281,a893)),a897),f34(a897,f904(x44281,a893))),f292(a897,f2(a897)))),x44282)),f317(f317(f34(a897,f904(x44281,a893)),f232(f904(a897,a893))),x44282))
% 94.68/94.43 [4450]P1(f317(f28(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),x44501)),f317(f317(f7(a897,a897,a893),f225(a897)),x44502)))))
% 94.68/94.43 [4562]E(f317(f252(f903(f898(x45621),f898(x45621))),f317(f247(f898(x45621),f898(x45621),a893),f317(f317(f18(f898(x45621),f904(f898(x45621),a893),f904(f898(x45621),a893)),f317(f317(f8(f904(f898(x45621),f904(a893,a893)),f904(f904(f898(x45621),a893),f904(f898(x45621),a893)),f898(x45621)),f18(f898(x45621),a893,a893)),f317(f317(f8(f904(f898(x45621),a893),f904(f898(x45621),f904(a893,a893)),f898(x45621)),f317(f8(a893,f904(a893,a893),f898(x45621)),a316)),f317(f317(f7(f898(x45621),f904(f898(x45621),a897),f904(f898(x45621),a893)),f317(f317(f8(f904(a897,a893),f904(f904(f898(x45621),a897),f904(f898(x45621),a893)),f898(x45621)),f8(a897,a893,f898(x45621))),f317(f317(f8(a897,f904(a897,a893),f898(x45621)),f225(a897)),f179(f898(x45621))))),f179(f898(x45621)))))),f317(f317(f18(f898(x45621),f904(f898(x45621),a893),f904(f898(x45621),a893)),f317(f317(f8(f904(f898(x45621),f904(a893,a893)),f904(f904(f898(x45621),a893),f904(f898(x45621),a893)),f898(x45621)),f18(f898(x45621),a893,a893)),f317(f317(f8(f904(f898(x45621),a893),f904(f898(x45621),f904(a893,a893)),f898(x45621)),f317(f8(a893,f904(a893,a893),f898(x45621)),a315)),f317(f317(f7(f898(x45621),f904(f898(x45621),a897),f904(f898(x45621),a893)),f317(f317(f8(f904(a897,a893),f904(f904(f898(x45621),a897),f904(f898(x45621),a893)),f898(x45621)),f8(a897,a893,f898(x45621))),f317(f317(f8(a897,f904(a897,a893),f898(x45621)),a314),f179(f898(x45621))))),f179(f898(x45621)))))),f317(f317(f7(f898(x45621),f904(f903(f898(x45621),f898(x45621)),a893),f904(f898(x45621),a893)),f317(f317(f8(f904(f898(x45621),f904(f904(f903(f898(x45621),f898(x45621)),a893),a893)),f904(f904(f903(f898(x45621),f898(x45621)),a893),f904(f898(x45621),a893)),f898(x45621)),f7(f898(x45621),f904(f903(f898(x45621),f898(x45621)),a893),a893)),f317(f317(f8(f904(f898(x45621),f903(f898(x45621),f898(x45621))),f904(f898(x45621),f904(f904(f903(f898(x45621),f898(x45621)),a893),a893)),f898(x45621)),f317(f8(f903(f898(x45621),f898(x45621)),f904(f904(f903(f898(x45621),f898(x45621)),a893),a893),f898(x45621)),f319(f903(f898(x45621),f898(x45621))))),f242(f898(x45621),f898(x45621))))),f135(x45621,x45622)))))),f136(x45621,x45622))
% 94.68/94.43 [4240]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),x42401),x42402)),f317(f317(f75(a1),x42401),x42402))),x42402),f317(f317(f75(a1),f317(f317(f23(a1),f317(f317(f74(a1),x42401),x42401)),a87)),x42402))
% 94.68/94.43 [4341]E(f317(a95,f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x43411),x43412)),f178(f904(f903(a897,a897),a893)))))),f317(f317(f23(a897),x43411),x43412))
% 94.68/94.43 [4345]E(f317(f317(f279(x43451,x43451,x43451),f317(f317(f91(f904(f903(x43451,x43451),a893)),x43452),f297(x43451,f178(f904(f903(x43451,x43451),a893))))),f297(x43451,f317(f317(f91(f904(f903(x43451,x43451),a893)),x43452),f297(x43451,f178(f904(f903(x43451,x43451),a893)))))),f297(x43451,x43452))
% 94.68/94.43 [4382]E(f258(x43821,f317(f126(f903(a89,x43821),f317(f247(a89,x43821,a893),f317(f317(f8(a893,f904(x43821,a893),a89),f16(a893,x43821)),f317(f225(a89),f2(a89))))),x43822)),f258(x43821,x43822))
% 94.68/94.43 [4383]E(f256(x43831,f317(f126(f903(a89,x43831),f317(f247(a89,x43831,a893),f317(f317(f8(a893,f904(x43831,a893),a89),f16(a893,x43831)),f317(f225(a89),f2(a89))))),x43832)),f256(x43831,x43832))
% 94.68/94.43 [4385]E(f317(f73(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x43851),x43852)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x43852),x43851)),f178(f904(f903(a897,a897),a893))))))
% 94.68/94.43 [4441]E(f317(f317(f278(f898(a897),x44411),f135(a897,a230)),f317(f317(f7(x44411,f898(f904(x44411,a897)),f898(a897)),f317(f317(f8(f904(f904(x44411,a897),a897),f904(f898(f904(x44411,a897)),f898(a897)),x44411),f144(f904(x44411,a897),a897)),f317(f7(f904(x44411,a897),x44411,a897),f5(f904(x44411,a897))))),x44412)),f143(x44411,x44412))
% 94.68/94.43 [4462]E(f317(f317(f80(a1,a897),f317(f94(a1),f317(f317(f74(a1),x44621),a87))),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f2(a897))),f317(f317(f8(a897,a897,a1),a102),f317(f317(f8(a897,a897,a1),f317(f228(a897),x44622)),a95)))),f317(f317(f228(a897),f317(a102,x44622)),f317(f94(a897),x44621)))
% 94.68/94.43 [4463]E(f317(f317(f80(a1,a897),f317(f94(a1),f317(f317(f74(a1),x44631),a87))),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f317(a102,x44632))),f317(f317(f8(a897,a897,a1),a102),f317(f317(f8(a897,a897,a1),f317(f223(a897),x44632)),a95)))),f317(f317(f223(a897),f317(a102,x44632)),f317(f94(a897),x44631)))
% 94.68/94.43 [4483]E(f317(f132(f898(x44831),f898(x44831),f124(x44831),f103(x44831)),f317(f317(f144(f898(x44831),f898(x44831)),f146(f898(x44831),x44831,f103(x44831),f317(f317(f8(f898(x44831),f904(f898(x44831),f898(x44831)),x44831),f16(f898(x44831),f898(x44831))),f317(f317(f7(x44831,f898(x44831),f898(x44831)),f141(x44831)),f103(x44831))))),x44832)),f317(f317(f144(f898(x44831),x44831),f131(x44831)),f317(f126(f898(x44831),f317(f317(f8(a893,a893,f898(x44831)),a312),f317(f317(f7(f898(x44831),f898(x44831),a893),a314),f103(x44831)))),x44832)))
% 94.68/94.43 [4545]E(f317(f247(a1,a1,a893),f317(f317(f7(a1,f904(a1,a893),f904(a1,a893)),f317(f317(f8(f904(a1,f904(a893,a893)),f904(f904(a1,a893),f904(a1,a893)),a1),f18(a1,a893,a893)),f317(f317(f8(f904(a1,a893),f904(a1,f904(a893,a893)),a1),f317(f8(a893,f904(a893,a893),a1),a315)),f317(f317(f8(f904(a1,a1),f904(a1,a893),a1),f317(f8(a1,a893,a1),f317(a314,x45451))),f317(f317(f8(a1,f904(a1,a1),a1),f74(a1)),f317(f75(a1),x45452)))))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),f317(a320,f317(f317(f225(a1),f2(a1)),x45452))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),f317(f317(f7(a1,a1,a893),f225(a1)),x45452))))),f317(f317(f8(a893,a893,a1),f317(a320,f317(a312,f317(f317(f225(a1),f2(a1)),x45452)))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f225(a1),x45452))),f317(f317(f7(a1,a1,a893),f224(a1)),f2(a1))))))),f44(x45451,x45452))
% 94.68/94.43 [4548]E(f317(f252(x45481),f317(f317(f8(f904(a897,a893),a893,x45481),f81(a897)),f317(f317(f7(x45481,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),x45481),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),x45481),f317(f8(a893,f904(a893,a893),a897),a315)),f317(f317(f7(x45481,f904(a897,x45481),f904(a897,a893)),f317(f317(f8(f904(x45481,a893),f904(f904(a897,x45481),f904(a897,a893)),x45481),f8(x45481,a893,a897)),a314)),f317(f154(x45481),x45482))))),f317(f317(f7(a897,a897,a893),f225(a897)),f317(f179(f898(x45481)),x45482))))),f317(f162(x45481),x45482))
% 94.68/94.43 [4355]E(f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),x43551),a87)),x43552)),f317(f317(f23(a1),f317(f317(f74(a1),x43551),a87)),x43552))),a87),f317(f317(f23(a1),f317(f317(f74(a1),x43551),x43551)),f317(f317(f23(a1),f317(f317(f74(a1),x43552),x43552)),a87)))
% 94.68/94.43 [4478]E(f317(f132(f898(f898(x44781)),f898(f898(x44781)),f124(f898(x44781)),f103(f898(x44781))),f317(f317(f144(f898(x44781),f898(f898(x44781))),f146(f898(f898(x44781)),x44781,f103(f898(x44781)),f317(f16(f904(f898(x44781),f898(f898(x44781))),x44781),f317(f317(f7(f898(x44781),f898(f898(x44781)),f898(f898(x44781))),f141(f898(x44781))),f103(f898(x44781)))))),x44782)),f317(f317(f144(f898(x44781),f898(x44781)),f161(x44781)),f317(f126(f898(x44781),f317(f317(f8(a893,a893,f898(x44781)),a312),f317(f317(f7(f898(x44781),f898(x44781),a893),a314),f103(x44781)))),x44782)))
% 94.68/94.43 [4488]E(f317(f317(f80(a1,a897),f317(f94(a1),f317(f317(f74(a1),x44881),a87))),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f2(a897))),f317(f317(f8(a897,a897,a1),a102),f317(f317(f7(a1,a897,a897),f317(f317(f8(a897,f904(a897,a897),a1),f228(a897)),a95)),x44882)))),f317(f317(f228(a897),f317(f94(a897),x44881)),f317(a102,x44882)))
% 94.68/94.43 [4489]E(f317(f317(f80(a1,a897),f317(f94(a1),f317(f317(f74(a1),x44891),a87))),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f317(a102,x44892))),f317(f317(f8(a897,a897,a1),a102),f317(f317(f7(a1,a897,a897),f317(f317(f8(a897,f904(a897,a897),a1),f223(a897)),a95)),x44892)))),f317(f317(f223(a897),f317(f94(a897),x44891)),f317(a102,x44892)))
% 94.68/94.43 [4477]E(f317(f247(x44771,x44771,a893),f317(f317(f18(x44771,a893,f904(x44771,a893)),f317(f317(f8(f904(x44771,f904(a893,a893)),f904(a893,f904(x44771,a893)),x44771),f7(x44771,a893,a893)),f317(f317(f8(f904(x44771,a893),f904(x44771,f904(a893,a893)),x44771),f317(f8(a893,f904(a893,a893),x44771),a315)),a314))),x44772)),f253(x44771,x44772))
% 94.68/94.43 [4522]E(f317(f317(f30(a897),x45221),f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45222)),f317(f317(f30(a897),x45221),f317(a102,f317(a102,f317(a102,x45222)))))
% 94.68/94.43 [4523]E(f40(a897,x45231,f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45232)),f40(a897,x45231,f317(a102,f317(a102,f317(a102,x45232)))))
% 94.68/94.43 [4524]E(f40(a897,f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45241),x45242),f40(a897,f317(a102,f317(a102,f317(a102,x45241))),x45242))
% 94.68/94.43 [4536]E(f113(f317(x45361,f317(f317(f75(a89),f317(f94(a89),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45362))),f317(f190(x45361),x45362))
% 94.68/94.43 [4537]E(f317(f317(f30(a897),f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),x45371)),x45372),f317(f317(f30(a897),f317(a102,f317(a102,f317(a102,x45371)))),x45372))
% 94.68/94.43 [4589]~E(f116(x45891,x45892,x45893),f109(x45891))
% 94.68/94.43 [3343]E(f317(f182(x33431,x33432),x33433),f111(x33431,x33432))
% 94.68/94.43 [3362]E(f317(f189(x33621,x33622),x33623),f317(f119(x33621),x33622))
% 94.68/94.43 [3439]E(f317(f317(f144(x34391,x34392),x34393),f103(x34391)),f103(x34392))
% 94.68/94.43 [3478]E(f317(f174(x34781,x34782,x34783),f2(a897)),x34782)
% 94.68/94.43 [3480]E(f317(f317(f171(x34801,x34802),x34803),f103(x34802)),f103(f903(x34801,x34802)))
% 94.68/94.43 [3493]E(f317(f179(f898(x34931)),f159(x34931,x34932,x34933)),x34932)
% 94.68/94.43 [3512]E(f79(x35121,f56(x35121,x35122,x35123)),f317(f57(x35121,x35122),x35123))
% 94.68/94.43 [3516]E(f233(x35161,x35162,f233(x35162,x35161,x35163)),x35163)
% 94.68/94.43 [3536]E(f317(f158(x35361),f159(x35361,x35362,x35363)),f159(x35361,x35362,x35363))
% 94.68/94.43 [3561]E(f130(x35611,x35612,f142(x35611,x35613)),f142(x35611,f130(x35611,x35612,x35613)))
% 94.68/94.43 [3580]E(f317(f241(f898(x35801),f898(x35801)),f156(x35801,x35802,x35803)),f317(f126(x35801,x35802),x35803))
% 94.68/94.43 [3623]E(f317(f317(f141(x36231),x36232),f159(x36231,x36233,x36232)),f159(x36231,f317(a102,x36233),x36232))
% 94.68/94.43 [3655]E(f175(x36551,x36552,x36553,f2(a897)),x36552)
% 94.68/94.43 [3656]E(f17(x36561,x36562,x36563,f2(a89)),x36562)
% 94.68/94.43 [3657]E(f19(x36571,x36572,x36573,f2(a89)),x36572)
% 94.68/94.43 [3664]E(f153(x36641,x36642,x36643,f103(x36641)),f103(x36642))
% 94.68/94.43 [3665]E(f120(x36651,x36652,x36653,f109(x36651)),f109(x36652))
% 94.68/94.43 [3671]E(f317(f317(f154(x36711),f317(f317(f141(x36711),x36712),x36713)),f2(a897)),x36712)
% 94.68/94.43 [3699]E(f54(x36991,x36992,f103(x36991),x36993),f103(f903(x36991,x36992)))
% 94.68/94.43 [3719]P24(x37191,x37192,x37193,f178(f904(x37191,a893)))
% 94.68/94.43 [3821]E(f255(x38211,x38212,x38213),f317(f242(f904(a89,f904(a893,f900(f899(x38211)))),f903(a89,a89)),f36(x38211)))
% 94.68/94.43 [3878]E(f317(f67(x38781,x38782,x38781,x38783),f25(x38781)),x38783)
% 94.68/94.43 [4055]P1(f317(f317(f319(f903(x40551,x40551)),f317(f317(f242(x40551,x40551),x40552),x40552)),f297(x40551,x40553)))
% 94.68/94.43 [4633]~P1(f317(f317(f319(f903(f898(x46331),f898(x46331))),f317(f317(f242(f898(x46331),f898(x46331)),x46332),f103(x46331))),f135(x46331,x46333)))
% 94.68/94.43 [4634]~P1(f317(f317(f319(f903(f898(x46341),f898(x46341))),f317(f317(f242(f898(x46341),f898(x46341)),x46342),f103(x46341))),f137(x46341,x46343)))
% 94.68/94.43 [4635]~P1(f317(f317(f319(f903(f898(x46351),f898(x46351))),f317(f317(f242(f898(x46351),f898(x46351)),x46352),f103(x46351))),f147(x46351,x46353)))
% 94.68/94.43 [4636]~P1(f317(f317(f319(f903(f898(x46361),f898(x46361))),f317(f317(f242(f898(x46361),f898(x46361)),f103(x46361)),x46362)),f135(x46361,x46363)))
% 94.68/94.43 [4637]~P1(f317(f317(f319(f903(f898(x46371),f898(x46371))),f317(f317(f242(f898(x46371),f898(x46371)),f103(x46371)),x46372)),f147(x46371,x46373)))
% 94.68/94.43 [3414]E(f317(f317(f191(x34141),x34142),x34143),f192(x34141,f205(x34142,x34143)))
% 94.68/94.43 [3467]E(f317(f276(x34671,x34672),f317(f276(x34672,x34671),x34673)),x34673)
% 94.68/94.43 [3488]E(f317(f317(f171(x34881,x34882),f103(x34881)),x34883),f103(f903(x34881,x34882)))
% 94.68/94.43 [3491]E(f166(x34911,x34912,f317(f272(a897),x34913)),f317(f317(f165(x34911),x34913),x34912))
% 94.68/94.43 [3509]E(f142(x35091,f317(f126(x35091,x35092),x35093)),f317(f126(x35091,x35092),f142(x35091,x35093)))
% 94.68/94.43 [3510]E(f317(f274(x35101,x35102),f317(f276(x35102,x35101),x35103)),f317(f254(x35102,x35101),x35103))
% 94.68/94.43 [3511]E(f317(f254(x35111,x35112),f317(f276(x35112,x35111),x35113)),f317(f274(x35112,x35111),x35113))
% 94.68/94.43 [3529]E(f317(f126(x35291,x35292),f317(f158(x35291),x35293)),f317(f158(x35291),f317(f126(x35291,x35292),x35293)))
% 94.68/94.43 [3541]E(f317(f317(f128(x35411),x35412),f317(f161(x35411),x35413)),f317(f317(f128(x35411),f317(a102,x35412)),x35413))
% 94.68/94.43 [3557]E(f317(f300(x35571,x35572,x35573),f178(f904(x35571,a893))),f178(f904(x35572,a893)))
% 94.68/94.43 [3558]E(f317(f275(x35581,x35582,x35583),f178(f904(x35581,a893))),f178(f904(x35582,a893)))
% 94.68/94.43 [3559]E(f317(f301(x35591,x35592,x35593),f178(f904(x35592,a893))),f178(f904(x35591,a893)))
% 94.68/94.43 [3560]E(f317(f301(x35601,x35602,x35603),f232(f904(x35602,a893))),f232(f904(x35601,a893)))
% 94.68/94.43 [3586]E(f110(x35861,f116(f899(x35861),x35862,x35863)),f106(x35861,x35862,f110(x35861,x35863)))
% 94.68/94.43 [3588]E(f317(f317(f299(x35881),x35882),f317(f162(x35881),x35883)),f317(f162(x35881),f130(x35881,x35882,x35883)))
% 94.68/94.43 [3675]E(f317(f300(f903(x36751,x36752),x36752,f246(x36751,x36752)),x36753),f317(f274(x36751,x36752),x36753))
% 94.68/94.43 [3676]E(f317(f300(f903(x36761,x36762),x36761,f241(x36761,x36762)),x36763),f317(f254(x36761,x36762),x36763))
% 94.68/94.43 [3691]E(f317(f162(x36911),f159(x36911,f317(a102,x36912),x36913)),f317(f317(f299(x36911),x36913),f178(f904(x36911,a893))))
% 94.68/94.43 [3748]E(f317(f317(f242(x37481,x37482),f317(f241(x37481,x37482),x37483)),f317(f246(x37481,x37482),x37483)),x37483)
% 94.68/94.43 [3755]E(f317(f179(f899(x37551)),f116(x37551,x37552,x37553)),f317(f317(f74(a897),f317(f179(f899(x37551)),x37553)),f317(a102,f2(a897))))
% 94.68/94.43 [3757]E(f317(f317(f247(x37571,x37572,x37571),f16(x37571,x37572)),x37573),f317(f241(x37571,x37572),x37573))
% 94.68/94.43 [3883]E(f317(f67(x38831,x38831,x38832,f25(x38831)),x38833),x38833)
% 94.68/94.43 [3890]E(f317(f317(f124(x38901),f159(x38901,x38902,x38903)),f317(f317(f141(x38901),x38903),f103(x38901))),f317(f317(f141(x38901),x38903),f159(x38901,x38902,x38903)))
% 94.68/94.43 [4065]P1(f317(f317(f224(f904(x40651,a893)),f317(f162(x40651),f317(f126(x40651,x40652),x40653))),f317(f162(x40651),x40653)))
% 94.68/94.43 [4107]P1(f317(f317(f224(f904(x41071,a893)),f317(f162(x41071),f317(f317(f165(x41071),x41072),x41073))),f317(f162(x41071),x41073)))
% 94.68/94.43 [4108]P1(f317(f317(f224(f904(x41081,a893)),f317(f162(x41081),f317(f317(f128(x41081),x41082),x41083))),f317(f162(x41081),x41083)))
% 94.68/94.43 [4112]P1(f317(f317(f224(f904(x41121,a893)),f317(f162(x41121),f166(x41121,x41122,x41123))),f317(f162(x41121),x41122)))
% 94.68/94.43 [4113]P1(f317(f317(f224(f904(x41131,a893)),f317(f162(x41131),f160(x41131,x41132,x41133))),f317(f162(x41131),x41133)))
% 94.68/94.43 [4134]P24(f903(x41341,x41342),f903(x41342,x41341),f317(f247(x41341,x41342,f903(x41342,x41341)),f317(f7(x41342,x41341,f903(x41342,x41341)),f242(x41342,x41341))),x41343)
% 94.68/94.43 [4145]E(f317(f317(f317(f173(f898(x41451),f898(x41451)),f40(a897,x41452,f317(f179(f898(x41451)),x41453))),f157(x41451)),x41453),f317(f317(f317(f173(f898(x41451),f898(x41451)),x41452),f157(x41451)),x41453))
% 94.68/94.43 [4189]P1(f317(f317(f319(f903(f898(x41891),f898(x41891))),f317(f317(f242(f898(x41891),f898(x41891)),x41892),x41892)),f148(x41891,f297(x41891,x41893))))
% 94.68/94.43 [4328]E(f79(f903(x43281,x43282),f317(f317(f18(f903(x43281,x43282),x43282,a893),f317(f317(f8(x43281,f904(x43282,a893),f903(x43281,x43282)),x43283),f241(x43281,x43282))),f246(x43281,x43282))),f79(f903(x43281,x43282),f317(f247(x43281,x43282,a893),x43283)))
% 94.68/94.43 [4329]E(f84(f903(x43291,x43292),f317(f317(f18(f903(x43291,x43292),x43292,a893),f317(f317(f8(x43291,f904(x43292,a893),f903(x43291,x43292)),x43293),f241(x43291,x43292))),f246(x43291,x43292))),f84(f903(x43291,x43292),f317(f247(x43291,x43292,a893),x43293)))
% 94.68/94.43 [4362]E(f317(f317(f278(f903(a897,x43621),x43621),f309(a897,x43621,a230,x43622)),f317(f317(f18(x43621,x43621,f903(a897,x43621)),f317(f317(f8(a897,f904(x43621,f903(a897,x43621)),x43621),f242(a897,x43621)),x43623)),f5(x43621))),f311(x43621,x43623,x43622))
% 94.68/94.43 [4424]E(f317(f248(x44241,x44241,x44242,x44242,f5(x44241),f5(x44242)),x44243),x44243)
% 94.68/94.43 [4497]E(f317(f132(f898(f898(x44971)),f898(f898(x44971)),f124(f898(x44971)),f103(f898(x44971))),f317(f317(f144(f898(x44971),f898(f898(x44971))),f317(f317(f7(f898(x44971),f898(x44971),f898(f898(x44971))),f317(f317(f8(f904(x44971,f898(x44971)),f904(f898(x44971),f898(f898(x44971))),f898(x44971)),f144(x44971,f898(x44971))),f317(f7(x44971,f898(x44971),f898(x44971)),f141(x44971)))),x44972)),f50(x44971,x44973,x44972))),f50(x44971,f317(a102,x44973),x44972))
% 94.68/94.43 [4553]E(f213(a897,f903(x45531,f899(x45531)),f2(a897),f317(f247(x45531,f899(x45531),a897),f317(f317(f7(x45531,a897,f904(f899(x45531),a897)),f317(f317(f8(f904(f899(x45531),f904(a897,a897)),f904(a897,f904(f899(x45531),a897)),x45531),f7(f899(x45531),a897,a897)),f317(f317(f8(f904(f899(x45531),a897),f904(f899(x45531),f904(a897,a897)),x45531),f317(f8(a897,f904(a897,a897),f899(x45531)),f74(a897))),f317(f317(f7(x45531,f904(f899(x45531),a897),f904(f899(x45531),a897)),f317(f317(f8(f904(a897,a897),f904(f904(f899(x45531),a897),f904(f899(x45531),a897)),x45531),f8(a897,a897,f899(x45531))),f317(f317(f8(a897,f904(a897,a897),x45531),f74(a897)),x45532))),f115(x45531,x45532))))),f72(a897))),f317(f125(x45531),x45533)),f317(f115(x45531,x45532),x45533))
% 94.68/94.43 [4561]E(f317(f317(f80(a1,x45611),f208(f317(f317(f67(f903(a1,a1),a1,x45611,f246(a1,a1)),f202(x45611)),x45612),f317(f317(f67(f903(a1,a1),a1,x45611,f246(a1,a1)),f202(x45611)),x45613))),f317(f317(f18(a1,a1,x45611),f317(f317(f8(a1,f904(a1,x45611),a1),f191(x45611)),f317(f317(f18(a1,a1,a1),f317(f317(f8(a1,f904(a1,a1),a1),f74(a1)),f317(f317(f8(a1,a1,a1),f317(f75(a1),f317(f317(f67(f903(a1,a1),a1,x45611,f241(a1,a1)),f202(x45611)),x45612))),f317(f317(f7(a1,a1,a1),f30(a1)),f317(f317(f67(f903(a1,a1),a1,x45611,f246(a1,a1)),f202(x45611)),x45612))))),f317(f317(f8(a1,a1,a1),f317(f75(a1),f317(f317(f67(f903(a1,a1),a1,x45611,f241(a1,a1)),f202(x45611)),x45613))),f317(f317(f7(a1,a1,a1),f30(a1)),f317(f317(f67(f903(a1,a1),a1,x45611,f246(a1,a1)),f202(x45611)),x45613)))))),f5(a1))),f220(x45611,x45612,x45613))
% 94.68/94.43 [4584]~E(f317(f317(f141(x45841),x45842),x45843),x45843)
% 94.68/94.43 [4587]~E(f317(f317(f141(x45871),x45872),x45873),f103(x45871))
% 94.68/94.43 [4593]~E(f317(f317(f299(x45931),x45932),x45933),f178(f904(x45931,a893)))
% 94.68/94.43 [4614]~E(f317(f300(x46141,f904(x46141,a893),x46142),x46143),f317(f298(x46141),x46143))
% 94.68/94.43 [3472]E(f317(f317(f149(x34721,f103(x34721)),x34722),x34723),f103(x34721))
% 94.68/94.43 [3473]E(f317(f131(x34731),f317(f317(f141(x34731),x34732),x34733)),x34732)
% 94.68/94.43 [3474]E(f317(f161(x34741),f317(f317(f141(x34741),x34742),x34743)),x34743)
% 94.68/94.43 [3515]E(f317(f317(f128(x35151),f72(a897)),f317(f317(f141(x35151),x35152),x35153)),x35153)
% 94.68/94.43 [3548]E(f104(x35481,f317(f317(f128(x35481),x35482),x35483)),f317(f317(f128(x35481),x35482),f104(x35481,x35483)))
% 94.68/94.43 [3550]E(f317(f317(f149(x35501,x35502),x35503),f317(f317(f154(x35501),x35502),x35503)),x35502)
% 94.68/94.43 [3570]E(f317(f317(f299(x35701),x35702),f317(f317(f299(x35701),x35702),x35703)),f317(f317(f299(x35701),x35702),x35703))
% 94.68/94.43 [3583]E(f317(f317(f299(x35831),x35832),f317(f162(x35831),x35833)),f317(f162(x35831),f317(f317(f141(x35831),x35832),x35833)))
% 94.68/94.43 [3585]E(f317(f317(f128(x35851),x35852),f317(f161(x35851),x35853)),f317(f161(x35851),f317(f317(f128(x35851),x35852),x35853)))
% 94.68/94.43 [3597]E(f317(f317(f165(x35971),f72(a897)),f317(f317(f141(x35971),x35972),x35973)),f317(f317(f141(x35971),x35972),f103(x35971)))
% 94.68/94.43 [3640]E(f317(f57(x36401,x36402),f317(f317(f299(x36401),x36403),f178(f904(x36401,a893)))),x36403)
% 94.68/94.43 [3681]E(f317(f317(f74(a897),x36811),f317(f317(f74(a897),x36812),x36813)),f317(f317(f74(a897),x36812),f317(f317(f74(a897),x36811),x36813)))
% 94.68/94.43 [3682]E(f317(f317(f74(a1),x36821),f317(f317(f74(a1),x36822),x36823)),f317(f317(f74(a1),x36822),f317(f317(f74(a1),x36821),x36823)))
% 94.68/94.43 [3687]E(f317(f317(f244(x36871,x36872),f178(f904(x36871,a893))),x36873),f178(f904(f903(x36871,x36872),a893)))
% 94.68/94.43 [3711]E(f317(f317(f91(f904(x37111,a893)),x37112),x37113),f317(f317(f91(f904(x37111,a893)),x37113),x37112))
% 94.68/94.43 [3712]E(f317(f317(f92(f904(x37121,a893)),x37122),x37123),f317(f317(f92(f904(x37121,a893)),x37123),x37122))
% 94.68/94.43 [3714]E(f317(f317(f124(x37141),x37142),f317(f317(f141(x37141),x37143),f103(x37141))),f317(f157(x37141),f317(f317(f141(x37141),x37143),x37142)))
% 94.68/94.43 [3715]E(f317(f317(f124(x37151),f317(f158(x37151),x37152)),f317(f158(x37151),x37153)),f317(f158(x37151),f317(f317(f124(x37151),x37153),x37152)))
% 94.68/94.43 [3725]E(f317(f161(x37251),f317(f317(f165(x37251),f317(a102,x37252)),x37253)),f317(f317(f165(x37251),x37252),f317(f161(x37251),x37253)))
% 94.68/94.43 [3733]P1(f317(f317(f319(x37331),x37332),f317(f317(f299(x37331),x37332),x37333)))
% 94.68/94.43 [3737]E(f317(f317(f35(x37371,f904(x37372,a893)),f178(f904(x37371,a893))),x37373),f232(f904(x37372,a893)))
% 94.68/94.43 [3740]E(f317(f275(x37401,x37401,f253(x37401,x37402)),x37403),f317(f317(f92(f904(x37401,a893)),x37402),x37403))
% 94.68/94.43 [3754]E(f317(f179(f898(x37541)),f317(f317(f141(x37541),x37542),x37543)),f317(f317(f74(a897),f317(f179(f898(x37541)),x37543)),f317(a102,f2(a897))))
% 94.68/94.43 [3759]E(f104(x37591,f317(f317(f124(x37591),x37592),f317(f317(f141(x37591),x37593),f103(x37591)))),x37592)
% 94.68/94.43 [3760]E(f134(x37601,f317(f317(f124(x37601),x37602),f317(f317(f141(x37601),x37603),f103(x37601)))),x37603)
% 94.68/94.43 [3768]E(f317(f317(f124(x37681),f317(f317(f165(x37681),x37682),x37683)),f317(f317(f128(x37681),x37682),x37683)),x37683)
% 94.68/94.43 [3777]E(f317(f317(f23(a897),f317(f317(f74(a897),x37771),x37772)),f317(f317(f74(a897),x37773),x37772)),f317(f317(f23(a897),x37771),x37773))
% 94.68/94.43 [3778]E(f317(f317(f23(a897),f317(f317(f74(a897),x37781),x37782)),f317(f317(f74(a897),x37781),x37783)),f317(f317(f23(a897),x37782),x37783))
% 94.68/94.43 [3784]E(f317(f317(f124(x37841),f317(f158(x37841),x37842)),f317(f317(f141(x37841),x37843),f103(x37841))),f317(f158(x37841),f317(f317(f141(x37841),x37843),x37842)))
% 94.68/94.43 [3786]E(f317(f317(f74(a897),f317(f179(f898(x37861)),x37862)),f317(f179(f898(x37861)),x37863)),f317(f179(f898(x37861)),f317(f317(f124(x37861),x37862),x37863)))
% 94.68/94.43 [3789]E(f317(f317(f74(a897),f317(f179(f898(x37891)),x37892)),f317(f179(f898(x37891)),x37893)),f317(f179(f898(x37891)),f163(x37891,x37892,x37893)))
% 94.68/94.43 [3796]E(f317(f317(f91(f904(x37961,a893)),f317(f162(x37961),x37962)),f317(f162(x37961),x37963)),f317(f162(x37961),f317(f317(f124(x37961),x37962),x37963)))
% 94.68/94.43 [3797]E(f40(a897,f317(f317(f75(a897),x37971),x37972),f317(f317(f75(a897),x37971),x37973)),f317(f317(f75(a897),x37971),f40(a897,x37972,x37973)))
% 94.68/94.43 [3809]E(f317(f317(f165(x38091),f317(f317(f23(a897),x38092),f72(a897))),f317(f161(x38091),x38093)),f317(f161(x38091),f317(f317(f165(x38091),x38092),x38093)))
% 94.68/94.43 [3814]E(f317(f317(f92(f904(x38141,a893)),x38142),f317(f73(f904(x38141,a893)),x38143)),f317(f317(f23(f904(x38141,a893)),x38142),x38143))
% 94.68/94.43 [3815]E(f317(f317(f23(f904(x38151,a893)),x38152),f317(f73(f904(x38151,a893)),x38153)),f317(f317(f92(f904(x38151,a893)),x38152),x38153))
% 94.68/94.43 [3837]E(f317(f317(f244(x38371,x38372),x38373),f317(f16(f904(x38372,a893),x38371),f178(f904(x38372,a893)))),f178(f904(f903(x38371,x38372),a893)))
% 94.68/94.43 [3839]E(f317(f317(f23(a897),f317(f317(f75(a897),x38391),x38392)),f317(f317(f75(a897),x38391),x38393)),f317(f317(f75(a897),x38391),f317(f317(f23(a897),x38392),x38393)))
% 94.68/94.43 [3840]E(f317(f317(f74(a897),f317(f317(f75(a897),x38401),x38402)),f317(f317(f75(a897),x38401),x38403)),f317(f317(f75(a897),x38401),f317(f317(f74(a897),x38402),x38403)))
% 94.68/94.43 [3841]E(f317(f317(f23(a1),f317(f317(f75(a1),x38411),x38412)),f317(f317(f75(a1),x38411),x38413)),f317(f317(f75(a1),x38411),f317(f317(f23(a1),x38412),x38413)))
% 94.68/94.43 [3842]E(f317(f317(f74(a1),f317(f317(f75(a1),x38421),x38422)),f317(f317(f75(a1),x38421),x38423)),f317(f317(f75(a1),x38421),f317(f317(f74(a1),x38422),x38423)))
% 94.68/94.43 [3843]E(f317(f317(f75(a1),f317(f317(f234(a1),x38431),x38432)),f317(f317(f234(a1),x38431),x38433)),f317(f317(f234(a1),x38431),f317(f317(f74(a897),x38432),x38433)))
% 94.68/94.43 [3857]E(f317(f317(f34(x38571,f904(x38572,a893)),x38573),f317(f16(f904(x38572,a893),x38571),f178(f904(x38572,a893)))),f178(f904(x38572,a893)))
% 94.68/94.43 [3859]E(f40(a897,f317(f317(f75(a897),x38591),x38592),f317(f317(f75(a897),x38593),x38592)),f317(f317(f75(a897),f40(a897,x38591,x38593)),x38592))
% 94.68/94.43 [3864]E(f40(a1,f317(f317(f23(a1),x38641),f40(a1,x38642,x38643)),x38643),f40(a1,f317(f317(f23(a1),x38641),x38642),x38643))
% 94.68/94.43 [3865]E(f40(a1,f317(f317(f75(a1),x38651),f40(a1,x38652,x38653)),x38653),f40(a1,f317(f317(f75(a1),x38651),x38652),x38653))
% 94.68/94.43 [3866]P1(f317(f317(f224(f904(x38661,a893)),x38662),f317(f317(f299(x38661),x38663),x38662)))
% 94.68/94.43 [3941]E(f317(f317(f35(f904(x39411,a893),f904(x39411,a893)),x39412),f317(f91(f904(x39411,a893)),x39413)),f317(f317(f91(f904(x39411,a893)),x39413),f32(f904(x39411,a893),x39412)))
% 94.68/94.43 [3942]E(f317(f317(f34(f904(x39421,a893),f904(x39421,a893)),x39422),f317(f92(f904(x39421,a893)),x39423)),f317(f317(f92(f904(x39421,a893)),x39423),f31(f904(x39421,a893),x39422)))
% 94.68/94.43 [3954]E(f317(f162(x39541),f317(f317(f317(f173(f898(x39541),f898(x39541)),x39542),f157(x39541)),x39543)),f317(f162(x39541),x39543))
% 94.68/94.43 [3958]E(f317(f317(f165(x39581),f317(f179(f898(x39581)),f167(x39581,x39582,x39583))),x39583),f167(x39581,x39582,x39583))
% 94.68/94.43 [3962]E(f317(f179(f898(x39621)),f317(f317(f317(f173(f898(x39621),f898(x39621)),x39622),f157(x39621)),x39623)),f317(f179(f898(x39621)),x39623))
% 94.68/94.43 [3965]E(f317(f317(f247(x39651,x39652,x39652),f317(f16(f904(x39652,x39652),x39651),f5(x39652))),x39653),f317(f246(x39651,x39652),x39653))
% 94.68/94.43 [3972]E(f40(a1,f317(f317(f23(a1),f40(a1,x39721,x39722)),x39723),x39722),f40(a1,f317(f317(f23(a1),x39721),x39723),x39722))
% 94.68/94.43 [3973]E(f40(a1,f317(f317(f234(a1),f40(a1,x39731,x39732)),x39733),x39732),f40(a1,f317(f317(f234(a1),x39731),x39733),x39732))
% 94.68/94.43 [3976]E(f317(f317(f34(f904(f903(x39761,x39762),a893),f904(x39762,a893)),x39763),f274(x39761,x39762)),f317(f274(x39761,x39762),f31(f904(f903(x39761,x39762),a893),x39763)))
% 94.68/94.43 [3977]E(f317(f317(f34(f904(f903(x39771,x39772),a893),f904(x39771,a893)),x39773),f254(x39771,x39772)),f317(f254(x39771,x39772),f31(f904(f903(x39771,x39772),a893),x39773)))
% 94.68/94.43 [4000]E(f317(f67(x40001,x40001,x40001,x40002),f317(f317(f173(x40001,x40001),x40003),x40002)),f317(f317(f173(x40001,x40001),f317(a102,x40003)),x40002))
% 94.68/94.43 [4018]E(f317(f317(f128(x40181),f317(f317(f23(a897),f317(f179(f898(x40181)),x40182)),x40183)),f317(f158(x40181),x40182)),f317(f158(x40181),f317(f317(f165(x40181),x40183),x40182)))
% 94.68/94.43 [4019]E(f317(f317(f165(x40191),f317(f317(f23(a897),f317(f179(f898(x40191)),x40192)),x40193)),f317(f158(x40191),x40192)),f317(f158(x40191),f317(f317(f128(x40191),x40193),x40192)))
% 94.68/94.43 [4021]E(f317(f317(f74(a897),f317(f155(a897),f317(f317(f144(x40211,a897),x40212),x40213))),f317(f179(f898(x40211)),x40213)),f145(x40211,x40212,x40213))
% 94.68/94.43 [4042]E(f317(f157(x40421),f317(f317(f317(f173(f898(x40421),f898(x40421)),x40422),f157(x40421)),x40423)),f317(f317(f317(f173(f898(x40421),f898(x40421)),f317(a102,x40422)),f157(x40421)),x40423))
% 94.68/94.43 [4056]P1(f317(f317(f224(a897),f317(f179(f898(x40561)),f317(f126(x40561,x40562),x40563))),f317(f179(f898(x40561)),x40563)))
% 94.68/94.43 [4073]E(f317(f317(f91(f904(f904(x40731,a893),a893)),f317(f298(x40731),x40732)),f317(f300(f904(x40731,a893),f904(x40731,a893),f317(f299(x40731),x40733)),f317(f298(x40731),x40732))),f317(f298(x40731),f317(f317(f299(x40731),x40733),x40732)))
% 94.68/94.43 [4104]P1(f317(f317(f224(a897),f317(f179(f898(x41041)),f167(x41041,x41042,x41043))),f317(f179(f898(x41041)),x41043)))
% 94.68/94.43 [4111]E(f317(f254(x41111,x41112),f317(f252(f903(x41111,x41112)),f317(f247(x41111,x41112,a893),x41113))),f317(f252(x41111),f317(f317(f8(f904(x41112,a893),a893,x41111),f81(x41112)),x41113)))
% 94.68/94.43 [4123]E(f317(f300(a897,a897,f317(f317(f7(a897,a897,a897),f74(a897)),x41231)),f293(a897,x41232,x41233)),f293(a897,f317(f317(f74(a897),x41232),x41231),f317(f317(f74(a897),x41233),x41231)))
% 94.68/94.43 [4137]E(f317(f300(a897,a897,f317(f317(f7(a897,a897,a897),f74(a897)),x41371)),f317(f292(a897,x41372),x41373)),f317(f292(a897,f317(f317(f74(a897),x41372),x41371)),f317(f317(f74(a897),x41373),x41371)))
% 94.68/94.43 [4155]E(f317(f317(f171(x41551,x41552),f317(f317(f144(f903(x41551,x41552),x41551),f241(x41551,x41552)),x41553)),f317(f317(f144(f903(x41551,x41552),x41552),f246(x41551,x41552)),x41553)),x41553)
% 94.68/94.43 [4160]E(f317(f317(f74(a897),f317(f317(f75(a897),x41601),f40(a897,f317(f317(f30(a897),x41602),x41601),x41603))),f40(a897,x41602,x41601)),f40(a897,x41602,f317(f317(f75(a897),x41601),x41603)))
% 94.68/94.43 [4173]E(f317(f317(f124(x41731),x41732),f317(f132(f898(x41731),f898(x41731),f124(x41731),f103(x41731)),x41733)),f317(f132(f898(x41731),f898(x41731),f124(x41731),x41732),x41733))
% 94.68/94.43 [4194]P1(f317(f317(f319(f903(x41941,x41941)),f317(f317(f242(x41941,x41941),x41942),x41942)),f317(f317(f173(f903(x41941,x41941),a893),f2(a897)),x41943)))
% 94.68/94.43 [4199]E(f317(f252(x41991),f317(f317(f8(f904(x41992,a893),a893,x41991),f81(x41992)),f317(f7(x41992,x41991,a893),x41993))),f317(f274(x41992,x41991),f317(f252(f903(x41992,x41991)),f317(f247(x41992,x41991,a893),x41993))))
% 94.68/94.43 [4216]E(f317(f317(f91(f904(x42161,a893)),f317(f317(f34(a897,f904(x42161,a893)),f293(a897,f72(a897),x42162)),x42163)),f317(x42163,f2(a897))),f317(f317(f34(a897,f904(x42161,a893)),f317(f291(a897),x42162)),x42163))
% 94.68/94.43 [4231]E(f317(f132(f898(x42311),f898(x42311),f124(x42311),f103(x42311)),f317(f317(f144(f898(x42311),f898(x42311)),f126(x42311,x42312)),x42313)),f317(f126(x42311,x42312),f317(f132(f898(x42311),f898(x42311),f124(x42311),f103(x42311)),x42313)))
% 94.68/94.43 [4235]E(f317(f246(f898(x42351),f898(x42351)),f156(x42351,x42352,x42353)),f317(f126(x42351,f317(f67(a893,a893,x42351,a312),x42352)),x42353))
% 94.68/94.43 [4280]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),x42801),f317(f317(f30(a1),x42802),x42801))),f40(a1,x42802,x42801))),x42803),f317(f317(f74(a1),x42802),x42803))
% 94.68/94.43 [4317]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f75(a1),f317(f317(f30(a1),x43171),x43172)),x43172)),f40(a1,x43171,x43172))),x43173),f317(f317(f74(a1),x43171),x43173))
% 94.68/94.43 [4343]E(f79(f903(x43431,x43432),f317(f247(x43431,x43432,a893),f317(f317(f8(f904(x43432,f903(x43431,x43432)),f904(x43432,a893),x43431),f317(f8(f903(x43431,x43432),a893,x43432),x43433)),f242(x43431,x43432)))),f79(f903(x43431,x43432),x43433))
% 94.68/94.43 [4344]E(f84(f903(x43441,x43442),f317(f247(x43441,x43442,a893),f317(f317(f8(f904(x43442,f903(x43441,x43442)),f904(x43442,a893),x43441),f317(f8(f903(x43441,x43442),a893,x43442),x43443)),f242(x43441,x43442)))),f84(f903(x43441,x43442),x43443))
% 94.68/94.43 [4371]P1(f317(f317(f224(f904(x43711,a893)),f31(f904(x43711,a893),f317(f317(f92(f904(f904(x43711,a893),a893)),x43712),x43713))),f317(f317(f92(f904(x43711,a893)),f31(f904(x43711,a893),x43712)),f31(f904(x43711,a893),x43713))))
% 94.68/94.43 [4372]E(f317(f158(x43721),f317(f317(f317(f173(f898(x43721),f898(x43721)),f317(f317(f23(a897),f317(f179(f898(x43721)),x43722)),f40(a897,x43723,f317(f179(f898(x43721)),x43722)))),f157(x43721)),x43722)),f317(f317(f317(f173(f898(x43721),f898(x43721)),x43723),f157(x43721)),f317(f158(x43721),x43722)))
% 94.68/94.43 [4409]P1(f317(f317(f224(a897),f317(f179(f898(x44091)),f317(f317(f128(x44091),f317(f179(f898(x44091)),f167(x44091,x44092,x44093))),x44093))),f317(f179(f898(x44091)),x44093)))
% 94.68/94.43 [4626]~P1(f317(f56(x46261,x46262,f178(f904(x46261,a893))),x46263))
% 94.68/94.43 [4631]~P1(f317(f317(f319(f903(x46311,x46311)),f317(f317(f242(x46311,x46311),x46312),x46313)),f143(x46311,f103(f904(x46311,a897)))))
% 94.68/94.43 [3726]E(f317(f179(f898(x37261)),f317(f317(f165(x37261),x37262),x37263)),f317(f317(f228(a897),f317(f179(f898(x37261)),x37263)),x37262))
% 94.68/94.43 [3727]E(f317(f179(f898(x37271)),f317(f317(f128(x37271),x37272),x37273)),f317(f317(f23(a897),f317(f179(f898(x37271)),x37273)),x37272))
% 94.68/94.43 [3753]E(f317(f179(f898(f898(x37531))),f50(x37531,x37532,x37533)),f317(f317(f234(a897),f317(f179(f898(x37531)),x37533)),x37532))
% 94.68/94.43 [3770]E(f317(f317(f30(a897),f317(f317(f30(a897),x37701),x37702)),x37703),f317(f317(f30(a897),x37701),f317(f317(f75(a897),x37702),x37703)))
% 94.68/94.43 [3771]E(f317(f317(f23(a897),f317(f317(f23(a897),x37711),x37712)),x37713),f317(f317(f23(a897),x37711),f317(f317(f74(a897),x37712),x37713)))
% 94.68/94.43 [3772]E(f317(f317(f74(a897),f317(f317(f74(a897),x37721),x37722)),x37723),f317(f317(f74(a897),x37721),f317(f317(f74(a897),x37722),x37723)))
% 94.68/94.43 [3773]E(f317(f317(f74(a1),f317(f317(f74(a1),x37731),x37732)),x37733),f317(f317(f74(a1),x37731),f317(f317(f74(a1),x37732),x37733)))
% 94.68/94.43 [3774]E(f317(f317(f75(a897),f317(f317(f75(a897),x37741),x37742)),x37743),f317(f317(f75(a897),x37741),f317(f317(f75(a897),x37742),x37743)))
% 94.68/94.43 [3775]E(f317(f317(f75(a1),f317(f317(f75(a1),x37751),x37752)),x37753),f317(f317(f75(a1),x37751),f317(f317(f75(a1),x37752),x37753)))
% 94.68/94.43 [3776]E(f317(f317(f234(a1),f317(f317(f234(a1),x37761),x37762)),x37763),f317(f317(f234(a1),x37761),f317(f317(f75(a897),x37762),x37763)))
% 94.68/94.43 [3795]E(f152(x37951,f317(f317(f141(f904(x37951,a893)),x37952),x37953)),f164(x37951,x37952,f152(x37951,x37953)))
% 94.68/94.43 [3838]E(f317(f317(f23(a897),f317(f317(f23(a897),x38381),x38382)),x38383),f317(f317(f23(a897),f317(f317(f23(a897),x38381),x38383)),x38382))
% 94.68/94.43 [3846]E(f317(f317(f92(f904(x38461,a893)),x38462),f317(f317(f23(f904(x38461,a893)),x38463),x38462)),f178(f904(x38461,a893)))
% 94.68/94.43 [3850]E(f317(f317(f144(a897,x38501),f317(f16(x38501,a897),x38502)),f129(a897,f317(f292(a897,f2(a897)),x38503))),f159(x38501,x38503,x38502))
% 94.68/94.43 [3888]E(f32(f904(x38881,a893),f317(f317(f299(f904(x38881,a893)),x38882),x38883)),f317(f317(f92(f904(x38881,a893)),x38882),f32(f904(x38881,a893),x38883)))
% 94.68/94.43 [3889]E(f31(f904(x38891,a893),f317(f317(f299(f904(x38891,a893)),x38892),x38893)),f317(f317(f91(f904(x38891,a893)),x38892),f31(f904(x38891,a893),x38893)))
% 94.68/94.43 [3891]E(f159(x38911,f317(f179(f898(x38911)),f317(f126(x38911,f317(a314,x38912)),x38913)),x38912),f317(f126(x38911,f317(a314,x38912)),x38913))
% 94.68/94.43 [3893]E(f317(f317(f23(a897),f317(f317(f75(a897),x38931),x38932)),f317(f317(f75(a897),x38933),x38932)),f317(f317(f75(a897),f317(f317(f23(a897),x38931),x38933)),x38932))
% 94.68/94.43 [3894]E(f317(f317(f74(a897),f317(f317(f75(a897),x38941),x38942)),f317(f317(f75(a897),x38943),x38942)),f317(f317(f75(a897),f317(f317(f74(a897),x38941),x38943)),x38942))
% 94.68/94.43 [3895]E(f317(f317(f23(a1),f317(f317(f75(a1),x38951),x38952)),f317(f317(f75(a1),x38953),x38952)),f317(f317(f75(a1),f317(f317(f23(a1),x38951),x38953)),x38952))
% 94.68/94.43 [3896]E(f317(f317(f74(a1),f317(f317(f75(a1),x38961),x38962)),f317(f317(f75(a1),x38963),x38962)),f317(f317(f75(a1),f317(f317(f74(a1),x38961),x38963)),x38962))
% 94.68/94.43 [3898]E(f317(f317(f228(a897),f317(f317(f23(a897),x38981),x38982)),f317(f317(f23(a897),x38983),x38982)),f317(f317(f23(a897),f317(f317(f228(a897),x38981),x38983)),x38982))
% 94.68/94.43 [3918]E(f317(f317(f92(f904(f898(x39181),a893)),f150(x39181,x39182)),f150(x39181,x39183)),f150(x39181,f317(f317(f92(f904(x39181,a893)),x39182),x39183)))
% 94.68/94.43 [3921]E(f317(f317(f91(f904(x39211,a893)),x39212),f317(f317(f23(f904(x39211,a893)),x39213),x39212)),f317(f317(f91(f904(x39211,a893)),x39212),x39213))
% 94.68/94.43 [3922]E(f317(f317(f91(f904(x39221,a893)),x39222),f317(f317(f91(f904(x39221,a893)),x39222),x39223)),f317(f317(f91(f904(x39221,a893)),x39222),x39223))
% 94.68/94.43 [3923]E(f317(f317(f92(f904(x39231,a893)),x39232),f317(f317(f92(f904(x39231,a893)),x39232),x39233)),f317(f317(f92(f904(x39231,a893)),x39232),x39233))
% 94.68/94.43 [3935]E(f317(f317(f279(x39351,x39352,x39352),x39353),f297(x39352,f178(f904(f903(x39352,x39352),a893)))),x39353)
% 94.68/94.43 [3938]E(f317(f317(f91(f904(x39381,a893)),f317(f317(f299(x39381),x39382),f178(f904(x39381,a893)))),x39383),f317(f317(f299(x39381),x39382),x39383))
% 94.68/94.43 [3957]E(f317(f317(f23(a897),f317(f317(f23(a897),f317(a102,x39571)),x39572)),f317(a102,x39573)),f317(f317(f23(a897),f317(f317(f23(a897),x39571),x39572)),x39573))
% 94.68/94.43 [3985]E(f317(f317(f92(f904(f904(x39851,a893),a893)),f317(f298(x39851),x39852)),f317(f298(x39851),x39853)),f317(f298(x39851),f317(f317(f92(f904(x39851,a893)),x39852),x39853)))
% 94.68/94.43 [3988]E(f317(f317(f91(f904(x39881,a893)),f317(f73(f904(x39881,a893)),x39882)),x39883),f317(f73(f904(x39881,a893)),f317(f317(f23(f904(x39881,a893)),x39882),x39883)))
% 94.68/94.43 [3997]E(f317(f317(f299(x39971),x39972),f317(f317(f23(f904(x39971,a893)),x39973),f317(f317(f299(x39971),x39972),f178(f904(x39971,a893))))),f317(f317(f299(x39971),x39972),x39973))
% 94.68/94.43 [4007]P1(f317(f317(f224(f904(x40071,a893)),x40072),f317(f317(f91(f904(x40071,a893)),x40073),x40072)))
% 94.68/94.43 [4008]P1(f317(f317(f224(f904(x40081,a893)),x40082),f317(f317(f91(f904(x40081,a893)),x40082),x40083)))
% 94.68/94.43 [4012]E(f317(f317(f92(f904(x40121,a893)),f317(f73(f904(x40121,a893)),x40122)),f317(f73(f904(x40121,a893)),x40123)),f317(f73(f904(x40121,a893)),f317(f317(f91(f904(x40121,a893)),x40122),x40123)))
% 94.68/94.43 [4013]E(f317(f317(f91(f904(x40131,a893)),f317(f73(f904(x40131,a893)),x40132)),f317(f73(f904(x40131,a893)),x40133)),f317(f73(f904(x40131,a893)),f317(f317(f92(f904(x40131,a893)),x40132),x40133)))
% 94.68/94.43 [4027]P1(f317(f317(f224(f904(x40271,a893)),f317(f162(x40271),x40272)),f317(f162(x40271),f317(f317(f141(x40271),x40273),x40272))))
% 94.68/94.43 [4039]E(f317(f317(f91(f904(x40391,a893)),f317(f317(f23(f904(x40391,a893)),x40392),x40393)),f317(f317(f92(f904(x40391,a893)),x40392),x40393)),x40392)
% 94.68/94.43 [4091]E(f317(f317(f9(x40911,a1),f317(f317(f8(a897,a1,x40911),f90(a1)),x40912)),x40913),f317(f90(a1),f317(f317(f9(x40911,a897),x40912),x40913)))
% 94.68/94.43 [4092]E(f317(f317(f6(x40921,a1),f317(f317(f8(a897,a1,x40921),f90(a1)),x40922)),x40923),f317(f90(a1),f317(f317(f6(x40921,a897),x40922),x40923)))
% 94.68/94.43 [4139]E(f317(f317(f124(x41391),f167(x41391,x41392,x41393)),f317(f317(f128(x41391),f317(f179(f898(x41391)),f167(x41391,x41392,x41393))),x41393)),x41393)
% 94.68/94.43 [4143]E(f317(f73(f904(f903(x41431,x41432),a893)),f317(f317(f244(x41431,x41432),x41433),f317(f16(f904(x41432,a893),x41431),f232(f904(x41432,a893))))),f317(f317(f244(x41431,x41432),f317(f73(f904(x41431,a893)),x41433)),f317(f16(f904(x41432,a893),x41431),f232(f904(x41432,a893)))))
% 94.68/94.43 [4144]E(f317(f73(f904(f903(x41441,x41442),a893)),f317(f317(f244(x41441,x41442),f232(f904(x41441,a893))),f317(f16(f904(x41442,a893),x41441),x41443))),f317(f317(f244(x41441,x41442),f232(f904(x41441,a893))),f317(f16(f904(x41442,a893),x41441),f317(f73(f904(x41442,a893)),x41443))))
% 94.68/94.43 [4195]E(f317(f317(f34(f904(x41951,a893),f904(x41951,a893)),x41952),f317(f317(f7(f904(x41951,a893),f904(x41951,a893),f904(x41951,a893)),f92(f904(x41951,a893))),x41953)),f317(f317(f92(f904(x41951,a893)),f31(f904(x41951,a893),x41952)),x41953))
% 94.68/94.43 [4201]E(f317(f132(f898(x42011),f898(x42011),f124(x42011),f103(x42011)),f317(f317(f141(f898(x42011)),x42012),x42013)),f317(f317(f124(x42011),x42012),f317(f132(f898(x42011),f898(x42011),f124(x42011),f103(x42011)),x42013)))
% 94.68/94.43 [4222]E(f317(f317(f299(f904(x42221,a893)),f317(f275(x42221,x42221,x42222),f317(f317(f299(x42221),x42223),f178(f904(x42221,a893))))),f178(f904(f904(x42221,a893),a893))),f317(f317(f55(x42221),f317(f317(f299(x42221),x42223),f178(f904(x42221,a893)))),x42222))
% 94.68/94.43 [4232]E(f317(f317(f74(a897),f317(f317(f75(a897),x42321),f317(f317(f30(a897),x42322),x42323))),f317(f317(f30(a897),f317(f317(f75(a897),x42321),f40(a897,x42322,x42323))),x42323)),f317(f317(f30(a897),f317(f317(f75(a897),x42321),x42322)),x42323))
% 94.68/94.43 [4233]E(f317(f317(f74(a1),f317(f317(f75(a1),x42331),f317(f317(f30(a1),x42332),x42333))),f317(f317(f30(a1),f317(f317(f75(a1),x42331),f40(a1,x42332,x42333))),x42333)),f317(f317(f30(a1),f317(f317(f75(a1),x42331),x42332)),x42333))
% 94.68/94.43 [4265]E(f317(f317(f23(f904(x42651,a893)),f317(f162(x42651),x42652)),f317(f317(f299(x42651),x42653),f178(f904(x42651,a893)))),f317(f162(x42651),f317(f126(x42651,f317(f317(f8(a893,a893,x42651),a312),f317(a314,x42653))),x42652)))
% 94.68/94.43 [4315]E(f317(f317(f124(x43151),f317(f132(f898(x43151),f898(x43151),f124(x43151),f103(x43151)),x43152)),f317(f132(f898(x43151),f898(x43151),f124(x43151),f103(x43151)),x43153)),f317(f132(f898(x43151),f898(x43151),f124(x43151),f103(x43151)),f317(f317(f124(f898(x43151)),x43152),x43153)))
% 94.68/94.43 [4318]E(f317(f317(f242(f898(x43181),f898(x43181)),f317(f126(x43181,x43182),x43183)),f317(f126(x43181,f317(f67(a893,a893,x43181,a312),x43182)),x43183)),f156(x43181,x43182,x43183))
% 94.68/94.43 [4321]E(f317(f317(f74(a897),f317(f317(f74(a897),f317(f317(f30(a897),x43211),x43212)),f317(f317(f30(a897),x43213),x43212))),f317(f317(f30(a897),f317(f317(f74(a897),f40(a897,x43211,x43212)),f40(a897,x43213,x43212))),x43212)),f317(f317(f30(a897),f317(f317(f74(a897),x43211),x43213)),x43212))
% 94.68/94.43 [4322]E(f317(f317(f74(a1),f317(f317(f74(a1),f317(f317(f30(a1),x43221),x43222)),f317(f317(f30(a1),x43223),x43222))),f317(f317(f30(a1),f317(f317(f74(a1),f40(a1,x43221,x43222)),f40(a1,x43223,x43222))),x43222)),f317(f317(f30(a1),f317(f317(f74(a1),x43221),x43223)),x43222))
% 94.68/94.43 [4375]E(f317(f317(f92(f904(f898(x43751),a893)),f317(f317(f7(f898(x43751),f904(f898(x43751),a893),a893),f319(f898(x43751))),f151(x43751,x43752))),f317(f317(f7(f898(x43751),f904(f898(x43751),a893),a893),f319(f898(x43751))),f151(x43751,x43753))),f150(x43751,f317(f317(f92(f904(x43751,a893)),f317(f317(f7(x43751,f904(x43751,a893),a893),f319(x43751)),x43752)),f317(f317(f7(x43751,f904(x43751,a893),a893),f319(x43751)),x43753))))
% 94.68/94.43 [4387]E(f317(f252(x43871),f317(f317(f18(x43871,a893,a893),f317(f317(f8(a893,f904(a893,a893),x43871),a316),f317(f317(f7(x43871,x43871,a893),a314),x43872))),f317(f317(f7(x43871,f904(x43871,a893),a893),f319(x43871)),x43873))),f317(f317(f299(x43871),x43872),x43873))
% 94.68/94.43 [4407]E(f317(f317(f80(f898(f898(x44071)),f898(f898(x44071))),f49(x44071,x44072)),f317(f317(f18(f898(f898(x44071)),f898(f898(x44071)),f898(f898(x44071))),f317(f317(f8(f898(f898(x44071)),f904(f898(f898(x44071)),f898(f898(x44071))),f898(f898(x44071))),f124(f898(x44071))),f317(f144(f898(x44071),f898(x44071)),f317(f141(x44071),x44073)))),f5(f898(f898(x44071))))),f49(x44071,f317(f317(f141(x44071),x44073),x44072)))
% 94.68/94.43 [4410]E(f317(f252(x44101),f317(f317(f18(x44101,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44101),a316),f317(f317(f7(x44101,f904(x44101,a893),a893),f319(x44101)),x44102))),f317(f317(f7(x44101,f904(x44101,a893),a893),f319(x44101)),x44103))),f317(f317(f91(f904(x44101,a893)),x44102),x44103))
% 94.68/94.43 [4411]E(f317(f252(x44111),f317(f317(f18(x44111,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44111),a315),f317(f317(f7(x44111,f904(x44111,a893),a893),f319(x44111)),x44112))),f317(f317(f7(x44111,f904(x44111,a893),a893),f319(x44111)),x44113))),f317(f317(f92(f904(x44111,a893)),x44112),x44113))
% 94.68/94.43 [4500]E(f317(f317(f34(x45001,f904(f904(x45001,a893),a893)),x45002),f317(f317(f7(x45001,f904(f904(x45001,a893),a893),f904(f904(x45001,a893),a893)),f317(f317(f8(f904(x45001,a893),f904(f904(f904(x45001,a893),a893),f904(f904(x45001,a893),a893)),x45001),f299(f904(x45001,a893))),f317(f317(f8(f904(x45001,a893),f904(x45001,a893),x45001),f275(x45001,x45001,x45003)),f317(f317(f7(x45001,f904(x45001,a893),f904(x45001,a893)),f299(x45001)),f178(f904(x45001,a893)))))),f178(f904(f904(x45001,a893),a893)))),f317(f317(f55(x45001),x45002),x45003))
% 94.68/94.43 [4502]E(f317(f317(f191(x45021),f317(f317(f75(a1),f317(f317(f67(f903(a1,a1),a1,x45021,f241(a1,a1)),f202(x45021)),x45022)),f317(f317(f67(f903(a1,a1),a1,x45021,f241(a1,a1)),f202(x45021)),x45023))),f317(f317(f75(a1),f317(f317(f67(f903(a1,a1),a1,x45021,f246(a1,a1)),f202(x45021)),x45022)),f317(f317(f67(f903(a1,a1),a1,x45021,f246(a1,a1)),f202(x45021)),x45023))),f218(x45021,x45022,x45023))
% 94.68/94.43 [4505]E(f317(f252(f898(x45051)),f317(f317(f18(f898(x45051),a893,a893),f317(f317(f8(a893,f904(a893,a893),f898(x45051)),a315),f317(f317(f7(f898(x45051),a897,a893),f317(f317(f8(a897,f904(a897,a893),f898(x45051)),a314),f179(f898(x45051)))),x45052))),f317(f317(f7(f898(x45051),f904(x45051,a893),a893),f317(f317(f8(f904(x45051,a893),f904(f904(x45051,a893),a893),f898(x45051)),f224(f904(x45051,a893))),f162(x45051))),f317(f162(x45051),x45053)))),f317(f162(f898(x45051)),f50(x45051,x45052,x45053)))
% 94.68/94.43 [3911]E(f40(a897,f317(f317(f74(a897),f317(f317(f75(a897),x39111),x39112)),x39113),x39112),f40(a897,x39113,x39112))
% 94.68/94.43 [3956]E(f129(a897,f317(f292(a897,f317(f317(f74(a897),x39561),x39562)),x39563)),f317(f317(f128(a897),x39562),f129(a897,f317(f292(a897,x39561),x39563))))
% 94.68/94.43 [3996]E(f317(f317(f74(a1),f317(f90(a1),x39961)),f317(f317(f74(a1),f317(f90(a1),x39962)),x39963)),f317(f317(f74(a1),f317(f90(a1),f317(f317(f74(a897),x39961),x39962))),x39963))
% 94.68/94.43 [4003]E(f317(f317(f23(f904(x40031,a893)),f317(f317(f23(f904(x40031,a893)),x40032),x40033)),x40033),f317(f317(f23(f904(x40031,a893)),x40032),x40033))
% 94.68/94.43 [4004]E(f317(f317(f91(f904(x40041,a893)),f317(f317(f23(f904(x40041,a893)),x40042),x40043)),x40043),f317(f317(f91(f904(x40041,a893)),x40042),x40043))
% 94.68/94.43 [4028]E(f317(f317(f279(x40281,x40281,x40282),f297(x40281,f178(f904(f903(x40281,x40281),a893)))),x40283),x40283)
% 94.68/94.43 [4036]E(f317(f317(f91(f904(x40361,a893)),f317(f271(x40361),x40362)),f317(f271(x40361),x40363)),f317(f271(x40361),f317(f317(f91(f904(f903(x40361,x40361),a893)),x40362),x40363)))
% 94.68/94.43 [4047]E(f256(x40471,f317(f317(f141(f903(a89,x40471)),f317(f317(f242(a89,x40471),f2(a89)),x40472)),x40473)),f256(x40471,x40473))
% 94.68/94.43 [4049]E(f317(f317(f92(f904(x40491,a893)),f32(f904(x40491,a893),x40492)),f32(f904(x40491,a893),x40493)),f32(f904(x40491,a893),f317(f317(f91(f904(f904(x40491,a893),a893)),x40492),x40493)))
% 94.68/94.43 [4050]E(f317(f317(f91(f904(x40501,a893)),f31(f904(x40501,a893),x40502)),f31(f904(x40501,a893),x40503)),f31(f904(x40501,a893),f317(f317(f91(f904(f904(x40501,a893),a893)),x40502),x40503)))
% 94.68/94.43 [4088]E(f317(f317(f279(x40881,x40881,x40881),f317(f317(f173(f903(x40881,x40881),a893),x40882),x40883)),x40883),f317(f317(f173(f903(x40881,x40881),a893),f317(a102,x40882)),x40883))
% 94.68/94.43 [4131]P1(f317(f317(f224(f904(x41311,a893)),f317(f317(f23(f904(x41311,a893)),x41312),x41313)),x41312))
% 94.68/94.43 [4132]P1(f317(f317(f224(f904(x41321,a893)),f317(f317(f92(f904(x41321,a893)),x41322),x41323)),x41323))
% 94.68/94.43 [4133]P1(f317(f317(f224(f904(x41331,a893)),f317(f317(f92(f904(x41331,a893)),x41332),x41333)),x41332))
% 94.68/94.43 [4157]E(f297(x41571,f317(f317(f91(f904(f903(x41571,x41571),a893)),f297(x41571,x41572)),f297(x41571,x41573))),f297(x41571,f317(f317(f91(f904(f903(x41571,x41571),a893)),x41572),x41573)))
% 94.68/94.44 [4161]E(f31(f904(x41611,a893),f317(f317(f299(f904(x41611,a893)),x41612),f317(f317(f299(f904(x41611,a893)),x41613),f178(f904(f904(x41611,a893),a893))))),f317(f317(f91(f904(x41611,a893)),x41612),x41613))
% 94.68/94.44 [4162]E(f32(f904(x41621,a893),f317(f317(f299(f904(x41621,a893)),x41622),f317(f317(f299(f904(x41621,a893)),x41623),f178(f904(f904(x41621,a893),a893))))),f317(f317(f92(f904(x41621,a893)),x41622),x41623))
% 94.68/94.44 [4167]E(f317(f317(f279(x41671,x41671,x41671),f317(f317(f173(f903(x41671,x41671),a893),x41672),x41673)),x41673),f317(f317(f279(x41671,x41671,x41671),x41673),f317(f317(f173(f903(x41671,x41671),a893),x41672),x41673)))
% 94.68/94.44 [4236]E(f317(f317(f91(f904(x42361,a893)),f317(f252(x42361),f317(f317(f7(x42361,x42361,a893),a314),x42362))),x42363),f317(f317(f299(x42361),x42362),x42363))
% 94.68/94.44 [4238]E(f317(a95,f317(f317(f9(x42381,a1),f317(f317(f8(a897,a1,x42381),f90(a1)),x42382)),x42383)),f317(f317(f9(x42381,a897),x42382),x42383))
% 94.68/94.44 [4239]E(f317(a95,f317(f317(f6(x42391,a1),f317(f317(f8(a897,a1,x42391),f90(a1)),x42392)),x42393)),f317(f317(f6(x42391,a897),x42392),x42393))
% 94.68/94.44 [4312]E(f317(f146(f898(x43121),x43121,f317(f161(x43121),x43122),f317(f16(f904(f898(x43121),f898(x43121)),x43121),f317(f317(f7(f898(x43121),f898(x43121),f898(x43121)),f124(x43121)),x43122))),x43123),f317(f161(x43121),f317(f317(f124(x43121),x43123),x43122)))
% 94.68/94.44 [4340]P1(f317(f317(f224(f904(f904(x43401,a893),a893)),f317(f317(f91(f904(f904(x43401,a893),a893)),f317(f298(x43401),x43402)),f317(f298(x43401),x43403))),f317(f298(x43401),f317(f317(f91(f904(x43401,a893)),x43402),x43403))))
% 94.68/94.44 [4429]E(f317(f252(x44291),f317(f317(f18(x44291,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44291),a315),f317(f317(f7(x44291,f904(x44291,a893),a893),f319(x44291)),x44292))),f317(f317(f8(a893,a893,x44291),a312),f317(f317(f7(x44291,f904(x44291,a893),a893),f319(x44291)),x44293)))),f317(f317(f23(f904(x44291,a893)),x44292),x44293))
% 94.68/94.44 [4453]E(f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,a897,a893),f225(a897)),f317(f179(f898(x44531)),x44532)))),f317(f317(f8(x44531,a893,a897),x44533),f317(f154(x44531),x44532))))),f317(f179(f898(x44531)),f317(f126(x44531,x44533),x44532)))
% 94.68/94.44 [4455]E(f317(f179(f898(x44551)),f166(x44551,x44552,x44553)),f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,a897,a893),f225(a897)),f317(f179(f898(x44551)),x44552)))),f317(f317(f7(a897,f904(a897,a893),a893),f319(a897)),x44553)))))
% 94.68/94.44 [4551]E(f317(f317(f92(f904(f903(f898(x45511),f898(x45511)),a893)),f317(f300(f903(f903(x45511,f898(x45511)),f903(x45511,f898(x45511))),f903(f898(x45511),f898(x45511)),f248(f903(x45511,f898(x45511)),f898(x45511),f903(x45511,f898(x45511)),f898(x45511),f317(f247(x45511,f898(x45511),f898(x45511)),f141(x45511)),f317(f247(x45511,f898(x45511),f898(x45511)),f141(x45511)))),f309(x45511,f898(x45511),x45512,f317(f133(x45511,x45512),x45513)))),f317(f252(f903(f898(x45511),f898(x45511))),f317(f247(f898(x45511),f898(x45511),a893),f317(f317(f7(f898(x45511),f904(f898(x45511),a893),f904(f898(x45511),a893)),f317(f317(f8(f904(a893,a893),f904(f904(f898(x45511),a893),f904(f898(x45511),a893)),f898(x45511)),f8(a893,a893,f898(x45511))),f317(f317(f8(a893,f904(a893,a893),f898(x45511)),a315),f317(f317(f7(f898(x45511),a897,a893),f317(f317(f8(a897,f904(a897,a893),f898(x45511)),a314),f179(f898(x45511)))),f317(a102,x45513))))),f317(f317(f7(f898(x45511),a897,a893),f317(f317(f8(a897,f904(a897,a893),f898(x45511)),a314),f179(f898(x45511)))),f317(a102,x45513)))))),f317(f133(x45511,x45512),f317(a102,x45513)))
% 94.68/94.44 [4051]E(f40(a897,f317(a102,f317(f317(f74(a897),f317(f317(f75(a897),x40511),x40512)),x40513)),x40512),f40(a897,f317(a102,x40513),x40512))
% 94.68/94.44 [4298]E(f317(f252(x42981),f317(f317(f18(x42981,a893,a893),f317(f317(f8(a893,f904(a893,a893),x42981),a315),x42982)),x42983)),f317(f317(f92(f904(x42981,a893)),f317(f252(x42981),x42982)),f317(f252(x42981),x42983)))
% 94.68/94.44 [4299]E(f317(f252(x42991),f317(f317(f18(x42991,a893,a893),f317(f317(f8(a893,f904(a893,a893),x42991),a316),x42992)),x42993)),f317(f317(f91(f904(x42991,a893)),f317(f252(x42991),x42992)),f317(f252(x42991),x42993)))
% 94.68/94.44 [4301]E(f317(f317(f124(x43011),f317(f317(f128(x43011),f40(a897,x43012,f317(f179(f898(x43011)),x43013))),x43013)),f317(f317(f165(x43011),f40(a897,x43012,f317(f179(f898(x43011)),x43013))),x43013)),f317(f317(f317(f173(f898(x43011),f898(x43011)),x43012),f157(x43011)),x43013))
% 94.68/94.44 [4307]E(f317(f252(x43071),f317(f317(f18(x43071,a893,a893),f317(f317(f8(a893,f904(a893,a893),x43071),a320),x43072)),x43073)),f317(f317(f91(f904(x43071,a893)),f317(f73(f904(x43071,a893)),f317(f252(x43071),x43072))),f317(f252(x43071),x43073)))
% 94.68/94.44 [4323]E(f317(f317(f74(a897),f317(f179(f898(x43231)),f317(f126(x43231,x43232),x43233))),f317(f179(f898(x43231)),f317(f126(x43231,f317(f317(f8(a893,a893,x43231),a312),x43232)),x43233))),f317(f179(f898(x43231)),x43233))
% 94.68/94.44 [4346]P1(f317(f317(f224(f904(x43461,a893)),f317(f317(f91(f904(x43461,a893)),f32(f904(x43461,a893),x43462)),f32(f904(x43461,a893),x43463))),f32(f904(x43461,a893),f317(f317(f92(f904(f904(x43461,a893),a893)),x43462),x43463))))
% 94.68/94.44 [4360]E(f317(f162(x43601),f317(f126(x43601,f317(f317(f8(a893,a893,x43601),a312),f317(f317(f7(x43601,x43601,a893),a314),x43602))),x43603)),f317(f317(f23(f904(x43601,a893)),f317(f162(x43601),x43603)),f317(f317(f299(x43601),x43602),f178(f904(x43601,a893)))))
% 94.68/94.44 [4369]P1(f317(f317(f224(f904(f903(x43691,x43691),a893)),f317(f317(f91(f904(f903(x43691,x43691),a893)),f297(x43691,x43692)),f297(x43691,x43693))),f297(x43691,f317(f317(f91(f904(f903(x43691,x43691),a893)),x43692),x43693))))
% 94.68/94.44 [4392]E(f317(f317(f75(a897),f317(a102,f317(a102,f2(a897)))),f317(f317(f6(a897,a897),f317(f317(f8(a897,a897,a897),f317(f74(a897),x43921)),f317(f317(f7(a897,a897,a897),f75(a897)),x43922))),f317(f272(a897),x43923))),f317(f317(f75(a897),x43923),f317(f317(f74(a897),x43921),f317(f317(f74(a897),x43921),f317(f317(f75(a897),f317(f317(f23(a897),x43923),f72(a897))),x43922)))))
% 94.68/94.44 [4402]E(f317(f252(x44021),f317(f317(f18(x44021,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44021),a315),f317(f317(f7(x44021,f904(x44021,a893),a893),f319(x44021)),f317(f162(x44021),x44022)))),x44023)),f317(f162(x44021),f317(f126(x44021,x44023),x44022)))
% 94.68/94.44 [4550]E(f317(f252(x45501),f317(f317(f8(f904(a897,a893),a893,x45501),f81(a897)),f317(f317(f7(x45501,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),x45501),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),x45501),f317(f8(a893,f904(a893,a893),a897),a315)),f317(f317(f7(x45501,f904(a897,x45501),f904(a897,a893)),f317(f317(f8(f904(x45501,a893),f904(f904(a897,x45501),f904(a897,a893)),x45501),f8(x45501,a893,a897)),a314)),f317(f154(x45501),x45502))))),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,a897,a893),f225(a897)),f317(f179(f898(x45501)),x45502)))),f317(f317(f7(a897,f904(a897,a893),a893),f319(a897)),x45503))))),f317(f162(x45501),f166(x45501,x45502,x45503)))
% 94.68/94.44 [4442]E(f317(f252(x44421),f317(f317(f18(x44421,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44421),a320),f317(f317(f8(a893,a893,x44421),a312),f317(f317(f7(x44421,x44421,a893),a314),x44422)))),x44423)),f317(f317(f299(x44421),x44422),f317(f252(x44421),x44423)))
% 94.68/94.44 [4474]E(f317(f317(f144(f903(x44741,a897),x44741),f241(x44741,a897)),f317(f126(f903(x44741,a897),f317(f317(f7(f903(x44741,a897),f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),f903(x44741,a897)),f319(a897)),f246(x44741,a897))),x44742)),f317(f317(f171(x44741,a897),x44743),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(x44741)),x44743)))))),f166(x44741,x44743,x44742))
% 94.68/94.44 [4501]E(f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f6(a897,a1),f317(f317(f8(a1,a1,a897),f317(f74(a1),x45011)),f317(f317(f7(a897,a1,a1),f317(f317(f8(a1,f904(a1,a1),a897),f75(a1)),f90(a1))),x45012))),f317(f272(a897),x45013))),f317(f317(f75(a1),f317(f90(a1),x45013)),f317(f317(f74(a1),x45011),f317(f317(f74(a1),x45011),f317(f317(f75(a1),f317(f90(a1),f317(f317(f23(a897),x45013),f72(a897)))),x45012)))))
% 94.68/94.44 [4543]E(f317(f252(f903(x45431,x45432)),f317(f247(x45431,x45432,a893),f317(f317(f7(x45431,f904(f903(x45432,x45431),a893),f904(x45432,a893)),f317(f317(f8(f904(x45432,f904(f904(f903(x45432,x45431),a893),a893)),f904(f904(f903(x45432,x45431),a893),f904(x45432,a893)),x45431),f7(x45432,f904(f903(x45432,x45431),a893),a893)),f317(f317(f8(f904(x45432,f903(x45432,x45431)),f904(x45432,f904(f904(f903(x45432,x45431),a893),a893)),x45431),f317(f8(f903(x45432,x45431),f904(f904(f903(x45432,x45431),a893),a893),x45432),f319(f903(x45432,x45431)))),f317(f7(x45432,x45431,f903(x45432,x45431)),f242(x45432,x45431))))),x45433))),f317(f276(x45432,x45431),x45433))
% 94.68/94.44 [4563]E(f317(f252(f898(x45631)),f317(f317(f8(f904(x45631,a893),a893,f898(x45631)),f81(x45631)),f317(f317(f8(f904(x45631,f904(f898(x45631),a893)),f904(x45631,a893),f898(x45631)),f317(f8(f904(f898(x45631),a893),a893,x45631),f81(f898(x45631)))),f317(f317(f7(f898(x45631),f904(x45631,f904(f898(x45631),a893)),f904(x45631,f904(f898(x45631),a893))),f317(f317(f8(f904(x45631,f904(f904(f898(x45631),a893),f904(f898(x45631),a893))),f904(f904(x45631,f904(f898(x45631),a893)),f904(x45631,f904(f898(x45631),a893))),f898(x45631)),f18(x45631,f904(f898(x45631),a893),f904(f898(x45631),a893))),f317(f317(f8(f904(x45631,f904(f898(x45631),f904(a893,a893))),f904(x45631,f904(f904(f898(x45631),a893),f904(f898(x45631),a893))),f898(x45631)),f317(f8(f904(f898(x45631),f904(a893,a893)),f904(f904(f898(x45631),a893),f904(f898(x45631),a893)),x45631),f18(f898(x45631),a893,a893))),f317(f317(f8(f904(x45631,f904(f898(x45631),a893)),f904(x45631,f904(f898(x45631),f904(a893,a893))),f898(x45631)),f317(f8(f904(f898(x45631),a893),f904(f898(x45631),f904(a893,a893)),x45631),f317(f8(a893,f904(a893,a893),f898(x45631)),a315))),f317(f317(f7(f898(x45631),f904(x45631,f904(f898(x45631),f898(x45631))),f904(x45631,f904(f898(x45631),a893))),f317(f317(f8(f904(f904(f898(x45631),f898(x45631)),f904(f898(x45631),a893)),f904(f904(x45631,f904(f898(x45631),f898(x45631))),f904(x45631,f904(f898(x45631),a893))),f898(x45631)),f8(f904(f898(x45631),f898(x45631)),f904(f898(x45631),a893),x45631)),f317(f317(f8(f904(f898(x45631),a893),f904(f904(f898(x45631),f898(x45631)),f904(f898(x45631),a893)),f898(x45631)),f8(f898(x45631),a893,f898(x45631))),a314))),f141(x45631)))))),f317(f317(f7(x45631,f904(f898(x45631),a893),f904(f898(x45631),a893)),f317(f317(f8(f904(a893,a893),f904(f904(f898(x45631),a893),f904(f898(x45631),a893)),x45631),f8(a893,a893,f898(x45631))),f317(f317(f8(a893,f904(a893,a893),x45631),a315),f317(f317(f7(x45631,f904(x45631,a893),a893),f319(x45631)),x45632)))),f317(f317(f7(f898(x45631),f904(f898(x45631),a893),a893),f319(f898(x45631))),x45633)))))),f164(x45631,x45632,x45633))
% 94.68/94.44 [4560]E(f317(f317(f80(a1,f903(a1,a1)),f317(f317(f23(a1),x45601),x45602)),f317(f317(f7(a1,f903(a1,a1),f903(a1,a1)),f317(f317(f18(a1,f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),f317(f317(f8(a893,f904(f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),a1),f86(f903(a1,a1))),f317(f224(a1),f2(a1)))),f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x45603)),f72(a1))))),f317(f317(f242(a1,a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x45603)),x45601))),f317(f38(x45602),f317(f317(f242(a1,a1),x45603),x45601)))
% 94.68/94.44 [3613]E(f106(x36131,f317(x36132,x36133),f317(x36134,x36133)),f317(f193(x36131,x36132,x36134),x36133))
% 94.68/94.44 [3666]E(f317(f317(f235(x36661,x36662,x36663),x36664),f2(a897)),x36662)
% 94.68/94.44 [3704]E(f175(x37041,x37042,x37043,f317(a102,x37044)),f317(x37043,x37044))
% 94.68/94.44 [3745]E(f160(x37451,x37452,f160(x37451,x37453,x37454)),f160(x37451,x37453,f160(x37451,x37452,x37454)))
% 94.68/94.44 [3746]E(f116(x37461,x37462,f106(x37461,x37463,x37464)),f106(x37461,f116(x37461,x37462,x37463),x37464))
% 94.68/94.44 [3879]E(f317(f146(x38791,x38792,x38793,x38794),f103(x38792)),x38793)
% 94.68/94.44 [3880]E(f317(f132(x38801,x38802,x38803,x38804),f103(x38802)),x38804)
% 94.68/94.44 [3917]E(f317(f179(f901(x39171,x39172)),f210(x39171,x39172,x39173,x39174)),f2(a897))
% 94.68/94.44 [3940]E(f317(f247(x39401,x39402,x39403),f245(x39401,x39402,x39403,x39404)),x39404)
% 94.68/94.44 [3984]E(f317(f317(f124(x39841),f159(x39841,x39842,x39843)),f159(x39841,x39844,x39843)),f317(f317(f124(x39841),f159(x39841,x39844,x39843)),f159(x39841,x39842,x39843)))
% 94.68/94.44 [4071]E(f317(f317(f249(x40711,x40712,x40713,f903(x40712,x40713)),x40714),f242(x40712,x40713)),x40714)
% 94.68/94.44 [4081]E(f117(x40811,x40812,x40813,x40814,f109(x40812)),x40813)
% 94.68/94.44 [4087]E(f69(x40871,x40872,x40873,x40874,f317(x40873,x40874)),x40873)
% 94.68/94.44 [4353]P41(x43531,x43532,x43533,x43534,f178(f904(x43531,a893)),x43534)
% 94.68/94.44 [3420]E(f317(f317(f16(x34201,x34202),x34203),x34204),x34203)
% 94.68/94.44 [3694]E(f160(x36941,x36942,f317(f126(x36941,x36943),x36944)),f317(f126(x36941,x36943),f160(x36941,x36942,x36944)))
% 94.68/94.44 [3728]E(f317(f317(f58(x37281,x37282,x37283),x37284),f178(f904(x37281,a893))),x37284)
% 94.68/94.44 [3752]E(f317(f317(f154(x37521),f317(f317(f141(x37521),x37522),x37523)),f317(a102,x37524)),f317(f317(f154(x37521),x37523),x37524))
% 94.68/94.44 [3819]E(f317(f317(x38191,x38192),f317(f174(x38193,x38194,x38191),x38192)),f317(f174(x38193,x38194,x38191),f317(a102,x38192)))
% 94.68/94.44 [3860]E(f245(x38601,x38602,x38603,f317(f247(x38601,x38602,x38603),x38604)),x38604)
% 94.68/94.44 [3915]E(f317(f317(f149(x39151,f317(f317(f141(x39151),x39152),x39153)),f2(a897)),x39154),f317(f317(f141(x39151),x39154),x39153))
% 94.68/94.44 [3925]E(f317(f317(f34(f904(x39251,a893),f904(x39252,a893)),x39253),f300(x39251,x39252,x39254)),f317(f300(x39251,x39252,x39254),f31(f904(x39251,a893),x39253)))
% 94.68/94.44 [3926]E(f317(f317(f34(f904(x39261,a893),f904(x39262,a893)),x39263),f301(x39262,x39261,x39264)),f317(f301(x39262,x39261,x39264),f31(f904(x39261,a893),x39263)))
% 94.68/94.44 [3951]E(f110(x39511,f120(x39512,f899(x39511),x39513,x39514)),f317(f108(x39512,x39511,x39514),x39513))
% 94.68/94.44 [4024]E(f317(f115(x40241,x40242),f116(x40241,x40243,x40244)),f317(f317(f74(a897),f317(f317(f74(a897),f317(x40242,x40243)),f317(f115(x40241,x40242),x40244))),f317(a102,f2(a897))))
% 94.68/94.44 [4046]E(f317(f132(x40461,x40462,f317(f7(x40462,x40461,x40461),x40463),x40464),f317(f158(x40462),f103(x40462))),x40464)
% 94.68/94.44 [4151]E(f213(x41511,f903(x41512,f899(x41512)),x41513,f317(f247(x41512,f899(x41512),x41511),x41514),f317(f125(x41512),f109(x41512))),x41513)
% 94.68/94.44 [4283]E(f317(f247(x42831,x42832,x42833),f317(f317(f8(f904(x42832,f903(x42831,x42832)),f904(x42832,x42833),x42831),f317(f8(f903(x42831,x42832),x42833,x42832),x42834)),f242(x42831,x42832))),x42834)
% 94.68/94.44 [3604]E(f317(f246(x36041,x36042),f317(f317(f242(x36041,x36042),x36043),x36044)),x36044)
% 94.68/94.44 [3605]E(f317(f241(x36051,x36052),f317(f317(f242(x36051,x36052),x36053),x36054)),x36053)
% 94.68/94.44 [3638]E(f317(f179(f898(x36381)),f317(f317(f149(x36381,x36382),x36383),x36384)),f317(f179(f898(x36381)),x36382))
% 94.68/94.44 [3639]E(f317(f179(f898(x36391)),f317(f317(f144(x36392,x36391),x36393),x36394)),f317(f179(f898(x36392)),x36394))
% 94.68/94.44 [3660]E(f317(f317(f128(x36601),f317(a102,x36602)),f317(f317(f141(x36601),x36603),x36604)),f317(f317(f128(x36601),x36602),x36604))
% 94.68/94.44 [3723]E(f317(f317(f165(x37231),x37232),f159(x37231,x37233,x37234)),f159(x37231,f317(f317(f228(a897),x37232),x37233),x37234))
% 94.68/94.44 [3724]E(f317(f317(f128(x37241),x37242),f159(x37241,x37243,x37244)),f159(x37241,f317(f317(f23(a897),x37243),x37242),x37244))
% 94.68/94.44 [3730]E(f317(f317(f299(x37301),x37302),f317(f317(f299(x37301),x37303),x37304)),f317(f317(f299(x37301),x37303),f317(f317(f299(x37301),x37302),x37304)))
% 94.68/94.44 [3734]E(f317(f317(f144(x37341,x37342),x37343),f104(x37341,x37344)),f104(x37342,f317(f317(f144(x37341,x37342),x37343),x37344)))
% 94.68/94.44 [3750]E(f317(f158(x37501),f317(f317(f144(x37502,x37501),x37503),x37504)),f317(f317(f144(x37502,x37501),x37503),f317(f158(x37502),x37504)))
% 94.68/94.44 [3751]E(f317(f317(f144(x37511,x37512),x37513),f317(f161(x37511),x37514)),f317(f161(x37512),f317(f317(f144(x37511,x37512),x37513),x37514)))
% 94.68/94.44 [3766]E(f317(f317(f165(x37661),f317(a102,x37662)),f317(f317(f141(x37661),x37663),x37664)),f317(f317(f141(x37661),x37663),f317(f317(f165(x37661),x37662),x37664)))
% 94.68/94.44 [3769]E(f317(f162(x37691),f317(f317(f144(x37692,x37691),x37693),x37694)),f317(f300(x37692,x37691,x37693),f317(f162(x37692),x37694)))
% 94.68/94.44 [3782]E(f317(f317(f144(x37821,x37822),f317(f16(x37822,x37821),x37823)),x37824),f159(x37822,f317(f179(f898(x37821)),x37824),x37823))
% 94.68/94.44 [3818]E(f17(x38181,x38182,x38183,f317(a3,f317(a102,f317(a20,x38184)))),f317(x38183,x38184))
% 94.68/94.44 [3822]E(f317(f317(f124(x38221),f317(f126(x38221,x38222),x38223)),f317(f126(x38221,x38222),x38224)),f317(f126(x38221,x38222),f317(f317(f124(x38221),x38223),x38224)))
% 94.68/94.44 [3834]E(f142(x38341,f317(f317(f144(x38342,x38341),x38343),f142(x38342,x38344))),f142(x38341,f317(f317(f144(x38342,x38341),x38343),x38344)))
% 94.68/94.44 [3849]E(f317(f276(x38491,x38491),f317(f317(f278(x38492,x38491),x38493),x38494)),f317(f317(f278(x38492,x38491),f317(f276(x38492,x38492),x38493)),x38494))
% 94.68/94.44 [3861]E(f317(f317(f279(x38611,x38612,x38613),x38614),f178(f904(f903(x38612,x38613),a893))),f178(f904(f903(x38611,x38613),a893)))
% 94.68/94.44 [3862]E(f317(f317(f165(x38621),f317(f317(f23(a897),x38622),x38623)),f317(f317(f128(x38621),x38623),x38624)),f317(f317(f128(x38621),x38623),f317(f317(f165(x38621),x38622),x38624)))
% 94.68/94.44 [3881]E(f317(f317(f124(x38811),f159(x38811,x38812,x38813)),f159(x38811,x38814,x38813)),f159(x38811,f317(f317(f74(a897),x38812),x38814),x38813))
% 94.68/94.44 [3882]E(f317(f317(f317(f268(x38821),x38822),x38823),x38824),f317(f242(f904(a89,f904(a893,f900(f899(x38821)))),f903(a89,a89)),f317(f37(x38821),x38822)))
% 94.68/94.44 [3908]E(f32(f904(x39081,a893),f317(f300(x39082,f904(x39081,a893),x39083),x39084)),f317(f317(f35(x39082,f904(x39081,a893)),x39084),x39083))
% 94.68/94.44 [3909]E(f31(f904(x39091,a893),f317(f300(x39092,f904(x39091,a893),x39093),x39094)),f317(f317(f34(x39092,f904(x39091,a893)),x39094),x39093))
% 94.68/94.44 [3910]E(f317(f179(f898(f903(x39101,x39102))),f317(f317(f171(x39101,x39102),x39103),x39104)),f317(f317(f228(a897),f317(f179(f898(x39101)),x39103)),f317(f179(f898(x39102)),x39104)))
% 94.68/94.44 [3912]E(f317(f301(x39121,x39122,x39123),f317(f73(f904(x39122,a893)),x39124)),f317(f73(f904(x39121,a893)),f317(f301(x39121,x39122,x39123),x39124)))
% 94.68/94.44 [3961]E(f317(f301(x39611,x39612,x39613),f317(f252(x39612),x39614)),f317(f252(x39611),f317(f317(f8(x39612,a893,x39611),x39614),x39613)))
% 94.68/94.44 [3979]E(f317(f317(f154(x39791),f317(f317(f124(x39791),x39792),f317(f317(f141(x39791),x39793),x39794))),f317(f179(f898(x39791)),x39792)),x39793)
% 94.68/94.44 [4001]E(f317(f300(x40011,x40012,x40013),f317(f301(x40011,x40012,x40013),x40014)),f317(f317(f92(f904(x40012,a893)),x40014),f317(f300(x40011,x40012,x40013),f232(f904(x40011,a893)))))
% 94.68/94.44 [4020]P1(f317(f317(f319(x40201),f317(x40202,x40203)),f317(f300(x40204,x40201,x40202),f232(f904(x40204,a893)))))
% 94.68/94.44 [4029]E(f19(x40291,x40292,x40293,f317(a3,f317(a102,f317(a20,x40294)))),f317(f317(x40293,x40294),f19(x40291,x40292,x40293,x40294)))
% 94.68/94.44 [4033]E(f317(f317(f124(x40331),f159(x40331,x40332,x40333)),f317(f317(f141(x40331),x40333),x40334)),f317(f317(f141(x40331),x40333),f317(f317(f124(x40331),f159(x40331,x40332,x40333)),x40334)))
% 94.68/94.44 [4035]E(f317(f317(f244(x40351,x40352),f317(f162(x40351),x40353)),f317(f16(f904(x40352,a893),x40351),f317(f162(x40352),x40354))),f317(f162(f903(x40351,x40352)),f54(x40351,x40352,x40353,x40354)))
% 94.68/94.44 [4048]E(f145(x40481,x40482,f317(f317(f141(x40481),x40483),x40484)),f317(f317(f74(a897),f317(f317(f74(a897),f317(x40482,x40483)),f145(x40481,x40482,x40484))),f317(a102,f2(a897))))
% 94.68/94.44 [4062]E(f175(f898(x40621),f317(f317(f141(x40621),x40622),x40623),f317(f317(f7(a897,f898(x40621),f898(x40621)),f128(x40621)),x40623),x40624),f317(f317(f128(x40621),x40624),f317(f317(f141(x40621),x40622),x40623)))
% 94.68/94.44 [4063]P24(x40631,f903(x40632,x40631),f321(x40633,x40634,x40632,x40631),f317(f317(f34(x40632,f904(x40631,a893)),x40634),x40633))
% 94.68/94.44 [4072]E(f317(f317(f23(f904(x40721,a893)),f317(f317(f23(f904(x40721,a893)),x40722),x40723)),f317(f317(f299(x40721),x40724),f178(f904(x40721,a893)))),f317(f317(f23(f904(x40721,a893)),x40722),f317(f317(f299(x40721),x40724),x40723)))
% 94.68/94.44 [4085]E(f317(f317(f173(f904(x40851,x40852),f904(x40851,x40852)),x40853),f67(x40852,x40852,x40851,x40854)),f67(x40852,x40852,x40851,f317(f317(f173(x40852,x40852),x40853),x40854)))
% 94.68/94.44 [4156]E(f317(f317(f317(f173(f898(x41561),f898(x41561)),x41562),f157(x41561)),f317(f317(f317(f173(f898(x41561),f898(x41561)),x41563),f157(x41561)),x41564)),f317(f317(f317(f173(f898(x41561),f898(x41561)),f317(f317(f74(a897),x41562),x41563)),f157(x41561)),x41564))
% 94.68/94.44 [4241]P1(f317(f317(f224(f904(x42411,a893)),f317(f162(x42411),f317(f317(f149(x42411,x42412),x42413),x42414))),f317(f317(f299(x42411),x42414),f317(f162(x42411),x42412))))
% 94.68/94.44 [4273]E(f317(f317(f34(f904(x42731,a893),f904(f903(x42731,x42732),a893)),x42733),f317(f317(f7(f904(x42731,a893),f904(x42731,f904(x42732,a893)),f904(f903(x42731,x42732),a893)),f244(x42731,x42732)),x42734)),f317(f317(f244(x42731,x42732),f31(f904(x42731,a893),x42733)),x42734))
% 94.68/94.44 [4311]E(f199(x43111,x43112,x43113,f317(f67(x43112,f904(a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(x43112))))),x43111,f198(x43112)),x43114)),f200(x43111,x43112,x43114,x43113))
% 94.68/94.44 [4326]E(f195(x43261,x43262,x43263,f317(f67(x43262,f904(a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(f900(x43262)))))),x43261,f194(x43262)),x43264)),f196(x43261,x43262,x43264,x43263))
% 94.68/94.44 [4331]P1(f317(f60(x43311,x43312,x43313,x43314,f178(f904(x43311,a893))),x43314))
% 94.68/94.44 [4370]E(f317(f317(f34(x43701,f904(x43702,a893)),x43703),f317(f317(f7(x43701,f904(x43702,a893),f904(x43702,a893)),f317(f317(f8(x43702,f904(f904(x43702,a893),f904(x43702,a893)),x43701),f299(x43702)),x43704)),f178(f904(x43702,a893)))),f317(f300(x43701,x43702,x43704),x43703))
% 94.68/94.44 [4377]P1(f317(f317(f224(f904(x43771,a893)),f317(f274(x43772,x43771),f317(f317(f92(f904(f903(x43772,x43771),a893)),x43773),x43774))),f317(f317(f92(f904(x43771,a893)),f317(f274(x43772,x43771),x43773)),f317(f274(x43772,x43771),x43774))))
% 94.68/94.44 [4378]P1(f317(f317(f224(f904(x43781,a893)),f317(f254(x43781,x43782),f317(f317(f92(f904(f903(x43781,x43782),a893)),x43783),x43784))),f317(f317(f92(f904(x43781,a893)),f317(f254(x43781,x43782),x43783)),f317(f254(x43781,x43782),x43784))))
% 94.68/94.44 [4438]P1(f317(f317(f224(f904(f903(x44381,x44382),a893)),f317(f300(x44382,f903(x44381,x44382),f321(x44383,x44384,x44381,x44382)),f317(f317(f34(x44381,f904(x44382,a893)),x44384),x44383))),f317(f317(f244(x44381,x44382),x44384),x44383)))
% 94.68/94.44 [4439]E(f317(f108(x44391,f903(x44391,x44392),x44393),f317(f317(f8(f904(x44392,f899(f903(x44391,x44392))),f899(f903(x44391,x44392)),x44391),f108(x44392,f903(x44391,x44392),x44394)),f317(f317(f8(f904(x44392,f903(x44391,x44392)),f904(x44392,f899(f903(x44391,x44392))),x44391),f317(f8(f903(x44391,x44392),f899(f903(x44391,x44392)),x44392),f119(f903(x44391,x44392)))),f242(x44391,x44392)))),f121(x44391,x44392,x44393,x44394))
% 94.68/94.44 [4440]E(f266(x44401,x44402,x44403,f317(f67(x44402,f904(a89,f904(a89,f904(f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x44402)))),f903(a89,a89))))),x44401,f268(x44402)),x44404)),f269(x44401,x44402,x44404,x44403))
% 94.68/94.44 [4480]E(f79(f903(x44801,x44802),f317(f247(x44801,x44802,a893),f317(f317(f7(x44801,f904(x44802,a893),f904(x44802,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x44802,a893),f904(x44802,a893)),x44801),f8(a893,a893,x44802)),f317(f317(f8(a893,f904(a893,a893),x44801),a315),f317(a314,x44803)))),f317(a314,x44804)))),f317(f317(f242(x44801,x44802),x44803),x44804))
% 94.68/94.44 [4481]E(f84(f903(x44811,x44812),f317(f247(x44811,x44812,a893),f317(f317(f7(x44811,f904(x44812,a893),f904(x44812,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x44812,a893),f904(x44812,a893)),x44811),f8(a893,a893,x44812)),f317(f317(f8(a893,f904(a893,a893),x44811),a315),f317(a314,x44813)))),f317(a314,x44814)))),f317(f317(f242(x44811,x44812),x44813),x44814))
% 94.68/94.44 [4552]E(f317(f317(f247(f898(x45521),f898(x45521),f903(f898(x45521),f898(x45521))),f317(f317(f18(f898(x45521),f904(f898(x45521),f903(f898(x45521),f898(x45521))),f904(f898(x45521),f903(f898(x45521),f898(x45521)))),f317(f317(f8(f904(f898(x45521),f904(f903(f898(x45521),f898(x45521)),f903(f898(x45521),f898(x45521)))),f904(f904(f898(x45521),f903(f898(x45521),f898(x45521))),f904(f898(x45521),f903(f898(x45521),f898(x45521)))),f898(x45521)),f18(f898(x45521),f903(f898(x45521),f898(x45521)),f903(f898(x45521),f898(x45521)))),f317(f317(f8(f904(f898(x45521),f903(f898(x45521),f898(x45521))),f904(f898(x45521),f904(f903(f898(x45521),f898(x45521)),f903(f898(x45521),f898(x45521)))),f898(x45521)),f317(f8(f903(f898(x45521),f898(x45521)),f904(f903(f898(x45521),f898(x45521)),f903(f898(x45521),f898(x45521))),f898(x45521)),f317(f86(f903(f898(x45521),f898(x45521))),f317(x45522,x45523)))),f317(f317(f8(f898(x45521),f904(f898(x45521),f903(f898(x45521),f898(x45521))),f898(x45521)),f242(f898(x45521),f898(x45521))),f317(f141(x45521),x45523))))),f317(f317(f7(f898(x45521),f904(f898(x45521),f898(x45521)),f904(f898(x45521),f903(f898(x45521),f898(x45521)))),f317(f317(f8(f904(f898(x45521),f903(f898(x45521),f898(x45521))),f904(f904(f898(x45521),f898(x45521)),f904(f898(x45521),f903(f898(x45521),f898(x45521)))),f898(x45521)),f8(f898(x45521),f903(f898(x45521),f898(x45521)),f898(x45521))),f242(f898(x45521),f898(x45521)))),f317(f141(x45521),x45523)))),f156(x45521,x45522,x45524)),f156(x45521,x45522,f317(f317(f141(x45521),x45523),x45524)))
% 94.68/94.44 [3798]E(f317(f317(f165(x37981),x37982),f317(f317(f165(x37981),x37983),x37984)),f317(f317(f165(x37981),f317(f317(f228(a897),x37982),x37983)),x37984))
% 94.68/94.44 [3799]E(f317(f317(f128(x37991),x37992),f317(f317(f128(x37991),x37993),x37994)),f317(f317(f128(x37991),f317(f317(f74(a897),x37992),x37993)),x37994))
% 94.68/94.44 [3810]E(f317(f317(f124(x38101),f317(f317(f141(x38101),x38102),x38103)),x38104),f317(f317(f141(x38101),x38102),f317(f317(f124(x38101),x38103),x38104)))
% 94.68/94.44 [3811]E(f317(f317(f124(x38111),f317(f317(f124(x38111),x38112),x38113)),x38114),f317(f317(f124(x38111),x38112),f317(f317(f124(x38111),x38113),x38114)))
% 94.68/94.44 [3892]E(f317(f317(f154(x38921),f317(f317(f141(x38921),x38922),x38923)),x38924),f175(x38921,x38922,f317(f154(x38921),x38923),x38924))
% 94.68/94.44 [3901]E(f317(f317(f173(x39011,x39011),x39012),f317(f317(f173(x39011,x39011),x39013),x39014)),f317(f317(f173(x39011,x39011),f317(f317(f75(a897),x39013),x39012)),x39014))
% 94.68/94.44 [3928]E(f317(f317(f91(f904(x39281,a893)),x39282),f317(f317(f299(x39281),x39283),x39284)),f317(f317(f299(x39281),x39283),f317(f317(f91(f904(x39281,a893)),x39282),x39284)))
% 94.68/94.44 [3943]E(f317(f317(f317(f173(x39431,x39431),x39432),x39433),f317(x39433,x39434)),f317(x39433,f317(f317(f317(f173(x39431,x39431),x39432),x39433),x39434)))
% 94.68/94.44 [3952]E(f317(f317(f279(x39521,x39522,x39523),f178(f904(f903(x39521,x39522),a893))),x39524),f178(f904(f903(x39521,x39523),a893)))
% 94.68/94.44 [3966]E(f317(f317(f91(f904(x39661,a893)),f317(f317(f299(x39661),x39662),x39663)),x39664),f317(f317(f299(x39661),x39662),f317(f317(f91(f904(x39661,a893)),x39663),x39664)))
% 94.68/94.44 [3986]E(f317(f29(f903(x39861,x39862)),f317(f317(f244(x39861,x39862),x39863),f317(f16(f904(x39862,a893),x39861),x39864))),f317(f317(f75(a897),f317(f29(x39861),x39863)),f317(f29(x39862),x39864)))
% 94.68/94.44 [3992]E(f317(f317(f92(f904(x39921,a893)),f317(f317(f299(x39921),x39922),x39923)),f317(f317(f299(x39921),x39922),x39924)),f317(f317(f299(x39921),x39922),f317(f317(f92(f904(x39921,a893)),x39923),x39924)))
% 94.68/94.44 [4005]E(f317(f317(f91(f904(x40051,a893)),x40052),f317(f317(f91(f904(x40051,a893)),x40053),x40054)),f317(f317(f91(f904(x40051,a893)),x40053),f317(f317(f91(f904(x40051,a893)),x40052),x40054)))
% 94.68/94.44 [4006]E(f317(f317(f92(f904(x40061,a893)),x40062),f317(f317(f92(f904(x40061,a893)),x40063),x40064)),f317(f317(f92(f904(x40061,a893)),x40063),f317(f317(f92(f904(x40061,a893)),x40062),x40064)))
% 94.68/94.44 [4016]E(f58(x40161,x40162,f317(f317(f8(x40162,f904(x40162,x40162),x40161),x40163),x40164)),f317(f59(x40162,x40161,x40163),x40164))
% 94.68/94.44 [4025]E(f169(x40251,f317(f317(f144(f898(x40252),f898(x40251)),f317(f144(x40252,x40251),x40253)),x40254)),f317(f317(f144(f898(x40252),f898(x40251)),f317(f144(x40252,x40251),x40253)),f169(x40252,x40254)))
% 94.68/94.44 [4045]E(f317(f132(f898(x40451),f898(x40451),f124(x40451),f103(x40451)),f317(f317(f144(x40452,f898(x40451)),x40453),x40454)),f153(x40452,x40451,x40453,x40454))
% 94.68/94.44 [4103]E(f317(f67(x41031,x41031,x41031,f317(f317(f173(x41031,x41031),x41032),x41033)),f317(f317(f173(x41031,x41031),x41034),x41033)),f317(f317(f173(x41031,x41031),f317(f317(f74(a897),x41032),x41034)),x41033))
% 94.68/94.44 [4126]E(f317(f317(f92(f904(x41261,a893)),f317(f317(f23(f904(x41261,a893)),x41262),x41263)),f317(f317(f23(f904(x41261,a893)),x41262),x41264)),f317(f317(f23(f904(x41261,a893)),x41262),f317(f317(f91(f904(x41261,a893)),x41263),x41264)))
% 94.68/94.44 [4127]E(f317(f317(f91(f904(x41271,a893)),f317(f317(f23(f904(x41271,a893)),x41272),x41273)),f317(f317(f23(f904(x41271,a893)),x41272),x41274)),f317(f317(f23(f904(x41271,a893)),x41272),f317(f317(f92(f904(x41271,a893)),x41273),x41274)))
% 94.68/94.44 [4128]E(f317(f317(f92(f904(x41281,a893)),f317(f317(f91(f904(x41281,a893)),x41282),x41283)),f317(f317(f91(f904(x41281,a893)),x41282),x41284)),f317(f317(f91(f904(x41281,a893)),x41282),f317(f317(f92(f904(x41281,a893)),x41283),x41284)))
% 94.68/94.44 [4129]E(f317(f317(f23(f904(x41291,a893)),f317(f317(f92(f904(x41291,a893)),x41292),x41293)),f317(f317(f92(f904(x41291,a893)),x41292),x41294)),f317(f317(f92(f904(x41291,a893)),x41292),f317(f317(f23(f904(x41291,a893)),x41293),x41294)))
% 94.68/94.44 [4130]E(f317(f317(f91(f904(x41301,a893)),f317(f317(f92(f904(x41301,a893)),x41302),x41303)),f317(f317(f92(f904(x41301,a893)),x41302),x41304)),f317(f317(f92(f904(x41301,a893)),x41302),f317(f317(f91(f904(x41301,a893)),x41303),x41304)))
% 94.68/94.44 [4135]E(f317(f29(f903(x41351,x41352)),f317(f317(f244(x41351,x41352),f317(f317(f299(x41351),x41353),f178(f904(x41351,a893)))),f317(f16(f904(x41352,a893),x41351),x41354))),f317(f29(x41352),x41354))
% 94.68/94.44 [4170]E(f317(f317(f35(x41701,f904(x41702,a893)),x41703),f317(f317(f8(f904(x41702,a893),f904(x41702,a893),x41701),f73(f904(x41702,a893))),x41704)),f317(f73(f904(x41702,a893)),f317(f317(f34(x41701,f904(x41702,a893)),x41703),x41704)))
% 94.68/94.44 [4171]E(f317(f317(f34(x41711,f904(x41712,a893)),x41713),f317(f317(f8(f904(x41712,a893),f904(x41712,a893),x41711),f73(f904(x41712,a893))),x41714)),f317(f73(f904(x41712,a893)),f317(f317(f35(x41711,f904(x41712,a893)),x41713),x41714)))
% 94.68/94.44 [4187]E(f317(f317(f279(x41871,x41871,x41871),f317(f317(f173(f903(x41871,x41871),a893),x41872),x41873)),f317(f317(f173(f903(x41871,x41871),a893),x41874),x41873)),f317(f317(f173(f903(x41871,x41871),a893),f317(f317(f74(a897),x41872),x41874)),x41873))
% 94.68/94.44 [4217]E(f317(f317(f35(x42171,f904(f904(x42172,a893),a893)),x42173),f317(f317(f8(f904(x42172,a893),f904(f904(x42172,a893),a893),x42171),f298(x42172)),x42174)),f317(f298(x42172),f317(f317(f35(x42171,f904(x42172,a893)),x42173),x42174)))
% 94.68/94.44 [4246]E(f317(f317(f34(f904(x42461,a893),f904(x42462,a893)),x42463),f317(f317(f7(f904(x42461,a893),f904(x42461,f904(x42462,a893)),f904(x42462,a893)),f34(x42461,f904(x42462,a893))),x42464)),f317(f317(f34(x42461,f904(x42462,a893)),f31(f904(x42461,a893),x42463)),x42464))
% 94.68/94.44 [4247]E(f317(f317(f35(f904(x42471,a893),f904(x42472,a893)),x42473),f317(f317(f7(f904(x42471,a893),f904(x42471,f904(x42472,a893)),f904(x42472,a893)),f35(x42471,f904(x42472,a893))),x42474)),f317(f317(f35(x42471,f904(x42472,a893)),f31(f904(x42471,a893),x42473)),x42474))
% 94.68/94.44 [4252]E(f317(f317(f144(x42521,x42522),x42523),f317(f132(f898(x42521),f898(x42521),f124(x42521),f103(x42521)),x42524)),f317(f132(f898(x42522),f898(x42522),f124(x42522),f103(x42522)),f317(f317(f144(f898(x42521),f898(x42522)),f317(f144(x42521,x42522),x42523)),x42524)))
% 94.68/94.44 [4254]E(f175(f898(x42541),f103(x42541),f317(f317(f8(f898(x42541),f898(x42541),a897),f317(f141(x42541),x42542)),f317(f317(f7(a897,f898(x42541),f898(x42541)),f165(x42541)),x42543)),x42544),f317(f317(f165(x42541),x42544),f317(f317(f141(x42541),x42542),x42543)))
% 94.68/94.44 [4292]P1(f317(f317(f224(f904(x42921,a893)),f317(f300(x42922,x42921,x42923),f317(f301(x42922,x42921,x42923),x42924))),x42924))
% 94.68/94.44 [4294]E(f317(f300(f903(x42941,x42942),f903(x42942,x42941),f317(f247(x42941,x42942,f903(x42942,x42941)),f317(f7(x42942,x42941,f903(x42942,x42941)),f242(x42942,x42941)))),f317(f317(f244(x42941,x42942),x42943),f317(f16(f904(x42942,a893),x42941),x42944))),f317(f317(f244(x42942,x42941),x42944),f317(f16(f904(x42941,a893),x42942),x42943)))
% 94.68/94.44 [4303]E(f317(f317(f34(x43031,f904(x43032,a893)),x43033),f317(f317(f8(f904(x43031,a893),f904(x43032,a893),x43031),f275(x43031,x43032,x43034)),f317(f317(f7(x43031,f904(x43031,a893),f904(x43031,a893)),f299(x43031)),f178(f904(x43031,a893))))),f317(f275(x43031,x43032,x43034),x43033))
% 94.68/94.44 [4304]E(f317(f317(f34(x43041,f904(x43042,a893)),x43043),f317(f317(f8(f904(x43041,a893),f904(x43042,a893),x43041),f301(x43042,x43041,x43044)),f317(f317(f7(x43041,f904(x43041,a893),f904(x43041,a893)),f299(x43041)),f178(f904(x43041,a893))))),f317(f301(x43042,x43041,x43044),x43043))
% 94.68/94.44 [4391]E(f317(f317(f92(f904(x43911,a893)),f317(f317(f92(f904(x43911,a893)),f317(f317(f91(f904(x43911,a893)),x43912),x43913)),f317(f317(f91(f904(x43911,a893)),x43913),x43914))),f317(f317(f91(f904(x43911,a893)),x43914),x43912)),f317(f317(f91(f904(x43911,a893)),f317(f317(f91(f904(x43911,a893)),f317(f317(f92(f904(x43911,a893)),x43912),x43913)),f317(f317(f92(f904(x43911,a893)),x43913),x43914))),f317(f317(f92(f904(x43911,a893)),x43914),x43912)))
% 94.68/94.44 [4454]E(f317(f132(f898(x44541),f898(x44541),f124(x44541),f103(x44541)),f317(f317(f144(x44542,f898(x44541)),f317(f317(f7(x44542,f898(x44541),f898(x44541)),f317(f317(f8(x44541,f904(f898(x44541),f898(x44541)),x44542),f141(x44541)),x44543)),f103(x44541))),x44544)),f317(f317(f144(x44542,x44541),x44543),x44544))
% 94.68/94.44 [4464]E(f317(f317(f80(a1,x44641),f317(f94(a1),f317(f317(f74(a1),x44642),a87))),f317(f317(f18(a1,x44641,x44641),f317(f317(f7(a1,x44641,f904(x44641,x44641)),f317(f317(f8(a893,f904(x44641,f904(x44641,x44641)),a1),f86(x44641)),a183)),x44643)),f317(f317(f8(a897,x44641,a1),x44644),a95))),f175(x44641,x44643,x44644,f317(f94(a897),x44642)))
% 94.68/94.44 [4495]E(f317(f252(x44951),f317(f317(f8(f904(x44952,a893),a893,x44951),f81(x44952)),f317(f317(f8(f904(x44952,a893),f904(x44952,a893),x44951),f317(f18(x44952,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44952),a315),f317(f317(f7(x44952,f904(x44952,a893),a893),f319(x44952)),x44953)))),f317(f7(x44952,x44951,a893),x44954)))),f317(f275(x44952,x44951,f317(f252(f903(x44952,x44951)),f317(f247(x44952,x44951,a893),x44954))),x44953))
% 94.68/94.44 [4630]~P1(f317(f317(f178(f904(x46301,f904(x46302,a893))),x46303),x46304))
% 94.68/94.44 [3955]E(f317(f317(f154(x39551),f317(f317(f124(x39551),x39552),x39553)),f317(f317(f74(a897),f317(f179(f898(x39551)),x39552)),x39554)),f317(f317(f154(x39551),x39553),x39554))
% 94.68/94.44 [3960]E(f317(f317(f128(x39601),x39602),f317(f317(f165(x39601),f317(f317(f74(a897),x39603),x39602)),x39604)),f317(f317(f165(x39601),x39603),f317(f317(f128(x39601),x39602),x39604)))
% 94.68/94.44 [4060]E(f317(f317(f91(f904(x40601,a893)),f317(f274(x40602,x40601),x40603)),f317(f274(x40602,x40601),x40604)),f317(f274(x40602,x40601),f317(f317(f91(f904(f903(x40602,x40601),a893)),x40603),x40604)))
% 94.68/94.44 [4061]E(f317(f317(f91(f904(x40611,a893)),f317(f254(x40611,x40612),x40613)),f317(f254(x40611,x40612),x40614)),f317(f254(x40611,x40612),f317(f317(f91(f904(f903(x40611,x40612),a893)),x40613),x40614)))
% 94.68/94.44 [4066]E(f317(f317(f23(f904(x40661,a893)),f317(f317(f92(f904(x40661,a893)),x40662),x40663)),x40664),f317(f317(f92(f904(x40661,a893)),x40662),f317(f317(f23(f904(x40661,a893)),x40663),x40664)))
% 94.68/94.44 [4067]E(f317(f317(f91(f904(x40671,a893)),f317(f317(f91(f904(x40671,a893)),x40672),x40673)),x40674),f317(f317(f91(f904(x40671,a893)),x40672),f317(f317(f91(f904(x40671,a893)),x40673),x40674)))
% 94.68/94.44 [4068]E(f317(f317(f92(f904(x40681,a893)),f317(f317(f92(f904(x40681,a893)),x40682),x40683)),x40684),f317(f317(f92(f904(x40681,a893)),x40682),f317(f317(f92(f904(x40681,a893)),x40683),x40684)))
% 94.68/94.44 [4105]E(f317(f317(f91(f904(f903(x41051,x41052),a893)),f317(f276(x41052,x41051),x41053)),f317(f276(x41052,x41051),x41054)),f317(f276(x41052,x41051),f317(f317(f91(f904(f903(x41052,x41051),a893)),x41053),x41054)))
% 94.68/94.44 [4106]E(f317(f317(f92(f904(f903(x41061,x41062),a893)),f317(f276(x41062,x41061),x41063)),f317(f276(x41062,x41061),x41064)),f317(f276(x41062,x41061),f317(f317(f92(f904(f903(x41062,x41061),a893)),x41063),x41064)))
% 94.68/94.44 [4119]E(f317(f317(f91(f904(x41191,f904(x41192,a893))),f233(x41192,x41191,x41193)),f233(x41192,x41191,x41194)),f233(x41192,x41191,f317(f317(f91(f904(x41192,f904(x41191,a893))),x41193),x41194)))
% 94.68/94.44 [4120]E(f317(f317(f92(f904(x41201,f904(x41202,a893))),f233(x41202,x41201,x41203)),f233(x41202,x41201,x41204)),f233(x41202,x41201,f317(f317(f92(f904(x41202,f904(x41201,a893))),x41203),x41204)))
% 94.68/94.44 [4174]E(f317(f317(f91(f904(x41741,a893)),f317(f317(f23(f904(x41741,a893)),x41742),x41743)),f317(f317(f23(f904(x41741,a893)),x41744),x41743)),f317(f317(f23(f904(x41741,a893)),f317(f317(f91(f904(x41741,a893)),x41742),x41744)),x41743))
% 94.68/94.44 [4175]E(f317(f317(f92(f904(x41751,a893)),f317(f317(f91(f904(x41751,a893)),x41752),x41753)),f317(f317(f91(f904(x41751,a893)),x41754),x41753)),f317(f317(f91(f904(x41751,a893)),f317(f317(f92(f904(x41751,a893)),x41752),x41754)),x41753))
% 94.68/94.44 [4176]E(f317(f317(f23(f904(x41761,a893)),f317(f317(f92(f904(x41761,a893)),x41762),x41763)),f317(f317(f92(f904(x41761,a893)),x41764),x41763)),f317(f317(f92(f904(x41761,a893)),f317(f317(f23(f904(x41761,a893)),x41762),x41764)),x41763))
% 94.68/94.44 [4177]E(f317(f317(f91(f904(x41771,a893)),f317(f317(f92(f904(x41771,a893)),x41772),x41773)),f317(f317(f92(f904(x41771,a893)),x41774),x41773)),f317(f317(f92(f904(x41771,a893)),f317(f317(f91(f904(x41771,a893)),x41772),x41774)),x41773))
% 94.68/94.44 [4178]E(f317(f317(f23(f904(x41781,a893)),f317(f317(f92(f904(x41781,a893)),x41782),x41783)),f317(f317(f92(f904(x41781,a893)),x41784),x41783)),f317(f317(f23(f904(x41781,a893)),f317(f317(f92(f904(x41781,a893)),x41782),x41783)),x41784))
% 94.68/94.44 [4190]E(f317(f317(f23(f904(x41901,a893)),f317(f317(f23(f904(x41901,a893)),x41902),f317(f317(f299(x41901),x41903),f178(f904(x41901,a893))))),x41904),f317(f317(f23(f904(x41901,a893)),x41902),f317(f317(f299(x41901),x41903),x41904)))
% 94.68/94.44 [4243]E(f317(f317(f91(f904(x42431,a893)),f317(f317(f299(x42431),x42432),f317(f317(f299(x42431),x42433),f178(f904(x42431,a893))))),f317(f271(x42431),x42434)),f317(f271(x42431),f317(f317(f299(f903(x42431,x42431)),f317(f317(f242(x42431,x42431),x42432),x42433)),x42434)))
% 94.68/94.44 [4268]E(f317(f317(f34(a897,f904(x42681,a893)),f317(f291(a897),x42682)),f317(f317(f8(a897,f904(x42681,a893),a897),x42683),f317(f317(f7(a897,a897,a897),f74(a897)),x42684))),f317(f317(f34(a897,f904(x42681,a893)),f293(a897,x42684,f317(f317(f74(a897),x42682),x42684))),x42683))
% 94.68/94.44 [4269]E(f164(x42691,f317(f275(x42691,x42691,x42692),f317(f317(f299(x42691),x42693),f178(f904(x42691,a893)))),f317(f275(f898(x42691),f898(x42691),f148(x42691,x42692)),f317(f317(f299(f898(x42691)),x42694),f178(f904(f898(x42691),a893))))),f317(f275(f898(x42691),f898(x42691),f148(x42691,x42692)),f317(f317(f299(f898(x42691)),f317(f317(f141(x42691),x42693),x42694)),f178(f904(f898(x42691),a893)))))
% 94.68/94.44 [4333]E(f317(f252(x43331),f317(f317(f7(x43331,f904(x43332,a893),a893),f317(f317(f8(x43332,f904(f904(x43332,a893),a893),x43331),f319(x43332)),x43333)),x43334)),f317(f301(x43331,x43332,x43333),x43334))
% 94.68/94.44 [4423]E(f317(f252(x44231),f317(f317(f7(x44231,f904(f903(x44232,x44231),a893),a893),f317(f317(f8(f903(x44232,x44231),f904(f904(f903(x44232,x44231),a893),a893),x44231),f319(f903(x44232,x44231))),f317(f242(x44232,x44231),x44233))),x44234)),f317(f275(x44232,x44231,x44234),f317(f317(f299(x44232),x44233),f178(f904(x44232,a893)))))
% 94.68/94.44 [4437]E(f317(f317(f144(f903(x44371,a897),x44371),f241(x44371,a897)),f317(f126(f903(x44371,a897),f317(f317(f8(a897,a893,f903(x44371,a897)),x44372),f317(f317(f8(a897,a897,f903(x44371,a897)),a102),f246(x44371,a897)))),f317(f317(f171(x44371,a897),x44373),x44374))),f317(f317(f144(f903(x44371,a897),x44371),f241(x44371,a897)),f317(f126(f903(x44371,a897),f317(f317(f8(a897,a893,f903(x44371,a897)),x44372),f246(x44371,a897))),f317(f317(f171(x44371,a897),x44373),f317(f317(f144(a897,a897),a102),x44374)))))
% 94.68/94.44 [4446]P1(f317(f317(f224(f904(f904(x44461,a893),a893)),f317(f317(f34(x44462,f904(f904(x44461,a893),a893)),x44463),f317(f317(f8(f904(x44461,a893),f904(f904(x44461,a893),a893),x44462),f298(x44461)),x44464))),f317(f298(x44461),f317(f317(f34(x44462,f904(x44461,a893)),x44463),x44464))))
% 94.68/94.44 [4487]E(f317(f317(f80(a1,x44871),f317(f94(a1),f317(f317(f74(a1),x44872),a87))),f317(f317(f18(a1,x44871,x44871),f317(f317(f7(a1,x44871,f904(x44871,x44871)),f317(f317(f8(a893,f904(x44871,f904(x44871,x44871)),a1),f86(x44871)),a183)),x44873)),f317(f317(f18(a1,x44871,x44871),f317(f317(f8(a897,f904(x44871,x44871),a1),x44874),a95)),f317(f317(f8(a897,x44871,a1),f174(x44871,x44873,x44874)),a95)))),f317(f174(x44871,x44873,x44874),f317(f94(a897),x44872)))
% 94.68/94.44 [4511]E(f317(f252(f903(x45111,x45112)),f317(f247(x45111,x45112,a893),f317(f317(f7(x45111,f904(x45112,a893),f904(x45112,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x45112,a893),f904(x45112,a893)),x45111),f8(a893,a893,x45112)),f317(f317(f8(a893,f904(a893,a893),x45111),a315),f317(f317(f7(x45111,f904(x45111,a893),a893),f319(x45111)),x45113)))),f317(f317(f7(x45112,f904(x45112,a893),a893),f319(x45112)),x45114)))),f219(x45111,x45112,x45113,x45114))
% 94.68/94.44 [4547]E(f317(f317(f34(x45471,f904(f903(x45471,x45472),a893)),x45473),f317(f317(f18(x45471,f904(x45472,f904(f903(x45471,x45472),a893)),f904(f903(x45471,x45472),a893)),f317(f317(f8(f904(x45472,a893),f904(f904(x45472,f904(f903(x45471,x45472),a893)),f904(f903(x45471,x45472),a893)),x45471),f34(x45472,f904(f903(x45471,x45472),a893))),x45474)),f317(f317(f7(x45471,f904(f903(x45471,x45472),a893),f904(x45472,f904(f903(x45471,x45472),a893))),f317(f317(f8(f904(x45472,f904(f904(f903(x45471,x45472),a893),f904(f903(x45471,x45472),a893))),f904(f904(f903(x45471,x45472),a893),f904(x45472,f904(f903(x45471,x45472),a893))),x45471),f7(x45472,f904(f903(x45471,x45472),a893),f904(f903(x45471,x45472),a893))),f317(f317(f8(f904(x45472,f903(x45471,x45472)),f904(x45472,f904(f904(f903(x45471,x45472),a893),f904(f903(x45471,x45472),a893))),x45471),f317(f8(f903(x45471,x45472),f904(f904(f903(x45471,x45472),a893),f904(f903(x45471,x45472),a893)),x45472),f299(f903(x45471,x45472)))),f242(x45471,x45472)))),f178(f904(f903(x45471,x45472),a893))))),f317(f317(f244(x45471,x45472),x45473),x45474))
% 94.68/94.44 [4114]E(f317(f317(f124(x41141),f317(f317(f165(x41141),x41142),x41143)),f317(f317(f165(x41141),f317(f317(f23(a897),x41142),f317(f179(f898(x41141)),x41143))),x41144)),f317(f317(f165(x41141),x41142),f317(f317(f124(x41141),x41143),x41144)))
% 94.68/94.44 [4115]E(f317(f317(f124(x41151),f317(f317(f128(x41151),x41152),x41153)),f317(f317(f128(x41151),f317(f317(f23(a897),x41152),f317(f179(f898(x41151)),x41153))),x41154)),f317(f317(f128(x41151),x41152),f317(f317(f124(x41151),x41153),x41154)))
% 94.68/94.44 [4164]E(f317(f317(f74(a897),f317(f317(f75(a897),x41641),x41642)),f317(f317(f74(a897),f317(f317(f75(a897),x41643),x41642)),x41644)),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f74(a897),x41641),x41643)),x41642)),x41644))
% 94.68/94.44 [4309]E(f84(x43091,f317(f317(f7(x43091,x43092,a893),f317(f317(f8(x43092,f904(x43092,a893),x43091),a314),x43093)),x43094)),f317(f85(x43091,x43092,f232(f904(x43091,a893)),x43093),x43094))
% 94.68/94.44 [4357]P1(f317(f317(f224(f904(x43571,a893)),f317(f317(f23(f904(x43571,a893)),f317(f274(x43572,x43571),x43573)),f317(f274(x43572,x43571),x43574))),f317(f274(x43572,x43571),f317(f317(f23(f904(f903(x43572,x43571),a893)),x43573),x43574))))
% 94.68/94.44 [4358]P1(f317(f317(f224(f904(x43581,a893)),f317(f317(f23(f904(x43581,a893)),f317(f254(x43581,x43582),x43583)),f317(f254(x43581,x43582),x43584))),f317(f254(x43581,x43582),f317(f317(f23(f904(f903(x43581,x43582),a893)),x43583),x43584))))
% 94.68/94.44 [4466]E(f317(f317(f74(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x44661),x44662)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x44663),x44664)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),f317(f317(f74(a897),x44661),x44663)),f317(f317(f74(a897),x44662),x44664))),f178(f904(f903(a897,a897),a893))))))
% 94.68/94.44 [4506]E(f317(f317(f75(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x45061),x45062)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x45063),x45064)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),f317(f317(f74(a897),f317(f317(f75(a897),x45061),x45063)),f317(f317(f75(a897),x45062),x45064))),f317(f317(f74(a897),f317(f317(f75(a897),x45061),x45064)),f317(f317(f75(a897),x45062),x45063)))),f178(f904(f903(a897,a897),a893))))))
% 94.68/94.44 [4527]E(f317(f252(x45271),f317(f317(f8(f904(x45272,a893),a893,x45271),f82(x45272)),f317(f317(f8(f904(x45272,a893),f904(x45272,a893),x45271),f317(f18(x45272,a893,a893),f317(f317(f8(a893,f904(a893,a893),x45272),a320),f317(f317(f7(x45272,f904(x45272,a893),a893),f319(x45272)),x45273)))),f317(f317(f7(x45271,f904(x45272,f904(x45271,a893)),f904(x45272,a893)),f317(f317(f8(f904(f904(x45271,a893),a893),f904(f904(x45272,f904(x45271,a893)),f904(x45272,a893)),x45271),f8(f904(x45271,a893),a893,x45272)),f319(x45271))),x45274)))),f317(f317(f35(x45272,f904(x45271,a893)),x45273),x45274))
% 94.68/94.44 [4559]E(f317(f317(f279(x45591,x45591,x45591),f317(f317(f299(f903(x45591,x45591)),f317(f317(f242(x45591,x45591),x45592),x45593)),x45594)),f297(x45591,f317(f317(f299(f903(x45591,x45591)),f317(f317(f242(x45591,x45591),x45592),x45593)),x45594))),f317(f317(f91(f904(f903(x45591,x45591),a893)),f317(f317(f279(x45591,x45591,x45591),x45594),f297(x45591,x45594))),f317(f252(f903(x45591,x45591)),f317(f247(x45591,x45591,a893),f317(f317(f7(x45591,f904(x45591,a893),f904(x45591,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x45591,a893),f904(x45591,a893)),x45591),f8(a893,a893,x45591)),f317(f317(f8(a893,f904(a893,a893),x45591),a315),f317(f317(f7(x45591,f904(f903(x45591,x45591),a893),a893),f317(f317(f8(f903(x45591,x45591),f904(f904(f903(x45591,x45591),a893),a893),x45591),f319(f903(x45591,x45591))),f317(f317(f7(x45591,x45591,f903(x45591,x45591)),f242(x45591,x45591)),x45592))),f297(x45591,x45594))))),f317(f317(f7(x45591,f904(f903(x45591,x45591),a893),a893),f317(f317(f8(f903(x45591,x45591),f904(f904(f903(x45591,x45591),a893),a893),x45591),f319(f903(x45591,x45591))),f317(f242(x45591,x45591),x45593))),f297(x45591,x45594)))))))
% 94.68/94.44 [4359]E(f317(f126(x43591,f317(f317(f18(x43591,a893,a893),f317(f317(f8(a893,f904(a893,a893),x43591),a315),x43592)),x43593)),x43594),f317(f126(x43591,x43593),f317(f126(x43591,x43592),x43594)))
% 94.68/94.44 [4460]E(f317(f317(f124(x44601),f317(f317(f317(f86(f898(x44601)),f317(f317(f319(a897),f2(a897)),x44602)),f317(f317(f141(x44601),x44603),f103(x44601))),f103(x44601))),f166(x44601,x44604,f317(f252(a897),f317(f317(f7(a897,f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),a897),f319(a897)),a102)),x44602)))),f166(x44601,f317(f317(f141(x44601),x44603),x44604),x44602))
% 94.68/94.44 [4555]E(f317(f252(f903(x45551,x45552)),f317(f317(f8(f904(a897,a893),a893,f903(x45551,x45552)),f81(a897)),f317(f317(f7(f903(x45551,x45552),f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),f903(x45551,x45552)),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),f903(x45551,x45552)),f317(f8(a893,f904(a893,a893),a897),a315)),f317(f317(f7(f903(x45551,x45552),f904(a897,f903(x45551,x45552)),f904(a897,a893)),f317(f317(f8(f904(f903(x45551,x45552),a893),f904(f904(a897,f903(x45551,x45552)),f904(a897,a893)),f903(x45551,x45552)),f8(f903(x45551,x45552),a893,a897)),a314)),f317(f317(f18(a897,x45552,f903(x45551,x45552)),f317(f317(f8(x45551,f904(x45552,f903(x45551,x45552)),a897),f242(x45551,x45552)),f317(f154(x45551),x45553))),f317(f154(x45552),x45554)))))),f317(f317(f7(a897,a897,a893),f225(a897)),f317(f317(f228(a897),f317(f179(f898(x45551)),x45553)),f317(f179(f898(x45552)),x45554)))))),f317(f162(f903(x45551,x45552)),f317(f317(f171(x45551,x45552),x45553),x45554)))
% 94.68/94.44 [4479]E(f317(f252(f903(x44791,x44792)),f317(f247(x44791,x44792,a893),f317(f317(f7(x44791,f904(x44792,a893),f904(x44792,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x44792,a893),f904(x44792,a893)),x44791),f8(a893,a893,x44792)),f317(f317(f8(a893,f904(a893,a893),x44791),a315),x44793))),x44794))),f317(f317(f244(x44791,x44792),f317(f252(x44791),x44793)),f317(f16(f904(x44792,a893),x44791),f317(f252(x44792),x44794))))
% 94.68/94.44 [4482]E(f317(f252(f903(x44821,x44822)),f317(f247(x44821,x44822,a893),f317(f317(f18(x44821,f904(x44822,a893),f904(x44822,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x44822,a893),f904(x44822,a893)),x44821),f8(a893,a893,x44822)),f317(f317(f8(a893,f904(a893,a893),x44821),a315),x44823))),x44824))),f317(f317(f244(x44821,x44822),f317(f252(x44821),x44823)),f317(f317(f8(f904(x44822,a893),f904(x44822,a893),x44821),f252(x44822)),x44824)))
% 94.68/94.44 [4494]E(f317(f252(x44941),f317(f317(f8(f904(x44942,a893),a893,x44941),f82(x44942)),f317(f317(f8(f904(x44942,a893),f904(x44942,a893),x44941),f317(f18(x44942,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44942),a320),f317(f317(f7(x44942,f904(x44942,a893),a893),f319(x44942)),x44943)))),x44944))),f317(f317(f35(x44942,f904(x44941,a893)),x44943),f317(f317(f8(f904(x44941,a893),f904(x44941,a893),x44942),f252(x44941)),f317(f7(x44941,x44942,a893),x44944))))
% 94.68/94.44 [4539]E(f317(f317(f144(f903(x45391,a897),x45391),f241(x45391,a897)),f317(f126(f903(x45391,a897),f317(f317(f7(f903(x45391,a897),f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),f903(x45391,a897)),f319(a897)),f246(x45391,a897))),x45392)),f317(f317(f171(x45391,a897),x45393),f129(a897,f317(f292(a897,x45394),f317(f317(f74(a897),x45394),f317(f179(f898(x45391)),x45393))))))),f317(f317(f144(f903(x45391,a897),x45391),f241(x45391,a897)),f317(f126(f903(x45391,a897),f317(f317(f7(f903(x45391,a897),f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),f903(x45391,a897)),f319(a897)),f317(f317(f7(f903(x45391,a897),a897,a897),f317(f317(f8(a897,f904(a897,a897),f903(x45391,a897)),f74(a897)),f246(x45391,a897))),x45394))),x45392)),f317(f317(f171(x45391,a897),x45393),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(x45391)),x45393)))))))
% 94.68/94.44 [4540]E(f317(a102,f317(f317(f223(a897),f317(f179(f898(x45401)),x45402)),f317(f132(a897,f898(x45403),f317(f7(f898(x45403),a897,a897),f317(f317(f8(a897,f904(a897,a897),f898(x45403)),f223(a897)),f317(f317(f7(f898(x45403),a897,a897),f317(f317(f8(a897,f904(a897,a897),f898(x45403)),f23(a897)),f179(f898(x45403)))),f317(a102,f2(a897))))),f2(a897)),f317(f158(f898(x45403)),f317(f126(f898(x45403),f317(f317(f8(a893,a893,f898(x45403)),a312),f317(f317(f7(f898(x45403),f898(x45403),a893),a314),f103(x45403)))),x45404))))),f317(f317(f223(a897),f317(a102,f317(f179(f898(x45401)),x45402))),f317(f132(a897,f898(x45403),f317(f7(f898(x45403),a897,a897),f317(f317(f8(a897,f904(a897,a897),f898(x45403)),f223(a897)),f179(f898(x45403)))),f2(a897)),f317(f158(f898(x45403)),x45404))))
% 94.68/94.44 [4493]E(f317(f317(f124(x44931),f166(x44931,x44932,x44933)),f166(x44931,x44934,f317(f252(a897),f317(f317(f7(a897,f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),a897),f319(a897)),f317(f317(f7(a897,a897,a897),f74(a897)),f317(f179(f898(x44931)),x44932)))),x44933)))),f166(x44931,f317(f317(f124(x44931),x44932),x44934),x44933))
% 94.68/94.44 [4541]E(f31(f904(x45411,a893),f317(f252(f904(x45411,a893)),f317(f317(f8(f904(x45412,a893),a893,f904(x45411,a893)),f81(x45412)),f317(f317(f8(f904(x45412,a893),f904(x45412,a893),f904(x45411,a893)),f317(f18(x45412,a893,a893),f317(f317(f8(a893,f904(a893,a893),x45412),a315),f317(f317(f7(x45412,f904(x45412,a893),a893),f319(x45412)),x45413)))),f317(f317(f7(f904(x45411,a893),f904(x45412,f904(x45411,a893)),f904(x45412,a893)),f317(f317(f8(f904(f904(x45411,a893),a893),f904(f904(x45412,f904(x45411,a893)),f904(x45412,a893)),f904(x45411,a893)),f8(f904(x45411,a893),a893,x45412)),a314)),x45414))))),f317(f317(f34(x45412,f904(x45411,a893)),x45413),x45414))
% 94.68/94.44 [4542]E(f32(f904(x45421,a893),f317(f252(f904(x45421,a893)),f317(f317(f8(f904(x45422,a893),a893,f904(x45421,a893)),f81(x45422)),f317(f317(f8(f904(x45422,a893),f904(x45422,a893),f904(x45421,a893)),f317(f18(x45422,a893,a893),f317(f317(f8(a893,f904(a893,a893),x45422),a315),f317(f317(f7(x45422,f904(x45422,a893),a893),f319(x45422)),x45423)))),f317(f317(f7(f904(x45421,a893),f904(x45422,f904(x45421,a893)),f904(x45422,a893)),f317(f317(f8(f904(f904(x45421,a893),a893),f904(f904(x45422,f904(x45421,a893)),f904(x45422,a893)),f904(x45421,a893)),f8(f904(x45421,a893),a893,x45422)),a314)),x45424))))),f317(f317(f35(x45422,f904(x45421,a893)),x45423),x45424))
% 94.68/94.44 [4549]E(f317(f317(f141(f898(x45491)),f317(f317(f141(x45491),x45492),f317(f132(f898(x45491),f898(x45491),f124(x45491),f103(x45491)),f317(f317(f144(f898(x45491),f898(x45491)),f146(f898(x45491),x45491,f103(x45491),f317(f317(f8(f898(x45491),f904(f898(x45491),f898(x45491)),x45491),f16(f898(x45491),f898(x45491))),f317(f317(f7(x45491,f898(x45491),f898(x45491)),f141(x45491)),f103(x45491))))),x45493)))),f169(x45491,f317(f317(f141(f898(x45491)),x45494),f317(f132(f898(f898(x45491)),f898(f898(x45491)),f124(f898(x45491)),f103(f898(x45491))),f317(f317(f144(f898(x45491),f898(f898(x45491))),f146(f898(f898(x45491)),x45491,f103(f898(x45491)),f317(f16(f904(f898(x45491),f898(f898(x45491))),x45491),f317(f317(f7(f898(x45491),f898(f898(x45491)),f898(f898(x45491))),f141(f898(x45491))),f103(f898(x45491)))))),x45493))))),f169(x45491,f317(f317(f141(f898(x45491)),f317(f317(f141(x45491),x45492),x45494)),x45493)))
% 94.68/94.44 [4556]E(f317(f252(f903(x45561,x45561)),f317(f247(x45561,x45561,a893),f317(f317(f7(x45561,f904(f903(x45562,x45562),a893),f904(x45561,a893)),f317(f317(f8(f904(x45561,f904(f904(f903(x45562,x45562),a893),a893)),f904(f904(f903(x45562,x45562),a893),f904(x45561,a893)),x45561),f7(x45561,f904(f903(x45562,x45562),a893),a893)),f317(f317(f8(f904(x45561,f903(x45562,x45562)),f904(x45561,f904(f904(f903(x45562,x45562),a893),a893)),x45561),f317(f8(f903(x45562,x45562),f904(f904(f903(x45562,x45562),a893),a893),x45561),f319(f903(x45562,x45562)))),f317(f317(f7(x45561,f904(x45561,x45562),f904(x45561,f903(x45562,x45562))),f317(f317(f8(f904(x45562,f903(x45562,x45562)),f904(f904(x45561,x45562),f904(x45561,f903(x45562,x45562))),x45561),f8(x45562,f903(x45562,x45562),x45561)),f317(f317(f8(x45562,f904(x45562,f903(x45562,x45562)),x45561),f242(x45562,x45562)),x45563))),x45563)))),x45564))),f317(f317(f278(x45562,x45561),x45564),x45563))
% 94.68/94.44 [3695]E(f317(f317(f144(x36951,x36952),x36953),f159(x36951,x36954,x36955)),f159(x36952,x36954,f317(x36953,x36955)))
% 94.68/94.44 [4026]E(f120(x40261,x40262,x40263,f116(x40261,x40264,x40265)),f116(x40262,f317(x40263,x40264),f120(x40261,x40262,x40263,x40265)))
% 94.68/94.44 [4258]E(f317(f69(x42581,x42582,x42583,x42584,x42585),x42584),x42585)
% 94.68/94.44 [4310]E(f243(x43101,x43102,x43103,f233(x43102,x43101,x43104),f233(x43103,x43102,x43105)),f233(x43103,x43101,f243(x43103,x43102,x43101,x43105,x43104)))
% 94.68/94.44 [3886]E(f317(f317(f247(x38861,x38862,x38863),x38864),x38865),f317(f317(x38864,f317(f241(x38861,x38862),x38865)),f317(f246(x38861,x38862),x38865)))
% 94.68/94.44 [3920]E(f317(f317(f317(f59(x39201,x39202,x39203),x39204),x39205),f178(f904(x39202,a893))),x39205)
% 94.68/94.44 [4198]E(f317(f67(f898(x41981),f898(x41982),f898(x41983),f317(f144(x41981,x41982),x41984)),f317(f144(x41983,x41981),x41985)),f317(f144(x41983,x41982),f317(f67(x41981,x41982,x41983,x41984),x41985)))
% 94.68/94.44 [4272]E(f79(x42721,f60(x42722,x42721,x42723,x42724,x42725)),f317(f317(f58(x42722,x42721,x42723),x42724),x42725))
% 94.68/94.44 [4306]E(f317(f317(f74(a897),f317(f317(f74(a897),f317(x43061,f317(f241(x43062,x43063),x43064))),f317(x43065,f317(f246(x43062,x43063),x43064)))),f317(a102,f2(a897))),f251(x43062,x43063,x43061,x43065,x43064))
% 94.68/94.44 [3823]E(f317(f317(f165(x38231),x38232),f317(f317(f144(x38233,x38231),x38234),x38235)),f317(f317(f144(x38233,x38231),x38234),f317(f317(f165(x38233),x38232),x38235)))
% 94.68/94.44 [3824]E(f317(f317(f128(x38241),x38242),f317(f317(f144(x38243,x38241),x38244),x38245)),f317(f317(f144(x38243,x38241),x38244),f317(f317(f128(x38243),x38242),x38245)))
% 94.68/94.44 [3855]E(f317(f317(f144(x38551,x38552),x38553),f317(f317(f141(x38551),x38554),x38555)),f317(f317(f141(x38552),f317(x38553,x38554)),f317(f317(f144(x38551,x38552),x38553),x38555)))
% 94.68/94.44 [3916]E(f317(f300(x39161,x39162,x39163),f317(f317(f299(x39161),x39164),x39165)),f317(f317(f299(x39162),f317(x39163,x39164)),f317(f300(x39161,x39162,x39163),x39165)))
% 94.68/94.44 [3944]E(f163(x39441,f317(f317(f141(x39441),x39442),x39443),f317(f317(f141(x39441),x39444),x39445)),f317(f317(f141(x39441),x39442),f317(f317(f141(x39441),x39444),f163(x39441,x39443,x39445))))
% 94.68/94.44 [3981]E(f317(f317(f171(x39811,x39812),f317(f317(f165(x39811),x39813),x39814)),f317(f317(f165(x39812),x39813),x39815)),f317(f317(f165(f903(x39811,x39812)),x39813),f317(f317(f171(x39811,x39812),x39814),x39815)))
% 94.68/94.44 [3982]E(f317(f317(f171(x39821,x39822),f317(f317(f128(x39821),x39823),x39824)),f317(f317(f128(x39822),x39823),x39825)),f317(f317(f128(f903(x39821,x39822)),x39823),f317(f317(f171(x39821,x39822),x39824),x39825)))
% 94.68/94.44 [3991]E(f317(f317(f149(x39911,f317(f317(f141(x39911),x39912),x39913)),f317(a102,x39914)),x39915),f317(f317(f141(x39911),x39912),f317(f317(f149(x39911,x39913),x39914),x39915)))
% 94.68/94.44 [3994]E(f317(f317(f124(x39941),f317(f317(f144(x39942,x39941),x39943),x39944)),f317(f317(f144(x39942,x39941),x39943),x39945)),f317(f317(f144(x39942,x39941),x39943),f317(f317(f124(x39942),x39944),x39945)))
% 94.68/94.44 [3998]E(f317(f317(x39981,x39982),f317(f317(f235(x39983,x39984,x39981),x39982),x39985)),f317(f317(f235(x39983,x39984,x39981),x39982),f317(a102,x39985)))
% 94.68/94.44 [4030]E(f153(x40301,x40302,x40303,f317(f317(f141(x40301),x40304),x40305)),f317(f317(f124(x40302),f317(x40303,x40304)),f153(x40301,x40302,x40303,x40305)))
% 94.68/94.44 [4043]E(f317(f317(f279(x40431,x40432,x40433),f317(f276(x40432,x40431),x40434)),f317(f276(x40433,x40432),x40435)),f317(f276(x40433,x40431),f317(f317(f279(x40433,x40432,x40431),x40435),x40434)))
% 94.68/94.44 [4076]E(f317(f317(f317(f173(f898(x40761),f898(x40761)),x40762),f157(x40761)),f317(f317(f144(x40763,x40761),x40764),x40765)),f317(f317(f144(x40763,x40761),x40764),f317(f317(f317(f173(f898(x40763),f898(x40763)),x40762),f157(x40763)),x40765)))
% 94.68/94.44 [4077]E(f317(f317(f249(x40771,x40772,x40771,x40773),f317(f242(x40772,x40771),x40774)),x40775),f317(x40775,x40774))
% 94.68/94.44 [4100]E(f145(x41001,x41002,f317(f317(f144(x41003,x41001),x41004),x41005)),f145(x41003,f317(f67(x41001,a897,x41003,x41002),x41004),x41005))
% 94.68/94.44 [4163]E(f167(f903(x41631,x41632),f317(f67(x41632,a893,f903(x41631,x41632),x41633),f246(x41631,x41632)),f317(f317(f171(x41631,x41632),x41634),x41635)),f317(f317(f171(x41631,x41632),x41634),f167(x41632,x41633,x41635)))
% 94.68/94.44 [4168]E(f317(f300(x41681,x41682,f317(f317(f8(x41683,x41682,x41681),x41684),x41685)),f232(f904(x41681,a893))),f317(f300(x41683,x41682,x41684),f317(f300(x41681,x41683,x41685),f232(f904(x41681,a893)))))
% 94.68/94.44 [4181]E(f167(f903(x41811,x41812),f317(f67(x41811,a893,f903(x41811,x41812),x41813),f241(x41811,x41812)),f317(f317(f171(x41811,x41812),x41814),x41815)),f317(f317(f171(x41811,x41812),f167(x41811,x41813,x41814)),x41815))
% 94.68/94.44 [4202]E(f317(f317(f91(f904(x42021,a893)),f317(f301(x42021,x42022,x42023),f317(f317(f299(x42022),x42024),f178(f904(x42022,a893))))),f317(f301(x42021,x42022,x42023),x42025)),f317(f301(x42021,x42022,x42023),f317(f317(f299(x42022),x42024),x42025)))
% 94.68/94.44 [4257]E(f317(f317(f124(f903(x42571,x42572)),f317(f317(f144(x42572,f903(x42571,x42572)),f317(f242(x42571,x42572),x42573)),x42574)),f54(x42571,x42572,x42575,x42574)),f54(x42571,x42572,f317(f317(f141(x42571),x42573),x42575),x42574))
% 94.68/94.44 [4259]E(f317(f317(f144(x42591,x42592),x42593),f167(x42591,f317(f67(x42592,a893,x42591,x42594),x42593),x42595)),f167(x42592,x42594,f317(f317(f144(x42591,x42592),x42593),x42595)))
% 94.68/94.44 [4264]E(f317(f132(x42641,x42642,f317(f7(x42642,x42641,x42641),f317(f7(x42641,x42642,x42641),x42643)),x42644),f317(f158(x42642),f317(f158(x42642),x42645))),f317(f132(x42641,x42642,x42643,x42644),x42645))
% 94.68/94.44 [4367]P1(f317(f317(f224(f904(x43671,a893)),f317(f300(x43672,x43671,x43673),f317(f317(f92(f904(x43672,a893)),x43674),x43675))),f317(f317(f92(f904(x43671,a893)),f317(f300(x43672,x43671,x43673),x43674)),f317(f300(x43672,x43671,x43673),x43675))))
% 94.68/94.44 [4368]P1(f317(f317(f224(f904(x43681,a893)),f317(f275(x43682,x43681,x43683),f317(f317(f92(f904(x43682,a893)),x43684),x43685))),f317(f317(f92(f904(x43681,a893)),f317(f275(x43682,x43681,x43683),x43684)),f317(f275(x43682,x43681,x43683),x43685))))
% 94.68/94.44 [4467]E(f317(f246(x44671,x44672),f317(f248(x44673,x44671,x44672,x44672,x44674,f25(x44672)),x44675)),f317(f246(x44673,x44672),x44675))
% 94.68/94.44 [4468]E(f317(f241(x44681,x44682),f317(f248(x44681,x44681,x44683,x44682,f25(x44681),x44684),x44685)),f317(f241(x44681,x44683),x44685))
% 94.68/94.44 [3667]E(f317(f317(f317(f317(f194(x36671),x36672),x36673),x36674),x36675),f182(x36671,x36672))
% 94.68/94.44 [3668]E(f317(f317(f317(f317(f198(x36681),x36682),x36683),x36684),x36685),f189(x36681,x36682))
% 94.68/94.44 [4031]E(f317(f317(f34(x40311,f904(x40312,a893)),f317(f317(f299(x40311),x40313),x40314)),x40315),f317(f317(f91(f904(x40312,a893)),f317(x40315,x40313)),f317(f317(f34(x40311,f904(x40312,a893)),x40314),x40315)))
% 94.68/94.44 [4032]E(f317(f317(f35(x40321,f904(x40322,a893)),f317(f317(f299(x40321),x40323),x40324)),x40325),f317(f317(f92(f904(x40322,a893)),f317(x40325,x40323)),f317(f317(f35(x40321,f904(x40322,a893)),x40324),x40325)))
% 94.68/94.44 [4084]E(f317(f108(x40841,x40842,f317(x40843,x40844)),f317(f317(f7(x40841,a89,f899(x40842)),x40845),x40844)),f317(f187(x40841,x40842,x40843,x40845),x40844))
% 94.68/94.44 [4094]E(f317(f317(f91(f904(x40941,a893)),f317(f300(x40942,x40941,x40943),x40944)),f317(f300(x40942,x40941,x40943),x40945)),f317(f300(x40942,x40941,x40943),f317(f317(f91(f904(x40942,a893)),x40944),x40945)))
% 94.68/94.44 [4095]E(f317(f317(f91(f904(x40951,a893)),f317(f275(x40952,x40951,x40953),x40954)),f317(f275(x40952,x40951,x40953),x40955)),f317(f275(x40952,x40951,x40953),f317(f317(f91(f904(x40952,a893)),x40954),x40955)))
% 94.68/94.44 [4096]E(f317(f317(f23(f904(x40961,a893)),f317(f301(x40961,x40962,x40963),x40964)),f317(f301(x40961,x40962,x40963),x40965)),f317(f301(x40961,x40962,x40963),f317(f317(f23(f904(x40962,a893)),x40964),x40965)))
% 94.68/94.44 [4097]E(f317(f317(f91(f904(x40971,a893)),f317(f301(x40971,x40972,x40973),x40974)),f317(f301(x40971,x40972,x40973),x40975)),f317(f301(x40971,x40972,x40973),f317(f317(f91(f904(x40972,a893)),x40974),x40975)))
% 94.68/94.44 [4098]E(f317(f317(f92(f904(x40981,a893)),f317(f301(x40981,x40982,x40983),x40984)),f317(f301(x40981,x40982,x40983),x40985)),f317(f301(x40981,x40982,x40983),f317(f317(f92(f904(x40982,a893)),x40984),x40985)))
% 94.68/94.44 [4159]E(f317(f317(f149(x41591,f317(f317(f124(x41591),x41592),f317(f317(f141(x41591),x41593),x41594))),f317(f179(f898(x41591)),x41592)),x41595),f317(f317(f124(x41591),x41592),f317(f317(f141(x41591),x41595),x41594)))
% 94.68/94.44 [4166]E(f317(f317(f35(x41661,f904(x41662,a893)),x41663),f317(f317(f8(f904(x41662,a893),f904(x41662,a893),x41661),f317(f299(x41662),x41664)),x41665)),f317(f317(f299(x41662),x41664),f317(f317(f35(x41661,f904(x41662,a893)),x41663),x41665)))
% 94.68/94.44 [4319]E(f317(f317(f144(x43191,x43192),x43193),f317(f126(x43191,f317(f67(x43192,a893,x43191,x43194),x43193)),x43195)),f317(f126(x43192,x43194),f317(f317(f144(x43191,x43192),x43193),x43195)))
% 94.68/94.44 [4325]E(f317(f179(f898(x43251)),f317(f126(x43251,x43252),f317(f317(f144(x43253,x43251),x43254),x43255))),f317(f179(f898(x43253)),f317(f126(x43253,f317(f67(x43251,a893,x43253,x43252),x43254)),x43255)))
% 94.68/94.44 [4532]E(f317(f146(f898(f903(x45321,x45322)),x45322,f103(f903(x45321,x45322)),f317(f317(f7(x45322,f904(f898(x45322),f898(f903(x45321,x45322))),f904(f898(x45322),f898(f903(x45321,x45322)))),f317(f317(f8(f904(f898(f903(x45321,x45322)),f898(f903(x45321,x45322))),f904(f904(f898(x45322),f898(f903(x45321,x45322))),f904(f898(x45322),f898(f903(x45321,x45322)))),x45322),f8(f898(f903(x45321,x45322)),f898(f903(x45321,x45322)),f898(x45322))),f317(f317(f8(f903(x45321,x45322),f904(f898(f903(x45321,x45322)),f898(f903(x45321,x45322))),x45322),f141(f903(x45321,x45322))),f317(f242(x45321,x45322),x45323)))),f317(f171(x45321,x45322),x45324))),x45325),f317(f317(f171(x45321,x45322),f317(f317(f141(x45321),x45323),x45324)),x45325))
% 94.68/94.44 [4023]E(f317(f317(f149(x40231,f317(f317(f149(x40231,x40232),x40233),x40234)),x40233),x40235),f317(f317(f149(x40231,x40232),x40233),x40235))
% 94.68/94.44 [4078]E(f317(f274(x40781,x40782),f317(f317(f299(f903(x40781,x40782)),f317(f317(f242(x40781,x40782),x40783),x40784)),x40785)),f317(f317(f299(x40782),x40784),f317(f274(x40781,x40782),x40785)))
% 94.68/94.44 [4079]E(f317(f254(x40791,x40792),f317(f317(f299(f903(x40791,x40792)),f317(f317(f242(x40791,x40792),x40793),x40794)),x40795)),f317(f317(f299(x40791),x40793),f317(f254(x40791,x40792),x40795)))
% 94.68/94.44 [4124]E(f112(x41241,x41242,f317(x41243,x41244),f317(f317(f7(x41241,a89,f899(f900(x41242))),x41245),x41244)),f317(f185(x41241,x41242,x41243,x41245),x41244))
% 94.68/94.44 [4152]E(f317(f317(f23(f904(f903(x41521,x41522),a893)),f317(f317(f244(x41521,x41522),x41523),x41524)),f317(f317(f244(x41521,x41522),x41525),x41524)),f317(f317(f244(x41521,x41522),f317(f317(f23(f904(x41521,a893)),x41523),x41525)),x41524))
% 94.68/94.44 [4153]E(f317(f317(f91(f904(f903(x41531,x41532),a893)),f317(f317(f244(x41531,x41532),x41533),x41534)),f317(f317(f244(x41531,x41532),x41535),x41534)),f317(f317(f244(x41531,x41532),f317(f317(f91(f904(x41531,a893)),x41533),x41535)),x41534))
% 94.68/94.44 [4154]E(f317(f317(f92(f904(f903(x41541,x41542),a893)),f317(f317(f244(x41541,x41542),x41543),x41544)),f317(f317(f244(x41541,x41542),x41545),x41544)),f317(f317(f244(x41541,x41542),f317(f317(f92(f904(x41541,a893)),x41543),x41545)),x41544))
% 94.68/94.44 [4213]E(f317(f317(f91(f904(x42131,a893)),f317(f317(f34(x42132,f904(x42131,a893)),x42133),x42134)),f317(f317(f34(x42132,f904(x42131,a893)),x42135),x42134)),f317(f317(f34(x42132,f904(x42131,a893)),f317(f317(f91(f904(x42132,a893)),x42133),x42135)),x42134))
% 94.68/94.44 [4214]E(f317(f317(f92(f904(x42141,a893)),f317(f317(f35(x42142,f904(x42141,a893)),x42143),x42144)),f317(f317(f35(x42142,f904(x42141,a893)),x42145),x42144)),f317(f317(f35(x42142,f904(x42141,a893)),f317(f317(f91(f904(x42142,a893)),x42143),x42145)),x42144))
% 94.68/94.44 [4228]E(f317(f317(f34(x42281,f904(x42282,a893)),x42283),f317(f317(f8(f904(x42282,a893),f904(x42282,a893),x42281),f317(f23(f904(x42282,a893)),x42284)),x42285)),f317(f317(f23(f904(x42282,a893)),x42284),f317(f317(f35(x42281,f904(x42282,a893)),x42283),x42285)))
% 94.68/94.44 [4229]E(f317(f317(f34(x42291,f904(x42292,a893)),x42293),f317(f317(f8(f904(x42292,a893),f904(x42292,a893),x42291),f317(f92(f904(x42292,a893)),x42294)),x42295)),f317(f317(f92(f904(x42292,a893)),x42294),f317(f317(f34(x42291,f904(x42292,a893)),x42293),x42295)))
% 94.68/94.44 [4230]E(f317(f317(f35(x42301,f904(x42302,a893)),x42303),f317(f317(f8(f904(x42302,a893),f904(x42302,a893),x42301),f317(f91(f904(x42302,a893)),x42304)),x42305)),f317(f317(f91(f904(x42302,a893)),x42304),f317(f317(f35(x42301,f904(x42302,a893)),x42303),x42305)))
% 94.68/94.44 [4284]E(f175(f898(x42841),f317(f317(f141(x42841),x42842),x42843),f317(f317(f8(f898(x42841),f898(x42841),a897),f317(f141(x42841),x42844)),f317(f317(f7(a897,x42841,f898(x42841)),f149(x42841,x42843)),x42842)),x42845),f317(f317(f149(x42841,f317(f317(f141(x42841),x42844),x42843)),x42845),x42842))
% 94.68/94.44 [4288]E(f317(f317(f34(x42881,f904(f903(x42882,x42883),a893)),x42884),f317(f317(f8(f904(f903(x42883,x42882),a893),f904(f903(x42882,x42883),a893),x42881),f276(x42883,x42882)),x42885)),f317(f276(x42883,x42882),f317(f317(f34(x42881,f904(f903(x42883,x42882),a893)),x42884),x42885)))
% 94.68/94.44 [4289]E(f317(f317(f35(x42891,f904(f903(x42892,x42893),a893)),x42894),f317(f317(f8(f904(f903(x42893,x42892),a893),f904(f903(x42892,x42893),a893),x42891),f276(x42893,x42892)),x42895)),f317(f276(x42893,x42892),f317(f317(f35(x42891,f904(f903(x42893,x42892),a893)),x42894),x42895)))
% 94.68/94.44 [4390]P1(f317(f317(f224(f904(x43901,a893)),f317(f317(f23(f904(x43901,a893)),f317(f300(x43902,x43901,x43903),x43904)),f317(f300(x43902,x43901,x43903),x43905))),f317(f300(x43902,x43901,x43903),f317(f317(f23(f904(x43902,a893)),x43904),x43905))))
% 94.68/94.44 [4535]E(f317(f146(f898(f903(x45351,x45352)),x45351,f103(f903(x45351,x45352)),f317(f317(f7(x45351,f904(f898(x45351),f898(f903(x45351,x45352))),f904(f898(x45351),f898(f903(x45351,x45352)))),f317(f317(f8(f904(f898(f903(x45351,x45352)),f898(f903(x45351,x45352))),f904(f904(f898(x45351),f898(f903(x45351,x45352))),f904(f898(x45351),f898(f903(x45351,x45352)))),x45351),f8(f898(f903(x45351,x45352)),f898(f903(x45351,x45352)),f898(x45351))),f317(f317(f8(f903(x45351,x45352),f904(f898(f903(x45351,x45352)),f898(f903(x45351,x45352))),x45351),f141(f903(x45351,x45352))),f317(f317(f7(x45351,x45352,f903(x45351,x45352)),f242(x45351,x45352)),x45353)))),f317(f317(f7(f898(x45351),f898(x45352),f898(f903(x45351,x45352))),f171(x45351,x45352)),x45354))),x45355),f317(f317(f171(x45351,x45352),x45355),f317(f317(f141(x45352),x45353),x45354)))
% 94.68/94.44 [4253]E(f317(f317(f91(f904(x42531,a893)),f317(f275(x42532,x42531,x42533),x42534)),f317(f275(x42532,x42531,x42535),x42534)),f317(f275(x42532,x42531,f317(f317(f91(f904(f903(x42532,x42531),a893)),x42533),x42535)),x42534))
% 94.68/94.44 [4290]E(f317(f317(f124(f903(x42901,x42902)),f317(f317(f171(x42901,x42902),x42903),f317(f317(f165(x42902),f317(f179(f898(x42901)),x42903)),x42904))),f317(f317(f171(x42901,x42902),x42905),f317(f317(f128(x42902),f317(f179(f898(x42901)),x42903)),x42904))),f317(f317(f171(x42901,x42902),f317(f317(f124(x42901),x42903),x42905)),x42904))
% 94.68/94.44 [4393]E(f317(f317(f244(x43931,x43932),x43933),f317(f317(f18(x43931,f904(x43932,a893),f904(x43932,a893)),f317(f317(f8(f904(x43932,a893),f904(f904(x43932,a893),f904(x43932,a893)),x43931),f23(f904(x43932,a893))),x43934)),x43935)),f317(f317(f23(f904(f903(x43931,x43932),a893)),f317(f317(f244(x43931,x43932),x43933),x43934)),f317(f317(f244(x43931,x43932),x43933),x43935)))
% 94.68/94.44 [4394]E(f317(f317(f244(x43941,x43942),x43943),f317(f317(f18(x43941,f904(x43942,a893),f904(x43942,a893)),f317(f317(f8(f904(x43942,a893),f904(f904(x43942,a893),f904(x43942,a893)),x43941),f91(f904(x43942,a893))),x43944)),x43945)),f317(f317(f91(f904(f903(x43941,x43942),a893)),f317(f317(f244(x43941,x43942),x43943),x43944)),f317(f317(f244(x43941,x43942),x43943),x43945)))
% 94.68/94.44 [4395]E(f317(f317(f244(x43951,x43952),x43953),f317(f317(f18(x43951,f904(x43952,a893),f904(x43952,a893)),f317(f317(f8(f904(x43952,a893),f904(f904(x43952,a893),f904(x43952,a893)),x43951),f92(f904(x43952,a893))),x43954)),x43955)),f317(f317(f92(f904(f903(x43951,x43952),a893)),f317(f317(f244(x43951,x43952),x43953),x43954)),f317(f317(f244(x43951,x43952),x43953),x43955)))
% 94.68/94.44 [4399]E(f317(f317(f34(x43991,f904(x43992,a893)),x43993),f317(f317(f7(x43991,f904(x43992,a893),f904(x43992,a893)),f317(f317(f8(f904(x43992,a893),f904(f904(x43992,a893),f904(x43992,a893)),x43991),f23(f904(x43992,a893))),x43994)),x43995)),f317(f317(f23(f904(x43992,a893)),f317(f317(f34(x43991,f904(x43992,a893)),x43993),x43994)),x43995))
% 94.68/94.44 [4400]E(f317(f317(f34(x44001,f904(x44002,a893)),x44003),f317(f317(f7(x44001,f904(x44002,a893),f904(x44002,a893)),f317(f317(f8(f904(x44002,a893),f904(f904(x44002,a893),f904(x44002,a893)),x44001),f92(f904(x44002,a893))),x44004)),x44005)),f317(f317(f92(f904(x44002,a893)),f317(f317(f34(x44001,f904(x44002,a893)),x44003),x44004)),x44005))
% 94.68/94.44 [4401]E(f317(f317(f35(x44011,f904(x44012,a893)),x44013),f317(f317(f7(x44011,f904(x44012,a893),f904(x44012,a893)),f317(f317(f8(f904(x44012,a893),f904(f904(x44012,a893),f904(x44012,a893)),x44011),f91(f904(x44012,a893))),x44014)),x44015)),f317(f317(f91(f904(x44012,a893)),f317(f317(f35(x44011,f904(x44012,a893)),x44013),x44014)),x44015))
% 94.68/94.44 [4405]E(f317(f317(f34(x44051,f904(x44052,a893)),x44053),f317(f317(f18(x44051,f904(x44052,a893),f904(x44052,a893)),f317(f317(f8(f904(x44052,a893),f904(f904(x44052,a893),f904(x44052,a893)),x44051),f91(f904(x44052,a893))),x44054)),x44055)),f317(f317(f91(f904(x44052,a893)),f317(f317(f34(x44051,f904(x44052,a893)),x44053),x44054)),f317(f317(f34(x44051,f904(x44052,a893)),x44053),x44055)))
% 94.68/94.44 [4406]E(f317(f317(f35(x44061,f904(x44062,a893)),x44063),f317(f317(f18(x44061,f904(x44062,a893),f904(x44062,a893)),f317(f317(f8(f904(x44062,a893),f904(f904(x44062,a893),f904(x44062,a893)),x44061),f92(f904(x44062,a893))),x44064)),x44065)),f317(f317(f92(f904(x44062,a893)),f317(f317(f35(x44061,f904(x44062,a893)),x44063),x44064)),f317(f317(f35(x44061,f904(x44062,a893)),x44063),x44065)))
% 94.68/94.44 [4419]E(f317(f317(f34(x44191,f904(x44192,a893)),x44193),f317(f317(f18(x44191,f904(x44192,a893),f904(x44192,a893)),f317(f317(f8(f904(x44192,a893),f904(f904(x44192,a893),f904(x44192,a893)),x44191),f91(f904(x44192,a893))),x44194)),x44195)),f317(f317(f91(f904(x44192,a893)),f31(f904(x44192,a893),f317(f300(x44191,f904(x44192,a893),x44194),x44193))),f31(f904(x44192,a893),f317(f300(x44191,f904(x44192,a893),x44195),x44193))))
% 94.68/94.44 [4420]E(f317(f317(f35(x44201,f904(x44202,a893)),x44203),f317(f317(f18(x44201,f904(x44202,a893),f904(x44202,a893)),f317(f317(f8(f904(x44202,a893),f904(f904(x44202,a893),f904(x44202,a893)),x44201),f92(f904(x44202,a893))),x44204)),x44205)),f317(f317(f92(f904(x44202,a893)),f32(f904(x44202,a893),f317(f300(x44201,f904(x44202,a893),x44204),x44203))),f32(f904(x44202,a893),f317(f300(x44201,f904(x44202,a893),x44205),x44203))))
% 94.68/94.44 [4456]E(f317(f317(f128(x44561),f317(f179(f898(x44561)),f167(x44561,x44562,f317(f317(f144(x44563,x44561),x44564),x44565)))),f317(f317(f144(x44563,x44561),x44564),x44565)),f317(f317(f144(x44563,x44561),x44564),f317(f317(f128(x44563),f317(f179(f898(x44563)),f167(x44563,f317(f67(x44561,a893,x44563,x44562),x44564),x44565))),x44565)))
% 94.68/94.44 [4332]E(f317(f317(f124(f903(x43321,x43322)),f317(f317(f171(x43321,x43322),f317(f317(f165(x43321),f317(f179(f898(x43322)),x43323)),x43324)),x43323)),f317(f317(f171(x43321,x43322),f317(f317(f128(x43321),f317(f179(f898(x43322)),x43323)),x43324)),x43325)),f317(f317(f171(x43321,x43322),x43324),f317(f317(f124(x43322),x43323),x43325)))
% 94.68/94.44 [4447]E(f79(x44471,f317(f317(f18(x44471,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44471),a315),f317(f317(f7(x44471,f904(x44471,a893),a893),f319(x44471)),x44472))),f317(f317(f7(x44471,x44473,a893),f317(f317(f8(x44473,f904(x44473,a893),x44471),a314),x44474)),x44475))),f317(f71(x44471,x44473,x44472,x44474),x44475))
% 94.68/94.44 [4448]E(f84(x44481,f317(f317(f18(x44481,a893,a893),f317(f317(f8(a893,f904(a893,a893),x44481),a315),f317(f317(f7(x44481,f904(x44481,a893),a893),f319(x44481)),x44482))),f317(f317(f7(x44481,x44483,a893),f317(f317(f8(x44483,f904(x44483,a893),x44481),a314),x44484)),x44485))),f317(f85(x44481,x44483,x44482,x44484),x44485))
% 94.68/94.44 [4496]E(f317(f317(f80(a1,x44961),f317(f94(a1),f317(f317(f74(a1),x44962),a87))),f317(f317(f18(a1,x44961,x44961),f317(f317(f7(a1,x44961,f904(x44961,x44961)),f317(f317(f8(a893,f904(x44961,f904(x44961,x44961)),a1),f86(x44961)),a183)),f175(x44961,x44963,x44964,x44965))),f317(f317(f8(a897,x44961,a1),x44964),f317(f317(f7(a1,a897,a897),f317(f317(f8(a897,f904(a897,a897),a1),f74(a897)),a95)),x44965)))),f175(x44961,x44963,x44964,f317(f317(f74(a897),f317(f94(a897),x44962)),x44965)))
% 94.68/94.44 [4531]E(f317(f317(f80(a1,x45311),f317(f94(a1),f317(f317(f74(a1),x45312),a87))),f317(f317(f18(a1,x45311,x45311),f317(f317(f7(a1,x45311,f904(x45311,x45311)),f317(f317(f8(a893,f904(x45311,f904(x45311,x45311)),a1),f86(x45311)),a183)),f317(f174(x45311,x45313,x45314),x45315))),f317(f317(f18(a1,x45311,x45311),f317(f317(f8(a897,f904(x45311,x45311),a1),x45314),f317(f317(f7(a1,a897,a897),f317(f317(f8(a897,f904(a897,a897),a1),f74(a897)),a95)),x45315))),f317(f317(f8(a897,x45311,a1),f174(x45311,x45313,x45314)),f317(f317(f7(a1,a897,a897),f317(f317(f8(a897,f904(a897,a897),a1),f74(a897)),a95)),x45315))))),f317(f174(x45311,x45313,x45314),f317(f317(f74(a897),f317(f94(a897),x45312)),x45315)))
% 94.68/94.44 [4564]E(f317(f252(f903(x45641,x45642)),f317(f247(x45641,x45642,a893),f317(f317(f8(f904(x45642,f904(x45643,a893)),f904(x45642,a893),x45641),f317(f8(f904(x45643,a893),a893,x45642),f81(x45643))),f317(f317(f7(x45641,f904(x45642,f904(x45643,a893)),f904(x45642,f904(x45643,a893))),f317(f317(f8(f904(f904(x45643,a893),f904(x45643,a893)),f904(f904(x45642,f904(x45643,a893)),f904(x45642,f904(x45643,a893))),x45641),f8(f904(x45643,a893),f904(x45643,a893),x45642)),f317(f317(f8(f904(x45643,f904(a893,a893)),f904(f904(x45643,a893),f904(x45643,a893)),x45641),f18(x45643,a893,a893)),f317(f317(f8(f904(x45643,a893),f904(x45643,f904(a893,a893)),x45641),f317(f8(a893,f904(a893,a893),x45643),a315)),f317(f317(f7(x45641,f904(f903(x45641,x45643),a893),f904(x45643,a893)),f317(f317(f8(f904(x45643,f904(f904(f903(x45641,x45643),a893),a893)),f904(f904(f903(x45641,x45643),a893),f904(x45643,a893)),x45641),f7(x45643,f904(f903(x45641,x45643),a893),a893)),f317(f317(f8(f904(x45643,f903(x45641,x45643)),f904(x45643,f904(f904(f903(x45641,x45643),a893),a893)),x45641),f317(f8(f903(x45641,x45643),f904(f904(f903(x45641,x45643),a893),a893),x45643),f319(f903(x45641,x45643)))),f242(x45641,x45643)))),x45644))))),f317(f317(f7(x45642,f904(f903(x45643,x45642),a893),f904(x45643,a893)),f317(f317(f8(f904(x45643,f904(f904(f903(x45643,x45642),a893),a893)),f904(f904(f903(x45643,x45642),a893),f904(x45643,a893)),x45642),f7(x45643,f904(f903(x45643,x45642),a893),a893)),f317(f317(f8(f904(x45643,f903(x45643,x45642)),f904(x45643,f904(f904(f903(x45643,x45642),a893),a893)),x45642),f317(f8(f903(x45643,x45642),f904(f904(f903(x45643,x45642),a893),a893),x45643),f319(f903(x45643,x45642)))),f317(f7(x45643,x45642,f903(x45643,x45642)),f242(x45643,x45642))))),x45645))))),f317(f317(f279(x45641,x45643,x45642),x45644),x45645))
% 94.68/94.44 [4182]E(f214(x41821,x41822,x41823,x41824,f210(x41821,x41822,x41825,x41826)),f317(f317(x41824,x41825),x41826))
% 94.68/94.44 [4183]E(f215(x41831,x41832,x41833,x41834,f210(x41831,x41832,x41835,x41836)),f317(f317(x41834,x41835),x41836))
% 94.68/94.44 [4308]E(f117(x43081,x43082,x43083,x43084,f116(x43082,x43085,x43086)),f317(f317(f317(x43084,x43085),x43086),f117(x43081,x43082,x43083,x43084,x43086)))
% 94.68/94.44 [4327]E(f69(x43271,x43272,f69(x43271,x43272,x43273,x43274,x43275),x43274,x43276),f69(x43271,x43272,x43273,x43274,x43276))
% 94.68/94.44 [4435]E(f317(f67(f903(x44351,x44352),x44352,f903(x44353,x44354),f246(x44351,x44352)),f248(x44353,x44351,x44354,x44352,x44355,x44356)),f317(f67(x44354,x44352,f903(x44353,x44354),x44356),f246(x44353,x44354)))
% 94.68/94.44 [4436]E(f317(f67(f903(x44361,x44362),x44361,f903(x44363,x44364),f241(x44361,x44362)),f248(x44363,x44361,x44364,x44362,x44365,x44366)),f317(f67(x44363,x44361,f903(x44363,x44364),x44365),f241(x44363,x44364)))
% 94.68/94.44 [4053]E(f317(f317(f67(x40531,x40532,x40533,x40534),x40535),x40536),f317(x40534,f317(x40535,x40536)))
% 94.68/94.44 [4192]E(f213(x41921,f903(x41922,f899(x41922)),x41923,f317(f247(x41922,f899(x41922),x41921),x41924),f317(f125(x41922),f116(x41922,x41925,x41926))),f317(f317(x41924,x41925),x41926))
% 94.68/94.44 [4242]E(f216(x42421,x42422,x42423,x42424,f210(x42421,x42422,x42425,x42426)),f317(f317(f74(a897),f317(f317(f74(a897),f317(x42423,x42425)),f317(x42424,x42426))),f317(a102,f2(a897))))
% 94.68/94.44 [3853]E(f317(f317(f247(x38531,x38532,x38533),x38534),f317(f317(f242(x38531,x38532),x38535),x38536)),f317(f317(x38534,x38535),x38536))
% 94.68/94.44 [3913]E(f317(f317(f317(f8(x39131,x39132,x39133),x39134),x39135),x39136),f317(x39134,f317(x39135,x39136)))
% 94.68/94.44 [3914]E(f317(f317(f317(f7(x39141,x39142,x39143),x39144),x39145),x39146),f317(f317(x39144,x39146),x39145))
% 94.68/94.44 [3930]E(f317(f317(f317(f18(x39301,x39302,x39303),x39304),x39305),x39306),f317(f317(x39304,x39306),f317(x39305,x39306)))
% 94.68/94.44 [3953]E(f317(f146(x39531,x39532,x39533,x39534),f317(f317(f141(x39532),x39535),x39536)),f317(f317(x39534,x39535),x39536))
% 94.68/94.44 [3990]E(f159(f903(x39901,x39902),f317(f317(f228(a897),x39903),x39904),f317(f317(f242(x39901,x39902),x39905),x39906)),f317(f317(f171(x39901,x39902),f159(x39901,x39903,x39905)),f159(x39902,x39904,x39906)))
% 94.68/94.44 [4057]E(f317(f317(f141(f903(x40571,x40572)),f317(f317(f242(x40571,x40572),x40573),x40574)),f317(f317(f171(x40571,x40572),x40575),x40576)),f317(f317(f171(x40571,x40572),f317(f317(f141(x40571),x40573),x40575)),f317(f317(f141(x40572),x40574),x40576)))
% 94.68/94.44 [4059]E(f317(f317(f144(x40591,x40592),x40593),f317(f317(f149(x40591,x40594),x40595),x40596)),f317(f317(f149(x40592,f317(f317(f144(x40591,x40592),x40593),x40594)),x40595),f317(x40593,x40596)))
% 94.68/94.44 [4083]E(f317(f317(f245(x40831,x40832,x40833,x40834),x40835),x40836),f317(x40834,f317(f317(f242(x40831,x40832),x40835),x40836)))
% 94.68/94.44 [4099]E(f317(f132(x40991,x40992,x40993,x40994),f317(f317(f141(x40992),x40995),x40996)),f317(f132(x40991,x40992,x40993,f317(f317(x40993,x40994),x40995)),x40996))
% 94.68/94.44 [4125]E(f250(x41251,x41252,x41253,x41254,f317(f317(f242(x41251,x41252),x41255),x41256)),f317(f317(x41254,x41255),x41256))
% 94.68/94.44 [4206]E(f317(f317(f34(x42061,f904(x42062,a893)),x42063),f317(f67(x42064,f904(x42062,a893),x42061,x42065),x42066)),f317(f317(f34(x42064,f904(x42062,a893)),f317(f300(x42061,x42064,x42066),x42063)),x42065))
% 94.68/94.44 [4256]E(f317(f317(f144(x42561,x42562),x42563),f317(f317(f144(x42564,x42561),x42565),x42566)),f317(f317(f144(x42564,x42562),f317(f67(x42561,x42562,x42564,x42563),x42565)),x42566))
% 94.68/94.44 [4262]E(f317(f300(x42621,x42622,f317(f67(x42623,x42622,x42621,x42624),x42625)),x42626),f317(f300(x42623,x42622,x42624),f317(f300(x42621,x42623,x42625),x42626)))
% 94.68/94.44 [4263]E(f317(f301(x42631,x42632,f317(f67(x42633,x42632,x42631,x42634),x42635)),x42636),f317(f301(x42631,x42633,x42635),f317(f301(x42633,x42632,x42634),x42636)))
% 94.68/94.44 [4291]E(f317(f132(x42911,x42912,x42913,f317(f132(x42911,x42912,x42913,x42914),x42915)),x42916),f317(f132(x42911,x42912,x42913,x42914),f317(f317(f124(x42912),x42915),x42916)))
% 94.68/94.44 [4425]E(f317(f248(x44251,x44251,x44252,x44253,f25(x44251),x44254),f317(f317(f242(x44251,x44252),x44255),x44256)),f317(f317(f242(x44251,x44253),x44255),f317(x44254,x44256)))
% 94.68/94.44 [4426]E(f317(f248(x44261,x44262,x44263,x44263,x44264,f25(x44263)),f317(f317(f242(x44261,x44263),x44265),x44266)),f317(f317(f242(x44262,x44263),f317(x44264,x44265)),x44266))
% 94.68/94.44 [4514]E(f317(f317(f144(f903(x45141,x45142),f903(x45141,x45143)),f317(f247(x45141,x45142,f903(x45141,x45143)),f317(f317(f7(x45141,f904(x45142,x45143),f904(x45142,f903(x45141,x45143))),f317(f317(f8(f904(x45143,f903(x45141,x45143)),f904(f904(x45142,x45143),f904(x45142,f903(x45141,x45143))),x45141),f8(x45143,f903(x45141,x45143),x45142)),f242(x45141,x45143))),x45144))),f317(f317(f171(x45141,x45142),x45145),x45146)),f317(f317(f171(x45141,x45143),x45145),f317(f317(f144(x45142,x45143),x45144),x45146)))
% 94.68/94.44 [4109]E(f317(f317(f67(x41091,x41092,x41093,f317(f16(x41092,x41091),x41094)),x41095),x41096),x41094)
% 94.68/94.44 [4141]E(f317(f300(x41411,x41412,x41413),f317(f300(x41414,x41411,x41415),x41416)),f317(f300(x41414,x41412,f317(f317(f8(x41411,x41412,x41414),x41413),x41415)),x41416))
% 94.68/94.44 [4147]E(f317(f317(f34(x41471,f904(x41472,a893)),f317(f300(x41473,x41471,x41474),x41475)),x41476),f317(f317(f34(x41473,f904(x41472,a893)),x41475),f317(f317(f8(x41471,f904(x41472,a893),x41473),x41476),x41474)))
% 94.68/94.44 [4148]E(f317(f317(f35(x41481,f904(x41482,a893)),f317(f300(x41483,x41481,x41484),x41485)),x41486),f317(f317(f35(x41483,f904(x41482,a893)),x41485),f317(f317(f8(x41481,f904(x41482,a893),x41483),x41486),x41484)))
% 94.68/94.44 [4149]E(f317(f317(f34(x41491,f904(x41492,a893)),x41493),f317(f317(f8(x41494,f904(x41492,a893),x41491),x41495),x41496)),f317(f317(f34(x41494,f904(x41492,a893)),f317(f300(x41491,x41494,x41496),x41493)),x41495))
% 94.68/94.44 [4150]E(f317(f317(f35(x41501,f904(x41502,a893)),x41503),f317(f317(f8(x41504,f904(x41502,a893),x41501),x41505),x41506)),f317(f317(f35(x41504,f904(x41502,a893)),f317(f300(x41501,x41504,x41506),x41503)),x41505))
% 94.68/94.44 [4208]E(f317(f317(f34(x42081,f904(x42082,a893)),x42083),f317(f317(f8(f904(x42084,a893),f904(x42082,a893),x42081),f300(x42084,x42082,x42085)),x42086)),f317(f300(x42084,x42082,x42085),f317(f317(f34(x42081,f904(x42084,a893)),x42083),x42086)))
% 94.68/94.44 [4209]E(f317(f317(f34(x42091,f904(x42092,a893)),x42093),f317(f317(f8(f904(x42094,a893),f904(x42092,a893),x42091),f275(x42094,x42092,x42095)),x42096)),f317(f275(x42094,x42092,x42095),f317(f317(f34(x42091,f904(x42094,a893)),x42093),x42096)))
% 94.68/94.44 [4210]E(f317(f317(f34(x42101,f904(x42102,a893)),x42103),f317(f317(f8(f904(x42104,a893),f904(x42102,a893),x42101),f301(x42102,x42104,x42105)),x42106)),f317(f301(x42102,x42104,x42105),f317(f317(f34(x42101,f904(x42104,a893)),x42103),x42106)))
% 94.68/94.44 [4211]E(f317(f317(f35(x42111,f904(x42112,a893)),x42113),f317(f317(f8(f904(x42114,a893),f904(x42112,a893),x42111),f301(x42112,x42114,x42115)),x42116)),f317(f301(x42112,x42114,x42115),f317(f317(f35(x42111,f904(x42114,a893)),x42113),x42116)))
% 94.68/94.44 [4296]E(f317(f132(x42961,x42962,f317(f7(x42962,x42961,x42961),x42963),x42964),f317(f158(x42962),f317(f317(f141(x42962),x42965),x42966))),f317(f317(x42963,x42965),f317(f132(x42961,x42962,f317(f7(x42962,x42961,x42961),x42963),x42964),f317(f158(x42962),x42966))))
% 94.68/94.44 [4354]E(f317(f317(f18(f903(x43541,x43542),x43542,x43543),f317(f317(f8(x43544,f904(x43542,x43543),f903(x43541,x43542)),x43545),f317(f317(f8(x43541,x43544,f903(x43541,x43542)),x43546),f241(x43541,x43542)))),f246(x43541,x43542)),f317(f247(x43541,x43542,x43543),f317(f317(f8(x43544,f904(x43542,x43543),x43541),x43545),x43546)))
% 94.68/94.44 [4361]E(f317(f132(x43611,x43612,f317(f7(x43612,x43611,x43611),x43613),f317(f132(x43611,x43612,f317(f7(x43612,x43611,x43611),x43613),x43614),f317(f158(x43612),x43615))),f317(f158(x43612),x43616)),f317(f132(x43611,x43612,f317(f7(x43612,x43611,x43611),x43613),x43614),f317(f158(x43612),f317(f317(f124(x43612),x43616),x43615))))
% 94.68/94.44 [4363]E(f317(f317(f144(f903(x43631,x43632),f903(x43633,x43632)),f317(f247(x43631,x43632,f903(x43633,x43632)),f317(f317(f8(x43633,f904(x43632,f903(x43633,x43632)),x43631),f242(x43633,x43632)),x43634))),f317(f317(f171(x43631,x43632),x43635),x43636)),f317(f317(f171(x43633,x43632),f317(f317(f144(x43631,x43633),x43634),x43635)),x43636))
% 94.68/94.44 [4408]P1(f317(f317(f224(f904(x44081,a893)),f317(f275(x44082,x44081,x44083),f317(f317(f35(x44084,f904(x44082,a893)),x44085),x44086))),f317(f317(f35(x44084,f904(x44081,a893)),x44085),f317(f317(f8(f904(x44082,a893),f904(x44081,a893),x44084),f275(x44082,x44081,x44083)),x44086))))
% 94.68/94.44 [4221]E(f317(f317(f171(x42211,x42212),f317(f317(f149(x42211,x42213),x42214),f317(f241(x42211,x42212),x42215))),f317(f317(f149(x42212,x42216),x42214),f317(f246(x42211,x42212),x42215))),f317(f317(f149(f903(x42211,x42212),f317(f317(f171(x42211,x42212),x42213),x42216)),x42214),x42215))
% 94.68/94.44 [4279]E(f317(f317(f91(f904(f903(x42791,x42792),a893)),f317(f317(f279(x42791,x42793,x42792),x42794),x42795)),f317(f317(f279(x42791,x42793,x42792),x42794),x42796)),f317(f317(f279(x42791,x42793,x42792),x42794),f317(f317(f91(f904(f903(x42793,x42792),a893)),x42795),x42796)))
% 94.68/94.44 [4373]E(f317(f317(f299(f903(x43731,x43732)),f317(f317(f242(x43731,x43732),x43733),x43734)),f317(f317(f91(f904(f903(x43731,x43732),a893)),f317(f317(f244(x43731,x43732),x43735),f317(f16(f904(x43732,a893),x43731),f317(f317(f299(x43732),x43734),x43736)))),f317(f317(f244(x43731,x43732),f317(f317(f299(x43731),x43733),x43735)),f317(f16(f904(x43732,a893),x43731),x43736)))),f317(f317(f244(x43731,x43732),f317(f317(f299(x43731),x43733),x43735)),f317(f16(f904(x43732,a893),x43731),f317(f317(f299(x43732),x43734),x43736))))
% 94.68/94.44 [4452]E(f317(f317(f92(f904(x44521,a893)),f317(f301(x44521,x44522,f317(f67(f903(x44522,x44523),x44522,x44521,f241(x44522,x44523)),x44524)),x44525)),f317(f301(x44521,x44523,f317(f67(f903(x44522,x44523),x44523,x44521,f246(x44522,x44523)),x44524)),x44526)),f317(f301(x44521,f903(x44522,x44523),x44524),f317(f317(f244(x44522,x44523),x44525),f317(f16(f904(x44523,a893),x44522),x44526))))
% 94.68/94.44 [4302]E(f317(f317(f91(f904(f903(x43021,x43022),a893)),f317(f317(f279(x43021,x43023,x43022),x43024),x43025)),f317(f317(f279(x43021,x43023,x43022),x43026),x43025)),f317(f317(f279(x43021,x43023,x43022),f317(f317(f91(f904(f903(x43021,x43023),a893)),x43024),x43026)),x43025))
% 94.68/94.44 [4433]E(f317(f317(f34(x44331,f904(x44332,a893)),x44333),f317(f317(f7(x44331,f904(x44334,f904(x44332,a893)),f904(x44332,a893)),f317(f317(f8(f904(x44334,a893),f904(f904(x44334,f904(x44332,a893)),f904(x44332,a893)),x44331),f34(x44334,f904(x44332,a893))),x44335)),x44336)),f317(f317(f34(x44334,f904(x44332,a893)),f317(f317(f34(x44331,f904(x44334,a893)),x44333),x44335)),x44336))
% 94.68/94.44 [4434]E(f317(f317(f35(x44341,f904(x44342,a893)),x44343),f317(f317(f7(x44341,f904(x44344,f904(x44342,a893)),f904(x44342,a893)),f317(f317(f8(f904(x44344,a893),f904(f904(x44344,f904(x44342,a893)),f904(x44342,a893)),x44341),f35(x44344,f904(x44342,a893))),x44345)),x44346)),f317(f317(f35(x44344,f904(x44342,a893)),f317(f317(f34(x44341,f904(x44344,a893)),x44343),x44345)),x44346))
% 94.68/94.44 [4486]E(f317(f247(x44861,x44862,f903(x44863,x44864)),f317(f317(f7(x44861,f904(x44862,x44864),f904(x44862,f903(x44863,x44864))),f317(f317(f8(f904(x44864,f903(x44863,x44864)),f904(f904(x44862,x44864),f904(x44862,f903(x44863,x44864))),x44861),f8(x44864,f903(x44863,x44864),x44862)),f317(f317(f8(x44863,f904(x44864,f903(x44863,x44864)),x44861),f242(x44863,x44864)),x44865))),x44866)),f248(x44861,x44863,x44862,x44864,x44865,x44866))
% 94.68/94.44 [4509]E(f317(f300(x45091,x45092,f317(f317(f18(x45091,x45092,x45092),f317(f317(f18(x45091,x45092,f904(x45092,x45092)),f317(f317(f8(a893,f904(x45092,f904(x45092,x45092)),x45091),f86(x45092)),x45093)),x45094)),x45095)),x45096),f317(f317(f91(f904(x45092,a893)),f317(f300(x45091,x45092,x45094),f317(f317(f92(f904(x45091,a893)),x45096),f317(f252(x45091),x45093)))),f317(f300(x45091,x45092,x45095),f317(f317(f92(f904(x45091,a893)),x45096),f317(f252(x45091),f317(f317(f8(a893,a893,x45091),a312),x45093))))))
% 94.68/94.44 [4521]E(f317(f300(x45211,f903(x45212,x45213),f317(f317(f18(x45211,x45213,f903(x45212,x45213)),f317(f317(f8(x45212,f904(x45213,f903(x45212,x45213)),x45211),f242(x45212,x45213)),x45214)),x45215)),x45216),f317(f317(f244(x45212,x45213),f317(f300(x45211,x45212,x45214),x45216)),f317(f317(f8(f904(x45211,a893),f904(x45213,a893),x45212),f300(x45211,x45213,x45215)),f317(f317(f7(x45212,f904(x45211,a893),f904(x45211,a893)),f317(f317(f8(f904(x45211,a893),f904(f904(x45211,a893),f904(x45211,a893)),x45212),f92(f904(x45211,a893))),f317(f317(f8(f904(x45212,a893),f904(x45211,a893),x45212),f301(x45211,x45212,x45214)),f317(f317(f7(x45212,f904(x45212,a893),f904(x45212,a893)),f299(x45212)),f178(f904(x45212,a893)))))),x45216))))
% 94.68/94.44 [4546]E(f236(x45461,x45462,x45463,x45464,x45465,x45466),f317(x45464,f317(f252(x45461),f317(f317(f8(f904(f904(x45463,x45461),a893),a893,x45461),f81(f904(x45463,x45461))),f317(f317(f8(f904(f904(x45463,x45461),a893),f904(f904(x45463,x45461),a893),x45461),f317(f18(f904(x45463,x45461),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x45463,x45461)),a315),f317(f317(f7(f904(x45463,x45461),f904(f904(x45463,x45461),a893),a893),f319(f904(x45463,x45461))),x45465)))),f317(f317(f7(x45461,f904(f904(x45463,x45461),x45461),f904(f904(x45463,x45461),a893)),f317(f317(f8(f904(x45461,a893),f904(f904(f904(x45463,x45461),x45461),f904(f904(x45463,x45461),a893)),x45461),f8(x45461,a893,f904(x45463,x45461))),a314)),f317(f317(f7(f904(x45463,x45461),x45463,x45461),f5(f904(x45463,x45461))),x45466)))))))
% 94.68/94.44 [4335]E(f317(f67(x43351,x43352,x43353,x43354),f69(x43353,x43351,x43355,x43356,x43357)),f69(x43353,x43352,f317(f67(x43351,x43352,x43353,x43354),x43355),x43356,f317(x43354,x43357)))
% 94.68/94.44 [4469]E(f317(f246(x44691,x44692),f317(f248(x44693,x44691,x44694,x44692,x44695,x44696),x44697)),f317(x44696,f317(f246(x44693,x44694),x44697)))
% 94.68/94.44 [4470]E(f317(f241(x44701,x44702),f317(f248(x44703,x44701,x44704,x44702,x44705,x44706),x44707)),f317(x44705,f317(f241(x44703,x44704),x44707)))
% 94.68/94.44 [4184]E(f317(f317(f171(x41841,x41842),f317(f317(f149(x41841,x41843),x41844),x41845)),f317(f317(f149(x41842,x41846),x41844),x41847)),f317(f317(f149(f903(x41841,x41842),f317(f317(f171(x41841,x41842),x41843),x41846)),x41844),f317(f317(f242(x41841,x41842),x41845),x41847)))
% 94.68/94.44 [4251]E(f317(f317(f317(f249(x42511,x42512,x42513,x42514),x42515),x42516),x42517),f317(f317(f247(x42512,x42513,x42514),x42516),f317(x42515,x42517)))
% 94.68/94.44 [4261]E(f317(f317(f317(f249(x42611,x42612,x42613,x42614),x42615),x42616),x42617),f317(f317(x42616,f317(f241(x42612,x42613),f317(x42615,x42617))),f317(f246(x42612,x42613),f317(x42615,x42617))))
% 94.68/94.44 [4313]E(f317(f67(x43131,x43132,x43133,x43134),f317(f67(x43135,x43131,x43133,x43136),x43137)),f317(f67(x43135,x43132,x43133,f317(f67(x43131,x43132,x43135,x43134),x43136)),x43137))
% 94.68/94.44 [4490]E(f317(f248(x44901,x44902,x44903,x44903,x44904,f25(x44903)),f317(f248(x44901,x44901,x44905,x44903,f25(x44901),x44906),x44907)),f317(f317(f242(x44902,x44903),f317(x44904,f317(f241(x44901,x44905),x44907))),f317(x44906,f317(f246(x44901,x44905),x44907))))
% 94.68/94.44 [4491]E(f317(f248(x44911,x44911,x44912,x44913,f25(x44911),x44914),f317(f248(x44915,x44911,x44912,x44912,x44916,f25(x44912)),x44917)),f317(f317(f242(x44911,x44913),f317(x44916,f317(f241(x44915,x44912),x44917))),f317(x44914,f317(f246(x44915,x44912),x44917))))
% 94.68/94.44 [4507]E(f317(f248(x45071,x45072,x45073,x45073,x45074,f25(x45073)),f317(f248(x45075,x45071,x45073,x45073,x45076,f25(x45073)),x45077)),f317(f248(x45075,x45072,x45073,x45073,f317(f67(x45071,x45072,x45075,x45074),x45076),f25(x45073)),x45077))
% 94.68/94.44 [4508]E(f317(f248(x45081,x45081,x45082,x45083,f25(x45081),x45084),f317(f248(x45081,x45081,x45085,x45082,f25(x45081),x45086),x45087)),f317(f248(x45081,x45081,x45085,x45083,f25(x45081),f317(f67(x45082,x45083,x45085,x45084),x45086)),x45087))
% 94.68/94.44 [4518]E(f317(f248(x45181,x45182,x45183,x45183,x45184,f25(x45183)),f317(f248(x45181,x45181,x45185,x45183,f25(x45181),x45186),x45187)),f317(f248(x45182,x45182,x45185,x45183,f25(x45182),x45186),f317(f248(x45181,x45182,x45185,x45185,x45184,f25(x45185)),x45187)))
% 94.68/94.44 [4218]E(f317(f317(f279(x42181,x42182,x42183),f317(f317(f279(x42181,x42184,x42182),x42185),x42186)),x42187),f317(f317(f279(x42181,x42184,x42183),x42185),f317(f317(f279(x42184,x42182,x42183),x42186),x42187)))
% 94.68/94.44 [4285]E(f317(f317(f247(x42851,x42852,x42853),f317(f67(x42854,f904(x42852,x42853),x42851,x42855),x42856)),x42857),f317(f317(x42855,f317(x42856,f317(f241(x42851,x42852),x42857))),f317(f246(x42851,x42852),x42857)))
% 94.68/94.44 [4366]E(f317(f132(x43661,x43662,f317(f7(x43662,x43661,x43661),x43663),x43664),f317(f158(x43662),f317(f317(f144(x43665,x43662),x43666),x43667))),f317(f132(x43661,x43665,f317(f7(x43665,x43661,x43661),f317(f67(x43662,f904(x43661,x43661),x43665,x43663),x43666)),x43664),f317(f158(x43665),x43667)))
% 94.68/94.44 [4314]E(f317(f317(f34(x43141,f904(f903(x43142,x43143),a893)),x43144),f317(f317(f8(f904(f903(x43145,x43143),a893),f904(f903(x43142,x43143),a893),x43141),f317(f279(x43142,x43145,x43143),x43146)),x43147)),f317(f317(f279(x43142,x43145,x43143),x43146),f317(f317(f34(x43141,f904(f903(x43145,x43143),a893)),x43144),x43147)))
% 94.68/94.44 [4457]E(f317(f317(f34(x44571,f904(f903(x44572,x44573),a893)),x44574),f317(f317(f7(x44571,f904(f903(x44575,x44573),a893),f904(f903(x44572,x44573),a893)),f317(f317(f8(f904(f903(x44572,x44575),a893),f904(f904(f903(x44575,x44573),a893),f904(f903(x44572,x44573),a893)),x44571),f279(x44572,x44575,x44573)),x44576)),x44577)),f317(f317(f279(x44572,x44575,x44573),f317(f317(f34(x44571,f904(f903(x44572,x44575),a893)),x44574),x44576)),x44577))
% 94.68/94.44 [4458]E(f317(f132(x44581,x44582,f317(f317(f7(x44581,f904(x44582,x44583),f904(x44582,x44581)),f317(f317(f8(f904(x44583,x44581),f904(f904(x44582,x44583),f904(x44582,x44581)),x44581),f8(x44583,x44581,x44582)),x44584)),x44585),x44586),x44587),f317(f132(x44581,x44583,x44584,x44586),f317(f317(f144(x44582,x44583),x44585),x44587)))
% 94.68/94.44 [4519]E(f317(f317(f35(x45191,f904(x45192,a893)),x45193),f317(f317(f8(f904(x45194,f904(x45192,a893)),f904(x45192,a893),x45191),f317(f35(x45194,f904(x45192,a893)),x45195)),f317(f317(f7(x45191,f904(x45194,f904(x45192,a893)),f904(x45194,f904(x45192,a893))),f317(f317(f8(f904(f904(x45192,a893),f904(x45192,a893)),f904(f904(x45194,f904(x45192,a893)),f904(x45194,f904(x45192,a893))),x45191),f8(f904(x45192,a893),f904(x45192,a893),x45194)),f317(f317(f8(f904(x45192,a893),f904(f904(x45192,a893),f904(x45192,a893)),x45191),f91(f904(x45192,a893))),x45196))),x45197))),f317(f317(f91(f904(x45192,a893)),f317(f317(f35(x45191,f904(x45192,a893)),x45193),x45196)),f317(f317(f35(x45194,f904(x45192,a893)),x45195),x45197)))
% 94.68/94.44 [4520]E(f317(f317(f34(x45201,f904(x45202,a893)),x45203),f317(f317(f8(f904(x45204,f904(x45202,a893)),f904(x45202,a893),x45201),f317(f34(x45204,f904(x45202,a893)),x45205)),f317(f317(f7(x45201,f904(x45204,f904(x45202,a893)),f904(x45204,f904(x45202,a893))),f317(f317(f8(f904(f904(x45202,a893),f904(x45202,a893)),f904(f904(x45204,f904(x45202,a893)),f904(x45204,f904(x45202,a893))),x45201),f8(f904(x45202,a893),f904(x45202,a893),x45204)),f317(f317(f8(f904(x45202,a893),f904(f904(x45202,a893),f904(x45202,a893)),x45201),f92(f904(x45202,a893))),x45206))),x45207))),f317(f317(f92(f904(x45202,a893)),f317(f317(f34(x45201,f904(x45202,a893)),x45203),x45206)),f317(f317(f34(x45204,f904(x45202,a893)),x45205),x45207)))
% 94.68/94.44 [4512]E(f187(x45121,x45122,f317(f317(f317(x45123,x45124),x45125),x45126),f317(f317(f7(x45121,f903(a89,a89),f904(a89,f899(x45122))),f317(f317(f7(x45121,a89,f904(f903(a89,a89),f904(a89,f899(x45122)))),f317(f317(f7(x45121,a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(x45122))))),x45127),x45124)),x45125)),x45126)),f317(f317(f317(f199(x45121,x45122,x45123,x45127),x45124),x45125),x45126))
% 94.68/94.44 [4526]E(f188(x45261,x45262,f317(f317(f317(x45263,x45264),x45265),x45266),f317(f317(f7(x45261,f903(a89,a89),f904(a89,f899(x45262))),f317(f317(f7(x45261,a89,f904(f903(a89,a89),f904(a89,f899(x45262)))),f317(f317(f7(x45261,a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(x45262))))),x45267),x45264)),x45265)),x45266)),f201(x45261,x45262,x45263,x45267,x45264,x45265,x45266))
% 94.68/94.44 [4517]E(f185(x45171,x45172,f317(f317(f317(x45173,x45174),x45175),x45176),f317(f317(f7(x45171,f903(a89,a89),f904(a89,f899(f900(x45172)))),f317(f317(f7(x45171,a89,f904(f903(a89,a89),f904(a89,f899(f900(x45172))))),f317(f317(f7(x45171,a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(f900(x45172)))))),x45177),x45174)),x45175)),x45176)),f317(f317(f317(f195(x45171,x45172,x45173,x45177),x45174),x45175),x45176))
% 94.68/94.44 [4528]E(f186(x45281,x45282,f317(f317(f317(x45283,x45284),x45285),x45286),f317(f317(f7(x45281,f903(a89,a89),f904(a89,f899(f900(x45282)))),f317(f317(f7(x45281,a89,f904(f903(a89,a89),f904(a89,f899(f900(x45282))))),f317(f317(f7(x45281,a89,f904(a89,f904(f903(a89,a89),f904(a89,f899(f900(x45282)))))),x45287),x45284)),x45285)),x45286)),f197(x45281,x45282,x45283,x45287,x45284,x45285,x45286))
% 94.68/94.44 [4427]E(f317(f248(x44271,x44272,x44273,x44274,x44275,x44276),f317(f317(f242(x44271,x44273),x44277),x44278)),f317(f317(f242(x44272,x44274),f317(x44275,x44277)),f317(x44276,x44278)))
% 94.68/94.44 [4530]E(f317(f317(f144(f903(x45301,x45302),f903(x45303,x45304)),f317(f247(x45301,x45302,f903(x45303,x45304)),f317(f317(f7(x45301,f904(x45302,x45304),f904(x45302,f903(x45303,x45304))),f317(f317(f8(f904(x45304,f903(x45303,x45304)),f904(f904(x45302,x45304),f904(x45302,f903(x45303,x45304))),x45301),f8(x45304,f903(x45303,x45304),x45302)),f317(f317(f8(x45303,f904(x45304,f903(x45303,x45304)),x45301),f242(x45303,x45304)),x45305))),x45306))),f317(f317(f171(x45301,x45302),x45307),x45308)),f317(f317(f171(x45303,x45304),f317(f317(f144(x45301,x45303),x45305),x45307)),f317(f317(f144(x45302,x45304),x45306),x45308)))
% 94.68/94.44 [4533]E(f317(f317(f144(f903(x45331,x45332),x45333),f317(f247(x45331,x45332,x45333),f317(f317(f8(f904(x45332,f903(x45331,x45334)),f904(x45332,x45333),x45331),f317(f8(f903(x45331,x45334),x45333,x45332),x45335)),f317(f317(f7(x45331,f904(x45332,x45334),f904(x45332,f903(x45331,x45334))),f317(f317(f8(f904(x45334,f903(x45331,x45334)),f904(f904(x45332,x45334),f904(x45332,f903(x45331,x45334))),x45331),f8(x45334,f903(x45331,x45334),x45332)),f242(x45331,x45334))),x45336)))),f317(f317(f171(x45331,x45332),x45337),x45338)),f317(f317(f144(f903(x45331,x45334),x45333),x45335),f317(f317(f171(x45331,x45334),x45337),f317(f317(f144(x45332,x45334),x45336),x45338))))
% 94.68/94.44 [4461]E(f317(f317(f144(f903(x44611,x44612),x44613),f317(f247(x44611,x44612,x44613),f317(f317(f8(f904(x44612,f903(x44614,x44612)),f904(x44612,x44613),x44611),f317(f8(f903(x44614,x44612),x44613,x44612),x44615)),f317(f317(f8(x44614,f904(x44612,f903(x44614,x44612)),x44611),f242(x44614,x44612)),x44616)))),f317(f317(f171(x44611,x44612),x44617),x44618)),f317(f317(f144(f903(x44614,x44612),x44613),x44615),f317(f317(f171(x44614,x44612),f317(f317(f144(x44611,x44614),x44616),x44617)),x44618)))
% 94.68/94.44 [4418]E(f317(f317(f247(x44181,x44182,x44183),f317(f317(f8(f904(x44182,f903(x44184,x44185)),f904(x44182,x44183),x44181),f317(f8(f903(x44184,x44185),x44183,x44182),f317(f247(x44184,x44185,x44183),x44186))),x44187)),x44188),f317(f317(f247(x44184,x44185,x44183),x44186),f317(f317(f247(x44181,x44182,f903(x44184,x44185)),x44187),x44188)))
% 94.68/94.44 [4534]E(f317(f317(f34(f903(x45341,x45342),f904(f903(x45343,x45344),a893)),f317(f317(f244(x45341,x45342),x45345),f317(f16(f904(x45342,a893),x45341),x45346))),f317(f247(x45341,x45342,f904(f903(x45343,x45344),a893)),f317(f317(f7(x45341,f904(x45342,f904(x45343,f904(x45344,a893))),f904(x45342,f904(f903(x45343,x45344),a893))),f317(f317(f8(f904(f904(x45343,f904(x45344,a893)),f904(f903(x45343,x45344),a893)),f904(f904(x45342,f904(x45343,f904(x45344,a893))),f904(x45342,f904(f903(x45343,x45344),a893))),x45341),f8(f904(x45343,f904(x45344,a893)),f904(f903(x45343,x45344),a893),x45342)),f317(f317(f8(f904(x45343,a893),f904(f904(x45343,f904(x45344,a893)),f904(f903(x45343,x45344),a893)),x45341),f244(x45343,x45344)),x45347))),f317(f317(f8(f904(x45344,a893),f904(x45343,f904(x45344,a893)),x45342),f16(f904(x45344,a893),x45343)),x45348)))),f317(f317(f244(x45343,x45344),f317(f317(f34(x45341,f904(x45343,a893)),x45345),x45347)),f317(f16(f904(x45344,a893),x45343),f317(f317(f34(x45342,f904(x45344,a893)),x45346),x45348))))
% 94.68/94.44 [4475]E(f317(f317(f249(x44751,x44752,x44753,x44754),f317(f317(f249(x44751,x44755,x44756,f903(x44752,x44753)),x44757),x44758)),x44759),f317(f317(f249(x44751,x44755,x44756,x44754),x44757),f317(f317(f7(x44755,f904(x44752,f904(x44753,x44754)),f904(x44756,x44754)),f317(f317(f8(f904(x44756,f903(x44752,x44753)),f904(f904(x44752,f904(x44753,x44754)),f904(x44756,x44754)),x44755),f249(x44756,x44752,x44753,x44754)),x44758)),x44759)))
% 94.68/94.44 [4504]E(f317(f67(f903(x45041,x45042),f903(x45043,x45044),f903(x45045,x45046),f248(x45041,x45043,x45042,x45044,x45047,x45048)),f248(x45045,x45041,x45046,x45042,x45049,x450410)),f248(x45045,x45043,x45046,x45044,f317(f67(x45041,x45043,x45045,x45047),x45049),f317(f67(x45042,x45044,x45046,x45048),x450410)))
% 94.68/94.44 [4510]E(f317(f248(x45101,x45102,x45103,x45104,x45105,x45106),f317(f248(x45107,x45101,x45108,x45103,x45109,x451010),x451011)),f317(f248(x45107,x45102,x45108,x45104,f317(f67(x45101,x45102,x45107,x45105),x45109),f317(f67(x45103,x45104,x45108,x45106),x451010)),x451011))
% 94.68/94.44 [4638]~P2(x46381)+P2(f900(x46381))
% 94.68/94.44 [4639]~P60(x46391)+P60(f900(x46391))
% 94.68/94.44 [4640]~P106(x46401)+P106(f898(x46401))
% 94.68/94.44 [4643]~P127(x46431)+~E(f72(x46431),f2(x46431))
% 94.68/94.44 [4645]~E(x46451,f2(a89))+E(f317(a22,x46451),f2(a1))
% 94.68/94.44 [4646]~E(x46461,f2(a1))+E(f76(a1,x46461),f2(a1))
% 94.68/94.44 [4652]~P144(x46521)+P27(x46521,f2(x46521))
% 94.68/94.44 [4654]~P66(x46541)+P13(x46541,f103(x46541))
% 94.68/94.44 [4663]P1(x46631)+P1(f317(a312,x46631))
% 94.68/94.44 [4717]~P144(x47171)+~P27(x47171,f72(x47171))
% 94.68/94.44 [4754]~P1(x47541)+~P1(f317(a312,x47541))
% 94.68/94.44 [4775]E(f317(a95,x47751),f2(a897))+~P1(f317(a183,x47751))
% 94.68/94.44 [4841]~P98(x48411)+P14(x48411,x48411,f75(x48411))
% 94.68/94.44 [4842]~P66(x48421)+P14(x48421,x48421,f228(x48421))
% 94.68/94.44 [4843]~P66(x48431)+P14(x48431,x48431,f223(x48431))
% 94.68/94.44 [4844]~P99(x48441)+P14(x48441,x48441,f91(x48441))
% 94.68/94.44 [4845]~P105(x48451)+P14(x48451,x48451,f92(x48451))
% 94.68/94.44 [4846]~P73(x48461)+P16(x48461,x48461,f75(x48461))
% 94.68/94.44 [4649]~E(x46491,f2(a897))+E(f317(f90(a1),x46491),f2(a1))
% 94.68/94.44 [4656]~P94(x46561)+E(f317(f94(x46561),a77),f2(x46561))
% 94.68/94.44 [4659]~E(f515(x46591),f2(a897))+E(f317(f155(a897),x46591),f2(a897))
% 94.68/94.44 [4660]~P109(x46601)+E(f226(x46601,f224(x46601)),f228(x46601))
% 94.68/94.44 [4661]~P109(x46611)+E(f227(x46611,f224(x46611)),f223(x46611))
% 94.68/94.44 [4662]~P91(x46621)+E(f76(x46621,f2(x46621)),f2(x46621))
% 94.68/94.44 [4671]~P144(x46711)+E(f317(f90(x46711),f72(a897)),f72(x46711))
% 94.68/94.44 [4672]~P144(x46721)+E(f317(f90(x46721),f2(a897)),f2(x46721))
% 94.68/94.44 [4673]~P141(x46731)+E(f317(f93(x46731),f72(a1)),f72(x46731))
% 94.68/94.44 [4674]~P141(x46741)+E(f317(f93(x46741),f2(a1)),f2(x46741))
% 94.68/94.44 [4675]E(x46751,f2(a897))+~E(f317(f90(a1),x46751),f2(a1))
% 94.68/94.44 [4711]~P97(x47111)+E(f317(f73(x47111),f178(x47111)),f232(x47111))
% 94.68/94.44 [4712]~P75(x47121)+E(f317(f73(x47121),f2(x47121)),f2(x47121))
% 94.68/94.44 [4713]~P97(x47131)+E(f317(f73(x47131),f232(x47131)),f178(x47131))
% 94.68/94.44 [4714]~P111(x47141)+E(f317(f70(x47141),f72(x47141)),f72(x47141))
% 94.68/94.44 [4715]~P86(x47151)+E(f317(f70(x47151),f2(x47151)),f2(x47151))
% 94.68/94.44 [4716]~P81(x47161)+E(f317(f155(x47161),f103(x47161)),f2(x47161))
% 94.68/94.44 [4734]~P35(x47341)+P39(f317(f162(a1),x47341))
% 94.68/94.44 [4759]~P94(x47591)+E(f317(f73(x47591),f72(x47591)),f317(f94(x47591),a87))
% 94.68/94.44 [4774]~P94(x47741)+P27(x47741,f317(f94(x47741),a77))
% 94.68/94.44 [4800]P35(x48001)+~P39(f317(f162(a1),x48001))
% 94.68/94.44 [4847]E(f317(f90(a1),f317(a95,x48471)),x48471)+P1(f317(a183,x48471))
% 94.68/94.44 [4917]~P115(x49171)+E(f235(x49171,f72(x49171),f75(x49171)),f234(x49171))
% 94.68/94.44 [4950]~P94(x49501)+~P27(x49501,f317(f94(x49501),a87))
% 94.68/94.44 [5103]E(f317(f70(a1),x51031),x51031)+P1(f317(f317(f225(a1),x51031),f2(a1)))
% 94.68/94.44 [5121]~E(f317(a95,x51211),f2(a897))+P1(f317(f317(f224(a1),x51211),f2(a1)))
% 94.68/94.44 [5187]~P1(f317(a183,x51871))+P1(f317(f317(f225(a1),x51871),f2(a1)))
% 94.68/94.44 [5227]~P110(x52271)+P1(f317(f317(f224(x52271),f2(x52271)),f72(x52271)))
% 94.68/94.44 [5228]~P141(x52281)+P1(f317(f317(f319(x52281),f72(x52281)),f100(x52281)))
% 94.68/94.44 [5229]~P144(x52291)+P1(f317(f317(f319(x52291),f72(x52291)),f176(x52291)))
% 94.68/94.44 [5230]~P141(x52301)+P1(f317(f317(f319(x52301),f2(x52301)),f100(x52301)))
% 94.68/94.44 [5231]~P144(x52311)+P1(f317(f317(f319(x52311),f2(x52311)),f176(x52311)))
% 94.68/94.44 [5232]~P110(x52321)+P1(f317(f317(f225(x52321),f2(x52321)),f72(x52321)))
% 94.68/94.44 [5284]E(x52841,f72(a897))+~P1(f317(f317(f277(a897),x52841),f72(a897)))
% 94.68/94.44 [5285]E(x52851,f2(a897))+~P1(f317(f317(f224(a897),x52851),f2(a897)))
% 94.68/94.44 [5327]E(f317(a95,x53271),f2(a897))+~P1(f317(f317(f224(a1),x53271),f2(a1)))
% 94.68/94.44 [5385]P1(f317(a183,x53851))+~P1(f317(f317(f225(a1),x53851),f2(a1)))
% 94.68/94.44 [5392]~P66(x53921)+P16(x53921,f898(x53921),f138(x53921,x53921,f5(x53921)))
% 94.68/94.44 [5410]P39(x54101)+~P1(f317(f317(f224(a1),f2(a1)),f796(x54101)))
% 94.68/94.44 [5415]E(f317(f70(a1),x54151),f317(f73(a1),x54151))+~P1(f317(f317(f225(a1),x54151),f2(a1)))
% 94.68/94.44 [5587]~P110(x55871)+~P1(f317(f317(f224(x55871),f72(x55871)),f2(x55871)))
% 94.68/94.44 [5588]~P110(x55881)+~P1(f317(f317(f225(x55881),f72(x55881)),f2(x55881)))
% 94.68/94.44 [5604]~E(x56041,f2(a897))+P1(f317(f317(f224(a1),f317(f90(a1),x56041)),f2(a1)))
% 94.68/94.44 [5605]~E(x56051,f2(a1))+P1(f317(f317(f225(a1),f317(f70(a1),x56051)),f72(a1)))
% 94.68/94.44 [5727]~P81(x57271)+E(f132(x57271,x57271,f74(x57271),f2(x57271)),f155(x57271))
% 94.68/94.44 [5910]~P96(x59101)+P24(a897,x59101,f90(x59101),f232(f904(a897,a893)))
% 94.68/94.44 [6117]E(x61171,f2(a897))+~P1(f317(f317(f224(a1),f317(f90(a1),x61171)),f2(a1)))
% 94.68/94.44 [6118]E(x61181,f2(a1))+~P1(f317(f317(f225(a1),f317(f70(a1),x61181)),f72(a1)))
% 94.68/94.44 [6941]~P1(f317(f317(f225(a1),x69411),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x69411),x69411)),f2(a1)))
% 94.68/94.44 [7504]P1(f317(f317(f225(a1),x75041),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x75041),x75041)),f2(a1)))
% 94.68/94.44 [8055]E(x80551,f317(a3,f2(a897)))+P1(f317(f317(f225(a897),f317(f317(f23(a897),f317(a20,x80551)),f317(a102,f2(a897)))),f317(a20,x80551)))
% 94.68/94.44 [8821]~P1(f317(f317(f225(a1),x88211),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x88211),x88211)),a87)),f2(a1)))
% 94.68/94.44 [8918]~P1(f317(f317(f225(a1),x89181),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x89181)),x89181)),f2(a1)))
% 94.68/94.44 [9237]P1(f317(f317(f225(a1),x92371),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92371),x92371)),a87)),f2(a1)))
% 94.68/94.44 [9299]P1(f317(f317(f225(a1),x92991),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f74(a1),f72(a1)),x92991)),x92991)),f2(a1)))
% 94.68/94.44 [4748]~E(a77,x47481)+E(f317(f317(f74(a1),x47481),x47481),a77)
% 94.68/94.44 [4749]~E(x47491,a77)+E(f317(f317(f74(a1),x47491),x47491),a77)
% 94.68/94.44 [4760]E(x47601,f2(a1))+E(f317(f317(f30(a1),x47601),x47601),f72(a1))
% 94.68/94.44 [4894]E(x48941,a77)+~E(f317(f317(f74(a1),x48941),x48941),a77)
% 94.68/94.44 [4895]E(a77,x48951)+~E(f317(f317(f74(a1),x48951),x48951),a77)
% 94.68/94.44 [4907]~P5(x49071)+E(f32(x49071,f178(f904(x49071,a893))),f232(x49071))
% 94.68/94.44 [4908]~P5(x49081)+E(f32(x49081,f232(f904(x49081,a893))),f178(x49081))
% 94.68/94.44 [4909]~P5(x49091)+E(f31(x49091,f178(f904(x49091,a893))),f178(x49091))
% 94.68/94.44 [4910]~P5(x49101)+E(f31(x49101,f232(f904(x49101,a893))),f232(x49101))
% 94.68/94.44 [4911]~P66(x49111)+E(f129(x49111,f178(f904(x49111,a893))),f103(x49111))
% 94.68/94.44 [5058]E(x50581,f2(a897))+P1(f317(f317(f225(a897),f2(a897)),x50581))
% 94.68/94.44 [5078]~P6(x50781)+P1(f317(f317(f224(a1),f2(a1)),x50781))
% 94.68/94.44 [5112]~E(f317(f94(a897),x51121),f2(a897))+P1(f317(f317(f224(a1),x51121),a77))
% 94.68/94.44 [5117]P39(x51171)+P1(f317(f317(f319(a1),f796(x51171)),x51171))
% 94.68/94.44 [5118]E(x51181,f317(a3,f2(a897)))+P1(f317(f317(f224(a89),f72(a89)),x51181))
% 94.68/94.44 [5159]P1(f317(a183,x51591))+P1(f317(f317(f224(a1),f2(a1)),x51591))
% 94.68/94.44 [5209]E(f317(f90(a1),f317(a95,x52091)),f2(a1))+P1(f317(f317(f224(a1),f2(a1)),x52091))
% 94.68/94.44 [5266]E(f317(f90(a1),f317(f94(a897),x52661)),f317(f94(a1),x52661))+P1(f317(a183,f317(f94(a1),x52661)))
% 94.68/94.44 [5291]E(f317(f94(a897),x52911),f2(a897))+~P1(f317(a183,f317(f94(a1),x52911)))
% 94.68/94.44 [5292]E(f317(f94(a897),x52921),f2(a897))+~P1(f317(f317(f224(a1),x52921),a77))
% 94.68/94.44 [5324]P6(x53241)+~P1(f317(f317(f224(a1),f2(a1)),x53241))
% 94.68/94.44 [5380]P149(f222(a894,f33(x53801)))+~P1(f317(f317(f319(a895),x53801),a905))
% 94.68/94.44 [5395]E(f317(a102,f534(x53951)),x53951)+~P1(f317(f317(f225(a897),f2(a897)),x53951))
% 94.68/94.44 [5404]E(f317(a102,f317(f94(a897),x54041)),f72(a897))+~P1(f317(a183,f317(f94(a1),x54041)))
% 94.68/94.44 [5411]E(f317(f90(a1),f323(x54111)),x54111)+~P1(f317(f317(f225(a1),f2(a1)),x54111))
% 94.68/94.44 [5418]~E(x54181,f317(a3,f2(a897)))+~P1(f317(f317(f224(a89),f72(a89)),x54181))
% 94.68/94.44 [5425]E(f317(f90(a1),f317(f94(a897),x54251)),f2(a1))+~P1(f317(a183,f317(f94(a1),x54251)))
% 94.68/94.44 [5451]E(f317(f155(a897),x54511),f2(a897))+P1(f317(f317(f319(a897),f515(x54511)),f317(f162(a897),x54511)))
% 94.68/94.44 [5472]E(f317(f90(a1),f317(a95,x54721)),x54721)+~P1(f317(f317(f224(a1),f2(a1)),x54721))
% 94.68/94.44 [5480]~P1(f317(a183,x54801))+~P1(f317(f317(f224(a1),f2(a1)),x54801))
% 94.68/94.44 [5580]E(f317(f317(f74(a897),f72(a897)),f317(f94(a897),x55801)),f72(a897))+~P1(f317(f317(f225(a1),x55801),a77))
% 94.68/94.44 [5646]E(x56461,f2(a897))+~P1(f317(f317(f225(a897),x56461),f317(a102,f2(a897))))
% 94.68/94.44 [5668]E(x56681,f317(a102,f2(a897)))+~P1(f317(f317(f277(a897),x56681),f317(a102,f2(a897))))
% 94.68/94.44 [5686]E(f317(f317(f23(a897),f317(f94(a897),x56861)),f72(a897)),f2(a897))+~P1(f317(f317(f224(a1),x56861),a77))
% 94.68/94.44 [5687]E(f317(f317(f74(a897),f317(f94(a897),x56871)),f72(a897)),f72(a897))+~P1(f317(f317(f225(a1),x56871),a77))
% 94.68/94.44 [5699]~P39(x56991)+E(f317(f29(a897),f317(f300(a1,a897,a95),x56991)),f317(f29(a1),x56991))
% 94.68/94.44 [5728]~P66(x57281)+E(f227(x57281,f317(f7(x57281,x57281,a893),f224(x57281))),f228(x57281))
% 94.68/94.44 [5729]~P66(x57291)+E(f226(x57291,f317(f7(x57291,x57291,a893),f224(x57291))),f223(x57291))
% 94.68/94.44 [5739]E(f40(a897,f317(a102,f2(a897)),f317(f94(a897),x57391)),f317(a102,f2(a897)))+~P1(f317(a183,f317(f94(a1),x57391)))
% 94.68/94.44 [5748]~P1(f317(f317(f225(a1),f2(a1)),x57481))+P1(f317(f317(f224(a1),f72(a1)),x57481))
% 94.68/94.44 [5749]P1(f317(f317(f225(a1),f2(a1)),x57491))+~P1(f317(f317(f224(a1),f72(a1)),x57491))
% 94.68/94.44 [5760]E(f317(a102,f317(f317(f23(a897),x57601),f72(a897))),x57601)+~P1(f317(f317(f225(a897),f2(a897)),x57601))
% 94.68/94.44 [5816]P1(f317(f317(f225(a897),f2(a897)),f323(x58161)))+~P1(f317(f317(f225(a1),f2(a1)),x58161))
% 94.68/94.44 [5877]E(f40(a1,f317(f94(a1),a87),x58771),f317(f317(f23(a1),x58771),f72(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x58771))
% 94.68/94.44 [5923]~P1(f317(f317(f225(a1),a77),x59231))+P1(f317(f317(f225(a897),f2(a897)),f317(f94(a897),x59231)))
% 94.68/94.44 [5928]E(f317(a20,f786(x59281)),x59281)+~P1(f317(f317(f319(a897),x59281),f232(f904(a897,a893))))
% 94.68/94.44 [5981]P1(f317(f317(f225(a897),f2(a897)),f317(a95,x59811)))+~P1(f317(f317(f225(a1),f2(a1)),x59811))
% 94.68/94.44 [6032]~P1(f317(f317(f225(a897),f2(a897)),x60321))+P1(f317(f317(f225(a1),f2(a1)),f317(f90(a1),x60321)))
% 94.68/94.44 [6068]~P1(f317(f317(f225(a897),f2(a897)),f317(a95,x60681)))+P1(f317(f317(f225(a1),f2(a1)),x60681))
% 94.68/94.44 [6083]~P39(x60831)+E(f317(f300(a897,a1,f90(a1)),f317(f300(a1,a897,a95),x60831)),x60831)
% 94.68/94.44 [6096]P1(f317(f317(f225(a1),a77),x60961))+~P1(f317(f317(f225(a897),f2(a897)),f317(f94(a897),x60961)))
% 94.68/94.44 [6155]P1(f317(f317(f225(a897),f2(a897)),x61551))+~P1(f317(f317(f225(a1),f2(a1)),f317(f90(a1),x61551)))
% 94.68/94.44 [6273]E(f317(f300(a897,a1,f90(a1)),f317(f272(a897),f317(a95,x62731))),f317(f292(a1,f2(a1)),x62731))+~P1(f317(f317(f224(a1),f2(a1)),x62731))
% 94.68/94.44 [6291]~P110(x62911)+P1(f317(f317(f225(x62911),f2(x62911)),f317(f317(f74(x62911),f72(x62911)),f72(x62911))))
% 94.68/94.44 [6342]P1(f317(f317(f225(a897),f317(a102,f2(a897))),f317(a95,x63421)))+~P1(f317(f317(f225(a1),f72(a1)),x63421))
% 94.68/94.44 [6444]E(x64441,f2(a1))+P1(f317(f44(f2(a1),x64441),f317(f317(f242(a1,a1),f2(a1)),f2(a1))))
% 94.68/94.44 [6618]~P1(f317(f317(f225(a897),f317(a102,f2(a897))),f317(a95,x66181)))+P1(f317(f317(f225(a1),f72(a1)),x66181))
% 94.68/94.44 [7059]~P117(x70591)+P36(x70591,f317(f252(f903(x70591,x70591)),f317(f247(x70591,x70591,a893),f225(x70591))))
% 94.68/94.44 [5633]E(f317(f94(a897),f317(f317(f23(a1),x56331),a87)),f317(a102,f317(f94(a897),x56331)))+P1(f317(a183,f317(f94(a1),x56331)))
% 94.68/94.44 [5649]~P35(x56491)+E(f317(f317(f144(a897,a1),f90(a1)),f317(f317(f144(a1,a897),a95),x56491)),x56491)
% 94.68/94.44 [5766]E(f317(f73(a1),f317(f90(a1),f317(a102,f324(x57661)))),x57661)+~P1(f317(f317(f225(a1),x57661),f2(a1)))
% 94.68/94.44 [5776]E(f317(f317(f74(a897),f72(a897)),f317(f94(a897),x57761)),f317(f94(a897),f317(f317(f23(a1),x57761),a87)))+P1(f317(f317(f225(a1),x57761),a77))
% 94.68/94.44 [5818]E(f317(f317(f30(a1),f317(f94(a1),a87)),x58181),f317(f94(a1),a87))+~P1(f317(f317(f225(a1),f2(a1)),x58181))
% 94.68/94.44 [5919]E(f317(f317(f23(a897),f317(f94(a897),x59191)),f72(a897)),f317(f94(a897),f317(f317(f74(a1),x59191),a87)))+P1(f317(f317(f224(a1),x59191),a77))
% 94.68/94.44 [5920]E(f317(f317(f74(a897),f317(f94(a897),x59201)),f72(a897)),f317(f94(a897),f317(f317(f23(a1),x59201),a87)))+P1(f317(f317(f225(a1),x59201),a77))
% 94.68/94.44 [5966]E(f317(a95,f317(f317(f74(a1),f72(a1)),x59661)),f317(a102,f317(a95,x59661)))+~P1(f317(f317(f224(a1),f2(a1)),x59661))
% 94.68/94.44 [6003]E(f317(a102,f317(f317(f23(a897),x60031),f317(a102,f2(a897)))),x60031)+~P1(f317(f317(f225(a897),f2(a897)),x60031))
% 94.68/94.44 [6222]E(f40(a897,f317(a102,f2(a897)),f317(f94(a897),x62221)),f317(a95,f40(a1,f72(a1),f317(f94(a1),x62221))))+P1(f317(a183,f317(f94(a1),x62221)))
% 94.68/94.44 [6266]~P1(f317(f317(f224(a1),a77),x62661))+P1(f317(f317(f224(a1),a77),f317(f317(f74(a1),x62661),x62661)))
% 94.68/94.44 [6267]~P1(f317(f317(f225(a1),a87),x62671))+P1(f317(f317(f224(a1),a87),f317(f317(f74(a1),x62671),x62671)))
% 94.68/94.44 [6268]~P1(f317(f317(f225(a1),a77),x62681))+P1(f317(f317(f225(a1),a77),f317(f317(f74(a1),x62681),x62681)))
% 94.68/94.44 [6269]~P1(f317(f317(f225(a1),a87),x62691))+P1(f317(f317(f225(a1),a87),f317(f317(f74(a1),x62691),x62691)))
% 94.68/94.44 [6458]~P1(f317(f28(x64581),f232(f904(x64581,a893))))+P1(f317(f28(f900(x64581)),f232(f904(f900(x64581),a893))))
% 94.68/94.44 [6545]~P1(f317(f317(f224(a1),f2(a1)),x65451))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f74(a1),f72(a1)),x65451)))
% 94.68/94.44 [6552]E(f317(f241(a1,a1),f42(f72(a1),f317(f94(a1),x65521))),f317(f317(f30(a1),f72(a1)),f317(f94(a1),x65521)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x65521)))
% 94.68/94.44 [6577]E(f317(f246(a1,a1),f42(f72(a1),f317(f94(a1),x65771))),f40(a1,f72(a1),f317(f94(a1),x65771)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x65771)))
% 94.68/94.44 [6589]P1(f317(f28(x65891),f232(f904(x65891,a893))))+~P1(f317(f28(f900(x65891)),f232(f904(f900(x65891),a893))))
% 94.68/94.44 [6619]P1(f317(f317(f224(a1),a77),x66191))+~P1(f317(f317(f224(a1),a77),f317(f317(f74(a1),x66191),x66191)))
% 94.68/94.44 [6620]P1(f317(f317(f225(a1),a77),x66201))+~P1(f317(f317(f225(a1),a77),f317(f317(f74(a1),x66201),x66201)))
% 94.68/94.44 [6621]P1(f317(f317(f225(a1),a87),x66211))+~P1(f317(f317(f224(a1),a87),f317(f317(f74(a1),x66211),x66211)))
% 94.68/94.44 [6622]P1(f317(f317(f225(a1),a87),x66221))+~P1(f317(f317(f225(a1),a87),f317(f317(f74(a1),x66221),x66221)))
% 94.68/94.44 [6945]~P1(f317(f28(x69451),f232(f904(x69451,a893))))+P1(f317(f317(f225(a897),f2(a897)),f317(f29(x69451),f232(f904(x69451,a893)))))
% 94.68/94.44 [7542]P1(f317(f28(a897),x75421))+~P1(f317(f28(a1),f317(f300(a897,a1,f90(a1)),x75421)))
% 94.68/94.44 [5556]~E(a87,x55561)+E(f317(f317(f23(a1),f317(f317(f74(a1),x55561),x55561)),a87),a87)
% 94.68/94.44 [5557]~E(x55571,a87)+E(f317(f317(f23(a1),f317(f317(f74(a1),x55571),x55571)),a87),a87)
% 94.68/94.44 [6091]E(x60911,a87)+~E(f317(f317(f23(a1),f317(f317(f74(a1),x60911),x60911)),a87),a87)
% 94.68/94.44 [6092]E(a87,x60921)+~E(f317(f317(f23(a1),f317(f317(f74(a1),x60921),x60921)),a87),a87)
% 94.68/94.44 [6514]~E(f317(f94(a897),x65141),f2(a897))+P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x65141),a87))))
% 94.68/94.44 [6875]~P1(f317(a183,f317(f94(a1),x68751)))+P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x68751),x68751))))
% 94.68/94.44 [6876]~P1(f317(f317(f224(a1),x68761),a77))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x68761),x68761)),a77))
% 94.68/94.44 [6877]~P1(f317(f317(f224(a1),x68771),a87))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x68771),x68771)),a87))
% 94.68/94.44 [6878]~P1(f317(f317(f225(a1),x68781),a77))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68781),x68781)),a77))
% 94.68/94.44 [6879]~P1(f317(f317(f224(a1),x68791),a87))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68791),x68791)),a87))
% 94.68/94.44 [7205]E(f317(f94(a897),x72051),f2(a897))+~P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x72051),a87))))
% 94.68/94.44 [7457]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x74571)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f74(a1),x74571),x74571))))
% 94.68/94.44 [7458]P1(f317(a183,f317(f94(a1),x74581)))+~P1(f317(a183,f317(f94(a1),f317(f317(f74(a1),x74581),x74581))))
% 94.68/94.44 [7459]P1(f317(f317(f224(a1),x74591),a77))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x74591),x74591)),a77))
% 94.68/94.44 [7460]P1(f317(f317(f224(a1),x74601),a87))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x74601),x74601)),a87))
% 94.68/94.44 [7461]P1(f317(f317(f224(a1),x74611),a87))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74611),x74611)),a87))
% 94.68/94.44 [7462]P1(f317(f317(f225(a1),x74621),a77))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74621),x74621)),a77))
% 94.68/94.44 [7824]E(f317(a97,f478(x78241)),x78241)+~P1(f317(f317(f319(f904(f903(a897,a897),a893)),x78241),a88))
% 94.68/94.44 [6431]~P94(x64311)+E(f317(f94(x64311),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f72(x64311))
% 94.68/94.44 [6925]~P1(f317(a183,f317(f94(a1),x69251)))+E(f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x69251),x69251)),a87)),f2(a897))
% 94.68/94.44 [8000]~P1(f317(f317(f225(a1),f317(f94(a1),x80001)),f2(a1)))+E(f317(f241(a1,a1),f317(a46,f45(f317(f73(a1),f72(a1)),f317(f73(a1),f317(f94(a1),x80001))))),f317(f317(f30(a1),f72(a1)),f317(f94(a1),x80001)))
% 94.68/94.44 [8013]~P1(f317(f317(f225(a1),f317(f94(a1),x80131)),f2(a1)))+E(f317(f246(a1,a1),f317(a46,f45(f317(f73(a1),f72(a1)),f317(f73(a1),f317(f94(a1),x80131))))),f40(a1,f72(a1),f317(f94(a1),x80131)))
% 94.68/94.44 [8062]~P1(f317(f317(f224(a1),a77),x80621))+P1(f317(f317(f224(a1),a77),f317(f317(f23(a1),f317(f317(f74(a1),x80621),x80621)),a87)))
% 94.68/94.44 [8063]~P1(f317(f317(f224(a1),a87),x80631))+P1(f317(f317(f224(a1),a87),f317(f317(f23(a1),f317(f317(f74(a1),x80631),x80631)),a87)))
% 94.68/94.44 [8064]~P1(f317(f317(f224(a1),a77),x80641))+P1(f317(f317(f225(a1),a77),f317(f317(f23(a1),f317(f317(f74(a1),x80641),x80641)),a87)))
% 94.68/94.44 [8065]~P1(f317(f317(f225(a1),a87),x80651))+P1(f317(f317(f225(a1),a87),f317(f317(f23(a1),f317(f317(f74(a1),x80651),x80651)),a87)))
% 94.68/94.44 [8363]~P94(x83631)+~P27(x83631,f317(f94(x83631),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))
% 94.68/94.44 [8546]P1(f317(f317(f224(a1),a77),x85461))+~P1(f317(f317(f224(a1),a77),f317(f317(f23(a1),f317(f317(f74(a1),x85461),x85461)),a87)))
% 94.68/94.44 [8547]P1(f317(f317(f224(a1),a77),x85471))+~P1(f317(f317(f225(a1),a77),f317(f317(f23(a1),f317(f317(f74(a1),x85471),x85471)),a87)))
% 94.68/94.44 [8548]P1(f317(f317(f224(a1),a87),x85481))+~P1(f317(f317(f224(a1),a87),f317(f317(f23(a1),f317(f317(f74(a1),x85481),x85481)),a87)))
% 94.68/94.44 [8549]P1(f317(f317(f225(a1),a87),x85491))+~P1(f317(f317(f225(a1),a87),f317(f317(f23(a1),f317(f317(f74(a1),x85491),x85491)),a87)))
% 94.68/94.44 [8868]E(f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x88681),x88681)),a87)),f317(f317(f80(a897,a897),f317(f94(a897),x88681)),f317(f317(f8(a897,a897,a897),a102),f317(f317(f18(a897,a897,a897),f74(a897)),f5(a897)))))+P1(f317(a183,f317(f94(a1),x88681)))
% 94.68/94.44 [9736]E(x97361,f178(f904(f903(a897,a897),a893)))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x97361),f178(f904(f903(a897,a897),a893)))),a63))
% 94.68/94.44 [8795]~P1(f317(a183,f317(f94(a1),x87951)))+P1(f317(a183,f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x87951),x87951)),a87))))
% 94.68/94.44 [8796]~P1(f317(f317(f225(a1),x87961),a77))+P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x87961),x87961)),a87)),a77))
% 94.68/94.44 [8797]~P1(f317(f317(f224(a1),x87971),a87))+P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x87971),x87971)),a87)),a87))
% 94.68/94.44 [8798]~P1(f317(f317(f225(a1),x87981),a77))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x87981),x87981)),a87)),a77))
% 94.68/94.44 [8799]~P1(f317(f317(f225(a1),x87991),a87))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x87991),x87991)),a87)),a87))
% 94.68/94.44 [8909]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x89091)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x89091),x89091)),a87))))
% 94.68/94.44 [9067]~P94(x90671)+E(f317(f317(f74(x90671),f72(x90671)),f72(x90671)),f317(f94(x90671),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))
% 94.68/94.44 [9221]P1(f317(a183,f317(f94(a1),x92211)))+~P1(f317(a183,f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92211),x92211)),a87))))
% 94.68/94.44 [9222]P1(f317(f317(f224(a1),x92221),a87))+~P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92221),x92221)),a87)),a87))
% 94.68/94.44 [9223]P1(f317(f317(f225(a1),x92231),a77))+~P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92231),x92231)),a87)),a77))
% 94.68/94.44 [9224]P1(f317(f317(f225(a1),x92241),a77))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92241),x92241)),a87)),a77))
% 94.68/94.44 [9225]P1(f317(f317(f225(a1),x92251),a87))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92251),x92251)),a87)),a87))
% 94.68/94.44 [9781]~P1(f317(f28(f903(a897,a897)),x97811))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f178(f904(f903(a897,a897),a893))),x97811)),a64))
% 94.68/94.44 [9558]~P144(x95581)+E(f317(f317(f234(x95581),f72(x95581)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95581))
% 94.68/94.44 [9559]~P144(x95591)+E(f317(f317(f234(x95591),f2(x95591)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(x95591))
% 94.68/94.44 [10004]~P1(f317(f317(f225(a897),f72(a897)),x100041))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f30(a897),x100041),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.44 [10010]~P1(f317(f317(f225(a897),f2(a897)),x100101))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f30(a897),f317(f317(f74(a897),x100101),f72(a897))),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.44 [10048]~E(f40(a897,x100481,f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(a897))+P1(f317(f317(f225(a897),f2(a897)),f40(a897,x100481,f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.44 [10078]E(f40(a897,x100781,f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(a897))+~P1(f317(f317(f225(a897),f2(a897)),f40(a897,x100781,f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.44 [4680]~P7(x46801,x46802)+P42(x46801,x46802)
% 94.68/94.44 [4681]~P36(x46811,x46812)+P57(x46811,x46812)
% 94.68/94.44 [4682]~P43(x46821,x46822)+P57(x46821,x46822)
% 94.68/94.44 [4684]~P7(x46841,x46842)+P49(x46841,x46842)
% 94.68/94.44 [4686]~P15(x46861,x46862)+P49(x46861,x46862)
% 94.68/94.44 [4688]~P7(x46881,x46882)+P50(x46881,x46882)
% 94.68/94.44 [4690]~P15(x46901,x46902)+P50(x46901,x46902)
% 94.68/94.44 [4691]~P7(x46911,x46912)+P15(x46911,x46912)
% 94.68/94.44 [4641]~E(x46411,x46412)+E(f259(x46411,x46412),f72(a89))
% 94.68/94.44 [4644]E(f206(x46441,x46442),x46441)+~E(x46442,f2(a897))
% 94.68/94.44 [4651]~E(x46512,f103(x46511))+E(f142(x46511,x46512),f103(x46511))
% 94.68/94.44 [4670]~E(f142(x46702,x46701),f103(x46702))+E(x46701,f103(x46702))
% 94.68/94.44 [4695]~P65(x46952)+P65(f904(x46951,x46952))
% 94.68/94.44 [4696]~P108(x46962)+P108(f904(x46961,x46962))
% 94.68/94.44 [4697]~P109(x46972)+P109(f904(x46971,x46972))
% 94.68/94.44 [4698]~P68(x46982)+P68(f904(x46981,x46982))
% 94.68/94.44 [4699]~P83(x46992)+P83(f904(x46991,x46992))
% 94.68/94.44 [4700]~P90(x47002)+P90(f904(x47001,x47002))
% 94.68/94.44 [4701]~P97(x47012)+P97(f904(x47011,x47012))
% 94.68/94.44 [4702]~P100(x47022)+P99(f904(x47021,x47022))
% 94.68/94.44 [4703]~P100(x47032)+P100(f904(x47031,x47032))
% 94.68/94.44 [4704]~P102(x47042)+P101(f904(x47041,x47042))
% 94.68/94.44 [4705]~P100(x47052)+P105(f904(x47051,x47052))
% 94.68/94.44 [4706]~P103(x47062)+P103(f904(x47061,x47062))
% 94.68/94.44 [4707]~P5(x47072)+P5(f904(x47071,x47072))
% 94.68/94.44 [4708]~P116(x47082)+P116(f904(x47081,x47082))
% 94.68/94.44 [4709]~P102(x47092)+P104(f904(x47091,x47092))
% 94.68/94.44 [4710]~P102(x47102)+P102(f904(x47101,x47102))
% 94.68/94.44 [4723]E(x47231,x47232)+~E(f317(a102,x47231),f317(a102,x47232))
% 94.68/94.44 [4724]E(x47241,x47242)+~E(f317(a97,x47241),f317(a97,x47242))
% 94.68/94.44 [4725]E(x47251,x47252)+~E(f317(a3,x47251),f317(a3,x47252))
% 94.68/94.44 [4727]E(x47271,x47272)+~E(f317(a20,x47271),f317(a20,x47272))
% 94.68/94.44 [4776]P38(x47761,x47762)+~E(f683(x47762,x47761),f684(x47762,x47761))
% 94.68/94.44 [4806]~P57(x48061,x48062)+P38(x48061,f297(x48061,x48062))
% 94.68/94.44 [4807]~P51(x48071,x48072)+P51(x48071,f297(x48071,x48072))
% 94.68/94.44 [4820]~P3(x48201)+E(f40(x48201,x48202,x48202),f2(x48201))
% 94.68/94.44 [4854]~P36(x48541,x48542)+P36(f898(x48541),f136(x48541,x48542))
% 94.68/94.44 [4855]~P36(x48551,x48552)+P36(f898(x48551),f135(x48551,x48552))
% 94.68/94.44 [4856]~P37(x48561,x48562)+P37(f898(x48561),f137(x48561,x48562))
% 94.68/94.44 [4857]~P37(x48571,x48572)+P37(f898(x48571),f148(x48571,x48572))
% 94.68/94.44 [4858]~P51(x48581,x48582)+P51(f898(x48581),f148(x48581,x48582))
% 94.68/94.44 [4955]~P36(x49551,x49552)+P36(f904(x49551,a893),f310(x49551,x49552))
% 94.68/94.44 [4956]~P36(x49561,x49562)+P36(f904(x49561,a893),f308(x49561,x49562))
% 94.68/94.44 [5087]~P6(x50871)+P39(f293(a1,x50871,x50872))
% 94.68/94.44 [5190]~P36(x51901,x51902)+P59(x51901,f61(x51901,x51901,x51902))
% 94.68/94.44 [5693]~P67(x56931)+P24(x56931,x56931,f73(x56931),x56932)
% 94.68/94.44 [4665]~E(x46652,f103(x46651))+E(f317(f157(x46651),x46652),f103(x46651))
% 94.68/94.44 [4666]~E(x46662,f103(x46661))+E(f317(f158(x46661),x46662),f103(x46661))
% 94.68/94.44 [4729]E(x47291,f317(a95,x47292))+~E(f317(f90(a1),x47291),x47292)
% 94.68/94.44 [4732]E(x47321,f103(x47322))+~E(f317(f157(x47322),x47321),f103(x47322))
% 94.68/94.44 [4733]E(x47331,f103(x47332))+~E(f317(f158(x47332),x47331),f103(x47332))
% 94.68/94.44 [4745]~P94(x47451)+E(f317(f94(x47451),x47452),f317(f93(x47451),x47452))
% 94.68/94.44 [4753]~P2(x47531)+P1(f317(f28(x47531),x47532))
% 94.68/94.44 [4761]~E(f643(x47612,x47611),f103(x47611))+E(f169(x47611,x47612),f103(f898(x47611)))
% 94.68/94.44 [4770]~E(x47702,f103(x47701))+E(f317(f162(x47701),x47702),f178(f904(x47701,a893)))
% 94.68/94.44 [4771]~E(x47712,f103(x47711))+E(f178(f904(x47711,a893)),f317(f162(x47711),x47712))
% 94.68/94.44 [4773]E(x47731,x47732)+~E(f317(f90(a1),x47731),f317(f90(a1),x47732))
% 94.68/94.44 [4777]E(f204(x47771,x47772),f2(a897))+P1(f317(f28(x47771),x47772))
% 94.68/94.44 [4795]~P111(x47951)+E(f76(x47951,f76(x47951,x47952)),f76(x47951,x47952))
% 94.68/94.44 [4809]~P112(x48091)+E(f317(f317(f234(x48091),x48092),f72(a897)),x48092)
% 94.68/94.44 [4810]~P82(x48101)+E(f317(f317(f234(x48101),x48102),f72(a897)),x48102)
% 94.68/94.44 [4811]~P51(x48111,x48112)+E(f317(f276(x48111,x48111),x48112),x48112)
% 94.68/94.44 [4815]E(x48151,x48152)+E(f259(x48151,x48152),f317(f317(f74(a89),x48152),f72(a89)))
% 94.68/94.44 [4818]E(f317(f29(x48181),x48182),f2(a897))+P1(f317(f28(x48181),x48182))
% 94.68/94.44 [4821]~E(f142(x48211,x48212),x48212)+P1(f317(f127(x48211),x48212))
% 94.68/94.44 [4824]~P75(x48241)+E(f317(f317(f23(x48241),x48242),f2(x48241)),x48242)
% 94.68/94.44 [4825]~P76(x48251)+E(f317(f317(f74(x48251),x48252),f2(x48251)),x48252)
% 94.68/94.44 [4826]~P81(x48261)+E(f317(f317(f74(x48261),x48262),f2(x48261)),x48262)
% 94.68/94.44 [4827]~P112(x48271)+E(f317(f317(f74(x48271),x48272),f2(x48271)),x48272)
% 94.68/94.44 [4828]~P112(x48281)+E(f317(f317(f75(x48281),x48282),f72(x48281)),x48282)
% 94.68/94.44 [4829]~P77(x48291)+E(f317(f317(f75(x48291),x48292),f72(x48291)),x48292)
% 94.68/94.44 [4830]~P82(x48301)+E(f317(f317(f75(x48301),x48302),f72(x48301)),x48302)
% 94.68/94.44 [4831]~P3(x48311)+E(f317(f317(f30(x48311),x48312),f72(x48311)),x48312)
% 94.68/94.44 [4832]~P122(x48321)+E(f317(f317(f281(x48321),x48322),f72(x48321)),x48322)
% 94.68/94.44 [4833]~P101(x48331)+E(f317(f317(f91(x48331),x48332),f178(x48331)),x48332)
% 94.68/94.44 [4834]~P104(x48341)+E(f317(f317(f92(x48341),x48342),f232(x48341)),x48342)
% 94.68/94.44 [4835]~P112(x48351)+E(f317(f317(f234(x48351),x48352),f2(a897)),f72(x48351))
% 94.68/94.44 [4836]~P115(x48361)+E(f317(f317(f234(x48361),x48362),f2(a897)),f72(x48361))
% 94.68/94.44 [4837]~E(x48372,f178(f904(x48371,a893)))+E(f317(f29(x48371),x48372),f2(a897))
% 94.68/94.44 [4848]~P3(x48481)+E(f40(x48481,x48482,f2(x48481)),x48482)
% 94.68/94.44 [4859]~P112(x48591)+E(f317(f317(f75(x48591),x48592),f2(x48591)),f2(x48591))
% 94.68/94.44 [4860]~P132(x48601)+E(f317(f317(f75(x48601),x48602),f2(x48601)),f2(x48601))
% 94.68/94.44 [4861]~P3(x48611)+E(f317(f317(f30(x48611),x48612),f2(x48611)),f2(x48611))
% 94.68/94.44 [4862]~P123(x48621)+E(f317(f317(f281(x48621),x48622),f2(x48621)),f2(x48621))
% 94.68/94.44 [4863]~P104(x48631)+E(f317(f317(f91(x48631),x48632),f232(x48631)),f232(x48631))
% 94.68/94.44 [4864]~P101(x48641)+E(f317(f317(f92(x48641),x48642),f178(x48641)),f178(x48641))
% 94.68/94.44 [4866]~P3(x48661)+E(f40(x48661,x48662,f72(x48661)),f2(x48661))
% 94.68/94.44 [4867]~P3(x48671)+E(f40(x48671,f2(x48671),x48672),f2(x48671))
% 94.68/94.44 [4896]E(x48961,f2(a897))+E(f50(x48962,x48961,f103(x48962)),f103(f898(x48962)))
% 94.68/94.44 [4919]P51(x49191,x49192)+~E(f317(f276(x49191,x49191),x49192),x49192)
% 94.68/94.44 [4920]P36(x49201,x49202)+~E(f516(x49202,x49201),f178(f904(x49201,a893)))
% 94.68/94.44 [4921]E(x49211,f103(x49212))+~E(f317(f162(x49212),x49211),f178(f904(x49212,a893)))
% 94.68/94.44 [4922]E(x49221,f103(x49222))+~E(f178(f904(x49222,a893)),f317(f162(x49222),x49221))
% 94.68/94.44 [4925]~E(x49251,x49252)+P1(f317(f317(a314,x49251),x49252))
% 94.68/94.44 [4935]P1(x49351)+P1(f317(f317(a320,x49351),x49352))
% 94.68/94.44 [4936]E(x49361,f103(x49362))+E(f317(f317(f154(x49362),x49361),f2(a897)),f317(f131(x49362),x49361))
% 94.68/94.44 [4939]E(f142(x49391,x49392),x49392)+~P1(f317(f127(x49391),x49392))
% 94.68/94.44 [4946]~P1(x49462)+P1(f317(f317(a320,x49461),x49462))
% 94.68/94.44 [4947]~P1(x49472)+P1(f317(f317(a316,x49471),x49472))
% 94.68/94.44 [4948]~P1(x49481)+P1(f317(f317(a316,x49481),x49482))
% 94.68/94.44 [4958]~E(f644(x49582,x49581),f648(x49582,x49581))+P1(f317(f127(x49581),x49582))
% 94.68/94.44 [4965]E(f317(f252(x49651),x49652),f178(f904(x49651,a893)))+P1(f317(x49652,f469(x49652)))
% 94.68/94.44 [4966]E(f178(f904(x49661,a893)),f317(f252(x49661),x49662))+P1(f317(x49662,f470(x49662)))
% 94.68/94.44 [5039]~P111(x50391)+E(f317(f317(f75(x50391),x50392),f76(x50391,x50392)),f317(f70(x50391),x50392))
% 94.68/94.44 [5051]~E(x50511,f2(a1))+E(f41(x50511,x50512),f317(f317(f242(a1,a1),f2(a1)),f2(a1)))
% 94.68/94.44 [5083]~P57(x50831,x50832)+P57(x50831,f317(f276(x50831,x50831),x50832))
% 94.68/94.44 [5084]~P37(x50841,x50842)+P37(x50841,f317(f276(x50841,x50841),x50842))
% 94.68/94.44 [5085]~P38(x50851,x50852)+P38(x50851,f317(f276(x50851,x50851),x50852))
% 94.68/94.44 [5086]~P51(x50861,x50862)+P51(x50861,f317(f276(x50861,x50861),x50862))
% 94.68/94.44 [5108]E(x51081,x51082)+~P1(f317(f317(a314,x51081),x51082))
% 94.68/94.44 [5119]P1(x51191)+~P1(f317(f317(a315,x51192),x51191))
% 94.68/94.44 [5120]P1(x51201)+~P1(f317(f317(a315,x51201),x51202))
% 94.68/94.44 [5125]~P116(x51251)+P1(f317(f317(f224(x51251),x51252),f232(x51251)))
% 94.68/94.44 [5126]~P112(x51261)+P1(f317(f317(f277(x51261),x51262),f2(x51261)))
% 94.68/94.44 [5130]E(x51301,x51302)+~E(f317(x51301,f379(x51302,x51301)),f317(x51302,f379(x51302,x51301)))
% 94.68/94.44 [5161]E(x51611,f2(a897))+E(f206(x51611,f40(a897,x51612,x51611)),f206(x51612,x51611))
% 94.68/94.44 [5166]~P66(x51661)+P13(x51661,f317(f317(f141(x51661),x51662),f103(x51661)))
% 94.68/94.44 [5168]E(x51681,f2(a1))+P1(f317(f44(x51682,x51681),f41(x51682,x51681)))
% 94.68/94.44 [5185]~P15(x51852,x51851)+P1(f317(f317(x51851,f779(x51851)),f779(x51851)))
% 94.68/94.44 [5188]~E(x51881,x51882)+P1(f317(f317(f225(a897),x51881),f317(a102,x51882)))
% 94.68/94.44 [5198]~E(x51981,f2(a897))+P1(f317(f317(f225(a897),x51981),f317(a102,x51982)))
% 94.68/94.44 [5208]P1(f317(x52081,x52082))+P1(f317(f317(f224(a1),f2(a1)),f842(x52081)))
% 94.68/94.44 [5271]P57(x52711,x52712)+~P57(x52711,f317(f276(x52711,x52711),x52712))
% 94.68/94.44 [5272]P37(x52721,x52722)+~P37(x52721,f317(f276(x52721,x52721),x52722))
% 94.68/94.44 [5273]P38(x52731,x52732)+~P38(x52731,f317(f276(x52731,x52731),x52732))
% 94.68/94.44 [5274]P51(x52741,x52742)+~P51(x52741,f317(f276(x52741,x52741),x52742))
% 94.68/94.44 [5277]~E(f40(a897,x52772,x52771),f2(a897))+E(f317(f317(f75(a897),x52771),f848(x52771,x52772)),x52772)
% 94.68/94.44 [5278]~E(f40(a1,x52782,x52781),f2(a1))+E(f317(f317(f75(a1),x52781),f849(x52781,x52782)),x52782)
% 94.68/94.44 [5305]~P1(f317(x53051,x53052))+P1(f317(f317(f224(a1),f2(a1)),f797(x53051)))
% 94.68/94.44 [5316]E(f317(f317(f23(a897),f317(a95,x53161)),f317(a95,x53162)),f317(a95,x53161))+~P1(f317(a183,x53162))
% 94.68/94.44 [5339]E(f262(x53391,x53392),f72(a89))+~P1(f317(f317(f224(a89),x53391),f72(a89)))
% 94.68/94.44 [5437]E(f317(f317(f154(x54371),x54372),f644(x54372,x54371)),f317(f317(f154(x54371),x54372),f648(x54372,x54371)))+P1(f317(f127(x54371),x54372))
% 94.68/94.44 [5481]~P1(f317(x54811,f84(x54812,x54811)))+P1(f317(x54811,f517(x54812,x54811)))
% 94.68/94.44 [5546]P59(x55461,x55462)+~P1(f317(f305(x55461,x55462),f488(x55462,x55461)))
% 94.68/94.44 [5690]~P15(x56902,x56901)+P1(f317(f317(x56901,f780(x56901,x56902)),f780(x56901,x56902)))
% 94.68/94.44 [5691]~P15(x56912,x56911)+P1(f317(f317(x56911,f783(x56911,x56912)),f783(x56911,x56912)))
% 94.68/94.44 [5700]~E(f317(a102,f40(a897,x57001,x57002)),x57002)+E(f40(a897,f317(a102,x57001),x57002),f2(a897))
% 94.68/94.44 [5755]P36(x57551,x57552)+P1(f317(f317(f319(x57551),f610(x57552,x57551)),f611(x57552,x57551)))
% 94.68/94.44 [5762]~P94(x57621)+P1(f317(f317(f319(x57621),f317(f94(x57621),x57622)),f100(x57621)))
% 94.68/94.44 [5763]~P141(x57631)+P1(f317(f317(f319(x57631),f317(f90(x57631),x57632)),f100(x57631)))
% 94.68/94.44 [5764]~P144(x57641)+P1(f317(f317(f319(x57641),f317(f90(x57641),x57642)),f176(x57641)))
% 94.68/94.44 [5765]~P141(x57651)+P1(f317(f317(f319(x57651),f317(f93(x57651),x57652)),f100(x57651)))
% 94.68/94.44 [5908]~P37(x59081,x59082)+E(f317(f317(f279(x59081,x59081,x59081),x59082),f297(x59081,x59082)),x59082)
% 94.68/94.44 [5922]E(f317(a102,f40(a897,x59221,x59222)),x59222)+E(f40(a897,f317(a102,x59221),x59222),f317(a102,f40(a897,x59221,x59222)))
% 94.68/94.44 [6355]P36(x63551,x63552)+~P1(f317(f317(f319(x63551),f489(x63552,x63551)),f306(x63551,x63552)))
% 94.68/94.44 [6394]~P110(x63941)+~P1(f317(f317(f225(x63941),f317(f90(x63941),x63942)),f2(x63941)))
% 94.68/94.44 [6395]~P86(x63951)+~P1(f317(f317(f225(x63951),f317(f70(x63951),x63952)),f2(x63951)))
% 94.68/94.44 [6485]P1(f317(f317(f225(a1),x64851),f40(a1,x64852,x64851)))+~P1(f317(f317(f225(a1),x64851),f2(a1)))
% 94.68/94.44 [6591]E(f317(f317(f299(a897),f317(a102,x65911)),f293(a897,x65912,x65911)),f293(a897,x65912,f317(a102,x65911)))+~P1(f317(f317(f224(a897),x65912),f317(a102,x65911)))
% 94.68/94.44 [6683]~P66(x66831)+P13(x66831,f140(x66831,x66831,f5(x66831),x66832))
% 94.68/94.44 [6815]E(f317(f157(x68151),x68152),x68152)+~P1(f317(f317(f224(a897),f317(f179(f898(x68151)),x68152)),f72(a897)))
% 94.68/94.44 [6837]~P86(x68371)+P1(f317(f317(f224(x68371),f317(f73(x68371),f317(f70(x68371),x68372))),f2(x68371)))
% 94.68/94.44 [6871]~P36(x68711,x68712)+P36(x68711,f317(f317(f279(x68711,x68711,x68711),x68712),f297(x68711,x68712)))
% 94.68/94.44 [6872]~P51(x68721,x68722)+P51(x68721,f317(f317(f279(x68721,x68721,x68721),x68722),f297(x68721,x68722)))
% 94.68/94.44 [7099]~P1(f317(f317(f225(a1),x70992),f2(a1)))+P1(f317(f317(f224(a1),f40(a1,x70991,x70992)),f2(a1)))
% 94.68/94.44 [7499]~P144(x74991)+E(f180(x74991,f317(f317(f7(x74991,x74991,x74991),f74(x74991)),f72(x74991)),x74992,f2(x74991)),f317(f90(x74991),x74992))
% 94.68/94.44 [7528]~P126(x75281)+~P1(f317(f317(f225(x75281),f317(f317(f75(x75281),x75282),x75282)),f2(x75281)))
% 94.68/94.44 [10170]~P111(x101701)+~P1(f317(f317(f225(x101701),f317(f317(f234(x101701),x101702),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101701)))
% 94.68/94.44 [4730]~E(x47302,f103(x47301))+E(f317(f179(f898(x47301)),x47302),f2(a897))
% 94.68/94.44 [4762]~E(x47621,f2(a897))+E(f317(f317(f74(a897),x47621),x47622),x47622)
% 94.68/94.44 [4763]~E(x47632,f2(a897))+E(f317(f317(f75(a897),x47631),x47632),f2(a897))
% 94.68/94.44 [4765]~E(x47651,f2(a897))+E(f317(f317(f75(a897),x47651),x47652),f2(a897))
% 94.68/94.44 [4766]~E(x47662,f2(a897))+E(f317(f317(f234(a897),x47661),x47662),f72(a897))
% 94.68/94.44 [4767]~E(x47672,f2(a1))+E(f317(f317(f30(a1),x47671),x47672),f2(a1))
% 94.68/94.44 [4778]E(x47781,f103(x47782))+~E(f317(f179(f898(x47782)),x47781),f2(a897))
% 94.68/94.44 [4780]~P98(x47801)+E(f317(f317(f75(x47801),x47802),x47802),x47802)
% 94.68/94.44 [4782]~P66(x47821)+E(f317(f317(f228(x47821),x47822),x47822),x47822)
% 94.68/94.44 [4784]~P66(x47841)+E(f317(f317(f223(x47841),x47842),x47842),x47842)
% 94.68/94.44 [4786]~P99(x47861)+E(f317(f317(f91(x47861),x47862),x47862),x47862)
% 94.68/94.44 [4787]~P100(x47871)+E(f317(f317(f91(x47871),x47872),x47872),x47872)
% 94.68/94.44 [4788]~P100(x47881)+E(f317(f317(f92(x47881),x47882),x47882),x47882)
% 94.68/94.44 [4790]~P105(x47901)+E(f317(f317(f92(x47901),x47902),x47902),x47902)
% 94.68/94.44 [4808]~P75(x48081)+E(f317(f317(f23(x48081),x48082),x48082),f2(x48081))
% 94.68/94.44 [4822]~P75(x48221)+E(f317(f73(x48221),f317(f73(x48221),x48222)),x48222)
% 94.68/94.44 [4823]~P97(x48231)+E(f317(f73(x48231),f317(f73(x48231),x48232)),x48232)
% 94.68/94.44 [4840]~E(x48402,f2(a897))+E(f317(f317(f234(a897),x48401),x48402),f317(a102,f2(a897)))
% 94.68/94.44 [4875]~P76(x48751)+E(f317(f317(f74(x48751),f2(x48751)),x48752),x48752)
% 94.68/94.44 [4876]~P81(x48761)+E(f317(f317(f74(x48761),f2(x48761)),x48762),x48762)
% 94.68/94.44 [4877]~P112(x48771)+E(f317(f317(f74(x48771),f2(x48771)),x48772),x48772)
% 94.68/94.44 [4878]~P112(x48781)+E(f317(f317(f75(x48781),f72(x48781)),x48782),x48782)
% 94.68/94.44 [4879]~P77(x48791)+E(f317(f317(f75(x48791),f72(x48791)),x48792),x48792)
% 94.68/94.44 [4880]~P82(x48801)+E(f317(f317(f75(x48801),f72(x48801)),x48802),x48802)
% 94.68/94.44 [4881]~P101(x48811)+E(f317(f317(f91(x48811),f178(x48811)),x48812),x48812)
% 94.68/94.44 [4882]~P104(x48821)+E(f317(f317(f92(x48821),f232(x48821)),x48822),x48822)
% 94.68/94.44 [4900]~P112(x49001)+E(f317(f317(f75(x49001),f2(x49001)),x49002),f2(x49001))
% 94.68/94.44 [4901]~P132(x49011)+E(f317(f317(f75(x49011),f2(x49011)),x49012),f2(x49011))
% 94.68/94.44 [4902]~P82(x49021)+E(f317(f317(f234(x49021),f72(x49021)),x49022),f72(x49021))
% 94.68/94.44 [4903]~P3(x49031)+E(f317(f317(f30(x49031),f2(x49031)),x49032),f2(x49031))
% 94.68/94.44 [4904]~P122(x49041)+E(f317(f317(f281(x49041),f2(x49041)),x49042),f2(x49041))
% 94.68/94.44 [4905]~P104(x49051)+E(f317(f317(f91(x49051),f232(x49051)),x49052),f232(x49051))
% 94.68/94.44 [4906]~P101(x49061)+E(f317(f317(f92(x49061),f178(x49061)),x49062),f178(x49061))
% 94.68/94.44 [4914]E(x49141,f103(x49142))+E(f134(x49142,f317(f158(x49142),x49141)),f317(f131(x49142),x49141))
% 94.68/94.44 [4915]E(x49151,f103(x49152))+E(f317(f131(x49152),f317(f158(x49152),x49151)),f134(x49152,x49151))
% 94.68/94.44 [4916]E(x49161,f2(a897))+~E(f317(f317(f74(a897),x49162),x49161),x49162)
% 94.68/94.44 [4923]~P94(x49231)+E(f317(f93(x49231),f317(f94(a1),x49232)),f317(f94(x49231),x49232))
% 94.68/94.44 [4924]~P141(x49241)+E(f317(f93(x49241),f317(f90(a1),x49242)),f317(f90(x49241),x49242))
% 94.68/94.44 [4931]E(x49311,f72(a897))+~E(f317(f317(f75(a897),x49312),x49311),f72(a897))
% 94.68/94.44 [4932]E(x49321,f72(a897))+~E(f317(f317(f75(a897),x49321),x49322),f72(a897))
% 94.68/94.44 [4933]E(x49331,f2(a897))+~E(f317(f317(f74(a897),x49332),x49331),f2(a897))
% 94.68/94.44 [4934]E(x49341,f2(a897))+~E(f317(f317(f74(a897),x49341),x49342),f2(a897))
% 94.68/94.44 [4951]~P111(x49511)+E(f317(f70(x49511),f317(f90(x49511),x49512)),f317(f90(x49511),x49512))
% 94.68/94.44 [4952]~P86(x49521)+E(f317(f70(x49521),f317(f73(x49521),x49522)),f317(f70(x49521),x49522))
% 94.68/94.44 [4953]~P86(x49531)+E(f317(f70(x49531),f317(f70(x49531),x49532)),f317(f70(x49531),x49532))
% 94.68/94.44 [4954]~P76(x49541)+E(f317(f155(x49541),f317(f158(x49541),x49542)),f317(f155(x49541),x49542))
% 94.68/94.44 [4959]~E(x49591,f317(a102,f2(a897)))+E(f317(f317(f234(a897),x49591),x49592),f317(a102,f2(a897)))
% 94.68/94.44 [4968]~P75(x49681)+E(f317(f317(f23(x49681),f2(x49681)),x49682),f317(f73(x49681),x49682))
% 94.68/94.44 [4969]~E(x49692,f2(a897))+E(f129(a897,f317(f292(a897,x49691),x49692)),f103(a897))
% 94.68/94.44 [4978]~P94(x49781)+E(f317(f317(f74(x49781),x49782),f317(f94(x49781),a77)),x49782)
% 94.68/94.44 [4979]E(x49791,f2(a1))+E(f42(f317(f70(a1),x49792),f317(f70(a1),x49791)),f48(x49792,x49791))
% 94.68/94.44 [4995]~E(x49951,x49952)+P1(f317(f317(f224(a897),x49951),x49952))
% 94.68/94.44 [4999]~E(x49991,x49992)+P1(f317(f317(f277(a897),x49991),x49992))
% 94.68/94.44 [5006]~E(x50061,f2(a89))+E(f317(f317(f74(a897),f317(a20,x50061)),x50062),x50062)
% 94.68/94.44 [5020]~P6(x50201)+P6(f317(f317(f234(a1),x50201),x50202))
% 94.68/94.44 [5021]~P75(x50211)+E(f317(f317(f74(x50211),x50212),f317(f73(x50211),x50212)),f2(x50211))
% 94.68/94.44 [5022]~P97(x50221)+E(f317(f317(f91(x50221),x50222),f317(f73(x50221),x50222)),f232(x50221))
% 94.68/94.44 [5023]~P97(x50231)+E(f317(f317(f92(x50231),x50232),f317(f73(x50231),x50232)),f178(x50231))
% 94.68/94.44 [5048]E(x50481,f2(a897))+~E(f317(f73(a1),f317(f90(a1),x50482)),f317(f90(a1),x50481))
% 94.68/94.44 [5049]E(x50491,f2(a897))+~E(f317(f73(a1),f317(f90(a1),x50491)),f317(f90(a1),x50492))
% 94.68/94.44 [5059]E(f184(x50591,x50592),f2(a1))+P1(f317(f317(f224(a1),x50592),x50591))
% 94.68/94.44 [5060]E(f168(x50601,x50602),f103(a1))+P1(f317(f317(f224(a1),x50601),x50602))
% 94.68/94.44 [5061]E(f231(x50611,x50612),f2(a89))+P1(f317(f317(f225(a89),x50611),x50612))
% 94.68/94.44 [5074]E(x50741,f317(a102,f2(a897)))+~E(f317(f317(f75(a897),x50742),x50741),f317(a102,f2(a897)))
% 94.68/94.44 [5075]E(x50751,f317(a102,f2(a897)))+~E(f317(f317(f75(a897),x50751),x50752),f317(a102,f2(a897)))
% 94.68/94.44 [5076]~P65(x50761)+P1(f317(f317(f224(x50761),x50762),x50762))
% 94.68/94.44 [5077]~P112(x50771)+P1(f317(f317(f277(x50771),x50772),x50772))
% 94.68/94.44 [5080]~P94(x50801)+E(f317(f317(f75(x50801),x50802),f317(f94(x50801),a87)),f317(f73(x50801),x50802))
% 94.68/94.44 [5100]~P94(x51001)+E(f317(f73(x51001),f317(f94(x51001),x51002)),f317(f94(x51001),f317(f73(a1),x51002)))
% 94.68/94.44 [5101]~P141(x51011)+E(f317(f73(x51011),f317(f93(x51011),x51012)),f317(f93(x51011),f317(f73(a1),x51012)))
% 94.68/94.44 [5131]~E(x51311,f317(a102,x51312))+P1(f317(f317(f225(a897),f2(a897)),x51311))
% 94.68/94.44 [5149]~P66(x51491)+E(f317(f73(f904(x51491,a893)),f317(f291(x51491),x51492)),f317(f294(x51491),x51492))
% 94.68/94.44 [5150]~P66(x51501)+E(f317(f73(f904(x51501,a893)),f317(f272(x51501),x51502)),f317(f273(x51501),x51502))
% 94.68/94.44 [5151]~P66(x51511)+E(f317(f73(f904(x51511,a893)),f317(f273(x51511),x51512)),f317(f272(x51511),x51512))
% 94.68/94.44 [5152]~P66(x51521)+E(f317(f73(f904(x51521,a893)),f317(f294(x51521),x51522)),f317(f291(x51521),x51522))
% 94.68/94.44 [5160]~E(f317(f90(a1),x51602),x51601)+P1(f317(f317(f224(a1),f2(a1)),x51601))
% 94.68/94.44 [5167]~E(x51672,f2(a1))+E(f48(x51671,x51672),f317(f317(f242(a1,a1),f2(a1)),f317(f70(a1),x51671)))
% 94.68/94.44 [5169]~P83(x51691)+P1(f317(f317(f224(x51691),f178(x51691)),x51692))
% 94.68/94.44 [5170]~P112(x51701)+P1(f317(f317(f277(x51701),f72(x51701)),x51702))
% 94.68/94.44 [5203]E(x52031,x52032)+~E(f317(f317(f74(a1),x52031),x52031),f317(f317(f74(a1),x52032),x52032))
% 94.68/94.44 [5207]~P1(f317(x52071,x52072))+P1(f317(x52071,f317(a95,f797(x52071))))
% 94.68/94.44 [5233]~P111(x52331)+E(f317(f317(f75(x52331),f76(x52331,x52332)),f317(f70(x52331),x52332)),x52332)
% 94.68/94.44 [5240]~E(x52402,f2(a897))+E(f79(f903(a897,a897),f43(x52401,x52402)),f317(f317(f242(a897,a897),f2(a897)),x52401))
% 94.68/94.44 [5245]~E(x52451,x52452)+~P1(f317(f317(f225(a897),x52451),x52452))
% 94.68/94.44 [5246]~E(x52461,x52462)+~P1(f317(f317(f225(a1),x52461),x52462))
% 94.68/94.44 [5249]~P144(x52491)+E(f317(f317(f74(x52491),f72(x52491)),f317(f90(x52491),x52492)),f317(f90(x52491),f317(a102,x52492)))
% 94.68/94.44 [5253]~E(x52531,f2(a897))+~P1(f317(f317(f225(a897),x52532),x52531))
% 94.68/94.44 [5267]E(f142(x52671,x52672),x52672)+~E(f317(f179(f898(x52671)),f142(x52671,x52672)),f317(f179(f898(x52671)),x52672))
% 94.68/94.44 [5268]E(f317(f29(x52681),f317(f162(x52681),x52682)),f317(f179(f898(x52681)),x52682))+~P1(f317(f127(x52681),x52682))
% 94.68/94.44 [5282]~P1(f317(x52821,f712(x52821)))+P1(f317(x52821,f317(f90(a1),x52822)))
% 94.68/94.44 [5293]E(f231(x52931,x52932),x52932)+~P1(f317(f317(f225(a89),x52931),x52932))
% 94.68/94.44 [5295]E(f262(x52951,x52952),f72(a89))+~P1(f317(f317(f225(a89),x52952),x52951))
% 94.68/94.44 [5296]E(f168(x52961,x52962),f103(a1))+~P1(f317(f317(f225(a1),x52962),x52961))
% 94.68/94.44 [5297]E(f118(x52971,x52972),f105(a1))+~P1(f317(f317(f225(a1),x52971),x52972))
% 94.68/94.44 [5299]~P108(x52991)+E(f293(x52991,x52992,x52992),f317(f317(f299(x52991),x52992),f178(f904(x52991,a893))))
% 94.68/94.44 [5319]~E(f317(f317(f23(a897),x53191),x53192),f2(a897))+P1(f317(f317(f224(a897),x53191),x53192))
% 94.68/94.44 [5336]~E(x53362,f2(a897))+E(f50(x53361,x53362,f103(x53361)),f317(f317(f141(f898(x53361)),f103(x53361)),f103(f898(x53361))))
% 94.68/94.44 [5340]~P65(x53401)+~P1(f317(f317(f225(x53401),x53402),x53402))
% 94.68/94.44 [5342]~E(f40(a1,x53421,x53422),f2(a1))+E(f40(a1,x53421,f317(f73(a1),x53422)),f2(a1))
% 94.68/94.44 [5344]~E(f40(a1,x53441,x53442),f2(a1))+E(f40(a1,f317(f73(a1),x53441),x53442),f2(a1))
% 94.68/94.44 [5352]E(f317(f292(a897,x53521),f317(a102,x53522)),f178(f904(a897,a893)))+P1(f317(f317(f224(a897),x53521),x53522))
% 94.68/94.44 [5376]E(f129(a897,f317(f292(a897,x53761),x53762)),f103(a897))+P1(f317(f317(f225(a897),x53761),x53762))
% 94.68/94.44 [5382]~E(f317(f29(x53821),f317(f162(x53821),x53822)),f317(f179(f898(x53821)),x53822))+P1(f317(f127(x53821),x53822))
% 94.68/94.44 [5386]~P1(f317(f127(x53861),x53862))+P1(f317(f127(x53861),f317(f157(x53861),x53862)))
% 94.68/94.44 [5387]~P1(f317(f127(x53871),x53872))+P1(f317(f127(x53871),f317(f161(x53871),x53872)))
% 94.68/94.44 [5388]~P1(f317(f127(x53881),x53882))+P1(f317(f127(x53881),f317(f158(x53881),x53882)))
% 94.68/94.44 [5396]P1(f317(x53961,x53962))+~P1(f317(x53961,f317(a95,f842(x53961))))
% 94.68/94.44 [5397]P1(f317(f317(f224(a897),x53972),x53971))+P1(f317(f317(f224(a897),x53971),x53972))
% 94.68/94.44 [5398]P1(f317(f317(f224(a1),x53982),x53981))+P1(f317(f317(f224(a1),x53981),x53982))
% 94.68/94.44 [5402]~P86(x54021)+P1(f317(f317(f224(x54021),x54022),f317(f70(x54021),x54022)))
% 94.68/94.44 [5405]P1(f317(x54051,f728(x54051)))+~P1(f317(x54051,f317(f90(a1),x54052)))
% 94.68/94.44 [5429]E(f317(f317(f23(a897),x54291),x54292),f2(a897))+~P1(f317(f317(f224(a897),x54291),x54292))
% 94.68/94.44 [5430]E(f317(f317(f30(a897),x54301),x54302),f2(a897))+~P1(f317(f317(f225(a897),x54301),x54302))
% 94.68/94.44 [5449]E(f40(a897,x54491,x54492),x54491)+~P1(f317(f317(f225(a897),x54491),x54492))
% 94.68/94.44 [5457]E(f40(a1,x54571,f317(f73(a1),x54572)),f282(x54571,x54572))+P1(f317(f317(f224(a1),f2(a1)),x54572))
% 94.68/94.44 [5470]E(f317(f317(f23(a1),x54701),x54702),f184(x54701,x54702))+~P1(f317(f317(f224(a1),x54702),x54701))
% 94.68/94.44 [5490]P1(f317(f317(f224(a1),f2(a1)),f712(x54901)))+P1(f317(x54901,f317(f90(a1),x54902)))
% 94.68/94.44 [5503]~P110(x55031)+P1(f317(f317(f224(x55031),f2(x55031)),f317(f90(x55031),x55032)))
% 94.68/94.44 [5504]~P86(x55041)+P1(f317(f317(f224(x55041),f2(x55041)),f317(f70(x55041),x55042)))
% 94.68/94.44 [5532]E(f317(f317(f74(a897),x55321),f434(x55322,x55321)),x55322)+~P1(f317(f317(f224(a897),x55321),x55322))
% 94.68/94.44 [5547]E(f293(a1,x55471,x55472),f178(f904(a1,a893)))+~P1(f317(f317(f225(a1),x55472),x55471))
% 94.68/94.44 [5550]~P111(x55501)+E(f317(f317(f75(x55501),f317(f70(x55501),x55502)),f317(f70(x55501),x55502)),f317(f317(f75(x55501),x55502),x55502))
% 94.68/94.44 [5555]E(f129(a897,f317(f292(a897,x55551),f317(a102,x55552))),f103(a897))+P1(f317(f317(f224(a897),x55551),x55552))
% 94.68/94.44 [5558]E(f317(f317(f30(a1),x55581),x55582),f283(x55581,x55582))+~P1(f317(f317(f224(a1),f2(a1)),x55582))
% 94.68/94.44 [5578]P1(f317(f127(x55781),x55782))+~P1(f317(f127(x55781),f317(f157(x55781),x55782)))
% 94.68/94.44 [5579]P1(f317(f127(x55791),x55792))+~P1(f317(f127(x55791),f317(f158(x55791),x55792)))
% 94.68/94.44 [5606]P1(f317(f28(a897),x56061))+P1(f317(f317(f319(a897),f380(x56061,x56062)),x56061))
% 94.68/94.44 [5607]P1(f317(f28(a897),x56071))+P1(f317(f317(f319(a897),f528(x56071,x56072)),x56071))
% 94.68/94.44 [5610]P1(f317(f317(f225(a897),x56102),f317(a102,x56101)))+P1(f317(f317(f225(a897),x56101),x56102))
% 94.68/94.44 [5611]E(f40(a1,x56111,x56112),f282(x56111,x56112))+~P1(f317(f317(f224(a1),f2(a1)),x56112))
% 94.68/94.44 [5614]E(f129(a897,f317(f292(a897,x56141),x56142)),f103(a897))+~P1(f317(f317(f224(a897),x56142),x56141))
% 94.68/94.44 [5615]~P67(x56151)+E(f317(f300(x56151,x56151,f73(x56151)),f317(f291(x56151),x56152)),f317(f273(x56151),f317(f73(x56151),x56152)))
% 94.68/94.44 [5616]~P67(x56161)+E(f317(f300(x56161,x56161,f73(x56161)),f317(f272(x56161),x56162)),f317(f294(x56161),f317(f73(x56161),x56162)))
% 94.68/94.44 [5617]~P67(x56171)+E(f317(f300(x56171,x56171,f73(x56171)),f317(f273(x56171),x56172)),f317(f291(x56171),f317(f73(x56171),x56172)))
% 94.68/94.44 [5618]~P67(x56181)+E(f317(f300(x56181,x56181,f73(x56181)),f317(f294(x56181),x56182)),f317(f272(x56181),f317(f73(x56181),x56182)))
% 94.68/94.44 [5629]E(x56291,f178(f904(x56292,a893)))+P1(f317(f317(f319(x56292),f863(x56291,x56292)),x56291))
% 94.68/94.44 [5630]E(x56301,f178(f904(x56302,a893)))+P1(f317(f317(f319(x56302),f864(x56301,x56302)),x56301))
% 94.68/94.44 [5641]~P1(f317(f317(f225(a897),x56411),x56412))+P1(f317(f317(f224(a897),x56411),x56412))
% 94.68/94.44 [5642]~P1(f317(f317(f225(a1),x56421),x56422))+P1(f317(f317(f224(a1),x56421),x56422))
% 94.68/94.44 [5658]E(f42(x56581,x56582),f317(f317(f242(a1,a1),f2(a1)),x56581))+~P1(f317(f317(f225(a1),x56581),x56582))
% 94.68/94.44 [5660]E(f205(f317(f73(a1),x56601),f317(f73(a1),x56602)),f205(x56601,x56602))+~P1(f317(f317(f225(a1),x56602),f2(a1)))
% 94.68/94.44 [5672]E(x56721,x56722)+~E(f317(a3,f317(a102,f317(a20,x56721))),f317(a3,f317(a102,f317(a20,x56722))))
% 94.68/94.44 [5677]E(f42(x56771,x56772),f317(f317(f242(a1,a1),f2(a1)),x56771))+~P1(f317(f317(f224(a1),x56772),f2(a1)))
% 94.68/94.44 [5706]E(f40(a897,f317(f94(a897),x57061),f317(f94(a897),x57062)),f2(a897))+~P1(f317(a183,f317(f94(a1),x57061)))
% 94.68/94.44 [5720]P1(f317(f317(f224(a1),f2(a1)),f728(x57201)))+~P1(f317(x57201,f317(f90(a1),x57202)))
% 94.68/94.44 [5753]P39(f293(a1,x57531,x57532))+~P1(f317(f317(f224(a1),f2(a1)),x57531))
% 94.68/94.44 [5758]~P1(f317(f28(x57581),x57582))+P1(f317(f28(f904(x57581,a893)),f317(f298(x57581),x57582)))
% 94.68/94.44 [5771]E(f317(f317(f74(a1),x57711),f317(f90(a1),f746(x57712,x57711))),x57712)+~P1(f317(f317(f224(a1),x57711),x57712))
% 94.68/94.44 [5779]P1(f317(f317(f224(a897),x57791),x57792))+P1(f317(f317(f224(a897),f317(a102,x57792)),x57791))
% 94.68/94.44 [5823]E(f317(f317(f30(a897),f317(f94(a897),x58231)),f317(f94(a897),x58232)),f2(a897))+~P1(f317(a183,f317(f94(a1),x58231)))
% 94.68/94.44 [5824]E(f317(f317(f75(a897),f317(f94(a897),x58241)),f317(f94(a897),x58242)),f2(a897))+~P1(f317(f317(f225(a1),x58241),a77))
% 94.68/94.44 [5826]P1(f317(f317(f224(a897),x58261),f317(a102,x58262)))+~P1(f317(f317(f224(a897),x58261),x58262))
% 94.68/94.44 [5828]P1(f317(f317(f225(a897),x58281),f317(a102,x58282)))+~P1(f317(f317(f224(a897),x58281),x58282))
% 94.68/94.44 [5830]P1(f317(f317(f225(a897),x58301),f317(a102,x58302)))+~P1(f317(f317(f225(a897),x58301),x58302))
% 94.68/94.44 [5833]~E(x58331,x58332)+P1(f317(f317(f225(a1),x58331),f317(f317(f74(a1),x58332),f72(a1))))
% 94.68/94.44 [5836]E(f40(a1,x58361,x58362),f2(a1))+E(f317(f317(f23(a1),x58362),f40(a1,x58361,x58362)),f40(a1,f317(f73(a1),x58361),x58362))
% 94.68/94.44 [5845]E(x58451,f103(x58452))+P1(f317(f317(f319(x58452),f134(x58452,x58451)),f317(f162(x58452),x58451)))
% 94.68/94.44 [5857]E(f79(f903(a897,a897),f43(x58571,x58572)),f317(f317(f242(a897,a897),f2(a897)),x58571))+~P1(f317(f317(f225(a897),x58571),x58572))
% 94.68/94.44 [5901]E(f317(f317(f23(a897),f317(f94(a897),x59011)),f317(f94(a897),x59012)),f317(f94(a897),x59011))+~P1(f317(f317(f225(a1),x59012),a77))
% 94.68/94.44 [5902]E(f317(f317(f74(a897),f317(f94(a897),x59021)),f317(f94(a897),x59022)),f317(f94(a897),x59022))+~P1(f317(f317(f225(a1),x59021),a77))
% 94.68/94.44 [5909]E(f317(a102,f317(f317(f74(a897),x59091),f537(x59092,x59091))),x59092)+~P1(f317(f317(f225(a897),x59091),x59092))
% 94.68/94.44 [5933]P1(f317(x59331,x59332))+~P1(f317(x59331,f317(a83,f508(x59332,x59331))))
% 94.68/94.44 [5934]P1(f317(x59341,x59342))+~P1(f317(x59341,f317(a3,f795(x59342,x59341))))
% 94.68/94.44 [5943]~P1(f317(f317(f225(a897),x59431),f317(a102,x59432)))+P1(f317(f317(f224(a897),x59431),x59432))
% 94.68/94.44 [5993]E(f317(f317(f299(a897),x59931),f317(f292(a897,x59932),x59931)),f317(f292(a897,x59932),f317(a102,x59931)))+~P1(f317(f317(f224(a897),x59932),x59931))
% 94.68/94.44 [5996]E(x59961,f103(x59962))+E(f317(f317(f124(x59962),f104(x59962,x59961)),f317(f317(f141(x59962),f134(x59962,x59961)),f103(x59962))),x59961)
% 94.68/94.44 [6013]P1(f317(f28(x60131),x60132))+~P1(f317(f317(f225(a897),f2(a897)),f317(f29(x60131),x60132)))
% 94.68/94.44 [6017]~E(x60171,f178(f904(x60172,a893)))+~P1(f317(f317(f225(a897),f2(a897)),f317(f29(x60172),x60171)))
% 94.68/94.44 [6029]~P1(f317(f317(f225(a897),x60291),x60292))+P1(f317(f317(f224(a897),f317(a102,x60291)),x60292))
% 94.68/94.44 [6033]~P66(x60331)+E(f140(x60331,x60331,f5(x60331),f142(x60331,x60332)),f129(x60331,f317(f162(x60331),x60332)))
% 94.68/94.44 [6036]E(x60361,f103(x60362))+P1(f317(f317(f319(x60362),f317(f131(x60362),x60361)),f317(f162(x60362),x60361)))
% 94.68/94.44 [6042]~P110(x60421)+P1(f317(f317(f225(x60421),x60422),f317(f317(f74(x60421),x60422),f72(x60421))))
% 94.68/94.44 [6044]~P86(x60441)+P1(f317(f317(f224(x60441),f317(f73(x60441),x60442)),f317(f70(x60441),x60442)))
% 94.68/94.44 [6058]~E(x60581,x60582)+E(f280(a897,f277(a897),x60581,x60582),f317(f317(f299(a897),x60581),f178(f904(a897,a893))))
% 94.68/94.44 [6076]P1(f317(f28(a897),x60761))+~P1(f317(f317(f224(a897),f380(x60761,x60762)),x60762))
% 94.68/94.44 [6077]P1(f317(f28(a897),x60771))+~P1(f317(f317(f225(a897),f528(x60771,x60772)),x60772))
% 94.68/94.44 [6080]~P1(f317(f28(f903(x60801,x60801)),x60802))+P1(f317(f28(x60801),f317(f271(x60801),x60802)))
% 94.68/94.44 [6136]E(f280(a897,f277(a897),x61361,x61362),f178(f904(a897,a893)))+P1(f317(f317(f277(a897),x61361),x61362))
% 94.68/94.44 [6139]~P1(f317(f317(f225(a897),x61392),f317(a102,x61391)))+~P1(f317(f317(f225(a897),x61391),x61392))
% 94.68/94.44 [6140]~P108(x61401)+E(f317(f317(f92(f904(x61401,a893)),f317(f291(x61401),x61402)),f317(f273(x61401),x61402)),f317(f317(f299(x61401),x61402),f178(f904(x61401,a893))))
% 94.68/94.44 [6152]P1(f317(f28(x61521),x61522))+~P1(f317(f28(f904(x61521,a893)),f317(f298(x61521),x61522)))
% 94.68/94.44 [6174]P1(f317(f317(f224(a897),f317(a102,x61741)),f317(a102,x61742)))+~P1(f317(f317(f224(a897),x61741),x61742))
% 94.68/94.44 [6175]P1(f317(f317(f224(a897),f317(a20,x61751)),f317(a20,x61752)))+~P1(f317(f317(f224(a89),x61751),x61752))
% 94.68/94.44 [6176]P1(f317(f317(f224(a89),f317(a3,x61761)),f317(a3,x61762)))+~P1(f317(f317(f224(a897),x61761),x61762))
% 94.68/94.44 [6178]P1(f317(f317(f225(a897),f317(a102,x61781)),f317(a102,x61782)))+~P1(f317(f317(f225(a897),x61781),x61782))
% 94.68/94.44 [6179]P1(f317(f317(f225(a897),f317(a20,x61791)),f317(a20,x61792)))+~P1(f317(f317(f225(a89),x61791),x61792))
% 94.68/94.44 [6180]P1(f317(f317(f225(a89),f317(a3,x61801)),f317(a3,x61802)))+~P1(f317(f317(f225(a897),x61801),x61802))
% 94.68/94.44 [6185]E(x61851,x61852)+~E(f317(f300(a897,a1,f90(a1)),x61851),f317(f300(a897,a1,f90(a1)),x61852))
% 94.68/94.44 [6201]P1(f317(f317(f224(a897),x62011),x62012))+~P1(f317(f317(f224(a897),f317(a102,x62011)),x62012))
% 94.68/94.44 [6204]P1(f317(f317(f225(a897),x62041),x62042))+~P1(f317(f317(f224(a897),f317(a102,x62041)),x62042))
% 94.68/94.44 [6205]P1(f317(f317(f225(a897),x62051),x62052))+~P1(f317(f317(f225(a897),f317(a102,x62051)),x62052))
% 94.68/94.44 [6225]E(f40(a1,x62251,x62252),f2(a1))+E(f317(f317(f23(a1),f40(a1,x62251,x62252)),x62252),f40(a1,x62251,f317(f73(a1),x62252)))
% 94.68/94.44 [6294]E(f317(f29(f904(x62941,a893)),f317(f298(x62941),x62942)),f317(f317(f234(a897),f317(a102,f317(a102,f2(a897)))),f317(f29(x62941),x62942)))+~P1(f317(f28(x62941),x62942))
% 94.68/94.44 [6297]E(x62971,f103(x62972))+E(f317(f317(f154(x62972),x62971),f317(f317(f23(a897),f317(f179(f898(x62972)),x62971)),f72(a897))),f134(x62972,x62971))
% 94.68/94.44 [6319]E(x63191,f103(x63192))+E(f317(f317(f124(x63192),f317(f161(x63192),x63191)),f317(f317(f141(x63192),f317(f131(x63192),x63191)),f103(x63192))),f317(f157(x63192),x63191))
% 94.68/94.44 [6352]~P1(f317(f28(x63521),f31(f904(x63521,a893),x63522)))+P1(f317(f28(f904(x63521,a893)),x63522))
% 94.68/94.44 [6374]P1(f317(f317(f224(a897),f317(f94(a897),x63741)),f317(f94(a897),x63742)))+~P1(f317(f317(f224(a1),x63741),a77))
% 94.68/94.44 [6398]~P1(f317(f317(f225(a1),x63981),x63982))+P1(f317(f317(f224(a1),x63981),f317(f317(f23(a1),x63982),f72(a1))))
% 94.68/94.44 [6399]~P1(f317(f317(f224(a1),x63991),x63992))+P1(f317(f317(f225(a1),x63991),f317(f317(f74(a1),x63992),f72(a1))))
% 94.68/94.44 [6400]~P1(f317(f317(f225(a1),x64001),x64002))+P1(f317(f317(f225(a1),x64001),f317(f317(f74(a1),x64002),f72(a1))))
% 94.68/94.44 [6402]~P1(f317(f317(f224(a1),x64021),x64022))+P1(f317(f317(f224(a897),f317(f94(a897),x64021)),f317(f94(a897),x64022)))
% 94.68/94.44 [6403]~P1(f317(f317(f224(a1),x64031),x64032))+P1(f317(f317(f224(a1),f317(f94(a1),x64031)),f317(f94(a1),x64032)))
% 94.68/94.44 [6405]~P1(f317(f317(f224(a897),x64051),x64052))+P1(f317(f317(f224(a1),f317(f90(a1),x64051)),f317(f90(a1),x64052)))
% 94.68/94.44 [6406]~P1(f317(f317(f225(a1),x64061),x64062))+P1(f317(f317(f225(a1),f317(f94(a1),x64061)),f317(f94(a1),x64062)))
% 94.68/94.44 [6408]~P1(f317(f317(f225(a897),x64081),x64082))+P1(f317(f317(f225(a1),f317(f90(a1),x64081)),f317(f90(a1),x64082)))
% 94.68/94.44 [6428]~P1(f317(f317(f224(a897),x64281),x64282))+~P1(f317(f317(f224(a897),f317(a102,x64282)),x64281))
% 94.68/94.44 [6471]~P1(f317(f317(f224(a897),f317(a102,x64711)),f317(a102,x64712)))+P1(f317(f317(f224(a897),x64711),x64712))
% 94.68/94.44 [6472]~P1(f317(f317(f224(a89),f317(a3,x64721)),f317(a3,x64722)))+P1(f317(f317(f224(a897),x64721),x64722))
% 94.68/94.44 [6473]~P1(f317(f317(f224(a897),f317(a20,x64731)),f317(a20,x64732)))+P1(f317(f317(f224(a89),x64731),x64732))
% 94.68/94.44 [6475]~P1(f317(f317(f225(a897),f317(a102,x64751)),f317(a102,x64752)))+P1(f317(f317(f225(a897),x64751),x64752))
% 94.68/94.44 [6476]~P1(f317(f317(f225(a89),f317(a3,x64761)),f317(a3,x64762)))+P1(f317(f317(f225(a897),x64761),x64762))
% 94.68/94.44 [6477]~P1(f317(f317(f225(a897),f317(a95,x64771)),f317(a95,x64772)))+P1(f317(f317(f225(a1),x64771),x64772))
% 94.68/94.44 [6478]~P1(f317(f317(f225(a897),f317(a20,x64781)),f317(a20,x64782)))+P1(f317(f317(f225(a89),x64781),x64782))
% 94.68/94.44 [6520]~P1(f317(f317(f225(a897),f317(a95,x65202)),f317(a95,x65201)))+P1(f317(f317(f225(a1),f2(a1)),x65201))
% 94.68/94.44 [6551]P1(f317(f317(f224(a1),f2(a1)),f40(a1,x65511,x65512)))+~P1(f317(f317(f225(a1),f2(a1)),x65512))
% 94.68/94.44 [6717]P36(x67171,x67172)+~E(f317(f317(f279(x67171,x67171,x67171),x67172),x67172),f178(f904(f903(x67171,x67171),a893)))
% 94.68/94.44 [6733]~P36(x67331,x67332)+P36(x67331,f317(f317(f279(x67331,x67331,x67331),x67332),x67332))
% 94.68/94.44 [6744]P1(f317(f317(f224(a1),x67441),x67442))+~P1(f317(f317(f225(a1),x67441),f317(f317(f74(a1),x67442),f72(a1))))
% 94.68/94.44 [6745]P1(f317(f317(f225(a1),x67451),x67452))+~P1(f317(f317(f224(a1),x67451),f317(f317(f23(a1),x67452),f72(a1))))
% 94.68/94.44 [6748]P1(f317(f317(f224(a897),x67481),x67482))+~P1(f317(f317(f224(a1),f317(f90(a1),x67481)),f317(f90(a1),x67482)))
% 94.68/94.44 [6749]P1(f317(f317(f224(a1),x67491),x67492))+~P1(f317(f317(f224(a1),f317(f94(a1),x67491)),f317(f94(a1),x67492)))
% 94.68/94.44 [6751]P1(f317(f317(f225(a897),x67511),x67512))+~P1(f317(f317(f225(a1),f317(f90(a1),x67511)),f317(f90(a1),x67512)))
% 94.68/94.44 [6752]P1(f317(f317(f225(a1),x67521),x67522))+~P1(f317(f317(f225(a897),f317(f94(a897),x67521)),f317(f94(a897),x67522)))
% 94.68/94.44 [6753]P1(f317(f317(f225(a1),x67531),x67532))+~P1(f317(f317(f225(a1),f317(f94(a1),x67531)),f317(f94(a1),x67532)))
% 94.68/94.44 [6826]~E(f280(a897,f277(a897),x68261,x68262),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x68261),x68262))
% 94.68/94.44 [6853]~E(f674(x68532,x68531),f103(x68531))+E(f317(f132(f898(x68531),f898(x68531),f124(x68531),f103(x68531)),x68532),f103(x68531))
% 94.68/94.44 [6854]~E(f675(x68542,x68541),f103(x68541))+E(f317(f132(f898(x68541),f898(x68541),f124(x68541),f103(x68541)),x68542),f103(x68541))
% 94.68/94.44 [6858]~P5(x68581)+E(f317(f132(x68581,x68581,f92(x68581),f232(x68581)),x68582),f32(x68581,f317(f162(x68581),x68582)))
% 94.68/94.44 [6859]~P5(x68591)+E(f317(f132(x68591,x68591,f91(x68591),f178(x68591)),x68592),f31(x68591,f317(f162(x68591),x68592)))
% 94.68/94.44 [6873]E(x68731,f2(a89))+E(f317(f317(f74(a897),f317(a20,f317(f317(f23(a89),x68731),f72(a89)))),f317(a102,x68732)),f317(f317(f74(a897),f317(a20,x68731)),x68732))
% 94.68/94.44 [6922]P1(f317(f317(f225(a1),f317(f317(f23(a1),x69221),x69222)),f2(a1)))+~P1(f317(f317(f225(a1),x69221),x69222))
% 94.68/94.44 [6947]~P66(x69471)+E(f317(f317(f91(f904(x69471,a893)),f317(f317(f299(x69471),x69472),f178(f904(x69471,a893)))),f317(f294(x69471),x69472)),f317(f273(x69471),x69472))
% 94.68/94.44 [7027]~P59(x70271,x70272)+P36(x70271,f317(f252(f903(x70271,x70271)),f317(f247(x70271,x70271,a893),x70272)))
% 94.68/94.44 [7028]~P59(x70281,x70282)+P57(x70281,f317(f252(f903(x70281,x70281)),f317(f247(x70281,x70281,a893),x70282)))
% 94.68/94.44 [7029]~P49(x70291,x70292)+P37(x70291,f317(f252(f903(x70291,x70291)),f317(f247(x70291,x70291,a893),x70292)))
% 94.68/94.44 [7030]~P50(x70301,x70302)+P51(x70301,f317(f252(f903(x70301,x70301)),f317(f247(x70301,x70301,a893),x70302)))
% 94.68/94.44 [7031]E(x70311,f178(f904(x70312,a893)))+~P1(f317(f317(f224(f904(x70312,a893)),x70311),f178(f904(x70312,a893))))
% 94.68/94.44 [7115]~P1(f317(f317(f225(a897),f2(a897)),x71152))+P1(f317(f317(f224(a897),f40(a897,x71151,x71152)),x71152))
% 94.68/94.44 [7116]~P1(f317(f317(f224(a1),f2(a1)),x71161))+P1(f317(f317(f224(a1),f40(a1,x71161,x71162)),x71161))
% 94.68/94.44 [7117]~P1(f317(f317(f225(a897),f2(a897)),x71172))+P1(f317(f317(f225(a897),f40(a897,x71171,x71172)),x71172))
% 94.68/94.44 [7119]~P1(f317(f317(f225(a1),f2(a1)),x71192))+P1(f317(f317(f225(a1),f40(a1,x71191,x71192)),x71192))
% 94.68/94.44 [7195]~P108(x71951)+E(f317(f317(f23(f904(x71951,a893)),f317(f317(f299(x71951),x71952),f178(f904(x71951,a893)))),f317(f272(x71951),x71952)),f317(f317(f299(x71951),x71952),f178(f904(x71951,a893))))
% 94.68/94.44 [7270]~P42(x72701,x72702)+P52(x72701,f232(f904(x72701,a893)),f317(f252(f903(x72701,x72701)),f317(f247(x72701,x72701,a893),x72702)))
% 94.68/94.44 [7271]P1(f317(x72711,x72712))+P1(f317(f317(f319(f904(f903(a897,a897),a893)),f508(x72712,x72711)),a88))
% 94.68/94.44 [7314]E(f317(f317(f124(a897),f129(a897,f317(f292(a897,x73141),x73142))),f317(f317(f141(a897),x73142),f103(a897))),f129(a897,f317(f292(a897,x73141),f317(a102,x73142))))+~P1(f317(f317(f224(a897),x73141),x73142))
% 94.68/94.44 [7466]E(x74661,f2(a897))+~E(f317(f132(a897,a897,f74(a897),x74661),x74662),f2(a897))
% 94.68/94.44 [7491]~P1(f317(f317(f225(a1),f317(f317(f23(a1),x74911),x74912)),f2(a1)))+P1(f317(f317(f225(a1),x74911),x74912))
% 94.68/94.44 [7520]P36(x75201,x75202)+~P36(x75201,f317(f317(f279(x75201,x75201,x75201),x75202),x75202))
% 94.68/94.44 [7545]~P1(f317(f317(f224(a897),f317(a102,x75451)),x75452))+P1(f175(a893,a229,f317(f224(a897),x75451),x75452))
% 94.68/94.44 [7700]P24(a897,a897,f317(f317(f7(a897,a897,a897),f23(a897)),x77001),x77002)+P1(f317(f317(f319(a897),f487(x77001,x77002)),x77002))
% 94.68/94.44 [7758]E(f317(f317(f317(f59(a897,x77581,f74(a897)),f317(f16(a897,x77581),f72(a897))),f2(a897)),x77582),f317(f29(x77581),x77582))+~P1(f317(f28(x77581),x77582))
% 94.68/94.44 [7800]P24(a897,a897,f317(f317(f7(a897,a897,a897),f23(a897)),x78001),x78002)+~P1(f317(f317(f224(a897),x78001),f487(x78001,x78002)))
% 94.68/94.44 [7856]P36(x78561,x78562)+P1(f317(f317(f224(f904(x78561,a893)),f516(x78562,x78561)),f317(f275(x78561,x78561,x78562),f516(x78562,x78561))))
% 94.68/94.44 [7861]P59(x78611,x78612)+~P36(x78611,f317(f252(f903(x78611,x78611)),f317(f247(x78611,x78611,a893),x78612)))
% 94.68/94.44 [7862]P49(x78621,x78622)+~P37(x78621,f317(f252(f903(x78621,x78621)),f317(f247(x78621,x78621,a893),x78622)))
% 94.68/94.44 [7863]P50(x78631,x78632)+~P51(x78631,f317(f252(f903(x78631,x78631)),f317(f247(x78631,x78631,a893),x78632)))
% 94.68/94.44 [7931]P1(f317(f317(f224(a897),f317(a102,x79311)),x79312))+~P1(f175(a893,a229,f317(f224(a897),x79311),x79312))
% 94.68/94.44 [7988]P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x79881),x79882)),f297(a897,a307)))+~P1(f317(f317(f224(a897),x79881),x79882))
% 94.68/94.44 [8084]P42(x80841,x80842)+~P52(x80841,f232(f904(x80841,a893)),f317(f252(f903(x80841,x80841)),f317(f247(x80841,x80841,a893),x80842)))
% 94.68/94.44 [8139]~P1(f317(f127(x81391),x81392))+P1(f317(f127(f904(x81391,a893)),f317(f317(f144(f898(x81391),f904(x81391,a893)),f162(x81391)),f49(x81391,x81392))))
% 94.68/94.44 [8340]~P36(x83401,f317(f276(x83401,x83401),x83402))+P36(x83401,f317(f276(x83401,x83401),f317(f317(f279(x83401,x83401,x83401),x83402),f297(x83401,x83402))))
% 94.68/94.44 [8352]P150(x83521,f317(f317(f299(a892),f317(a908,x83522)),f178(f904(a892,a893))))+~P150(f317(f317(f299(a892),f317(a908,x83522)),x83521),f317(f317(f299(a892),f909(f222(a894,f33(x83522)))),f178(f904(a892,a893))))
% 94.68/94.44 [8439]P25(x84391,a897,f800(x84392,x84391),x84392,f317(f292(a897,f2(a897)),f317(f29(x84391),x84392)))+~P1(f317(f28(x84391),x84392))
% 94.68/94.44 [8440]P25(a897,x84401,f801(x84402,x84401),f317(f292(a897,f2(a897)),f317(f29(x84401),x84402)),x84402)+~P1(f317(f28(x84401),x84402))
% 94.68/94.44 [8457]P25(a897,x84571,f802(x84572,x84571),f293(a897,f72(a897),f317(f29(x84571),x84572)),x84572)+~P1(f317(f28(x84571),x84572))
% 94.68/94.44 [8467]P1(f317(f28(f903(x84671,x84671)),f317(f317(f279(x84671,x84671,x84671),x84672),f297(x84671,x84672))))+~P1(f317(f28(f903(x84671,x84671)),x84672))
% 94.68/94.44 [8494]E(x84941,f2(a1))+P1(f317(f44(x84942,x84941),f317(f317(f242(a1,a1),f317(f317(f30(a1),x84942),x84941)),f40(a1,x84942,x84941))))
% 94.68/94.44 [8507]~P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x85071),x85072)),f297(a897,a307)))+P1(f317(f317(f224(a897),x85071),x85072))
% 94.68/94.44 [8524]~P81(x85241)+E(f317(f132(x85241,x85241,f317(f7(x85241,x85241,x85241),f74(x85241)),f2(x85241)),f317(f158(x85241),x85242)),f317(f132(x85241,x85241,f74(x85241),f2(x85241)),x85242))
% 94.68/94.44 [8695]~P66(x86951)+E(f317(f132(f898(x86951),x86951,f317(f7(x86951,f898(x86951),f898(x86951)),f138(x86951,x86951,f5(x86951))),f103(x86951)),x86952),f140(x86951,x86951,f5(x86951),x86952))
% 94.68/94.44 [8806]~P57(x88061,f317(f252(f903(x88061,x88061)),f317(f247(x88061,x88061,a893),x88062)))+P57(x88061,f317(f252(f903(x88061,x88061)),f317(f247(x88061,x88061,a893),f233(x88061,x88061,x88062))))
% 94.68/94.44 [8820]P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x88201),x88202)),f317(f317(f279(a897,a897,a897),a307),f297(a897,a307))))+~P1(f317(f317(f225(a897),x88201),x88202))
% 94.68/94.44 [8866]~P1(f317(f28(f903(x88661,x88661)),f317(f317(f279(x88661,x88661,x88661),x88662),f297(x88661,x88662))))+P1(f317(f28(f903(x88661,x88661)),x88662))
% 94.68/94.44 [8924]~P57(x89241,f317(f252(f903(x89241,x89241)),f317(f247(x89241,x89241,a893),f233(x89241,x89241,x89242))))+P57(x89241,f317(f252(f903(x89241,x89241)),f317(f247(x89241,x89241,a893),x89242)))
% 94.68/94.44 [9122]P57(x91221,x91222)+P1(f317(f317(f319(f903(x91221,x91221)),f317(f317(f242(x91221,x91221),f553(x91222,x91221)),f553(x91222,x91221))),f317(f317(f279(x91221,x91221,x91221),x91222),f297(x91221,x91222))))
% 94.68/94.44 [9123]P57(x91231,x91232)+P1(f317(f317(f319(f903(x91231,x91231)),f317(f317(f242(x91231,x91231),f555(x91232,x91231)),f555(x91232,x91231))),f317(f317(f279(x91231,x91231,x91231),x91232),f297(x91231,x91232))))
% 94.68/94.44 [9240]~P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x92401),x92402)),f317(f317(f279(a897,a897,a897),a307),f297(a897,a307))))+P1(f317(f317(f225(a897),x92401),x92402))
% 94.68/94.44 [5145]~P94(x51451)+E(f317(f317(f74(x51451),f317(f94(x51451),a77)),x51452),x51452)
% 94.68/94.44 [5175]~P69(x51751)+E(f317(f317(f74(x51751),f317(f73(x51751),x51752)),x51752),f2(x51751))
% 94.68/94.44 [5176]~P75(x51761)+E(f317(f317(f74(x51761),f317(f73(x51761),x51762)),x51762),f2(x51761))
% 94.68/94.44 [5177]~P97(x51771)+E(f317(f317(f91(x51771),f317(f73(x51771),x51772)),x51772),f232(x51771))
% 94.68/94.44 [5178]~P97(x51781)+E(f317(f317(f92(x51781),f317(f73(x51781),x51782)),x51782),f178(x51781))
% 94.68/94.44 [5211]~P94(x52111)+E(f317(f317(f75(x52111),f317(f94(x52111),a87)),x52112),f317(f73(x52111),x52112))
% 94.68/94.44 [5368]~P114(x53681)+E(f317(f317(f75(x53681),f317(f73(x53681),f72(x53681))),x53682),f317(f73(x53681),x53682))
% 94.68/94.44 [5414]E(f317(f70(a1),x54141),f72(a1))+~E(f317(f70(a1),f317(f317(f75(a1),x54141),x54142)),f72(a1))
% 94.68/94.44 [5506]~P94(x55061)+E(f317(f317(f74(x55061),f72(x55061)),f317(f94(x55061),x55062)),f317(f94(x55061),f317(f317(f23(a1),x55062),a87)))
% 94.68/94.44 [5559]~P66(x55591)+E(f14(x55591,f317(f317(f299(x55591),x55592),f178(f904(x55591,a893)))),x55592)
% 94.68/94.44 [5560]~P66(x55601)+E(f15(x55601,f317(f317(f299(x55601),x55602),f178(f904(x55601,a893)))),x55602)
% 94.68/94.44 [5561]~P100(x55611)+E(f13(x55611,f317(f317(f299(x55611),x55612),f178(f904(x55611,a893)))),x55612)
% 94.68/94.44 [5562]~P100(x55621)+E(f10(x55621,f317(f317(f299(x55621),x55622),f178(f904(x55621,a893)))),x55622)
% 94.68/94.44 [5563]~P5(x55631)+E(f32(x55631,f317(f317(f299(x55631),x55632),f178(f904(x55631,a893)))),x55632)
% 94.68/94.44 [5564]~P5(x55641)+E(f31(x55641,f317(f317(f299(x55641),x55642),f178(f904(x55641,a893)))),x55642)
% 94.68/94.44 [5586]E(f317(f317(f74(a897),x55861),f317(f317(f23(a897),x55862),x55861)),x55862)+P1(f317(f317(f225(a897),x55862),x55861))
% 94.68/94.44 [5624]E(x56241,f103(x56242))+P1(f317(f317(f225(a897),f2(a897)),f317(f179(f898(x56242)),x56241)))
% 94.68/94.44 [5750]~P66(x57501)+E(f11(x57501,f228(x57501),f317(f317(f299(x57501),x57502),f178(f904(x57501,a893)))),x57502)
% 94.68/94.44 [5751]~P66(x57511)+E(f12(x57511,f223(x57511),f317(f317(f299(x57511),x57512),f178(f904(x57511,a893)))),x57512)
% 94.68/94.44 [5812]E(f317(f317(f23(a897),x58121),f317(f317(f23(a897),x58121),x58122)),x58122)+~P1(f317(f317(f224(a897),x58122),x58121))
% 94.68/94.44 [5813]E(f317(f317(f74(a897),x58131),f317(f317(f23(a897),x58132),x58131)),x58132)+~P1(f317(f317(f224(a897),x58131),x58132))
% 94.68/94.44 [5835]E(f40(a897,f317(f317(f23(a897),x58351),x58352),x58352),f40(a897,x58351,x58352))+P1(f317(f317(f225(a897),x58351),x58352))
% 94.68/94.44 [5846]E(f317(f73(a1),f317(f317(f30(a1),x58461),f317(f73(a1),x58462))),f283(x58461,x58462))+P1(f317(f317(f224(a1),f2(a1)),x58462))
% 94.68/94.44 [5848]~E(x58482,f2(a897))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f234(a897),x58481),x58482)))
% 94.68/94.44 [5911]~P94(x59111)+E(f317(f317(f74(x59111),f317(f73(x59111),f72(x59111))),f317(f94(x59111),x59112)),f317(f94(x59111),f317(f317(f74(a1),x59112),a87)))
% 94.68/94.44 [5913]E(f317(f317(f234(a897),f317(f94(a897),x59131)),x59132),f317(f317(f234(a897),f2(a897)),x59132))+~P1(f317(a183,f317(f94(a1),x59131)))
% 94.68/94.44 [6021]E(f317(f131(a897),f129(a897,f317(f292(a897,x60211),x60212))),x60211)+~P1(f317(f317(f225(a897),x60211),x60212))
% 94.68/94.44 [6037]E(f317(f317(f75(a897),f317(f94(a897),x60371)),f317(f94(a897),x60372)),f317(f94(a897),f317(f317(f75(a1),x60371),x60372)))+P1(f317(f317(f225(a1),x60371),a77))
% 94.68/94.44 [6043]~P126(x60431)+P1(f317(f317(f224(x60431),f2(x60431)),f317(f317(f75(x60431),x60432),x60432)))
% 94.68/94.44 [6055]E(f317(f317(f23(a897),f317(a102,x60551)),x60552),f317(a102,f317(f317(f23(a897),x60551),x60552)))+~P1(f317(f317(f224(a897),x60552),x60551))
% 94.68/94.44 [6059]E(f40(a897,f317(f317(f23(a897),x60591),x60592),x60592),f40(a897,x60591,x60592))+~P1(f317(f317(f224(a897),x60592),x60591))
% 94.68/94.44 [6113]E(f317(f317(f234(a897),f317(a95,x61131)),x61132),f317(a95,f317(f317(f234(a1),x61131),x61132)))+~P1(f317(f317(f224(a1),f2(a1)),x61131))
% 94.68/94.44 [6131]P1(f317(f127(x61311),x61312))+P1(f317(f317(f225(a897),f644(x61312,x61311)),f317(f179(f898(x61311)),x61312)))
% 94.68/94.44 [6132]P1(f317(f127(x61321),x61322))+P1(f317(f317(f225(a897),f648(x61322,x61321)),f317(f179(f898(x61321)),x61322)))
% 94.68/94.44 [6146]~E(x61461,f103(x61462))+~P1(f317(f317(f225(a897),f2(a897)),f317(f179(f898(x61462)),x61461)))
% 94.68/94.44 [6157]E(f134(a897,f129(a897,f317(f292(a897,x61571),x61572))),f317(f317(f23(a897),x61572),f72(a897)))+~P1(f317(f317(f225(a897),x61571),x61572))
% 94.68/94.44 [6160]E(f317(f317(f74(a1),x61601),f317(f90(a1),f317(a102,f760(x61602,x61601)))),x61602)+~P1(f317(f317(f225(a1),x61601),x61602))
% 94.68/94.44 [6167]E(x61671,f2(a897))+E(f317(f317(f75(a897),x61672),f317(f317(f234(a897),x61672),f317(f317(f23(a897),x61671),f72(a897)))),f317(f317(f234(a897),x61672),x61671))
% 94.68/94.44 [6195]E(f317(f317(f75(a897),f317(a95,x61951)),f317(a95,x61952)),f317(a95,f317(f317(f75(a1),x61951),x61952)))+~P1(f317(f317(f224(a1),f2(a1)),x61951))
% 94.68/94.44 [6196]E(f317(f317(f30(a897),f317(a95,x61961)),f317(a95,x61962)),f317(a95,f317(f317(f30(a1),x61961),x61962)))+~P1(f317(f317(f224(a1),f2(a1)),x61961))
% 94.68/94.44 [6211]~P112(x62111)+E(f317(f317(f74(x62111),x62112),x62112),f317(f317(f75(x62111),f317(f317(f74(x62111),f72(x62111)),f72(x62111))),x62112))
% 94.68/94.44 [6234]E(f317(f317(f23(a1),f317(f90(a1),x62341)),f317(f90(a1),x62342)),f317(f90(a1),f317(f317(f23(a897),x62341),x62342)))+~P1(f317(f317(f224(a897),x62342),x62341))
% 94.68/94.44 [6236]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f74(a1),x62361),x62362)),f45(x62361,x62362))+~P1(f317(f317(f224(a1),x62362),f2(a1)))
% 94.68/94.44 [6270]E(f169(x62701,x62702),f103(f898(x62701)))+P1(f317(f317(f319(f898(x62701)),f643(x62702,x62701)),f317(f162(f898(x62701)),x62702)))
% 94.68/94.44 [6281]E(f106(a1,f317(f119(a1),x62811),f118(x62812,f317(f317(f74(a1),x62811),f72(a1)))),f118(x62812,x62811))+P1(f317(f317(f225(a1),x62812),x62811))
% 94.68/94.44 [6336]~P1(f317(f317(f277(a897),x63361),x63362))+P1(f317(f317(f277(a897),x63361),f317(f317(f74(a897),x63362),x63361)))
% 94.68/94.44 [6358]E(f317(f317(f141(a1),x63581),f168(f317(f317(f74(a1),x63581),f72(a1)),x63582)),f168(x63581,x63582))+~P1(f317(f317(f224(a1),x63581),x63582))
% 94.68/94.44 [6380]P150(x63801,x63802)+~P1(f317(f317(f224(f904(a892,a893)),x63802),x63801))
% 94.68/94.44 [6401]~P1(f317(f317(f225(a897),x64012),x64011))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f23(a897),x64011),x64012)))
% 94.68/94.44 [6433]~P1(f317(f317(f225(a897),x64331),f317(a95,x64332)))+P1(f317(f317(f225(a1),f317(f90(a1),x64331)),x64332))
% 94.68/94.44 [6462]~P66(x64621)+E(f317(f317(f91(f904(x64621,a893)),f317(f272(x64621),x64622)),f317(f317(f299(x64621),x64622),f178(f904(x64621,a893)))),f317(f291(x64621),x64622))
% 94.68/94.44 [6463]~P1(f317(f317(f224(a1),f2(a1)),x64631))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),x64631),x64632)))
% 94.68/94.44 [6466]~P1(f317(f317(f225(a897),f2(a897)),x64661))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f234(a897),x64661),x64662)))
% 94.68/94.44 [6493]~E(f317(x64931,f2(a897)),f2(a897))+E(f317(f317(f6(a897,a897),x64931),f293(a897,f317(a102,f2(a897)),x64932)),f317(f317(f6(a897,a897),x64931),f293(a897,f2(a897),x64932)))
% 94.68/94.44 [6559]~P94(x65591)+E(f317(f317(f75(x65591),f317(f317(f74(x65591),f72(x65591)),f72(x65591))),f317(f94(x65591),x65592)),f317(f94(x65591),f317(f317(f74(a1),x65592),x65592)))
% 94.68/94.44 [6579]E(f317(f317(f299(a1),x65791),f293(a1,f317(f317(f74(a1),x65791),f72(a1)),x65792)),f293(a1,x65791,x65792))+P1(f317(f317(f225(a1),x65792),x65791))
% 94.68/94.44 [6580]P1(f317(f317(f225(a897),x65801),f317(a95,x65802)))+~P1(f317(f317(f225(a1),f317(f90(a1),x65801)),x65802))
% 94.68/94.44 [6680]P1(f317(f317(f277(a897),x66801),x66802))+~P1(f317(f317(f277(a897),x66801),f317(f317(f74(a897),x66802),x66801)))
% 94.68/94.44 [6686]E(f317(a95,f317(f317(f30(a1),f317(f94(a1),x66861)),f317(f94(a1),x66862))),f317(f317(f30(a897),f317(f94(a897),x66861)),f317(f94(a897),x66862)))+P1(f317(a183,f317(f94(a1),x66861)))
% 94.68/94.44 [6746]P1(f317(f317(f225(a897),x67461),x67462))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f23(a897),x67462),x67461)))
% 94.68/94.44 [6789]P1(f317(f317(f225(a897),f2(a897)),x67891))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f75(a897),x67892),x67891)))
% 94.68/94.44 [6790]P1(f317(f317(f225(a897),f2(a897)),x67901))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f75(a897),x67901),x67902)))
% 94.68/94.44 [6809]~P1(f317(f317(f224(a1),x68091),f2(a1)))+E(f317(f317(f75(a897),f317(a95,f317(f73(a1),x68091))),f317(a95,f317(f73(a1),x68092))),f317(a95,f317(f317(f75(a1),x68091),x68092)))
% 94.68/94.44 [6870]~E(x68702,f178(f904(x68701,a893)))+P1(f317(f317(f224(f904(x68701,a893)),x68702),f317(f73(f904(x68701,a893)),x68702)))
% 94.68/94.44 [6932]~P94(x69321)+E(f317(f317(f74(x69321),f317(f317(f74(x69321),f2(x69321)),f317(f94(x69321),x69322))),f317(f94(x69321),x69322)),f317(f94(x69321),f317(f317(f74(a1),x69322),x69322)))
% 94.68/94.44 [6988]~P1(f317(f317(f225(a1),x69881),x69882))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x69881),f72(a1))),x69882))
% 94.68/94.44 [7060]E(x70601,f2(a897))+~P1(f317(f317(f224(a1),f317(f90(a1),x70602)),f317(f73(a1),f317(f90(a1),x70601))))
% 94.68/94.44 [7061]E(x70611,f2(a897))+~P1(f317(f317(f224(a1),f317(f90(a1),x70611)),f317(f73(a1),f317(f90(a1),x70612))))
% 94.68/94.44 [7163]E(f317(f317(f242(a1,a1),f317(f94(a1),a87)),f317(f317(f74(a1),x71631),x71632)),f45(x71631,x71632))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x71631),x71632)))
% 94.68/94.44 [7207]~P26(x72071,x72072)+P36(x72071,f317(f241(f904(f903(x72071,x72071),a893),f904(f903(x72071,x72071),a893)),x72072))
% 94.68/94.44 [7226]~P1(f317(f317(f224(a897),f317(a102,f2(a897))),x72261))+P1(f317(f317(f224(a897),f317(a102,f2(a897))),f317(f317(f234(a897),x72261),x72262)))
% 94.68/94.44 [7404]~P1(f317(f317(f224(a1),x74041),x74042))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x74041),x74041)),f317(f317(f74(a1),x74042),x74042)))
% 94.68/94.44 [7409]~P1(f317(f317(f225(a1),x74091),x74092))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x74091),x74091)),f317(f317(f74(a1),x74092),x74092)))
% 94.68/94.44 [7467]~P1(f317(f317(f225(a897),f2(a897)),x74671))+P1(f317(f317(f225(a897),f317(f317(f23(a897),x74671),f317(a102,x74672))),x74671))
% 94.68/94.44 [7502]P1(f317(f317(f224(a897),f317(a102,f2(a897))),x75021))+~P1(f317(f317(f224(a897),f317(a102,f2(a897))),f317(f317(f75(a897),x75022),x75021)))
% 94.68/94.44 [7503]P1(f317(f317(f224(a897),f317(a102,f2(a897))),x75031))+~P1(f317(f317(f224(a897),f317(a102,f2(a897))),f317(f317(f75(a897),x75031),x75032)))
% 94.68/94.44 [7507]P1(f317(f317(f224(a897),f317(f317(f154(a897),x75071),x75072)),f317(f155(a897),x75071)))+~P1(f317(f317(f225(a897),x75072),f317(f179(f898(a897)),x75071)))
% 94.68/94.44 [7544]P1(f317(f317(f225(a1),x75441),x75442))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x75441),f72(a1))),x75442))
% 94.68/94.44 [7585]P1(f317(f28(x75851),f232(f904(x75851,a893))))+~P1(f317(f28(f904(x75852,x75851)),f232(f904(f904(x75852,x75851),a893))))
% 94.68/94.44 [7586]P1(f317(f28(x75861),f232(f904(x75861,a893))))+~P1(f317(f28(f902(x75862,x75861)),f232(f904(f902(x75862,x75861),a893))))
% 94.68/94.44 [7587]P1(f317(f28(x75871),f232(f904(x75871,a893))))+~P1(f317(f28(f902(x75871,x75872)),f232(f904(f902(x75871,x75872),a893))))
% 94.68/94.44 [7627]E(x76271,f178(f904(x76272,a893)))+~P1(f317(f317(f224(f904(x76272,a893)),x76271),f317(f73(f904(x76272,a893)),x76271)))
% 94.68/94.44 [7768]E(f317(f132(f898(x77681),f898(x77681),f124(x77681),f103(x77681)),x77682),f103(x77681))+P1(f317(f317(f319(f898(x77681)),f674(x77682,x77681)),f317(f162(f898(x77681)),x77682)))
% 94.68/94.44 [7769]E(f317(f132(f898(x77691),f898(x77691),f124(x77691),f103(x77691)),x77692),f103(x77691))+P1(f317(f317(f319(f898(x77691)),f675(x77692,x77691)),f317(f162(f898(x77691)),x77692)))
% 94.68/94.44 [8006]P1(f317(f317(f224(a1),x80061),x80062))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x80061),x80061)),f317(f317(f74(a1),x80062),x80062)))
% 94.68/94.44 [8011]P1(f317(f317(f225(a1),x80111),x80112))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x80111),x80111)),f317(f317(f74(a1),x80112),x80112)))
% 94.68/94.44 [8104]~P112(x81041)+E(f317(f317(f75(x81041),f317(f317(f74(x81041),f72(x81041)),f72(x81041))),f317(f317(f6(a897,x81041),f90(x81041)),f293(a897,f72(a897),x81042))),f317(f317(f75(x81041),f317(f90(x81041),x81042)),f317(f317(f74(x81041),f317(f90(x81041),x81042)),f72(x81041))))
% 94.68/94.44 [8153]P1(f317(f317(f319(a897),x81531),x81532))+~P1(f317(f317(f319(a1),f317(f90(a1),x81531)),f317(f300(a897,a1,f90(a1)),x81532)))
% 94.68/94.44 [8312]~P1(f317(f28(x83121),x83122))+E(f317(f300(a897,x83121,f491(x83122,x83121)),f317(f252(a897),f317(f317(f7(a897,a897,a893),f225(a897)),f492(x83122,x83121)))),x83122)
% 94.68/94.44 [8592]P53(x85921,x85922)+P1(f317(f317(f319(f903(x85921,x85921)),f317(f317(f242(x85921,x85921),f328(x85922,x85921)),f328(x85922,x85921))),x85922))
% 94.68/94.44 [8593]P37(x85931,x85932)+P1(f317(f317(f319(f903(x85931,x85931)),f317(f317(f242(x85931,x85931),f768(x85932,x85931)),f770(x85932,x85931))),x85932))
% 94.68/94.44 [8594]P37(x85941,x85942)+P1(f317(f317(f319(f903(x85941,x85941)),f317(f317(f242(x85941,x85941),f770(x85942,x85941)),f771(x85942,x85941))),x85942))
% 94.68/94.44 [8595]P38(x85951,x85952)+P1(f317(f317(f319(f903(x85951,x85951)),f317(f317(f242(x85951,x85951),f684(x85952,x85951)),f683(x85952,x85951))),x85952))
% 94.68/94.44 [8596]P38(x85961,x85962)+P1(f317(f317(f319(f903(x85961,x85961)),f317(f317(f242(x85961,x85961),f683(x85962,x85961)),f684(x85962,x85961))),x85962))
% 94.68/94.44 [8597]P51(x85971,x85972)+P1(f317(f317(f319(f903(x85971,x85971)),f317(f317(f242(x85971,x85971),f781(x85972,x85971)),f782(x85972,x85971))),x85972))
% 94.68/94.44 [8738]~P94(x87381)+E(f317(f317(f23(x87381),f72(x87381)),f317(f94(x87381),x87382)),f317(f94(x87381),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x87382))))
% 94.68/94.44 [8863]~P1(f317(f317(f225(f904(a897,a893)),x88631),x88632))+P1(f317(f317(f225(f904(a1,a893)),f317(f300(a897,a1,f90(a1)),x88631)),f317(f300(a897,a1,f90(a1)),x88632)))
% 94.68/94.44 [8897]~P1(f317(f317(f225(a1),x88971),x88972))+P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x88971),x88971)),a87)),f317(f317(f74(a1),x88972),x88972)))
% 94.68/94.44 [8899]~P1(f317(f317(f225(a1),x88991),x88992))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x88991),x88991)),a87)),f317(f317(f74(a1),x88992),x88992)))
% 94.68/94.44 [8972]~P1(f317(f317(f319(a897),x89721),f317(f162(a897),x89722)))+P1(f317(f317(f224(a897),x89721),f317(f132(a897,a897,f74(a897),f2(a897)),x89722)))
% 94.68/94.44 [9061]P45(x90611,x90612)+~P1(f317(f317(f319(f903(x90611,x90611)),f317(f317(f242(x90611,x90611),f879(x90612,x90611)),f879(x90612,x90611))),x90612))
% 94.68/94.44 [9062]P37(x90621,x90622)+~P1(f317(f317(f319(f903(x90621,x90621)),f317(f317(f242(x90621,x90621),f768(x90622,x90621)),f771(x90622,x90621))),x90622))
% 94.68/94.44 [9063]P51(x90631,x90632)+~P1(f317(f317(f319(f903(x90631,x90631)),f317(f317(f242(x90631,x90631),f782(x90632,x90631)),f781(x90632,x90631))),x90632))
% 94.68/94.44 [9203]~P1(f317(f317(f224(f904(a1,a893)),f317(f300(a897,a1,f90(a1)),x92031)),f317(f300(a897,a1,f90(a1)),x92032)))+P1(f317(f317(f224(f904(a897,a893)),x92031),x92032))
% 94.68/94.44 [9204]~P1(f317(f317(f225(f904(a1,a893)),f317(f300(a897,a1,f90(a1)),x92041)),f317(f300(a897,a1,f90(a1)),x92042)))+P1(f317(f317(f225(f904(a897,a893)),x92041),x92042))
% 94.68/94.44 [9289]P1(f317(f317(f225(a1),x92891),x92892))+~P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92891),x92891)),a87)),f317(f317(f74(a1),x92892),x92892)))
% 94.68/94.44 [9291]P1(f317(f317(f225(a1),x92911),x92912))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x92911),x92911)),a87)),f317(f317(f74(a1),x92912),x92912)))
% 94.68/94.44 [10188]~P106(x101881)+E(f106(f898(x101881),f317(f119(f898(x101881)),f103(x101881)),f317(f317(f317(f86(f899(f898(x101881))),f317(f317(f225(a1),f2(a1)),x101882)),f317(f108(f903(x101881,f898(x101881)),f898(x101881),f121(x101881,f898(x101881),f122(x101881,f317(f317(f23(a1),x101882),f72(a1))),f122(f898(x101881),f317(f317(f23(a1),x101882),f72(a1))))),f317(f247(x101881,f898(x101881),f899(f898(x101881))),f317(f317(f8(f904(f898(x101881),f898(x101881)),f904(f898(x101881),f899(f898(x101881))),x101881),f317(f8(f898(x101881),f899(f898(x101881)),f898(x101881)),f119(f898(x101881)))),f141(x101881))))),f105(f898(x101881)))),f122(f898(x101881),x101882))
% 94.68/94.44 [10210]~P1(f317(f28(x102101),x102102))+E(f317(f179(f898(x102101)),f84(f898(x102101),f317(f317(f18(f898(x102101),a893,a893),f317(f317(f8(a893,f904(a893,a893),f898(x102101)),a315),f317(f317(f7(f898(x102101),f904(x102101,a893),a893),f317(f317(f8(f904(x102101,a893),f904(f904(x102101,a893),a893),f898(x102101)),a314),f162(x102101))),x102102))),f127(x102101)))),f204(x102101,x102102))
% 94.68/94.44 [6156]E(f317(f317(f74(a897),f317(f317(f23(a897),x61561),x61562)),x61562),x61561)+~P1(f317(f317(f224(a897),x61562),x61561))
% 94.68/94.44 [6230]E(f317(f317(f30(a897),f317(f317(f75(a897),x62301),x62302)),x62302),x62301)+~P1(f317(f317(f225(a897),f2(a897)),x62302))
% 94.68/94.44 [6231]E(f317(f317(f30(a897),f317(f317(f75(a897),x62311),x62312)),x62311),x62312)+~P1(f317(f317(f225(a897),f2(a897)),x62311))
% 94.68/94.44 [6235]~P76(x62351)+E(f317(f317(f6(a897,x62351),f317(f154(x62351),x62352)),f317(f292(a897,f2(a897)),f317(f179(f898(x62351)),x62352))),f317(f155(x62351),x62352))
% 94.68/94.44 [6350]E(f40(a897,f317(a102,f317(f317(f75(a897),x63501),x63502)),x63501),f72(a897))+~P1(f317(f317(f225(a897),f72(a897)),x63501))
% 94.68/94.44 [6356]E(f317(a102,f317(f317(f74(a897),f317(f94(a897),x63561)),x63562)),f317(f317(f74(a897),f72(a897)),x63562))+~P1(f317(a183,f317(f94(a1),x63561)))
% 94.68/94.44 [6386]E(f317(a95,f317(f317(f234(a1),f317(f94(a1),x63861)),x63862)),f317(f317(f234(a897),f317(f94(a897),x63861)),x63862))+P1(f317(a183,f317(f94(a1),x63861)))
% 94.68/94.44 [6634]E(f317(f317(f23(a897),x66341),f317(f94(a897),f317(f317(f74(a1),x66342),a87))),f317(f317(f23(a897),f317(a102,x66341)),f317(f94(a897),x66342)))+~P1(f317(f317(f225(a1),a77),x66342))
% 94.68/94.44 [6716]E(x67161,f2(a897))+E(f317(a102,f317(f317(f74(a897),f317(f317(f23(a897),x67161),f72(a897))),x67162)),f317(f317(f74(a897),x67161),x67162))
% 94.68/94.44 [6759]E(x67591,f2(a1))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x67591)),x67592)))
% 94.68/94.44 [6774]~E(x67742,f2(a897))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x67741)),x67742)))
% 94.68/94.44 [6812]E(x68121,f2(a897))+E(f317(f317(f74(a897),x68122),f317(f317(f75(a897),f317(f317(f23(a897),x68121),f72(a897))),x68122)),f317(f317(f75(a897),x68121),x68122))
% 94.68/94.44 [6863]~P1(f317(f317(f224(a1),x68631),x68632))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x68631),a87)),x68632))
% 94.68/94.44 [6992]E(f317(f317(f141(a897),x69921),f129(a897,f317(f292(a897,f317(a102,x69921)),x69922))),f129(a897,f317(f292(a897,x69921),x69922)))+~P1(f317(f317(f225(a897),x69921),x69922))
% 94.68/94.44 [7198]E(x71981,x71982)+~E(f317(f317(f23(a1),f317(f317(f74(a1),x71981),x71981)),a87),f317(f317(f23(a1),f317(f317(f74(a1),x71982),x71982)),a87))
% 94.68/94.44 [7201]E(x72011,f103(x72012))+E(f256(x72012,f317(f317(f144(x72012,f903(a89,x72012)),f317(f242(a89,x72012),f72(a89))),x72011)),f265(x72012,x72011))
% 94.68/94.44 [7437]P1(f317(f317(f224(a1),x74371),x74372))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x74371),a87)),x74372))
% 94.68/94.44 [7910]~P1(f317(f317(f225(a897),x79101),x79102))+P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x79101),x79102)),a230))
% 94.68/94.44 [8130]~P1(f317(f317(f225(a89),f2(a89)),x81301))+P1(f317(f317(f225(a89),f317(f241(a89,f903(a89,a89)),f317(f257(x81301),x81302))),x81301))
% 94.68/94.44 [8394]~P37(x83941,x83942)+P37(x83941,f317(f317(f91(f904(f903(x83941,x83941),a893)),x83942),f297(x83941,f178(f904(f903(x83941,x83941),a893)))))
% 94.68/94.44 [8395]~P38(x83951,x83952)+P38(x83951,f317(f317(f91(f904(f903(x83951,x83951),a893)),x83952),f297(x83951,f178(f904(f903(x83951,x83951),a893)))))
% 94.68/94.44 [8443]~P86(x84431)+P1(f317(f317(f224(x84431),f317(f70(x84431),f317(f155(x84431),x84432))),f317(f155(x84431),f317(f317(f144(x84431,x84431),f70(x84431)),x84432))))
% 94.68/94.44 [8469]P1(f317(f317(f225(a897),x84691),x84692))+~P1(f317(f317(f319(f903(a897,a897)),f317(f317(f242(a897,a897),x84691),x84692)),a230))
% 94.68/94.44 [8616]E(f317(f317(f242(x86161,x86161),f568(x86162,x86161)),f568(x86162,x86161)),x86162)+~P1(f317(f317(f319(f903(x86161,x86161)),x86162),f297(x86161,f178(f904(f903(x86161,x86161),a893)))))
% 94.68/94.44 [8660]E(f317(f292(a897,x86601),f317(f317(f74(a897),x86601),f317(f29(a897),x86602))),x86602)+~P1(f317(f317(f224(f904(a897,a893)),x86602),f317(f292(a897,x86601),f317(f317(f74(a897),x86601),f317(f29(a897),x86602)))))
% 94.68/94.44 [8890]P38(x88901,x88902)+~P38(x88901,f317(f317(f91(f904(f903(x88901,x88901),a893)),x88902),f297(x88901,f178(f904(f903(x88901,x88901),a893)))))
% 94.68/94.44 [9016]E(f317(f317(f30(a1),f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x90161),x90161)),a87))),f317(f94(a1),f317(f317(f74(a1),x90162),x90162))),f317(f317(f30(a1),f317(f94(a1),x90161)),f317(f94(a1),x90162)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x90162)))
% 94.68/94.44 [9106]~P37(x91061,x91062)+P1(f317(f317(f224(f904(f903(x91061,x91061),a893)),f317(f317(f279(x91061,x91061,x91061),x91062),x91062)),x91062))
% 94.68/94.44 [9133]E(f167(f898(x91331),f317(f317(f8(a893,a893,f898(x91331)),a312),f317(f317(f7(f898(x91331),f898(x91331),a893),a314),f103(x91331))),x91332),f169(x91331,f169(x91331,x91332)))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x91331),a897),f179(f898(x91331))),x91332)))
% 94.68/94.44 [9136]E(f317(f317(f30(a1),f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x91361),x91361)),a87))),f317(f94(a1),f317(f317(f74(a1),x91362),x91362))),f317(f317(f30(a1),f317(f317(f74(a1),f317(f94(a1),x91361)),f72(a1))),f317(f94(a1),x91362)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x91362)))
% 94.68/94.44 [9985]P1(f317(a183,x99852))+E(f317(f317(f80(a1,a897),f317(f317(f23(a1),x99851),x99852)),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f2(a897))),a95)),f317(f317(f23(a897),f317(a95,x99851)),f317(a95,x99852)))
% 94.68/94.44 [9993]E(f317(f317(f80(a1,a897),f317(f94(a1),f317(f317(f74(a1),x99931),f317(f73(a1),x99932)))),f317(f317(f18(a1,a897,a897),f317(f317(f7(a1,a897,f904(a897,a897)),f317(f317(f8(a893,f904(a897,f904(a897,a897)),a1),f86(a897)),a183)),f2(a897))),a95)),f317(f317(f23(a897),f317(f94(a897),x99931)),f317(f94(a897),x99932)))+P1(f317(f317(f225(a1),x99932),a77))
% 94.68/94.44 [9994]~P26(x99941,x99942)+P1(f317(f317(f224(f904(f903(x99941,x99941),a893)),f317(f317(f279(x99941,x99941,x99941),f317(f241(f904(f903(x99941,x99941),a893),f904(f903(x99941,x99941),a893)),x99942)),f317(f246(f904(f903(x99941,x99941),a893),f904(f903(x99941,x99941),a893)),x99942))),f317(f241(f904(f903(x99941,x99941),a893),f904(f903(x99941,x99941),a893)),x99942)))
% 94.68/94.44 [10049]~E(f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,f904(a897,a893),a893),f319(a897)),x100491))),f317(f317(f7(a897,a897,a893),f225(a897)),f317(a102,x100492))))),f2(a897))+~P1(f317(f317(f319(a897),f2(a897)),x100491))
% 94.68/94.44 [10060]E(f289(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x100601,x100602),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x100602),x100601))
% 94.68/94.44 [10065]E(f287(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x100651,x100652),f178(f904(a897,a893)))+P1(f317(f317(f277(a897),x100651),x100652))
% 94.68/94.44 [10066]E(f290(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x100661,x100662),f178(f904(a897,a893)))+P1(f317(f317(f277(a897),x100661),x100662))
% 94.68/94.44 [10070]E(f287(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x100701,x100702),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x100702),x100701))
% 94.68/94.44 [10072]E(f290(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x100721,x100722),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x100722),x100721))
% 94.68/94.44 [10115]E(f40(a1,f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x101151),x101151)),a87)),f317(f94(a1),f317(f317(f74(a1),x101152),x101152))),f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a1,f317(f94(a1),x101151),f317(f94(a1),x101152)))),f72(a1)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x101152)))
% 94.68/94.44 [10124]E(f40(a1,f317(f94(a1),f317(f317(f23(a1),f317(f317(f74(a1),x101241),x101241)),a87)),f317(f94(a1),f317(f317(f74(a1),x101242),x101242))),f317(f317(f23(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a1,f317(f317(f74(a1),f317(f94(a1),x101241)),f72(a1)),f317(f94(a1),x101242)))),f72(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x101242)))
% 94.68/94.44 [10179]~P5(x101791)+E(f31(x101791,f317(f252(x101791),f317(f317(f8(f904(x101791,a893),a893,x101791),f82(x101791)),f317(f317(f8(f904(x101791,a893),f904(x101791,a893),x101791),f317(f18(x101791,a893,a893),f317(f317(f8(a893,f904(a893,a893),x101791),a320),f317(f317(f7(x101791,f904(x101791,a893),a893),f319(x101791)),x101792)))),f224(x101791))))),f32(x101791,x101792))
% 94.68/94.44 [10203]~P36(x102031,x102032)+P59(x102031,f317(f317(f7(x102031,f904(f903(x102031,x102031),a893),f904(x102031,a893)),f317(f317(f8(f904(x102031,f904(f904(f903(x102031,x102031),a893),a893)),f904(f904(f903(x102031,x102031),a893),f904(x102031,a893)),x102031),f7(x102031,f904(f903(x102031,x102031),a893),a893)),f317(f317(f8(f904(x102031,f903(x102031,x102031)),f904(x102031,f904(f904(f903(x102031,x102031),a893),a893)),x102031),f317(f8(f903(x102031,x102031),f904(f904(f903(x102031,x102031),a893),a893),x102031),f319(f903(x102031,x102031)))),f242(x102031,x102031)))),x102032))
% 94.68/94.44 [10204]~P8(x102041,f232(f904(x102041,a893)),x102042)+P7(x102041,f317(f317(f7(x102041,f904(f903(x102041,x102041),a893),f904(x102041,a893)),f317(f317(f8(f904(x102041,f904(f904(f903(x102041,x102041),a893),a893)),f904(f904(f903(x102041,x102041),a893),f904(x102041,a893)),x102041),f7(x102041,f904(f903(x102041,x102041),a893),a893)),f317(f317(f8(f904(x102041,f903(x102041,x102041)),f904(x102041,f904(f904(f903(x102041,x102041),a893),a893)),x102041),f317(f8(f903(x102041,x102041),f904(f904(f903(x102041,x102041),a893),a893),x102041),f319(f903(x102041,x102041)))),f242(x102041,x102041)))),x102042))
% 94.68/94.44 [10247]P36(x102471,x102472)+~P59(x102471,f317(f317(f7(x102471,f904(f903(x102471,x102471),a893),f904(x102471,a893)),f317(f317(f8(f904(x102471,f904(f904(f903(x102471,x102471),a893),a893)),f904(f904(f903(x102471,x102471),a893),f904(x102471,a893)),x102471),f7(x102471,f904(f903(x102471,x102471),a893),a893)),f317(f317(f8(f904(x102471,f903(x102471,x102471)),f904(x102471,f904(f904(f903(x102471,x102471),a893),a893)),x102471),f317(f8(f903(x102471,x102471),f904(f904(f903(x102471,x102471),a893),a893),x102471),f319(f903(x102471,x102471)))),f242(x102471,x102471)))),x102472))
% 94.68/94.44 [10248]P8(x102481,f232(f904(x102481,a893)),x102482)+~P7(x102481,f317(f317(f7(x102481,f904(f903(x102481,x102481),a893),f904(x102481,a893)),f317(f317(f8(f904(x102481,f904(f904(f903(x102481,x102481),a893),a893)),f904(f904(f903(x102481,x102481),a893),f904(x102481,a893)),x102481),f7(x102481,f904(f903(x102481,x102481),a893),a893)),f317(f317(f8(f904(x102481,f903(x102481,x102481)),f904(x102481,f904(f904(f903(x102481,x102481),a893),a893)),x102481),f317(f8(f903(x102481,x102481),f904(f904(f903(x102481,x102481),a893),a893),x102481),f319(f903(x102481,x102481)))),f242(x102481,x102481)))),x102482))
% 94.68/94.44 [7384]E(f317(f317(f74(a897),f317(f94(a897),f317(f317(f23(a1),x73841),a87))),x73842),f317(a102,f317(f317(f74(a897),f317(f94(a897),x73841)),x73842)))+P1(f317(a183,f317(f94(a1),x73841)))
% 94.68/94.44 [7827]~P94(x78271)+E(f317(f317(f74(x78271),f317(f317(f74(x78271),f72(x78271)),f317(f94(x78271),x78272))),f317(f94(x78271),x78272)),f317(f94(x78271),f317(f317(f23(a1),f317(f317(f74(a1),x78272),x78272)),a87)))
% 94.68/94.44 [8471]~P1(f317(f317(f224(a1),x84711),x84712))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x84711),x84711)),f317(f317(f23(a1),f317(f317(f74(a1),x84712),x84712)),a87)))
% 94.68/94.44 [8473]~P1(f317(f317(f224(a1),x84731),x84732))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x84731),x84731)),f317(f317(f23(a1),f317(f317(f74(a1),x84732),x84732)),a87)))
% 94.68/94.44 [8901]P1(f317(f317(f224(a1),x89011),x89012))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x89011),x89011)),f317(f317(f23(a1),f317(f317(f74(a1),x89012),x89012)),a87)))
% 94.68/94.44 [8903]P1(f317(f317(f224(a1),x89031),x89032))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),x89031),x89031)),f317(f317(f23(a1),f317(f317(f74(a1),x89032),x89032)),a87)))
% 94.68/94.44 [9192]~P1(f317(f317(f224(a1),x91921),x91922))+P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x91921),x91921)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x91922),x91922)),a87)))
% 94.68/94.44 [9194]~P1(f317(f317(f225(a1),x91941),x91942))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x91941),x91941)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x91942),x91942)),a87)))
% 94.68/94.44 [9466]P1(f317(f317(f224(a1),x94661),x94662))+~P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),x94661),x94661)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x94662),x94662)),a87)))
% 94.68/94.44 [9468]P1(f317(f317(f225(a1),x94681),x94682))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),x94681),x94681)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),x94682),x94682)),a87)))
% 94.68/94.44 [9501]~P1(f317(f28(x95011),x95012))+P1(f317(f28(f904(x95011,a893)),f317(f252(f904(x95011,a893)),f317(f317(f7(f904(x95011,a893),f904(x95011,a893),a893),f224(f904(x95011,a893))),x95012))))
% 94.68/94.44 [9553]~E(f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),x95531),f178(f904(f903(a897,a897),a893)))),f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),x95532),f178(f904(f903(a897,a897),a893)))))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x95531),x95532)),a99))
% 94.68/94.44 [9647]E(f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),x96471),f178(f904(f903(a897,a897),a893)))),f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),x96472),f178(f904(f903(a897,a897),a893)))))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x96471),x96472)),a99))
% 94.68/94.44 [9683]P1(f317(f317(f224(a1),f2(a1)),f617(x96831,x96832)))+E(f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96831)),f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96832)))
% 94.68/94.44 [10187]~P5(x101871)+E(f32(x101871,f317(f252(x101871),f317(f317(f8(f904(x101871,a893),a893,x101871),f82(x101871)),f317(f317(f8(f904(x101871,a893),f904(x101871,a893),x101871),f317(f18(x101871,a893,a893),f317(f317(f8(a893,f904(a893,a893),x101871),a320),f317(f317(f7(x101871,f904(x101871,a893),a893),f319(x101871)),x101872)))),f317(f7(x101871,x101871,a893),f224(x101871)))))),f31(x101871,x101872))
% 94.68/94.44 [10209]P1(f317(f317(f319(a897),f2(a897)),x102091))+E(f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),a897),f319(a897)),a102)),x102091))),f317(f317(f7(a897,a897,a893),f225(a897)),x102092)))),f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,f904(a897,a893),a893),f319(a897)),x102091))),f317(f317(f7(a897,a897,a893),f225(a897)),f317(a102,x102092))))))
% 94.68/94.44 [10267]P1(f317(f317(f277(a897),x102671),x102672))+~P1(f317(f317(f319(a897),x102672),f285(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102671)))
% 94.68/94.44 [10268]P1(f317(f317(f277(a897),x102681),x102682))+~P1(f317(f317(f319(a897),x102681),f288(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102682)))
% 94.68/94.44 [10269]~P1(f317(f317(f277(a897),x102691),x102692))+~P1(f317(f317(f319(a897),x102692),f288(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102691)))
% 94.68/94.44 [10270]~P1(f317(f317(f277(a897),x102701),x102702))+~P1(f317(f317(f319(a897),x102701),f285(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102702)))
% 94.68/94.44 [7694]~P94(x76941)+E(f317(f317(f75(x76941),x76942),f317(f94(x76941),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),x76942)
% 94.68/94.44 [7958]~P94(x79581)+E(f317(f317(f74(x79581),f317(f94(x79581),x79582)),f72(x79581)),f317(f94(x79581),f317(f317(f74(a1),x79582),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))
% 94.68/94.44 [8102]P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x81022)))+E(f317(f317(f234(a1),x81021),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x81022),x81022)),a87))),f72(a1))
% 94.68/94.44 [9528]~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x95282)))+E(f317(f317(f234(a1),x95281),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x95282),x95282)),a87))),f317(f317(f80(a1,a1),f317(f317(f234(a1),x95281),f317(f94(a897),x95282))),f317(f317(f18(a1,a1,a1),f317(f317(f8(a1,f904(a1,a1),a1),f75(a1)),f317(f75(a1),x95281))),f5(a1))))
% 94.68/94.44 [9904]~P1(f317(f317(f224(a897),f629(x99042,x99041)),f317(x99041,f629(x99042,x99041))))+P1(f317(f28(a897),f317(f252(a897),f317(f317(f7(a897,a897,a893),f317(f317(f8(a897,f904(a897,a893),a897),f224(a897)),x99041)),x99042))))
% 94.68/94.44 [10039]~P1(f317(f317(f224(a897),f317(f94(a897),x100391)),f317(a102,x100392)))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x100391),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),f224(a897)),a95)),x100392))))
% 94.68/94.44 [10040]~P1(f317(f317(f225(a897),f317(f94(a897),x100401)),f317(a102,x100402)))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x100401),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),f225(a897)),a95)),x100402))))
% 94.68/94.44 [10099]P1(f317(f317(f224(a897),f317(f94(a897),x100991)),f317(a102,x100992)))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x100991),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),f224(a897)),a95)),x100992))))
% 94.68/94.44 [10100]P1(f317(f317(f225(a897),f317(f94(a897),x101001)),f317(a102,x101002)))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101001),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),f225(a897)),a95)),x101002))))
% 94.68/94.44 [10130]~P1(f317(f317(f224(a897),f317(a102,x101302)),f317(f94(a897),x101301)))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101301),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f8(a897,a893,a1),f317(f224(a897),x101302)),a95)))))
% 94.68/94.44 [10131]~P1(f317(f317(f225(a897),f317(a102,x101312)),f317(f94(a897),x101311)))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101311),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f8(a897,a893,a1),f317(f225(a897),x101312)),a95)))))
% 94.68/94.44 [10177]P1(f317(f317(f224(a897),f317(a102,x101771)),f317(f94(a897),x101772)))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101772),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f8(a897,a893,a1),f317(f224(a897),x101771)),a95)))))
% 94.68/94.44 [10178]P1(f317(f317(f225(a897),f317(a102,x101781)),f317(f94(a897),x101782)))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101782),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f8(a897,a893,a1),f317(f225(a897),x101781)),a95)))))
% 94.68/94.44 [10257]~P1(f317(f317(f319(a897),f2(a897)),x102571))+E(f317(a102,f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,f904(a897,a893),a893),f317(f317(f8(a897,f904(f904(a897,a893),a893),a897),f319(a897)),a102)),x102571))),f317(f317(f7(a897,a897,a893),f225(a897)),x102572))))),f317(f29(a897),f317(f252(a897),f317(f317(f18(a897,a893,a893),f317(f317(f8(a893,f904(a893,a893),a897),a315),f317(f317(f7(a897,f904(a897,a893),a893),f319(a897)),x102571))),f317(f317(f7(a897,a897,a893),f225(a897)),f317(a102,x102572))))))
% 94.68/94.44 [8643]~P94(x86431)+E(f317(f317(f75(x86431),f317(f94(x86431),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),x86432),x86432)
% 94.68/94.44 [8704]~P94(x87041)+E(f317(f317(f74(x87041),f72(x87041)),f317(f94(x87041),x87042)),f317(f94(x87041),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),x87042)))
% 94.68/94.44 [8766]~P94(x87661)+E(f317(f317(f23(x87661),f317(f94(x87661),x87662)),f72(x87661)),f317(f94(x87661),f317(f317(f74(a1),x87662),f317(f73(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [8920]~P1(f317(f317(f225(a897),f317(f94(a897),a77)),x89202))+E(f317(f317(f23(a897),x89201),f317(f317(f23(a897),x89202),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f23(a897),f317(a102,x89201)),x89202))
% 94.68/94.44 [9571]~P112(x95711)+E(f317(f317(f75(x95711),x95712),x95712),f317(f317(f234(x95711),x95712),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [9572]~P82(x95721)+E(f317(f317(f234(x95721),x95722),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f75(x95721),x95722),x95722))
% 94.68/94.44 [9574]~P94(x95741)+E(f317(f317(f75(x95741),x95742),f317(f94(x95741),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f74(x95741),x95742),x95742))
% 94.68/94.44 [9822]~P141(x98221)+E(f317(f317(f234(x98221),f317(f73(x98221),x98222)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x98221),x98222),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [9823]~P111(x98231)+E(f317(f317(f234(x98231),f317(f70(x98231),x98232)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x98231),x98232),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [9819]~P94(x98191)+E(f317(f317(f75(x98191),f317(f94(x98191),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x98192),f317(f317(f74(x98191),x98192),x98192))
% 94.68/94.44 [9937]~P111(x99371)+E(f317(f70(x99371),f317(f317(f234(x99371),x99372),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x99371),x99372),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [10001]~P111(x100011)+P1(f317(f317(f224(x100011),f2(x100011)),f317(f317(f234(x100011),x100012),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.44 [10168]~E(f317(a102,x101682),f317(f94(a897),x101681))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101681),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),a314),a95)),x101682)))))
% 94.68/94.44 [10169]~E(f317(f94(a897),x101691),f317(a102,x101692))+P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x101691),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),a314),a95)),x101692)))))
% 94.68/94.44 [10212]E(f317(a102,x102121),f317(f94(a897),x102122))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x102122),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),a314),a95)),x102121)))))
% 94.68/94.44 [10213]E(f317(f94(a897),x102131),f317(a102,x102132))+~P1(f317(f317(f80(a1,a893),f317(f94(a1),f317(f317(f74(a1),x102131),a87))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a320),f317(f317(f8(a893,a893,a1),a312),a183))),f317(f317(f7(a1,a897,a893),f317(f317(f8(a897,f904(a897,a893),a1),a314),a95)),x102132)))))
% 94.68/94.44 [10258]~P15(x102581,x102582)+P1(f317(f317(f319(f904(x102581,a893)),f790(x102582,x102581)),f317(f317(f8(f904(x102581,a893),a893,f904(x102581,a893)),f81(x102581)),f317(f317(f8(f904(x102581,a893),f904(x102581,a893),f904(x102581,a893)),f317(f18(x102581,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102581),a315),f317(f317(f18(x102581,x102581,a893),x102582),f5(x102581))))),f317(f317(f7(f904(x102581,a893),f904(x102581,f904(x102581,a893)),f904(x102581,a893)),f317(f317(f8(f904(f904(x102581,a893),a893),f904(f904(x102581,f904(x102581,a893)),f904(x102581,a893)),f904(x102581,a893)),f8(f904(x102581,a893),a893,x102581)),a314)),x102582)))))
% 94.68/94.44 [9999]~P94(x99991)+E(f317(f317(f234(x99991),f317(f94(x99991),a87)),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x99992)),f72(x99991))
% 94.68/94.44 [10000]~P141(x100001)+E(f317(f317(f234(x100001),f317(f73(x100001),f72(x100001))),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100002)),f72(x100001))
% 94.68/94.44 [10003]~P82(x100031)+E(f317(f317(f234(x100031),x100032),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),a87))),f317(f317(f75(x100031),f317(f317(f75(x100031),x100032),x100032)),x100032))
% 94.68/94.44 [10192]~P1(f317(f317(f224(a1),f2(a1)),x101922))+E(f40(a1,f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101921)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101922)),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a1,x101921,x101922))))
% 94.68/94.44 [10215]~P1(f317(f317(f224(a1),f2(a1)),x102152))+E(f317(f317(f30(a1),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102151))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102152)),f317(f317(f30(a1),x102151),x102152))
% 94.68/94.44 [10217]~P1(f317(f317(f224(a1),x102172),f2(a1)))+E(f317(f317(f30(a1),f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102171))),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102172)),f317(f317(f30(a1),f317(f317(f74(a1),x102171),f72(a1))),x102172))
% 94.68/94.44 [10218]~P1(f317(f317(f224(a1),x102182),f2(a1)))+E(f40(a1,f317(f317(f74(a1),f72(a1)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102181)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102182)),f317(f317(f23(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f40(a1,f317(f317(f74(a1),x102181),f72(a1)),x102182))),f72(a1)))
% 94.68/94.44 [10090]~P94(x100901)+E(f317(f317(f234(x100901),f317(f94(x100901),a87)),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100902))),f317(f94(x100901),a87))
% 94.68/94.44 [10092]~P141(x100921)+E(f317(f317(f234(x100921),f317(f73(x100921),f72(x100921))),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100922))),f317(f73(x100921),f72(x100921)))
% 94.68/94.44 [5009]P37(x50091,x50092)+~P8(x50091,x50093,x50092)
% 94.68/94.44 [5011]P51(x50111,x50112)+~P8(x50111,x50113,x50112)
% 94.68/94.44 [5184]~P8(x51841,x51842,x51843)+P52(x51841,x51842,x51843)
% 94.68/94.44 [8168]~E(x81682,x81683)+P33(x81681,x81681,a314,x81682,x81683)
% 94.68/94.44 [8717]E(x87171,x87172)+~P33(x87173,x87173,a314,x87171,x87172)
% 94.68/94.44 [4813]E(f159(x48131,x48132,x48133),f103(x48131))+~E(x48132,f2(a897))
% 94.68/94.44 [4981]~E(f159(x49812,x49811,x49813),f103(x49812))+E(x49811,f2(a897))
% 94.68/94.44 [5189]~P36(x51891,x51893)+P36(x51891,f311(x51891,x51892,x51893))
% 94.68/94.44 [5298]~P28(x52981,x52982,x52983)+P30(a1,x52981,f168(x52982,x52983))
% 94.68/94.44 [5366]P28(x53661,x53662,x53663)+~P30(a1,x53661,f168(x53662,x53663))
% 94.68/94.44 [5438]~P8(x54381,x54382,x54383)+P8(f898(x54381),f151(x54381,x54382),f148(x54381,x54383))
% 94.68/94.44 [5439]~P52(x54391,x54392,x54393)+P52(f898(x54391),f151(x54391,x54392),f148(x54391,x54393))
% 94.68/94.44 [5552]P55(x55521,x55522,x55523)+~E(f535(x55523,x55522,x55521),f536(x55523,x55522,x55521))
% 94.68/94.44 [5553]P54(x55531,x55532,x55533)+~E(f556(x55533,x55532,x55531),f557(x55533,x55532,x55531))
% 94.68/94.44 [8174]~E(x81742,x81743)+P25(x81741,x81741,f25(x81741),x81742,x81743)
% 94.68/94.44 [8725]E(x87251,x87252)+~P25(x87253,x87253,f25(x87253),x87251,x87252)
% 94.68/94.44 [4768]~E(f317(f158(x47682),x47681),x47683)+E(x47681,f317(f158(x47682),x47683))
% 94.68/94.44 [4769]~E(x47692,f317(f158(x47691),x47693))+E(f317(f158(x47691),x47692),x47693)
% 94.68/94.44 [4819]E(x48191,x48192)+~E(f317(f158(x48193),x48191),f317(f158(x48193),x48192))
% 94.68/94.44 [5035]~P7(x50353,x50351)+P1(f317(f317(x50351,x50352),x50352))
% 94.68/94.44 [5036]~P42(x50363,x50361)+P1(f317(f317(x50361,x50362),x50362))
% 94.68/94.44 [5038]~P59(x50381,x50382)+P1(f317(f305(x50381,x50382),x50383))
% 94.68/94.44 [5104]~P36(x51041,x51042)+P36(f898(x51041),f317(f133(x51041,x51042),x51043))
% 94.68/94.44 [5109]~P1(f317(x51092,x51093))+~E(f317(f252(x51091),x51092),f178(f904(x51091,a893)))
% 94.68/94.44 [5110]~P1(f317(x51102,x51103))+~E(f178(f904(x51101,a893)),f317(f252(x51101),x51102))
% 94.68/94.44 [5122]E(x51221,f2(a897))+E(f134(x51222,f159(x51222,x51221,x51223)),x51223)
% 94.68/94.44 [5141]~P1(f317(x51411,x51413))+P1(f317(x51411,f84(x51412,x51411)))
% 94.68/94.44 [5142]~P1(f317(x51421,x51423))+P1(f317(x51421,f715(x51421,x51422)))
% 94.68/94.44 [5154]E(x51541,f2(a897))+E(f317(f131(x51542),f159(x51542,x51541,x51543)),x51543)
% 94.68/94.44 [5260]~E(x52602,x52603)+P1(f317(f317(f319(x52601),x52602),f317(a314,x52603)))
% 94.68/94.44 [5275]~E(x52752,f2(a897))+E(f317(f162(x52751),f159(x52751,x52752,x52753)),f178(f904(x52751,a893)))
% 94.68/94.44 [5320]E(f317(f158(x53201),x53202),f317(f317(f141(x53201),x53203),f103(x53201)))+~E(x53202,f317(f317(f141(x53201),x53203),f103(x53201)))
% 94.68/94.44 [5321]~E(x53213,f317(f317(f141(x53211),x53212),f103(x53211)))+E(f317(f317(f141(x53211),x53212),f103(x53211)),f317(f158(x53211),x53213))
% 94.68/94.44 [5362]~P32(x53621,x53622,x53623)+P32(x53621,x53622,f317(f158(x53621),x53623))
% 94.68/94.44 [5363]~P30(x53631,x53632,x53633)+P30(x53631,x53632,f317(f158(x53631),x53633))
% 94.68/94.44 [5367]E(f317(f29(x53671),f533(x53672,x53673,x53671)),x53672)+~E(f317(f29(x53671),x53673),f317(a102,x53672))
% 94.68/94.44 [5374]~P36(x53741,x53743)+P1(f317(f317(f319(x53741),x53742),f306(x53741,x53743)))
% 94.68/94.44 [5378]~E(f317(f158(x53782),x53781),f317(f317(f141(x53782),x53783),f103(x53782)))+E(x53781,f317(f317(f141(x53782),x53783),f103(x53782)))
% 94.68/94.44 [5379]~E(f317(f317(f141(x53792),x53793),f103(x53792)),f317(f158(x53792),x53791))+E(x53791,f317(f317(f141(x53792),x53793),f103(x53792)))
% 94.68/94.44 [5403]E(f79(f903(a897,a897),f43(x54031,x54032)),x54033)+~P1(f317(f43(x54031,x54032),x54033))
% 94.68/94.44 [5442]P32(x54421,x54422,x54423)+~P32(x54421,x54422,f317(f158(x54421),x54423))
% 94.68/94.44 [5443]P30(x54431,x54432,x54433)+~P30(x54431,x54432,f317(f158(x54431),x54433))
% 94.68/94.44 [5482]P1(f317(f317(x54821,x54822),x54822))+~P1(f317(f260(x54823,x54821),x54822))
% 94.68/94.44 [5483]~P1(f317(f317(x54832,x54833),x54833))+P1(f317(f260(x54831,x54832),x54833))
% 94.68/94.44 [5505]~E(x55052,f103(x55051))+P1(f317(f317(f319(f898(x55051)),x55052),f151(x55051,x55053)))
% 94.68/94.44 [5515]~P52(x55151,x55152,x55153)+P52(x55151,x55152,f317(f276(x55151,x55151),x55153))
% 94.68/94.44 [5516]~P55(x55161,x55162,x55163)+P55(x55161,x55162,f317(f276(x55161,x55161),x55163))
% 94.68/94.44 [5533]~P3(x55331)+E(f40(x55331,f40(x55331,x55332,x55333),x55333),f40(x55331,x55332,x55333))
% 94.68/94.44 [5635]E(x56351,x56352)+~P1(f317(f317(f319(x56353),x56351),f317(a314,x56352)))
% 94.68/94.44 [5682]~P144(x56821)+E(f180(x56821,x56822,f2(a897),x56823),x56823)
% 94.68/94.44 [5704]P52(x57041,x57042,x57043)+~P52(x57041,x57042,f317(f276(x57041,x57041),x57043))
% 94.68/94.44 [5705]P55(x57051,x57052,x57053)+~P55(x57051,x57052,f317(f276(x57051,x57051),x57053))
% 94.68/94.44 [5709]~P66(x57092)+E(f140(x57091,x57092,x57093,f103(x57091)),f103(x57091))
% 94.68/94.44 [5721]E(f160(x57211,x57212,f142(x57211,x57213)),f142(x57211,f160(x57211,x57212,x57213)))+~P1(f317(f127(x57211),x57213))
% 94.68/94.44 [5820]~P1(f317(f317(x58203,x58202),x58202))+P1(f317(f317(f319(x58201),x58202),f260(x58201,x58203)))
% 94.68/94.44 [5822]E(f317(f126(x58221,x58222),x58223),f103(x58221))+P1(f317(x58222,f649(x58223,x58222,x58221)))
% 94.68/94.44 [5890]E(f62(x58901,x58902,x58903),x58902)+P1(f317(x58903,f716(x58902,x58901,x58903)))
% 94.68/94.44 [5986]~P1(f317(f127(x59861),x59862))+P1(f317(f127(x59861),f166(x59861,x59862,x59863)))
% 94.68/94.44 [5987]~P1(f317(f127(x59871),x59873))+P1(f317(f127(x59871),f160(x59871,x59872,x59873)))
% 94.68/94.44 [5988]~P1(f317(f127(x59881),x59883))+P1(f317(f127(x59881),f167(x59881,x59882,x59883)))
% 94.68/94.44 [5989]~P1(f317(f127(x59891),x59893))+P1(f317(f127(x59891),f130(x59891,x59892,x59893)))
% 94.68/94.44 [5990]~P147(x59901,x59903,x59902)+P1(f317(x59901,f40(a1,x59902,x59903)))
% 94.68/94.44 [6007]~P32(x60073,x60071,x60072)+P1(f317(x60071,f729(x60072,x60071,x60073)))
% 94.68/94.44 [6008]~P34(x60083,x60081,x60082)+P1(f317(x60081,f735(x60082,x60081,x60083)))
% 94.68/94.44 [6009]~P34(x60093,x60091,x60092)+P1(f317(x60091,f747(x60092,x60091,x60093)))
% 94.68/94.44 [6010]~P32(x60103,x60101,x60102)+P1(f317(x60101,f772(x60102,x60101,x60103)))
% 94.68/94.44 [6011]~P32(x60113,x60111,x60112)+P1(f317(x60111,f774(x60111,x60112,x60113)))
% 94.68/94.44 [6016]P1(f317(f317(x60161,x60162),x60162))+~P1(f317(f317(f319(x60163),x60162),f260(x60163,x60161)))
% 94.68/94.44 [6031]E(f317(f126(x60311,x60312),x60313),f167(x60311,x60312,x60313))+P1(f317(x60312,f700(x60313,x60312,x60311)))
% 94.68/94.44 [6071]~P1(f317(f127(x60711),x60713))+P1(f317(f127(f898(x60711)),f50(x60711,x60712,x60713)))
% 94.68/94.44 [6107]~P108(x61071)+E(f317(f317(f92(f904(x61071,a893)),f317(f291(x61071),x61072)),f296(x61071,x61072,x61073)),f178(f904(x61071,a893)))
% 94.68/94.44 [6108]~P108(x61081)+E(f317(f317(f92(f904(x61081,a893)),f317(f291(x61081),x61082)),f295(x61081,x61082,x61083)),f178(f904(x61081,a893)))
% 94.68/94.44 [6109]~P108(x61091)+E(f317(f317(f92(f904(x61091,a893)),f317(f272(x61091),x61092)),f293(x61091,x61092,x61093)),f178(f904(x61091,a893)))
% 94.68/94.44 [6345]E(f317(f126(x63451,x63452),x63453),x63453)+~P1(f317(x63452,f650(x63453,x63452,x63451)))
% 94.68/94.44 [6347]E(f317(f317(f299(x63471),f589(x63472,x63473,x63471)),f533(x63472,x63473,x63471)),x63473)+~E(f317(f29(x63471),x63473),f317(a102,x63472))
% 94.68/94.44 [6363]P147(x63631,x63632,x63633)+~P1(f317(x63631,f40(a1,x63633,x63632)))
% 94.68/94.44 [6416]P30(x64161,x64162,x64163)+~P1(f317(x64162,f737(x64163,x64162,x64161)))
% 94.68/94.44 [6417]P30(x64171,x64172,x64173)+~P1(f317(x64172,f743(x64172,x64173,x64171)))
% 94.68/94.44 [6418]P30(x64181,x64182,x64183)+~P1(f317(x64182,f744(x64183,x64182,x64181)))
% 94.68/94.44 [6419]P28(x64191,x64192,x64193)+~P1(f317(x64191,f761(x64193,x64192,x64191)))
% 94.68/94.44 [6420]P29(x64201,x64202,x64203)+~P1(f317(x64201,f807(x64203,x64202,x64201)))
% 94.68/94.44 [6422]E(f167(x64221,x64222,x64223),x64223)+~P1(f317(x64222,f695(x64223,x64222,x64221)))
% 94.68/94.44 [6503]~P1(f317(x65032,f512(x65033,x65032,x65031)))+P1(f317(f238(x65031,x65032),x65033))
% 94.68/94.44 [6504]~P1(f317(x65042,f651(x65043,x65042,x65041)))+P1(f317(f150(x65041,x65042),x65043))
% 94.68/94.44 [6760]~P1(f317(f305(x67601,x67602),f882(x67603,x67602,x67601)))+P1(f317(f305(x67601,x67602),x67603))
% 94.68/94.44 [6761]~P1(f317(f305(x67611,x67612),f884(x67613,x67612,x67611)))+P1(f317(f305(x67611,x67612),x67613))
% 94.68/94.44 [7385]~P3(x73851)+E(f317(f317(f74(x73851),f317(f317(f75(x73851),x73852),f317(f317(f30(x73851),x73853),x73852))),f40(x73851,x73853,x73852)),x73853)
% 94.68/94.44 [7415]P28(x74151,x74152,x74153)+P1(f317(f317(f319(a1),f761(x74153,x74152,x74151)),f293(a1,x74152,x74153)))
% 94.68/94.44 [7848]E(f317(f317(f242(x78481,x78481),f435(x78482,x78483,x78481)),f435(x78482,x78483,x78481)),x78483)+~P1(f317(f317(f319(f903(x78481,x78481)),x78483),f253(x78481,x78482)))
% 94.68/94.44 [7966]~P1(f317(f317(f319(x79661),f461(x79663,x79662,x79661)),f306(x79661,x79663)))+P1(f317(f317(f319(x79661),x79662),f306(x79661,x79663)))
% 94.68/94.44 [7967]~P1(f317(f317(f319(x79671),f539(x79673,x79672,x79671)),f306(x79671,x79673)))+P1(f317(f317(f319(x79671),x79672),f306(x79671,x79673)))
% 94.68/94.44 [7968]~P1(f317(f317(f319(x79681),f541(x79683,x79682,x79681)),f306(x79681,x79683)))+P1(f317(f317(f319(x79681),x79682),f306(x79681,x79683)))
% 94.68/94.44 [8061]P32(a1,x80611,f168(x80612,x80613))+P28(f317(f67(a893,a893,a1,a312),x80611),x80612,x80613)
% 94.68/94.44 [8149]~P3(x81491)+E(f317(f317(f74(x81491),f317(f317(f75(x81491),f317(f317(f30(x81491),x81492),x81493)),x81493)),f40(x81491,x81492,x81493)),x81492)
% 94.68/94.44 [8195]~E(f317(f29(x81951),x81952),f317(a102,x81953))+~P1(f317(f317(f319(x81951),f589(x81953,x81952,x81951)),f533(x81953,x81952,x81951)))
% 94.68/94.44 [8635]~P32(a1,x86351,f168(x86352,x86353))+~P28(f317(f67(a893,a893,a1,a312),x86351),x86352,x86353)
% 94.68/94.44 [8822]P1(f317(f317(f224(f904(f903(x88221,x88221),a893)),f297(x88221,x88222)),f297(x88221,x88223)))+~P1(f317(f317(f224(f904(f903(x88221,x88221),a893)),x88222),f297(x88221,x88223)))
% 94.68/94.44 [9102]E(x91021,f103(x91022))+~P1(f317(f317(f319(f903(f898(x91022),f898(x91022))),f317(f317(f242(f898(x91022),f898(x91022)),x91021),f103(x91022))),f148(x91022,x91023)))
% 94.68/94.44 [9127]E(x91271,f103(x91272))+~P1(f317(f317(f319(f903(f898(x91272),f898(x91272))),f317(f317(f242(f898(x91272),f898(x91272)),f103(x91272)),x91271)),f148(x91272,x91273)))
% 94.68/94.44 [9252]E(f317(f317(f141(x92521),f668(x92522,x92523,x92521)),f669(x92522,x92523,x92521)),x92523)+~P1(f317(f317(f319(f903(f898(x92521),f898(x92521))),f317(f317(f242(f898(x92521),f898(x92521)),f103(x92521)),x92523)),f137(x92521,x92522)))
% 94.68/94.44 [9494]~P126(x94941)+~P1(f317(f317(f225(x94941),f317(f317(f74(x94941),f317(f317(f75(x94941),x94942),x94942)),f317(f317(f75(x94941),x94943),x94943))),f2(x94941)))
% 94.68/94.44 [9545]P1(f317(f28(x95451),x95452))+~P1(f317(f317(f319(f903(f904(x95451,a893),f904(x95451,a893))),f317(f317(f242(f904(x95451,a893),f904(x95451,a893)),x95453),x95452)),f304(x95451)))
% 94.68/94.44 [9848]~P46(x98481,x98482,x98483)+P1(f317(f317(f224(a1),f317(f317(f67(f903(a1,a1),a1,x98481,f241(a1,a1)),f202(x98481)),f220(x98481,x98482,f217(x98481,x98483)))),f2(a1)))
% 94.68/94.44 [9849]~P47(x98491,x98492,x98493)+P1(f317(f317(f225(a1),f317(f317(f67(f903(a1,a1),a1,x98491,f241(a1,a1)),f202(x98491)),f220(x98491,x98492,f217(x98491,x98493)))),f2(a1)))
% 94.68/94.44 [9967]P47(x99671,x99672,x99673)+~P1(f317(f317(f225(a1),f317(f317(f67(f903(a1,a1),a1,x99671,f241(a1,a1)),f202(x99671)),f220(x99671,x99672,f217(x99671,x99673)))),f2(a1)))
% 94.68/94.44 [9968]P46(x99681,x99682,x99683)+~P1(f317(f317(f224(a1),f317(f317(f67(f903(a1,a1),a1,x99681,f241(a1,a1)),f202(x99681)),f220(x99681,x99682,f217(x99681,x99683)))),f2(a1)))
% 94.68/94.44 [10320]~P111(x103201)+~P1(f317(f317(f225(x103201),f317(f317(f74(x103201),f317(f317(f234(x103201),x103202),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103201),x103203),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103201)))
% 94.68/94.44 [4798]~E(x47983,f103(x47981))+E(f317(f317(f124(x47981),x47982),x47983),x47982)
% 94.68/94.44 [4799]~E(x47992,f103(x47991))+E(f317(f317(f124(x47991),x47992),x47993),x47993)
% 94.68/94.44 [4805]~E(x48052,f2(a897))+E(f317(f317(f165(x48051),x48052),x48053),f103(x48051))
% 94.68/94.44 [4814]~E(x48143,f103(x48141))+E(f317(f317(f165(x48141),x48142),x48143),f103(x48141))
% 94.68/94.44 [4853]~E(x48531,x48533)+E(x48531,f317(f317(f124(x48532),f103(x48532)),x48533))
% 94.68/94.44 [4944]~P83(x49442)+E(f317(f178(f904(x49441,x49442)),x49443),f178(x49442))
% 94.68/94.44 [4945]~P116(x49452)+E(f317(f232(f904(x49451,x49452)),x49453),f232(x49452))
% 94.68/94.44 [4963]E(x49631,f103(x49632))+~E(f317(f317(f124(x49632),x49633),x49631),x49633)
% 94.68/94.44 [4964]E(x49641,f103(x49642))+~E(f317(f317(f124(x49642),x49641),x49643),x49643)
% 94.68/94.44 [4972]E(x49721,f103(x49722))+~E(f317(f317(f124(x49722),x49723),x49721),f103(x49722))
% 94.68/94.44 [4973]E(x49731,f103(x49732))+~E(f317(f317(f124(x49732),x49731),x49733),f103(x49732))
% 94.68/94.44 [5002]~E(x50022,f2(a897))+E(f317(f317(f75(a897),x50021),x50022),f317(f317(f75(a897),x50023),x50022))
% 94.68/94.44 [5004]~E(x50041,f2(a897))+E(f317(f317(f75(a897),x50041),x50042),f317(f317(f75(a897),x50041),x50043))
% 94.68/94.44 [5062]~P112(x50621)+E(f317(f317(f74(x50621),x50622),x50623),f317(f317(f74(x50621),x50623),x50622))
% 94.68/94.44 [5063]~P112(x50631)+E(f317(f317(f75(x50631),x50632),x50633),f317(f317(f75(x50631),x50633),x50632))
% 94.68/94.44 [5065]~P66(x50651)+E(f317(f317(f228(x50651),x50652),x50653),f317(f317(f228(x50651),x50653),x50652))
% 94.68/94.44 [5067]~P66(x50671)+E(f317(f317(f223(x50671),x50672),x50673),f317(f317(f223(x50671),x50673),x50672))
% 94.68/94.44 [5069]~P99(x50691)+E(f317(f317(f91(x50691),x50692),x50693),f317(f317(f91(x50691),x50693),x50692))
% 94.68/94.44 [5070]~P100(x50701)+E(f317(f317(f91(x50701),x50702),x50703),f317(f317(f91(x50701),x50703),x50702))
% 94.68/94.44 [5071]~P100(x50711)+E(f317(f317(f92(x50711),x50712),x50713),f317(f317(f92(x50711),x50713),x50712))
% 94.68/94.44 [5073]~P105(x50731)+E(f317(f317(f92(x50731),x50732),x50733),f317(f317(f92(x50731),x50733),x50732))
% 94.68/94.44 [5136]E(f40(a897,x51361,x51362),f2(a897))+~E(x51361,f317(f317(f75(a897),x51362),x51363))
% 94.68/94.44 [5137]E(f40(a1,x51371,x51372),f2(a1))+~E(x51371,f317(f317(f75(a1),x51372),x51373))
% 94.68/94.44 [5201]E(x52011,x52012)+~E(f317(f317(f74(a897),x52013),x52011),f317(f317(f74(a897),x52013),x52012))
% 94.68/94.44 [5202]E(x52021,x52022)+~E(f317(f317(f74(a897),x52021),x52023),f317(f317(f74(a897),x52022),x52023))
% 94.68/94.44 [5212]~P69(x52121)+E(f317(f317(f74(x52121),x52122),f317(f73(x52121),x52123)),f317(f317(f23(x52121),x52122),x52123))
% 94.68/94.44 [5213]~P75(x52131)+E(f317(f317(f74(x52131),x52132),f317(f73(x52131),x52133)),f317(f317(f23(x52131),x52132),x52133))
% 94.68/94.44 [5214]~P114(x52141)+E(f317(f317(f74(x52141),x52142),f317(f73(x52141),x52143)),f317(f317(f23(x52141),x52142),x52143))
% 94.68/94.44 [5215]~P97(x52151)+E(f317(f317(f92(x52151),x52152),f317(f73(x52151),x52153)),f317(f317(f23(x52151),x52152),x52153))
% 94.68/94.44 [5216]~P75(x52161)+E(f317(f317(f23(x52161),x52162),f317(f73(x52161),x52163)),f317(f317(f74(x52161),x52162),x52163))
% 94.68/94.44 [5254]~P1(f317(x52543,x52542))+P1(f317(f317(f319(x52541),x52542),x52543))
% 94.68/94.44 [5256]~P77(x52562)+E(f317(f317(f9(x52561,x52562),x52563),f178(f904(x52561,a893))),f72(x52562))
% 94.68/94.44 [5258]~P76(x52582)+E(f317(f317(f6(x52581,x52582),x52583),f178(f904(x52581,a893))),f2(x52582))
% 94.68/94.44 [5310]~E(x53102,f317(f317(f74(a897),x53101),x53103))+P1(f317(f317(f224(a897),x53101),x53102))
% 94.68/94.44 [5313]~E(x53132,f178(f904(x53131,a893)))+E(f317(f317(f55(x53131),x53132),x53133),f178(f904(f904(x53131,a893),a893)))
% 94.68/94.44 [5314]~E(x53142,f178(f904(x53141,a893)))+E(f178(f904(f904(x53141,a893),a893)),f317(f317(f55(x53141),x53142),x53143))
% 94.68/94.44 [5383]~E(f317(f274(x53832,x53833),x53831),f178(f904(x53833,a893)))+E(x53831,f178(f904(f903(x53832,x53833),a893)))
% 94.68/94.44 [5384]~E(f317(f254(x53842,x53843),x53841),f178(f904(x53842,a893)))+E(x53841,f178(f904(f903(x53842,x53843),a893)))
% 94.68/94.44 [5416]E(f317(f274(x54161,x54162),x54163),f178(f904(x54162,a893)))+~E(x54163,f178(f904(f903(x54161,x54162),a893)))
% 94.68/94.44 [5417]E(f317(f254(x54171,x54172),x54173),f178(f904(x54171,a893)))+~E(x54173,f178(f904(f903(x54171,x54172),a893)))
% 94.68/94.44 [5420]E(f264(x54201,x54202,x54203),f317(f317(f23(a89),x54202),x54203))+P1(f317(f317(f225(a89),x54202),x54203))
% 94.68/94.44 [5436]P1(f317(x54361,x54362))+~P1(f317(f317(f319(x54363),x54362),x54361))
% 94.68/94.44 [5475]E(x54751,x54752)+~E(f317(f73(f904(x54753,a893)),x54751),f317(f73(f904(x54753,a893)),x54752))
% 94.68/94.44 [5486]~E(x54861,f178(f904(x54862,a893)))+~P1(f317(f317(f319(x54862),x54863),x54861))
% 94.68/94.44 [5517]~E(x55172,f317(f317(f74(a1),x55171),f317(f90(a1),x55173)))+P1(f317(f317(f224(a1),x55171),x55172))
% 94.68/94.44 [5531]E(f317(f317(f299(x55311),x55312),x55313),x55313)+~P1(f317(f317(f319(x55311),x55312),x55313))
% 94.68/94.44 [5542]E(x55421,f178(f904(x55422,a893)))+~E(f317(f317(f55(x55422),x55421),x55423),f178(f904(f904(x55422,a893),a893)))
% 94.68/94.44 [5543]E(x55431,f178(f904(x55432,a893)))+~E(f178(f904(f904(x55432,a893),a893)),f317(f317(f55(x55432),x55431),x55433))
% 94.68/94.44 [5549]~P131(x55491)+E(f317(f317(f75(x55491),f317(f73(x55491),x55492)),f317(f73(x55491),x55493)),f317(f317(f75(x55491),x55492),x55493))
% 94.68/94.44 [5551]~P61(x55511)+E(f317(f317(f281(x55511),f317(f73(x55511),x55512)),f317(f73(x55511),x55513)),f317(f317(f281(x55511),x55512),x55513))
% 94.68/94.44 [5582]~P1(f317(x55823,x55822))+P1(f317(f317(f319(x55821),x55822),f317(f252(x55821),x55823)))
% 94.68/94.44 [5609]E(x56091,f2(a897))+E(f317(f162(x56092),f159(x56092,x56091,x56093)),f317(f317(f299(x56092),x56093),f178(f904(x56092,a893))))
% 94.68/94.44 [5628]E(f160(x56281,x56282,x56283),x56283)+P1(f317(f317(f319(x56281),x56282),f317(f162(x56281),x56283)))
% 94.68/94.44 [5713]~P1(f317(f127(x57131),x57133))+P1(f317(f127(x57131),f317(f126(x57131,x57132),x57133)))
% 94.68/94.44 [5756]~P3(x57561)+E(f317(f317(f30(x57561),f40(x57561,x57562,x57563)),x57563),f2(x57561))
% 94.68/94.44 [5775]E(f166(x57751,f317(f317(f141(x57751),x57752),f103(x57751)),x57753),f103(x57751))+P1(f317(f317(f319(a897),f2(a897)),x57753))
% 94.68/94.44 [5781]E(x57811,f2(a897))+E(f317(f161(x57812),f159(x57812,x57811,x57813)),f159(x57812,f317(f317(f23(a897),x57811),f72(a897)),x57813))
% 94.68/94.44 [5832]E(f317(f317(f141(x58321),x58322),x58323),f130(x58321,x58322,x58323))+P1(f317(f317(f319(x58321),x58322),f317(f162(x58321),x58323)))
% 94.68/94.44 [5841]E(x58411,x58412)+~E(f317(f317(f75(a897),f317(a102,x58413)),x58411),f317(f317(f75(a897),f317(a102,x58413)),x58412))
% 94.68/94.44 [5842]~E(x58422,f317(f317(f74(a1),x58421),f317(f90(a1),f317(a102,x58423))))+P1(f317(f317(f225(a1),x58421),x58422))
% 94.68/94.44 [5912]~P29(x59121,x59122,x59123)+P30(a897,x59121,f129(a897,f317(f292(a897,x59122),x59123)))
% 94.68/94.44 [5965]~E(x59653,f103(x59651))+E(f317(f317(f317(f173(f898(x59651),f898(x59651)),x59652),f157(x59651)),x59653),f103(x59651))
% 94.68/94.44 [5969]P1(f317(x59691,x59692))+~P1(f317(f317(f319(x59693),x59692),f317(f252(x59693),x59691)))
% 94.68/94.44 [6002]E(x60021,x60022)+~E(f317(f317(f299(x60023),x60021),f178(f904(x60023,a893))),f317(f317(f299(x60023),x60022),f178(f904(x60023,a893))))
% 94.68/94.44 [6018]~P108(x60181)+E(f317(f317(f92(f904(x60181,a893)),f317(f272(x60181),x60182)),f317(f292(x60181,x60182),x60183)),f178(f904(x60181,a893)))
% 94.68/94.44 [6057]E(f130(x60571,x60572,x60573),x60573)+~P1(f317(f317(f319(x60571),x60572),f317(f162(x60571),x60573)))
% 94.68/94.44 [6079]~P67(x60791)+E(f317(f300(x60791,x60791,f73(x60791)),f317(f292(x60791,x60792),x60793)),f295(x60791,f317(f73(x60791),x60793),f317(f73(x60791),x60792)))
% 94.68/94.44 [6090]E(f317(f179(f898(x60901)),f160(x60901,x60902,x60903)),f317(f179(f898(x60901)),x60903))+P1(f317(f317(f319(x60901),x60902),f317(f162(x60901),x60903)))
% 94.68/94.44 [6145]~P108(x61451)+E(f317(f317(f92(f904(x61451,a893)),f317(f292(x61451,x61452),x61453)),f317(f273(x61451),x61453)),f178(f904(x61451,a893)))
% 94.68/94.44 [6165]~P67(x61651)+E(f317(f300(x61651,x61651,f73(x61651)),f296(x61651,x61652,x61653)),f296(x61651,f317(f73(x61651),x61653),f317(f73(x61651),x61652)))
% 94.68/94.44 [6166]~P67(x61661)+E(f317(f300(x61661,x61661,f73(x61661)),f293(x61661,x61662,x61663)),f293(x61661,f317(f73(x61661),x61663),f317(f73(x61661),x61662)))
% 94.68/94.44 [6232]E(f166(x62321,f317(f317(f141(x62321),x62322),f103(x62321)),x62323),f317(f317(f141(x62321),x62322),f103(x62321)))+~P1(f317(f317(f319(a897),f2(a897)),x62323))
% 94.68/94.44 [6237]P29(x62371,x62372,x62373)+~P30(a897,x62371,f129(a897,f317(f292(a897,x62372),x62373)))
% 94.68/94.44 [6240]~P67(x62401)+E(f317(f300(x62401,x62401,f73(x62401)),f295(x62401,x62402,x62403)),f317(f292(x62401,f317(f73(x62401),x62403)),f317(f73(x62401),x62402)))
% 94.68/94.44 [6262]~P4(x62621)+E(f40(x62621,f317(f73(x62621),f40(x62621,x62622,x62623)),x62623),f40(x62621,f317(f73(x62621),x62622),x62623))
% 94.68/94.44 [6361]~P1(f317(f28(f903(x63612,x63611)),x63613))+P1(f317(f28(x63611),f317(f274(x63612,x63611),x63613)))
% 94.68/94.44 [6362]~P1(f317(f28(f903(x63621,x63622)),x63623))+P1(f317(f28(x63621),f317(f254(x63621,x63622),x63623)))
% 94.68/94.44 [6367]~P108(x63671)+E(f317(f317(f92(f904(x63671,a893)),f296(x63671,x63672,x63673)),f317(f273(x63671),x63673)),f178(f904(x63671,a893)))
% 94.68/94.44 [6368]~P108(x63681)+E(f317(f317(f92(f904(x63681,a893)),f295(x63681,x63682,x63683)),f317(f294(x63681),x63683)),f178(f904(x63681,a893)))
% 94.68/94.44 [6369]~P108(x63691)+E(f317(f317(f92(f904(x63691,a893)),f293(x63691,x63692,x63693)),f317(f294(x63691),x63693)),f178(f904(x63691,a893)))
% 94.68/94.44 [6442]E(f317(f317(f154(x64421),x64422),f613(x64422,x64423,x64421)),x64423)+~P1(f317(f317(f319(x64421),x64423),f317(f162(x64421),x64422)))
% 94.68/94.44 [6590]E(x65901,f103(x65902))+~E(f317(f317(f317(f173(f898(x65902),f898(x65902)),x65903),f157(x65902)),x65901),f103(x65902))
% 94.68/94.44 [6696]~P1(f317(f28(f903(x66962,x66961)),x66963))+P1(f317(f28(f903(x66961,x66962)),f317(f276(x66962,x66961),x66963)))
% 94.68/94.44 [6719]E(x67191,x67192)+~E(f280(a897,f277(a897),x67193,x67191),f317(f317(f299(a897),x67192),f178(f904(a897,a893))))
% 94.68/94.44 [6720]E(x67201,x67202)+~E(f280(a897,f277(a897),x67201,x67202),f317(f317(f299(a897),x67203),f178(f904(a897,a893))))
% 94.68/94.44 [6855]P55(x68551,x68552,x68553)+P1(f317(f317(f319(x68551),f536(x68553,x68552,x68551)),x68552))
% 94.68/94.44 [6856]P55(x68561,x68562,x68563)+P1(f317(f317(f319(x68561),f535(x68563,x68562,x68561)),x68562))
% 94.68/94.44 [6866]P1(f317(f305(x68661,x68662),x68663))+P1(f317(f317(x68662,f882(x68663,x68662,x68661)),x68663))
% 94.68/94.44 [6867]P1(f317(f305(x68671,x68672),x68673))+P1(f317(f317(x68672,f884(x68673,x68672,x68671)),x68673))
% 94.68/94.44 [6898]E(f317(f179(f898(x68981)),f160(x68981,x68982,x68983)),f317(f317(f23(a897),f317(f179(f898(x68981)),x68983)),f72(a897)))+~P1(f317(f317(f319(x68981),x68982),f317(f162(x68981),x68983)))
% 94.68/94.44 [6937]P1(f317(f238(x69371,x69372),x69373))+P1(f317(f317(f319(x69371),f512(x69373,x69372,x69371)),x69373))
% 94.68/94.44 [6946]~P1(f317(f28(f903(x69462,x69461)),f317(f276(x69461,x69462),x69463)))+P1(f317(f28(f903(x69461,x69462)),x69463))
% 94.68/94.44 [7006]~P1(f317(f317(f319(x70061),x70062),f317(f162(x70061),f104(x70061,x70063))))+P1(f317(f317(f319(x70061),x70062),f317(f162(x70061),x70063)))
% 94.68/94.44 [7042]E(f317(f126(x70421,x70422),x70423),x70423)+P1(f317(f317(f319(x70421),f650(x70423,x70422,x70421)),f317(f162(x70421),x70423)))
% 94.68/94.44 [7058]E(f317(f126(x70581,x70582),x70583),f103(x70581))+P1(f317(f317(f319(x70581),f649(x70583,x70582,x70581)),f317(f162(x70581),x70583)))
% 94.68/94.44 [7083]P30(x70831,x70832,x70833)+P1(f317(f317(f319(x70831),f737(x70833,x70832,x70831)),f317(f162(x70831),x70833)))
% 94.68/94.44 [7084]P30(x70841,x70842,x70843)+P1(f317(f317(f319(x70841),f744(x70843,x70842,x70841)),f317(f162(x70841),x70843)))
% 94.68/94.44 [7085]P30(x70851,x70852,x70853)+P1(f317(f317(f319(x70851),f743(x70852,x70853,x70851)),f317(f162(x70851),x70853)))
% 94.68/94.44 [7088]E(f167(x70881,x70882,x70883),x70883)+P1(f317(f317(f319(x70881),f695(x70883,x70882,x70881)),f317(f162(x70881),x70883)))
% 94.68/94.44 [7164]P1(f317(f150(x71641,x71642),x71643))+P1(f317(f317(f319(x71641),f651(x71643,x71642,x71641)),f317(f162(x71641),x71643)))
% 94.68/94.44 [7173]~P32(x71731,x71733,x71732)+P1(f317(f317(f319(x71731),f729(x71732,x71733,x71731)),f317(f162(x71731),x71732)))
% 94.68/94.44 [7174]~P34(x71741,x71743,x71742)+P1(f317(f317(f319(x71741),f735(x71742,x71743,x71741)),f317(f162(x71741),x71742)))
% 94.68/94.44 [7175]~P34(x71751,x71753,x71752)+P1(f317(f317(f319(x71751),f747(x71752,x71753,x71751)),f317(f162(x71751),x71752)))
% 94.68/94.44 [7176]~P32(x71761,x71763,x71762)+P1(f317(f317(f319(x71761),f772(x71762,x71763,x71761)),f317(f162(x71761),x71762)))
% 94.68/94.44 [7177]~P32(x71771,x71772,x71773)+P1(f317(f317(f319(x71771),f774(x71772,x71773,x71771)),f317(f162(x71771),x71773)))
% 94.68/94.44 [7211]P1(f317(f317(f319(x72111),x72112),f615(x72113,x72112,x72111)))+~P1(f317(f317(f319(x72111),x72112),f31(f904(x72111,a893),x72113)))
% 94.68/94.44 [7212]~P76(x72121)+E(f317(f317(f74(x72121),f317(f317(f6(a897,x72121),x72122),f317(f272(a897),x72123))),f317(x72122,x72123)),f317(f317(f6(a897,x72121),x72122),f317(f272(a897),f317(a102,x72123))))
% 94.68/94.44 [7224]P29(x72241,x72242,x72243)+P1(f317(f317(f319(a897),f807(x72243,x72242,x72241)),f317(f292(a897,x72242),x72243)))
% 94.68/94.44 [7304]~P32(x73042,x73041,x73043)+P1(f317(x73041,f317(f317(f154(x73042),x73043),f732(x73043,x73041,x73042))))
% 94.68/94.44 [7315]~P1(f317(f317(f319(x73151),x73152),f601(x73152,x73153,x73151)))+P1(f317(f317(f319(x73151),x73152),f32(f904(x73151,a893),x73153)))
% 94.68/94.44 [7348]~P76(x73481)+E(f317(f317(f74(x73481),f317(f317(f6(a897,x73481),x73482),f317(f291(a897),x73483))),f317(x73482,f317(a102,x73483))),f317(f317(f6(a897,x73481),x73482),f317(f291(a897),f317(a102,x73483))))
% 94.68/94.44 [7489]P1(f317(f317(f319(f898(x74891)),x74892),f151(x74891,x74893)))+P1(f317(f317(f319(x74891),f637(x74893,x74892,x74891)),f317(f162(x74891),x74892)))
% 94.68/94.44 [7505]~P1(f317(f317(f319(f898(x75051)),x75052),f151(x75051,f306(x75051,x75053))))+P1(f317(f317(f319(f898(x75051)),x75052),f306(f898(x75051),f147(x75051,x75053))))
% 94.68/94.44 [7529]~P1(f317(f317(f319(f898(x75291)),x75292),f306(f898(x75291),f147(x75291,x75293))))+P1(f317(f317(f319(f898(x75291)),x75292),f151(x75291,f306(x75291,x75293))))
% 94.68/94.44 [7561]E(f317(f317(f317(f173(f898(x75611),f898(x75611)),x75612),f157(x75611)),x75613),x75613)+~P1(f317(f317(f224(a897),f317(f179(f898(x75611)),x75613)),f72(a897)))
% 94.68/94.44 [7594]E(f317(f317(f124(x75941),f733(x75942,x75943,x75941)),f317(f317(f141(x75941),x75943),f734(x75942,x75943,x75941))),x75942)+~P1(f317(f317(f319(x75941),x75943),f317(f162(x75941),x75942)))
% 94.68/94.44 [7595]E(f317(f317(f124(x75951),f739(x75952,x75953,x75951)),f317(f317(f141(x75951),x75953),f740(x75952,x75953,x75951))),x75952)+~P1(f317(f317(f319(x75951),x75953),f317(f162(x75951),x75952)))
% 94.68/94.44 [7596]E(f317(f317(f124(x75961),f741(x75962,x75963,x75961)),f317(f317(f141(x75961),x75963),f742(x75962,x75963,x75961))),x75962)+~P1(f317(f317(f319(x75961),x75963),f317(f162(x75961),x75962)))
% 94.68/94.44 [7617]~P24(x76171,x76172,x76173,f232(f904(x76171,a893)))+P24(f898(x76171),f898(x76172),f317(f144(x76171,x76172),x76173),f232(f904(f898(x76171),a893)))
% 94.68/94.44 [7770]E(x77701,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x77702)),x77703)),f317(f246(a897,a897),x77702)))+~P1(f317(f43(x77701,x77703),x77702))
% 94.68/94.44 [7778]P24(x77781,x77782,x77783,f232(f904(x77781,a893)))+~P24(f898(x77781),f898(x77782),f317(f144(x77781,x77782),x77783),f232(f904(f898(x77781),a893)))
% 94.68/94.44 [7823]P1(f317(f317(f319(f904(x78231,a893)),f601(x78232,x78233,x78231)),x78233))+P1(f317(f317(f319(x78231),x78232),f32(f904(x78231,a893),x78233)))
% 94.68/94.44 [7914]P1(f317(f317(f319(f898(x79141)),x79142),f151(x79141,x79143)))+~P1(f317(f317(f319(x79141),f637(x79143,x79142,x79141)),x79143))
% 94.68/94.44 [8015]P30(x80151,x80152,x80153)+~P1(f317(x80152,f317(f317(f154(x80151),x80153),f738(x80153,x80152,x80151))))
% 94.68/94.44 [8040]E(x80401,x80402)+~E(f317(f317(f7(x80403,f904(x80403,a893),a893),f319(x80403)),x80401),f317(f317(f7(x80403,f904(x80403,a893),a893),f319(x80403)),x80402))
% 94.68/94.44 [8048]~P1(f317(f317(f319(f903(x80481,x80481)),x80483),f253(x80481,x80482)))+P1(f317(f317(f319(x80481),f435(x80482,x80483,x80481)),x80482))
% 94.68/94.44 [8050]~P1(f317(f317(f319(x80501),x80503),f31(f904(x80501,a893),x80502)))+P1(f317(f317(f319(f904(x80501,a893)),f615(x80502,x80503,x80501)),x80502))
% 94.68/94.44 [8169]P24(x81691,x81692,f85(x81692,x81691,f232(f904(x81692,a893)),x81693),f232(f904(x81691,a893)))+~E(f317(f300(x81692,x81691,x81693),f232(f904(x81692,a893))),f232(f904(x81691,a893)))
% 94.68/94.44 [8223]~P1(f317(f317(f319(x82231),x82232),f317(f162(x82231),f739(x82233,x82232,x82231))))+~P1(f317(f317(f319(x82231),x82232),f317(f162(x82231),x82233)))
% 94.68/94.44 [8224]~P1(f317(f317(f319(x82241),x82242),f317(f162(x82241),f742(x82243,x82242,x82241))))+~P1(f317(f317(f319(x82241),x82242),f317(f162(x82241),x82243)))
% 94.68/94.44 [8253]P29(f317(f67(a893,a893,a897,a312),x82531),x82532,x82533)+P32(a897,x82531,f129(a897,f317(f292(a897,x82532),x82533)))
% 94.68/94.44 [8414]E(x84141,f103(x84142))+P1(f317(f317(f319(x84142),f317(f241(x84142,f903(a89,a89)),f317(f265(x84142,x84141),x84143))),f317(f162(x84142),x84141)))
% 94.68/94.44 [8513]~P72(x85131)+E(f317(f132(x85131,x85131,f317(f7(x85131,x85131,x85131),f74(x85131)),x85132),f317(f158(x85131),x85133)),f317(f132(x85131,x85131,f74(x85131),x85132),x85133))
% 94.68/94.44 [8705]~P24(x87052,x87051,x87053,f232(f904(x87052,a893)))+E(f317(f300(x87051,x87052,f85(x87052,x87051,f232(f904(x87052,a893)),x87053)),f232(f904(x87051,a893))),f232(f904(x87052,a893)))
% 94.68/94.44 [8775]~P29(f317(f67(a893,a893,a897,a312),x87751),x87752,x87753)+~P32(a897,x87751,f129(a897,f317(f292(a897,x87752),x87753)))
% 94.68/94.44 [9022]~P66(x90221)+E(f317(f162(x90221),f139(x90221,x90221,f5(x90221),x90222,x90223)),f317(f317(f299(x90221),x90222),f317(f162(x90221),x90223)))
% 94.68/94.44 [9031]~E(f317(x90313,f317(f85(x90311,x90312,f232(f904(x90311,a893)),x90313),f788(x90313,x90312,x90311))),f788(x90313,x90312,x90311))+E(f317(f300(x90311,x90312,x90313),f232(f904(x90311,a893))),f232(f904(x90312,a893)))
% 94.68/94.44 [9033]P1(f317(f317(f225(a897),f2(a897)),f561(x90331,x90332,x90333)))+~P1(f317(f317(f319(f903(x90333,x90333)),x90332),f317(f317(f279(x90333,x90333,x90333),x90331),f297(x90333,x90331))))
% 94.68/94.44 [9310]~P57(x93101,x93102)+~P1(f317(f317(f319(f903(x93101,x93101)),f317(f317(f242(x93101,x93101),x93103),x93103)),f317(f317(f279(x93101,x93101,x93101),x93102),f297(x93101,x93102))))
% 94.68/94.44 [9449]~E(f317(f317(f92(f904(f903(x94491,x94491),a893)),f317(f276(x94491,x94491),x94492)),f297(x94491,x94492)),f178(f904(f903(x94491,x94491),a893)))+~P1(f317(f317(f319(f903(x94491,x94491)),f317(f317(f242(x94491,x94491),x94493),x94493)),f317(f317(f279(x94491,x94491,x94491),x94492),f297(x94491,x94492))))
% 94.68/94.44 [9640]~P1(f317(f28(x96401),x96402))+P1(f317(f317(f224(a897),f317(f29(x96401),f317(f317(f23(f904(x96401,a893)),x96402),f317(f317(f299(x96401),x96403),f178(f904(x96401,a893)))))),f317(f29(x96401),x96402)))
% 94.68/94.44 [5124]~E(x51243,f103(x51241))+E(f134(x51241,f317(f317(f141(x51241),x51242),x51243)),x51242)
% 94.68/94.44 [5133]~E(x51333,f103(x51331))+E(f104(x51331,f317(f317(f141(x51331),x51332),x51333)),f103(x51331))
% 94.68/94.44 [5163]E(x51631,f103(x51632))+E(f134(x51632,f317(f317(f141(x51632),x51633),x51631)),f134(x51632,x51631))
% 94.68/94.44 [5165]E(x51651,f103(x51652))+E(f134(x51652,f317(f317(f124(x51652),x51653),x51651)),f134(x51652,x51651))
% 94.68/94.44 [5171]~E(x51713,f103(x51711))+E(f104(x51711,f317(f317(f124(x51711),x51712),x51713)),f104(x51711,x51712))
% 94.68/94.44 [5173]~E(x51733,f103(x51731))+E(f134(x51731,f317(f317(f124(x51731),x51732),x51733)),f134(x51731,x51732))
% 94.68/94.44 [5206]E(x52061,f103(x52062))+E(f317(f131(x52062),f317(f317(f124(x52062),x52061),x52063)),f317(f131(x52062),x52061))
% 94.68/94.44 [5234]~E(x52342,f103(x52341))+E(f317(f131(x52341),f317(f317(f124(x52341),x52342),x52343)),f317(f131(x52341),x52343))
% 94.68/94.44 [5286]~P66(x52861)+E(f317(f317(f228(x52861),x52862),f317(f317(f223(x52861),x52862),x52863)),x52862)
% 94.68/94.44 [5287]~P66(x52871)+E(f317(f317(f223(x52871),x52872),f317(f317(f228(x52871),x52872),x52873)),x52872)
% 94.68/94.44 [5288]~P100(x52881)+E(f317(f317(f91(x52881),x52882),f317(f317(f92(x52881),x52882),x52883)),x52882)
% 94.68/94.44 [5289]~P100(x52891)+E(f317(f317(f92(x52891),x52892),f317(f317(f91(x52891),x52892),x52893)),x52892)
% 94.68/94.44 [5308]~P3(x53081)+E(f40(x53081,f317(f317(f75(x53081),x53082),x53083),x53083),f2(x53081))
% 94.68/94.44 [5309]~P3(x53091)+E(f40(x53091,f317(f317(f75(x53091),x53092),x53093),x53092),f2(x53091))
% 94.68/94.44 [5377]~P69(x53771)+E(f317(f73(x53771),f317(f317(f23(x53771),x53772),x53773)),f317(f317(f23(x53771),x53773),x53772))
% 94.68/94.44 [5440]E(x54401,f103(x54402))+E(f104(x54402,f317(f317(f141(x54402),x54403),x54401)),f317(f317(f141(x54402),x54403),f104(x54402,x54401)))
% 94.68/94.44 [5441]E(x54411,f103(x54412))+E(f104(x54412,f317(f317(f124(x54412),x54413),x54411)),f317(f317(f124(x54412),x54413),f104(x54412,x54411)))
% 94.68/94.44 [5444]~P5(x54441)+E(f32(x54441,f317(f317(f299(x54441),x54442),x54443)),f317(f317(f92(x54441),x54442),f32(x54441,x54443)))
% 94.68/94.44 [5445]~P5(x54451)+E(f31(x54451,f317(f317(f299(x54451),x54452),x54453)),f317(f317(f91(x54451),x54452),f31(x54451,x54453)))
% 94.68/94.44 [5491]~P98(x54911)+E(f317(f317(f75(x54911),x54912),f317(f317(f75(x54911),x54912),x54913)),f317(f317(f75(x54911),x54912),x54913))
% 94.68/94.44 [5493]~P66(x54931)+E(f317(f317(f228(x54931),x54932),f317(f317(f228(x54931),x54932),x54933)),f317(f317(f228(x54931),x54932),x54933))
% 94.68/94.44 [5495]~P66(x54951)+E(f317(f317(f223(x54951),x54952),f317(f317(f223(x54951),x54952),x54953)),f317(f317(f223(x54951),x54952),x54953))
% 94.68/94.44 [5497]~P99(x54971)+E(f317(f317(f91(x54971),x54972),f317(f317(f91(x54971),x54972),x54973)),f317(f317(f91(x54971),x54972),x54973))
% 94.68/94.44 [5498]~P100(x54981)+E(f317(f317(f91(x54981),x54982),f317(f317(f91(x54981),x54982),x54983)),f317(f317(f91(x54981),x54982),x54983))
% 94.68/94.44 [5499]~P100(x54991)+E(f317(f317(f92(x54991),x54992),f317(f317(f92(x54991),x54992),x54993)),f317(f317(f92(x54991),x54992),x54993))
% 94.68/94.44 [5501]~P105(x55011)+E(f317(f317(f92(x55011),x55012),f317(f317(f92(x55011),x55012),x55013)),f317(f317(f92(x55011),x55012),x55013))
% 94.68/94.44 [5508]~P3(x55081)+E(f40(x55081,f317(f317(f74(x55081),x55082),x55083),x55083),f40(x55081,x55082,x55083))
% 94.68/94.44 [5509]~P3(x55091)+E(f40(x55091,f317(f317(f74(x55091),x55092),x55093),x55092),f40(x55091,x55093,x55092))
% 94.68/94.44 [5518]~P131(x55181)+E(f317(f317(f75(x55181),x55182),f317(f73(x55181),x55183)),f317(f73(x55181),f317(f317(f75(x55181),x55182),x55183)))
% 94.68/94.44 [5519]~P61(x55191)+E(f317(f317(f281(x55191),x55192),f317(f73(x55191),x55193)),f317(f73(x55191),f317(f317(f281(x55191),x55192),x55193)))
% 94.68/94.44 [5520]~P81(x55201)+E(f317(f317(f74(x55201),x55202),f317(f155(x55201),x55203)),f317(f155(x55201),f317(f317(f141(x55201),x55202),x55203)))
% 94.68/94.44 [5548]~P131(x55481)+E(f317(f317(f75(x55481),f317(f73(x55481),x55482)),x55483),f317(f317(f75(x55481),x55482),f317(f73(x55481),x55483)))
% 94.68/94.44 [5554]~P8(x55541,x55542,x55543)+E(f31(f904(x55541,a893),f317(f317(f55(x55541),x55542),x55543)),x55542)
% 94.68/94.44 [5620]~P115(x56201)+E(f317(f317(f75(x56201),x56202),f317(f317(f234(x56201),x56202),x56203)),f317(f317(f234(x56201),x56202),f317(a102,x56203)))
% 94.68/94.44 [5621]~P112(x56211)+E(f317(f317(f75(x56211),x56212),f317(f317(f234(x56211),x56212),x56213)),f317(f317(f234(x56211),x56212),f317(a102,x56213)))
% 94.68/94.44 [5631]~P75(x56311)+E(f317(f317(f74(x56311),f317(f73(x56311),x56312)),f317(f317(f74(x56311),x56312),x56313)),x56313)
% 94.68/94.44 [5654]~P144(x56541)+E(f317(f317(f234(x56541),f317(f90(x56541),x56542)),x56543),f317(f90(x56541),f317(f317(f234(a897),x56542),x56543)))
% 94.68/94.44 [5655]~P141(x56551)+E(f317(f317(f234(x56551),f317(f93(x56551),x56552)),x56553),f317(f93(x56551),f317(f317(f234(a1),x56552),x56553)))
% 94.68/94.44 [5661]~P86(x56611)+E(f317(f70(x56611),f317(f317(f23(x56611),x56612),x56613)),f317(f70(x56611),f317(f317(f23(x56611),x56613),x56612)))
% 94.68/94.44 [5663]~P111(x56631)+E(f317(f317(f75(x56631),f76(x56631,x56632)),f76(x56631,x56633)),f76(x56631,f317(f317(f75(x56631),x56632),x56633)))
% 94.68/94.44 [5667]E(x56671,f103(x56672))+E(f317(f317(f124(x56672),f317(f161(x56672),x56671)),x56673),f317(f161(x56672),f317(f317(f124(x56672),x56671),x56673)))
% 94.68/94.44 [5673]~E(x56732,f317(a102,f317(f317(f74(a897),x56731),x56733)))+P1(f317(f317(f225(a897),x56731),x56732))
% 94.68/94.44 [5674]~P131(x56741)+E(f317(f317(f75(x56741),f317(f73(x56741),x56742)),x56743),f317(f73(x56741),f317(f317(f75(x56741),x56742),x56743)))
% 94.68/94.44 [5675]~P122(x56751)+E(f317(f317(f281(x56751),f317(f73(x56751),x56752)),x56753),f317(f73(x56751),f317(f317(f281(x56751),x56752),x56753)))
% 94.68/94.44 [5676]~P111(x56761)+E(f317(f317(f234(x56761),f317(f70(x56761),x56762)),x56763),f317(f70(x56761),f317(f317(f234(x56761),x56762),x56763)))
% 94.68/94.44 [5774]E(f392(x57741,x57742,x57743),f396(x57741,x57742,x57743))+E(f317(f317(f92(f904(x57743,a893)),x57742),x57741),f178(f904(x57743,a893)))
% 94.68/94.44 [5789]~P77(x57892)+E(f317(f317(f9(x57891,x57892),f317(f16(x57892,x57891),f72(x57892))),x57893),f72(x57892))
% 94.68/94.44 [5790]~P76(x57902)+E(f317(f317(f6(x57901,x57902),f317(f16(x57902,x57901),f2(x57902))),x57903),f2(x57902))
% 94.68/94.44 [5792]~P94(x57921)+E(f317(f317(f23(x57921),f317(f94(x57921),x57922)),f317(f94(x57921),x57923)),f317(f94(x57921),f317(f317(f23(a1),x57922),x57923)))
% 94.68/94.44 [5795]~P144(x57951)+E(f317(f317(f74(x57951),f317(f90(x57951),x57952)),f317(f90(x57951),x57953)),f317(f90(x57951),f317(f317(f74(a897),x57952),x57953)))
% 94.68/94.44 [5796]~P144(x57961)+E(f317(f317(f75(x57961),f317(f90(x57961),x57962)),f317(f90(x57961),x57963)),f317(f90(x57961),f317(f317(f75(a897),x57962),x57963)))
% 94.68/94.44 [5797]~P141(x57971)+E(f317(f317(f23(x57971),f317(f93(x57971),x57972)),f317(f93(x57971),x57973)),f317(f93(x57971),f317(f317(f23(a1),x57972),x57973)))
% 94.68/94.44 [5798]~P141(x57981)+E(f317(f317(f74(x57981),f317(f93(x57981),x57982)),f317(f93(x57981),x57983)),f317(f93(x57981),f317(f317(f74(a1),x57982),x57983)))
% 94.68/94.44 [5799]~P141(x57991)+E(f317(f317(f75(x57991),f317(f93(x57991),x57992)),f317(f93(x57991),x57993)),f317(f93(x57991),f317(f317(f75(a1),x57992),x57993)))
% 94.68/94.44 [5800]~P94(x58001)+E(f317(f317(f74(x58001),f317(f94(x58001),x58002)),f317(f94(x58001),x58003)),f317(f94(x58001),f317(f317(f74(a1),x58002),x58003)))
% 94.68/94.44 [5801]~P94(x58011)+E(f317(f317(f75(x58011),f317(f94(x58011),x58012)),f317(f94(x58011),x58013)),f317(f94(x58011),f317(f317(f75(a1),x58012),x58013)))
% 94.68/94.44 [5849]~E(x58493,x58492)+P1(f317(f317(f224(f904(x58491,a893)),x58492),x58493))
% 94.68/94.44 [5855]~E(x58552,x58553)+P1(f317(f317(f224(f904(x58551,a893)),x58552),x58553))
% 94.68/94.44 [5860]~P75(x58601)+E(f317(f317(f74(x58601),f317(f73(x58601),x58602)),f317(f73(x58601),x58603)),f317(f73(x58601),f317(f317(f74(x58601),x58603),x58602)))
% 94.68/94.44 [5861]~P69(x58611)+E(f317(f317(f74(x58611),f317(f73(x58611),x58612)),f317(f73(x58611),x58613)),f317(f73(x58611),f317(f317(f74(x58611),x58612),x58613)))
% 94.68/94.44 [5862]~P78(x58621)+E(f317(f317(f223(x58621),f317(f73(x58621),x58622)),f317(f73(x58621),x58623)),f317(f73(x58621),f317(f317(f228(x58621),x58622),x58623)))
% 94.68/94.44 [5863]~P78(x58631)+E(f317(f317(f228(x58631),f317(f73(x58631),x58632)),f317(f73(x58631),x58633)),f317(f73(x58631),f317(f317(f223(x58631),x58632),x58633)))
% 94.68/94.44 [5864]~P97(x58641)+E(f317(f317(f92(x58641),f317(f73(x58641),x58642)),f317(f73(x58641),x58643)),f317(f73(x58641),f317(f317(f91(x58641),x58642),x58643)))
% 94.68/94.44 [5865]~P97(x58651)+E(f317(f317(f91(x58651),f317(f73(x58651),x58652)),f317(f73(x58651),x58653)),f317(f73(x58651),f317(f317(f92(x58651),x58652),x58653)))
% 94.68/94.44 [5866]~P111(x58661)+E(f317(f317(f75(x58661),f317(f70(x58661),x58662)),f317(f70(x58661),x58663)),f317(f70(x58661),f317(f317(f75(x58661),x58662),x58663)))
% 94.68/94.44 [5867]~P63(x58671)+E(f317(f317(f281(x58671),f317(f70(x58671),x58672)),f317(f70(x58671),x58673)),f317(f70(x58671),f317(f317(f281(x58671),x58672),x58673)))
% 94.68/94.44 [5868]~P81(x58681)+E(f317(f317(f74(x58681),f317(f155(x58681),x58682)),f317(f155(x58681),x58683)),f317(f155(x58681),f317(f317(f124(x58681),x58682),x58683)))
% 94.68/94.44 [5869]E(x58691,f178(f904(x58692,a893)))+~E(f317(f317(f91(f904(x58692,a893)),x58693),x58691),f178(f904(x58692,a893)))
% 94.68/94.44 [5870]E(x58701,f178(f904(x58702,a893)))+~E(f317(f317(f91(f904(x58702,a893)),x58701),x58703),f178(f904(x58702,a893)))
% 94.68/94.44 [5871]~P148(x58711,x58713,x58712)+P1(f317(x58711,f317(f317(f30(a1),x58712),x58713)))
% 94.68/94.44 [5936]~P1(f317(f28(x59361),x59363))+P1(f317(f28(x59361),f317(f317(f299(x59361),x59362),x59363)))
% 94.68/94.44 [5937]~P1(f317(f127(x59371),x59373))+P1(f317(f127(x59371),f317(f317(f165(x59371),x59372),x59373)))
% 94.68/94.44 [5938]~P1(f317(f127(x59381),x59383))+P1(f317(f127(x59381),f317(f317(f128(x59381),x59382),x59383)))
% 94.68/94.44 [5970]~P66(x59701)+P1(f317(f317(f224(x59701),x59702),f317(f317(f223(x59701),x59703),x59702)))
% 94.68/94.44 [5971]~P66(x59711)+P1(f317(f317(f224(x59711),x59712),f317(f317(f223(x59711),x59712),x59713)))
% 94.68/94.44 [5972]~P99(x59721)+P1(f317(f317(f224(x59721),x59722),f317(f317(f91(x59721),x59723),x59722)))
% 94.68/94.44 [5973]~P100(x59731)+P1(f317(f317(f224(x59731),x59732),f317(f317(f91(x59731),x59733),x59732)))
% 94.68/94.44 [5974]~P99(x59741)+P1(f317(f317(f224(x59741),x59742),f317(f317(f91(x59741),x59742),x59743)))
% 94.68/94.44 [5975]~P100(x59751)+P1(f317(f317(f224(x59751),x59752),f317(f317(f91(x59751),x59752),x59753)))
% 94.68/94.44 [5976]~P112(x59761)+P1(f317(f317(f277(x59761),x59762),f317(f317(f75(x59761),x59763),x59762)))
% 94.68/94.44 [5977]~P112(x59771)+P1(f317(f317(f277(x59771),x59772),f317(f317(f75(x59771),x59772),x59773)))
% 94.68/94.44 [5991]~E(x59911,f2(a897))+E(f317(f317(f30(a897),f317(f317(f75(a897),x59911),x59912)),f317(f317(f75(a897),x59911),x59913)),f2(a897))
% 94.68/94.44 [6073]~P94(x60731)+E(f317(f317(f23(x60731),f317(f94(x60731),x60732)),f317(f94(x60731),x60733)),f317(f94(x60731),f317(f317(f74(a1),x60732),f317(f73(a1),x60733))))
% 94.68/94.44 [6133]E(x61331,f2(a897))+E(f317(f317(f30(a897),f317(f317(f75(a897),x61331),x61332)),f317(f317(f75(a897),x61331),x61333)),f317(f317(f30(a897),x61332),x61333))
% 94.68/94.44 [6163]E(f142(x61631,f317(f317(f141(x61631),x61632),x61633)),f317(f317(f141(x61631),x61632),f142(x61631,x61633)))+P1(f317(f317(f319(x61631),x61632),f317(f162(x61631),x61633)))
% 94.68/94.44 [6199]P148(x61991,x61992,x61993)+~P1(f317(x61991,f317(f317(f30(a1),x61993),x61992)))
% 94.68/94.44 [6275]E(x62751,f103(x62752))+E(f317(f317(f141(x62752),f317(f131(x62752),x62751)),f317(f317(f165(x62752),x62753),f317(f161(x62752),x62751))),f317(f317(f165(x62752),f317(a102,x62753)),x62751))
% 94.68/94.44 [6284]E(f317(f317(f23(f904(x62841,a893)),x62842),x62843),x62842)+~E(f317(f317(f92(f904(x62841,a893)),x62842),x62843),f178(f904(x62841,a893)))
% 94.68/94.44 [6298]E(f142(x62981,f317(f317(f141(x62981),x62982),x62983)),f142(x62981,x62983))+~P1(f317(f317(f319(x62981),x62982),f317(f162(x62981),x62983)))
% 94.68/94.44 [6329]~P1(f317(f317(f224(a897),x63291),x63293))+P1(f317(f317(f224(a897),x63291),f317(f317(f74(a897),x63292),x63293)))
% 94.68/94.44 [6331]~P1(f317(f317(f224(a897),x63311),x63312))+P1(f317(f317(f224(a897),x63311),f317(f317(f74(a897),x63312),x63313)))
% 94.68/94.44 [6333]~P1(f317(f317(f225(a897),x63331),x63333))+P1(f317(f317(f225(a897),x63331),f317(f317(f74(a897),x63332),x63333)))
% 94.68/94.44 [6335]~P1(f317(f317(f225(a897),x63351),x63352))+P1(f317(f317(f225(a897),x63351),f317(f317(f74(a897),x63352),x63353)))
% 94.68/94.44 [6375]P1(f317(f28(x63751),x63752))+~P1(f317(f28(x63751),f317(f317(f299(x63751),x63753),x63752)))
% 94.68/94.44 [6376]P1(f317(f127(x63761),x63762))+~P1(f317(f127(x63761),f317(f317(f141(x63761),x63763),x63762)))
% 94.68/94.44 [6377]P1(f317(f127(x63771),x63772))+~P1(f317(f127(x63771),f317(f317(f124(x63771),x63773),x63772)))
% 94.68/94.44 [6378]P1(f317(f127(x63781),x63782))+~P1(f317(f127(x63781),f317(f317(f124(x63781),x63782),x63783)))
% 94.68/94.44 [6432]~P112(x64321)+E(f317(f317(f74(x64321),x64322),f317(f317(f75(x64321),x64323),x64322)),f317(f317(f75(x64321),f317(f317(f74(x64321),x64323),f72(x64321))),x64322))
% 94.68/94.44 [6479]~E(x64791,x64792)+~P1(f317(f317(f225(f904(x64793,a893)),x64791),x64792))
% 94.68/94.44 [6525]P1(f317(f317(f319(x65251),x65252),x65253))+P1(f317(f317(f319(x65251),x65252),f317(f73(f904(x65251,a893)),x65253)))
% 94.68/94.44 [6531]E(f134(x65311,f317(f317(f128(x65311),x65312),x65313)),f134(x65311,x65313))+~P1(f317(f317(f225(a897),x65312),f317(f179(f898(x65311)),x65313)))
% 94.68/94.44 [6532]E(f317(f317(f165(x65321),x65322),f104(x65321,x65323)),f317(f317(f165(x65321),x65322),x65323))+~P1(f317(f317(f225(a897),x65322),f317(f179(f898(x65321)),x65323)))
% 94.68/94.44 [6592]E(f317(f317(f317(f173(f898(x65921),f898(x65921)),x65922),f157(x65921)),x65923),x65923)+~E(f40(a897,x65922,f317(f179(f898(x65921)),x65923)),f2(a897))
% 94.68/94.44 [6599]~P8(x65991,x65993,x65992)+E(f317(f317(f279(x65991,x65991,x65991),f317(f276(x65991,x65991),x65992)),x65992),x65992)
% 94.68/94.44 [6642]~E(f317(f317(f91(f904(x66421,a893)),x66422),x66423),x66423)+P1(f317(f317(f224(f904(x66421,a893)),x66422),x66423))
% 94.68/94.44 [6647]~P54(x66471,x66471,x66473)+P54(x66471,x66471,f317(f317(f173(f903(x66471,x66471),a893),x66472),x66473))
% 94.68/94.44 [6650]~P1(f317(f317(f319(x66501),x66503),f317(f162(x66501),x66502)))+P1(f317(f317(f225(a897),f2(a897)),f317(f179(f898(x66501)),x66502)))
% 94.68/94.44 [6678]~P86(x66781)+E(f317(f70(x66781),f317(f317(f74(x66781),f317(f70(x66781),x66782)),f317(f70(x66781),x66783))),f317(f317(f74(x66781),f317(f70(x66781),x66782)),f317(f70(x66781),x66783)))
% 94.68/94.44 [6689]E(f317(f317(f30(a897),f317(f317(f75(a897),x66891),x66892)),f317(f317(f75(a897),x66891),x66893)),f317(f317(f30(a897),x66892),x66893))+~P1(f317(f317(f225(a897),f2(a897)),x66891))
% 94.68/94.44 [6832]~P1(f317(f28(x68321),x68323))+E(f317(f317(f58(x68321,f904(x68321,a893),f299(x68321)),x68322),x68323),f317(f317(f91(f904(x68321,a893)),x68323),x68322))
% 94.68/94.44 [6891]E(f317(f317(f91(f904(x68911,a893)),x68912),x68913),x68912)+~P1(f317(f317(f224(f904(x68911,a893)),x68913),x68912))
% 94.68/94.44 [6893]E(f317(f317(f91(f904(x68931,a893)),x68932),x68933),x68933)+~P1(f317(f317(f224(f904(x68931,a893)),x68932),x68933))
% 94.68/94.44 [6894]E(f317(f317(f92(f904(x68941,a893)),x68942),x68943),x68943)+~P1(f317(f317(f224(f904(x68941,a893)),x68943),x68942))
% 94.68/94.44 [6895]E(f317(f317(f92(f904(x68951,a893)),x68952),x68953),x68952)+~P1(f317(f317(f224(f904(x68951,a893)),x68952),x68953))
% 94.68/94.44 [6944]~P1(f317(f127(x69441),x69442))+E(f317(f317(f23(f904(x69441,a893)),f317(f162(x69441),x69442)),f317(f317(f299(x69441),x69443),f178(f904(x69441,a893)))),f317(f162(x69441),f160(x69441,x69443,x69442)))
% 94.68/94.44 [7001]P36(x70011,x70012)+~P36(x70011,f317(f317(f173(f903(x70011,x70011),a893),x70013),x70012))
% 94.68/94.44 [7019]~E(x70191,f2(a897))+P1(f317(f317(f277(a897),f317(f317(f75(a897),x70191),x70192)),f317(f317(f75(a897),x70191),x70193)))
% 94.68/94.44 [7070]P1(f317(f44(x70701,x70702),f317(a46,x70703)))+~P1(f317(f44(f317(f73(a1),x70701),f317(f73(a1),x70702)),x70703))
% 94.68/94.44 [7075]E(f317(f317(f23(f904(x70751,a893)),f317(f317(f299(x70751),x70752),x70753)),f317(f317(f299(x70751),x70752),f178(f904(x70751,a893)))),x70753)+P1(f317(f317(f319(x70751),x70752),x70753))
% 94.68/94.44 [7097]E(f317(f317(f92(f904(x70971,a893)),f317(f162(x70971),x70972)),f317(f162(x70971),x70973)),f178(f904(x70971,a893)))+~P1(f317(f127(x70971),f317(f317(f124(x70971),x70972),x70973)))
% 94.68/94.44 [7112]~P1(f317(f317(f319(x71121),x71122),f317(f162(x71121),x71123)))+~P1(f317(f127(x71121),f317(f317(f141(x71121),x71122),x71123)))
% 94.68/94.44 [7183]P30(x71831,x71832,x71833)+P1(f317(f317(f225(a897),f738(x71833,x71832,x71831)),f317(f179(f898(x71831)),x71833)))
% 94.68/94.44 [7193]E(f317(f317(f92(f904(x71931,a893)),x71932),x71933),f178(f904(x71931,a893)))+P1(f317(f317(f319(x71931),f392(x71933,x71932,x71931)),x71932))
% 94.68/94.44 [7194]E(f317(f317(f92(f904(x71941,a893)),x71942),x71943),f178(f904(x71941,a893)))+P1(f317(f317(f319(x71941),f396(x71943,x71942,x71941)),x71943))
% 94.68/94.44 [7197]E(f104(x71971,f317(f317(f165(x71971),x71972),x71973)),f317(f317(f165(x71971),f317(f317(f23(a897),x71972),f72(a897))),x71973))+~P1(f317(f317(f224(a897),x71972),f317(f179(f898(x71971)),x71973)))
% 94.68/94.44 [7257]~P32(x72573,x72572,x72571)+P1(f317(f317(f225(a897),f732(x72571,x72572,x72573)),f317(f179(f898(x72573)),x72571)))
% 94.68/94.44 [7277]P1(f317(f317(f225(a897),f2(a897)),x72771))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x72772),x72771)),f317(f317(f75(a897),x72773),x72771)))
% 94.68/94.44 [7278]P1(f317(f317(f225(a897),f2(a897)),x72781))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x72781),x72782)),f317(f317(f75(a897),x72781),x72783)))
% 94.68/94.44 [7281]~P1(f317(f317(f319(x72811),x72812),x72813))+~P1(f317(f317(f319(x72811),x72812),f317(f73(f904(x72811,a893)),x72813)))
% 94.68/94.44 [7287]~P1(f317(f317(f225(f904(x72871,a893)),x72872),x72873))+P1(f317(f317(f224(f904(x72871,a893)),x72872),x72873))
% 94.68/94.44 [7393]~P1(f317(f317(f224(a897),x73933),x73932))+P1(f317(f317(f224(a897),f317(f317(f23(a897),x73931),x73932)),f317(f317(f23(a897),x73931),x73933)))
% 94.68/94.44 [7394]~P1(f317(f317(f224(a897),x73941),x73943))+P1(f317(f317(f224(a897),f317(f317(f23(a897),x73941),x73942)),f317(f317(f23(a897),x73943),x73942)))
% 94.68/94.44 [7395]~P1(f317(f317(f224(a897),x73952),x73953))+P1(f317(f317(f224(a897),f317(f317(f74(a897),x73951),x73952)),f317(f317(f74(a897),x73951),x73953)))
% 94.68/94.44 [7396]~P1(f317(f317(f224(a897),x73961),x73963))+P1(f317(f317(f224(a897),f317(f317(f74(a897),x73961),x73962)),f317(f317(f74(a897),x73963),x73962)))
% 94.68/94.44 [7398]~P1(f317(f317(f224(a897),x73982),x73983))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x73981),x73982)),f317(f317(f75(a897),x73981),x73983)))
% 94.68/94.44 [7400]~P1(f317(f317(f224(a897),x74001),x74003))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x74001),x74002)),f317(f317(f75(a897),x74003),x74002)))
% 94.68/94.44 [7401]~P1(f317(f317(f224(a897),x74011),x74013))+P1(f317(f317(f224(a897),f317(f317(f30(a897),x74011),x74012)),f317(f317(f30(a897),x74013),x74012)))
% 94.68/94.44 [7402]~P1(f317(f317(f224(a1),x74022),x74023))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x74021),x74022)),f317(f317(f74(a1),x74021),x74023)))
% 94.68/94.44 [7405]~P1(f317(f317(f225(a897),x74052),x74053))+P1(f317(f317(f225(a897),f317(f317(f74(a897),x74051),x74052)),f317(f317(f74(a897),x74051),x74053)))
% 94.68/94.44 [7406]~P1(f317(f317(f225(a897),x74061),x74063))+P1(f317(f317(f225(a897),f317(f317(f74(a897),x74061),x74062)),f317(f317(f74(a897),x74063),x74062)))
% 94.68/94.44 [7407]~P1(f317(f317(f225(a1),x74071),x74073))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x74071),x74072)),f317(f317(f74(a1),x74073),x74072)))
% 94.68/94.44 [7410]~P1(f317(f317(f277(a897),x74102),x74103))+P1(f317(f317(f277(a897),f317(f317(f75(a897),x74101),x74102)),f317(f317(f75(a897),x74101),x74103)))
% 94.68/94.44 [7488]E(x74881,x74882)+~P1(f317(f317(f319(x74883),x74881),f317(f317(f299(x74883),x74882),f178(f904(x74883,a893)))))
% 94.68/94.44 [7490]~E(f317(f317(f92(f904(x74901,a893)),x74902),x74903),f178(f904(x74901,a893)))+P1(f317(f317(f224(f904(x74901,a893)),x74902),f317(f73(f904(x74901,a893)),x74903)))
% 94.68/94.44 [7495]P1(f317(f317(f319(f904(x74951,a893)),x74952),f317(f298(x74951),x74953)))+~P1(f317(f317(f224(f904(x74951,a893)),x74952),x74953))
% 94.68/94.44 [7546]E(f317(f317(f141(x75461),f317(f317(f154(x75461),x75462),x75463)),f317(f317(f128(x75461),f317(a102,x75463)),x75462)),f317(f317(f128(x75461),x75463),x75462))+~P1(f317(f317(f225(a897),x75463),f317(f179(f898(x75461)),x75462)))
% 94.68/94.44 [7571]P1(f317(f317(f319(f903(x75711,x75711)),x75712),f297(x75711,x75713)))+~P1(f317(f317(f319(f903(x75711,x75711)),x75712),x75713))
% 94.68/94.44 [7580]~P1(f317(f317(f319(f904(x75801,a893)),x75802),f317(f298(x75801),x75803)))+P1(f317(f317(f224(f904(x75801,a893)),x75802),x75803))
% 94.68/94.44 [7625]P1(f317(f317(f224(f904(x76251,a893)),x76252),f31(f904(x76251,a893),x76253)))+~P1(f317(f317(f319(f904(x76251,a893)),x76252),x76253))
% 94.68/94.44 [7650]~P141(x76501)+E(f317(f317(f75(x76501),f317(f317(f234(x76501),f317(f73(x76501),f72(x76501))),x76502)),f317(f317(f234(x76501),x76503),x76502)),f317(f317(f234(x76501),f317(f73(x76501),x76503)),x76502))
% 94.68/94.44 [7672]E(f317(f317(f154(x76721),x76722),f317(f317(f23(a897),f317(f179(f898(x76721)),x76722)),f317(a102,x76723))),f317(f317(f154(x76721),f317(f158(x76721),x76722)),x76723))+~P1(f317(f317(f225(a897),x76723),f317(f179(f898(x76721)),x76722)))
% 94.68/94.44 [7689]~E(f317(f317(f92(f904(x76891,a893)),f580(x76893,x76892,x76891)),x76893),f178(f904(x76891,a893)))+E(f317(f317(f92(f904(x76891,a893)),f31(f904(x76891,a893),x76892)),x76893),f178(f904(x76891,a893)))
% 94.68/94.44 [7753]~P1(f317(f317(f319(x77533),x77532),f317(f162(x77533),x77531)))+P1(f317(f317(f225(a897),f613(x77531,x77532,x77533)),f317(f179(f898(x77533)),x77531)))
% 94.68/94.44 [7761]P1(f317(f317(f319(x77611),f317(f317(f154(x77611),x77612),x77613)),f317(f162(x77611),x77612)))+~P1(f317(f317(f225(a897),x77613),f317(f179(f898(x77611)),x77612)))
% 94.68/94.44 [7859]~P1(f317(x78592,f696(x78593,x78592,x78591)))+E(f317(f317(f128(x78591),f317(f179(f898(x78591)),f167(x78591,x78592,x78593))),x78593),f103(x78591))
% 94.68/94.44 [7872]P1(f317(f317(f224(f904(f898(x78721),a893)),f151(x78721,x78722)),f151(x78721,x78723)))+~P1(f317(f317(f224(f904(x78721,a893)),x78722),x78723))
% 94.68/94.44 [7873]P1(f317(f317(f224(f904(f898(x78731),a893)),f150(x78731,x78732)),f150(x78731,x78733)))+~P1(f317(f317(f224(f904(x78731,a893)),x78732),x78733))
% 94.68/94.44 [7900]E(f317(f317(f92(f904(x79001,a893)),f31(f904(x79001,a893),x79002)),x79003),f178(f904(x79001,a893)))+P1(f317(f317(f319(f904(x79001,a893)),f580(x79003,x79002,x79001)),x79002))
% 94.68/94.44 [7902]~P1(f317(f317(f319(f904(x79021,a893)),x79023),x79022))+P1(f317(f317(f224(f904(x79021,a893)),f32(f904(x79021,a893),x79022)),x79023))
% 94.68/94.44 [7904]E(f317(f317(f92(f904(x79041,a893)),x79042),x79043),f178(f904(x79041,a893)))+~P1(f317(f317(f224(f904(x79041,a893)),x79042),f317(f73(f904(x79041,a893)),x79043)))
% 94.68/94.44 [7953]E(f317(f317(f23(a897),f317(f317(f74(a897),f317(f155(a897),x79531)),x79532)),f317(f317(f154(a897),x79531),x79533)),f317(f155(a897),f317(f317(f149(a897,x79531),x79533),x79532)))+~P1(f317(f317(f225(a897),x79533),f317(f179(f898(a897)),x79531)))
% 94.68/94.44 [8004]P1(f317(f317(f224(a897),x80041),x80042))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x80043),x80041)),f317(f317(f74(a897),x80043),x80042)))
% 94.68/94.44 [8007]P1(f317(f317(f225(a897),x80071),x80072))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),x80073),x80071)),f317(f317(f74(a897),x80073),x80072)))
% 94.68/94.44 [8008]P1(f317(f317(f225(a897),x80081),x80082))+~P1(f317(f317(f225(a897),f317(f317(f75(a897),x80083),x80081)),f317(f317(f75(a897),x80083),x80082)))
% 94.68/94.44 [8009]P1(f317(f317(f225(a897),x80091),x80092))+~P1(f317(f317(f225(a897),f317(f317(f75(a897),x80091),x80093)),f317(f317(f75(a897),x80092),x80093)))
% 94.68/94.44 [8038]P1(f317(f317(f225(a897),f2(a897)),x80381))+~P1(f317(f317(f225(a897),f317(f317(f75(a897),x80382),x80381)),f317(f317(f75(a897),x80383),x80381)))
% 94.68/94.44 [8039]P1(f317(f317(f225(a897),f2(a897)),x80391))+~P1(f317(f317(f225(a897),f317(f317(f75(a897),x80391),x80392)),f317(f317(f75(a897),x80391),x80393)))
% 94.68/94.44 [8112]E(f237(x81121,x81122,x81123),x81122)+~P1(f317(f317(f224(f904(x81121,a893)),x81123),f317(f317(f299(x81121),x81122),f178(f904(x81121,a893)))))
% 94.68/94.44 [8162]~P1(f317(f127(x81621),x81623))+E(f317(f126(x81621,f317(f317(f8(a893,a893,x81621),a312),f317(a314,x81622))),x81623),f160(x81621,x81622,x81623))
% 94.68/94.44 [8187]E(f317(f317(f128(x81871),f317(f179(f898(x81871)),f167(x81871,x81872,x81873))),x81873),f103(x81871))+P1(f317(f317(f319(x81871),f696(x81873,x81872,x81871)),f317(f162(x81871),x81873)))
% 94.68/94.44 [8191]E(f317(f317(f124(x81911),f317(f317(f165(x81911),x81912),x81913)),f317(f317(f141(x81911),f317(f317(f154(x81911),x81913),x81912)),f103(x81911))),f317(f317(f165(x81911),f317(a102,x81912)),x81913))+~P1(f317(f317(f225(a897),x81912),f317(f179(f898(x81911)),x81913)))
% 94.68/94.44 [8258]E(f317(f126(x82581,f317(f317(f8(a893,a893,x82581),a312),f317(a314,x82582))),x82583),x82583)+P1(f317(f317(f319(x82581),x82582),f317(f162(x82581),x82583)))
% 94.68/94.44 [8264]P1(f317(f317(f224(f904(f904(x82641,a893),a893)),f238(x82641,x82642)),f238(x82641,x82643)))+~P1(f317(f317(f224(f904(x82641,a893)),x82642),x82643))
% 94.68/94.44 [8303]~P1(f317(f127(x83031),x83033))+P1(f317(f127(x83031),f317(f317(f317(f173(f898(x83031),f898(x83031)),x83032),f157(x83031)),x83033)))
% 94.68/94.44 [8309]~P1(f317(f317(f225(a897),x83092),x83093))+P1(f317(f317(f225(a897),f317(f317(f75(a897),f317(a102,x83091)),x83092)),f317(f317(f75(a897),f317(a102,x83091)),x83093)))
% 94.68/94.44 [8329]P1(f317(f317(f224(f904(f904(x83291,a893),a893)),f317(f298(x83291),x83292)),f317(f298(x83291),x83293)))+~P1(f317(f317(f224(f904(x83291,a893)),x83292),x83293))
% 94.68/94.44 [8399]~E(f317(f300(x83991,x83992,x83993),f232(f904(x83991,a893))),f232(f904(x83992,a893)))+E(f317(f67(x83991,x83992,x83992,x83993),f85(x83991,x83992,f232(f904(x83991,a893)),x83993)),f25(x83992))
% 94.68/94.44 [8493]~P1(f317(f317(f224(f904(x84931,a893)),x84933),x84932))+P1(f317(f317(f224(f904(x84931,a893)),f317(f73(f904(x84931,a893)),x84932)),f317(f73(f904(x84931,a893)),x84933)))
% 94.68/94.44 [8527]E(f317(f300(a897,a897,f317(f317(f7(a897,a897,a897),f23(a897)),x85271)),f317(f292(a897,x85272),x85273)),f317(f292(a897,f317(f317(f23(a897),x85272),x85271)),f317(f317(f23(a897),x85273),x85271)))+~P1(f317(f317(f225(a897),x85271),x85273))
% 94.68/94.44 [8553]~P81(x85531)+E(f317(f317(f74(x85531),x85532),f317(f132(x85531,x85531,f74(x85531),f2(x85531)),x85533)),f317(f132(x85531,x85531,f74(x85531),x85532),x85533))
% 94.68/94.44 [8629]~P86(x86291)+P1(f317(f317(f224(x86291),f317(f70(x86291),f317(f317(f23(x86291),x86292),x86293))),f317(f317(f74(x86291),f317(f70(x86291),x86292)),f317(f70(x86291),x86293))))
% 94.68/94.44 [8630]~P86(x86301)+P1(f317(f317(f224(x86301),f317(f70(x86301),f317(f317(f74(x86301),x86302),x86303))),f317(f317(f74(x86301),f317(f70(x86301),x86302)),f317(f70(x86301),x86303))))
% 94.68/94.44 [8641]E(f317(f317(f74(a1),f317(f317(f75(a1),x86411),f40(a1,f317(f317(f30(a1),x86412),x86411),x86413))),f40(a1,x86412,x86411)),f40(a1,x86412,f317(f317(f75(a1),x86411),x86413)))+~P1(f317(f317(f225(a1),f2(a1)),x86413))
% 94.68/94.44 [8647]E(f317(f317(f124(x86471),f317(f317(f165(x86471),x86472),x86473)),f317(f317(f141(x86471),f317(f131(x86471),f317(f317(f128(x86471),x86472),x86473))),f103(x86471))),f317(f317(f165(x86471),f317(a102,x86472)),x86473))+~P1(f317(f317(f225(a897),x86472),f317(f179(f898(x86471)),x86473)))
% 94.68/94.44 [8667]E(f317(f258(x86671,f317(f317(f144(x86671,f903(a89,x86671)),f317(f242(a89,x86671),f72(a89))),x86672)),f317(a3,x86673)),f317(f317(f154(x86671),x86672),x86673))+~P1(f317(f317(f225(a897),x86673),f317(f179(f898(x86671)),x86672)))
% 94.68/94.44 [8735]P1(f317(f317(f319(f903(x87351,x87351)),x87352),f317(f317(f279(x87351,x87351,x87351),x87353),f297(x87351,x87353))))+~P1(f317(f317(f319(f903(x87351,x87351)),x87352),x87353))
% 94.68/94.44 [8746]E(f317(f300(x87461,x87462,x87463),f232(f904(x87461,a893))),f232(f904(x87462,a893)))+~E(f317(f67(x87461,x87462,x87462,x87463),f85(x87461,x87462,f232(f904(x87461,a893)),x87463)),f25(x87462))
% 94.68/94.44 [8755]P1(f317(f317(f224(a897),x87551),x87552))+~P1(f317(f317(f224(a897),f317(f317(f75(a897),f317(a102,x87553)),x87551)),f317(f317(f75(a897),f317(a102,x87553)),x87552)))
% 94.68/94.44 [8771]P1(f317(f317(f224(f904(x87711,a893)),x87712),x87713))+~P1(f317(f317(f224(f904(x87711,a893)),f317(f73(f904(x87711,a893)),x87713)),f317(f73(f904(x87711,a893)),x87712)))
% 94.68/94.44 [8794]P1(f317(f127(x87941),x87942))+~P1(f317(f127(x87941),f317(f317(f317(f173(f898(x87941),f898(x87941)),x87943),f157(x87941)),x87942)))
% 94.68/94.44 [8867]E(f317(f275(x88671,x88671,f297(x88671,x88672)),x88673),x88673)+~P1(f317(f317(f224(f904(x88671,a893)),f317(f275(x88671,x88671,x88672),x88673)),x88673))
% 94.68/94.44 [8915]~P66(x89151)+P13(x89151,f317(f126(x89151,f317(f317(f7(x89151,x89151,a893),a314),f317(x89152,x89153))),x89153))
% 94.68/94.44 [8922]~P1(f317(f317(f224(a897),x89221),x89222))+P1(f317(f317(f224(a897),x89221),f317(f132(a897,a897,f74(a897),x89222),x89223)))
% 94.68/94.44 [9008]~P1(f317(f317(f319(f903(x90081,x90081)),x90082),f297(x90081,x90083)))+P1(f317(f317(f319(f903(x90081,x90081)),x90082),f317(f317(f173(f903(x90081,x90081),a893),f558(x90083,x90082,x90081)),x90083)))
% 94.68/94.44 [9089]~P81(x90891)+E(f317(f317(f74(x90891),x90892),f317(f132(x90891,x90891,f317(f7(x90891,x90891,x90891),f74(x90891)),f2(x90891)),f317(f158(x90891),x90893))),f317(f132(x90891,x90891,f74(x90891),x90892),x90893))
% 94.68/94.44 [9207]~P25(x92072,x92071,x92073,f232(f904(x92072,a893)),f232(f904(x92071,a893)))+E(f85(x92071,x92072,f232(f904(x92071,a893)),f85(x92072,x92071,f232(f904(x92072,a893)),x92073)),x92073)
% 94.68/94.44 [9362]P54(x93621,x93622,x93623)+P1(f317(f317(f319(f903(x93621,x93622)),f317(f317(f242(x93621,x93622),f559(x93623,x93622,x93621)),f557(x93623,x93622,x93621))),x93623))
% 94.68/94.44 [9363]P54(x93631,x93632,x93633)+P1(f317(f317(f319(f903(x93631,x93632)),f317(f317(f242(x93631,x93632),f559(x93633,x93632,x93631)),f556(x93633,x93632,x93631))),x93633))
% 94.68/94.44 [9434]~P1(f317(f317(f319(f903(x94341,x94341)),x94342),f317(f317(f279(x94341,x94341,x94341),x94343),f297(x94341,x94343))))+P1(f317(f317(f319(f903(x94341,x94341)),x94342),f317(f317(f173(f903(x94341,x94341),a893),f561(x94343,x94342,x94341)),x94343)))
% 94.68/94.44 [9435]~P1(f317(x94351,f317(f317(f154(x94352),x94353),f317(f179(f898(x94352)),f167(x94352,x94351,x94353)))))+~P1(f317(f317(f225(a897),f317(f179(f898(x94352)),f167(x94352,x94351,x94353))),f317(f179(f898(x94352)),x94353)))
% 94.68/94.44 [9526]~P1(f317(f317(f224(f904(x95261,a893)),x95262),x95263))+P1(f317(f317(f224(f904(x95261,a893)),f317(f317(f7(x95261,f904(x95261,a893),a893),f319(x95261)),x95262)),f317(f317(f7(x95261,f904(x95261,a893),a893),f319(x95261)),x95263)))
% 94.68/94.44 [9588]~P1(f317(f317(f319(f903(f904(x95881,a893),f904(x95881,a893))),f317(f317(f242(f904(x95881,a893),f904(x95881,a893)),x95882),x95883)),f304(x95881)))+P1(f317(f317(f225(f904(x95881,a893)),x95882),x95883))
% 94.68/94.44 [9616]P55(x96161,x96162,x96163)+~P1(f317(f317(f319(f903(x96161,x96161)),f317(f317(f242(x96161,x96161),f536(x96163,x96162,x96161)),f535(x96163,x96162,x96161))),x96163))
% 94.68/94.44 [9617]P55(x96171,x96172,x96173)+~P1(f317(f317(f319(f903(x96171,x96171)),f317(f317(f242(x96171,x96171),f535(x96173,x96172,x96171)),f536(x96173,x96172,x96171))),x96173))
% 94.68/94.44 [9654]~P1(f317(f317(f319(f903(f898(x96541),f898(x96541))),f317(f317(f242(f898(x96541),f898(x96541)),x96542),x96542)),f137(x96541,x96543)))+P1(f317(f317(f319(f903(x96541,x96541)),f317(f317(f242(x96541,x96541),f636(x96542,x96543,x96541)),f636(x96542,x96543,x96541))),x96543))
% 94.68/94.44 [9704]P1(f317(f317(f224(f904(x97041,a893)),x97042),x97043))+~P1(f317(f317(f224(f904(x97041,a893)),f317(f317(f7(x97041,f904(x97041,a893),a893),f319(x97041)),x97042)),f317(f317(f7(x97041,f904(x97041,a893),a893),f319(x97041)),x97043)))
% 94.68/94.44 [9785]E(f317(f317(f23(a897),f317(f317(f6(a897,a897),x97851),f317(f272(a897),x97852))),f317(f317(f6(a897,a897),x97853),f317(f272(a897),x97852))),f317(f317(f6(a897,a897),f317(f317(f18(a897,a897,a897),f317(f317(f8(a897,f904(a897,a897),a897),f23(a897)),x97851)),x97853)),f317(f272(a897),x97852)))+~P1(f317(f317(f224(a897),f317(x97853,f417(x97852,x97851,x97853))),f317(x97851,f417(x97852,x97851,x97853))))
% 94.68/94.44 [5710]~P75(x57101)+E(f317(f317(f23(x57101),f317(f317(f74(x57101),x57102),x57103)),x57103),x57102)
% 94.68/94.44 [5711]~P75(x57111)+E(f317(f317(f74(x57111),f317(f317(f23(x57111),x57112),x57113)),x57113),x57112)
% 94.68/94.44 [5945]~P75(x59451)+E(f317(f317(f74(x59451),x59452),f317(f317(f74(x59451),f317(f73(x59451),x59452)),x59453)),x59453)
% 94.68/94.44 [6034]~P82(x60341)+E(f317(f317(f75(x60341),f317(f317(f234(x60341),x60342),x60343)),x60342),f317(f317(f234(x60341),x60342),f317(a102,x60343)))
% 94.68/94.44 [6035]~P112(x60351)+E(f317(f317(f75(x60351),f317(f317(f234(x60351),x60352),x60353)),x60352),f317(f317(f234(x60351),x60352),f317(a102,x60353)))
% 94.68/94.44 [6259]~P111(x62591)+E(f317(f70(x62591),f317(f317(f234(x62591),f317(f73(x62591),x62592)),x62593)),f317(f70(x62591),f317(f317(f234(x62591),x62592),x62593)))
% 94.68/94.44 [6306]~P82(x63061)+E(f317(f317(f75(x63061),f317(f317(f234(x63061),x63062),x63063)),x63062),f317(f317(f75(x63061),x63062),f317(f317(f234(x63061),x63062),x63063)))
% 94.68/94.44 [6366]E(f317(f317(f23(a89),f317(f317(f74(a89),x63661),x63662)),x63663),f264(x63661,x63662,x63663))+~P1(f317(f317(f225(a89),x63662),x63663))
% 94.68/94.44 [6391]~E(f317(f317(f128(x63911),x63913),x63912),f103(x63911))+P1(f317(f317(f224(a897),f317(f179(f898(x63911)),x63912)),x63913))
% 94.68/94.44 [6530]E(f317(f317(f75(a897),f317(f94(a897),x65301)),f317(f317(f75(a897),f317(f94(a897),x65302)),x65303)),f2(a897))+~P1(f317(f317(f225(a1),x65301),a77))
% 94.68/94.44 [6546]~P61(x65461)+E(f317(f317(f234(x65461),f317(f317(f281(x65461),f72(x65461)),x65462)),x65463),f317(f317(f281(x65461),f72(x65461)),f317(f317(f234(x65461),x65462),x65463)))
% 94.68/94.44 [6628]E(f317(f317(f23(a897),f317(f317(f74(a897),x66281),x66282)),x66283),f317(f317(f23(a897),x66281),f317(f317(f23(a897),x66283),x66282)))+~P1(f317(f317(f224(a897),x66282),x66283))
% 94.68/94.44 [6630]E(f317(f317(f23(a897),f317(f317(f74(a897),x66301),x66302)),x66303),f317(f317(f74(a897),x66301),f317(f317(f23(a897),x66302),x66303)))+~P1(f317(f317(f224(a897),x66303),x66302))
% 94.68/94.44 [6669]~P66(x66691)+P1(f317(f317(f224(x66691),f317(f317(f228(x66691),x66692),x66693)),x66693))
% 94.68/94.44 [6670]~P66(x66701)+P1(f317(f317(f224(x66701),f317(f317(f228(x66701),x66702),x66703)),x66702))
% 94.68/94.44 [6671]~P100(x66711)+P1(f317(f317(f224(x66711),f317(f317(f92(x66711),x66712),x66713)),x66713))
% 94.68/94.44 [6672]~P105(x66721)+P1(f317(f317(f224(x66721),f317(f317(f92(x66721),x66722),x66723)),x66723))
% 94.68/94.44 [6673]~P100(x66731)+P1(f317(f317(f224(x66731),f317(f317(f92(x66731),x66732),x66733)),x66732))
% 94.68/94.44 [6674]~P105(x66741)+P1(f317(f317(f224(x66741),f317(f317(f92(x66741),x66742),x66743)),x66742))
% 94.68/94.44 [6688]E(f317(f317(f30(a1),f317(f317(f30(a1),x66881),x66882)),x66883),f317(f317(f30(a1),x66881),f317(f317(f75(a1),x66882),x66883)))+~P1(f317(f317(f225(a1),f2(a1)),x66883))
% 94.68/94.44 [6742]~P112(x67421)+E(f317(f317(f74(x67421),f317(f317(f75(x67421),x67422),x67423)),x67423),f317(f317(f75(x67421),f317(f317(f74(x67421),x67422),f72(x67421))),x67423))
% 94.68/94.44 [6743]~P94(x67431)+E(f317(f317(f75(x67431),f317(f73(x67431),f317(f94(x67431),x67432))),x67433),f317(f317(f75(x67431),f317(f94(x67431),f317(f73(a1),x67432))),x67433))
% 94.68/94.44 [6816]~P81(x68161)+E(f317(f155(x68161),f317(f317(f144(x68162,x68161),f317(f16(x68161,x68162),f2(x68161))),x68163)),f2(x68161))
% 94.68/94.44 [6834]E(f317(f317(f74(a897),f317(f94(a897),x68341)),f317(f317(f74(a897),f317(f94(a897),x68342)),x68343)),f317(f317(f74(a897),f317(f94(a897),x68342)),x68343))+~P1(f317(a183,f317(f94(a1),x68341)))
% 94.68/94.44 [6849]~P5(x68491)+E(f32(x68491,f317(f317(f299(x68491),x68492),f317(f317(f299(x68491),x68493),f178(f904(x68491,a893))))),f317(f317(f92(x68491),x68492),x68493))
% 94.68/94.44 [6850]~P5(x68501)+E(f31(x68501,f317(f317(f299(x68501),x68502),f317(f317(f299(x68501),x68503),f178(f904(x68501,a893))))),f317(f317(f91(x68501),x68502),x68503))
% 94.68/94.44 [6874]E(f317(f317(f165(x68741),x68742),x68743),x68743)+~P1(f317(f317(f224(a897),f317(f179(f898(x68741)),x68743)),x68742))
% 94.68/94.44 [6886]E(f317(f317(f128(x68861),x68862),x68863),f103(x68861))+~P1(f317(f317(f224(a897),f317(f179(f898(x68861)),x68863)),x68862))
% 94.68/94.44 [6897]E(f317(f317(f74(a897),f317(f317(f23(a897),x68971),x68972)),x68973),f317(f317(f23(a897),f317(f317(f74(a897),x68971),x68973)),x68972))+~P1(f317(f317(f224(a897),x68972),x68971))
% 94.68/94.44 [6911]~P1(f317(f317(f225(a897),x69111),x69113))+P1(f317(f317(f225(a897),f317(f317(f23(a897),x69111),x69112)),x69113))
% 94.68/94.44 [6938]~P66(x69381)+E(f160(x69381,x69382,f317(f317(f138(x69381,x69381,f5(x69381)),x69382),x69383)),x69383)
% 94.68/94.44 [7032]E(f317(f317(f23(a897),f317(f317(f74(a897),x70321),x70322)),f317(a102,x70323)),f317(f317(f23(a897),x70321),f317(a102,f317(f317(f23(a897),x70323),x70322))))+~P1(f317(f317(f224(a897),x70322),x70323))
% 94.68/94.44 [7033]~P111(x70331)+P1(f317(f317(f224(x70331),f2(x70331)),f317(f317(f234(x70331),f317(f70(x70331),x70332)),x70333)))
% 94.68/94.44 [7124]~P1(f317(f28(x71241),x71242))+P1(f317(f28(x71241),f317(f317(f23(f904(x71241,a893)),x71242),x71243)))
% 94.68/94.44 [7125]~P1(f317(f28(x71251),x71253))+P1(f317(f28(x71251),f317(f317(f92(f904(x71251,a893)),x71252),x71253)))
% 94.68/94.44 [7126]~P1(f317(f28(x71261),x71262))+P1(f317(f28(x71261),f317(f317(f92(f904(x71261,a893)),x71262),x71263)))
% 94.68/94.44 [7267]~P36(x72671,x72673)+P36(x72671,f317(f317(f92(f904(f903(x72671,x72671),a893)),x72672),x72673))
% 94.68/94.44 [7268]~P36(x72681,x72682)+P36(x72681,f317(f317(f92(f904(f903(x72681,x72681),a893)),x72682),x72683))
% 94.68/94.44 [7389]~P66(x73891)+E(f14(x73891,f317(f162(x73891),f317(f317(f141(x73891),x73892),x73893))),f317(f132(x73891,x73891,f228(x73891),x73892),x73893))
% 94.68/94.44 [7390]~P66(x73901)+E(f15(x73901,f317(f162(x73901),f317(f317(f141(x73901),x73902),x73903))),f317(f132(x73901,x73901,f223(x73901),x73902),x73903))
% 94.68/94.44 [7391]~P100(x73911)+E(f13(x73911,f317(f162(x73911),f317(f317(f141(x73911),x73912),x73913))),f317(f132(x73911,x73911,f91(x73911),x73912),x73913))
% 94.68/94.44 [7392]~P100(x73921)+E(f10(x73921,f317(f162(x73921),f317(f317(f141(x73921),x73922),x73923))),f317(f132(x73921,x73921,f92(x73921),x73922),x73923))
% 94.68/94.44 [7456]~P1(f317(f28(x74561),x74562))+P1(f317(f317(f224(a897),f317(f29(x74561),x74562)),f317(f29(x74561),f317(f317(f299(x74561),x74563),x74562))))
% 94.68/94.44 [7463]E(f317(f317(f91(f904(a897,a893)),f317(f292(a897,x74631),x74632)),f317(f292(a897,x74632),f317(f317(f74(a897),x74632),x74633))),f317(f292(a897,x74631),f317(f317(f74(a897),x74632),x74633)))+~P1(f317(f317(f224(a897),x74631),x74632))
% 94.68/94.44 [7472]P1(f317(f317(f224(a897),x74721),x74722))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x74723),x74721)),x74722))
% 94.68/94.44 [7473]P1(f317(f317(f224(a897),x74731),x74732))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x74731),x74733)),x74732))
% 94.68/94.44 [7474]P1(f317(f317(f225(a897),x74741),x74742))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),x74741),x74743)),x74742))
% 94.68/94.44 [7514]~P66(x75141)+E(f11(x75141,f228(x75141),f317(f162(x75141),f317(f317(f141(x75141),x75142),x75143))),f317(f132(x75141,x75141,f228(x75141),x75142),x75143))
% 94.68/94.44 [7515]~P66(x75151)+E(f12(x75151,f223(x75151),f317(f162(x75151),f317(f317(f141(x75151),x75152),x75153))),f317(f132(x75151,x75151,f223(x75151),x75152),x75153))
% 94.68/94.44 [7519]~E(x75192,f178(f904(f903(x75191,x75191),a893)))+P1(f317(f317(f224(f904(f903(x75191,x75191),a893)),x75192),x75193))
% 94.68/94.44 [7618]E(f317(f317(f91(f904(x76181,a893)),x76182),f317(f317(f23(f904(x76181,a893)),x76183),x76182)),x76183)+~P1(f317(f317(f224(f904(x76181,a893)),x76182),x76183))
% 94.68/94.44 [7621]~P1(f317(f317(f224(a897),x76211),f317(f317(f74(a897),x76213),x76212)))+P1(f317(f317(f224(a897),f317(f317(f23(a897),x76211),x76212)),x76213))
% 94.68/94.44 [7622]~P1(f317(f317(f225(a897),x76221),f317(f317(f23(a897),x76223),x76222)))+P1(f317(f317(f225(a897),f317(f317(f74(a897),x76221),x76222)),x76223))
% 94.68/94.44 [7679]E(x76791,f103(x76792))+E(f317(f131(x76792),f317(f317(f317(f173(f898(x76792),f898(x76792)),x76793),f157(x76792)),x76791)),f317(f317(f154(x76792),x76791),f40(a897,x76793,f317(f179(f898(x76792)),x76791))))
% 94.68/94.44 [7688]E(f317(f317(f299(x76881),x76882),f317(f317(f23(f904(x76881,a893)),x76883),f317(f317(f299(x76881),x76882),f178(f904(x76881,a893))))),x76883)+~P1(f317(f317(f319(x76881),x76882),x76883))
% 94.68/94.44 [7850]P1(f317(f317(f224(a897),x78501),f317(f317(f74(a897),x78502),x78503)))+~P1(f317(f317(f224(a897),f317(f317(f23(a897),x78501),x78503)),x78502))
% 94.68/94.44 [7851]P1(f317(f317(f225(a897),x78511),f317(f317(f23(a897),x78512),x78513)))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),x78511),x78513)),x78512))
% 94.68/94.44 [7877]P1(f317(f28(x78771),x78772))+~P1(f317(f28(x78771),f317(f317(f91(f904(x78771,a893)),x78773),x78772)))
% 94.68/94.44 [7878]P1(f317(f28(x78781),x78782))+~P1(f317(f28(x78781),f317(f317(f91(f904(x78781,a893)),x78782),x78783)))
% 94.68/94.44 [7952]~P45(x79521,x79523)+P1(f317(f317(f319(f903(x79521,x79521)),f317(f317(f242(x79521,x79521),x79522),x79522)),x79523))
% 94.68/94.44 [8085]E(f317(f317(f154(a897),f129(a897,f317(f292(a897,x80851),x80852))),x80853),f317(f317(f74(a897),x80851),x80853))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),x80851),x80853)),x80852))
% 94.68/94.44 [8151]E(f317(f317(f165(a897),x81511),f129(a897,f317(f292(a897,x81512),x81513))),f129(a897,f317(f292(a897,x81512),f317(f317(f74(a897),x81512),x81511))))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x81512),x81511)),x81513))
% 94.68/94.44 [8208]~P94(x82081)+E(f317(f317(f234(x82081),x82082),f317(f94(a897),f317(f317(f74(a1),x82083),x82083))),f317(f317(f80(x82081,x82081),f317(f317(f234(x82081),x82082),f317(f94(a897),x82083))),f317(f317(f18(x82081,x82081,x82081),f75(x82081)),f5(x82081))))
% 94.68/94.44 [8474]E(f317(f317(f124(x84741),f317(f317(f165(x84741),x84742),x84743)),f317(f317(f141(x84741),f317(f317(f154(x84741),x84743),x84742)),f317(f317(f128(x84741),f317(a102,x84742)),x84743))),x84743)+~P1(f317(f317(f225(a897),x84742),f317(f179(f898(x84741)),x84743)))
% 94.68/94.44 [8481]P1(f317(f317(f224(f904(x84811,a893)),f305(x84811,x84812)),f305(x84811,x84813)))+~P1(f317(f317(f224(f904(x84811,f904(x84811,a893))),x84813),x84812))
% 94.68/94.44 [8482]~P55(x84821,x84822,x84823)+P55(x84821,x84822,f317(f317(f23(f904(f903(x84821,x84821),a893)),x84823),f297(x84821,f178(f904(f903(x84821,x84821),a893)))))
% 94.68/94.44 [8501]P1(f317(f317(f224(f904(x85011,a893)),f306(x85011,x85012)),f306(x85011,x85013)))+~P1(f317(f317(f224(f904(f903(x85011,x85011),a893)),x85013),x85012))
% 94.68/94.44 [8508]~P126(x85081)+P1(f317(f317(f224(x85081),f2(x85081)),f317(f317(f74(x85081),f317(f317(f75(x85081),x85082),x85082)),f317(f317(f75(x85081),x85083),x85083))))
% 94.68/94.44 [8542]P1(f317(f317(f224(f904(x85421,a893)),f317(f271(x85421),x85422)),f317(f271(x85421),x85423)))+~P1(f317(f317(f224(f904(f903(x85421,x85421),a893)),x85422),x85423))
% 94.68/94.44 [8571]~P53(x85711,x85712)+~P1(f317(f317(f319(f903(x85711,x85711)),f317(f317(f242(x85711,x85711),x85713),x85713)),x85712))
% 94.68/94.44 [8573]~P36(x85731,x85732)+~P1(f317(f317(f319(f903(x85731,x85731)),f317(f317(f242(x85731,x85731),x85733),x85733)),x85732))
% 94.68/94.44 [8631]P1(f317(f317(f224(f904(x86311,a893)),f32(f904(x86311,a893),x86312)),f32(f904(x86311,a893),x86313)))+~P1(f317(f317(f224(f904(f904(x86311,a893),a893)),x86313),x86312))
% 94.68/94.44 [8632]P1(f317(f317(f224(f904(x86321,a893)),f31(f904(x86321,a893),x86322)),f31(f904(x86321,a893),x86323)))+~P1(f317(f317(f224(f904(f904(x86321,a893),a893)),x86322),x86323))
% 94.68/94.44 [8686]~P8(x86861,x86863,x86862)+P1(f317(f317(f224(f904(f903(x86861,x86861),a893)),x86862),f317(f317(f244(x86861,x86861),x86863),f317(f16(f904(x86861,a893),x86861),x86863))))
% 94.68/94.44 [8687]~P52(x86871,x86873,x86872)+P1(f317(f317(f224(f904(f903(x86871,x86871),a893)),x86872),f317(f317(f244(x86871,x86871),x86873),f317(f16(f904(x86871,a893),x86871),x86873))))
% 94.68/94.44 [8736]~P86(x87361)+P1(f317(f317(f224(x87361),f317(f317(f23(x87361),f317(f70(x87361),x87362)),f317(f70(x87361),x87363))),f317(f70(x87361),f317(f317(f23(x87361),x87363),x87362))))
% 94.68/94.44 [8737]~P86(x87371)+P1(f317(f317(f224(x87371),f317(f317(f23(x87371),f317(f70(x87371),x87372)),f317(f70(x87371),x87373))),f317(f70(x87371),f317(f317(f23(x87371),x87372),x87373))))
% 94.68/94.44 [8769]P1(f317(f317(f224(f904(f903(x87691,x87691),a893)),f297(x87691,x87692)),f297(x87691,x87693)))+~P1(f317(f317(f224(f904(f903(x87691,x87691),a893)),x87692),x87693))
% 94.68/94.44 [8880]~P24(x88802,x88801,x88803,f232(f904(x88802,a893)))+E(f317(f67(x88801,x88802,x88802,f85(x88802,x88801,f232(f904(x88802,a893)),x88803)),x88803),f25(x88802))
% 94.68/94.44 [8940]P55(x89401,x89402,x89403)+~P55(x89401,x89402,f317(f317(f23(f904(f903(x89401,x89401),a893)),x89403),f297(x89401,f178(f904(f903(x89401,x89401),a893)))))
% 94.68/94.44 [8960]P1(f317(f317(f224(f904(f903(f898(x89601),f898(x89601)),a893)),f147(x89601,x89602)),f147(x89601,x89603)))+~P1(f317(f317(f224(f904(f903(x89601,x89601),a893)),x89602),x89603))
% 94.68/94.44 [8961]P1(f317(f317(f224(f904(f903(f898(x89611),f898(x89611)),a893)),f148(x89611,x89612)),f148(x89611,x89613)))+~P1(f317(f317(f224(f904(f903(x89611,x89611),a893)),x89612),x89613))
% 94.68/94.44 [8982]~P52(x89821,x89823,x89822)+P1(f317(f317(f224(f904(f903(x89821,x89821),a893)),x89822),f317(f317(f279(x89821,x89821,x89821),f317(f276(x89821,x89821),x89822)),x89822)))
% 94.68/94.44 [9034]~P1(f317(f127(x90341),x90342))+E(f317(f126(x90341,f317(f317(f7(x90341,f904(x90341,a893),a893),f319(x90341)),f317(f162(x90341),f166(x90341,x90342,x90343)))),x90342),f166(x90341,x90342,x90343))
% 94.68/94.44 [9087]E(x90871,x90872)+~P1(f317(f317(f319(f903(x90873,x90873)),f317(f317(f242(x90873,x90873),x90871),x90872)),f297(x90873,f178(f904(f903(x90873,x90873),a893)))))
% 94.68/94.44 [9170]P1(f317(f317(f319(x91701),x91702),f306(x91701,x91703)))+P1(f317(f317(f319(f903(x91701,x91701)),f317(f317(f242(x91701,x91701),f461(x91703,x91702,x91701)),x91702)),x91703))
% 94.68/94.44 [9171]P1(f317(f317(f319(x91711),x91712),f306(x91711,x91713)))+P1(f317(f317(f319(f903(x91711,x91711)),f317(f317(f242(x91711,x91711),f539(x91713,x91712,x91711)),x91712)),x91713))
% 94.68/94.44 [9172]P1(f317(f317(f319(x91721),x91722),f306(x91721,x91723)))+P1(f317(f317(f319(f903(x91721,x91721)),f317(f317(f242(x91721,x91721),f541(x91723,x91722,x91721)),x91722)),x91723))
% 94.68/94.44 [9208]P24(x92081,x92082,x92083,f232(f904(x92081,a893)))+~E(f317(f67(x92082,x92081,x92081,f85(x92081,x92082,f232(f904(x92081,a893)),x92083)),x92083),f25(x92081))
% 94.68/94.44 [9261]~P1(f317(f317(f319(f898(x92611)),x92613),f151(x92611,x92612)))+P1(f317(f150(x92611,f317(f317(f7(x92611,f904(x92611,a893),a893),f319(x92611)),x92612)),x92613))
% 94.68/94.44 [9284]P1(f317(x92843,x92842))+E(f317(f252(x92841),f317(f317(f18(x92841,a893,a893),f317(f317(f8(a893,f904(a893,a893),x92841),a315),f317(a314,x92842))),x92843)),f178(f904(x92841,a893)))
% 94.68/94.44 [9301]~P86(x93011)+P1(f317(f317(f224(x93011),f317(f70(x93011),f317(f317(f23(x93011),f317(f70(x93011),x93012)),f317(f70(x93011),x93013)))),f317(f70(x93011),f317(f317(f23(x93011),x93012),x93013))))
% 94.68/94.44 [9315]~P1(f317(x93153,x93152))+E(f317(f252(x93151),f317(f317(f18(x93151,a893,a893),f317(f317(f8(a893,f904(a893,a893),x93151),a315),f317(a314,x93152))),x93153)),f317(f317(f299(x93151),x93152),f178(f904(x93151,a893))))
% 94.68/94.44 [9324]~P1(f317(f317(f319(f904(x93241,a893)),x93243),f317(f298(x93241),x93242)))+P1(f317(f238(x93241,f317(f317(f7(x93241,f904(x93241,a893),a893),f319(x93241)),x93242)),x93243))
% 94.68/94.44 [9361]P36(x93611,x93612)+P1(f317(f317(f319(f903(x93611,x93611)),f317(f317(f242(x93611,x93611),f317(f502(x93612,x93611),f317(a102,x93613))),f317(f502(x93612,x93611),x93613))),x93612))
% 94.68/94.44 [9503]P1(f317(f317(f319(f898(x95031)),x95032),f151(x95031,x95033)))+~P1(f317(f150(x95031,f317(f317(f7(x95031,f904(x95031,a893),a893),f319(x95031)),x95033)),x95032))
% 94.68/94.44 [9518]P1(f317(f317(f319(f904(x95181,a893)),x95182),f317(f298(x95181),x95183)))+~P1(f317(f238(x95181,f317(f317(f7(x95181,f904(x95181,a893),a893),f319(x95181)),x95183)),x95182))
% 94.68/94.44 [9583]P1(f317(f317(f319(x95831),f317(f258(x95831,x95832),x95833)),f317(f162(x95831),f317(f317(f144(f903(a89,x95831),x95831),f246(a89,x95831)),x95832))))+~P1(f317(f317(f225(a89),x95833),f317(f155(a89),f317(f317(f144(f903(a89,x95831),a89),f241(a89,x95831)),x95832))))
% 94.68/94.44 [9633]P1(f317(f317(f224(f904(f903(f898(x96331),f898(x96331)),a893)),f148(x96331,x96332)),f317(f317(f244(f898(x96331),f898(x96331)),f151(x96331,x96333)),f317(f16(f904(f898(x96331),a893),f898(x96331)),f151(x96331,x96333)))))+~P1(f317(f317(f224(f904(f903(x96331,x96331),a893)),x96332),f317(f317(f244(x96331,x96331),x96333),f317(f16(f904(x96331,a893),x96331),x96333))))
% 94.68/94.44 [9657]P1(f317(f317(f319(x96571),f317(f241(x96571,f903(a89,a89)),f317(f256(x96571,x96572),x96573))),f317(f162(x96571),f317(f317(f144(f903(a89,x96571),x96571),f246(a89,x96571)),x96572))))+~P1(f317(f317(f225(a89),f2(a89)),f317(f155(a89),f317(f317(f144(f903(a89,x96571),a89),f241(a89,x96571)),x96572))))
% 94.68/94.44 [9672]~P1(f317(f317(f224(f904(f903(x96721,x96721),a893)),x96722),f317(f317(f244(x96721,x96721),x96723),f317(f16(f904(x96721,a893),x96721),x96723))))+P1(f317(f317(f224(f904(f903(x96721,x96721),a893)),f317(f317(f279(x96721,x96721,x96721),x96722),f297(x96721,x96722))),f317(f317(f244(x96721,x96721),x96723),f317(f16(f904(x96721,a893),x96721),x96723))))
% 94.68/94.44 [9970]~P36(x99701,x99702)+~P1(f317(f317(f319(f903(x99701,x99701)),f317(f317(f242(x99701,x99701),f317(x99703,f317(a102,f503(x99702,x99701,x99703)))),f317(x99703,f503(x99702,x99701,x99703)))),x99702))
% 94.68/94.44 [9971]~P36(x99711,x99712)+~P1(f317(f317(f319(f903(x99711,x99711)),f317(f317(f242(x99711,x99711),f317(x99713,f317(a102,f550(x99713,x99712,x99711)))),f317(x99713,f550(x99713,x99712,x99711)))),x99712))
% 94.68/94.44 [10226]P1(f317(f317(f224(f904(f903(f904(x102261,a893),f904(x102261,a893)),a893)),f317(f317(f279(f904(x102261,a893),f904(x102261,a893),f904(x102261,a893)),f310(x102261,x102262)),f317(f317(f91(f904(f903(f904(x102261,a893),f904(x102261,a893)),a893)),f310(x102261,x102263)),f317(f317(f299(f903(f904(x102261,a893),f904(x102261,a893))),f317(f317(f242(f904(x102261,a893),f904(x102261,a893)),f178(f904(x102261,a893))),f178(f904(x102261,a893)))),f178(f904(f903(f904(x102261,a893),f904(x102261,a893)),a893)))))),f310(x102261,x102262)))+~P1(f317(f317(f224(f904(f903(x102261,x102261),a893)),f317(f317(f279(x102261,x102261,x102261),x102262),x102263)),x102262))
% 94.68/94.44 [10227]P1(f317(f317(f224(f904(f903(f904(x102271,a893),f904(x102271,a893)),a893)),f317(f317(f279(f904(x102271,a893),f904(x102271,a893),f904(x102271,a893)),f308(x102271,x102272)),f317(f317(f91(f904(f903(f904(x102271,a893),f904(x102271,a893)),a893)),f308(x102271,x102273)),f317(f317(f299(f903(f904(x102271,a893),f904(x102271,a893))),f317(f317(f242(f904(x102271,a893),f904(x102271,a893)),f178(f904(x102271,a893))),f178(f904(x102271,a893)))),f178(f904(f903(f904(x102271,a893),f904(x102271,a893)),a893)))))),f308(x102271,x102272)))+~P1(f317(f317(f224(f904(f903(x102271,x102271),a893)),f317(f317(f279(x102271,x102271,x102271),x102272),x102273)),x102272))
% 94.68/94.44 [7388]~P1(f317(f317(f224(a897),x73882),x73881))+E(f317(f317(f23(a897),f317(a102,f317(f317(f23(a897),x73881),x73882))),x73883),f317(f317(f23(a897),f317(a102,x73881)),f317(f317(f74(a897),x73882),x73883)))
% 94.68/94.44 [7428]~P3(x74281)+E(f317(f317(f74(x74281),f40(x74281,x74282,x74283)),f317(f317(f75(x74281),f317(f317(f30(x74281),x74282),x74283)),x74283)),x74282)
% 94.68/94.44 [7626]E(f317(f317(f75(a897),f317(f94(a897),x76261)),f317(f317(f75(a897),f317(f94(a897),x76262)),x76263)),f317(f317(f75(a897),f317(f94(a897),f317(f317(f75(a1),x76261),x76262))),x76263))+P1(f317(f317(f225(a1),x76261),a77))
% 94.68/94.44 [8094]~P1(f317(f317(f224(a897),x80943),x80942))+P1(f317(f317(f224(a897),x80941),f317(f317(f23(a897),f317(f317(f74(a897),x80942),x80941)),x80943)))
% 94.68/94.44 [8294]~P1(f317(f317(f224(a897),x82941),x82942))+E(f317(f317(f124(a897),f129(a897,f317(f292(a897,x82941),x82942))),f129(a897,f317(f292(a897,x82942),f317(f317(f74(a897),x82942),x82943)))),f129(a897,f317(f292(a897,x82941),f317(f317(f74(a897),x82942),x82943))))
% 94.68/94.44 [8550]~P1(f317(f28(x85501),x85502))+E(f317(a102,f317(f29(x85501),f317(f317(f23(f904(x85501,a893)),x85502),f317(f317(f299(x85501),x85503),f178(f904(x85501,a893)))))),f317(f29(x85501),f317(f317(f299(x85501),x85503),x85502)))
% 94.68/94.44 [8589]~P1(f317(f28(x85891),x85892))+E(f317(f317(f74(a897),f72(a897)),f317(f29(x85891),f317(f317(f23(f904(x85891,a893)),x85892),f317(f317(f299(x85891),x85893),f178(f904(x85891,a893)))))),f317(f29(x85891),f317(f317(f299(x85891),x85893),x85892)))
% 94.68/94.44 [8778]E(f317(f317(f23(a897),f317(f29(x87781),x87782)),f317(f29(x87781),f317(f317(f92(f904(x87781,a893)),x87782),x87783))),f317(f29(x87781),f317(f317(f23(f904(x87781,a893)),x87782),x87783)))+~P1(f317(f28(x87781),f317(f317(f92(f904(x87781,a893)),x87782),x87783)))
% 94.68/94.44 [9029]~P6(f317(x90292,f878(x90292,x90293,x90291)))+E(f317(f90(a1),f317(f317(f9(x90291,a897),f317(f317(f8(a1,a897,x90291),a95),x90292)),x90293)),f317(f317(f9(x90291,a1),x90292),x90293))
% 94.68/94.44 [9030]~P6(f317(x90302,f412(x90302,x90303,x90301)))+E(f317(f90(a1),f317(f317(f6(x90301,a897),f317(f317(f8(a1,a897,x90301),a95),x90302)),x90303)),f317(f317(f6(x90301,a1),x90302),x90303))
% 94.68/94.44 [9070]~P1(f317(f28(x90701),x90703))+P1(f317(f317(f224(a897),f317(f317(f23(a897),f317(f29(x90701),x90702)),f317(f29(x90701),x90703))),f317(f29(x90701),f317(f317(f23(f904(x90701,a893)),x90702),x90703))))
% 94.68/94.44 [9097]P1(f317(f317(f319(x90971),f878(x90972,x90973,x90971)),x90973))+E(f317(f90(a1),f317(f317(f9(x90971,a897),f317(f317(f8(a1,a897,x90971),a95),x90972)),x90973)),f317(f317(f9(x90971,a1),x90972),x90973))
% 94.68/94.44 [9098]P1(f317(f317(f319(x90981),f412(x90982,x90983,x90981)),x90983))+E(f317(f90(a1),f317(f317(f6(x90981,a897),f317(f317(f8(a1,a897,x90981),a95),x90982)),x90983)),f317(f317(f6(x90981,a1),x90982),x90983))
% 94.68/94.44 [9162]E(f79(x91621,f317(f317(f7(x91621,f904(x91621,a893),a893),f319(x91621)),f317(f317(f23(f904(x91621,a893)),x91622),f317(f317(f299(x91621),x91623),f178(f904(x91621,a893)))))),f237(x91621,x91623,x91622))+P1(f317(f317(f224(f904(x91621,a893)),x91622),f317(f317(f299(x91621),x91623),f178(f904(x91621,a893)))))
% 94.68/94.44 [9519]E(f317(f317(f144(f898(x95191),x95191),f317(f317(f7(f898(x95191),a897,x95191),f154(x95191)),x95192)),f317(f126(f898(x95191),f317(f317(f8(a897,a893,f898(x95191)),f317(f225(a897),x95192)),f179(f898(x95191)))),x95193)),f317(f317(f154(f898(x95191)),f169(x95191,x95193)),x95192))+~P1(f317(f317(f225(a897),x95192),f317(f179(f898(f898(x95191))),f169(x95191,x95193))))
% 94.68/94.44 [9606]E(f317(f126(x96061,x96062),x96063),f167(x96061,x96062,x96063))+P1(f317(f317(f319(x96061),f700(x96063,x96062,x96061)),f317(f162(x96061),f317(f317(f128(x96061),f317(f179(f898(x96061)),f167(x96061,x96062,x96063))),x96063))))
% 94.68/94.44 [9745]E(f317(f317(f128(x97451),f317(f179(f898(x97451)),f167(x97451,x97452,x97453))),x97453),f103(x97451))+~P1(f317(x97452,f317(f131(x97451),f317(f317(f128(x97451),f317(f179(f898(x97451)),f167(x97451,x97452,x97453))),x97453))))
% 94.68/94.44 [9837]~P1(f317(f317(f319(f903(x98371,x98371)),x98372),f297(x98371,x98373)))+P1(f317(f317(f319(f903(x98371,x98371)),x98372),f317(f317(f34(a897,f904(f903(x98371,x98371),a893)),f232(f904(a897,a893))),f317(f317(f7(a897,f904(f903(x98371,x98371),a893),f904(f903(x98371,x98371),a893)),f173(f903(x98371,x98371),a893)),x98373))))
% 94.68/94.44 [9897]~P1(f317(f317(f224(f904(x98971,a893)),f317(f317(f34(a897,f904(x98971,a893)),f317(f292(a897,f2(a897)),f456(x98973,x98972,x98971))),x98972)),x98973))+P1(f317(f317(f224(f904(x98971,a893)),f317(f317(f34(a897,f904(x98971,a893)),f232(f904(a897,a893))),x98972)),x98973))
% 94.68/94.44 [9943]~P1(f317(f317(f225(a1),f2(a1)),x99433))+P1(f317(f317(f225(a1),x99431),f317(f317(f74(a1),x99432),f317(f317(f75(a1),f317(f317(f74(a1),f317(f70(a1),f317(f317(f23(a1),x99432),x99431))),f72(a1))),x99433))))
% 94.68/94.44 [9957]~P36(x99571,f317(f317(f91(f904(f903(x99571,x99571),a893)),x99572),x99573))+P36(x99571,f317(f317(f91(f904(f903(x99571,x99571),a893)),f317(f317(f91(f904(f903(x99571,x99571),a893)),f317(f317(f279(x99571,x99571,x99571),x99572),x99572)),f317(f317(f279(x99571,x99571,x99571),x99573),x99572))),x99573))
% 94.68/94.44 [10032]P36(x100321,f317(f317(f91(f904(f903(x100321,x100321),a893)),x100322),x100323))+~P36(x100321,f317(f317(f91(f904(f903(x100321,x100321),a893)),f317(f317(f91(f904(f903(x100321,x100321),a893)),f317(f317(f279(x100321,x100321,x100321),x100322),x100322)),f317(f317(f279(x100321,x100321,x100321),x100323),x100322))),x100323))
% 94.68/94.44 [9610]~P141(x96101)+E(f317(f93(x96101),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x96102),x96103)),f178(f904(f903(a897,a897),a893)))))),f317(f317(f23(x96101),f317(f90(x96101),x96102)),f317(f90(x96101),x96103)))
% 94.68/94.44 [9692]P1(f317(x96923,x96922))+E(f317(f252(x96921),f317(f317(f18(x96921,a893,a893),f317(f317(f8(a893,f904(a893,a893),x96921),a315),f317(f317(f7(x96921,x96921,a893),a314),x96922))),x96923)),f178(f904(x96921,a893)))
% 94.68/94.44 [9694]~P1(f317(x96943,x96942))+E(f317(f252(x96941),f317(f317(f18(x96941,a893,a893),f317(f317(f8(a893,f904(a893,a893),x96941),a315),f317(f317(f7(x96941,x96941,a893),a314),x96942))),x96943)),f317(f317(f299(x96941),x96942),f178(f904(x96941,a893))))
% 94.68/94.44 [9923]E(x99231,x99232)+P1(f317(f317(f233(x99233,x99233,f317(f317(f8(f904(x99233,a893),f904(x99233,a893),x99233),f317(f8(a893,a893,x99233),a312)),a314)),x99231),x99232))
% 94.68/94.44 [10012]~E(x100121,x100122)+~P1(f317(f317(f233(x100123,x100123,f317(f317(f8(f904(x100123,a893),f904(x100123,a893),x100123),f317(f8(a893,a893,x100123),a312)),a314)),x100121),x100122))
% 94.68/94.44 [10024]~P1(f317(f28(x100241),x100243))+E(f317(f317(f58(x100241,f904(x100241,a893),f317(f317(f8(f904(x100241,a893),f904(f904(x100241,a893),f904(x100241,a893)),x100241),f317(f7(f904(x100241,a893),f904(x100241,a893),f904(x100241,a893)),f23(f904(x100241,a893)))),f317(f317(f7(x100241,f904(x100241,a893),f904(x100241,a893)),f299(x100241)),f178(f904(x100241,a893))))),x100242),x100243),f317(f317(f23(f904(x100241,a893)),x100242),x100243))
% 94.68/94.44 [10054]~P1(f317(f317(f225(a1),f2(a1)),x100543))+P1(f317(f317(f225(a1),f317(f317(f23(a1),x100541),f317(f317(f75(a1),f317(f317(f74(a1),f317(f70(a1),f317(f317(f23(a1),x100541),x100542))),f72(a1))),x100543))),x100542))
% 94.68/94.44 [10316]~P1(f317(f317(f319(x103161),x103163),f306(x103161,x103162)))+P1(f317(f305(x103161,f317(f317(f7(x103161,f904(f903(x103161,x103161),a893),f904(x103161,a893)),f317(f317(f8(f904(x103161,f904(f904(f903(x103161,x103161),a893),a893)),f904(f904(f903(x103161,x103161),a893),f904(x103161,a893)),x103161),f7(x103161,f904(f903(x103161,x103161),a893),a893)),f317(f317(f8(f904(x103161,f903(x103161,x103161)),f904(x103161,f904(f904(f903(x103161,x103161),a893),a893)),x103161),f317(f8(f903(x103161,x103161),f904(f904(f903(x103161,x103161),a893),a893),x103161),f319(f903(x103161,x103161)))),f242(x103161,x103161)))),x103162)),x103163))
% 94.68/94.44 [10329]P1(f317(f317(f319(x103291),x103292),f306(x103291,x103293)))+~P1(f317(f305(x103291,f317(f317(f7(x103291,f904(f903(x103291,x103291),a893),f904(x103291,a893)),f317(f317(f8(f904(x103291,f904(f904(f903(x103291,x103291),a893),a893)),f904(f904(f903(x103291,x103291),a893),f904(x103291,a893)),x103291),f7(x103291,f904(f903(x103291,x103291),a893),a893)),f317(f317(f8(f904(x103291,f903(x103291,x103291)),f904(x103291,f904(f904(f903(x103291,x103291),a893),a893)),x103291),f317(f8(f903(x103291,x103291),f904(f904(f903(x103291,x103291),a893),a893),x103291),f319(f903(x103291,x103291)))),f242(x103291,x103291)))),x103293)),x103292))
% 94.68/94.44 [9895]~P1(f317(f28(x98951),f317(f252(x98951),x98953)))+P1(f317(f28(x98951),f317(f252(x98951),f317(f317(f18(x98951,a893,a893),f317(f317(f8(a893,f904(a893,a893),x98951),a315),x98952)),x98953))))
% 94.68/94.44 [9896]~P1(f317(f28(x98961),f317(f252(x98961),x98962)))+P1(f317(f28(x98961),f317(f252(x98961),f317(f317(f18(x98961,a893,a893),f317(f317(f8(a893,f904(a893,a893),x98961),a315),x98962)),x98963))))
% 94.68/94.44 [9991]P1(f317(f28(x99911),f317(f252(x99911),x99912)))+~P1(f317(f28(x99911),f317(f252(x99911),f317(f317(f18(x99911,a893,a893),f317(f317(f8(a893,f904(a893,a893),x99911),a316),x99913)),x99912))))
% 94.68/94.44 [9992]P1(f317(f28(x99921),f317(f252(x99921),x99922)))+~P1(f317(f28(x99921),f317(f252(x99921),f317(f317(f18(x99921,a893,a893),f317(f317(f8(a893,f904(a893,a893),x99921),a316),x99922)),x99923))))
% 94.68/94.44 [10295]~P1(f317(f28(x102951),x102952))+P1(f317(f28(f898(x102951)),f317(f252(f898(x102951)),f317(f317(f18(f898(x102951),a893,a893),f317(f317(f8(a893,f904(a893,a893),f898(x102951)),a315),f317(f317(f7(f898(x102951),f904(x102951,a893),a893),f317(f317(f8(f904(x102951,a893),f904(f904(x102951,a893),a893),f898(x102951)),f224(f904(x102951,a893))),f162(x102951))),x102952))),f317(f317(f7(f898(x102951),a897,a893),f317(f317(f8(a897,f904(a897,a893),f898(x102951)),a314),f179(f898(x102951)))),x102953)))))
% 94.68/94.44 [10296]~P1(f317(f28(x102961),x102962))+P1(f317(f28(f898(x102961)),f317(f252(f898(x102961)),f317(f317(f18(f898(x102961),a893,a893),f317(f317(f8(a893,f904(a893,a893),f898(x102961)),a315),f317(f317(f7(f898(x102961),f904(x102961,a893),a893),f317(f317(f8(f904(x102961,a893),f904(f904(x102961,a893),a893),f898(x102961)),f224(f904(x102961,a893))),f162(x102961))),x102962))),f317(f317(f7(f898(x102961),a897,a893),f317(f317(f8(a897,f904(a897,a893),f898(x102961)),f224(a897)),f179(f898(x102961)))),x102963)))))
% 94.68/94.44 [10005]~P112(x100051)+E(f317(f317(f234(x100051),x100052),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100053)),f317(f317(f75(x100051),f317(f317(f234(x100051),x100052),x100053)),f317(f317(f234(x100051),x100052),x100053)))
% 94.68/94.44 [10035]~P82(x100351)+E(f317(f317(f234(x100351),f317(f317(f234(x100351),x100352),x100353)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x100351),x100352),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100353)))
% 94.68/94.44 [10091]~P141(x100911)+E(f317(f317(f234(x100911),f317(f73(x100911),x100912)),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100913)),f317(f317(f234(x100911),x100912),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100913)))
% 94.68/94.44 [10234]~P111(x102341)+P1(f317(f317(f224(x102341),f2(x102341)),f317(f317(f74(x102341),f317(f317(f234(x102341),x102342),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102341),x102343),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))))
% 94.68/94.44 [10101]~P112(x101011)+E(f317(f317(f234(x101011),x101012),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101013))),f317(f317(f75(x101011),x101012),f317(f317(f75(x101011),f317(f317(f234(x101011),x101012),x101013)),f317(f317(f234(x101011),x101012),x101013))))
% 94.68/94.44 [10151]~P82(x101511)+E(f317(f317(f75(x101511),x101512),f317(f317(f234(x101511),f317(f317(f234(x101511),x101512),x101513)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101511),x101512),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101513))))
% 94.68/94.44 [10191]~P111(x101911)+P1(f317(f317(f224(x101911),f2(x101911)),f317(f317(f234(x101911),x101912),f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x101913))))
% 94.68/94.44 [10271]~P94(x102711)+E(f317(f317(f23(x102711),f317(f317(f74(x102711),f317(f317(f234(x102711),x102712),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102711),x102713),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(f317(f75(x102711),f317(f317(f75(x102711),f317(f94(x102711),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102712)),x102713)),f317(f317(f234(x102711),f317(f317(f23(x102711),x102712),x102713)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [10272]~P94(x102721)+E(f317(f317(f74(x102721),f317(f317(f74(x102721),f317(f317(f234(x102721),x102722),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102721),x102723),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(f317(f75(x102721),f317(f317(f75(x102721),f317(f94(x102721),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102722)),x102723)),f317(f317(f234(x102721),f317(f317(f74(x102721),x102722),x102723)),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.44 [7894]P24(x78941,x78942,x78943,x78944)+~E(f858(x78944,x78943,x78942,x78941),f872(x78944,x78943,x78942,x78941))
% 94.68/94.44 [8185]P33(x81851,x81852,x81853,x81854,f103(x81852))+~E(x81854,f103(x81851))
% 94.68/94.44 [8186]P33(x81861,x81862,x81863,f103(x81861),x81864)+~E(x81864,f103(x81862))
% 94.68/94.44 [8726]~P33(x87262,x87263,x87264,x87261,f103(x87263))+E(x87261,f103(x87262))
% 94.68/94.44 [8727]~P33(x87273,x87272,x87274,f103(x87273),x87271)+E(x87271,f103(x87272))
% 94.68/94.44 [5129]~P17(x51293,x51291,x51294)+E(f317(f317(x51291,x51292),x51292),x51292)
% 94.68/94.44 [5375]P1(f317(x53752,x53754))+E(f317(f126(x53751,x53752),f159(x53751,x53753,x53754)),f103(x53751))
% 94.68/94.44 [5413]~E(x54134,f178(f904(x54131,a893)))+E(f317(f300(x54131,x54132,x54133),x54134),f178(f904(x54132,a893)))
% 94.68/94.44 [5659]~P1(f317(x56592,x56594))+E(f317(f126(x56591,x56592),f159(x56591,x56593,x56594)),f159(x56591,x56593,x56594))
% 94.68/94.44 [5689]~E(f317(f300(x56892,x56893,x56894),x56891),f178(f904(x56893,a893)))+E(x56891,f178(f904(x56892,a893)))
% 94.68/94.44 [5876]~P7(x58761,x58763)+E(f261(x58761,x58762,f260(x58761,x58763),x58764),x58764)
% 94.68/94.44 [5992]~P66(x59922)+E(f317(f317(f138(x59921,x59922,x59923),x59924),f103(x59921)),f317(f317(f141(x59921),x59924),f103(x59921)))
% 94.68/94.44 [6360]~E(x63601,f178(f904(x63602,a893)))+~P1(f317(f56(x63602,x63603,x63601),x63604))
% 94.68/94.44 [6383]~P58(x63831,x63833,x63834,x63832)+P1(f317(f28(x63831),x63832))
% 94.68/94.44 [6385]~P58(x63851,x63853,x63852,x63854)+P1(f317(f28(x63851),x63852))
% 94.68/94.44 [6393]~P58(x63932,x63933,x63934,x63931)+~E(x63931,f178(f904(x63932,a893)))
% 94.68/94.44 [6427]~P108(x64271)+E(f317(f317(f92(f904(x64271,a893)),f317(f292(x64271,x64272),x64273)),f293(x64271,x64273,x64274)),f178(f904(x64271,a893)))
% 94.68/94.44 [6454]~P1(f317(f317(x64543,x64544),x64542))+P1(f317(f317(f319(x64541),x64542),f284(x64541,x64543,x64544)))
% 94.68/94.44 [6455]~P1(f317(f317(x64553,x64554),x64552))+P1(f317(f317(f319(x64551),x64552),f285(x64551,x64553,x64554)))
% 94.68/94.44 [6456]~P1(f317(f317(x64563,x64562),x64564))+P1(f317(f317(f319(x64561),x64562),f286(x64561,x64563,x64564)))
% 94.68/94.44 [6457]~P1(f317(f317(x64573,x64572),x64574))+P1(f317(f317(f319(x64571),x64572),f288(x64571,x64573,x64574)))
% 94.68/94.44 [6603]~P108(x66031)+E(f317(f317(f92(f904(x66031,a893)),f296(x66031,x66032,x66033)),f293(x66031,x66033,x66034)),f178(f904(x66031,a893)))
% 94.68/94.44 [6604]~P108(x66041)+E(f317(f317(f92(f904(x66041,a893)),f295(x66041,x66042,x66043)),f296(x66041,x66043,x66044)),f178(f904(x66041,a893)))
% 94.68/94.44 [6605]~P108(x66051)+E(f317(f317(f92(f904(x66051,a893)),f295(x66051,x66052,x66053)),f295(x66051,x66053,x66054)),f178(f904(x66051,a893)))
% 94.68/94.44 [6606]~P108(x66061)+E(f317(f317(f92(f904(x66061,a893)),f293(x66061,x66062,x66063)),f296(x66061,x66063,x66064)),f178(f904(x66061,a893)))
% 94.68/94.44 [6607]~P108(x66071)+E(f317(f317(f92(f904(x66071,a893)),f293(x66071,x66072,x66073)),f295(x66071,x66073,x66074)),f178(f904(x66071,a893)))
% 94.68/94.44 [6645]P1(f317(f317(x66451,x66452),f501(x66452,x66451)))+~P1(f317(f239(x66453,x66454,x66451),x66452))
% 94.68/94.44 [6727]~P66(x67272)+E(f317(f162(x67271),f140(x67271,x67272,x67273,x67274)),f317(f162(x67271),x67274))
% 94.68/94.44 [6779]~P144(x67791)+E(f180(x67791,x67792,f317(a102,x67793),x67794),f180(x67791,x67792,x67793,f317(x67792,x67794)))
% 94.68/94.44 [6843]~P1(f317(f317(f319(x68434),x68433),f284(x68434,x68431,x68432)))+P1(f317(f317(x68431,x68432),x68433))
% 94.68/94.44 [6844]~P1(f317(f317(f319(x68444),x68443),f285(x68444,x68441,x68442)))+P1(f317(f317(x68441,x68442),x68443))
% 94.68/94.44 [6845]~P1(f317(f317(f319(x68454),x68452),f286(x68454,x68451,x68453)))+P1(f317(f317(x68451,x68452),x68453))
% 94.68/94.44 [6846]~P1(f317(f317(f319(x68464),x68462),f288(x68464,x68461,x68463)))+P1(f317(f317(x68461,x68462),x68463))
% 94.68/94.44 [6923]E(f317(f29(f902(x69231,x69232)),f303(x69231,x69232,x69233,x69234)),f2(a897))+P1(f317(f28(x69232),x69234))
% 94.68/94.44 [6924]E(f317(f29(f902(x69241,x69242)),f303(x69241,x69242,x69243,x69244)),f2(a897))+P1(f317(f28(x69241),x69243))
% 94.68/94.44 [7132]~P14(x71324,x71321,x71322)+E(f317(f67(x71321,x71321,x71321,f317(x71322,x71323)),f317(x71322,x71323)),f317(x71322,x71323))
% 94.68/94.44 [7373]E(f267(x73731,x73732,x73733,x73734),f317(f242(f904(a89,f904(a893,f900(f899(x73731)))),f903(a89,a89)),f36(x73731)))+~P1(f317(f317(f224(a89),x73733),f2(a89)))
% 94.68/94.44 [8017]~E(x80172,x80173)+P1(f317(f317(f319(f903(x80171,x80171)),f317(f317(f242(x80171,x80171),x80172),x80173)),f297(x80171,x80174)))
% 94.68/94.44 [8046]~P24(x80461,x80462,x80463,f232(f904(x80461,a893)))+E(f317(f71(x80461,x80462,f232(f904(x80461,a893)),x80463),f317(x80463,x80464)),x80464)
% 94.68/94.44 [8047]~P24(x80471,x80472,x80473,f232(f904(x80471,a893)))+E(f317(f85(x80471,x80472,f232(f904(x80471,a893)),x80473),f317(x80473,x80474)),x80474)
% 94.68/94.44 [8134]~P1(f317(f317(f319(f898(x81341)),f317(f317(f141(x81341),x81344),x81342)),f151(x81341,x81343)))+P1(f317(f317(f319(f898(x81341)),x81342),f151(x81341,x81343)))
% 94.68/94.44 [8135]~P1(f317(f317(f319(f898(x81351)),f317(f317(f124(x81351),x81354),x81352)),f151(x81351,x81353)))+P1(f317(f317(f319(f898(x81351)),x81352),f151(x81351,x81353)))
% 94.68/94.44 [8136]~P1(f317(f317(f319(f898(x81361)),f317(f317(f124(x81361),x81362),x81364)),f151(x81361,x81363)))+P1(f317(f317(f319(f898(x81361)),x81362),f151(x81361,x81363)))
% 94.68/94.44 [8147]~P66(x81471)+P13(x81471,f317(f317(f144(x81472,x81471),x81473),f140(x81472,x81471,x81473,x81474)))
% 94.68/94.44 [8252]P24(x82524,x82523,x82521,x82522)+E(f317(x82521,f858(x82522,x82521,x82523,x82524)),f317(x82521,f872(x82522,x82521,x82523,x82524)))
% 94.68/94.44 [8359]~P24(x83592,x83591,x83594,x83593)+P24(x83591,x83592,f71(x83592,x83591,x83593,x83594),f317(f300(x83592,x83591,x83594),x83593))
% 94.68/94.44 [8499]P36(f903(x84992,x84994),f270(x84992,x84994,x84991,x84993))+P1(f317(x84991,f506(x84992,x84993,x84994,x84991)))
% 94.68/94.44 [8614]E(x86141,x86142)+~P1(f317(f317(f319(f903(x86143,x86143)),f317(f317(f242(x86143,x86143),x86141),x86142)),f253(x86143,x86144)))
% 94.68/94.44 [8678]~P1(f317(f28(f902(x86783,x86781)),f303(x86783,x86781,x86784,x86782)))+P1(f317(f28(x86781),x86782))
% 94.68/94.44 [8679]~P1(f317(f28(f902(x86791,x86793)),f303(x86791,x86793,x86792,x86794)))+P1(f317(f28(x86791),x86792))
% 94.68/94.44 [8688]~P24(x86881,x86882,x86883,x86884)+P25(x86881,x86882,x86883,x86884,f317(f300(x86881,x86882,x86883),x86884))
% 94.68/94.44 [8689]P11(x86891,x86892,x86893,x86894)+~E(f317(x86894,f811(x86892,x86894,x86893,x86891)),f317(x86894,f812(x86892,x86894,x86893,x86891)))
% 94.68/94.44 [8779]~P25(x87792,x87793,x87794,x87791,f178(f904(x87793,a893)))+E(x87791,f178(f904(x87792,a893)))
% 94.68/94.44 [8780]~P25(x87803,x87802,x87804,f178(f904(x87803,a893)),x87801)+E(x87801,f178(f904(x87802,a893)))
% 94.68/94.44 [8872]P36(f903(x88721,x88722),f270(x88721,x88722,x88723,x88724))+~P36(x88722,f317(x88724,f506(x88721,x88724,x88722,x88723)))
% 94.68/94.44 [9439]E(f317(f317(f149(x94391,x94392),f646(x94393,x94394,x94392,x94391)),f647(x94393,x94394,x94392,x94391)),x94394)+~P1(f317(f317(f319(f903(f898(x94391),f898(x94391))),f317(f317(f242(f898(x94391),f898(x94391)),x94392),x94394)),f147(x94391,x94393)))
% 94.68/94.44 [9444]~P1(f317(f317(f319(f903(f898(x94441),f898(x94441))),f317(f317(f242(f898(x94441),f898(x94441)),x94442),x94443)),f135(x94441,x94444)))+P1(f317(f317(f319(f903(f898(x94441),f898(x94441))),f317(f317(f242(f898(x94441),f898(x94441)),x94442),x94443)),f137(x94441,x94444)))
% 94.68/94.44 [9556]P1(f317(f28(x95561),x95562))+~P1(f317(f317(f319(f903(f904(x95561,a893),f904(x95561,a893))),f317(f317(f242(f904(x95561,a893),f904(x95561,a893)),x95563),x95562)),f308(x95561,x95564)))
% 94.68/94.44 [9557]P1(f317(f28(x95571),x95572))+~P1(f317(f317(f319(f903(f904(x95571,a893),f904(x95571,a893))),f317(f317(f242(f904(x95571,a893),f904(x95571,a893)),x95572),x95573)),f308(x95571,x95574)))
% 94.68/94.44 [9560]~E(x95601,f178(f904(x95602,a893)))+~P1(f317(f317(f319(f903(f904(x95602,a893),f904(x95602,a893))),f317(f317(f242(f904(x95602,a893),f904(x95602,a893)),x95603),x95601)),f308(x95602,x95604)))
% 94.68/94.44 [10202]P11(x102021,x102022,x102023,x102024)+~P1(f317(f317(f247(x102021,x102021,a893),f317(f317(f7(x102021,f904(x102021,x102022),f904(x102021,a893)),f317(f317(f8(f904(x102022,a893),f904(f904(x102021,x102022),f904(x102021,a893)),x102021),f8(x102022,a893,x102021)),f317(f317(f8(x102022,f904(x102022,a893),x102021),a314),x102024))),x102024)),f513(x102024,x102023,x102022,x102021)))
% 94.68/94.44 [5027]~E(x50272,f103(x50271))+E(f317(f317(f149(x50271,x50272),x50273),x50274),f103(x50271))
% 94.68/94.44 [5028]~E(x50284,f103(x50281))+E(f317(f317(f144(x50281,x50282),x50283),x50284),f103(x50282))
% 94.68/94.44 [5262]E(x52621,f103(x52622))+~E(f317(f317(f144(x52622,x52623),x52624),x52621),f103(x52623))
% 94.68/94.44 [5263]E(x52631,f103(x52632))+~E(f317(f317(f149(x52632,x52631),x52633),x52634),f103(x52632))
% 94.68/94.44 [5300]E(x53001,x53002)+~E(f317(f317(f124(x53003),x53004),x53001),f317(f317(f124(x53003),x53004),x53002))
% 94.68/94.44 [5301]E(x53011,x53012)+~E(f317(f317(f124(x53013),x53011),x53014),f317(f317(f124(x53013),x53012),x53014))
% 94.68/94.44 [5450]P1(f317(x54503,x54502))+E(f160(x54501,x54502,f317(f126(x54501,x54503),x54504)),f317(f126(x54501,x54503),x54504))
% 94.68/94.44 [5452]~P1(f317(x54522,x54523))+P32(x54521,x54522,f317(f317(f141(x54521),x54523),x54524))
% 94.68/94.44 [5462]E(x54621,x54622)+~E(f129(a897,f317(f292(a897,x54621),x54623)),f317(f317(f141(a897),x54622),x54624))
% 94.68/94.44 [5511]~P26(x55112,x55113)+P26(x55111,f317(f317(f68(x55112,x55111),x55113),x55114))
% 94.68/94.44 [5512]~P36(x55122,x55123)+P36(x55121,f317(f317(f278(x55122,x55121),x55123),x55124))
% 94.68/94.44 [5513]~P37(x55132,x55133)+P37(x55131,f317(f317(f278(x55132,x55131),x55133),x55134))
% 94.68/94.44 [5514]~P51(x55142,x55143)+P51(x55141,f317(f317(f278(x55142,x55141),x55143),x55144))
% 94.68/94.44 [5643]~P32(x56431,x56432,x56434)+P32(x56431,x56432,f317(f317(f141(x56431),x56433),x56434))
% 94.68/94.44 [5644]~P32(x56441,x56442,x56444)+P32(x56441,x56442,f317(f317(f124(x56441),x56443),x56444))
% 94.68/94.44 [5645]~P32(x56451,x56452,x56453)+P32(x56451,x56452,f317(f317(f124(x56451),x56453),x56454))
% 94.68/94.44 [5732]~E(x57321,f103(x57322))+~E(f317(f317(f124(x57322),x57323),f317(f317(f141(x57322),x57324),f103(x57322))),x57321)
% 94.68/94.44 [5757]~P30(x57573,x57571,f317(f317(f141(x57573),x57572),x57574))+P1(f317(x57571,x57572))
% 94.68/94.44 [5767]E(f104(x57671,x57672),x57673)+~E(f317(f317(f124(x57671),x57673),f317(f317(f141(x57671),x57674),f103(x57671))),x57672)
% 94.68/94.44 [5768]E(f134(x57681,x57682),x57683)+~E(f317(f317(f124(x57681),x57684),f317(f317(f141(x57681),x57683),f103(x57681))),x57682)
% 94.68/94.44 [5878]~E(f129(a897,f317(f292(a897,x58781),x58782)),f317(f317(f141(a897),x58783),x58784))+P1(f317(f317(f225(a897),x58781),x58782))
% 94.68/94.44 [5896]P30(x58961,x58962,x58963)+~P30(x58961,x58962,f317(f317(f141(x58961),x58964),x58963))
% 94.68/94.44 [5897]P30(x58971,x58972,x58973)+~P30(x58971,x58972,f317(f317(f124(x58971),x58974),x58973))
% 94.68/94.44 [5898]P30(x58981,x58982,x58983)+~P30(x58981,x58982,f317(f317(f124(x58981),x58983),x58984))
% 94.68/94.44 [6097]E(x60971,f317(f317(f124(x60972),f317(f158(x60972),x60973)),f317(f317(f141(x60972),x60974),f103(x60972))))+~E(f317(f158(x60972),x60971),f317(f317(f141(x60972),x60974),x60973))
% 94.68/94.44 [6279]~P108(x62791)+E(f317(f317(f92(f904(x62791,a893)),f317(f292(x62791,x62792),x62793)),f317(f292(x62791,x62793),x62794)),f178(f904(x62791,a893)))
% 94.68/94.44 [6290]E(f317(f317(f154(x62901),f159(x62901,x62902,x62903)),x62904),x62903)+~P1(f317(f317(f225(a897),x62904),x62902))
% 94.68/94.44 [6317]~P76(x63171)+E(f317(f155(x63171),f317(f317(f144(a1,x63171),x63172),f168(x63173,x63174))),f317(f317(f6(a1,x63171),x63172),f317(f162(a1),f168(x63173,x63174))))
% 94.68/94.44 [6318]~P76(x63181)+E(f317(f317(f6(a1,x63181),x63182),f317(f162(a1),f168(x63183,x63184))),f317(f155(x63181),f317(f317(f144(a1,x63181),x63182),f168(x63183,x63184))))
% 94.68/94.44 [6467]~E(x64672,f317(f317(f124(x64671),f317(f158(x64671),x64674)),f317(f317(f141(x64671),x64673),f103(x64671))))+E(f317(f158(x64671),x64672),f317(f317(f141(x64671),x64673),x64674))
% 94.68/94.44 [6483]~P19(x64832,x64833,x64834,x64831)+E(f317(x64831,f178(f904(x64832,a893))),f25(x64833))
% 94.68/94.44 [6511]~P108(x65111)+E(f317(f317(f92(f904(x65111,a893)),f296(x65111,x65112,x65113)),f317(f292(x65111,x65113),x65114)),f178(f904(x65111,a893)))
% 94.68/94.44 [6730]E(x67301,f178(f904(x67302,a893)))+~E(f303(x67303,x67302,x67304,x67301),f178(f904(f902(x67303,x67302),a893)))
% 94.68/94.44 [6731]E(x67311,f178(f904(x67312,a893)))+~E(f303(x67312,x67313,x67311,x67314),f178(f904(f902(x67312,x67313),a893)))
% 94.68/94.44 [6800]~P66(x68002)+E(f317(f179(f898(x68001)),f140(x68001,x68002,x68003,x68004)),f317(f179(f898(x68001)),x68004))
% 94.68/94.44 [6811]~P1(f317(f240(x68113,x68114,x68111),x68112))+P1(f317(f317(x68111,f490(x68112,x68111)),x68112))
% 94.68/94.44 [6857]~P1(f317(f28(x68572),x68574))+P1(f317(f28(x68571),f317(f300(x68572,x68571,x68573),x68574)))
% 94.68/94.44 [7093]~P24(x70932,x70931,x70933,x70934)+E(f317(f29(x70931),f317(f300(x70932,x70931,x70933),x70934)),f317(f29(x70932),x70934))
% 94.68/94.44 [7111]E(f317(f300(x71111,x71112,x71113),f317(f301(x71111,x71112,x71113),x71114)),x71114)+~E(f317(f300(x71111,x71112,x71113),f232(f904(x71111,a893))),f232(f904(x71112,a893)))
% 94.68/94.44 [7527]~P24(x75271,x75272,x75273,f232(f904(x75271,a893)))+E(f317(f301(x75271,x75272,x75273),f317(f300(x75271,x75272,x75273),x75274)),x75274)
% 94.68/94.44 [7811]E(x78111,x78112)+~P1(f317(f317(f319(x78113),x78111),f317(f162(x78113),f159(x78113,x78114,x78112))))
% 94.68/94.44 [7820]~E(x78201,f2(a897))+~P1(f317(f317(f319(x78202),x78203),f317(f162(x78202),f159(x78202,x78201,x78204))))
% 94.68/94.44 [7853]P1(f317(x78531,x78532))+~P1(f317(f317(f319(x78533),x78532),f317(f162(x78533),f167(x78533,x78531,x78534))))
% 94.68/94.44 [7963]~P1(f317(f317(f319(f898(x79631)),f317(f317(f141(x79631),x79632),x79634)),f151(x79631,x79633)))+P1(f317(f317(f319(x79631),x79632),x79633))
% 94.68/94.44 [8091]~P1(f317(f317(f319(x80911),x80912),f317(f162(x80911),f166(x80911,x80913,x80914))))+P1(f317(f317(f319(x80911),x80912),f317(f162(x80911),x80913)))
% 94.68/94.44 [8092]~P1(f317(f317(f319(x80921),x80922),f317(f162(x80921),f160(x80921,x80924,x80923))))+P1(f317(f317(f319(x80921),x80922),f317(f162(x80921),x80923)))
% 94.68/94.44 [8093]~P1(f317(f317(f319(x80931),x80932),f317(f162(x80931),f167(x80931,x80934,x80933))))+P1(f317(f317(f319(x80931),x80932),f317(f162(x80931),x80933)))
% 94.68/94.44 [8103]E(f317(f179(f898(x81031)),x81032),x81033)+~P1(f317(f317(f319(f898(x81031)),x81032),f317(f162(f898(x81031)),f50(x81031,x81033,x81034))))
% 94.68/94.44 [8198]P1(f317(x81983,x81982))+E(f317(f126(x81981,f317(f317(f8(a893,a893,x81981),a312),f317(a314,x81982))),f317(f126(x81981,x81983),x81984)),f317(f126(x81981,x81983),x81984))
% 94.68/94.44 [8310]E(f317(f317(f154(x83101),f167(x83101,x83102,x83103)),x83104),f317(f317(f154(x83101),x83103),x83104))+~P1(f317(f317(f225(a897),x83104),f317(f179(f898(x83101)),f167(x83101,x83102,x83103))))
% 94.68/94.44 [8397]~P76(x83971)+E(f317(f317(f6(a897,x83971),f317(f317(f8(a897,x83971,a897),x83972),a102)),f317(f292(a897,x83973),x83974)),f317(f317(f6(a897,x83971),x83972),f317(f292(a897,f317(a102,x83973)),f317(a102,x83974))))
% 94.68/94.44 [8406]~P76(x84061)+E(f317(f317(f6(a897,x84061),f317(f317(f8(a897,x84061,a897),x84062),a102)),f293(a897,x84063,x84064)),f317(f317(f6(a897,x84061),x84062),f293(a897,f317(a102,x84063),f317(a102,x84064))))
% 94.68/94.44 [8535]~P24(x85351,x85353,x85354,f232(f904(x85351,a893)))+P24(x85351,f904(x85352,x85353),f317(f317(f8(x85353,f904(x85352,x85353),x85351),f16(x85353,x85352)),x85354),f232(f904(x85351,a893)))
% 94.68/94.44 [8620]~P24(x86202,x86201,x86204,x86203)+E(f317(f300(x86201,x86202,f71(x86202,x86201,x86203,x86204)),f317(f300(x86202,x86201,x86204),x86203)),x86203)
% 94.68/94.44 [8680]~P1(f317(f317(f319(f903(x86801,x86801)),f317(f317(f242(x86801,x86801),x86802),x86804)),f253(x86801,x86803)))+P1(f317(f317(f319(x86801),x86802),x86803))
% 94.68/94.44 [8803]~P24(x88032,x88031,x88033,f232(f904(x88032,a893)))+E(f317(f300(x88031,x88032,f85(x88032,x88031,f232(f904(x88032,a893)),x88033)),f317(f300(x88032,x88031,x88033),x88034)),x88034)
% 94.68/94.44 [8878]~P25(x88781,x88782,x88783,x88784,f232(f904(x88782,a893)))+E(f317(f300(x88781,x88782,x88783),f232(f904(x88781,a893))),f232(f904(x88782,a893)))
% 94.68/94.44 [8911]~E(f317(f317(f6(x89111,a897),x89114),x89113),f317(a102,x89112))+P1(f317(f317(f319(x89111),f523(x89112,x89113,x89114,x89111)),x89113))
% 94.68/94.44 [8932]~E(f317(f317(f6(x89324,a897),x89321),x89323),f317(a102,x89322))+P1(f317(f317(f225(a897),f2(a897)),f317(x89321,f523(x89322,x89323,x89321,x89324))))
% 94.68/94.44 [8943]~P1(f317(f28(x89432),x89434))+P1(f317(f317(f224(a897),f317(f29(x89431),f317(f300(x89432,x89431,x89433),x89434))),f317(f29(x89432),x89434)))
% 94.68/94.44 [8944]E(f317(f317(f242(x89441,x89442),f619(x89443,x89444,x89442,x89441)),f620(x89443,x89444,x89442,x89441)),x89444)+~P1(f317(f317(f319(f903(x89441,x89442)),x89444),f317(f276(x89442,x89441),x89443)))
% 94.68/94.44 [8952]P24(x89521,x89522,x89523,x89524)+P1(f317(f317(f319(x89521),f858(x89524,x89523,x89522,x89521)),x89524))
% 94.68/94.44 [8953]P24(x89531,x89532,x89533,x89534)+P1(f317(f317(f319(x89531),f872(x89534,x89533,x89532,x89531)),x89534))
% 94.68/94.44 [9021]P11(x90211,x90212,x90213,x90214)+P1(f317(f317(f319(f903(x90211,x90211)),f513(x90214,x90213,x90212,x90211)),x90213))
% 94.68/94.44 [9075]P1(f317(x90751,x90752))+~P1(f317(x90751,f317(f317(f242(x90753,x90754),f880(x90754,x90753,x90751)),f881(x90754,x90753,x90751))))
% 94.68/94.44 [9092]E(f317(f179(f898(x90921)),x90922),f317(f179(f898(x90921)),x90923))+~P1(f317(f317(f319(f903(f898(x90921),f898(x90921))),f317(f317(f242(f898(x90921),f898(x90921)),x90922),x90923)),f135(x90921,x90924)))
% 94.68/94.44 [9093]E(f317(f179(f898(x90931)),x90932),f317(f179(f898(x90931)),x90933))+~P1(f317(f317(f319(f903(f898(x90931),f898(x90931))),f317(f317(f242(f898(x90931),f898(x90931)),x90932),x90933)),f147(x90931,x90934)))
% 94.68/94.44 [9096]E(f317(f179(f898(x90961)),x90962),f317(f179(f898(x90961)),x90963))+~P1(f317(f317(f319(f903(f898(x90961),f898(x90961))),f317(f317(f242(f898(x90961),f898(x90961)),x90962),x90963)),f148(x90961,x90964)))
% 94.68/94.44 [9166]P1(f317(f317(f224(a897),f145(x91661,x91662,x91663)),f145(x91661,x91664,x91663)))+P1(f317(f317(f319(x91661),f645(x91664,x91662,x91663,x91661)),f317(f162(x91661),x91663)))
% 94.68/94.44 [9169]E(f317(f179(f898(x91691)),x91692),f317(f179(f898(x91691)),x91693))+~P1(f317(f317(f319(f903(f898(x91691),f898(x91691))),f317(f317(f242(f898(x91691),f898(x91691)),x91692),x91693)),f297(f898(x91691),f147(x91691,x91694))))
% 94.68/94.44 [9287]P1(f317(f317(f277(a897),x92871),x92872))+P1(f317(f317(f224(f904(a897,a893)),f280(a897,f277(a897),x92871,x92872)),f280(a897,f277(a897),x92873,x92874)))
% 94.68/94.44 [9410]~P24(x94101,x94102,x94103,x94104)+~P1(f317(f317(f225(a897),f317(f29(x94102),f317(f300(x94101,x94102,x94103),x94104))),f317(f29(x94101),x94104)))
% 94.68/94.44 [9457]~P1(f317(f317(f319(f903(f898(x94571),f898(x94571))),f317(f317(f242(f898(x94571),f898(x94571)),x94572),x94573)),f147(x94571,x94574)))+P1(f317(f317(f319(f903(f898(x94571),f898(x94571))),f317(f317(f242(f898(x94571),f898(x94571)),x94572),x94573)),f148(x94571,f297(x94571,x94574))))
% 94.68/94.44 [9461]~P1(f317(f317(f319(f903(f898(x94611),f898(x94611))),f317(f317(f242(f898(x94611),f898(x94611)),x94612),x94613)),f148(x94611,x94614)))+P1(f317(f317(f319(f903(f898(x94611),f898(x94611))),f317(f317(f242(f898(x94611),f898(x94611)),x94612),x94613)),f297(f898(x94611),f147(x94611,x94614))))
% 94.68/94.44 [9477]P1(f317(f317(f319(f903(x94771,x94771)),f317(f317(f242(x94771,x94771),x94772),x94773)),f297(x94771,x94774)))+~P1(f317(f317(f319(f903(x94771,x94771)),f317(f317(f242(x94771,x94771),x94772),x94773)),f317(f317(f279(x94771,x94771,x94771),x94774),f297(x94771,x94774))))
% 94.68/94.44 [9551]P1(f317(f317(f277(a897),x95511),x95512))+~P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x95513,x95514)),f280(a897,f277(a897),x95511,x95512)))
% 94.68/94.44 [9673]E(f317(f317(f124(x96731),f662(x96732,x96733,x96734,x96731)),f317(f317(f141(x96731),f663(x96732,x96733,x96734,x96731)),f665(x96732,x96733,x96734,x96731))),x96734)+~P1(f317(f317(f319(f903(f898(x96731),f898(x96731))),f317(f317(f242(f898(x96731),f898(x96731)),x96734),x96733)),f147(x96731,x96732)))
% 94.68/94.44 [9674]E(f317(f317(f124(x96741),f662(x96742,x96743,x96744,x96741)),f317(f317(f141(x96741),f664(x96742,x96743,x96744,x96741)),f665(x96742,x96743,x96744,x96741))),x96743)+~P1(f317(f317(f319(f903(f898(x96741),f898(x96741))),f317(f317(f242(f898(x96741),f898(x96741)),x96744),x96743)),f147(x96741,x96742)))
% 94.68/94.44 [9752]P1(f317(f317(f319(f903(x97521,x97521)),f317(f317(f242(x97521,x97521),x97522),f576(x97523,x97524,x97522,x97521))),f297(x97521,x97523)))+~P1(f317(f317(f319(f903(x97521,x97521)),f317(f317(f242(x97521,x97521),x97522),x97524)),f317(f317(f279(x97521,x97521,x97521),x97523),f297(x97521,x97523))))
% 94.68/94.44 [9820]P1(f317(f317(f224(a897),f145(x98201,x98202,x98203)),f145(x98201,x98204,x98203)))+~P1(f317(f317(f225(a897),f317(x98202,f645(x98204,x98202,x98203,x98201))),f317(x98204,f645(x98204,x98202,x98203,x98201))))
% 94.68/94.44 [9891]P1(f317(f317(f319(f903(x98911,x98911)),f317(f317(f242(x98911,x98911),f569(x98912,x98913,x98914,x98911)),x98913)),f297(x98911,x98912)))+~P1(f317(f317(f319(f903(x98911,x98911)),f317(f317(f242(x98911,x98911),x98914),x98913)),f317(f317(f279(x98911,x98911,x98911),x98912),f297(x98911,x98912))))
% 94.68/94.44 [5281]~E(x52812,x52813)+E(f160(x52811,x52812,f317(f317(f141(x52811),x52813),x52814)),x52814)
% 94.68/94.44 [5406]P1(f317(x54062,x54063))+E(f167(x54061,x54062,f317(f317(f141(x54061),x54063),x54064)),f103(x54061))
% 94.68/94.44 [5474]~P90(x54742)+E(f317(f317(f73(f904(x54741,x54742)),x54743),x54744),f317(f73(x54742),f317(x54743,x54744)))
% 94.68/94.44 [5487]~E(x54872,f2(a897))+E(f317(f317(f128(x54871),x54872),f317(f317(f141(x54871),x54873),x54874)),f317(f317(f141(x54871),x54873),x54874))
% 94.68/94.44 [5488]P1(f317(x54882,x54883))+E(f317(f126(x54881,x54882),f317(f317(f141(x54881),x54883),x54884)),f317(f126(x54881,x54882),x54884))
% 94.68/94.44 [5626]~E(x56262,x56264)+P1(f317(f317(f317(f299(x56261),x56262),x56263),x56264))
% 94.68/94.44 [5634]E(x56341,f103(x56342))+E(f134(x56343,f317(f317(f144(x56342,x56343),x56344),x56341)),f317(x56344,f134(x56342,x56341)))
% 94.68/94.44 [5648]~E(x56481,f57(x56482,x56484))+E(f317(x56481,f317(f317(f299(x56482),x56483),f178(f904(x56482,a893)))),x56483)
% 94.68/94.44 [5684]E(x56841,f103(x56842))+E(f317(f131(x56843),f317(f317(f144(x56842,x56843),x56844),x56841)),f317(x56844,f317(f131(x56842),x56841)))
% 94.68/94.44 [5787]~P1(f317(x57873,x57874))+P1(f317(f317(f317(f299(x57871),x57872),x57873),x57874))
% 94.68/94.44 [5915]~P18(x59152,x59154,x59151)+E(f317(x59151,f317(f317(f299(x59152),x59153),f178(f904(x59152,a893)))),x59153)
% 94.68/94.44 [5941]~E(x59412,x59413)+P1(f317(f317(f319(x59411),x59412),f317(f317(f299(x59411),x59413),x59414)))
% 94.68/94.44 [5946]~P112(x59461)+E(f317(f317(f74(x59461),x59462),f317(f317(f74(x59461),x59463),x59464)),f317(f317(f74(x59461),x59463),f317(f317(f74(x59461),x59462),x59464)))
% 94.68/94.44 [5947]~P112(x59471)+E(f317(f317(f75(x59471),x59472),f317(f317(f75(x59471),x59473),x59474)),f317(f317(f75(x59471),x59473),f317(f317(f75(x59471),x59472),x59474)))
% 94.68/94.44 [5949]~P66(x59491)+E(f317(f317(f228(x59491),x59492),f317(f317(f228(x59491),x59493),x59494)),f317(f317(f228(x59491),x59493),f317(f317(f228(x59491),x59492),x59494)))
% 94.68/94.44 [5951]~P66(x59511)+E(f317(f317(f223(x59511),x59512),f317(f317(f223(x59511),x59513),x59514)),f317(f317(f223(x59511),x59513),f317(f317(f223(x59511),x59512),x59514)))
% 94.68/94.44 [5953]~P99(x59531)+E(f317(f317(f91(x59531),x59532),f317(f317(f91(x59531),x59533),x59534)),f317(f317(f91(x59531),x59533),f317(f317(f91(x59531),x59532),x59534)))
% 94.68/94.44 [5954]~P100(x59541)+E(f317(f317(f91(x59541),x59542),f317(f317(f91(x59541),x59543),x59544)),f317(f317(f91(x59541),x59543),f317(f317(f91(x59541),x59542),x59544)))
% 94.68/94.44 [5955]~P100(x59551)+E(f317(f317(f92(x59551),x59552),f317(f317(f92(x59551),x59553),x59554)),f317(f317(f92(x59551),x59553),f317(f317(f92(x59551),x59552),x59554)))
% 94.68/94.44 [5957]~P105(x59571)+E(f317(f317(f92(x59571),x59572),f317(f317(f92(x59571),x59573),x59574)),f317(f317(f92(x59571),x59573),f317(f317(f92(x59571),x59572),x59574)))
% 94.68/94.44 [5964]E(x59641,x59642)+E(f160(x59643,x59641,f317(f317(f141(x59643),x59642),x59644)),f317(f317(f141(x59643),x59642),f160(x59643,x59641,x59644)))
% 94.68/94.44 [5979]~P1(f317(x59792,x59793))+E(f317(f126(x59791,x59792),f317(f317(f141(x59791),x59793),x59794)),f317(f317(f141(x59791),x59793),f317(f126(x59791,x59792),x59794)))
% 94.68/94.44 [6119]~P1(f317(x61192,x61193))+E(f167(x61191,x61192,f317(f317(f141(x61191),x61193),x61194)),f317(f317(f141(x61191),x61193),f167(x61191,x61192,x61194)))
% 94.68/94.44 [6183]E(x61831,f178(f904(x61832,a893)))+E(f317(f317(f34(x61832,f904(x61833,a893)),x61831),f317(f16(f904(x61833,a893),x61832),x61834)),x61834)
% 94.68/94.44 [6184]E(x61841,f178(f904(x61842,a893)))+E(f317(f317(f35(x61842,f904(x61843,a893)),x61841),f317(f16(f904(x61843,a893),x61842),x61844)),x61844)
% 94.68/94.44 [6193]~E(x61934,f178(f904(x61932,a893)))+E(f317(f317(f244(x61931,x61932),x61933),f317(f16(f904(x61932,a893),x61931),x61934)),f178(f904(f903(x61931,x61932),a893)))
% 94.68/94.44 [6194]~E(x61943,f178(f904(x61941,a893)))+E(f317(f317(f244(x61941,x61942),x61943),f317(f16(f904(x61942,a893),x61941),x61944)),f178(f904(f903(x61941,x61942),a893)))
% 94.68/94.44 [6250]E(x62501,f2(a897))+E(f317(f317(f128(x62502),x62501),f317(f317(f141(x62502),x62503),x62504)),f317(f317(f128(x62502),f317(f317(f23(a897),x62501),f72(a897))),x62504))
% 94.68/94.44 [6271]E(x62711,f178(f904(x62712,a893)))+E(f317(f300(x62712,x62713,f317(f16(x62713,x62712),x62714)),x62711),f317(f317(f299(x62713),x62714),f178(f904(x62713,a893))))
% 94.68/94.44 [6274]E(f317(f301(x62741,x62742,f317(f16(x62742,x62741),x62743)),x62744),f178(f904(x62741,a893)))+P1(f317(f317(f319(x62742),x62743),x62744))
% 94.68/94.44 [6343]~E(x63433,f178(f904(x63431,a893)))+E(f317(f317(f34(x63431,f904(x63432,a893)),x63433),f317(f16(f904(x63432,a893),x63431),x63434)),f178(f904(x63432,a893)))
% 94.68/94.44 [6344]~E(x63443,f178(f904(x63441,a893)))+E(f317(f317(f35(x63441,f904(x63442,a893)),x63443),f317(f16(f904(x63442,a893),x63441),x63444)),f232(f904(x63442,a893)))
% 94.68/94.44 [6346]~P3(x63461)+E(f40(x63461,f317(f317(f75(x63461),x63462),x63463),f317(f317(f75(x63461),x63462),x63464)),f317(f317(f75(x63461),x63462),f40(x63461,x63463,x63464)))
% 94.68/94.44 [6521]E(f317(f301(x65211,x65212,f317(f16(x65212,x65211),x65213)),x65214),f232(f904(x65211,a893)))+~P1(f317(f317(f319(x65212),x65213),x65214))
% 94.68/94.44 [6544]~P1(f317(f317(f319(x65441),x65442),x65444))+P1(f317(f317(f319(x65441),x65442),f317(f317(f299(x65441),x65443),x65444)))
% 94.68/94.44 [6549]P1(f317(x65491,x65492))+~P1(f317(f150(x65493,x65491),f317(f317(f141(x65493),x65492),x65494)))
% 94.68/94.44 [6558]~E(x65583,f317(f317(f23(a897),f317(f179(f898(x65581)),x65582)),f72(a897)))+E(f104(x65581,f317(f317(f149(x65581,x65582),x65583),x65584)),f104(x65581,x65582))
% 94.68/94.44 [6581]~P66(x65811)+E(f317(f317(f92(f904(x65811,a893)),f317(f291(x65811),x65812)),f293(x65811,x65813,x65814)),f293(x65811,x65813,f317(f317(f228(x65811),x65812),x65814)))
% 94.68/94.44 [6582]~P66(x65821)+E(f317(f317(f92(f904(x65821,a893)),f317(f273(x65821),x65822)),f293(x65821,x65823,x65824)),f293(x65821,f317(f317(f223(x65821),x65822),x65823),x65824))
% 94.68/94.44 [6598]E(f317(f317(f92(f904(x65981,a893)),x65982),f317(f317(f299(x65981),x65983),x65984)),f317(f317(f92(f904(x65981,a893)),x65982),x65984))+P1(f317(f317(f319(x65981),x65983),x65982))
% 94.68/94.44 [6610]E(f160(x66101,x66102,f317(f317(f124(x66101),x66103),x66104)),f317(f317(f124(x66101),x66103),f160(x66101,x66102,x66104)))+P1(f317(f317(f319(x66101),x66102),f317(f162(x66101),x66103)))
% 94.68/94.44 [6615]~P82(x66151)+E(f317(f317(f75(x66151),f317(f317(f234(x66151),x66152),x66153)),f317(f317(f234(x66151),x66152),x66154)),f317(f317(f234(x66151),x66152),f317(f317(f74(a897),x66153),x66154)))
% 94.68/94.44 [6616]~P112(x66161)+E(f317(f317(f75(x66161),f317(f317(f234(x66161),x66162),x66163)),f317(f317(f234(x66161),x66162),x66164)),f317(f317(f234(x66161),x66162),f317(f317(f74(a897),x66163),x66164)))
% 94.68/94.44 [6653]~P112(x66531)+E(f317(f317(f74(x66531),f317(f317(f75(x66531),x66532),x66533)),f317(f317(f75(x66531),x66532),x66534)),f317(f317(f75(x66531),x66532),f317(f317(f74(x66531),x66533),x66534)))
% 94.68/94.44 [6654]~P66(x66541)+E(f317(f317(f223(x66541),f317(f317(f228(x66541),x66542),x66543)),f317(f317(f228(x66541),x66542),x66544)),f317(f317(f228(x66541),x66542),f317(f317(f223(x66541),x66543),x66544)))
% 94.68/94.44 [6655]~P66(x66551)+E(f317(f317(f228(x66551),f317(f317(f223(x66551),x66552),x66553)),f317(f317(f223(x66551),x66552),x66554)),f317(f317(f223(x66551),x66552),f317(f317(f228(x66551),x66553),x66554)))
% 94.68/94.44 [6656]~P103(x66561)+E(f317(f317(f92(x66561),f317(f317(f91(x66561),x66562),x66563)),f317(f317(f91(x66561),x66562),x66564)),f317(f317(f91(x66561),x66562),f317(f317(f92(x66561),x66563),x66564)))
% 94.68/94.44 [6657]~P103(x66571)+E(f317(f317(f91(x66571),f317(f317(f92(x66571),x66572),x66573)),f317(f317(f92(x66571),x66572),x66574)),f317(f317(f92(x66571),x66572),f317(f317(f91(x66571),x66573),x66574)))
% 94.68/94.44 [6691]~P3(x66911)+E(f40(x66911,f317(f317(f75(x66911),x66912),x66913),f317(f317(f75(x66911),x66914),x66913)),f317(f317(f75(x66911),f40(x66911,x66912,x66914)),x66913))
% 94.68/94.44 [6694]~E(f317(f179(f898(x66941)),x66943),f317(f179(f898(x66942)),x66944))+E(f317(f317(f144(f903(x66941,x66942),x66942),f246(x66941,x66942)),f317(f317(f171(x66941,x66942),x66943),x66944)),x66944)
% 94.68/94.44 [6695]~E(f317(f179(f898(x66951)),x66953),f317(f179(f898(x66952)),x66954))+E(f317(f317(f144(f903(x66951,x66952),x66951),f241(x66951,x66952)),f317(f317(f171(x66951,x66952),x66953),x66954)),x66953)
% 94.68/94.44 [6700]P1(f317(f150(x67001,x67002),x67003))+~P1(f317(f150(x67001,x67002),f317(f317(f141(x67001),x67004),x67003)))
% 94.68/94.44 [6701]P1(f317(f150(x67011,x67012),x67013))+~P1(f317(f150(x67011,x67012),f317(f317(f124(x67011),x67014),x67013)))
% 94.68/94.44 [6702]P1(f317(f150(x67021,x67022),x67023))+~P1(f317(f150(x67021,x67022),f317(f317(f124(x67021),x67023),x67024)))
% 94.68/94.44 [6707]~P4(x67071)+E(f40(x67071,f317(f317(f23(x67071),x67072),f40(x67071,x67073,x67074)),x67074),f40(x67071,f317(f317(f23(x67071),x67072),x67073),x67074))
% 94.68/94.44 [6709]~P3(x67091)+E(f40(x67091,f317(f317(f75(x67091),x67092),f40(x67091,x67093,x67094)),x67094),f40(x67091,f317(f317(f75(x67091),x67092),x67093),x67094))
% 94.68/94.44 [6710]~P3(x67101)+E(f40(x67101,f317(f317(f74(x67101),x67102),f40(x67101,x67103,x67104)),x67104),f40(x67101,f317(f317(f74(x67101),x67102),x67103),x67104))
% 94.68/94.44 [6792]~P66(x67921)+E(f317(f317(f92(f904(x67921,a893)),f293(x67921,x67922,x67923)),f317(f291(x67921),x67924)),f293(x67921,x67922,f317(f317(f228(x67921),x67923),x67924)))
% 94.68/94.44 [6793]~P66(x67931)+E(f317(f317(f92(f904(x67931,a893)),f293(x67931,x67932,x67933)),f317(f273(x67931),x67934)),f293(x67931,f317(f317(f223(x67931),x67932),x67934),x67933))
% 94.68/94.44 [6796]~E(f317(f179(f898(x67961)),x67963),f317(f179(f898(x67962)),x67964))+E(f317(f317(f171(x67961,x67962),f317(f158(x67961),x67963)),f317(f158(x67962),x67964)),f317(f158(f903(x67961,x67962)),f317(f317(f171(x67961,x67962),x67963),x67964)))
% 94.68/94.44 [6808]E(x68081,f317(f317(f23(a897),f317(f179(f898(x68082)),x68083)),f72(a897)))+E(f104(x68082,f317(f317(f149(x68082,x68083),x68081),x68084)),f317(f317(f149(x68082,f104(x68082,x68083)),x68081),x68084))
% 94.68/94.44 [6823]~P1(f317(f127(x68232),x68234))+P1(f317(f127(f903(x68231,x68232)),f317(f317(f171(x68231,x68232),x68233),x68234)))
% 94.68/94.44 [6824]~P1(f317(f127(x68241),x68243))+P1(f317(f127(f903(x68241,x68242)),f317(f317(f171(x68241,x68242),x68243),x68244)))
% 94.68/94.44 [7096]E(f317(f317(f30(a897),x70961),x70962),x70963)+~P1(f317(f43(x70961,x70962),f317(f317(f242(a897,a897),x70963),x70964)))
% 94.68/94.44 [7120]E(f40(a897,x71201,x71202),x71203)+~P1(f317(f43(x71201,x71202),f317(f317(f242(a897,a897),x71204),x71203)))
% 94.68/94.44 [7123]P1(f317(f127(x71231),x71232))+~P1(f317(f127(x71233),f317(f317(f144(x71231,x71233),x71234),x71232)))
% 94.68/94.44 [7206]E(f160(x72061,x72062,f317(f317(f124(x72061),x72063),x72064)),f317(f317(f124(x72061),f160(x72061,x72062,x72063)),x72064))+~P1(f317(f317(f319(x72061),x72062),f317(f162(x72061),x72063)))
% 94.68/94.44 [7299]~P4(x72991)+E(f40(x72991,f317(f317(f23(x72991),f40(x72991,x72992,x72993)),x72994),x72993),f40(x72991,f317(f317(f23(x72991),x72992),x72994),x72993))
% 94.68/94.44 [7302]~P3(x73021)+E(f40(x73021,f317(f317(f74(x73021),f40(x73021,x73022,x73023)),x73024),x73023),f40(x73021,f317(f317(f74(x73021),x73022),x73024),x73023))
% 94.68/94.44 [7303]~P3(x73031)+E(f40(x73031,f317(f317(f75(x73031),f40(x73031,x73032,x73033)),x73034),x73033),f40(x73031,f317(f317(f75(x73031),x73032),x73034),x73033))
% 94.68/94.44 [7497]~E(x74971,f317(f317(f141(x74972),x74973),x74974))+~P1(f317(f317(f224(a897),f317(f179(f898(x74972)),x74971)),f317(f179(f898(x74972)),x74974)))
% 94.68/94.44 [7701]P24(x77011,x77012,x77013,f317(f162(x77011),x77014))+~P1(f317(f127(x77012),f317(f317(f144(x77011,x77012),x77013),x77014)))
% 94.68/94.44 [7776]~P1(f317(f317(f224(f904(x77761,a893)),x77762),x77764))+P1(f317(f317(f224(f904(x77761,a893)),x77762),f317(f317(f299(x77761),x77763),x77764)))
% 94.68/94.44 [7812]~P4(x78121)+E(f40(x78121,f317(f317(f23(x78121),f40(x78121,x78122,x78123)),f40(x78121,x78124,x78123)),x78123),f40(x78121,f317(f317(f23(x78121),x78122),x78124),x78123))
% 94.68/94.44 [7813]~P3(x78131)+E(f40(x78131,f317(f317(f74(x78131),f40(x78131,x78132,x78133)),f40(x78131,x78134,x78133)),x78133),f40(x78131,f317(f317(f74(x78131),x78132),x78134),x78133))
% 94.68/94.44 [7814]~P3(x78141)+E(f40(x78141,f317(f317(f75(x78141),f40(x78141,x78142,x78143)),f40(x78141,x78144,x78143)),x78143),f40(x78141,f317(f317(f75(x78141),x78142),x78144),x78143))
% 94.68/94.44 [7918]~E(f317(x79184,f436(x79184,x79183,x79181,x79182)),f178(f904(x79182,a893)))+E(f317(f317(f34(x79181,f904(x79182,a893)),x79183),x79184),f178(f904(x79182,a893)))
% 94.68/94.44 [7919]~E(f317(x79194,f581(x79194,x79193,x79191,x79192)),f232(f904(x79192,a893)))+E(f317(f317(f35(x79191,f904(x79192,a893)),x79193),x79194),f232(f904(x79192,a893)))
% 94.68/94.44 [7920]~E(f317(x79204,f437(x79204,x79203,x79202,x79201)),f178(f904(x79202,a893)))+E(f317(f317(f34(x79201,f904(x79202,a893)),x79203),x79204),f178(f904(x79202,a893)))
% 94.68/94.44 [7921]~E(f317(x79214,f582(x79214,x79213,x79212,x79211)),f232(f904(x79212,a893)))+E(f317(f317(f35(x79211,f904(x79212,a893)),x79213),x79214),f232(f904(x79212,a893)))
% 94.68/94.44 [8311]P1(f317(x83111,x83112))+~P1(f317(f317(f319(x83113),x83112),f317(f317(f92(f904(x83113,a893)),x83114),f317(f252(x83113),x83111))))
% 94.68/94.44 [8348]~P1(f317(f317(f224(f904(x83481,a893)),x83483),x83484))+P1(f317(f317(f224(f904(x83481,a893)),f317(f317(f299(x83481),x83482),x83483)),f317(f317(f299(x83481),x83482),x83484)))
% 94.68/94.44 [8528]P1(f317(x85282,x85283))+E(f317(f317(f128(x85281),f317(f179(f898(x85281)),f167(x85281,x85282,f317(f317(f141(x85281),x85283),x85284)))),f317(f317(f141(x85281),x85283),x85284)),f317(f317(f141(x85281),x85283),x85284))
% 94.68/94.44 [8634]~P1(f317(f317(f225(a897),f317(x86344,x86342)),f317(x86344,x86343)))+P1(f317(f317(f319(f903(x86341,x86341)),f317(f317(f242(x86341,x86341),x86342),x86343)),f317(f317(f278(a897,x86341),a230),x86344)))
% 94.68/94.44 [8730]~P1(f317(x87302,f719(x87304,x87302,x87303,x87301)))+E(f167(x87301,x87302,f317(f317(f124(x87301),x87303),x87304)),f317(f317(f124(x87301),x87303),f167(x87301,x87302,x87304)))
% 94.68/94.44 [8807]P24(f898(x88071),f898(x88072),f317(f144(x88071,x88072),x88073),x88074)+~P24(x88071,x88072,x88073,f31(f904(x88071,a893),f317(f300(f898(x88071),f904(x88071,a893),f162(x88071)),x88074)))
% 94.68/94.44 [8882]~P1(f317(x88822,x88823))+E(f317(f317(f128(x88821),f317(f179(f898(x88821)),f167(x88821,x88822,f317(f317(f141(x88821),x88823),x88824)))),f317(f317(f141(x88821),x88823),x88824)),f317(f317(f128(x88821),f317(f179(f898(x88821)),f167(x88821,x88822,x88824))),x88824))
% 94.68/94.44 [8923]~E(x89232,x89233)+E(f317(f126(x89231,f317(f317(f8(a893,a893,x89231),a312),f317(a314,x89232))),f317(f317(f141(x89231),x89233),x89234)),f317(f126(x89231,f317(f317(f8(a893,a893,x89231),a312),f317(a314,x89232))),x89234))
% 94.68/94.44 [8933]E(f317(f317(f34(x89331,f904(x89332,a893)),x89333),x89334),f178(f904(x89332,a893)))+P1(f317(f317(f319(x89331),f436(x89334,x89333,x89331,x89332)),x89333))
% 94.68/94.44 [8934]E(f317(f317(f35(x89341,f904(x89342,a893)),x89343),x89344),f232(f904(x89342,a893)))+P1(f317(f317(f319(x89341),f581(x89344,x89343,x89341,x89342)),x89343))
% 94.68/94.44 [8935]E(f317(f317(f34(x89351,f904(x89352,a893)),x89353),x89354),f178(f904(x89352,a893)))+P1(f317(f317(f319(x89351),f437(x89354,x89353,x89352,x89351)),x89353))
% 94.68/94.44 [8936]E(f317(f317(f35(x89361,f904(x89362,a893)),x89363),x89364),f232(f904(x89362,a893)))+P1(f317(f317(f319(x89361),f582(x89364,x89363,x89362,x89361)),x89363))
% 94.68/94.44 [8974]P1(f317(f317(f225(a897),f317(x89741,x89742)),f317(x89741,x89743)))+~P1(f317(f317(f319(f903(x89744,x89744)),f317(f317(f242(x89744,x89744),x89742),x89743)),f317(f317(f278(a897,x89744),a230),x89741)))
% 94.68/94.44 [9000]E(f167(x90001,x90002,f317(f317(f124(x90001),x90003),x90004)),f317(f317(f124(x90001),x90003),f167(x90001,x90002,x90004)))+P1(f317(f317(f319(x90001),f719(x90004,x90002,x90003,x90001)),f317(f162(x90001),x90003)))
% 94.68/94.44 [9051]~P25(x90511,x90512,x90513,f232(f904(x90511,a893)),f232(f904(x90512,a893)))+E(f317(f300(x90511,x90512,x90513),f317(f73(f904(x90511,a893)),x90514)),f317(f73(f904(x90512,a893)),f317(f300(x90511,x90512,x90513),x90514)))
% 94.68/94.44 [9155]P1(f317(f317(f319(x91551),f430(x91552,x91553,x91554,x91551)),x91553))+~P1(f317(f317(f319(f904(x91551,a893)),x91554),f317(f317(f55(x91551),x91553),x91552)))
% 94.68/94.44 [9158]E(x91581,x91582)+~P1(f317(f317(f319(f903(x91583,x91583)),f317(f317(f242(x91583,x91583),x91581),x91582)),f317(f317(f173(f903(x91583,x91583),a893),f2(a897)),x91584)))
% 94.68/94.44 [9239]E(f317(f275(x92391,x92391,x92392),f317(f317(f299(x92391),f430(x92392,x92393,x92394,x92391)),f178(f904(x92391,a893)))),x92394)+~P1(f317(f317(f319(f904(x92391,a893)),x92394),f317(f317(f55(x92391),x92393),x92392)))
% 94.68/94.44 [9244]~P1(f317(f317(f319(f903(x92441,x92441)),f317(f317(f242(x92441,x92441),x92443),x92442)),f297(x92441,x92444)))+P1(f317(f317(f319(f903(x92441,x92441)),f317(f317(f242(x92441,x92441),x92442),x92443)),f297(x92441,f317(f276(x92441,x92441),x92444))))
% 94.68/94.44 [9257]~P3(x92571)+E(f317(f317(f74(x92571),f317(f317(f74(x92571),f317(f317(f75(x92571),x92572),f317(f317(f30(x92571),x92573),x92572))),f40(x92571,x92573,x92572))),x92574),f317(f317(f74(x92571),x92573),x92574))
% 94.68/94.44 [9268]~P1(f317(f317(f319(x92681),x92683),x92684))+P1(f317(f317(f319(f904(x92681,a893)),f317(f275(x92681,x92681,x92682),f317(f317(f299(x92681),x92683),f178(f904(x92681,a893))))),f317(f317(f55(x92681),x92684),x92682)))
% 94.68/94.44 [9280]P1(f317(f317(f319(f903(x92801,x92801)),f317(f317(f242(x92801,x92801),x92802),x92803)),f297(x92801,x92804)))+~P1(f317(f317(f319(f903(x92801,x92801)),f317(f317(f242(x92801,x92801),x92803),x92802)),f297(x92801,f317(f276(x92801,x92801),x92804))))
% 94.68/94.44 [9369]E(f317(f317(f149(x93691,f317(f158(x93691),x93692)),f317(f317(f23(a897),f317(f317(f23(a897),f317(f179(f898(x93691)),x93692)),x93693)),f72(a897))),x93694),f317(f158(x93691),f317(f317(f149(x93691,x93692),x93693),x93694)))+~P1(f317(f317(f225(a897),x93693),f317(f179(f898(x93691)),x93692)))
% 94.68/94.44 [9372]~P1(f317(x93722,f713(x93724,x93722,x93723,x93721)))+E(f317(f317(f128(x93721),f317(f179(f898(x93721)),f167(x93721,x93722,f317(f317(f124(x93721),x93723),x93724)))),f317(f317(f124(x93721),x93723),x93724)),f317(f317(f128(x93721),f317(f179(f898(x93721)),f167(x93721,x93722,x93724))),x93724))
% 94.68/94.44 [9418]~P24(x94182,x94181,x94183,f232(f904(x94182,a893)))+P1(f317(f317(f224(f904(x94181,a893)),f317(f300(x94182,x94181,x94183),f317(f73(f904(x94182,a893)),x94184))),f317(f73(f904(x94181,a893)),f317(f300(x94182,x94181,x94183),x94184))))
% 94.68/94.44 [9430]~P5(x94301)+E(f317(f132(x94301,x94302,f317(f7(x94302,x94301,x94301),f317(f317(f8(x94301,f904(x94301,x94301),x94302),f91(x94301)),x94303)),f178(x94301)),x94304),f317(f317(f34(x94302,x94301),f317(f162(x94302),x94304)),x94303))
% 94.68/94.44 [9431]~P5(x94311)+E(f317(f132(x94311,x94312,f317(f7(x94312,x94311,x94311),f317(f317(f8(x94311,f904(x94311,x94311),x94312),f92(x94311)),x94313)),f232(x94311)),x94314),f317(f317(f35(x94312,x94311),f317(f162(x94312),x94314)),x94313))
% 94.68/94.44 [9441]E(f317(f317(f128(x94411),f317(f179(f898(x94411)),f167(x94411,x94412,f317(f317(f124(x94411),x94413),x94414)))),f317(f317(f124(x94411),x94413),x94414)),f317(f317(f128(x94411),f317(f179(f898(x94411)),f167(x94411,x94412,x94414))),x94414))+P1(f317(f317(f319(x94411),f713(x94414,x94412,x94413,x94411)),f317(f162(x94411),x94413)))
% 94.68/94.44 [9511]~P1(f317(f317(f319(f903(f898(x95114),f898(x95114))),f317(f317(f242(f898(x95114),f898(x95114)),x95113),x95112)),f147(x95114,x95111)))+P1(f317(f317(f225(a897),f646(x95111,x95112,x95113,x95114)),f317(f179(f898(x95114)),x95113)))
% 94.68/94.44 [9512]~P3(x95121)+E(f317(f317(f74(x95121),f317(f317(f74(x95121),f317(f317(f75(x95121),f317(f317(f30(x95121),x95122),x95123)),x95123)),f40(x95121,x95122,x95123))),x95124),f317(f317(f74(x95121),x95122),x95124))
% 94.68/94.44 [9541]~P1(f317(f317(f319(f903(f898(x95411),f898(x95411))),f317(f317(f242(f898(x95411),f898(x95411)),x95412),x95413)),f317(f276(f898(x95411),f898(x95411)),f147(x95411,x95414))))+P1(f317(f317(f319(f903(f898(x95411),f898(x95411))),f317(f317(f242(f898(x95411),f898(x95411)),x95412),x95413)),f147(x95411,f317(f276(x95411,x95411),x95414))))
% 94.68/94.44 [9542]P1(f317(f317(f319(f903(f898(x95421),f898(x95421))),f317(f317(f242(f898(x95421),f898(x95421)),x95422),x95423)),f317(f276(f898(x95421),f898(x95421)),f147(x95421,x95424))))+~P1(f317(f317(f319(f903(f898(x95421),f898(x95421))),f317(f317(f242(f898(x95421),f898(x95421)),x95422),x95423)),f147(x95421,f317(f276(x95421,x95421),x95424))))
% 94.68/94.44 [9586]~P1(f317(f317(f319(x95861),x95863),f317(f254(x95861,x95862),x95864)))+P1(f317(f317(f319(f903(x95861,x95862)),f317(f317(f242(x95861,x95862),x95863),f504(x95864,x95862,x95863,x95861))),x95864))
% 94.68/94.44 [9587]~P1(f317(f317(f319(x95871),x95873),f317(f254(x95871,x95872),x95874)))+P1(f317(f317(f319(f903(x95871,x95872)),f317(f317(f242(x95871,x95872),x95873),f505(x95874,x95872,x95873,x95871))),x95874))
% 94.68/94.44 [9747]~P1(f317(f317(f319(f903(x97471,x97471)),f317(f317(f242(x97471,x97471),x97472),x97474)),f317(f317(f279(x97471,x97471,x97471),x97473),f297(x97471,x97473))))+P1(f317(f317(f319(f903(x97471,x97471)),f317(f317(f242(x97471,x97471),x97472),f569(x97473,x97474,x97472,x97471))),x97473))
% 94.68/94.44 [9905]P11(x99051,x99052,x99053,x99054)+P1(f317(f317(f319(f903(x99051,x99051)),f317(f317(f242(x99051,x99051),f812(x99052,x99054,x99053,x99051)),f811(x99052,x99054,x99053,x99051))),x99053))
% 94.68/94.44 [9912]~P1(f317(f317(f319(f903(x99122,x99121)),x99124),f317(f276(x99121,x99122),x99123)))+P1(f317(f317(f319(f903(x99121,x99122)),f317(f317(f242(x99121,x99122),f620(x99123,x99124,x99121,x99122)),f619(x99123,x99124,x99121,x99122))),x99123))
% 94.68/94.44 [9936]~P1(f317(f317(f319(f903(f898(x99361),f898(x99361))),f317(f317(f242(f898(x99361),f898(x99361)),x99364),x99363)),f147(x99361,x99362)))+P1(f317(f317(f319(f903(x99361,x99361)),f317(f317(f242(x99361,x99361),f663(x99362,x99363,x99364,x99361)),f664(x99362,x99363,x99364,x99361))),x99362))
% 94.68/94.44 [10026]~P1(f317(f317(f319(f903(f898(x100261),f898(x100261))),f317(f317(f242(f898(x100261),f898(x100261)),x100262),x100264)),f147(x100261,x100263)))+P1(f317(f317(f319(f903(x100261,x100261)),f317(f317(f242(x100261,x100261),f317(f317(f154(x100261),x100262),f646(x100263,x100264,x100262,x100261))),f647(x100263,x100264,x100262,x100261))),x100263))
% 94.68/94.44 [10046]~P1(f317(f28(x100462),x100464))+E(f317(f317(f317(f59(f904(x100461,a893),x100462,f91(f904(x100461,a893))),f317(f317(f7(x100462,f904(x100461,a893),f904(x100461,a893)),f317(f317(f8(x100461,f904(f904(x100461,a893),f904(x100461,a893)),x100462),f299(x100461)),x100463)),f178(f904(x100461,a893)))),f178(f904(x100461,a893))),x100464),f317(f300(x100462,x100461,x100463),x100464))
% 94.68/94.44 [10157]~P24(x101571,x101572,x101573,f232(f904(x101571,a893)))+P1(f317(f317(f224(f904(x101571,a893)),f317(f301(x101571,x101572,x101573),f317(f317(f299(x101572),x101574),f178(f904(x101572,a893))))),f317(f317(f299(x101571),f79(x101571,f317(f317(f7(x101571,x101572,a893),f317(f317(f8(x101572,f904(x101572,a893),x101571),a314),x101573)),x101574))),f178(f904(x101571,a893)))))
% 94.68/94.44 [5695]~E(f317(f317(f124(x56951),x56952),x56954),x56953)+E(f317(f317(f165(x56951),f317(f179(f898(x56951)),x56952)),x56953),x56952)
% 94.68/94.44 [5696]~E(f317(f317(f124(x56962),x56963),x56961),x56964)+E(x56961,f317(f317(f128(x56962),f317(f179(f898(x56962)),x56963)),x56964))
% 94.68/94.44 [5707]~E(x57074,f2(a897))+E(f317(f317(f154(x57071),f317(f317(f141(x57071),x57072),x57073)),x57074),x57072)
% 94.68/94.44 [6263]~P112(x62631)+E(f317(f317(f234(x62631),f317(f317(f234(x62631),x62632),x62633)),x62634),f317(f317(f234(x62631),x62632),f317(f317(f75(a897),x62633),x62634)))
% 94.68/94.44 [6264]~P82(x62641)+E(f317(f317(f234(x62641),f317(f317(f234(x62641),x62642),x62643)),x62644),f317(f317(f234(x62641),x62642),f317(f317(f75(a897),x62643),x62644)))
% 94.68/94.44 [6272]E(x62721,f2(a897))+E(f317(f317(f154(x62722),f317(f317(f141(x62722),x62723),x62724)),x62721),f317(f317(f154(x62722),x62724),f317(f317(f23(a897),x62721),f72(a897))))
% 94.68/94.44 [6301]~P122(x63011)+E(f317(f317(f281(x63011),f317(f317(f75(x63011),x63012),x63013)),x63014),f317(f317(f75(x63011),x63012),f317(f317(f281(x63011),x63013),x63014)))
% 94.68/94.44 [6302]~P72(x63021)+E(f317(f317(f74(x63021),f317(f317(f74(x63021),x63022),x63023)),x63024),f317(f317(f74(x63021),x63022),f317(f317(f74(x63021),x63023),x63024)))
% 94.68/94.44 [6303]~P112(x63031)+E(f317(f317(f74(x63031),f317(f317(f74(x63031),x63032),x63033)),x63034),f317(f317(f74(x63031),x63032),f317(f317(f74(x63031),x63033),x63034)))
% 94.68/94.44 [6304]~P112(x63041)+E(f317(f317(f75(x63041),f317(f317(f75(x63041),x63042),x63043)),x63044),f317(f317(f75(x63041),x63042),f317(f317(f75(x63041),x63043),x63044)))
% 94.68/94.44 [6305]~P73(x63051)+E(f317(f317(f75(x63051),f317(f317(f75(x63051),x63052),x63053)),x63054),f317(f317(f75(x63051),x63052),f317(f317(f75(x63051),x63053),x63054)))
% 94.68/94.44 [6308]~P66(x63081)+E(f317(f317(f228(x63081),f317(f317(f228(x63081),x63082),x63083)),x63084),f317(f317(f228(x63081),x63082),f317(f317(f228(x63081),x63083),x63084)))
% 94.68/94.44 [6310]~P66(x63101)+E(f317(f317(f223(x63101),f317(f317(f223(x63101),x63102),x63103)),x63104),f317(f317(f223(x63101),x63102),f317(f317(f223(x63101),x63103),x63104)))
% 94.68/94.44 [6312]~P99(x63121)+E(f317(f317(f91(x63121),f317(f317(f91(x63121),x63122),x63123)),x63124),f317(f317(f91(x63121),x63122),f317(f317(f91(x63121),x63123),x63124)))
% 94.68/94.44 [6313]~P100(x63131)+E(f317(f317(f91(x63131),f317(f317(f91(x63131),x63132),x63133)),x63134),f317(f317(f91(x63131),x63132),f317(f317(f91(x63131),x63133),x63134)))
% 94.68/94.44 [6314]~P100(x63141)+E(f317(f317(f92(x63141),f317(f317(f92(x63141),x63142),x63143)),x63144),f317(f317(f92(x63141),x63142),f317(f317(f92(x63141),x63143),x63144)))
% 94.68/94.44 [6316]~P105(x63161)+E(f317(f317(f92(x63161),f317(f317(f92(x63161),x63162),x63163)),x63164),f317(f317(f92(x63161),x63162),f317(f317(f92(x63161),x63163),x63164)))
% 94.68/94.44 [6325]~P3(x63251)+E(f40(x63251,f317(f317(f74(x63251),x63252),f317(f317(f75(x63251),x63253),x63254)),x63254),f40(x63251,x63252,x63254))
% 94.68/94.44 [6326]~P3(x63261)+E(f40(x63261,f317(f317(f74(x63261),x63262),f317(f317(f75(x63261),x63263),x63264)),x63263),f40(x63261,x63262,x63263))
% 94.68/94.44 [6468]E(f317(f317(f154(x64681),f317(f317(f165(x64681),x64682),x64683)),x64684),f317(f317(f154(x64681),x64683),x64684))+~P1(f317(f317(f225(a897),x64684),x64682))
% 94.68/94.44 [6649]~E(x66492,x66494)+P1(f317(f317(f162(x66491),f317(f317(f141(x66491),x66492),x66493)),x66494))
% 94.68/94.44 [6651]~P112(x66511)+E(f317(f317(f74(x66511),f317(f317(f74(x66511),x66512),x66513)),x66514),f317(f317(f74(x66511),f317(f317(f74(x66511),x66512),x66514)),x66513))
% 94.68/94.44 [6652]~P112(x66521)+E(f317(f317(f75(x66521),f317(f317(f75(x66521),x66522),x66523)),x66524),f317(f317(f75(x66521),f317(f317(f75(x66521),x66522),x66524)),x66523))
% 94.68/94.44 [6713]~P144(x67132)+E(f317(f317(f6(x67131,x67132),f317(f16(x67132,x67131),x67133)),x67134),f317(f317(f75(x67132),f317(f90(x67132),f317(f29(x67131),x67134))),x67133))
% 94.68/94.44 [6889]E(f317(f317(f92(f904(x68891,a893)),f317(f317(f299(x68891),x68892),x68893)),x68894),f317(f317(f92(f904(x68891,a893)),x68893),x68894))+P1(f317(f317(f319(x68891),x68892),x68894))
% 94.68/94.44 [6958]~P67(x69581)+E(f317(f317(f228(x69581),f317(f317(f23(x69581),x69582),x69583)),f317(f317(f23(x69581),x69584),x69583)),f317(f317(f23(x69581),f317(f317(f228(x69581),x69582),x69584)),x69583))
% 94.68/94.44 [6959]~P67(x69591)+E(f317(f317(f223(x69591),f317(f317(f23(x69591),x69592),x69593)),f317(f317(f23(x69591),x69594),x69593)),f317(f317(f23(x69591),f317(f317(f223(x69591),x69592),x69594)),x69593))
% 94.68/94.44 [6960]~P84(x69601)+E(f317(f317(f228(x69601),f317(f317(f74(x69601),x69602),x69603)),f317(f317(f74(x69601),x69604),x69603)),f317(f317(f74(x69601),f317(f317(f228(x69601),x69602),x69604)),x69603))
% 94.68/94.44 [6961]~P84(x69611)+E(f317(f317(f223(x69611),f317(f317(f74(x69611),x69612),x69613)),f317(f317(f74(x69611),x69614),x69613)),f317(f317(f74(x69611),f317(f317(f223(x69611),x69612),x69614)),x69613))
% 94.68/94.44 [6963]~P113(x69631)+E(f317(f317(f74(x69631),f317(f317(f75(x69631),x69632),x69633)),f317(f317(f75(x69631),x69634),x69633)),f317(f317(f75(x69631),f317(f317(f74(x69631),x69632),x69634)),x69633))
% 94.68/94.44 [6964]~P112(x69641)+E(f317(f317(f75(x69641),f317(f317(f234(x69641),x69642),x69643)),f317(f317(f234(x69641),x69644),x69643)),f317(f317(f234(x69641),f317(f317(f75(x69641),x69642),x69644)),x69643))
% 94.68/94.44 [6965]~P77(x69651)+E(f317(f317(f75(x69651),f317(f317(f234(x69651),x69652),x69653)),f317(f317(f234(x69651),x69654),x69653)),f317(f317(f234(x69651),f317(f317(f75(x69651),x69652),x69654)),x69653))
% 94.68/94.44 [6966]~P61(x69661)+E(f317(f317(f281(x69661),f317(f317(f234(x69661),x69662),x69663)),f317(f317(f234(x69661),x69664),x69663)),f317(f317(f234(x69661),f317(f317(f281(x69661),x69662),x69664)),x69663))
% 94.68/94.44 [6967]~P66(x69671)+E(f317(f317(f223(x69671),f317(f317(f228(x69671),x69672),x69673)),f317(f317(f228(x69671),x69674),x69673)),f317(f317(f228(x69671),f317(f317(f223(x69671),x69672),x69674)),x69673))
% 94.68/94.44 [6968]~P122(x69681)+E(f317(f317(f23(x69681),f317(f317(f281(x69681),x69682),x69683)),f317(f317(f281(x69681),x69684),x69683)),f317(f317(f281(x69681),f317(f317(f23(x69681),x69682),x69684)),x69683))
% 94.68/94.44 [6969]~P122(x69691)+E(f317(f317(f74(x69691),f317(f317(f281(x69691),x69692),x69693)),f317(f317(f281(x69691),x69694),x69693)),f317(f317(f281(x69691),f317(f317(f74(x69691),x69692),x69694)),x69693))
% 94.68/94.44 [6970]~P66(x69701)+E(f317(f317(f228(x69701),f317(f317(f223(x69701),x69702),x69703)),f317(f317(f223(x69701),x69704),x69703)),f317(f317(f223(x69701),f317(f317(f228(x69701),x69702),x69704)),x69703))
% 94.68/94.44 [6971]~P103(x69711)+E(f317(f317(f92(x69711),f317(f317(f91(x69711),x69712),x69713)),f317(f317(f91(x69711),x69714),x69713)),f317(f317(f91(x69711),f317(f317(f92(x69711),x69712),x69714)),x69713))
% 94.68/94.44 [6972]~P103(x69721)+E(f317(f317(f91(x69721),f317(f317(f92(x69721),x69722),x69723)),f317(f317(f92(x69721),x69724),x69723)),f317(f317(f92(x69721),f317(f317(f91(x69721),x69722),x69724)),x69723))
% 94.68/94.44 [6973]~P112(x69731)+E(f317(f317(f74(x69731),f317(f317(f75(x69731),x69732),x69733)),f317(f317(f75(x69731),x69734),x69733)),f317(f317(f75(x69731),f317(f317(f74(x69731),x69732),x69734)),x69733))
% 94.68/94.44 [7007]E(f317(f317(f149(x70071,x70072),x70073),x70074),x70072)+~P1(f317(f317(f224(a897),f317(f179(f898(x70071)),x70072)),x70073))
% 94.68/94.44 [7035]~P1(f317(x70353,x70354))+P1(f317(f317(f317(f91(f904(x70351,a893)),x70352),x70353),x70354))
% 94.68/94.44 [7037]~P1(f317(x70372,x70374))+P1(f317(f317(f317(f91(f904(x70371,a893)),x70372),x70373),x70374))
% 94.68/94.44 [7057]E(f317(f317(f154(x70571),f317(f317(f124(x70571),x70572),x70573)),x70574),f317(f317(f154(x70571),x70572),x70574))+~P1(f317(f317(f225(a897),x70574),f317(f179(f898(x70571)),x70572)))
% 94.68/94.44 [7068]E(f317(f317(f23(f904(x70681,a893)),f317(f317(f299(x70681),x70682),x70683)),x70684),f317(f317(f23(f904(x70681,a893)),x70683),x70684))+~P1(f317(f317(f319(x70681),x70682),x70684))
% 94.68/94.44 [7109]~E(f129(a897,f317(f292(a897,x71091),x71092)),f317(f317(f141(a897),x71094),x71093))+E(f129(a897,f317(f292(a897,f317(f317(f74(a897),x71091),f72(a897))),x71092)),x71093)
% 94.68/94.44 [7131]~P1(f317(f317(f162(x71311),x71313),x71314))+P1(f317(f317(f162(x71311),f317(f317(f141(x71311),x71312),x71313)),x71314))
% 94.68/94.44 [7181]E(x71811,f2(a897))+E(f317(f317(f141(x71812),x71813),f317(f317(f165(x71812),f317(f317(f23(a897),x71811),f72(a897))),x71814)),f317(f317(f165(x71812),x71811),f317(f317(f141(x71812),x71813),x71814)))
% 94.68/94.44 [7283]E(f317(f317(f154(x72831),x72832),f317(f317(f23(a897),x72833),f317(f179(f898(x72831)),x72834))),f317(f317(f154(x72831),f317(f317(f124(x72831),x72834),x72832)),x72833))+P1(f317(f317(f225(a897),x72833),f317(f179(f898(x72831)),x72834)))
% 94.68/94.44 [7311]E(f317(f317(f92(f904(x73111,a893)),x73112),f317(f317(f299(x73111),x73113),x73114)),f317(f317(f299(x73111),x73113),f317(f317(f92(f904(x73111,a893)),x73112),x73114)))+~P1(f317(f317(f319(x73111),x73113),x73112))
% 94.68/94.44 [7349]E(f317(f317(f154(x73491),f317(f317(f149(x73491,x73492),x73493),x73494)),x73493),x73494)+~P1(f317(f317(f225(a897),x73493),f317(f179(f898(x73491)),x73492)))
% 94.68/94.44 [7371]E(x73711,f178(f904(x73712,a893)))+E(f317(f300(f903(x73713,x73712),x73713,f241(x73713,x73712)),f317(f317(f244(x73713,x73712),x73714),f317(f16(f904(x73712,a893),x73713),x73711))),x73714)
% 94.68/94.44 [7372]E(x73721,f178(f904(x73722,a893)))+E(f317(f300(f903(x73722,x73723),x73723,f246(x73722,x73723)),f317(f317(f244(x73722,x73723),x73721),f317(f16(f904(x73723,a893),x73722),x73724))),x73724)
% 94.68/94.44 [7447]E(f317(f317(f23(f904(x74471,a893)),f317(f317(f299(x74471),x74472),x74473)),x74474),f317(f317(f299(x74471),x74472),f317(f317(f23(f904(x74471,a893)),x74473),x74474)))+P1(f317(f317(f319(x74471),x74472),x74474))
% 94.68/94.44 [7483]~E(x74834,f178(f904(x74832,a893)))+E(f317(f300(f903(x74831,x74832),x74831,f241(x74831,x74832)),f317(f317(f244(x74831,x74832),x74833),f317(f16(f904(x74832,a893),x74831),x74834))),f178(f904(x74831,a893)))
% 94.68/94.44 [7484]~E(x74843,f178(f904(x74841,a893)))+E(f317(f300(f903(x74841,x74842),x74842,f246(x74841,x74842)),f317(f317(f244(x74841,x74842),x74843),f317(f16(f904(x74842,a893),x74841),x74844))),f178(f904(x74842,a893)))
% 94.68/94.44 [7536]~P1(f317(f317(f319(x75361),x75362),x75364))+P1(f317(f317(f319(x75361),x75362),f317(f317(f91(f904(x75361,a893)),x75363),x75364)))
% 94.68/94.44 [7539]~P1(f317(f317(f319(x75391),x75392),x75393))+P1(f317(f317(f319(x75391),x75392),f317(f317(f91(f904(x75391,a893)),x75393),x75394)))
% 94.68/94.44 [7557]E(f317(f317(f92(f904(x75571,a893)),f317(f317(f299(x75571),x75572),x75573)),x75574),f317(f317(f299(x75571),x75572),f317(f317(f92(f904(x75571,a893)),x75573),x75574)))+~P1(f317(f317(f319(x75571),x75572),x75574))
% 94.68/94.44 [7834]P1(f317(x78341,x78342))+~P1(f317(f317(f317(f92(f904(x78343,a893)),x78344),x78341),x78342))
% 94.68/94.44 [7835]P1(f317(x78351,x78352))+~P1(f317(f317(f317(f92(f904(x78353,a893)),x78351),x78354),x78352))
% 94.68/94.44 [7836]E(f317(f317(f6(x78361,a897),x78362),f317(f317(f23(f904(x78361,a893)),x78363),f317(f317(f299(x78361),x78364),f178(f904(x78361,a893))))),f317(f317(f6(x78361,a897),x78362),x78363))+P1(f317(f317(f319(x78361),x78364),x78363))
% 94.68/94.44 [7841]~P76(x78411)+E(f317(f155(x78411),f317(f317(f144(a897,x78411),x78412),f129(a897,f317(f292(a897,x78413),x78414)))),f317(f317(f6(a897,x78411),x78412),f317(f162(a897),f129(a897,f317(f292(a897,x78413),x78414)))))
% 94.68/94.44 [7842]~P76(x78421)+E(f317(f317(f6(a897,x78421),x78422),f317(f162(a897),f129(a897,f317(f292(a897,x78423),x78424)))),f317(f155(x78421),f317(f317(f144(a897,x78421),x78422),f129(a897,f317(f292(a897,x78423),x78424)))))
% 94.68/94.44 [7956]~E(x79563,x79564)+P1(f317(f56(x79561,x79562,f317(f317(f299(x79561),x79563),f178(f904(x79561,a893)))),x79564))
% 94.68/94.44 [8053]P1(f317(f317(f319(x80531),x80532),f317(f162(x80531),x80533)))+~P1(f317(f317(f319(x80531),x80532),f317(f162(x80531),f317(f317(f165(x80531),x80534),x80533))))
% 94.68/94.44 [8054]P1(f317(f317(f319(x80541),x80542),f317(f162(x80541),x80543)))+~P1(f317(f317(f319(x80541),x80542),f317(f162(x80541),f317(f317(f128(x80541),x80544),x80543))))
% 94.68/94.44 [8124]P1(f317(f317(f319(x81241),x81242),x81243))+~P1(f317(f317(f319(x81241),x81242),f317(f317(f23(f904(x81241,a893)),x81243),x81244)))
% 94.68/94.44 [8126]P1(f317(f317(f319(x81261),x81262),x81263))+~P1(f317(f317(f319(x81261),x81262),f317(f317(f92(f904(x81261,a893)),x81264),x81263)))
% 94.68/94.44 [8129]P1(f317(f317(f319(x81291),x81292),x81293))+~P1(f317(f317(f319(x81291),x81292),f317(f317(f92(f904(x81291,a893)),x81293),x81294)))
% 94.68/94.44 [8144]E(f317(f317(f124(x81441),f317(f317(f165(x81441),x81442),x81443)),f317(f317(f141(x81441),x81444),f317(f317(f128(x81441),f317(a102,x81442)),x81443))),f317(f317(f149(x81441,x81443),x81442),x81444))+~P1(f317(f317(f225(a897),x81442),f317(f179(f898(x81441)),x81443)))
% 94.68/94.44 [8167]P1(f317(f317(f319(x81671),x81672),x81673))+~P1(f317(f317(f224(f904(x81671,a893)),f317(f317(f299(x81671),x81672),x81674)),x81673))
% 94.68/94.44 [8204]~P1(f317(f317(f319(x82041),x82042),x82043))+~P1(f317(f317(f319(x82041),x82042),f317(f317(f23(f904(x82041,a893)),x82044),x82043)))
% 94.68/94.44 [8237]~P1(f317(f317(f225(a897),x82374),f317(f179(f898(x82371)),x82373)))+P1(f317(f317(f319(x82371),x82372),f317(f162(x82371),f317(f317(f149(x82371,x82373),x82374),x82372))))
% 94.68/94.44 [8290]E(f317(f317(f154(x82901),f317(f317(f128(x82901),x82902),x82903)),x82904),f317(f317(f154(x82901),x82903),f317(f317(f74(a897),x82902),x82904)))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x82902),x82904)),f317(f179(f898(x82901)),x82903)))
% 94.68/94.44 [8299]~P144(x82992)+E(f317(f317(f6(x82991,x82992),f317(f317(f8(a897,x82992,x82991),f90(x82992)),x82993)),x82994),f317(f90(x82992),f317(f317(f6(x82991,a897),x82993),x82994)))
% 94.68/94.44 [8300]~P141(x83002)+E(f317(f317(f6(x83001,x83002),f317(f317(f8(a1,x83002,x83001),f93(x83002)),x83003)),x83004),f317(f93(x83002),f317(f317(f6(x83001,a1),x83003),x83004)))
% 94.68/94.44 [8350]~P64(x83502)+E(f317(f317(f9(x83501,x83502),f317(f317(f8(x83502,x83502,x83501),f70(x83502)),x83503)),x83504),f317(f70(x83502),f317(f317(f9(x83501,x83502),x83503),x83504)))
% 94.68/94.44 [8351]~P69(x83512)+E(f317(f317(f6(x83511,x83512),f317(f317(f8(x83512,x83512,x83511),f73(x83512)),x83513)),x83514),f317(f73(x83512),f317(f317(f6(x83511,x83512),x83513),x83514)))
% 94.68/94.44 [8354]E(f317(f317(f6(x83541,a897),x83542),f317(f317(f23(f904(x83541,a893)),x83543),f317(f317(f299(x83541),x83544),f178(f904(x83541,a893))))),f317(f317(f23(a897),f317(f317(f6(x83541,a897),x83542),x83543)),f317(x83542,x83544)))+~P1(f317(f317(f319(x83541),x83544),x83543))
% 94.68/94.44 [8373]P1(f317(f317(f224(f904(x83731,a893)),x83732),x83733))+~P1(f317(f317(f224(f904(x83731,a893)),f317(f317(f299(x83731),x83734),x83732)),x83733))
% 94.68/94.44 [8497]~E(f317(f300(x84972,x84973,x84971),f232(f904(x84972,a893))),f232(f904(x84973,a893)))+E(f317(x84971,f317(f85(x84972,x84973,f232(f904(x84972,a893)),x84971),x84974)),x84974)
% 94.68/94.44 [8580]P36(x85801,x85802)+~P36(x85801,f317(f317(f299(f903(x85801,x85801)),f317(f317(f242(x85801,x85801),x85803),x85804)),x85802))
% 94.68/94.44 [8581]P57(x85811,x85812)+~P57(x85811,f317(f317(f299(f903(x85811,x85811)),f317(f317(f242(x85811,x85811),x85813),x85814)),x85812))
% 94.68/94.44 [8586]~P66(x85861)+E(f317(f317(f138(x85861,x85861,f5(x85861)),x85862),f317(f317(f138(x85861,x85861,f5(x85861)),x85863),x85864)),f317(f317(f138(x85861,x85861,f5(x85861)),x85863),f317(f317(f138(x85861,x85861,f5(x85861)),x85862),x85864)))
% 94.68/94.44 [8601]E(x86011,x86012)+~P1(f317(f56(x86013,x86014,f317(f317(f299(x86013),x86011),f178(f904(x86013,a893)))),x86012))
% 94.68/94.44 [8610]E(f317(f317(f124(x86101),f317(f317(f165(x86101),x86102),x86103)),f317(f317(f165(x86101),x86104),f317(f317(f128(x86101),x86102),x86103))),f317(f317(f165(x86101),f317(f317(f74(a897),x86102),x86104)),x86103))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x86102),x86104)),f317(f179(f898(x86101)),x86103)))
% 94.68/94.44 [8650]P1(f317(f28(x86501),x86502))+~E(x86502,f317(f300(a897,x86501,x86503),f317(f252(a897),f317(f317(f7(a897,a897,a893),f225(a897)),x86504))))
% 94.68/94.44 [8670]~P92(x86701)+E(f317(f132(x86701,x86701,f74(x86701),f317(f317(f74(x86701),x86702),x86703)),x86704),f317(f317(f74(x86701),x86702),f317(f132(x86701,x86701,f74(x86701),x86703),x86704)))
% 94.68/94.44 [8706]P1(f317(f317(f224(f904(x87061,a893)),f317(f254(x87061,x87062),x87063)),f317(f254(x87061,x87062),x87064)))+~P1(f317(f317(f224(f904(f903(x87061,x87062),a893)),x87063),x87064))
% 94.68/94.44 [8718]~P1(f317(f317(f224(a897),x87182),x87184))+P1(f317(f317(f224(f904(x87181,a893)),f317(f162(x87181),f317(f317(f165(x87181),x87182),x87183))),f317(f162(x87181),f317(f317(f165(x87181),x87184),x87183))))
% 94.68/94.44 [8719]~P1(f317(f317(f224(a897),x87194),x87192))+P1(f317(f317(f224(f904(x87191,a893)),f317(f162(x87191),f317(f317(f128(x87191),x87192),x87193))),f317(f162(x87191),f317(f317(f128(x87191),x87194),x87193))))
% 94.68/94.44 [8776]~P1(f317(f28(x87761),f317(f317(f23(f904(x87761,a893)),x87762),x87764)))+P1(f317(f28(x87761),f317(f317(f23(f904(x87761,a893)),x87762),f317(f317(f299(x87761),x87763),x87764))))
% 94.68/94.44 [8818]P1(f317(f317(f319(f903(x88181,x88181)),x88182),f297(x88181,x88183)))+~P1(f317(f317(f319(f903(x88181,x88181)),x88182),f317(f317(f173(f903(x88181,x88181),a893),x88184),x88183)))
% 94.68/94.44 [8904]~P1(f317(f28(x89041),f317(f317(f23(f904(x89041,a893)),x89042),f317(f317(f299(x89041),x89044),x89043))))+P1(f317(f28(x89041),f317(f317(f23(f904(x89041,a893)),x89042),x89043)))
% 94.68/94.44 [9115]~P66(x91151)+P1(f317(f317(f224(x91151),f317(f317(f223(x91151),x91152),f317(f317(f228(x91151),x91153),x91154))),f317(f317(f228(x91151),f317(f317(f223(x91151),x91152),x91153)),f317(f317(f223(x91151),x91152),x91154))))
% 94.68/94.44 [9116]~P100(x91161)+P1(f317(f317(f224(x91161),f317(f317(f91(x91161),x91162),f317(f317(f92(x91161),x91163),x91164))),f317(f317(f92(x91161),f317(f317(f91(x91161),x91162),x91163)),f317(f317(f91(x91161),x91162),x91164))))
% 94.68/94.44 [9264]E(x92641,x92642)+~P1(f317(f317(f319(f903(x92643,x92643)),f317(f317(f242(x92643,x92643),x92641),x92642)),f317(f162(f903(x92643,x92643)),f317(f317(f171(x92643,x92643),x92644),x92644))))
% 94.68/94.44 [9295]~P1(f317(f317(f319(f903(x92951,x92951)),f317(f317(f242(x92951,x92951),x92953),x92952)),f297(x92951,x92954)))+~P36(x92951,f317(f317(f299(f903(x92951,x92951)),f317(f317(f242(x92951,x92951),x92952),x92953)),x92954))
% 94.68/94.44 [9296]~P1(f317(f317(f319(f903(x92961,x92961)),f317(f317(f242(x92961,x92961),x92963),x92962)),f297(x92961,x92964)))+~P57(x92961,f317(f317(f299(f903(x92961,x92961)),f317(f317(f242(x92961,x92961),x92962),x92963)),x92964))
% 94.68/94.44 [9300]E(x93001,x93002)+E(f317(f126(x93003,f317(f317(f8(a893,a893,x93003),a312),f317(a314,x93001))),f317(f317(f141(x93003),x93002),x93004)),f317(f317(f141(x93003),x93002),f317(f126(x93003,f317(f317(f8(a893,a893,x93003),a312),f317(a314,x93001))),x93004)))
% 94.68/94.44 [9331]~P25(x93312,x93311,x93313,f232(f904(x93312,a893)),f232(f904(x93311,a893)))+E(f317(f300(x93311,x93312,f85(x93312,x93311,f232(f904(x93312,a893)),x93313)),x93314),f317(f301(x93312,x93311,x93313),x93314))
% 94.68/94.44 [9347]~P66(x93471)+P1(f317(f317(f224(x93471),f317(f317(f223(x93471),f317(f317(f228(x93471),x93472),x93473)),f317(f317(f228(x93471),x93472),x93474))),f317(f317(f228(x93471),x93472),f317(f317(f223(x93471),x93473),x93474))))
% 94.68/94.44 [9348]~P100(x93481)+P1(f317(f317(f224(x93481),f317(f317(f91(x93481),f317(f317(f92(x93481),x93482),x93483)),f317(f317(f92(x93481),x93482),x93484))),f317(f317(f92(x93481),x93482),f317(f317(f91(x93481),x93483),x93484))))
% 94.68/94.44 [9412]~P25(x94122,x94121,x94124,f232(f904(x94122,a893)),f232(f904(x94121,a893)))+E(f317(f252(x94121),f317(f317(f8(x94122,a893,x94121),x94123),f85(x94122,x94121,f232(f904(x94122,a893)),x94124))),f317(f300(x94122,x94121,x94124),f317(f252(x94122),x94123)))
% 94.68/94.44 [9426]~E(f317(f300(x94262,x94261,x94263),f232(f904(x94262,a893))),f232(f904(x94261,a893)))+P1(f317(f317(f224(f904(x94261,a893)),f317(f73(f904(x94261,a893)),f317(f300(x94262,x94261,x94263),x94264))),f317(f300(x94262,x94261,x94263),f317(f73(f904(x94262,a893)),x94264))))
% 94.68/94.44 [9760]P1(f317(f317(f319(f903(x97601,x97601)),f317(f317(f242(x97601,x97601),x97602),x97603)),f317(f276(x97601,x97601),f317(f317(f279(x97601,x97601,x97601),x97604),f297(x97601,x97604)))))+~P1(f317(f317(f319(f903(x97601,x97601)),f317(f317(f242(x97601,x97601),x97602),x97603)),f317(f317(f279(x97601,x97601,x97601),f317(f276(x97601,x97601),x97604)),f297(x97601,f317(f276(x97601,x97601),x97604)))))
% 94.68/94.44 [9761]~P1(f317(f317(f319(f903(x97611,x97611)),f317(f317(f242(x97611,x97611),x97612),x97613)),f317(f276(x97611,x97611),f317(f317(f279(x97611,x97611,x97611),x97614),f297(x97611,x97614)))))+P1(f317(f317(f319(f903(x97611,x97611)),f317(f317(f242(x97611,x97611),x97612),x97613)),f317(f317(f279(x97611,x97611,x97611),f317(f276(x97611,x97611),x97614)),f297(x97611,f317(f276(x97611,x97611),x97614)))))
% 94.68/94.44 [9782]~P1(f317(f317(f319(x97822),x97824),f317(f274(x97821,x97822),x97823)))+P1(f317(f317(f319(f903(x97821,x97822)),f317(f317(f242(x97821,x97822),f496(x97823,x97821,x97824,x97822)),x97824)),x97823))
% 94.68/94.44 [9783]~P1(f317(f317(f319(x97832),x97834),f317(f274(x97831,x97832),x97833)))+P1(f317(f317(f319(f903(x97831,x97832)),f317(f317(f242(x97831,x97832),f497(x97833,x97831,x97834,x97832)),x97834)),x97833))
% 94.68/94.44 [9808]~P1(f317(f317(f319(x98081),x98084),f317(f317(f91(f904(x98081,a893)),x98082),x98083)))+P1(f317(f317(f317(f91(f904(x98081,a893)),f317(f317(f7(x98081,f904(x98081,a893),a893),f319(x98081)),x98082)),f317(f317(f7(x98081,f904(x98081,a893),a893),f319(x98081)),x98083)),x98084))
% 94.68/94.44 [9809]~P1(f317(f317(f319(x98091),x98094),f317(f317(f92(f904(x98091,a893)),x98092),x98093)))+P1(f317(f317(f317(f92(f904(x98091,a893)),f317(f317(f7(x98091,f904(x98091,a893),a893),f319(x98091)),x98092)),f317(f317(f7(x98091,f904(x98091,a893),a893),f319(x98091)),x98093)),x98094))
% 94.68/94.44 [9889]~P1(f317(f317(f319(f903(x98891,x98891)),f317(f317(f242(x98891,x98891),x98894),x98893)),f317(f317(f279(x98891,x98891,x98891),x98892),f297(x98891,x98892))))+P1(f317(f317(f319(f903(x98891,x98891)),f317(f317(f242(x98891,x98891),f576(x98892,x98893,x98894,x98891)),x98893)),x98892))
% 94.68/94.44 [9924]P1(f317(f317(f319(x99241),x99242),f317(f317(f91(f904(x99241,a893)),x99243),x99244)))+~P1(f317(f317(f317(f91(f904(x99241,a893)),f317(f317(f7(x99241,f904(x99241,a893),a893),f319(x99241)),x99243)),f317(f317(f7(x99241,f904(x99241,a893),a893),f319(x99241)),x99244)),x99242))
% 94.68/94.44 [9925]P1(f317(f317(f319(x99251),x99252),f317(f317(f92(f904(x99251,a893)),x99253),x99254)))+~P1(f317(f317(f317(f92(f904(x99251,a893)),f317(f317(f7(x99251,f904(x99251,a893),a893),f319(x99251)),x99253)),f317(f317(f7(x99251,f904(x99251,a893),a893),f319(x99251)),x99254)),x99252))
% 94.68/94.44 [10207]P31(x102071,f317(f317(f7(x102071,f904(f903(x102071,x102071),a893),f904(x102071,a893)),f317(f317(f8(f904(x102071,f904(f904(f903(x102071,x102071),a893),a893)),f904(f904(f903(x102071,x102071),a893),f904(x102071,a893)),x102071),f7(x102071,f904(f903(x102071,x102071),a893),a893)),f317(f317(f8(f904(x102071,f903(x102071,x102071)),f904(x102071,f904(f904(f903(x102071,x102071),a893),a893)),x102071),f317(f8(f903(x102071,x102071),f904(f904(f903(x102071,x102071),a893),a893),x102071),f319(f903(x102071,x102071)))),f242(x102071,x102071)))),x102072),x102073,x102074)+~P1(f317(f317(f319(f903(f898(x102071),f898(x102071))),f317(f317(f242(f898(x102071),f898(x102071)),x102073),x102074)),f148(x102071,x102072)))
% 94.68/94.44 [10211]P58(x102111,f317(f317(f7(x102111,f904(f903(x102111,x102111),a893),f904(x102111,a893)),f317(f317(f8(f904(x102111,f904(f904(f903(x102111,x102111),a893),a893)),f904(f904(f903(x102111,x102111),a893),f904(x102111,a893)),x102111),f7(x102111,f904(f903(x102111,x102111),a893),a893)),f317(f317(f8(f904(x102111,f903(x102111,x102111)),f904(x102111,f904(f904(f903(x102111,x102111),a893),a893)),x102111),f317(f8(f903(x102111,x102111),f904(f904(f903(x102111,x102111),a893),a893),x102111),f319(f903(x102111,x102111)))),f242(x102111,x102111)))),x102112),x102113,x102114)+~P1(f317(f317(f319(f903(f904(x102111,a893),f904(x102111,a893))),f317(f317(f242(f904(x102111,a893),f904(x102111,a893)),x102113),x102114)),f308(x102111,x102112)))
% 94.68/94.44 [10246]E(x102461,x102462)+~E(f317(f317(f7(x102463,f904(f903(x102463,x102464),a893),f904(x102464,a893)),f317(f317(f8(f904(x102464,f904(f904(f903(x102463,x102464),a893),a893)),f904(f904(f903(x102463,x102464),a893),f904(x102464,a893)),x102463),f7(x102464,f904(f903(x102463,x102464),a893),a893)),f317(f317(f8(f904(x102464,f903(x102463,x102464)),f904(x102464,f904(f904(f903(x102463,x102464),a893),a893)),x102463),f317(f8(f903(x102463,x102464),f904(f904(f903(x102463,x102464),a893),a893),x102464),f319(f903(x102463,x102464)))),f242(x102463,x102464)))),x102461),f317(f317(f7(x102463,f904(f903(x102463,x102464),a893),f904(x102464,a893)),f317(f317(f8(f904(x102464,f904(f904(f903(x102463,x102464),a893),a893)),f904(f904(f903(x102463,x102464),a893),f904(x102464,a893)),x102463),f7(x102464,f904(f903(x102463,x102464),a893),a893)),f317(f317(f8(f904(x102464,f903(x102463,x102464)),f904(x102464,f904(f904(f903(x102463,x102464),a893),a893)),x102463),f317(f8(f903(x102463,x102464),f904(f904(f903(x102463,x102464),a893),a893),x102464),f319(f903(x102463,x102464)))),f242(x102463,x102464)))),x102462))
% 94.68/94.44 [10249]~P31(x102491,f317(f317(f7(x102491,f904(f903(x102491,x102491),a893),f904(x102491,a893)),f317(f317(f8(f904(x102491,f904(f904(f903(x102491,x102491),a893),a893)),f904(f904(f903(x102491,x102491),a893),f904(x102491,a893)),x102491),f7(x102491,f904(f903(x102491,x102491),a893),a893)),f317(f317(f8(f904(x102491,f903(x102491,x102491)),f904(x102491,f904(f904(f903(x102491,x102491),a893),a893)),x102491),f317(f8(f903(x102491,x102491),f904(f904(f903(x102491,x102491),a893),a893),x102491),f319(f903(x102491,x102491)))),f242(x102491,x102491)))),x102494),x102492,x102493)+P1(f317(f317(f319(f903(f898(x102491),f898(x102491))),f317(f317(f242(f898(x102491),f898(x102491)),x102492),x102493)),f148(x102491,x102494)))
% 94.68/94.44 [10250]~P58(x102501,f317(f317(f7(x102501,f904(f903(x102501,x102501),a893),f904(x102501,a893)),f317(f317(f8(f904(x102501,f904(f904(f903(x102501,x102501),a893),a893)),f904(f904(f903(x102501,x102501),a893),f904(x102501,a893)),x102501),f7(x102501,f904(f903(x102501,x102501),a893),a893)),f317(f317(f8(f904(x102501,f903(x102501,x102501)),f904(x102501,f904(f904(f903(x102501,x102501),a893),a893)),x102501),f317(f8(f903(x102501,x102501),f904(f904(f903(x102501,x102501),a893),a893),x102501),f319(f903(x102501,x102501)))),f242(x102501,x102501)))),x102504),x102502,x102503)+P1(f317(f317(f319(f903(f904(x102501,a893),f904(x102501,a893))),f317(f317(f242(f904(x102501,a893),f904(x102501,a893)),x102502),x102503)),f308(x102501,x102504)))
% 94.68/94.44 [7606]~P94(x76061)+E(f317(f317(f74(x76061),f317(f94(x76061),x76062)),f317(f317(f23(x76061),f317(f94(x76061),x76063)),x76064)),f317(f317(f23(x76061),f317(f94(x76061),f317(f317(f74(a1),x76062),x76063))),x76064))
% 94.68/94.44 [7607]~P94(x76071)+E(f317(f317(f74(x76071),f317(f94(x76071),x76072)),f317(f317(f74(x76071),f317(f94(x76071),x76073)),x76074)),f317(f317(f74(x76071),f317(f94(x76071),f317(f317(f74(a1),x76072),x76073))),x76074))
% 94.68/94.44 [7608]~P94(x76081)+E(f317(f317(f75(x76081),f317(f94(x76081),x76082)),f317(f317(f75(x76081),f317(f94(x76081),x76083)),x76084)),f317(f317(f75(x76081),f317(f94(x76081),f317(f317(f75(a1),x76082),x76083))),x76084))
% 94.68/94.44 [7651]~P144(x76511)+E(f317(f155(x76511),f317(f317(f144(x76512,x76511),f317(f16(x76511,x76512),x76513)),x76514)),f317(f317(f75(x76511),f317(f90(x76511),f317(f179(f898(x76512)),x76514))),x76513))
% 94.68/94.44 [7891]E(f317(f258(x78911,f317(f317(f141(f903(a89,x78911)),x78912),x78913)),x78914),f317(f246(a89,x78911),x78912))+~P1(f317(f317(f225(a89),x78914),f317(f241(a89,x78911),x78912)))
% 94.68/94.44 [7932]~P94(x79321)+E(f317(f317(f74(x79321),f317(f94(x79321),x79322)),f317(f317(f23(x79321),x79323),f317(f94(x79321),x79324))),f317(f317(f74(x79321),f317(f94(x79321),f317(f317(f74(a1),x79322),f317(f73(a1),x79324)))),x79323))
% 94.68/94.44 [8066]E(f317(f258(x80661,x80662),f317(f317(f23(a89),x80663),f317(f241(a89,x80661),x80664))),f317(f258(x80661,f317(f317(f141(f903(a89,x80661)),x80664),x80662)),x80663))+P1(f317(f317(f225(a89),x80663),f317(f241(a89,x80661),x80664)))
% 94.68/94.44 [8503]~P1(f317(f317(f319(x85031),x85032),f317(f162(x85031),f104(x85031,x85034))))+P1(f317(f317(f319(x85031),x85032),f317(f162(x85031),f104(x85031,f317(f317(f124(x85031),x85033),x85034)))))
% 94.68/94.44 [8504]~P1(f317(f317(f319(x85041),x85042),f317(f162(x85041),f104(x85041,x85043))))+P1(f317(f317(f319(x85041),x85042),f317(f162(x85041),f104(x85041,f317(f317(f124(x85041),x85043),x85044)))))
% 94.68/94.44 [8523]E(f317(f317(f91(f904(x85231,a893)),f317(f317(f92(f904(x85231,a893)),x85232),x85233)),x85234),f317(f317(f92(f904(x85231,a893)),x85232),f317(f317(f91(f904(x85231,a893)),x85233),x85234)))+~P1(f317(f317(f224(f904(x85231,a893)),x85234),x85232))
% 94.68/94.44 [8832]~E(f317(f317(f91(f904(x88321,a893)),f317(f317(f92(f904(x88321,a893)),x88323),x88324)),x88322),f317(f317(f92(f904(x88321,a893)),x88323),f317(f317(f91(f904(x88321,a893)),x88324),x88322)))+P1(f317(f317(f224(f904(x88321,a893)),x88322),x88323))
% 94.68/94.44 [9120]~P1(f317(f317(f224(f904(x91201,a893)),x91202),f317(f317(f91(f904(x91201,a893)),x91203),x91204)))+P1(f317(f317(f224(f904(x91201,a893)),f317(f317(f23(f904(x91201,a893)),x91202),x91203)),x91204))
% 94.68/94.44 [9236]~E(f317(f300(x92361,x92362,x92363),f232(f904(x92361,a893))),f232(f904(x92362,a893)))+E(f317(f300(x92361,x92362,x92363),f317(f300(x92362,x92361,f85(x92361,x92362,f232(f904(x92361,a893)),x92363)),x92364)),x92364)
% 94.68/94.44 [9241]P1(f317(f317(f224(f904(x92411,a893)),x92412),f317(f317(f91(f904(x92411,a893)),x92413),x92414)))+~P1(f317(f317(f224(f904(x92411,a893)),f317(f317(f23(f904(x92411,a893)),x92412),x92413)),x92414))
% 94.68/94.44 [9326]~P86(x93261)+E(f317(f70(x93261),f317(f317(f6(x93262,x93261),f317(f317(f8(x93261,x93261,x93262),f70(x93261)),x93263)),x93264)),f317(f317(f6(x93262,x93261),f317(f317(f8(x93261,x93261,x93262),f70(x93261)),x93263)),x93264))
% 94.68/94.44 [9502]~P86(x95021)+P1(f317(f317(f224(x95021),f2(x95021)),f317(f317(f6(x95022,x95021),f317(f317(f8(x95021,x95021,x95022),f70(x95021)),x95023)),x95024)))
% 94.68/94.44 [9506]~P69(x95061)+E(f317(f155(x95061),f317(f317(f144(x95062,x95061),f317(f67(x95061,x95061,x95062,f73(x95061)),x95063)),x95064)),f317(f73(x95061),f317(f155(x95061),f317(f317(f144(x95062,x95061),x95063),x95064))))
% 94.68/94.44 [9656]~P86(x96561)+P1(f317(f317(f224(x96561),f317(f70(x96561),f317(f317(f6(x96562,x96561),x96563),x96564))),f317(f317(f6(x96562,x96561),f317(f317(f8(x96561,x96561,x96562),f70(x96561)),x96563)),x96564)))
% 94.68/94.44 [9685]~E(f317(f317(f74(a897),x96851),x96854),f317(f317(f74(a897),x96853),x96852))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x96851),x96852)),f317(f317(f242(a897,a897),x96853),x96854))),a99))
% 94.68/94.44 [9686]~P1(f317(f317(f225(a897),x96861),x96863))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x96861),x96862)),f317(f317(f242(a897,a897),x96863),x96864))),a26))
% 94.68/94.44 [9687]~P1(f317(f317(f225(a897),x96871),x96873))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x96871),x96872)),f317(f317(f242(a897,a897),x96873),x96874))),a65))
% 94.68/94.44 [9833]E(f317(f317(f74(a897),x98331),x98332),f317(f317(f74(a897),x98333),x98334))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x98331),x98334)),f317(f317(f242(a897,a897),x98333),x98332))),a99))
% 94.68/94.44 [9864]E(f317(f317(f154(x98641),f317(f317(f128(x98641),f317(f179(f898(x98641)),f167(x98641,x98642,x98643))),x98643)),x98644),f317(f317(f154(x98641),x98643),f317(f317(f74(a897),x98644),f317(f179(f898(x98641)),f167(x98641,x98642,x98643)))))+~P1(f317(f317(f225(a897),x98644),f317(f179(f898(x98641)),f317(f317(f128(x98641),f317(f179(f898(x98641)),f167(x98641,x98642,x98643))),x98643))))
% 94.68/94.44 [9880]~P1(f317(f317(f319(x98802),x98804),f317(f317(f34(x98801,f904(x98802,a893)),f232(f904(x98801,a893))),x98803)))+P1(f317(f317(f317(f34(x98801,f904(x98802,a893)),f232(f904(x98801,a893))),f317(f317(f8(f904(x98802,a893),f904(x98802,a893),x98801),f317(f7(x98802,f904(x98802,a893),a893),f319(x98802))),x98803)),x98804))
% 94.68/94.44 [9881]~P1(f317(f317(f319(x98812),x98814),f317(f317(f35(x98811,f904(x98812,a893)),f232(f904(x98811,a893))),x98813)))+P1(f317(f317(f317(f35(x98811,f904(x98812,a893)),f232(f904(x98811,a893))),f317(f317(f8(f904(x98812,a893),f904(x98812,a893),x98811),f317(f7(x98812,f904(x98812,a893),a893),f319(x98812))),x98813)),x98814))
% 94.68/94.44 [9950]~P1(f317(f44(x99501,x99502),f317(f317(f242(a1,a1),x99504),x99503)))+P1(f317(f44(f317(f73(a1),x99501),x99502),f317(f317(f242(a1,a1),f317(f317(f317(f86(a1),f317(f317(a314,x99503),f2(a1))),f317(f73(a1),x99504)),f317(f317(f23(a1),f317(f73(a1),x99504)),f72(a1)))),f317(f317(f317(f86(a1),f317(f317(a314,x99503),f2(a1))),f2(a1)),f317(f317(f23(a1),x99502),x99503)))))
% 94.68/94.44 [9962]P1(f317(f317(f319(x99621),x99622),f317(f317(f34(x99623,f904(x99621,a893)),f232(f904(x99623,a893))),x99624)))+~P1(f317(f317(f317(f34(x99623,f904(x99621,a893)),f232(f904(x99623,a893))),f317(f317(f8(f904(x99621,a893),f904(x99621,a893),x99623),f317(f7(x99621,f904(x99621,a893),a893),f319(x99621))),x99624)),x99622))
% 94.68/94.44 [9963]P1(f317(f317(f319(x99631),x99632),f317(f317(f35(x99633,f904(x99631,a893)),f232(f904(x99633,a893))),x99634)))+~P1(f317(f317(f317(f35(x99633,f904(x99631,a893)),f232(f904(x99633,a893))),f317(f317(f8(f904(x99631,a893),f904(x99631,a893),x99633),f317(f7(x99631,f904(x99631,a893),a893),f319(x99631))),x99634)),x99632))
% 94.68/94.44 [9975]E(f317(f317(f34(a897,f904(x99751,a893)),f232(f904(a897,a893))),x99752),f317(f317(f34(a897,f904(x99751,a893)),f232(f904(a897,a893))),x99753))+~E(f317(f317(f34(a897,f904(x99751,a893)),f317(f292(a897,f2(a897)),f457(x99752,x99754,x99753,x99751))),x99753),f317(f317(f34(a897,f904(x99751,a893)),f317(f292(a897,f2(a897)),f317(f317(f74(a897),f457(x99752,x99754,x99753,x99751)),x99754))),x99752))
% 94.68/94.44 [10327]~P1(f317(f317(f224(f904(f903(x103271,x103272),a893)),x103273),x103274))+P1(f317(f317(f224(f904(x103271,f904(x103272,a893))),f317(f317(f7(x103271,f904(f903(x103271,x103272),a893),f904(x103272,a893)),f317(f317(f8(f904(x103272,f904(f904(f903(x103271,x103272),a893),a893)),f904(f904(f903(x103271,x103272),a893),f904(x103272,a893)),x103271),f7(x103272,f904(f903(x103271,x103272),a893),a893)),f317(f317(f8(f904(x103272,f903(x103271,x103272)),f904(x103272,f904(f904(f903(x103271,x103272),a893),a893)),x103271),f317(f8(f903(x103271,x103272),f904(f904(f903(x103271,x103272),a893),a893),x103272),f319(f903(x103271,x103272)))),f242(x103271,x103272)))),x103273)),f317(f317(f7(x103271,f904(f903(x103271,x103272),a893),f904(x103272,a893)),f317(f317(f8(f904(x103272,f904(f904(f903(x103271,x103272),a893),a893)),f904(f904(f903(x103271,x103272),a893),f904(x103272,a893)),x103271),f7(x103272,f904(f903(x103271,x103272),a893),a893)),f317(f317(f8(f904(x103272,f903(x103271,x103272)),f904(x103272,f904(f904(f903(x103271,x103272),a893),a893)),x103271),f317(f8(f903(x103271,x103272),f904(f904(f903(x103271,x103272),a893),a893),x103272),f319(f903(x103271,x103272)))),f242(x103271,x103272)))),x103274)))
% 94.68/94.44 [10343]P1(f317(f317(f224(f904(f903(x103431,x103432),a893)),x103433),x103434))+~P1(f317(f317(f224(f904(x103431,f904(x103432,a893))),f317(f317(f7(x103431,f904(f903(x103431,x103432),a893),f904(x103432,a893)),f317(f317(f8(f904(x103432,f904(f904(f903(x103431,x103432),a893),a893)),f904(f904(f903(x103431,x103432),a893),f904(x103432,a893)),x103431),f7(x103432,f904(f903(x103431,x103432),a893),a893)),f317(f317(f8(f904(x103432,f903(x103431,x103432)),f904(x103432,f904(f904(f903(x103431,x103432),a893),a893)),x103431),f317(f8(f903(x103431,x103432),f904(f904(f903(x103431,x103432),a893),a893),x103432),f319(f903(x103431,x103432)))),f242(x103431,x103432)))),x103433)),f317(f317(f7(x103431,f904(f903(x103431,x103432),a893),f904(x103432,a893)),f317(f317(f8(f904(x103432,f904(f904(f903(x103431,x103432),a893),a893)),f904(f904(f903(x103431,x103432),a893),f904(x103432,a893)),x103431),f7(x103432,f904(f903(x103431,x103432),a893),a893)),f317(f317(f8(f904(x103432,f903(x103431,x103432)),f904(x103432,f904(f904(f903(x103431,x103432),a893),a893)),x103431),f317(f8(f903(x103431,x103432),f904(f904(f903(x103431,x103432),a893),a893),x103432),f319(f903(x103431,x103432)))),f242(x103431,x103432)))),x103434)))
% 94.68/94.44 [9375]~P1(f317(f317(f319(f903(x93751,x93751)),x93752),f297(x93751,x93754)))+P1(f317(f317(f319(f903(x93751,x93751)),x93752),f297(x93751,f317(f317(f91(f904(f903(x93751,x93751),a893)),x93753),x93754))))
% 94.68/94.44 [9376]~P1(f317(f317(f319(f903(x93761,x93761)),x93762),f297(x93761,x93763)))+P1(f317(f317(f319(f903(x93761,x93761)),x93762),f297(x93761,f317(f317(f91(f904(f903(x93761,x93761),a893)),x93763),x93764))))
% 94.68/94.44 [10061]~P1(f317(f317(f224(a897),f317(f317(f74(a897),x100611),x100614)),f317(f317(f74(a897),x100613),x100612)))+P1(f317(f317(f224(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x100611),x100612)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x100613),x100614)),f178(f904(f903(a897,a897),a893)))))))
% 94.68/94.44 [10062]~P1(f317(f317(f225(a897),f317(f317(f74(a897),x100621),x100624)),f317(f317(f74(a897),x100623),x100622)))+P1(f317(f317(f225(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x100621),x100622)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x100623),x100624)),f178(f904(f903(a897,a897),a893)))))))
% 94.68/94.44 [10149]P1(f317(f317(f224(a897),f317(f317(f74(a897),x101491),x101492)),f317(f317(f74(a897),x101493),x101494)))+~P1(f317(f317(f224(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x101491),x101494)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x101493),x101492)),f178(f904(f903(a897,a897),a893)))))))
% 94.68/94.44 [10150]P1(f317(f317(f225(a897),f317(f317(f74(a897),x101501),x101502)),f317(f317(f74(a897),x101503),x101504)))+~P1(f317(f317(f225(a1),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x101501),x101504)),f178(f904(f903(a897,a897),a893)))))),f317(a83,f317(f275(f903(a897,a897),f903(a897,a897),a99),f317(f317(f299(f903(a897,a897)),f317(f317(f242(a897,a897),x101503),x101502)),f178(f904(f903(a897,a897),a893)))))))
% 94.68/94.44 [10193]P1(f317(f317(f224(f904(x101931,a893)),f317(f317(f34(a897,f904(x101931,a893)),f232(f904(a897,a893))),x101932)),f317(f317(f34(a897,f904(x101931,a893)),f232(f904(a897,a893))),x101933)))+~P1(f317(f317(f224(f904(x101931,a893)),f317(f317(f34(a897,f904(x101931,a893)),f317(f292(a897,f2(a897)),f458(x101933,x101934,x101932,x101931))),x101932)),f317(f317(f34(a897,f904(x101931,a893)),f317(f292(a897,f2(a897)),f317(f317(f74(a897),f458(x101933,x101934,x101932,x101931)),x101934))),x101933)))
% 94.68/94.44 [10253]P1(f317(f317(f224(a89),x102534),f2(a89)))+E(f317(f317(f249(f903(a89,a89),f903(x102531,f904(a896,a313)),f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89))),f317(x102532,x102533)),f317(f317(f8(f904(f904(a89,f904(a893,f900(f899(x102531)))),f904(f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89)))),f904(f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89))),f903(x102531,f904(a896,a313))),f317(f249(f903(a89,a89),f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89))),f267(x102531,x102532,f317(f317(f23(a89),x102534),f72(a89)),x102533))),f317(f317(f8(f904(f904(a89,f904(a893,f900(f899(x102531)))),f904(a89,f904(a893,f900(f899(x102531))))),f904(f904(a89,f904(a893,f900(f899(x102531)))),f904(f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89)))),f903(x102531,f904(a896,a313))),f317(f8(f904(a89,f904(a893,f900(f899(x102531)))),f904(f903(a89,a89),f903(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89))),f904(a89,f904(a893,f900(f899(x102531))))),f242(f904(a89,f904(a893,f900(f899(x102531)))),f903(a89,a89)))),f317(f317(f8(f904(a89,f904(a893,f900(f899(x102531)))),f904(f904(a89,f904(a893,f900(f899(x102531)))),f904(a89,f904(a893,f900(f899(x102531))))),f903(x102531,f904(a896,a313))),f39(x102531)),f317(f317(f8(x102531,f904(a89,f904(a893,f900(f899(x102531)))),f903(x102531,f904(a896,a313))),f37(x102531)),f241(x102531,f904(a896,a313))))))),f267(x102531,x102532,x102534,x102533))
% 94.68/94.44 [10317]~P1(f317(f317(f319(x103172),x103174),f317(f274(x103171,x103172),x103173)))+P1(f317(f240(x103171,x103172,f317(f317(f7(x103171,f904(f903(x103171,x103172),a893),f904(x103172,a893)),f317(f317(f8(f904(x103172,f904(f904(f903(x103171,x103172),a893),a893)),f904(f904(f903(x103171,x103172),a893),f904(x103172,a893)),x103171),f7(x103172,f904(f903(x103171,x103172),a893),a893)),f317(f317(f8(f904(x103172,f903(x103171,x103172)),f904(x103172,f904(f904(f903(x103171,x103172),a893),a893)),x103171),f317(f8(f903(x103171,x103172),f904(f904(f903(x103171,x103172),a893),a893),x103172),f319(f903(x103171,x103172)))),f242(x103171,x103172)))),x103173)),x103174))
% 94.68/94.44 [10318]~P1(f317(f317(f319(x103181),x103184),f317(f254(x103181,x103182),x103183)))+P1(f317(f239(x103181,x103182,f317(f317(f7(x103181,f904(f903(x103181,x103182),a893),f904(x103182,a893)),f317(f317(f8(f904(x103182,f904(f904(f903(x103181,x103182),a893),a893)),f904(f904(f903(x103181,x103182),a893),f904(x103182,a893)),x103181),f7(x103182,f904(f903(x103181,x103182),a893),a893)),f317(f317(f8(f904(x103182,f903(x103181,x103182)),f904(x103182,f904(f904(f903(x103181,x103182),a893),a893)),x103181),f317(f8(f903(x103181,x103182),f904(f904(f903(x103181,x103182),a893),a893),x103182),f319(f903(x103181,x103182)))),f242(x103181,x103182)))),x103183)),x103184))
% 94.68/94.44 [10330]P1(f317(f317(f319(x103301),x103302),f317(f274(x103303,x103301),x103304)))+~P1(f317(f240(x103303,x103301,f317(f317(f7(x103303,f904(f903(x103303,x103301),a893),f904(x103301,a893)),f317(f317(f8(f904(x103301,f904(f904(f903(x103303,x103301),a893),a893)),f904(f904(f903(x103303,x103301),a893),f904(x103301,a893)),x103303),f7(x103301,f904(f903(x103303,x103301),a893),a893)),f317(f317(f8(f904(x103301,f903(x103303,x103301)),f904(x103301,f904(f904(f903(x103303,x103301),a893),a893)),x103303),f317(f8(f903(x103303,x103301),f904(f904(f903(x103303,x103301),a893),a893),x103301),f319(f903(x103303,x103301)))),f242(x103303,x103301)))),x103304)),x103302))
% 94.68/94.44 [10331]P1(f317(f317(f319(x103311),x103312),f317(f254(x103311,x103313),x103314)))+~P1(f317(f239(x103311,x103313,f317(f317(f7(x103311,f904(f903(x103311,x103313),a893),f904(x103313,a893)),f317(f317(f8(f904(x103313,f904(f904(f903(x103311,x103313),a893),a893)),f904(f904(f903(x103311,x103313),a893),f904(x103313,a893)),x103311),f7(x103313,f904(f903(x103311,x103313),a893),a893)),f317(f317(f8(f904(x103313,f903(x103311,x103313)),f904(x103313,f904(f904(f903(x103311,x103313),a893),a893)),x103311),f317(f8(f903(x103311,x103313),f904(f904(f903(x103311,x103313),a893),a893),x103313),f319(f903(x103311,x103313)))),f242(x103311,x103313)))),x103314)),x103312))
% 94.68/94.44 [9986]P1(f317(f150(x99861,x99862),x99863))+~P1(f317(f150(x99861,f317(f317(f18(x99861,a893,a893),f317(f317(f8(a893,f904(a893,a893),x99861),a315),x99864)),x99862)),x99863))
% 94.68/94.44 [9987]P1(f317(f150(x99871,x99872),x99873))+~P1(f317(f150(x99871,f317(f317(f18(x99871,a893,a893),f317(f317(f8(a893,f904(a893,a893),x99871),a315),x99872)),x99874)),x99873))
% 94.68/94.44 [10073]~P112(x100731)+E(f317(f317(f75(x100731),f317(f317(f74(x100731),f72(x100731)),f72(x100731))),f317(f317(f6(a897,x100731),f317(f317(f8(x100731,x100731,a897),f317(f74(x100731),x100732)),f317(f317(f7(a897,x100731,x100731),f317(f317(f8(x100731,f904(x100731,x100731),a897),f75(x100731)),f90(x100731))),x100733))),f317(f272(a897),x100734))),f317(f317(f75(x100731),f317(f90(x100731),x100734)),f317(f317(f74(x100731),x100732),f317(f317(f74(x100731),x100732),f317(f317(f75(x100731),f317(f90(x100731),f317(f317(f23(a897),x100734),f72(a897)))),x100733)))))
% 94.68/94.44 [10214]P1(f317(x102141,f507(x102142,x102143,x102144,x102141)))+P36(x102142,f317(f252(f903(x102142,x102142)),f317(f247(x102142,x102142,a893),f317(f317(f8(f904(x102142,a893),f904(x102142,a893),x102142),f317(f18(x102142,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102142),a315),x102141))),f317(f317(f7(x102142,f904(x102142,x102142),f904(x102142,a893)),f317(f317(f8(f904(x102142,a893),f904(f904(x102142,x102142),f904(x102142,a893)),x102142),f8(x102142,a893,x102142)),a314)),x102143)))))
% 94.68/94.44 [10228]~P1(f317(f317(f225(a897),f317(x102284,f317(x102283,f507(x102281,x102283,x102284,x102282)))),f317(x102284,f507(x102281,x102283,x102284,x102282))))+P36(x102281,f317(f252(f903(x102281,x102281)),f317(f247(x102281,x102281,a893),f317(f317(f8(f904(x102281,a893),f904(x102281,a893),x102281),f317(f18(x102281,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102281),a315),x102282))),f317(f317(f7(x102281,f904(x102281,x102281),f904(x102281,a893)),f317(f317(f8(f904(x102281,a893),f904(f904(x102281,x102281),f904(x102281,a893)),x102281),f8(x102281,a893,x102281)),a314)),x102283)))))
% 94.68/94.44 [10304]~P5(x103041)+E(f32(x103041,f317(f252(x103041),f317(f317(f8(f904(f904(x103042,x103041),a893),a893,x103041),f81(f904(x103042,x103041))),f317(f317(f8(f904(f904(x103042,x103041),a893),f904(f904(x103042,x103041),a893),x103041),f317(f18(f904(x103042,x103041),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x103042,x103041)),a315),f317(f317(f7(f904(x103042,x103041),f904(f904(x103042,x103041),a893),a893),f319(f904(x103042,x103041))),x103043)))),f317(f317(f7(x103041,f904(f904(x103042,x103041),x103041),f904(f904(x103042,x103041),a893)),f317(f317(f8(f904(x103041,a893),f904(f904(f904(x103042,x103041),x103041),f904(f904(x103042,x103041),a893)),x103041),f8(x103041,a893,f904(x103042,x103041))),a314)),f317(f317(f7(f904(x103042,x103041),x103042,x103041),f5(f904(x103042,x103041))),x103044)))))),f317(f32(f904(x103042,x103041),x103043),x103044))
% 94.68/94.44 [10305]~P5(x103051)+E(f32(x103051,f317(f252(x103051),f317(f317(f8(f904(f904(x103052,x103051),a893),a893,x103051),f81(f904(x103052,x103051))),f317(f317(f8(f904(f904(x103052,x103051),a893),f904(f904(x103052,x103051),a893),x103051),f317(f18(f904(x103052,x103051),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x103052,x103051)),a315),f317(f317(f7(f904(x103052,x103051),f904(f904(x103052,x103051),a893),a893),f319(f904(x103052,x103051))),x103053)))),f317(f317(f7(x103051,f904(f904(x103052,x103051),x103051),f904(f904(x103052,x103051),a893)),f317(f317(f8(f904(x103051,a893),f904(f904(f904(x103052,x103051),x103051),f904(f904(x103052,x103051),a893)),x103051),f8(x103051,a893,f904(x103052,x103051))),a314)),f317(f317(f7(f904(x103052,x103051),x103052,x103051),f5(f904(x103052,x103051))),x103054)))))),f317(f32(f904(x103052,x103051),x103053),x103054))
% 94.68/94.44 [10306]~P5(x103061)+E(f31(x103061,f317(f252(x103061),f317(f317(f8(f904(f904(x103062,x103061),a893),a893,x103061),f81(f904(x103062,x103061))),f317(f317(f8(f904(f904(x103062,x103061),a893),f904(f904(x103062,x103061),a893),x103061),f317(f18(f904(x103062,x103061),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x103062,x103061)),a315),f317(f317(f7(f904(x103062,x103061),f904(f904(x103062,x103061),a893),a893),f319(f904(x103062,x103061))),x103063)))),f317(f317(f7(x103061,f904(f904(x103062,x103061),x103061),f904(f904(x103062,x103061),a893)),f317(f317(f8(f904(x103061,a893),f904(f904(f904(x103062,x103061),x103061),f904(f904(x103062,x103061),a893)),x103061),f8(x103061,a893,f904(x103062,x103061))),a314)),f317(f317(f7(f904(x103062,x103061),x103062,x103061),f5(f904(x103062,x103061))),x103064)))))),f317(f31(f904(x103062,x103061),x103063),x103064))
% 94.68/94.44 [10307]~P5(x103071)+E(f31(x103071,f317(f252(x103071),f317(f317(f8(f904(f904(x103072,x103071),a893),a893,x103071),f81(f904(x103072,x103071))),f317(f317(f8(f904(f904(x103072,x103071),a893),f904(f904(x103072,x103071),a893),x103071),f317(f18(f904(x103072,x103071),a893,a893),f317(f317(f8(a893,f904(a893,a893),f904(x103072,x103071)),a315),f317(f317(f7(f904(x103072,x103071),f904(f904(x103072,x103071),a893),a893),f319(f904(x103072,x103071))),x103073)))),f317(f317(f7(x103071,f904(f904(x103072,x103071),x103071),f904(f904(x103072,x103071),a893)),f317(f317(f8(f904(x103071,a893),f904(f904(f904(x103072,x103071),x103071),f904(f904(x103072,x103071),a893)),x103071),f8(x103071,a893,f904(x103072,x103071))),a314)),f317(f317(f7(f904(x103072,x103071),x103072,x103071),f5(f904(x103072,x103071))),x103074)))))),f317(f31(f904(x103072,x103071),x103073),x103074))
% 94.68/94.44 [10356]~P1(f317(f317(f319(f903(x103561,x103561)),f317(f317(f242(x103561,x103561),x103563),x103564)),f317(f317(f91(f904(f903(x103561,x103561),a893)),x103562),f297(x103561,f178(f904(f903(x103561,x103561),a893))))))+P1(f317(f317(f317(f317(f91(f904(x103561,f904(x103561,a893))),f317(f317(f7(x103561,f904(f903(x103561,x103561),a893),f904(x103561,a893)),f317(f317(f8(f904(x103561,f904(f904(f903(x103561,x103561),a893),a893)),f904(f904(f903(x103561,x103561),a893),f904(x103561,a893)),x103561),f7(x103561,f904(f903(x103561,x103561),a893),a893)),f317(f317(f8(f904(x103561,f903(x103561,x103561)),f904(x103561,f904(f904(f903(x103561,x103561),a893),a893)),x103561),f317(f8(f903(x103561,x103561),f904(f904(f903(x103561,x103561),a893),a893),x103561),f319(f903(x103561,x103561)))),f242(x103561,x103561)))),x103562)),a314),x103563),x103564))
% 94.68/94.44 [10366]P1(f317(f317(f319(f903(x103661,x103661)),f317(f317(f242(x103661,x103661),x103662),x103663)),f317(f317(f91(f904(f903(x103661,x103661),a893)),x103664),f297(x103661,f178(f904(f903(x103661,x103661),a893))))))+~P1(f317(f317(f317(f317(f91(f904(x103661,f904(x103661,a893))),f317(f317(f7(x103661,f904(f903(x103661,x103661),a893),f904(x103661,a893)),f317(f317(f8(f904(x103661,f904(f904(f903(x103661,x103661),a893),a893)),f904(f904(f903(x103661,x103661),a893),f904(x103661,a893)),x103661),f7(x103661,f904(f903(x103661,x103661),a893),a893)),f317(f317(f8(f904(x103661,f903(x103661,x103661)),f904(x103661,f904(f904(f903(x103661,x103661),a893),a893)),x103661),f317(f8(f903(x103661,x103661),f904(f904(f903(x103661,x103661),a893),a893),x103661),f319(f903(x103661,x103661)))),f242(x103661,x103661)))),x103664)),a314),x103662),x103663))
% 94.68/94.44 [10314]E(f317(f317(f141(f898(x103141)),f317(f317(f141(x103141),x103142),f317(f132(f898(x103141),f898(x103141),f124(x103141),f103(x103141)),f317(f317(f144(f898(x103141),f898(x103141)),f146(f898(x103141),x103141,f103(x103141),f317(f317(f8(f898(x103141),f904(f898(x103141),f898(x103141)),x103141),f16(f898(x103141),f898(x103141))),f317(f317(f7(x103141,f898(x103141),f898(x103141)),f141(x103141)),f103(x103141))))),x103143)))),f169(x103141,f317(f317(f141(f898(x103141)),x103144),f317(f132(f898(f898(x103141)),f898(f898(x103141)),f124(f898(x103141)),f103(f898(x103141))),f317(f317(f144(f898(x103141),f898(f898(x103141))),f146(f898(f898(x103141)),x103141,f103(f898(x103141)),f317(f16(f904(f898(x103141),f898(f898(x103141))),x103141),f317(f317(f7(f898(x103141),f898(f898(x103141)),f898(f898(x103141))),f141(f898(x103141))),f103(f898(x103141)))))),x103143))))),f169(x103141,f317(f317(f141(f898(x103141)),f317(f317(f141(x103141),x103142),x103144)),x103143)))+~P1(f317(f305(f898(f898(x103141)),f170(x103141)),f317(f317(f141(f898(x103141)),f317(f317(f141(x103141),x103142),x103144)),x103143)))
% 94.68/94.44 [10355]~P1(f317(f28(x103552),f317(f252(x103552),x103554)))+P1(f317(f28(x103551),f317(f252(x103551),f317(f317(f8(f904(x103552,a893),a893,x103551),f81(x103552)),f317(f317(f7(x103551,f904(x103552,a893),f904(x103552,a893)),f317(f317(f8(f904(x103552,f904(a893,a893)),f904(f904(x103552,a893),f904(x103552,a893)),x103551),f18(x103552,a893,a893)),f317(f317(f8(f904(x103552,a893),f904(x103552,f904(a893,a893)),x103551),f317(f8(a893,f904(a893,a893),x103552),a315)),f317(f317(f7(x103551,f904(x103552,x103551),f904(x103552,a893)),f317(f317(f8(f904(x103551,a893),f904(f904(x103552,x103551),f904(x103552,a893)),x103551),f8(x103551,a893,x103552)),a314)),x103553)))),x103554)))))
% 94.68/94.44 [8870]P24(x88701,x88702,x88703,x88704)+~P25(x88701,x88702,x88703,x88704,x88705)
% 94.68/94.44 [5328]E(x53281,x53282)+~E(f159(x53283,x53281,x53284),f159(x53283,x53282,x53285))
% 94.68/94.44 [5329]E(x53291,x53292)+~E(f116(x53293,x53294,x53291),f116(x53293,x53295,x53292))
% 94.68/94.44 [5330]E(x53301,x53302)+~E(f116(x53303,x53301,x53304),f116(x53303,x53302,x53305))
% 94.68/94.44 [8197]~E(f317(x81973,x81974),x81975)+E(f69(x81971,x81972,x81973,x81974,x81975),x81973)
% 94.68/94.44 [8728]~E(f69(x87284,x87285,x87281,x87282,x87283),x87281)+E(f317(x87281,x87282),x87283)
% 94.68/94.44 [9345]~P25(x93452,x93451,x93454,x93453,x93455)+P25(x93451,x93452,f71(x93452,x93451,x93453,x93454),x93455,x93453)
% 94.68/94.44 [9346]~P25(x93462,x93461,x93464,x93463,x93465)+P25(x93461,x93462,f85(x93462,x93461,x93463,x93464),x93465,x93463)
% 94.68/94.44 [6149]P1(f317(f240(x61491,x61492,x61493),x61494))+~P1(f317(f317(x61493,x61495),x61494))
% 94.68/94.44 [6151]P1(f317(f239(x61511,x61512,x61513),x61514))+~P1(f317(f317(x61513,x61514),x61515))
% 94.68/94.44 [6640]~E(x66405,f2(a89))+E(f317(f186(x66401,x66402,x66403,x66404),x66405),f114(x66402))
% 94.68/94.44 [6641]~E(x66415,f2(a89))+E(f317(f188(x66411,x66412,x66413,x66414),x66415),f105(x66412))
% 94.68/94.44 [6781]~E(x67813,f2(a89))+E(f317(f263(x67811,x67812,x67813,x67814),x67815),f317(f242(x67811,x67812),x67815))
% 94.68/94.44 [7846]~P20(x78464,x78461,x78462,x78465)+E(f317(f67(x78461,x78461,x78461,f317(x78462,x78463)),f317(x78462,x78463)),f317(x78462,x78463))
% 94.68/94.44 [8238]~P16(x82385,x82381,x82382)+E(f317(f67(x82381,x82381,x82381,f317(x82382,x82383)),f317(x82382,x82384)),f317(f67(x82381,x82381,x82381,f317(x82382,x82384)),f317(x82382,x82383)))
% 94.68/94.44 [8563]P1(f317(f317(f319(f903(x85631,x85631)),f317(f317(f242(x85631,x85631),x85632),x85633)),f311(x85631,x85634,x85635)))+~P1(f317(f317(f225(a897),f317(x85634,x85632)),f317(x85634,x85633)))
% 94.68/94.44 [8656]~P1(f317(f317(f319(x86564),x86563),f280(x86564,x86561,x86562,x86565)))+P1(f317(f317(x86561,x86562),x86563))
% 94.68/94.44 [8657]~P1(f317(f317(f319(x86574),x86573),f289(x86574,x86571,x86572,x86575)))+P1(f317(f317(x86571,x86572),x86573))
% 94.68/94.44 [8658]~P1(f317(f317(f319(x86584),x86582),f280(x86584,x86581,x86585,x86583)))+P1(f317(f317(x86581,x86582),x86583))
% 94.68/94.44 [8659]~P1(f317(f317(f319(x86594),x86592),f289(x86594,x86591,x86595,x86593)))+P1(f317(f317(x86591,x86592),x86593))
% 94.68/94.44 [8740]~P25(x87401,x87403,x87405,x87402,x87404)+E(f317(f29(x87401),x87402),f317(f29(x87403),x87404))
% 94.68/94.44 [8788]~P25(x87881,x87882,x87883,x87884,x87885)+E(f317(f300(x87881,x87882,x87883),x87884),x87885)
% 94.68/94.44 [8808]~P56(x88082,x88081,x88085,x88083,x88084)+E(f317(f300(x88081,x88082,x88083),x88084),f232(f904(x88082,a893)))
% 94.68/94.44 [9253]~P33(x92531,x92532,x92533,x92534,x92535)+P33(x92531,x92532,x92533,f317(f158(x92531),x92534),f317(f158(x92532),x92535))
% 94.68/94.44 [9255]~P33(x92551,x92552,x92553,f317(f158(x92551),x92554),x92555)+P33(x92551,x92552,x92553,x92554,f317(f158(x92552),x92555))
% 94.68/94.44 [9256]~P33(x92561,x92562,x92563,x92564,f317(f158(x92562),x92565))+P33(x92561,x92562,x92563,f317(f158(x92561),x92564),x92565)
% 94.68/94.44 [9262]P33(x92621,x92622,x92623,x92624,x92625)+~P33(x92621,x92622,x92623,f317(f158(x92621),x92624),f317(f158(x92622),x92625))
% 94.68/94.44 [9675]P1(f317(f317(f319(f903(f898(x96751),f898(x96751))),f317(f317(f242(f898(x96751),f898(x96751)),f317(f317(f141(x96751),x96752),x96753)),f317(f317(f141(x96751),x96752),x96754))),f147(x96751,x96755)))+~P1(f317(f317(f319(f903(f898(x96751),f898(x96751))),f317(f317(f242(f898(x96751),f898(x96751)),x96753),x96754)),f147(x96751,x96755)))
% 94.68/94.44 [9676]P1(f317(f317(f319(f903(f898(x96761),f898(x96761))),f317(f317(f242(f898(x96761),f898(x96761)),f317(f317(f124(x96761),x96762),x96763)),f317(f317(f124(x96761),x96762),x96764))),f137(x96761,x96765)))+~P1(f317(f317(f319(f903(f898(x96761),f898(x96761))),f317(f317(f242(f898(x96761),f898(x96761)),x96763),x96764)),f137(x96761,x96765)))
% 94.68/94.44 [9871]E(f317(f317(f141(x98711),f631(x98712,x98713,x98714,x98715,x98711)),f634(x98712,x98713,x98714,x98715,x98711)),x98715)+~P1(f317(f317(f319(f903(f898(x98711),f898(x98711))),f317(f317(f242(f898(x98711),f898(x98711)),x98715),f317(f317(f141(x98711),x98714),x98713))),f148(x98711,x98712)))
% 94.68/94.44 [9892]E(f317(f317(f141(x98921),f632(x98922,x98923,x98924,x98925,x98921)),f633(x98922,x98923,x98924,x98925,x98921)),x98923)+~P1(f317(f317(f319(f903(f898(x98921),f898(x98921))),f317(f317(f242(f898(x98921),f898(x98921)),f317(f317(f141(x98921),x98925),x98924)),x98923)),f148(x98921,x98922)))
% 94.68/94.44 [10036]~P1(f317(f317(f319(f903(f898(x100361),f898(x100361))),f317(f317(f242(f898(x100361),f898(x100361)),f317(f317(f141(x100361),x100365),x100362)),x100364)),f148(x100361,x100363)))+P1(f317(f317(f319(f903(f898(x100361),f898(x100361))),f317(f317(f242(f898(x100361),f898(x100361)),x100362),f633(x100363,x100364,x100362,x100365,x100361))),f148(x100361,x100363)))
% 94.68/94.44 [10116]~P1(f317(f317(f319(f903(f898(x101161),f898(x101161))),f317(f317(f242(f898(x101161),f898(x101161)),x101165),f317(f317(f141(x101161),x101164),x101163))),f148(x101161,x101162)))+P1(f317(f317(f319(f903(f898(x101161),f898(x101161))),f317(f317(f242(f898(x101161),f898(x101161)),f634(x101162,x101163,x101164,x101165,x101161)),x101163)),f148(x101161,x101162)))
% 94.68/94.44 [10308]P1(f317(f317(f319(f903(x103081,x103081)),f317(f317(f242(x103081,x103081),f317(x103082,f317(f317(f74(a897),x103083),x103084))),f317(x103082,x103083))),f297(x103081,x103085)))+~P1(f317(f317(f319(f903(x103081,x103081)),f317(f317(f242(x103081,x103081),f317(x103082,f317(a102,f554(x103084,x103083,x103085,x103082,x103081)))),f317(x103082,f554(x103084,x103083,x103085,x103082,x103081)))),f297(x103081,x103085)))
% 94.68/94.44 [5302]E(x53021,x53022)+~E(f317(f317(f141(x53023),x53024),x53021),f317(f317(f141(x53023),x53025),x53022))
% 94.68/94.44 [5303]E(x53031,x53032)+~E(f317(f317(f141(x53033),x53031),x53034),f317(f317(f141(x53033),x53032),x53035))
% 94.68/94.44 [5345]P1(f317(x53451,x53452))+~E(f317(f126(x53453,x53451),x53454),f317(f317(f141(x53453),x53452),x53455))
% 94.68/94.44 [5346]P1(f317(x53461,x53462))+~E(f317(f317(f141(x53463),x53462),x53464),f317(f126(x53463,x53461),x53465))
% 94.68/94.44 [5507]~E(f317(f317(f128(x55071),x55073),x55072),f317(f317(f141(x55071),x55074),x55075))+E(f317(f317(f154(x55071),x55072),x55073),x55074)
% 94.68/94.44 [5647]~P14(x56474,x56475,x56471)+E(f317(f317(x56471,x56472),f317(f317(x56471,x56472),x56473)),f317(f317(x56471,x56472),x56473))
% 94.68/94.44 [6208]~E(x62084,f2(a89))+E(f317(f317(f107(x62081,x62082,x62083),x62084),x62085),f317(f317(f242(f898(x62082),x62081),f103(x62082)),x62085))
% 94.68/94.44 [6283]~P66(x62832)+~E(f317(f317(f138(x62831,x62832,x62833),x62834),x62835),f103(x62831))
% 94.68/94.44 [6681]E(x66811,x66812)+~E(f317(f317(f124(x66813),x66814),f317(f317(f141(x66813),x66811),f103(x66813))),f317(f317(f124(x66813),x66815),f317(f317(f141(x66813),x66812),f103(x66813))))
% 94.68/94.44 [6682]E(x66821,x66822)+~E(f317(f317(f124(x66823),x66821),f317(f317(f141(x66823),x66824),f103(x66823))),f317(f317(f124(x66823),x66822),f317(f317(f141(x66823),x66825),f103(x66823))))
% 94.68/94.44 [7005]E(f317(f317(f299(x70051),f317(x70052,x70053)),f317(f300(x70054,x70051,x70052),x70055)),f317(f300(x70054,x70051,x70052),x70055))+~P1(f317(f317(f319(x70054),x70053),x70055))
% 94.68/94.44 [7013]~P1(f317(x70134,f317(x70133,x70135)))+P1(f317(f317(f301(x70131,x70132,x70133),x70134),x70135))
% 94.68/94.44 [7016]~P1(f317(f317(x70163,x70165),x70164))+P1(f317(f317(f233(x70161,x70162,x70163),x70164),x70165))
% 94.68/94.44 [7113]~E(f317(f300(x71131,x71132,x71133),x71134),x71135)+E(f317(f300(f904(x71131,a893),f904(x71132,a893),f300(x71131,x71132,x71133)),f317(f298(x71131),x71134)),f317(f298(x71132),x71135))
% 94.68/94.44 [7141]E(f317(f261(x71411,x71412,x71413,x71414),x71415),f317(x71414,x71415))+~P1(f317(f317(f319(x71411),x71415),x71413))
% 94.68/94.44 [7455]P24(x74551,x74552,x74553,x74554)+~P24(x74551,x74552,x74553,f317(f317(f299(x74551),x74555),x74554))
% 94.68/94.44 [7560]~P1(f317(f317(f319(x75604),x75603),x75605))+P1(f317(f317(f319(x75601),f317(x75602,x75603)),f317(f300(x75604,x75601,x75602),x75605)))
% 94.68/94.44 [7581]~P66(x75812)+E(f140(x75811,x75812,x75813,f317(f126(x75811,x75814),x75815)),f317(f126(x75811,x75814),f140(x75811,x75812,x75813,x75815)))
% 94.68/94.44 [7612]P1(f317(x76121,f317(x76122,x76123)))+~P1(f317(f317(f301(x76124,x76125,x76122),x76121),x76123))
% 94.68/94.44 [7615]P1(f317(f317(x76151,x76152),x76153))+~P1(f317(f317(f233(x76154,x76155,x76151),x76153),x76152))
% 94.68/94.44 [7681]~P1(f317(f317(f319(x76813),f317(x76814,x76812)),x76815))+P1(f317(f317(f319(x76811),x76812),f317(f301(x76811,x76813,x76814),x76815)))
% 94.68/94.44 [8079]~P1(f317(f317(f319(x80795),x80793),f317(f301(x80795,x80791,x80792),x80794)))+P1(f317(f317(f319(x80791),f317(x80792,x80793)),x80794))
% 94.68/94.44 [8378]~P16(x83782,x83781,x83783)+E(f317(f132(x83781,x83782,f317(f7(x83782,x83781,x83781),x83783),x83784),f142(x83782,x83785)),f317(f317(f58(x83782,x83781,x83783),x83784),f317(f162(x83782),x83785)))
% 94.68/94.44 [8400]E(f317(x84001,f547(x84002,x84001,x84003,x84004)),x84004)+~P1(f317(f317(f319(x84005),x84004),f317(f300(x84003,x84005,x84001),x84002)))
% 94.68/94.44 [8703]~E(x87032,f317(f317(f141(x87031),x87034),x87035))+P1(f317(f317(f319(f903(f898(x87031),f898(x87031))),f317(f317(f242(f898(x87031),f898(x87031)),f103(x87031)),x87032)),f137(x87031,x87033)))
% 94.68/94.44 [8749]E(f317(x87491,f317(f85(x87492,x87493,x87494,x87491),x87495)),x87495)+~P1(f317(f317(f319(x87493),x87495),f317(f300(x87492,x87493,x87491),x87494)))
% 94.68/94.44 [8752]P24(x87521,x87522,f85(x87522,x87521,x87523,x87524),x87525)+~P1(f317(f317(f224(f904(x87521,a893)),x87525),f317(f300(x87522,x87521,x87524),x87523)))
% 94.68/94.44 [8759]~P33(x87591,x87593,x87595,x87592,x87594)+E(f317(f179(f898(x87591)),x87592),f317(f179(f898(x87593)),x87594))
% 94.68/94.44 [8770]P1(f317(f317(f224(f904(x87701,a893)),f317(f317(f35(x87702,f904(x87701,a893)),x87703),x87704)),f317(x87704,x87705)))+~P1(f317(f317(f319(x87702),x87705),x87703))
% 94.68/94.44 [8824]~P56(x88241,x88242,x88243,x88245,x88244)+E(f317(f300(x88241,x88242,x88243),f232(f904(x88241,a893))),x88244)
% 94.68/94.44 [9049]E(f317(f126(x90491,x90492),f725(x90493,x90494,x90495,x90492,x90491)),x90493)+~E(f317(f126(x90491,x90492),x90495),f317(f317(f141(x90491),x90494),x90493))
% 94.68/94.44 [9050]E(f317(f126(x90501,x90502),f720(x90503,x90502,x90504,x90505,x90501)),x90504)+~E(f317(f317(f141(x90501),x90505),x90504),f317(f126(x90501,x90502),x90503))
% 94.68/94.44 [9142]E(f317(f179(f898(x91421)),x91422),x91423)+~P1(f317(f317(f319(f903(f898(x91421),f898(x91421))),f317(f317(f242(f898(x91421),f898(x91421)),x91424),x91422)),f317(f133(x91421,x91425),x91423)))
% 94.68/94.44 [9143]E(f317(f179(f898(x91431)),x91432),x91433)+~P1(f317(f317(f319(f903(f898(x91431),f898(x91431))),f317(f317(f242(f898(x91431),f898(x91431)),x91432),x91434)),f317(f133(x91431,x91435),x91433)))
% 94.68/94.44 [9212]P1(f317(f317(f319(x92121),f547(x92122,x92123,x92121,x92124)),x92122))+~P1(f317(f317(f319(x92125),x92124),f317(f300(x92121,x92125,x92123),x92122)))
% 94.68/94.44 [9373]E(f317(f300(x93731,x93732,x93733),f658(x93734,x93733,x93731,x93735,x93732)),x93735)+~P1(f317(f317(f224(f904(x93732,a893)),x93735),f317(f300(x93731,x93732,x93733),x93734)))
% 94.68/94.44 [9693]P1(f317(f317(f319(f903(f898(x96931),f898(x96931))),f317(f317(f242(f898(x96931),f898(x96931)),f317(f317(f141(x96931),x96932),x96933)),f317(f317(f141(x96931),x96932),x96934))),f297(f898(x96931),f147(x96931,x96935))))+~P1(f317(f317(f319(f903(f898(x96931),f898(x96931))),f317(f317(f242(f898(x96931),f898(x96931)),x96933),x96934)),f297(f898(x96931),f147(x96931,x96935))))
% 94.68/94.44 [9724]~E(f317(x97243,f672(x97245,x97244,x97243,x97242,x97241)),f317(x97245,f672(x97245,x97244,x97243,x97242,x97241)))+E(f317(f317(f144(x97241,x97242),x97243),x97244),f317(f317(f144(x97241,x97242),x97245),x97244))
% 94.68/94.44 [9799]~E(f317(f126(x97991,x97995),x97994),f317(f317(f141(x97991),x97993),x97992))+E(f317(f317(f124(x97991),f723(x97992,x97993,x97994,x97995,x97991)),f317(f317(f141(x97991),x97993),f725(x97992,x97993,x97994,x97995,x97991))),x97994)
% 94.68/94.44 [9800]~E(f317(f317(f141(x98001),x98005),x98004),f317(f126(x98001,x98003),x98002))+E(f317(f317(f124(x98001),f721(x98002,x98003,x98004,x98005,x98001)),f317(f317(f141(x98001),x98005),f720(x98002,x98003,x98004,x98005,x98001))),x98002)
% 94.68/94.44 [9804]E(f317(f317(f144(x98041,x98042),x98043),x98044),f317(f317(f144(x98041,x98042),x98045),x98044))+P1(f317(f317(f319(x98041),f672(x98043,x98044,x98045,x98042,x98041)),f317(f162(x98041),x98044)))
% 94.68/94.44 [9834]~P1(f317(f317(f319(x98345),x98344),f317(f275(x98341,x98345,x98343),x98342)))+P1(f317(f317(f319(x98341),f351(x98342,x98343,x98341,x98344,x98345)),x98342))
% 94.68/94.44 [9835]~P1(f317(f317(f319(x98355),x98354),f317(f275(x98351,x98355,x98353),x98352)))+P1(f317(f317(f319(x98351),f390(x98352,x98353,x98351,x98354,x98355)),x98352))
% 94.68/94.44 [9865]~P1(f317(f317(f224(f904(x98655,a893)),x98654),f317(f300(x98651,x98655,x98653),x98652)))+P1(f317(f317(f224(f904(x98651,a893)),f658(x98652,x98653,x98651,x98654,x98655)),x98652))
% 94.68/94.44 [10309]E(x103091,f2(a89))+E(f213(f903(f898(x103092),x103093),f903(x103092,x103093),f317(f317(f242(f898(x103092),x103093),f103(x103092)),x103094),f317(f247(x103092,x103093,f903(f898(x103092),x103093)),f317(f317(f7(x103092,f904(x103093,f903(f898(x103092),x103093)),f904(x103093,f903(f898(x103092),x103093))),f317(f317(f8(f904(f903(f898(x103092),x103093),f903(f898(x103092),x103093)),f904(f904(x103093,f903(f898(x103092),x103093)),f904(x103093,f903(f898(x103092),x103093))),x103092),f8(f903(f898(x103092),x103093),f903(f898(x103092),x103093),x103093)),f317(f317(f8(f904(f898(x103092),f904(x103093,f903(f898(x103092),x103093))),f904(f903(f898(x103092),x103093),f903(f898(x103092),x103093)),x103092),f247(f898(x103092),x103093,f903(f898(x103092),x103093))),f317(f317(f8(f904(f898(x103092),f898(x103092)),f904(f898(x103092),f904(x103093,f903(f898(x103092),x103093))),x103092),f317(f8(f898(x103092),f904(x103093,f903(f898(x103092),x103093)),f898(x103092)),f242(f898(x103092),x103093))),f141(x103092))))),f317(f107(x103093,x103092,x103095),f317(f317(f23(a89),x103091),f72(a89))))),f317(x103095,x103094)),f317(f317(f107(x103093,x103092,x103095),x103091),x103094))
% 94.68/94.44 [6086]E(x60861,x60862)+~E(f317(f246(x60863,x60864),f317(f317(f242(x60863,x60864),x60865),x60861)),x60862)
% 94.68/94.44 [6087]E(x60871,x60872)+~E(f317(f241(x60873,x60874),f317(f317(f242(x60873,x60874),x60871),x60875)),x60872)
% 94.68/94.44 [6359]~E(x63593,f317(f317(f124(x63591),x63594),f317(f317(f141(x63591),x63592),x63595)))+P1(f317(f317(f319(x63591),x63592),f317(f162(x63591),x63593)))
% 94.68/94.44 [6768]E(f317(f300(x67681,x67682,f317(f16(x67682,x67681),x67683)),x67684),f317(f317(f299(x67682),x67683),f178(f904(x67682,a893))))+~P1(f317(f317(f319(x67681),x67685),x67684))
% 94.68/94.44 [6842]E(f317(f317(f91(f904(x68421,a893)),f317(f162(x68421),x68422)),f317(f162(x68421),x68423)),f317(f162(x68421),x68424))+~E(f156(x68421,x68425,x68424),f317(f317(f242(f898(x68421),f898(x68421)),x68422),x68423))
% 94.68/94.44 [6943]~P66(x69432)+E(f317(f179(f898(x69431)),f317(f317(f138(x69431,x69432,x69433),x69434),x69435)),f317(a102,f317(f179(f898(x69431)),x69435)))
% 94.68/94.44 [6957]~P66(x69572)+E(f317(f162(x69571),f317(f317(f138(x69571,x69572,x69573),x69574),x69575)),f317(f317(f299(x69571),x69574),f317(f162(x69571),x69575)))
% 94.68/94.44 [7235]~P112(x72351)+E(f317(f317(f74(x72351),f317(f317(f74(x72351),x72352),x72353)),f317(f317(f74(x72351),x72354),x72355)),f317(f317(f74(x72351),f317(f317(f74(x72351),x72352),x72354)),f317(f317(f74(x72351),x72353),x72355)))
% 94.68/94.44 [7236]~P112(x72361)+E(f317(f317(f75(x72361),f317(f317(f75(x72361),x72362),x72363)),f317(f317(f75(x72361),x72364),x72365)),f317(f317(f75(x72361),f317(f317(f75(x72361),x72362),x72364)),f317(f317(f75(x72361),x72363),x72365)))
% 94.68/94.44 [7237]~P61(x72371)+E(f317(f317(f281(x72371),f317(f317(f75(x72371),x72372),x72373)),f317(f317(f75(x72371),x72374),x72375)),f317(f317(f75(x72371),f317(f317(f281(x72371),x72372),x72374)),f317(f317(f281(x72371),x72373),x72375)))
% 94.68/94.44 [7251]~P66(x72511)+E(f296(x72511,f317(f317(f223(x72511),x72512),x72513),f317(f317(f228(x72511),x72514),x72515)),f317(f317(f92(f904(x72511,a893)),f296(x72511,x72512,x72514)),f296(x72511,x72513,x72515)))
% 94.68/94.44 [7252]~P66(x72521)+E(f295(x72521,f317(f317(f223(x72521),x72522),x72523),f317(f317(f228(x72521),x72524),x72525)),f317(f317(f92(f904(x72521,a893)),f295(x72521,x72522,x72524)),f295(x72521,x72523,x72525)))
% 94.68/94.44 [7253]~P66(x72531)+E(f293(x72531,f317(f317(f223(x72531),x72532),x72533),f317(f317(f228(x72531),x72534),x72535)),f317(f317(f92(f904(x72531,a893)),f293(x72531,x72532,x72534)),f293(x72531,x72533,x72535)))
% 94.68/94.44 [7254]~P66(x72541)+E(f317(f317(f92(f904(x72541,a893)),f317(f292(x72541,x72542),x72543)),f317(f292(x72541,x72544),x72545)),f317(f292(x72541,f317(f317(f223(x72541),x72542),x72544)),f317(f317(f228(x72541),x72543),x72545)))
% 94.68/94.44 [7374]~P1(f317(x73741,f873(x73743,x73742,x73741)))+P1(f317(x73741,f317(f317(f242(x73742,x73743),x73744),x73745)))
% 94.68/94.44 [7486]~E(x74862,f317(x74864,x74865))+P1(f317(f317(f319(x74861),x74862),f317(f300(x74863,x74861,x74864),f232(f904(x74863,a893)))))
% 94.68/94.44 [7558]~P14(x75583,x75582,x75584)+P14(x75581,x75582,f317(f317(f8(x75583,f904(x75582,x75582),x75581),x75584),x75585))
% 94.68/94.44 [7559]~P16(x75593,x75592,x75594)+P16(x75591,x75592,f317(f317(f8(x75593,f904(x75592,x75592),x75591),x75594),x75595))
% 94.68/94.44 [7698]~P24(x76981,x76982,x76983,x76984)+P24(x76981,x76982,x76983,f317(f317(f23(f904(x76981,a893)),x76984),x76985))
% 94.68/94.44 [7855]~P1(f317(f317(x78553,x78554),x78555))+P1(f317(f317(f247(x78551,x78552,a893),x78553),f317(f317(f242(x78551,x78552),x78554),x78555)))
% 94.68/94.44 [7969]~P1(f317(x79692,x79694))+~E(f317(f317(f128(x79691),f317(f179(f898(x79691)),f167(x79691,x79692,x79693))),x79693),f317(f317(f141(x79691),x79694),x79695))
% 94.68/94.44 [7989]P24(x79891,x79892,x79893,x79894)+~P24(x79891,x79892,x79893,f317(f317(f91(f904(x79891,a893)),x79895),x79894))
% 94.68/94.44 [7990]P24(x79901,x79902,x79903,x79904)+~P24(x79901,x79902,x79903,f317(f317(f91(f904(x79901,a893)),x79904),x79905))
% 94.68/94.44 [8037]~P66(x80372)+E(f317(f317(f138(x80371,x80372,x80373),x80374),f140(x80371,x80372,x80373,x80375)),f140(x80371,x80372,x80373,f317(f317(f141(x80371),x80374),x80375)))
% 94.68/94.44 [8355]~P14(x83552,x83551,x83553)+E(f317(f132(x83551,x83552,f317(f7(x83552,x83551,x83551),x83553),x83554),x83555),f317(f317(f58(x83552,x83551,x83553),x83554),f317(f162(x83552),x83555)))
% 94.68/94.44 [8383]~E(f317(f317(f128(x83831),f317(f179(f898(x83831)),f167(x83831,x83832,x83833))),x83833),f317(f317(f141(x83831),x83834),x83835))+E(f317(f317(f124(x83831),f167(x83831,x83832,x83833)),f317(f317(f141(x83831),x83834),x83835)),x83833)
% 94.68/94.44 [8410]P1(f317(f317(x84101,x84102),x84103))+~P1(f317(f317(f247(x84104,x84105,a893),x84101),f317(f317(f242(x84104,x84105),x84102),x84103)))
% 94.68/94.44 [8887]P1(f317(f317(f224(f904(x88871,a893)),f317(f300(x88872,x88871,x88873),x88874)),f317(f300(x88872,x88871,x88873),x88875)))+~P1(f317(f317(f224(f904(x88872,a893)),x88874),x88875))
% 94.68/94.44 [8888]P1(f317(f317(f224(f904(x88881,a893)),f317(f301(x88881,x88882,x88883),x88884)),f317(f301(x88881,x88882,x88883),x88885)))+~P1(f317(f317(f224(f904(x88882,a893)),x88884),x88885))
% 94.68/94.44 [8967]E(x89671,f2(a89))+E(f317(f317(f249(x89672,x89673,x89672,f903(x89673,x89672)),f317(x89674,x89675)),f263(x89673,x89672,f317(f317(f23(a89),x89671),f72(a89)),x89674)),f317(f263(x89673,x89672,x89671,x89674),x89675))
% 94.68/94.44 [9074]P1(f317(f317(f245(x90741,x90742,a893,x90743),x90744),x90745))+~P1(f317(x90743,f317(f317(f242(x90741,x90742),x90744),x90745)))
% 94.68/94.44 [9351]~P1(f317(f317(f245(x93512,x93513,a893,x93511),x93514),x93515))+P1(f317(x93511,f317(f317(f242(x93512,x93513),x93514),x93515)))
% 94.68/94.44 [9536]~P1(f317(f317(f319(x95362),x95365),f317(f300(x95361,x95362,x95364),x95363)))+P1(f317(f317(f319(x95361),f317(f85(x95361,x95362,x95363,x95364),x95365)),x95363))
% 94.68/94.44 [9635]~P1(f317(f28(x96353),f317(f300(x96352,x96353,x96355),f232(f904(x96352,a893)))))+P1(f317(f28(x96351),f317(f300(x96352,x96351,f317(f317(f8(x96353,x96351,x96352),x96354),x96355)),f232(f904(x96352,a893)))))
% 94.68/94.44 [9660]P1(f317(f317(f224(f904(f904(x96601,a893),a893)),f317(f300(f904(x96602,a893),f904(x96601,a893),f300(x96602,x96601,x96603)),f317(f298(x96602),x96604))),f317(f298(x96601),x96605)))+~P1(f317(f317(f224(f904(x96601,a893)),f317(f300(x96602,x96601,x96603),x96604)),x96605))
% 94.68/94.44 [9732]E(x97321,x97322)+~P1(f317(f60(x97323,x97324,x97325,x97321,f178(f904(x97323,a893))),x97322))
% 94.68/94.44 [9748]E(f317(f317(f242(x97481,x97482),f477(x97483,x97484,x97485,x97482,x97481)),f481(x97483,x97484,x97485,x97482,x97481)),x97485)+~P1(f317(f317(f319(f903(x97481,x97482)),x97485),f317(f317(f244(x97481,x97482),x97484),x97483)))
% 94.68/94.44 [9840]P1(f317(f317(f319(x98401),f477(x98402,x98403,x98404,x98405,x98401)),x98403))+~P1(f317(f317(f319(f903(x98401,x98405)),x98404),f317(f317(f244(x98401,x98405),x98403),x98402)))
% 94.68/94.44 [9995]P1(f317(f317(f319(x99951),f481(x99952,x99953,x99954,x99951,x99955)),f317(x99952,f477(x99952,x99953,x99954,x99951,x99955))))+~P1(f317(f317(f319(f903(x99955,x99951)),x99954),f317(f317(f244(x99955,x99951),x99953),x99952)))
% 94.68/94.44 [10015]P1(f317(f317(f319(f903(x100151,x100151)),f317(f317(f242(x100151,x100151),x100152),f573(x100153,x100154,x100155,x100152,x100151))),x100153))+~P1(f317(f317(f319(f903(x100151,x100151)),f317(f317(f242(x100151,x100151),x100152),x100155)),f317(f317(f173(f903(x100151,x100151),a893),f317(a102,x100154)),x100153)))
% 94.68/94.44 [10016]P1(f317(f317(f319(f903(x100161,x100161)),f317(f317(f242(x100161,x100161),x100162),f574(x100163,x100164,x100165,x100162,x100161))),x100163))+~P1(f317(f317(f319(f903(x100161,x100161)),f317(f317(f242(x100161,x100161),x100162),x100165)),f317(f317(f173(f903(x100161,x100161),a893),f317(a102,x100164)),x100163)))
% 94.68/94.44 [10033]~P1(f317(f317(f319(f903(f898(x100331),f898(x100331))),f317(f317(f242(f898(x100331),f898(x100331)),f317(f317(f141(x100331),x100332),x100335)),x100334)),f148(x100331,x100333)))+P1(f317(f317(f319(f903(x100331,x100331)),f317(f317(f242(x100331,x100331),x100332),f632(x100333,x100334,x100335,x100332,x100331))),x100333))
% 94.68/94.44 [6439]P1(f317(x64392,x64394))+E(f167(x64391,x64392,f317(f317(f124(x64391),x64393),f317(f317(f141(x64391),x64394),x64395))),f167(x64391,x64392,x64393))
% 94.68/94.44 [6488]~P68(x64882)+E(f317(f317(f317(f23(f904(x64881,x64882)),x64883),x64884),x64885),f317(f317(f23(x64882),f317(x64883,x64885)),f317(x64884,x64885)))
% 94.68/94.44 [6490]~P100(x64902)+E(f317(f317(f317(f91(f904(x64901,x64902)),x64903),x64904),x64905),f317(f317(f91(x64902),f317(x64903,x64905)),f317(x64904,x64905)))
% 94.68/94.44 [6492]~P100(x64922)+E(f317(f317(f317(f92(f904(x64921,x64922)),x64923),x64924),x64925),f317(f317(f92(x64922),f317(x64923,x64925)),f317(x64924,x64925)))
% 94.68/94.44 [6512]E(x65121,x65122)+E(f317(f317(f154(x65123),f317(f317(f149(x65123,x65124),x65121),x65125)),x65122),f317(f317(f154(x65123),x65124),x65122))
% 94.68/94.44 [6786]~E(x67864,f178(f904(x67863,a893)))+E(f317(f317(f23(f904(x67861,a893)),x67862),f317(f317(f34(x67863,f904(x67861,a893)),x67864),x67865)),x67862)
% 94.68/94.44 [6787]~E(x67874,f178(f904(x67873,a893)))+E(f317(f317(f91(f904(x67871,a893)),x67872),f317(f317(f34(x67873,f904(x67871,a893)),x67874),x67875)),x67872)
% 94.68/94.44 [6788]~E(x67884,f178(f904(x67883,a893)))+E(f317(f317(f92(f904(x67881,a893)),x67882),f317(f317(f35(x67883,f904(x67881,a893)),x67884),x67885)),x67882)
% 94.68/94.44 [6804]~E(x68044,f178(f904(x68043,a893)))+E(f317(f317(f299(x68041),x68042),f317(f317(f34(x68043,f904(x68041,a893)),x68044),x68045)),f317(f317(f299(x68041),x68042),f178(f904(x68041,a893))))
% 94.68/94.44 [7604]E(f317(f317(f154(x76041),f317(f317(f144(x76042,x76041),x76043),x76044)),x76045),f317(x76043,f317(f317(f154(x76042),x76044),x76045)))+~P1(f317(f317(f225(a897),x76045),f317(f179(f898(x76042)),x76044)))
% 94.68/94.44 [7669]E(f317(f317(f91(f904(x76691,a893)),f317(x76692,x76693)),f317(f317(f34(x76694,f904(x76691,a893)),x76695),x76692)),f317(f317(f34(x76694,f904(x76691,a893)),x76695),x76692))+~P1(f317(f317(f319(x76694),x76693),x76695))
% 94.68/94.44 [7670]E(f317(f317(f92(f904(x76701,a893)),f317(x76702,x76703)),f317(f317(f35(x76704,f904(x76701,a893)),x76705),x76702)),f317(f317(f35(x76704,f904(x76701,a893)),x76705),x76702))+~P1(f317(f317(f319(x76704),x76703),x76705))
% 94.68/94.44 [8277]~E(x82773,f178(f904(x82771,a893)))+E(f317(f317(f34(x82771,f904(x82772,a893)),x82773),f317(f317(f8(f904(x82772,a893),f904(x82772,a893),x82771),f317(f299(x82772),x82774)),x82775)),f178(f904(x82772,a893)))
% 94.68/94.44 [8282]~P1(f317(f317(f319(x82824),x82823),x82825))+P1(f317(f317(f224(f904(x82821,a893)),f317(x82822,x82823)),f317(f317(f34(x82824,f904(x82821,a893)),x82825),x82822)))
% 94.68/94.44 [8409]~E(f317(x84094,x84092),x84095)+P1(f317(f317(f319(x84091),x84092),f317(f301(x84091,x84093,x84094),f317(f317(f299(x84093),x84095),f178(f904(x84093,a893))))))
% 94.68/94.44 [8456]~P54(x84561,x84562,f317(f276(x84562,x84561),x84563))+E(f317(f317(f92(f904(x84561,a893)),f317(f275(x84562,x84561,x84563),x84564)),f317(f275(x84562,x84561,x84563),x84565)),f317(f275(x84562,x84561,x84563),f317(f317(f92(f904(x84562,a893)),x84564),x84565)))
% 94.68/94.44 [8532]E(x85321,f2(a89))+E(f317(f108(x85322,x85323,f317(x85324,f317(f317(f23(a89),x85321),f72(a89)))),f317(f317(f7(x85322,a89,f899(x85323)),x85325),x85321)),f317(f188(x85322,x85323,x85324,x85325),x85321))
% 94.68/94.44 [8570]E(x85701,f178(f904(x85702,a893)))+E(f317(f317(f34(x85702,f904(x85703,a893)),x85701),f317(f317(f8(f904(x85703,a893),f904(x85703,a893),x85702),f317(f299(x85703),x85704)),x85705)),f317(f317(f299(x85703),x85704),f317(f317(f34(x85702,f904(x85703,a893)),x85701),x85705)))
% 94.68/94.44 [8621]~P24(x86212,x86211,x86213,f232(f904(x86212,a893)))+E(f317(f317(f23(f904(x86211,a893)),f317(f300(x86212,x86211,x86213),x86214)),f317(f300(x86212,x86211,x86213),x86215)),f317(f300(x86212,x86211,x86213),f317(f317(f23(f904(x86212,a893)),x86214),x86215)))
% 94.68/94.44 [8622]~P24(x86222,x86221,x86223,f232(f904(x86222,a893)))+E(f317(f317(f92(f904(x86221,a893)),f317(f300(x86222,x86221,x86223),x86224)),f317(f300(x86222,x86221,x86223),x86225)),f317(f300(x86222,x86221,x86223),f317(f317(f92(f904(x86222,a893)),x86224),x86225)))
% 94.68/94.44 [8690]~P1(f317(f317(f61(x86901,x86902,x86905),x86903),x86904))+P1(f317(f317(f319(f903(x86901,x86902)),f317(f317(f242(x86901,x86902),x86903),x86904)),x86905))
% 94.68/94.44 [8722]P1(f317(f317(f319(x87221),x87222),f317(f274(x87223,x87221),x87224)))+~P1(f317(f317(f319(f903(x87223,x87221)),f317(f317(f242(x87223,x87221),x87225),x87222)),x87224))
% 94.68/94.44 [8724]P1(f317(f317(f319(x87241),x87242),f317(f254(x87241,x87243),x87244)))+~P1(f317(f317(f319(f903(x87241,x87243)),f317(f317(f242(x87241,x87243),x87242),x87245)),x87244))
% 94.68/94.44 [8871]P1(f317(f317(f61(x88711,x88712,x88713),x88714),x88715))+~P1(f317(f317(f319(f903(x88711,x88712)),f317(f317(f242(x88711,x88712),x88714),x88715)),x88713))
% 94.68/94.44 [8910]E(f317(x89101,x89102),x89103)+~P1(f317(f317(f319(x89104),x89102),f317(f301(x89104,x89105,x89101),f317(f317(f299(x89105),x89103),f178(f904(x89105,a893))))))
% 94.68/94.44 [9139]P1(f317(f317(f319(f903(x91391,x91392)),f317(f317(f242(x91391,x91392),x91393),x91394)),f317(f276(x91392,x91391),x91395)))+~P1(f317(f317(f319(f903(x91392,x91391)),f317(f317(f242(x91392,x91391),x91394),x91393)),x91395))
% 94.68/94.44 [9157]~P1(f317(f317(x91571,x91575),x91574))+P1(f317(f317(x91571,f317(f246(x91572,x91573),f317(f317(f242(x91572,x91573),x91574),x91575))),f317(f241(x91572,x91573),f317(f317(f242(x91572,x91573),x91574),x91575))))
% 94.68/94.44 [9187]~P1(f317(f317(f319(f903(x91872,x91871)),f317(f317(f242(x91872,x91871),x91874),x91873)),f317(f276(x91871,x91872),x91875)))+P1(f317(f317(f319(f903(x91871,x91872)),f317(f317(f242(x91871,x91872),x91873),x91874)),x91875))
% 94.68/94.44 [9219]~P1(f317(f317(f319(f903(x92193,x92191)),f317(f317(f242(x92193,x92191),x92195),x92192)),x92194))+P1(f317(f317(f319(x92191),x92192),f317(f275(x92193,x92191,x92194),f317(f317(f299(x92193),x92195),f178(f904(x92193,a893))))))
% 94.68/94.44 [9266]P1(f317(f317(f319(f903(x92661,x92662)),f317(f317(f242(x92661,x92662),x92663),x92664)),x92665))+~P1(f317(f317(f319(x92662),x92664),f317(f275(x92661,x92662,x92665),f317(f317(f299(x92661),x92663),f178(f904(x92661,a893))))))
% 94.68/94.44 [9358]~P76(x93581)+E(f317(f317(f6(a897,x93581),x93582),f293(a897,f317(f317(f74(a897),x93583),x93584),f317(f317(f74(a897),x93585),x93584))),f317(f317(f6(a897,x93581),f317(f317(f8(a897,x93581,a897),x93582),f317(f317(f7(a897,a897,a897),f74(a897)),x93584))),f293(a897,x93583,x93585)))
% 94.68/94.44 [9378]~P76(x93781)+E(f317(f317(f6(a897,x93781),x93782),f317(f292(a897,f317(f317(f74(a897),x93783),x93784)),f317(f317(f74(a897),x93785),x93784))),f317(f317(f6(a897,x93781),f317(f317(f8(a897,x93781,a897),x93782),f317(f317(f7(a897,a897,a897),f74(a897)),x93784))),f317(f292(a897,x93783),x93785)))
% 94.68/94.44 [9436]~P24(x94361,x94362,x94363,f232(f904(x94361,a893)))+E(f317(f317(f144(x94361,x94362),x94363),f317(f126(x94361,f317(f317(f8(a893,a893,x94361),a312),f317(a314,x94364))),x94365)),f317(f126(x94362,f317(f317(f8(a893,a893,x94362),a312),f317(a314,f317(x94363,x94364)))),f317(f317(f144(x94361,x94362),x94363),x94365)))
% 94.68/94.44 [9454]~P24(x94541,x94542,x94543,f317(f317(f299(x94541),x94544),f317(f162(x94541),x94545)))+E(f317(f317(f144(x94541,x94542),x94543),f317(f126(x94541,f317(f317(f8(a893,a893,x94541),a312),f317(a314,x94544))),x94545)),f317(f126(x94542,f317(f317(f8(a893,a893,x94542),a312),f317(a314,f317(x94543,x94544)))),f317(f317(f144(x94541,x94542),x94543),x94545)))
% 94.68/94.44 [9623]P1(f317(f317(f319(f903(f898(x96231),f898(x96231))),f317(f317(f242(f898(x96231),f898(x96231)),f317(f317(f141(x96231),x96232),x96233)),f317(f317(f141(x96231),x96234),x96233))),f147(x96231,x96235)))+~P1(f317(f317(f319(f903(x96231,x96231)),f317(f317(f242(x96231,x96231),x96232),x96234)),x96235))
% 94.68/94.44 [9743]E(f317(f317(f299(x97431),f659(x97432,x97433,x97434,x97435,x97431)),f670(x97432,x97433,x97434,x97435,x97431)),f317(f317(f299(x97431),x97434),x97433))+~P1(f317(f56(x97431,x97435,f317(f317(f299(x97431),x97434),x97433)),x97432))
% 94.68/94.44 [9744]E(f317(f317(f299(x97441),f680(x97442,x97443,x97444,x97445,x97441)),f693(x97442,x97443,x97444,x97445,x97441)),f317(f317(f299(x97441),x97444),x97443))+~P1(f317(f56(x97441,x97445,f317(f317(f299(x97441),x97444),x97443)),x97442))
% 94.68/94.44 [9825]P1(f317(f317(f319(x98251),f585(x98252,x98253,x98254,x98255,x98251)),x98254))+P1(f317(f317(f317(f35(x98251,f904(x98255,a893)),x98254),x98253),x98252))
% 94.68/94.44 [9830]P1(f317(f317(f319(x98301),f583(x98302,x98303,x98301,x98304,x98305)),x98303))+P1(f317(f317(f319(x98305),x98304),f317(f317(f35(x98301,f904(x98305,a893)),x98303),x98302)))
% 94.68/94.44 [9838]P1(f317(f317(f319(x98381),f586(x98382,x98383,x98381,x98384,x98385)),x98383))+P1(f317(f317(f224(f904(x98385,a893)),x98384),f317(f317(f35(x98381,f904(x98385,a893)),x98383),x98382)))
% 94.68/94.44 [9839]P1(f317(f317(f319(x98391),f814(x98392,x98393,x98394,x98395,x98391)),x98395))+P1(f317(f317(f224(f904(x98394,a893)),x98393),f317(f317(f35(x98391,f904(x98394,a893)),x98395),x98392)))
% 94.68/94.44 [9841]P1(f317(f317(x98411,f439(x98412,x98411,x98413,x98414,x98415)),x98412))+~P1(f317(f317(f317(f34(x98415,f904(x98414,a893)),x98413),x98411),x98412))
% 94.68/94.44 [9845]P1(f317(f317(f319(x98451),f439(x98452,x98453,x98454,x98455,x98451)),x98454))+~P1(f317(f317(f317(f34(x98451,f904(x98455,a893)),x98454),x98453),x98452))
% 94.68/94.44 [9846]P52(x98464,f317(f317(f35(x98461,f904(x98464,a893)),x98465),x98463),f317(f317(f35(x98461,f904(f903(x98464,x98464),a893)),x98465),x98462))+P1(f317(f317(f319(x98461),f753(x98462,x98463,x98464,x98465,x98461)),x98465))
% 94.68/94.44 [9847]P52(x98474,f317(f317(f34(x98471,f904(x98474,a893)),x98475),x98473),f317(f317(f34(x98471,f904(f903(x98474,x98474),a893)),x98475),x98472))+P1(f317(f317(f319(x98471),f806(x98472,x98473,x98474,x98475,x98471)),x98475))
% 94.68/94.44 [9857]P1(f317(f317(f319(x98571),f444(x98572,x98573,x98571,x98574,x98575)),x98573))+~P1(f317(f317(f319(x98575),x98574),f317(f317(f34(x98571,f904(x98575,a893)),x98573),x98572)))
% 94.68/94.44 [9863]P1(f317(f317(f319(x98631),x98632),f317(x98633,f444(x98633,x98634,x98635,x98632,x98631))))+~P1(f317(f317(f319(x98631),x98632),f317(f317(f34(x98635,f904(x98631,a893)),x98634),x98633)))
% 94.68/94.44 [9944]~P1(f317(f317(x99444,f585(x99445,x99444,x99443,x99442,x99441)),x99445))+P1(f317(f317(f317(f35(x99441,f904(x99442,a893)),x99443),x99444),x99445))
% 94.68/94.44 [9947]~P1(f317(f317(f319(x99471),x99472),f317(x99475,f583(x99475,x99474,x99473,x99472,x99471))))+P1(f317(f317(f319(x99471),x99472),f317(f317(f35(x99473,f904(x99471,a893)),x99474),x99475)))
% 94.68/94.44 [9951]~P52(x99511,f317(x99514,f806(x99515,x99514,x99511,x99513,x99512)),f317(x99515,f806(x99515,x99514,x99511,x99513,x99512)))+P52(x99511,f317(f317(f34(x99512,f904(x99511,a893)),x99513),x99514),f317(f317(f34(x99512,f904(f903(x99511,x99511),a893)),x99513),x99515))
% 94.68/94.44 [9952]~P52(x99521,f317(x99524,f753(x99525,x99524,x99521,x99523,x99522)),f317(x99525,f753(x99525,x99524,x99521,x99523,x99522)))+P52(x99521,f317(f317(f35(x99522,f904(x99521,a893)),x99523),x99524),f317(f317(f35(x99522,f904(f903(x99521,x99521),a893)),x99523),x99525))
% 94.68/94.44 [9953]~P1(f317(f317(f224(f904(x99531,a893)),x99532),f317(x99535,f586(x99535,x99534,x99533,x99532,x99531))))+P1(f317(f317(f224(f904(x99531,a893)),x99532),f317(f317(f35(x99533,f904(x99531,a893)),x99534),x99535)))
% 94.68/94.44 [9954]~P1(f317(f317(f224(f904(x99541,a893)),x99542),f317(x99545,f814(x99545,x99542,x99541,x99544,x99543))))+P1(f317(f317(f224(f904(x99541,a893)),x99542),f317(f317(f35(x99543,f904(x99541,a893)),x99544),x99545)))
% 94.68/94.44 [10019]~P1(f317(f317(f319(x100191),f659(x100195,x100194,x100193,x100192,x100191)),f670(x100195,x100194,x100193,x100192,x100191)))+~P1(f317(f56(x100191,x100192,f317(f317(f299(x100191),x100193),x100194)),x100195))
% 94.68/94.45 [10020]~P1(f317(f317(f319(x100201),f680(x100205,x100204,x100203,x100202,x100201)),f693(x100205,x100204,x100203,x100202,x100201)))+~P1(f317(f56(x100201,x100202,f317(f317(f299(x100201),x100203),x100204)),x100205))
% 94.68/94.45 [10021]~P1(f317(f317(f319(f903(x100211,x100211)),f317(f317(f242(x100211,x100211),x100212),x100215)),f317(f317(f173(f903(x100211,x100211),a893),f317(a102,x100214)),x100213)))+P1(f317(f317(f319(f903(x100211,x100211)),f317(f317(f242(x100211,x100211),x100212),f575(x100213,x100214,x100215,x100212,x100211))),f317(f317(f173(f903(x100211,x100211),a893),x100214),x100213)))
% 94.68/94.45 [10027]P1(f317(f60(x100271,x100271,x100272,f659(x100273,x100274,x100275,x100272,x100271),f670(x100273,x100274,x100275,x100272,x100271)),x100273))+~P1(f317(f56(x100271,x100272,f317(f317(f299(x100271),x100275),x100274)),x100273))
% 94.68/94.45 [10028]P1(f317(f60(x100281,x100281,x100282,f680(x100283,x100284,x100285,x100282,x100281),f693(x100283,x100284,x100285,x100282,x100281)),x100283))+~P1(f317(f56(x100281,x100282,f317(f317(f299(x100281),x100285),x100284)),x100283))
% 94.68/94.45 [10038]~P66(x100381)+P13(x100381,f317(f317(f144(x100382,x100381),x100383),f317(f126(x100382,f317(f317(f7(x100382,x100381,a893),f317(f317(f8(x100381,f904(x100381,a893),x100382),a314),x100383)),f317(x100384,x100385))),x100385)))
% 94.68/94.45 [10088]~P1(f317(f317(f319(x100882),x100885),f317(f275(x100881,x100882,x100884),x100883)))+P1(f317(f317(f319(f903(x100881,x100882)),f317(f317(f242(x100881,x100882),f351(x100883,x100884,x100881,x100885,x100882)),x100885)),x100884))
% 94.68/94.45 [10089]~P1(f317(f317(f319(x100892),x100895),f317(f275(x100891,x100892,x100894),x100893)))+P1(f317(f317(f319(f903(x100891,x100892)),f317(f317(f242(x100891,x100892),f390(x100893,x100894,x100891,x100895,x100892)),x100895)),x100894))
% 94.68/94.45 [10109]~P1(f317(f317(f319(f903(x101091,x101091)),f317(f317(f242(x101091,x101091),x101095),x101094)),f317(f317(f173(f903(x101091,x101091),a893),f317(a102,x101093)),x101092)))+P1(f317(f317(f319(f903(x101091,x101091)),f317(f317(f242(x101091,x101091),f575(x101092,x101093,x101094,x101095,x101091)),x101094)),x101092))
% 94.68/94.45 [10112]~P1(f317(f317(f319(f903(x101121,x101121)),f317(f317(f242(x101121,x101121),x101125),x101124)),f317(f317(f173(f903(x101121,x101121),a893),f317(a102,x101123)),x101122)))+P1(f317(f317(f319(f903(x101121,x101121)),f317(f317(f242(x101121,x101121),f573(x101122,x101123,x101124,x101125,x101121)),x101124)),f317(f317(f173(f903(x101121,x101121),a893),x101123),x101122)))
% 94.68/94.45 [10113]~P1(f317(f317(f319(f903(x101131,x101131)),f317(f317(f242(x101131,x101131),x101135),x101134)),f317(f317(f173(f903(x101131,x101131),a893),f317(a102,x101133)),x101132)))+P1(f317(f317(f319(f903(x101131,x101131)),f317(f317(f242(x101131,x101131),f574(x101132,x101133,x101134,x101135,x101131)),x101134)),f317(f317(f173(f903(x101131,x101131),a893),x101133),x101132)))
% 94.68/94.45 [10114]~P1(f317(f317(f319(f903(f898(x101141),f898(x101141))),f317(f317(f242(f898(x101141),f898(x101141)),x101145),f317(f317(f141(x101141),x101144),x101143))),f148(x101141,x101142)))+P1(f317(f317(f319(f903(x101141,x101141)),f317(f317(f242(x101141,x101141),f631(x101142,x101143,x101144,x101145,x101141)),x101144)),x101142))
% 94.68/94.45 [7690]~E(x76903,f178(f904(x76902,a893)))+E(f317(f317(f91(f904(x76901,a893)),f317(f317(f34(x76902,f904(x76901,a893)),x76903),x76904)),x76905),x76905)
% 94.68/94.45 [7691]~E(x76913,f178(f904(x76912,a893)))+E(f317(f317(f92(f904(x76911,a893)),f317(f317(f35(x76912,f904(x76911,a893)),x76913),x76914)),x76915),x76915)
% 94.68/94.45 [8118]~E(x81183,f178(f904(x81182,a893)))+E(f317(f317(f23(f904(x81181,a893)),f317(f317(f35(x81182,f904(x81181,a893)),x81183),x81184)),x81185),f317(f317(f23(f904(x81181,a893)),f232(f904(x81181,a893))),x81185))
% 94.68/94.45 [8251]E(f317(f317(f149(x82511,f317(f317(f124(x82511),x82512),x82513)),x82514),x82515),f317(f317(f124(x82511),f317(f317(f149(x82511,x82512),x82514),x82515)),x82513))+~P1(f317(f317(f225(a897),x82514),f317(f179(f898(x82511)),x82512)))
% 94.68/94.45 [8522]E(f317(f317(f154(x85221),f317(f317(f144(a897,x85221),x85222),f129(a897,f317(f292(a897,x85223),x85224)))),x85225),f317(x85222,f317(f317(f74(a897),x85223),x85225)))+~P1(f317(f317(f225(a897),x85225),f317(f317(f23(a897),x85224),x85223)))
% 94.68/94.45 [8536]E(x85361,f2(a89))+E(f112(x85362,x85363,f317(x85364,f317(f317(f23(a89),x85361),f72(a89))),f317(f317(f7(x85362,a89,f899(f900(x85363))),x85365),x85361)),f317(f186(x85362,x85363,x85364,x85365),x85361))
% 94.68/94.45 [8560]~E(x85603,f178(f904(x85601,a893)))+E(f317(f317(f34(x85601,f904(x85602,a893)),x85603),f317(f317(f8(f904(x85602,a893),f904(x85602,a893),x85601),f317(f91(f904(x85602,a893)),x85604)),x85605)),f178(f904(x85602,a893)))
% 94.68/94.45 [8561]~E(x85613,f178(f904(x85611,a893)))+E(f317(f317(f35(x85611,f904(x85612,a893)),x85613),f317(f317(f8(f904(x85612,a893),f904(x85612,a893),x85611),f317(f23(f904(x85612,a893)),x85614)),x85615)),f232(f904(x85612,a893)))
% 94.68/94.45 [8562]~E(x85623,f178(f904(x85621,a893)))+E(f317(f317(f35(x85621,f904(x85622,a893)),x85623),f317(f317(f8(f904(x85622,a893),f904(x85622,a893),x85621),f317(f92(f904(x85622,a893)),x85624)),x85625)),f232(f904(x85622,a893)))
% 94.68/94.45 [8564]~P145(x85642)+E(f317(f317(f6(x85641,x85642),f317(f317(f8(x85642,x85642,x85641),f317(f75(x85642),x85643)),x85644)),x85645),f317(f317(f75(x85642),x85643),f317(f317(f6(x85641,x85642),x85644),x85645)))
% 94.68/94.45 [8855]E(x88551,f178(f904(x88552,a893)))+E(f317(f317(f34(x88552,f904(x88553,a893)),x88551),f317(f317(f8(f904(x88553,a893),f904(x88553,a893),x88552),f317(f91(f904(x88553,a893)),x88554)),x88555)),f317(f317(f91(f904(x88553,a893)),x88554),f317(f317(f34(x88552,f904(x88553,a893)),x88551),x88555)))
% 94.68/94.45 [8856]E(x88561,f178(f904(x88562,a893)))+E(f317(f317(f35(x88562,f904(x88563,a893)),x88561),f317(f317(f8(f904(x88563,a893),f904(x88563,a893),x88562),f317(f23(f904(x88563,a893)),x88564)),x88565)),f317(f317(f23(f904(x88563,a893)),x88564),f317(f317(f34(x88562,f904(x88563,a893)),x88561),x88565)))
% 94.68/94.45 [8857]E(x88571,f178(f904(x88572,a893)))+E(f317(f317(f35(x88572,f904(x88573,a893)),x88571),f317(f317(f8(f904(x88573,a893),f904(x88573,a893),x88572),f317(f92(f904(x88573,a893)),x88574)),x88575)),f317(f317(f92(f904(x88573,a893)),x88574),f317(f317(f35(x88572,f904(x88573,a893)),x88571),x88575)))
% 94.68/94.45 [9056]~P1(f317(f317(f225(a897),f317(x90564,x90562)),f317(x90564,x90563)))+P1(f317(f317(f319(f903(x90561,x90561)),f317(f317(f242(x90561,x90561),x90562),x90563)),f143(x90561,f317(f317(f141(f904(x90561,a897)),x90564),x90565))))
% 94.68/94.45 [9322]~P24(x93222,x93221,x93223,f317(f317(f91(f904(x93222,a893)),x93224),x93225))+E(f317(f317(f92(f904(x93221,a893)),f317(f300(x93222,x93221,x93223),f317(f317(f23(f904(x93222,a893)),x93224),x93225))),f317(f300(x93222,x93221,x93223),f317(f317(f23(f904(x93222,a893)),x93225),x93224))),f178(f904(x93221,a893)))
% 94.68/94.45 [9585]~P24(x95853,x95851,x95855,f232(f904(x95853,a893)))+E(f317(f67(x95851,x95852,x95853,f317(f67(x95853,x95852,x95851,x95854),f85(x95853,x95851,f232(f904(x95853,a893)),x95855))),x95855),x95854)
% 94.68/94.45 [9619]~P1(f317(f317(f224(f904(x96193,a893)),f317(f275(x96191,x96193,x96194),x96192)),x96195))+P1(f317(f317(f224(f904(x96191,a893)),x96192),f317(f73(f904(x96191,a893)),f317(f275(x96193,x96191,f317(f276(x96191,x96193),x96194)),f317(f73(f904(x96193,a893)),x96195)))))
% 94.68/94.45 [9644]~P24(x96441,x96442,x96443,f317(f317(f299(x96441),x96444),x96445))+~P1(f317(f317(f319(x96442),f317(x96443,x96444)),f317(f300(x96441,x96442,x96443),f317(f317(f23(f904(x96441,a893)),x96445),f317(f317(f299(x96441),x96444),f178(f904(x96441,a893)))))))
% 94.68/94.45 [9697]P1(f317(f317(f224(f904(x96971,a893)),f317(f275(x96972,x96971,x96973),x96974)),x96975))+~P1(f317(f317(f224(f904(x96972,a893)),x96974),f317(f73(f904(x96972,a893)),f317(f275(x96971,x96972,f317(f276(x96972,x96971),x96973)),f317(f73(f904(x96971,a893)),x96975)))))
% 94.68/94.45 [9770]~P86(x97701)+P1(f317(f317(f224(x97701),f317(f70(x97701),f317(f317(f23(x97701),f317(f317(f74(x97701),x97702),x97703)),f317(f317(f74(x97701),x97704),x97705)))),f317(f317(f74(x97701),f317(f70(x97701),f317(f317(f23(x97701),x97702),x97704))),f317(f70(x97701),f317(f317(f23(x97701),x97703),x97705)))))
% 94.68/94.45 [9878]P1(f317(f317(f319(x98781),f445(x98782,x98783,x98784,x98781,x98785)),x98784))+P1(f317(f317(f224(f904(x98785,a893)),f317(f317(f34(x98781,f904(x98785,a893)),x98784),x98783)),x98782))
% 94.68/94.45 [10056]~P1(f317(f317(f224(f904(x100561,a893)),f317(x100564,f445(x100565,x100564,x100563,x100562,x100561))),x100565))+P1(f317(f317(f224(f904(x100561,a893)),f317(f317(f34(x100562,f904(x100561,a893)),x100563),x100564)),x100565))
% 94.68/94.45 [8669]E(f317(f317(f124(x86691),x86692),f317(f317(f149(x86691,x86693),f317(f317(f23(a897),x86694),f317(f179(f898(x86691)),x86692))),x86695)),f317(f317(f149(x86691,f317(f317(f124(x86691),x86692),x86693)),x86694),x86695))+P1(f317(f317(f225(a897),x86694),f317(f179(f898(x86691)),x86692)))
% 94.68/94.45 [8697]~P140(x86971)+E(f317(f317(f74(x86971),f317(f317(f75(x86971),x86972),x86973)),f317(f317(f74(x86971),f317(f317(f75(x86971),x86974),x86973)),x86975)),f317(f317(f74(x86971),f317(f317(f75(x86971),f317(f317(f74(x86971),x86972),x86974)),x86973)),x86975))
% 94.68/94.45 [9275]~P145(x92751)+E(f317(f155(x92751),f317(f317(f144(x92752,x92751),f317(f317(f8(x92751,x92751,x92752),f317(f75(x92751),x92753)),x92754)),x92755)),f317(f317(f75(x92751),x92753),f317(f155(x92751),f317(f317(f144(x92752,x92751),x92754),x92755))))
% 94.68/94.45 [9453]E(f317(f179(f898(x94531)),f317(f317(f165(x94531),f317(f317(f228(a897),f317(f179(f898(x94531)),x94532)),f317(f179(f898(x94533)),x94534))),x94532)),f317(f179(f898(x94533)),f317(f317(f165(x94533),f317(f317(f228(a897),f317(f179(f898(x94531)),x94532)),f317(f179(f898(x94533)),x94534))),x94534)))+P1(f317(x94535,f317(f317(f171(x94531,x94533),x94532),x94534)))
% 94.68/94.45 [9707]~P145(x97072)+E(f317(f317(f6(x97071,x97072),f317(f317(f7(x97071,x97072,x97072),f317(f317(f8(x97072,f904(x97072,x97072),x97071),f75(x97072)),x97073)),x97074)),x97075),f317(f317(f75(x97072),f317(f317(f6(x97071,x97072),x97073),x97075)),x97074))
% 94.68/94.45 [9708]~P62(x97082)+E(f317(f317(f6(x97081,x97082),f317(f317(f7(x97081,x97082,x97082),f317(f317(f8(x97082,f904(x97082,x97082),x97081),f281(x97082)),x97083)),x97084)),x97085),f317(f317(f281(x97082),f317(f317(f6(x97081,x97082),x97083),x97085)),x97084))
% 94.68/94.45 [9715]~P77(x97152)+E(f317(f317(f9(x97151,x97152),f317(f317(f18(x97151,x97152,x97152),f317(f317(f8(x97152,f904(x97152,x97152),x97151),f75(x97152)),x97153)),x97154)),x97155),f317(f317(f75(x97152),f317(f317(f9(x97151,x97152),x97153),x97155)),f317(f317(f9(x97151,x97152),x97154),x97155)))
% 94.68/94.45 [9716]~P69(x97162)+E(f317(f317(f6(x97161,x97162),f317(f317(f18(x97161,x97162,x97162),f317(f317(f8(x97162,f904(x97162,x97162),x97161),f23(x97162)),x97163)),x97164)),x97165),f317(f317(f23(x97162),f317(f317(f6(x97161,x97162),x97163),x97165)),f317(f317(f6(x97161,x97162),x97164),x97165)))
% 94.68/94.45 [9717]~P76(x97172)+E(f317(f317(f6(x97171,x97172),f317(f317(f18(x97171,x97172,x97172),f317(f317(f8(x97172,f904(x97172,x97172),x97171),f74(x97172)),x97173)),x97174)),x97175),f317(f317(f74(x97172),f317(f317(f6(x97171,x97172),x97173),x97175)),f317(f317(f6(x97171,x97172),x97174),x97175)))
% 94.68/94.45 [9755]~E(x97553,f178(f904(x97551,a893)))+E(f317(f317(f34(x97551,f904(x97552,a893)),x97553),f317(f317(f7(x97551,f904(x97552,a893),f904(x97552,a893)),f317(f317(f8(f904(x97552,a893),f904(f904(x97552,a893),f904(x97552,a893)),x97551),f91(f904(x97552,a893))),x97554)),x97555)),f178(f904(x97552,a893)))
% 94.68/94.45 [9756]~E(x97563,f178(f904(x97561,a893)))+E(f317(f317(f35(x97561,f904(x97562,a893)),x97563),f317(f317(f7(x97561,f904(x97562,a893),f904(x97562,a893)),f317(f317(f8(f904(x97562,a893),f904(f904(x97562,a893),f904(x97562,a893)),x97561),f23(f904(x97562,a893))),x97564)),x97565)),f232(f904(x97562,a893)))
% 94.68/94.45 [9757]~E(x97573,f178(f904(x97571,a893)))+E(f317(f317(f35(x97571,f904(x97572,a893)),x97573),f317(f317(f7(x97571,f904(x97572,a893),f904(x97572,a893)),f317(f317(f8(f904(x97572,a893),f904(f904(x97572,a893),f904(x97572,a893)),x97571),f92(f904(x97572,a893))),x97574)),x97575)),f232(f904(x97572,a893)))
% 94.68/94.45 [9778]E(x97781,f178(f904(x97782,a893)))+E(f317(f317(f34(x97782,f904(x97783,a893)),x97781),f317(f317(f7(x97782,f904(x97783,a893),f904(x97783,a893)),f317(f317(f8(f904(x97783,a893),f904(f904(x97783,a893),f904(x97783,a893)),x97782),f91(f904(x97783,a893))),x97784)),x97785)),f317(f317(f91(f904(x97783,a893)),f317(f317(f34(x97782,f904(x97783,a893)),x97781),x97784)),x97785))
% 94.68/94.45 [9779]E(x97791,f178(f904(x97792,a893)))+E(f317(f317(f35(x97792,f904(x97793,a893)),x97791),f317(f317(f7(x97792,f904(x97793,a893),f904(x97793,a893)),f317(f317(f8(f904(x97793,a893),f904(f904(x97793,a893),f904(x97793,a893)),x97792),f23(f904(x97793,a893))),x97794)),x97795)),f317(f317(f23(f904(x97793,a893)),f317(f317(f35(x97792,f904(x97793,a893)),x97791),x97794)),x97795))
% 94.68/94.45 [9780]E(x97801,f178(f904(x97802,a893)))+E(f317(f317(f35(x97802,f904(x97803,a893)),x97801),f317(f317(f7(x97802,f904(x97803,a893),f904(x97803,a893)),f317(f317(f8(f904(x97803,a893),f904(f904(x97803,a893),f904(x97803,a893)),x97802),f92(f904(x97803,a893))),x97804)),x97805)),f317(f317(f92(f904(x97803,a893)),f317(f317(f35(x97802,f904(x97803,a893)),x97801),x97804)),x97805))
% 94.68/94.45 [9327]~P1(f317(f317(f224(a897),x93271),x93274))+E(f317(f317(f23(a897),f317(f317(f74(a897),f317(f317(f75(a897),x93271),x93272)),x93273)),f317(f317(f74(a897),f317(f317(f75(a897),x93274),x93272)),x93275)),f317(f317(f23(a897),x93273),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x93274),x93271)),x93272)),x93275)))
% 94.68/94.45 [9927]~P145(x99271)+E(f317(f155(x99271),f317(f317(f144(x99272,x99271),f317(f317(f7(x99272,x99271,x99271),f317(f317(f8(x99271,f904(x99271,x99271),x99272),f75(x99271)),x99273)),x99274)),x99275)),f317(f317(f75(x99271),f317(f155(x99271),f317(f317(f144(x99272,x99271),x99273),x99275))),x99274))
% 94.68/94.45 [9933]~P69(x99331)+E(f317(f155(x99331),f317(f317(f144(x99332,x99331),f317(f317(f18(x99332,x99331,x99331),f317(f317(f8(x99331,f904(x99331,x99331),x99332),f23(x99331)),x99333)),x99334)),x99335)),f317(f317(f23(x99331),f317(f155(x99331),f317(f317(f144(x99332,x99331),x99333),x99335))),f317(f155(x99331),f317(f317(f144(x99332,x99331),x99334),x99335))))
% 94.68/94.45 [9934]~P76(x99341)+E(f317(f155(x99341),f317(f317(f144(x99342,x99341),f317(f317(f18(x99342,x99341,x99341),f317(f317(f8(x99341,f904(x99341,x99341),x99342),f74(x99341)),x99343)),x99344)),x99345)),f317(f317(f74(x99341),f317(f155(x99341),f317(f317(f144(x99342,x99341),x99343),x99345))),f317(f155(x99341),f317(f317(f144(x99342,x99341),x99344),x99345))))
% 94.68/94.45 [10080]P1(f317(x100801,f317(f317(f171(x100802,x100803),x100804),x100805)))+~P1(f317(x100801,f317(f317(f171(x100802,x100803),f317(f317(f165(x100802),f317(f317(f228(a897),f317(f179(f898(x100802)),x100804)),f317(f179(f898(x100803)),x100805))),x100804)),f317(f317(f165(x100803),f317(f317(f228(a897),f317(f179(f898(x100802)),x100804)),f317(f179(f898(x100803)),x100805))),x100805))))
% 94.68/94.45 [10342]~P1(f317(f317(f319(f903(x103422,x103421)),f317(f317(f242(x103422,x103421),x103424),x103425)),f317(f276(x103421,x103422),x103423)))+P1(f317(f317(f233(x103421,x103422,f317(f317(f7(x103421,f904(f903(x103421,x103422),a893),f904(x103422,a893)),f317(f317(f8(f904(x103422,f904(f904(f903(x103421,x103422),a893),a893)),f904(f904(f903(x103421,x103422),a893),f904(x103422,a893)),x103421),f7(x103422,f904(f903(x103421,x103422),a893),a893)),f317(f317(f8(f904(x103422,f903(x103421,x103422)),f904(x103422,f904(f904(f903(x103421,x103422),a893),a893)),x103421),f317(f8(f903(x103421,x103422),f904(f904(f903(x103421,x103422),a893),a893),x103422),f319(f903(x103421,x103422)))),f242(x103421,x103422)))),x103423)),x103424),x103425))
% 94.68/94.45 [10352]P1(f317(f317(f319(f903(x103521,x103522)),f317(f317(f242(x103521,x103522),x103523),x103524)),f317(f276(x103522,x103521),x103525)))+~P1(f317(f317(f233(x103522,x103521,f317(f317(f7(x103522,f904(f903(x103522,x103521),a893),f904(x103521,a893)),f317(f317(f8(f904(x103521,f904(f904(f903(x103522,x103521),a893),a893)),f904(f904(f903(x103522,x103521),a893),f904(x103521,a893)),x103522),f7(x103521,f904(f903(x103522,x103521),a893),a893)),f317(f317(f8(f904(x103521,f903(x103522,x103521)),f904(x103521,f904(f904(f903(x103522,x103521),a893),a893)),x103522),f317(f8(f903(x103522,x103521),f904(f904(f903(x103522,x103521),a893),a893),x103521),f319(f903(x103522,x103521)))),f242(x103522,x103521)))),x103525)),x103523),x103524))
% 94.68/94.45 [9584]~P1(f317(f317(f224(a897),x95844),x95841))+E(f317(f317(f23(a897),f317(f317(f74(a897),f317(f317(f75(a897),x95841),x95842)),x95843)),f317(f317(f74(a897),f317(f317(f75(a897),x95844),x95842)),x95845)),f317(f317(f23(a897),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x95841),x95844)),x95842)),x95843)),x95845))
% 94.68/94.45 [7382]E(x73821,x73822)+~E(f210(x73823,x73824,x73825,x73821),f210(x73823,x73824,x73826,x73822))
% 94.68/94.45 [7383]E(x73831,x73832)+~E(f210(x73833,x73834,x73831,x73835),f210(x73833,x73834,x73832,x73836))
% 94.68/94.45 [8506]~P19(x85065,x85061,x85062,x85066)+E(f317(f67(x85061,x85061,x85061,f317(x85062,x85063)),f317(x85062,x85064)),f317(f67(x85061,x85061,x85061,f317(x85062,x85064)),f317(x85062,x85063)))
% 94.68/94.45 [8741]~P56(x87414,x87415,x87412,x87411,x87416)+E(f317(x87411,f317(x87412,x87413)),x87413)
% 94.68/94.45 [8908]P24(x89081,x89082,x89083,x89084)+~P24(x89081,x89085,f317(f67(x89082,x89085,x89081,x89086),x89083),x89084)
% 94.68/94.45 [8981]~E(x89816,x89814)+E(f317(f69(x89811,x89812,x89813,x89814,x89815),x89816),x89815)
% 94.68/94.45 [8987]E(x89871,x89872)+E(f317(f69(x89873,x89874,x89875,x89872,x89876),x89871),f317(x89875,x89871))
% 94.68/94.45 [8999]~P24(x89994,x89992,f317(f67(x89991,x89992,x89994,x89993),x89995),x89996)+P24(x89991,x89992,x89993,f317(f300(x89994,x89991,x89995),x89996))
% 94.68/94.45 [9718]P1(f317(f28(x97181),x97182))+~P1(f317(f60(x97181,x97183,x97184,x97185,x97182),x97186))
% 94.68/94.45 [9727]~P1(f317(f317(f319(x97274),x97273),f287(x97274,x97271,x97275,x97272,x97276)))+P1(f317(f317(x97271,x97272),x97273))
% 94.68/94.45 [9728]~P1(f317(f317(f319(x97284),x97283),f290(x97284,x97285,x97281,x97282,x97286)))+P1(f317(f317(x97281,x97282),x97283))
% 94.68/94.45 [9729]~P1(f317(f317(f319(x97294),x97292),f287(x97294,x97295,x97291,x97296,x97293)))+P1(f317(f317(x97291,x97292),x97293))
% 94.68/94.45 [9730]~P1(f317(f317(f319(x97304),x97302),f290(x97304,x97301,x97305,x97306,x97303)))+P1(f317(f317(x97301,x97302),x97303))
% 94.68/94.45 [10229]P12(x102291,x102292,x102293,x102294,x102295,x102296)+~E(f317(f317(x102296,f824(x102293,x102296,x102295,x102292,x102294,x102291)),f830(x102293,x102296,x102295,x102292,x102294,x102291)),f317(f317(x102296,f825(x102293,x102296,x102295,x102292,x102294,x102291)),f831(x102293,x102296,x102295,x102292,x102294,x102291)))
% 94.68/94.45 [5838]E(x58381,x58382)+~E(f317(f317(f242(x58383,x58384),x58385),x58381),f317(f317(f242(x58383,x58384),x58386),x58382))
% 94.68/94.45 [5840]E(x58401,x58402)+~E(f317(f317(f242(x58403,x58404),x58401),x58405),f317(f317(f242(x58403,x58404),x58402),x58406))
% 94.68/94.45 [5985]~P16(x59855,x59856,x59851)+E(f317(f317(x59851,x59852),f317(f317(x59851,x59853),x59854)),f317(f317(x59851,x59853),f317(f317(x59851,x59852),x59854)))
% 94.68/94.45 [7449]~P31(x74494,x74491,f317(f317(f141(x74494),x74492),x74495),f317(f317(f141(x74494),x74493),x74496))+P1(f317(f317(x74491,x74492),x74493))
% 94.68/94.45 [7808]P31(x78081,x78082,x78083,x78084)+~P31(x78081,x78082,f317(f317(f141(x78081),x78085),x78083),f317(f317(f141(x78081),x78086),x78084))
% 94.68/94.45 [8845]~P56(x88455,x88451,x88452,x88456,x88454)+P1(f317(f317(f319(x88451),f317(x88452,x88453)),x88454))
% 94.68/94.45 [9047]~E(x90473,f317(f317(f141(x90471),x90475),x90476))+P1(f317(f317(f319(f903(f898(x90471),f898(x90471))),f317(f317(f242(f898(x90471),f898(x90471)),x90472),f317(f317(f124(x90471),x90472),x90473))),f137(x90471,x90474)))
% 94.68/94.45 [9281]~P33(x92811,x92812,x92813,x92815,x92816)+P33(x92811,x92812,x92813,f317(f317(f165(x92811),x92814),x92815),f317(f317(f165(x92812),x92814),x92816))
% 94.68/94.45 [9282]~P33(x92821,x92822,x92823,x92825,x92826)+P33(x92821,x92822,x92823,f317(f317(f128(x92821),x92824),x92825),f317(f317(f128(x92822),x92824),x92826))
% 94.68/94.45 [9546]E(f317(f300(x95461,x95462,f69(x95461,x95462,x95463,x95464,x95465)),x95466),f317(f300(x95461,x95462,x95463),x95466))+P1(f317(f317(f319(x95461),x95464),x95466))
% 94.68/94.45 [9549]E(f317(f317(f144(x95491,x95492),f69(x95491,x95492,x95493,x95494,x95495)),x95496),f317(f317(f144(x95491,x95492),x95493),x95496))+P1(f317(f317(f319(x95491),x95494),f317(f162(x95491),x95496)))
% 94.68/94.45 [9790]~P23(x97904,x97902,x97905,x97903,x97906,x97901)+E(f317(x97901,f178(f904(x97902,a893))),x97903)
% 94.68/94.45 [10022]~E(f317(x100224,f317(f241(x100221,x100223),x100225)),f317(x100226,f317(f241(x100221,x100223),x100225)))+E(f317(f248(x100221,x100222,x100223,x100223,x100224,f25(x100223)),x100225),f317(f248(x100221,x100222,x100223,x100223,x100226,f25(x100223)),x100225))
% 94.68/94.45 [10023]~E(f317(x100234,f317(f246(x100231,x100232),x100235)),f317(x100236,f317(f246(x100231,x100232),x100235)))+E(f317(f248(x100231,x100231,x100232,x100233,f25(x100231),x100234),x100235),f317(f248(x100231,x100231,x100232,x100233,f25(x100231),x100236),x100235))
% 94.68/94.45 [10076]~E(f317(f248(x100762,x100766,x100763,x100763,x100761,f25(x100763)),x100764),f317(f248(x100762,x100766,x100763,x100763,x100765,f25(x100763)),x100764))+E(f317(x100761,f317(f241(x100762,x100763),x100764)),f317(x100765,f317(f241(x100762,x100763),x100764)))
% 94.68/94.45 [10077]~E(f317(f248(x100772,x100772,x100773,x100776,f25(x100772),x100771),x100774),f317(f248(x100772,x100772,x100773,x100776,f25(x100772),x100775),x100774))+E(f317(x100771,f317(f246(x100772,x100773),x100774)),f317(x100775,f317(f246(x100772,x100773),x100774)))
% 94.68/94.45 [8948]P1(f317(f317(f319(x89481),x89482),x89483))+~P1(f317(f317(f319(f903(x89481,x89484)),f317(f317(f242(x89481,x89484),x89482),x89485)),f317(f317(f244(x89481,x89484),x89483),x89486)))
% 94.68/94.45 [8964]P1(f317(f317(f319(x89641),x89642),f317(x89643,x89644)))+~P1(f317(f317(f319(f903(x89645,x89641)),f317(f317(f242(x89645,x89641),x89644),x89642)),f317(f317(f244(x89645,x89641),x89646),x89643)))
% 94.68/94.45 [9403]P1(f317(f317(f319(f903(x94031,x94031)),f317(f317(f242(x94031,x94031),f317(x94032,x94033)),f317(x94032,x94034))),x94035))+~P1(f317(f317(f319(f903(x94036,x94036)),f317(f317(f242(x94036,x94036),x94033),x94034)),f317(f317(f278(x94031,x94036),x94035),x94032)))
% 94.68/94.45 [9423]~P1(f317(f317(f319(f903(x94234,x94234)),f317(f317(f242(x94234,x94234),f317(x94236,x94232)),f317(x94236,x94233))),x94235))+P1(f317(f317(f319(f903(x94231,x94231)),f317(f317(f242(x94231,x94231),x94232),x94233)),f317(f317(f278(x94234,x94231),x94235),x94236)))
% 94.68/94.45 [10079]E(f317(f317(f242(x100791,x100792),f622(x100793,x100794,x100795,x100796,x100792,x100791)),f623(x100793,x100794,x100795,x100796,x100792,x100791)),x100796)+~P1(f317(f317(f319(f903(x100791,x100792)),x100796),f317(f317(f279(x100791,x100795,x100792),x100794),x100793)))
% 94.68/94.45 [10300]~P1(f317(f317(f319(f903(x103001,x103006)),x103005),f317(f317(f279(x103001,x103002,x103006),x103004),x103003)))+P1(f317(f317(f319(f903(x103001,x103002)),f317(f317(f242(x103001,x103002),f622(x103003,x103004,x103002,x103005,x103006,x103001)),f625(x103003,x103004,x103002,x103005,x103006,x103001))),x103004))
% 94.68/94.45 [10301]~P1(f317(f317(f319(f903(x103016,x103012)),x103015),f317(f317(f279(x103016,x103011,x103012),x103014),x103013)))+P1(f317(f317(f319(f903(x103011,x103012)),f317(f317(f242(x103011,x103012),f625(x103013,x103014,x103011,x103015,x103012,x103016)),f623(x103013,x103014,x103011,x103015,x103012,x103016))),x103013))
% 94.68/94.45 [10302]P12(x103021,x103022,x103023,x103024,x103025,x103026)+P1(f317(f317(f319(f903(x103022,x103022)),f317(f317(f242(x103022,x103022),f831(x103023,x103026,x103025,x103022,x103024,x103021)),f830(x103023,x103026,x103025,x103022,x103024,x103021))),x103025))
% 94.68/94.45 [10303]P12(x103031,x103032,x103033,x103034,x103035,x103036)+P1(f317(f317(f319(f903(x103031,x103031)),f317(f317(f242(x103031,x103031),f825(x103033,x103036,x103035,x103032,x103034,x103031)),f824(x103033,x103036,x103035,x103032,x103034,x103031))),x103034))
% 94.68/94.45 [7879]~P5(x78792)+E(f317(f317(f34(x78791,x78792),x78793),f317(f317(f7(x78791,x78794,x78792),x78795),x78796)),f317(f317(f317(f34(x78791,f904(x78794,x78792)),x78793),x78795),x78796))
% 94.68/94.45 [7880]~P5(x78802)+E(f317(f317(f35(x78801,x78802),x78803),f317(f317(f7(x78801,x78804,x78802),x78805),x78806)),f317(f317(f317(f35(x78801,f904(x78804,x78802)),x78803),x78805),x78806))
% 94.68/94.45 [8651]E(f317(f317(f34(x86511,f904(x86512,a893)),x86513),f317(f317(f8(f904(x86512,a893),f904(x86512,a893),x86511),f317(f299(x86512),x86514)),x86515)),f317(f317(f299(x86512),x86514),f317(f317(f34(x86511,f904(x86512,a893)),x86513),x86515)))+~P1(f317(f317(f319(x86511),x86516),x86513))
% 94.68/94.45 [9100]~P5(x91002)+E(f317(f317(f34(x91001,x91002),x91003),f317(f317(f8(f904(x91004,x91002),x91002,x91001),f317(f34(x91004,x91002),x91005)),f317(f7(x91004,x91001,x91002),x91006))),f317(f317(f34(x91004,x91002),x91005),f317(f317(f8(f904(x91001,x91002),x91002,x91004),f317(f34(x91001,x91002),x91003)),x91006)))
% 94.68/94.45 [9101]~P5(x91012)+E(f317(f317(f35(x91011,x91012),x91013),f317(f317(f8(f904(x91014,x91012),x91012,x91011),f317(f35(x91014,x91012),x91015)),f317(f7(x91014,x91011,x91012),x91016))),f317(f317(f35(x91014,x91012),x91015),f317(f317(f8(f904(x91011,x91012),x91012,x91014),f317(f35(x91011,x91012),x91013)),x91016)))
% 94.68/94.45 [9307]P1(f317(f317(f319(x93071),x93072),f317(f162(x93071),x93073)))+~P1(f317(f317(f319(f903(x93074,x93071)),f317(f317(f242(x93074,x93071),x93075),x93072)),f317(f162(f903(x93074,x93071)),f317(f317(f171(x93074,x93071),x93076),x93073))))
% 94.68/94.45 [9308]P1(f317(f317(f319(x93081),x93082),f317(f162(x93081),x93083)))+~P1(f317(f317(f319(f903(x93081,x93084)),f317(f317(f242(x93081,x93084),x93082),x93085)),f317(f162(f903(x93081,x93084)),f317(f317(f171(x93081,x93084),x93083),x93086))))
% 94.68/94.45 [9419]P1(f317(f317(f224(f904(x94191,a893)),f317(f275(x94192,x94191,x94193),x94194)),x94195))+~P1(f317(f317(f224(f904(f903(x94192,x94191),a893)),x94193),f317(f317(f244(x94192,x94191),x94196),f317(f16(f904(x94191,a893),x94192),x94195))))
% 94.68/94.45 [9424]~P25(x94244,x94242,x94245,f232(f904(x94244,a893)),f232(f904(x94242,a893)))+E(f317(f317(f35(x94241,f904(x94242,a893)),x94243),f317(f317(f8(f904(x94244,a893),f904(x94242,a893),x94241),f300(x94244,x94242,x94245)),x94246)),f317(f300(x94244,x94242,x94245),f317(f317(f35(x94241,f904(x94244,a893)),x94243),x94246)))
% 94.68/94.45 [9622]P1(f317(f317(f319(f903(f898(x96221),f898(x96221))),f317(f317(f242(f898(x96221),f898(x96221)),f317(f317(f141(x96221),x96222),x96223)),f317(f317(f141(x96221),x96224),x96225))),f137(x96221,x96226)))+~P1(f317(f317(f319(f903(x96221,x96221)),f317(f317(f242(x96221,x96221),x96222),x96224)),x96226))
% 94.68/94.45 [10075]E(f317(f317(f242(x100751,x100752),f524(x100753,x100754,x100755,x100752,x100751,x100756)),f527(x100753,x100754,x100755,x100752,x100751,x100756)),x100756)+P1(f317(f317(f319(x100755),x100754),f317(f317(f247(x100751,x100752,f904(x100755,a893)),x100753),x100756)))
% 94.68/94.45 [10081]E(f317(f317(f242(x100811,x100812),f525(x100813,x100814,x100812,x100811,x100815,x100816)),f526(x100813,x100814,x100812,x100811,x100815,x100816)),x100813)+~P1(f317(f317(f319(x100816),x100815),f317(f317(f247(x100811,x100812,f904(x100816,a893)),x100814),x100813)))
% 94.68/94.45 [10244]P1(f317(f317(f319(x102441),x102442),f317(f317(x102443,f525(x102444,x102443,x102445,x102446,x102442,x102441)),f526(x102444,x102443,x102445,x102446,x102442,x102441))))+~P1(f317(f317(f319(x102441),x102442),f317(f317(f247(x102446,x102445,f904(x102441,a893)),x102443),x102444)))
% 94.68/94.45 [10273]~P1(f317(f317(f319(x102731),x102732),f317(f317(x102735,f524(x102735,x102732,x102731,x102734,x102733,x102736)),f527(x102735,x102732,x102731,x102734,x102733,x102736))))+P1(f317(f317(f319(x102731),x102732),f317(f317(f247(x102733,x102734,f904(x102731,a893)),x102735),x102736)))
% 94.68/94.45 [8552]E(x85521,x85522)+E(f317(f317(f149(x85523,f317(f317(f149(x85523,x85524),x85521),x85525)),x85522),x85526),f317(f317(f149(x85523,f317(f317(f149(x85523,x85524),x85522),x85526)),x85521),x85525))
% 94.68/94.45 [9682]~P1(f317(f317(f319(x96823),x96826),x96825))+E(f317(f317(f299(x96821),x96822),f317(f300(x96823,x96821,x96824),f317(f317(f23(f904(x96823,a893)),x96825),f317(f317(f299(x96823),x96826),f178(f904(x96823,a893)))))),f317(f300(x96823,x96821,f69(x96823,x96821,x96824,x96826,x96822)),x96825))
% 94.68/94.45 [9180]~P1(f317(f317(x91804,x91805),x91806))+P1(f317(f317(f317(f317(f91(f904(x91801,f904(x91802,a893))),x91803),x91804),x91805),x91806))
% 94.68/94.45 [9182]~P1(f317(f317(x91823,x91825),x91826))+P1(f317(f317(f317(f317(f91(f904(x91821,f904(x91822,a893))),x91823),x91824),x91825),x91826))
% 94.68/94.45 [9474]P1(f317(f317(x94741,x94742),x94743))+~P1(f317(f317(f317(f317(f92(f904(x94744,f904(x94745,a893))),x94746),x94741),x94742),x94743))
% 94.68/94.45 [9475]P1(f317(f317(x94751,x94752),x94753))+~P1(f317(f317(f317(f317(f92(f904(x94754,f904(x94755,a893))),x94751),x94756),x94752),x94753))
% 94.68/94.45 [9915]~P77(x99152)+E(f317(f317(f9(x99151,x99152),f317(f317(f7(x99151,f904(x99153,a893),x99152),f317(f317(f8(f904(x99153,x99152),f904(f904(x99153,a893),x99152),x99151),f9(x99153,x99152)),x99154)),x99155)),x99156),f317(f317(f9(f903(x99151,x99153),x99152),f317(f247(x99151,x99153,x99152),x99154)),f317(f317(f244(x99151,x99153),x99156),f317(f16(f904(x99153,a893),x99151),x99155))))
% 94.68/94.45 [9916]~P76(x99162)+E(f317(f317(f6(x99161,x99162),f317(f317(f7(x99161,f904(x99163,a893),x99162),f317(f317(f8(f904(x99163,x99162),f904(f904(x99163,a893),x99162),x99161),f6(x99163,x99162)),x99164)),x99165)),x99166),f317(f317(f6(f903(x99161,x99163),x99162),f317(f247(x99161,x99163,x99162),x99164)),f317(f317(f244(x99161,x99163),x99166),f317(f16(f904(x99163,a893),x99161),x99165))))
% 94.68/94.45 [10047]~P76(x100472)+E(f317(f317(f6(x100471,x100472),f317(f317(f7(x100471,f904(x100473,a893),x100472),f317(f317(f8(f904(x100473,x100472),f904(f904(x100473,a893),x100472),x100471),f6(x100473,x100472)),f317(f7(x100473,x100471,x100472),x100474))),x100475)),x100476),f317(f317(f6(x100473,x100472),f317(f317(f7(x100473,f904(x100471,a893),x100472),f317(f317(f8(f904(x100471,x100472),f904(f904(x100471,a893),x100472),x100473),f6(x100471,x100472)),x100474)),x100476)),x100475))
% 94.68/94.45 [10364]~P1(f317(f317(f319(f903(x103641,x103642)),f317(f317(f242(x103641,x103642),x103645),x103646)),f317(f317(f91(f904(f903(x103641,x103642),a893)),x103643),x103644)))+P1(f317(f317(f317(f317(f91(f904(x103641,f904(x103642,a893))),f317(f317(f7(x103641,f904(f903(x103641,x103642),a893),f904(x103642,a893)),f317(f317(f8(f904(x103642,f904(f904(f903(x103641,x103642),a893),a893)),f904(f904(f903(x103641,x103642),a893),f904(x103642,a893)),x103641),f7(x103642,f904(f903(x103641,x103642),a893),a893)),f317(f317(f8(f904(x103642,f903(x103641,x103642)),f904(x103642,f904(f904(f903(x103641,x103642),a893),a893)),x103641),f317(f8(f903(x103641,x103642),f904(f904(f903(x103641,x103642),a893),a893),x103642),f319(f903(x103641,x103642)))),f242(x103641,x103642)))),x103643)),f317(f317(f7(x103641,f904(f903(x103641,x103642),a893),f904(x103642,a893)),f317(f317(f8(f904(x103642,f904(f904(f903(x103641,x103642),a893),a893)),f904(f904(f903(x103641,x103642),a893),f904(x103642,a893)),x103641),f7(x103642,f904(f903(x103641,x103642),a893),a893)),f317(f317(f8(f904(x103642,f903(x103641,x103642)),f904(x103642,f904(f904(f903(x103641,x103642),a893),a893)),x103641),f317(f8(f903(x103641,x103642),f904(f904(f903(x103641,x103642),a893),a893),x103642),f319(f903(x103641,x103642)))),f242(x103641,x103642)))),x103644)),x103645),x103646))
% 94.68/94.45 [10365]~P1(f317(f317(f319(f903(x103651,x103652)),f317(f317(f242(x103651,x103652),x103655),x103656)),f317(f317(f92(f904(f903(x103651,x103652),a893)),x103653),x103654)))+P1(f317(f317(f317(f317(f92(f904(x103651,f904(x103652,a893))),f317(f317(f7(x103651,f904(f903(x103651,x103652),a893),f904(x103652,a893)),f317(f317(f8(f904(x103652,f904(f904(f903(x103651,x103652),a893),a893)),f904(f904(f903(x103651,x103652),a893),f904(x103652,a893)),x103651),f7(x103652,f904(f903(x103651,x103652),a893),a893)),f317(f317(f8(f904(x103652,f903(x103651,x103652)),f904(x103652,f904(f904(f903(x103651,x103652),a893),a893)),x103651),f317(f8(f903(x103651,x103652),f904(f904(f903(x103651,x103652),a893),a893),x103652),f319(f903(x103651,x103652)))),f242(x103651,x103652)))),x103653)),f317(f317(f7(x103651,f904(f903(x103651,x103652),a893),f904(x103652,a893)),f317(f317(f8(f904(x103652,f904(f904(f903(x103651,x103652),a893),a893)),f904(f904(f903(x103651,x103652),a893),f904(x103652,a893)),x103651),f7(x103652,f904(f903(x103651,x103652),a893),a893)),f317(f317(f8(f904(x103652,f903(x103651,x103652)),f904(x103652,f904(f904(f903(x103651,x103652),a893),a893)),x103651),f317(f8(f903(x103651,x103652),f904(f904(f903(x103651,x103652),a893),a893),x103652),f319(f903(x103651,x103652)))),f242(x103651,x103652)))),x103654)),x103655),x103656))
% 94.68/94.45 [10374]P1(f317(f317(f319(f903(x103741,x103742)),f317(f317(f242(x103741,x103742),x103743),x103744)),f317(f317(f91(f904(f903(x103741,x103742),a893)),x103745),x103746)))+~P1(f317(f317(f317(f317(f91(f904(x103741,f904(x103742,a893))),f317(f317(f7(x103741,f904(f903(x103741,x103742),a893),f904(x103742,a893)),f317(f317(f8(f904(x103742,f904(f904(f903(x103741,x103742),a893),a893)),f904(f904(f903(x103741,x103742),a893),f904(x103742,a893)),x103741),f7(x103742,f904(f903(x103741,x103742),a893),a893)),f317(f317(f8(f904(x103742,f903(x103741,x103742)),f904(x103742,f904(f904(f903(x103741,x103742),a893),a893)),x103741),f317(f8(f903(x103741,x103742),f904(f904(f903(x103741,x103742),a893),a893),x103742),f319(f903(x103741,x103742)))),f242(x103741,x103742)))),x103745)),f317(f317(f7(x103741,f904(f903(x103741,x103742),a893),f904(x103742,a893)),f317(f317(f8(f904(x103742,f904(f904(f903(x103741,x103742),a893),a893)),f904(f904(f903(x103741,x103742),a893),f904(x103742,a893)),x103741),f7(x103742,f904(f903(x103741,x103742),a893),a893)),f317(f317(f8(f904(x103742,f903(x103741,x103742)),f904(x103742,f904(f904(f903(x103741,x103742),a893),a893)),x103741),f317(f8(f903(x103741,x103742),f904(f904(f903(x103741,x103742),a893),a893),x103742),f319(f903(x103741,x103742)))),f242(x103741,x103742)))),x103746)),x103743),x103744))
% 94.68/94.45 [10375]P1(f317(f317(f319(f903(x103751,x103752)),f317(f317(f242(x103751,x103752),x103753),x103754)),f317(f317(f92(f904(f903(x103751,x103752),a893)),x103755),x103756)))+~P1(f317(f317(f317(f317(f92(f904(x103751,f904(x103752,a893))),f317(f317(f7(x103751,f904(f903(x103751,x103752),a893),f904(x103752,a893)),f317(f317(f8(f904(x103752,f904(f904(f903(x103751,x103752),a893),a893)),f904(f904(f903(x103751,x103752),a893),f904(x103752,a893)),x103751),f7(x103752,f904(f903(x103751,x103752),a893),a893)),f317(f317(f8(f904(x103752,f903(x103751,x103752)),f904(x103752,f904(f904(f903(x103751,x103752),a893),a893)),x103751),f317(f8(f903(x103751,x103752),f904(f904(f903(x103751,x103752),a893),a893),x103752),f319(f903(x103751,x103752)))),f242(x103751,x103752)))),x103755)),f317(f317(f7(x103751,f904(f903(x103751,x103752),a893),f904(x103752,a893)),f317(f317(f8(f904(x103752,f904(f904(f903(x103751,x103752),a893),a893)),f904(f904(f903(x103751,x103752),a893),f904(x103752,a893)),x103751),f7(x103752,f904(f903(x103751,x103752),a893),a893)),f317(f317(f8(f904(x103752,f903(x103751,x103752)),f904(x103752,f904(f904(f903(x103751,x103752),a893),a893)),x103751),f317(f8(f903(x103751,x103752),f904(f904(f903(x103751,x103752),a893),a893),x103752),f319(f903(x103751,x103752)))),f242(x103751,x103752)))),x103756)),x103753),x103754))
% 94.68/94.45 [10358]~P1(f317(f317(f319(f903(x103582,x103583)),f317(f317(f242(x103582,x103583),x103585),x103586)),f317(f317(f34(x103581,f904(f903(x103582,x103583),a893)),f232(f904(x103581,a893))),x103584)))+P1(f317(f317(f317(f317(f34(x103581,f904(x103582,f904(x103583,a893))),f232(f904(x103581,a893))),f317(f317(f8(f904(f903(x103582,x103583),a893),f904(x103582,f904(x103583,a893)),x103581),f317(f7(x103582,f904(f903(x103582,x103583),a893),f904(x103583,a893)),f317(f317(f8(f904(x103583,f904(f904(f903(x103582,x103583),a893),a893)),f904(f904(f903(x103582,x103583),a893),f904(x103583,a893)),x103582),f7(x103583,f904(f903(x103582,x103583),a893),a893)),f317(f317(f8(f904(x103583,f903(x103582,x103583)),f904(x103583,f904(f904(f903(x103582,x103583),a893),a893)),x103582),f317(f8(f903(x103582,x103583),f904(f904(f903(x103582,x103583),a893),a893),x103583),f319(f903(x103582,x103583)))),f242(x103582,x103583))))),x103584)),x103585),x103586))
% 94.68/94.45 [10359]~P1(f317(f317(f319(f903(x103592,x103593)),f317(f317(f242(x103592,x103593),x103595),x103596)),f317(f317(f35(x103591,f904(f903(x103592,x103593),a893)),f232(f904(x103591,a893))),x103594)))+P1(f317(f317(f317(f317(f35(x103591,f904(x103592,f904(x103593,a893))),f232(f904(x103591,a893))),f317(f317(f8(f904(f903(x103592,x103593),a893),f904(x103592,f904(x103593,a893)),x103591),f317(f7(x103592,f904(f903(x103592,x103593),a893),f904(x103593,a893)),f317(f317(f8(f904(x103593,f904(f904(f903(x103592,x103593),a893),a893)),f904(f904(f903(x103592,x103593),a893),f904(x103593,a893)),x103592),f7(x103593,f904(f903(x103592,x103593),a893),a893)),f317(f317(f8(f904(x103593,f903(x103592,x103593)),f904(x103593,f904(f904(f903(x103592,x103593),a893),a893)),x103592),f317(f8(f903(x103592,x103593),f904(f904(f903(x103592,x103593),a893),a893),x103593),f319(f903(x103592,x103593)))),f242(x103592,x103593))))),x103594)),x103595),x103596))
% 94.68/94.45 [10368]P1(f317(f317(f319(f903(x103681,x103682)),f317(f317(f242(x103681,x103682),x103683),x103684)),f317(f317(f34(x103685,f904(f903(x103681,x103682),a893)),f232(f904(x103685,a893))),x103686)))+~P1(f317(f317(f317(f317(f34(x103685,f904(x103681,f904(x103682,a893))),f232(f904(x103685,a893))),f317(f317(f8(f904(f903(x103681,x103682),a893),f904(x103681,f904(x103682,a893)),x103685),f317(f7(x103681,f904(f903(x103681,x103682),a893),f904(x103682,a893)),f317(f317(f8(f904(x103682,f904(f904(f903(x103681,x103682),a893),a893)),f904(f904(f903(x103681,x103682),a893),f904(x103682,a893)),x103681),f7(x103682,f904(f903(x103681,x103682),a893),a893)),f317(f317(f8(f904(x103682,f903(x103681,x103682)),f904(x103682,f904(f904(f903(x103681,x103682),a893),a893)),x103681),f317(f8(f903(x103681,x103682),f904(f904(f903(x103681,x103682),a893),a893),x103682),f319(f903(x103681,x103682)))),f242(x103681,x103682))))),x103686)),x103683),x103684))
% 94.68/94.45 [10369]P1(f317(f317(f319(f903(x103691,x103692)),f317(f317(f242(x103691,x103692),x103693),x103694)),f317(f317(f35(x103695,f904(f903(x103691,x103692),a893)),f232(f904(x103695,a893))),x103696)))+~P1(f317(f317(f317(f317(f35(x103695,f904(x103691,f904(x103692,a893))),f232(f904(x103695,a893))),f317(f317(f8(f904(f903(x103691,x103692),a893),f904(x103691,f904(x103692,a893)),x103695),f317(f7(x103691,f904(f903(x103691,x103692),a893),f904(x103692,a893)),f317(f317(f8(f904(x103692,f904(f904(f903(x103691,x103692),a893),a893)),f904(f904(f903(x103691,x103692),a893),f904(x103692,a893)),x103691),f7(x103692,f904(f903(x103691,x103692),a893),a893)),f317(f317(f8(f904(x103692,f903(x103691,x103692)),f904(x103692,f904(f904(f903(x103691,x103692),a893),a893)),x103691),f317(f8(f903(x103691,x103692),f904(f904(f903(x103691,x103692),a893),a893),x103692),f319(f903(x103691,x103692)))),f242(x103691,x103692))))),x103696)),x103693),x103694))
% 94.68/94.45 [7554]E(f317(x75541,f317(x75542,x75543)),f317(x75544,x75543))+~E(f317(f67(x75545,x75546,x75547,x75541),x75542),x75544)
% 94.68/94.45 [9698]E(x96981,x96982)+E(f69(x96983,x96984,f69(x96983,x96984,x96985,x96981,x96986),x96982,x96987),f69(x96983,x96984,f69(x96983,x96984,x96985,x96982,x96987),x96981,x96986))
% 94.68/94.45 [9789]~P22(x97893,x97894,x97891,x97895,x97896,x97897)+E(f317(f317(x97891,x97892),x97892),x97892)
% 94.68/94.45 [6088]~E(f317(f317(f144(x60881,x60885),x60886),x60882),f317(f317(f144(x60883,x60885),x60887),x60884))+E(f317(f179(f898(x60881)),x60882),f317(f179(f898(x60883)),x60884))
% 94.68/94.45 [8583]E(f317(x85831,f317(x85832,x85833)),f317(x85834,x85833))+~E(f317(f67(x85835,x85836,x85837,x85831),x85832),f317(f67(x85836,x85836,x85837,f25(x85836)),x85834))
% 94.68/94.45 [8937]~P33(x89374,x89375,x89371,f317(f317(f141(x89374),x89372),x89376),f317(f317(f141(x89375),x89373),x89377))+P1(f317(f317(x89371,x89372),x89373))
% 94.68/94.45 [9314]P33(x93141,x93142,x93143,x93144,x93145)+~P33(x93141,x93142,x93143,f317(f317(f141(x93141),x93146),x93144),f317(f317(f141(x93142),x93147),x93145))
% 94.68/94.45 [9948]P1(f317(f317(x99481,x99482),f498(x99483,x99482,x99484,x99481)))+~P1(f317(f317(f243(x99485,x99486,x99487,x99481,x99484),x99482),x99483))
% 94.68/94.45 [9972]P1(f317(f317(x99721,f498(x99722,x99723,x99721,x99724)),x99722))+~P1(f317(f317(f243(x99725,x99726,x99727,x99724,x99721),x99723),x99722))
% 94.68/94.45 [9054]~P20(x90546,x90541,x90543,x90547)+E(f317(f67(x90541,x90541,x90542,f317(x90543,x90544)),f317(f67(x90541,x90541,x90542,f317(x90543,x90544)),x90545)),f317(f67(x90541,x90541,x90542,f317(x90543,x90544)),x90545))
% 94.68/94.45 [9427]~P33(x94273,x94272,x94274,f317(f317(f144(x94271,x94273),x94275),x94276),x94277)+P33(x94271,x94272,f317(f317(f8(x94273,f904(x94272,a893),x94271),x94274),x94275),x94276,x94277)
% 94.68/94.45 [9450]P33(x94501,x94502,x94503,f317(f317(f144(x94504,x94501),x94505),x94506),x94507)+~P33(x94504,x94502,f317(f317(f8(x94501,f904(x94502,a893),x94504),x94503),x94505),x94506,x94507)
% 94.68/94.45 [9053]~P1(f317(f317(f319(x90531),x90532),f317(f317(x90535,x90536),x90537)))+P1(f317(f317(f319(x90531),x90532),f317(f317(f247(x90533,x90534,f904(x90531,a893)),x90535),f317(f317(f242(x90533,x90534),x90536),x90537))))
% 94.68/94.45 [9340]P1(f317(f317(f317(x93401,x93402),x93403),x93404))+~P1(f317(f317(f317(f247(x93405,x93406,f904(x93407,a893)),x93401),f317(f317(f242(x93405,x93406),x93402),x93403)),x93404))
% 94.68/94.45 [9489]P1(f317(f317(f319(x94891),f317(f317(x94892,x94893),x94894)),f317(f300(f903(x94895,x94896),x94891,f317(f247(x94895,x94896,x94891),x94892)),x94897)))+~P1(f317(f317(f319(f903(x94895,x94896)),f317(f317(f242(x94895,x94896),x94893),x94894)),x94897))
% 94.68/94.45 [9836]P1(f317(f317(f319(f903(f898(x98361),f898(x98361))),f317(f317(f242(f898(x98361),f898(x98361)),f317(f317(f124(x98361),x98362),f317(f317(f141(x98361),x98363),x98364))),f317(f317(f124(x98361),x98362),f317(f317(f141(x98361),x98365),x98366)))),f137(x98361,x98367)))+~P1(f317(f317(f319(f903(x98361,x98361)),f317(f317(f242(x98361,x98361),x98363),x98365)),x98367))
% 94.68/94.45 [9900]~P33(x99001,x99003,x99004,x99006,f317(f317(f144(x99002,x99003),x99005),x99007))+P33(x99001,x99002,f317(f317(f7(x99001,f904(x99002,x99003),f904(x99002,a893)),f317(f317(f8(f904(x99003,a893),f904(f904(x99002,x99003),f904(x99002,a893)),x99001),f8(x99003,a893,x99002)),x99004)),x99005),x99006,x99007)
% 94.68/94.45 [9976]P33(x99761,x99762,x99763,x99764,f317(f317(f144(x99765,x99762),x99766),x99767))+~P33(x99761,x99765,f317(f317(f7(x99761,f904(x99765,x99762),f904(x99765,a893)),f317(f317(f8(f904(x99762,a893),f904(f904(x99765,x99762),f904(x99765,a893)),x99761),f8(x99762,a893,x99765)),x99763)),x99766),x99764,x99767)
% 94.68/94.45 [10287]P1(f317(f317(f319(x102871),f588(x102872,x102873,x102874,x102875,x102876,x102877,x102871)),x102875))+P1(f317(f317(f317(f317(f35(x102871,f904(x102877,f904(x102876,a893))),x102875),x102874),x102873),x102872))
% 94.68/94.45 [10288]P1(f317(f317(f319(x102881),f763(x102882,x102883,x102884,x102885,x102886,x102887,x102881)),x102887))+P1(f317(f317(f317(f317(f35(x102881,f904(x102883,f904(x102882,a893))),x102887),x102886),x102885),x102884))
% 94.68/94.45 [10289]P1(f317(f317(f319(x102891),f452(x102892,x102893,x102894,x102895,x102896,x102897,x102891)),x102895))+~P1(f317(f317(f317(f317(f34(x102891,f904(x102897,f904(x102896,a893))),x102895),x102894),x102893),x102892))
% 94.68/94.45 [10290]P1(f317(f317(f319(x102901),f764(x102902,x102903,x102904,x102905,x102906,x102907,x102901)),x102905))+~P1(f317(f317(f317(f317(f34(x102901,f904(x102907,f904(x102906,a893))),x102905),x102904),x102903),x102902))
% 94.68/94.45 [10323]P1(f317(f317(f317(x103231,f452(x103232,x103233,x103231,x103234,x103235,x103236,x103237)),x103233),x103232))+~P1(f317(f317(f317(f317(f34(x103237,f904(x103236,f904(x103235,a893))),x103234),x103231),x103233),x103232))
% 94.68/94.45 [10324]P1(f317(f317(f317(x103241,f764(x103242,x103243,x103241,x103244,x103245,x103246,x103247)),x103243),x103242))+~P1(f317(f317(f317(f317(f34(x103247,f904(x103246,f904(x103245,a893))),x103244),x103241),x103243),x103242))
% 94.68/94.45 [10339]~P1(f317(f317(f317(x103395,f588(x103397,x103396,x103395,x103394,x103393,x103392,x103391)),x103396),x103397))+P1(f317(f317(f317(f317(f35(x103391,f904(x103392,f904(x103393,a893))),x103394),x103395),x103396),x103397))
% 94.68/94.45 [10340]~P1(f317(f317(f317(x103405,f763(x103403,x103402,x103407,x103406,x103405,x103404,x103401)),x103406),x103407))+P1(f317(f317(f317(f317(f35(x103401,f904(x103402,f904(x103403,a893))),x103404),x103405),x103406),x103407))
% 94.68/94.45 [10357]~P1(f317(f317(f319(f903(x103571,x103573)),f317(f317(f242(x103571,x103573),x103576),x103577)),f317(f317(f279(x103571,x103572,x103573),x103574),x103575)))+P1(f317(f317(f243(x103571,x103572,x103573,f317(f317(f7(x103571,f904(f903(x103571,x103572),a893),f904(x103572,a893)),f317(f317(f8(f904(x103572,f904(f904(f903(x103571,x103572),a893),a893)),f904(f904(f903(x103571,x103572),a893),f904(x103572,a893)),x103571),f7(x103572,f904(f903(x103571,x103572),a893),a893)),f317(f317(f8(f904(x103572,f903(x103571,x103572)),f904(x103572,f904(f904(f903(x103571,x103572),a893),a893)),x103571),f317(f8(f903(x103571,x103572),f904(f904(f903(x103571,x103572),a893),a893),x103572),f319(f903(x103571,x103572)))),f242(x103571,x103572)))),x103574),f317(f317(f7(x103572,f904(f903(x103572,x103573),a893),f904(x103573,a893)),f317(f317(f8(f904(x103573,f904(f904(f903(x103572,x103573),a893),a893)),f904(f904(f903(x103572,x103573),a893),f904(x103573,a893)),x103572),f7(x103573,f904(f903(x103572,x103573),a893),a893)),f317(f317(f8(f904(x103573,f903(x103572,x103573)),f904(x103573,f904(f904(f903(x103572,x103573),a893),a893)),x103572),f317(f8(f903(x103572,x103573),f904(f904(f903(x103572,x103573),a893),a893),x103573),f319(f903(x103572,x103573)))),f242(x103572,x103573)))),x103575)),x103576),x103577))
% 94.68/94.45 [10367]P1(f317(f317(f319(f903(x103671,x103672)),f317(f317(f242(x103671,x103672),x103673),x103674)),f317(f317(f279(x103671,x103675,x103672),x103676),x103677)))+~P1(f317(f317(f243(x103671,x103675,x103672,f317(f317(f7(x103671,f904(f903(x103671,x103675),a893),f904(x103675,a893)),f317(f317(f8(f904(x103675,f904(f904(f903(x103671,x103675),a893),a893)),f904(f904(f903(x103671,x103675),a893),f904(x103675,a893)),x103671),f7(x103675,f904(f903(x103671,x103675),a893),a893)),f317(f317(f8(f904(x103675,f903(x103671,x103675)),f904(x103675,f904(f904(f903(x103671,x103675),a893),a893)),x103671),f317(f8(f903(x103671,x103675),f904(f904(f903(x103671,x103675),a893),a893),x103675),f319(f903(x103671,x103675)))),f242(x103671,x103675)))),x103676),f317(f317(f7(x103675,f904(f903(x103675,x103672),a893),f904(x103672,a893)),f317(f317(f8(f904(x103672,f904(f904(f903(x103675,x103672),a893),a893)),f904(f904(f903(x103675,x103672),a893),f904(x103672,a893)),x103675),f7(x103672,f904(f903(x103675,x103672),a893),a893)),f317(f317(f8(f904(x103672,f903(x103675,x103672)),f904(x103672,f904(f904(f903(x103675,x103672),a893),a893)),x103675),f317(f8(f903(x103675,x103672),f904(f904(f903(x103675,x103672),a893),a893),x103672),f319(f903(x103675,x103672)))),f242(x103675,x103672)))),x103677)),x103673),x103674))
% 94.68/94.45 [10299]~P145(x102992)+E(f317(f317(f6(x102991,x102992),f317(f317(f7(x102991,f904(x102993,a893),x102992),f317(f317(f8(f904(x102993,x102992),f904(f904(x102993,a893),x102992),x102991),f6(x102993,x102992)),f317(f317(f7(x102991,f904(x102993,x102992),f904(x102993,x102992)),f317(f317(f8(f904(x102992,x102992),f904(f904(x102993,x102992),f904(x102993,x102992)),x102991),f8(x102992,x102992,x102993)),f317(f317(f8(x102992,f904(x102992,x102992),x102991),f75(x102992)),x102994))),x102995))),x102996)),x102997),f317(f317(f75(x102992),f317(f317(f6(x102991,x102992),x102994),x102997)),f317(f317(f6(x102993,x102992),x102995),x102996)))
% 94.68/94.45 [9374]~P19(x93747,x93741,x93743,x93748)+E(f317(f67(x93741,x93741,x93742,f317(x93743,x93744)),f317(f67(x93741,x93741,x93742,f317(x93743,x93745)),x93746)),f317(f67(x93741,x93741,x93742,f317(x93743,x93745)),f317(f67(x93741,x93741,x93742,f317(x93743,x93744)),x93746)))
% 94.68/94.45 [10362]E(f317(f317(f242(x103621,x103622),f317(x103623,f482(x103624,x103625,x103623,x103626,x103627,x103628,x103622,x103621))),f317(x103625,f483(x103624,x103625,x103623,x103626,x103627,x103628,x103622,x103621))),x103628)+~P1(f317(f317(f319(f903(x103621,x103622)),x103628),f317(f300(f903(x103627,x103626),f903(x103621,x103622),f248(x103627,x103621,x103626,x103622,x103623,x103625)),x103624)))
% 94.68/94.45 [10380]~P1(f317(f317(f319(f903(x103808,x103807)),x103806),f317(f300(f903(x103801,x103802),f903(x103808,x103807),f248(x103801,x103808,x103802,x103807,x103805,x103804)),x103803)))+P1(f317(f317(f319(f903(x103801,x103802)),f317(f317(f242(x103801,x103802),f482(x103803,x103804,x103805,x103802,x103801,x103806,x103807,x103808)),f483(x103803,x103804,x103805,x103802,x103801,x103806,x103807,x103808))),x103803))
% 94.68/94.45 [9826]P1(f317(f317(f319(f903(f903(x98261,x98262),f903(x98261,x98262))),f317(f317(f242(f903(x98261,x98262),f903(x98261,x98262)),f317(f317(f242(x98261,x98262),x98263),x98264)),f317(f317(f242(x98261,x98262),x98265),x98266))),f309(x98261,x98262,x98267,x98268)))+~P1(f317(f317(f319(f903(x98261,x98261)),f317(f317(f242(x98261,x98261),x98263),x98265)),x98267))
% 94.68/94.45 [10351]E(f317(f132(x103511,x103512,f317(f7(x103512,x103511,x103511),x103513),f317(x103514,x103515)),x103516),f317(x103514,f317(f132(x103517,x103512,f317(f7(x103512,x103517,x103517),x103518),x103515),x103516)))+P1(f317(f317(f319(x103512),f710(x103515,x103518,x103514,x103513,x103517,x103511,x103516,x103512)),f317(f162(x103512),x103516)))
% 94.68/94.45 [10370]~E(f317(f67(x103701,x103701,x103707,f317(x103703,f710(x103705,x103708,x103704,x103703,x103707,x103701,x103706,x103702))),x103704),f317(f67(x103707,x103701,x103707,x103704),f317(x103708,f710(x103705,x103708,x103704,x103703,x103707,x103701,x103706,x103702))))+E(f317(f132(x103701,x103702,f317(f7(x103702,x103701,x103701),x103703),f317(x103704,x103705)),x103706),f317(x103704,f317(f132(x103707,x103702,f317(f7(x103702,x103707,x103707),x103708),x103705),x103706)))
% 94.68/94.45 [8588]E(f317(x85881,f317(x85882,x85883)),f317(x85884,f317(x85885,x85883)))+~E(f317(f67(x85886,x85887,x85888,x85881),x85882),f317(f67(x85889,x85887,x85888,x85884),x85885))
% 94.68/94.45 [10208]P1(f317(f317(f319(f903(x102081,x102082)),f317(f317(f242(x102081,x102082),f317(x102083,x102084)),f317(x102085,x102086))),f317(f300(f903(x102087,x102088),f903(x102081,x102082),f248(x102087,x102081,x102088,x102082,x102083,x102085)),x102089)))+~P1(f317(f317(f319(f903(x102087,x102088)),f317(f317(f242(x102087,x102088),x102084),x102086)),x102089))
% 94.68/94.45 [8883]~E(f317(x88834,f317(x88835,x88836)),f317(x88839,f317(x888310,x888311)))+E(f317(f317(f67(x88831,x88832,x88833,x88834),x88835),x88836),f317(f317(f67(x88837,x88832,x88838,x88839),x888310),x888311))
% 94.68/94.45 [4647]~P66(x46471)+~P99(x46471)+E(f223(x46471),f91(x46471))
% 94.68/94.45 [4648]~P66(x46481)+~P105(x46481)+E(f228(x46481),f92(x46481))
% 94.68/94.45 [4893]~P111(x48931)+~P94(x48931)+E(f317(f70(x48931),f317(f94(x48931),a87)),f72(x48931))
% 94.68/94.45 [5186]E(x51861,f2(a1))+E(f76(a1,x51861),f317(f73(a1),f72(a1)))+P1(f317(f317(f225(a1),f2(a1)),x51861))
% 94.68/94.45 [5391]E(x53911,f2(a1))+E(f76(a1,x53911),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x53911))
% 94.68/94.45 [7453]~P39(x74531)+P1(f317(f28(a1),x74531))+~P1(f317(f28(a897),f317(f300(a1,a897,a95),x74531)))
% 94.68/94.45 [9788]E(x97881,f178(f904(f903(a897,a897),a893)))+~P1(f317(f28(f903(a897,a897)),x97881))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f178(f904(f903(a897,a897),a893))),x97881)),a27))
% 94.68/94.45 [9949]E(x99491,f2(a897))+E(x99491,f317(a102,f2(a897)))+~P1(f317(f317(f225(a897),x99491),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.45 [10237]E(x102371,f2(a89))+E(f317(f317(f74(a1),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a22,f317(f317(f30(a89),x102371),f317(f94(a89),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))),f72(a1)),f317(a22,x102371))+E(f40(a89,x102371,f317(f94(a89),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(a89))
% 94.68/94.45 [10085]E(x100851,f2(a89))+~E(f40(a89,x100851,f317(f94(a89),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(a89))+E(f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(a22,f317(f317(f30(a89),x100851),f317(f94(a89),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f317(a22,x100851))
% 94.68/94.45 [4728]~P57(x47281,x47282)+P43(x47281,x47282)+~P44(a893)
% 94.68/94.45 [4657]~P144(x46571)+P27(x46571,x46572)+~E(x46572,f2(x46571))
% 94.68/94.45 [4658]~P66(x46581)+P13(x46581,x46582)+~E(x46582,f103(x46581))
% 94.68/94.45 [4667]~P111(x46671)+~E(x46672,f2(x46671))+E(f76(x46671,x46672),f2(x46671))
% 94.68/94.45 [4668]~P91(x46681)+~E(x46682,f2(x46681))+E(f76(x46681,x46682),f2(x46681))
% 94.68/94.45 [4676]~P144(x46762)+~P27(x46762,x46761)+E(x46761,f2(x46762))
% 94.68/94.45 [4721]~P111(x47212)+~E(f76(x47212,x47211),f2(x47212))+E(x47211,f2(x47212))
% 94.68/94.45 [4735]~P2(x47352)+~P2(x47351)+P2(f904(x47351,x47352))
% 94.68/94.45 [4736]~P2(x47362)+~P2(x47361)+P2(f902(x47361,x47362))
% 94.68/94.45 [4737]~P2(x47372)+~P2(x47371)+P2(f903(x47371,x47372))
% 94.68/94.45 [4738]~P6(x47382)+~P6(x47381)+P6(f184(x47381,x47382))
% 94.68/94.45 [4739]~P60(x47392)+~P60(x47391)+P60(f904(x47391,x47392))
% 94.68/94.45 [4740]~P60(x47402)+~P60(x47401)+P60(f902(x47401,x47402))
% 94.68/94.45 [4741]~P60(x47412)+~P60(x47411)+P60(f903(x47411,x47412))
% 94.68/94.45 [4742]~P106(x47422)+~P106(x47421)+P106(f903(x47421,x47422))
% 94.68/94.45 [4865]~P66(x48651)+~P13(x48651,x48652)+P13(x48651,f142(x48651,x48652))
% 94.68/94.45 [5113]~P6(x51132)+~P6(x51131)+P6(f40(a1,x51131,x51132))
% 94.68/94.45 [4678]~P78(x46781)+~E(x46782,f2(x46781))+E(f317(f73(x46781),x46782),x46782)
% 94.68/94.45 [4693]~P93(x46931)+~E(x46932,f2(a1))+E(f317(f93(x46931),x46932),f2(x46931))
% 94.68/94.45 [4694]~P141(x46941)+~E(x46942,f2(a1))+E(f317(f93(x46941),x46942),f2(x46941))
% 94.68/94.45 [4718]~P75(x47181)+~E(f2(x47181),x47182)+E(f317(f73(x47181),x47182),f2(x47181))
% 94.68/94.45 [4719]~P75(x47191)+~E(x47192,f2(x47191))+E(f317(f73(x47191),x47192),f2(x47191))
% 94.68/94.45 [4720]~P86(x47201)+~E(x47202,f2(x47201))+E(f317(f70(x47201),x47202),f2(x47201))
% 94.68/94.45 [4744]~P78(x47442)+E(x47441,f2(x47442))+~E(f317(f73(x47442),x47441),x47441)
% 94.68/94.45 [4746]E(x47461,f317(a95,x47462))+~E(x47461,f2(a897))+~E(x47462,f317(f90(a1),x47461))
% 94.68/94.45 [4747]E(f317(a95,x47471),x47472)+~E(x47472,f2(a897))+~E(x47471,f317(f90(a1),x47472))
% 94.68/94.45 [4751]~P93(x47512)+E(x47511,f2(a1))+~E(f317(f93(x47512),x47511),f2(x47512))
% 94.68/94.45 [4755]~P75(x47552)+E(x47551,f2(x47552))+~E(f317(f73(x47552),x47551),f2(x47552))
% 94.68/94.45 [4756]~P86(x47562)+E(x47561,f2(x47562))+~E(f317(f70(x47562),x47561),f2(x47562))
% 94.68/94.45 [4757]~P75(x47571)+E(f2(x47571),x47572)+~E(f317(f73(x47571),x47572),f2(x47571))
% 94.68/94.45 [4940]~P66(x49401)+~P13(x49401,x49402)+P13(x49401,f317(f161(x49401),x49402))
% 94.68/94.45 [4967]~P1(x49672)+~P1(x49671)+P1(f317(f317(a315,x49671),x49672))
% 94.68/94.45 [5005]~E(f72(a897),f2(a897))+E(f317(f29(x50051),x50052),f2(a897))+~P1(f317(f28(x50051),x50052))
% 94.68/94.45 [5041]~P115(x50411)+~P145(x50411)+E(f317(f317(f234(x50411),f2(x50411)),f317(a102,x50412)),f2(x50411))
% 94.68/94.45 [5081]~P66(x50811)+P13(x50811,f129(x50811,x50812))+~P1(f317(f28(x50811),x50812))
% 94.68/94.45 [5082]~P66(x50821)+P13(x50821,f703(x50822,x50821))+~P1(f317(f28(x50821),x50822))
% 94.68/94.45 [5105]~P66(x51051)+E(f317(f162(x51051),f129(x51051,x51052)),x51052)+~P1(f317(f28(x51051),x51052))
% 94.68/94.45 [5106]~P66(x51061)+E(f317(f162(x51061),f703(x51062,x51061)),x51062)+~P1(f317(f28(x51061),x51062))
% 94.68/94.45 [5135]P1(x51351)+P1(x51352)+~P1(f317(f317(a316,x51352),x51351))
% 94.68/94.45 [5148]E(x51481,f178(f904(x51482,a893)))+~E(f317(f29(x51482),x51481),f2(a897))+~P1(f317(f28(x51482),x51481))
% 94.68/94.45 [5153]P1(x51531)+~P1(x51532)+~P1(f317(f317(a320,x51532),x51531))
% 94.68/94.45 [5204]~P74(x52041)+E(f317(f70(x52041),x52042),x52042)+P1(f317(f317(f225(x52041),x52042),f2(x52041)))
% 94.68/94.45 [5264]~P60(x52642)+~P1(f317(f51(x52642),x52641))+P1(f317(x52641,f704(x52641,x52642)))
% 94.68/94.45 [5265]~P60(x52652)+~P1(f317(f51(x52652),x52651))+P1(f317(x52651,f711(x52651,x52652)))
% 94.68/94.45 [5306]E(x53061,f103(x53062))+P1(f317(f127(x53062),f104(x53062,x53061)))+~P1(f317(f127(x53062),x53061))
% 94.68/94.45 [5311]~P66(x53111)+~P1(f317(f28(x53111),x53112))+P1(f317(f127(x53111),f129(x53111,x53112)))
% 94.68/94.45 [5312]~P66(x53121)+~P1(f317(f28(x53121),x53122))+P1(f317(f127(x53121),f703(x53122,x53121)))
% 94.68/94.45 [5317]~P141(x53171)+E(f317(f90(x53171),f317(a95,x53172)),f317(f93(x53171),x53172))+P1(f317(f317(f225(a1),x53172),f2(a1)))
% 94.68/94.45 [5338]P7(x53382,x53381)+E(f317(x53381,f433(x53381)),f317(x53381,f459(x53381)))+P1(f317(f317(x53381,f433(x53381)),f459(x53381)))
% 94.68/94.45 [5351]E(f317(f90(a1),f850(x53511,x53512)),x53511)+P1(f317(x53512,f317(a95,x53511)))+~P1(f317(x53512,f2(a897)))
% 94.68/94.45 [5364]~P60(x53641)+~P1(f317(x53642,f717(x53642,x53641)))+P1(f317(f52(x53641),x53642))
% 94.68/94.45 [5365]~P60(x53651)+~P1(f317(x53652,f727(x53652,x53651)))+P1(f317(f52(x53651),x53652))
% 94.68/94.45 [5401]~P111(x54011)+~E(f76(x54011,x54012),f317(f73(x54011),f72(x54011)))+P1(f317(f317(f225(x54011),x54012),f2(x54011)))
% 94.68/94.45 [5476]~E(x54762,f2(a1))+E(f205(x54761,x54762),f317(f317(f242(a1,a1),f2(a1)),f72(a1)))+P1(f317(f317(f225(a1),x54762),f2(a1)))
% 94.68/94.45 [5477]~E(x54771,f2(a1))+E(f205(x54771,x54772),f317(f317(f242(a1,a1),f2(a1)),f72(a1)))+P1(f317(f317(f225(a1),x54772),f2(a1)))
% 94.68/94.45 [5530]E(f317(f90(a1),f850(x55301,x55302)),x55301)+P1(f317(x55302,f317(a95,x55301)))+P1(f317(f317(f225(a1),x55301),f2(a1)))
% 94.68/94.45 [5598]~P111(x55981)+E(f76(x55981,x55982),f317(f73(x55981),f72(x55981)))+~P1(f317(f317(f225(x55981),x55982),f2(x55981)))
% 94.68/94.45 [5599]~P86(x55991)+E(f317(f70(x55991),x55992),f317(f73(x55991),x55992))+~P1(f317(f317(f224(x55991),x55992),f2(x55991)))
% 94.68/94.45 [5600]~P86(x56001)+E(f317(f70(x56001),x56002),f317(f73(x56001),x56002))+~P1(f317(f317(f225(x56001),x56002),f2(x56001)))
% 94.68/94.45 [5601]~P74(x56011)+E(f317(f70(x56011),x56012),f317(f73(x56011),x56012))+~P1(f317(f317(f225(x56011),x56012),f2(x56011)))
% 94.68/94.45 [5701]~P1(f317(x57011,f850(x57012,x57011)))+P1(f317(x57011,f317(a95,x57012)))+~P1(f317(x57011,f2(a897)))
% 94.68/94.45 [5708]E(x57081,f2(a897))+E(f317(a102,f560(x57082,x57081)),x57081)+~P1(f317(f317(f225(a897),x57081),f317(a102,x57082)))
% 94.68/94.45 [5712]P7(x57121,x57122)+~E(f317(x57122,f433(x57122)),f317(x57122,f459(x57122)))+~P1(f317(f317(x57122,f433(x57122)),f459(x57122)))
% 94.68/94.45 [5730]~P66(x57301)+P13(x57301,x57302)+P1(f317(f317(f224(a897),f686(x57302,x57301)),f687(x57302,x57301)))
% 94.68/94.45 [5731]~P66(x57311)+P13(x57311,x57312)+P1(f317(f317(f224(a897),f694(x57312,x57311)),f698(x57312,x57311)))
% 94.68/94.45 [5817]~P86(x58171)+~E(x58172,f2(x58171))+P1(f317(f317(f224(x58171),f317(f70(x58171),x58172)),f2(x58171)))
% 94.68/94.45 [5914]~P1(f317(x59141,f850(x59142,x59141)))+P1(f317(x59141,f317(a95,x59142)))+P1(f317(f317(f225(a1),x59142),f2(a1)))
% 94.68/94.45 [5939]~P1(f317(x59391,f317(a95,x59392)))+P1(f317(x59391,f2(a897)))+~P1(f317(f317(f225(a1),x59392),f2(a1)))
% 94.68/94.45 [6293]~P111(x62931)+~P1(f317(f317(f225(x62931),x62932),f2(x62931)))+P1(f317(f317(f225(x62931),f76(x62931,x62932)),f2(x62931)))
% 94.68/94.45 [6413]~P111(x64131)+P1(f317(f317(f224(x64131),f317(f93(x64131),x64132)),f2(x64131)))+~P1(f317(f317(f224(a1),x64132),f2(a1)))
% 94.68/94.45 [6414]~P111(x64141)+P1(f317(f317(f225(x64141),f317(f93(x64141),x64142)),f2(x64141)))+~P1(f317(f317(f225(a1),x64142),f2(a1)))
% 94.68/94.45 [6423]~P86(x64232)+E(x64231,f2(x64232))+~P1(f317(f317(f224(x64232),f317(f70(x64232),x64231)),f2(x64232)))
% 94.68/94.45 [6501]~P141(x65011)+~P1(f317(f317(f319(x65011),x65012),f100(x65011)))+P1(f317(f317(f319(x65011),f317(f73(x65011),x65012)),f100(x65011)))
% 94.68/94.45 [6533]~P111(x65331)+~P1(f317(f317(f225(x65331),f76(x65331,x65332)),f2(x65331)))+P1(f317(f317(f225(x65331),x65332),f2(x65331)))
% 94.68/94.45 [6711]~P111(x67112)+~P1(f317(f317(f224(x67112),f317(f93(x67112),x67111)),f2(x67112)))+P1(f317(f317(f224(a1),x67111),f2(a1)))
% 94.68/94.45 [6712]~P111(x67122)+~P1(f317(f317(f225(x67122),f317(f93(x67122),x67121)),f2(x67122)))+P1(f317(f317(f225(a1),x67121),f2(a1)))
% 94.68/94.45 [7227]~P78(x72271)+~P1(f317(f317(f224(x72271),x72272),f2(x72271)))+P1(f317(f317(f224(x72271),f317(f317(f74(x72271),x72272),x72272)),f2(x72271)))
% 94.68/94.45 [7229]~P78(x72291)+~P1(f317(f317(f225(x72291),x72292),f2(x72291)))+P1(f317(f317(f225(x72291),f317(f317(f74(x72291),x72292),x72292)),f2(x72291)))
% 94.68/94.45 [7230]~P111(x72301)+~P1(f317(f317(f225(x72301),x72302),f2(x72301)))+P1(f317(f317(f225(x72301),f317(f317(f74(x72301),x72302),x72302)),f2(x72301)))
% 94.68/94.45 [7801]~P78(x78011)+~P1(f317(f317(f224(x78011),f317(f317(f74(x78011),x78012),x78012)),f2(x78011)))+P1(f317(f317(f224(x78011),x78012),f2(x78011)))
% 94.68/94.45 [7802]~P78(x78021)+~P1(f317(f317(f225(x78021),f317(f317(f74(x78021),x78022),x78022)),f2(x78021)))+P1(f317(f317(f225(x78021),x78022),f2(x78021)))
% 94.68/94.45 [7803]~P111(x78031)+~P1(f317(f317(f225(x78031),f317(f317(f74(x78031),x78032),x78032)),f2(x78031)))+P1(f317(f317(f225(x78031),x78032),f2(x78031)))
% 94.68/94.45 [4792]~E(x47922,f2(a897))+~E(x47921,f2(a897))+E(f317(f317(f74(a897),x47921),x47922),f2(a897))
% 94.68/94.45 [4793]~E(x47932,f72(a897))+~E(x47931,f72(a897))+E(f317(f317(f75(a897),x47931),x47932),f72(a897))
% 94.68/94.45 [4794]~E(x47942,f72(a1))+~E(x47941,f72(a1))+E(f317(f317(f75(a1),x47941),x47942),f72(a1))
% 94.68/94.45 [4849]~P3(x48492)+E(x48491,f2(x48492))+E(f317(f317(f30(x48492),x48491),x48491),f72(x48492))
% 94.68/94.45 [4850]~P122(x48502)+E(x48501,f2(x48502))+E(f317(f317(f281(x48502),x48501),x48501),f72(x48502))
% 94.68/94.45 [4851]~P123(x48512)+E(x48511,f2(x48512))+E(f317(f317(f281(x48512),x48511),x48511),f72(x48512))
% 94.68/94.45 [4869]~P78(x48691)+~E(x48692,f2(x48691))+E(f317(f317(f74(x48691),x48692),x48692),f2(x48691))
% 94.68/94.45 [4872]~P143(x48721)+~E(x48722,f72(x48721))+E(f317(f317(f75(x48721),x48722),x48722),f72(x48721))
% 94.68/94.45 [4873]~P123(x48731)+~E(x48732,f2(x48731))+E(f317(f317(f281(x48731),x48732),x48732),f2(x48731))
% 94.68/94.45 [4918]~E(x49182,f2(a897))+~E(x49181,f2(a897))+E(f317(f73(a1),f317(f90(a1),x49181)),f317(f90(a1),x49182))
% 94.68/94.45 [4937]E(x49371,f72(a897))+E(x49372,f2(a897))+~E(f317(f317(f75(a897),x49372),x49371),x49372)
% 94.68/94.45 [4949]E(x49491,f2(a897))+E(x49492,f2(a897))+~E(f317(f317(f75(a897),x49492),x49491),f2(a897))
% 94.68/94.45 [4976]~E(x49762,f2(a897))+~E(x49761,f317(a102,f2(a897)))+E(f317(f317(f74(a897),x49761),x49762),f317(a102,f2(a897)))
% 94.68/94.45 [4977]~E(x49771,f2(a897))+~E(x49772,f317(a102,f2(a897)))+E(f317(f317(f74(a897),x49771),x49772),f317(a102,f2(a897)))
% 94.68/94.45 [4984]E(x49841,f72(a1))+E(x49842,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49841),x49842),f72(a1))
% 94.68/94.45 [4985]E(x49851,f72(a1))+E(x49852,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49852),x49851),f72(a1))
% 94.68/94.45 [4986]E(x49861,f72(a1))+E(x49861,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49862),x49861),f72(a1))
% 94.68/94.45 [4988]E(x49881,f72(a1))+E(x49881,f317(f94(a1),a87))+~E(f317(f317(f75(a1),x49881),x49882),f72(a1))
% 94.68/94.45 [5013]~P78(x50132)+E(x50131,f2(x50132))+~E(f317(f317(f74(x50132),x50131),x50131),f2(x50132))
% 94.68/94.45 [5019]~E(x50191,f317(f94(a1),a87))+~E(x50192,f317(f94(a1),a87))+E(f317(f317(f75(a1),x50191),x50192),f72(a1))
% 94.68/94.45 [5030]E(x50301,f2(a897))+E(x50302,f2(a897))+~E(f317(f317(f74(a897),x50302),x50301),f317(a102,f2(a897)))
% 94.68/94.45 [5040]~P94(x50401)+~P61(x50401)+E(f317(f317(f281(x50401),x50402),f317(f94(x50401),a77)),f2(x50401))
% 94.68/94.45 [5047]~P143(x50471)+~E(x50472,f317(f73(x50471),f72(x50471)))+E(f317(f317(f75(x50471),x50472),x50472),f72(x50471))
% 94.68/94.45 [5052]~P6(x50522)+~P6(x50521)+P6(f317(f317(f74(a1),x50521),x50522))
% 94.68/94.45 [5053]~P6(x50532)+~P6(x50531)+P6(f317(f317(f75(a1),x50531),x50532))
% 94.68/94.45 [5054]~P6(x50542)+~P6(x50541)+P6(f317(f317(f30(a1),x50541),x50542))
% 94.68/94.45 [5056]~E(x50562,f2(a1))+E(x50561,f2(a1))+E(f41(x50561,x50562),f317(f317(f242(a1,a1),f2(a1)),x50561))
% 94.68/94.45 [5079]~E(x50792,f317(a102,f2(a897)))+~E(x50791,f317(a102,f2(a897)))+E(f317(f317(f75(a897),x50791),x50792),f317(a102,f2(a897)))
% 94.68/94.45 [5096]E(x50961,f2(a897))+E(x50962,f317(a102,f2(a897)))+~E(f317(f317(f234(a897),x50962),x50961),f317(a102,f2(a897)))
% 94.68/94.45 [5097]E(x50971,f2(a897))+E(x50971,f317(a102,f2(a897)))+~E(f317(f317(f74(a897),x50972),x50971),f317(a102,f2(a897)))
% 94.68/94.45 [5098]E(x50981,f2(a897))+E(x50981,f317(a102,f2(a897)))+~E(f317(f317(f74(a897),x50981),x50982),f317(a102,f2(a897)))
% 94.68/94.45 [5107]~P94(x51071)+~P61(x51071)+E(f317(f317(f281(x51071),x51072),f317(f94(x51071),a87)),f317(f73(x51071),x51072))
% 94.68/94.45 [5127]E(x51271,f317(a95,x51272))+~E(x51271,f2(a897))+P1(f317(f317(f224(a1),f2(a1)),x51272))
% 94.68/94.45 [5128]E(f317(a95,x51281),x51282)+~E(x51282,f2(a897))+P1(f317(f317(f224(a1),f2(a1)),x51281))
% 94.68/94.45 [5144]E(x51441,f317(a102,f2(a897)))+E(x51442,f317(a102,f2(a897)))+~E(f317(f317(f74(a897),x51441),x51442),f317(a102,f2(a897)))
% 94.68/94.45 [5155]~E(x51551,f317(a95,x51552))+E(x51551,f2(a897))+P1(f317(f317(f224(a1),f2(a1)),x51552))
% 94.68/94.45 [5156]~E(f317(a95,x51562),x51561)+E(x51561,f2(a897))+P1(f317(f317(f224(a1),f2(a1)),x51562))
% 94.68/94.45 [5179]~P66(x51791)+E(f317(f57(x51791,f228(x51791)),x51792),f14(x51791,x51792))+~P1(f317(f28(x51791),x51792))
% 94.68/94.45 [5180]~P66(x51801)+E(f317(f57(x51801,f223(x51801)),x51802),f15(x51801,x51802))+~P1(f317(f28(x51801),x51802))
% 94.68/94.45 [5181]~P100(x51811)+E(f317(f57(x51811,f91(x51811)),x51812),f13(x51811,x51812))+~P1(f317(f28(x51811),x51812))
% 94.68/94.45 [5182]~P100(x51821)+E(f317(f57(x51821,f92(x51821)),x51822),f10(x51821,x51822))+~P1(f317(f28(x51821),x51822))
% 94.68/94.45 [5259]E(x52591,x52592)+~E(f317(f317(f23(a897),x52592),x52591),f2(a897))+~E(f317(f317(f23(a897),x52591),x52592),f2(a897))
% 94.68/94.45 [5276]P6(x52761)+~P39(x52762)+~P1(f317(f317(f319(a1),x52761),x52762))
% 94.68/94.45 [5307]~P111(x53071)+~E(f76(x53071,x53072),f72(x53071))+P1(f317(f317(f225(x53071),f2(x53071)),x53072))
% 94.68/94.45 [5318]~P94(x53181)+E(f317(f90(x53181),f317(f94(a897),x53182)),f317(f94(x53181),x53182))+P1(f317(a183,f317(f94(a1),x53182)))
% 94.68/94.45 [5323]~P43(x53231,x53232)+P44(a893)+P1(f317(f28(f903(x53231,x53231)),x53232))
% 94.68/94.45 [5393]~P66(x53931)+E(f317(f57(x53931,f228(x53931)),x53932),f11(x53931,f228(x53931),x53932))+~P1(f317(f28(x53931),x53932))
% 94.68/94.45 [5394]~P66(x53941)+E(f317(f57(x53941,f223(x53941)),x53942),f12(x53941,f223(x53941),x53942))+~P1(f317(f28(x53941),x53942))
% 94.68/94.45 [5408]E(x54081,x54082)+P1(f317(f317(f225(a897),x54082),x54081))+P1(f317(f317(f225(a897),x54081),x54082))
% 94.68/94.45 [5409]E(x54091,x54092)+P1(f317(f317(f225(a1),x54092),x54091))+P1(f317(f317(f225(a1),x54091),x54092))
% 94.68/94.45 [5463]~P94(x54631)+E(f317(f90(x54631),f317(f94(a897),x54632)),f2(x54631))+~P1(f317(a183,f317(f94(a1),x54632)))
% 94.68/94.45 [5466]~E(x54662,f317(a95,x54661))+E(x54661,f317(f90(a1),x54662))+~P1(f317(f317(f224(a1),f2(a1)),x54661))
% 94.68/94.45 [5467]~E(f317(a95,x54671),x54672)+E(x54671,f317(f90(a1),x54672))+~P1(f317(f317(f224(a1),f2(a1)),x54671))
% 94.68/94.45 [5468]~E(x54681,f317(a95,x54682))+E(f317(f90(a1),x54681),x54682)+~P1(f317(f317(f224(a1),f2(a1)),x54682))
% 94.68/94.45 [5478]E(x54781,f317(a95,x54782))+~E(x54782,f317(f90(a1),x54781))+~P1(f317(f317(f224(a1),f2(a1)),x54782))
% 94.68/94.45 [5479]E(f317(a95,x54791),x54792)+~E(x54791,f317(f90(a1),x54792))+~P1(f317(f317(f224(a1),f2(a1)),x54791))
% 94.68/94.45 [5510]~P112(x55102)+E(x55101,f2(x55102))+~P1(f317(f317(f277(x55102),f2(x55102)),x55101))
% 94.68/94.45 [5521]~P86(x55212)+E(x55211,f2(x55212))+P1(f317(f317(f225(x55212),f2(x55212)),f317(f70(x55212),x55211)))
% 94.68/94.45 [5585]~P111(x55851)+E(f76(x55851,x55852),f72(x55851))+~P1(f317(f317(f225(x55851),f2(x55851)),x55852))
% 94.68/94.45 [5591]~P94(x55911)+E(f317(f90(x55911),f317(f94(a897),x55912)),f2(x55911))+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x55912)))
% 94.68/94.45 [5602]~P86(x56021)+E(f317(f70(x56021),x56022),x56022)+~P1(f317(f317(f224(x56021),f2(x56021)),x56022))
% 94.68/94.45 [5603]~P86(x56031)+E(f317(f70(x56031),x56032),x56032)+~P1(f317(f317(f225(x56031),f2(x56031)),x56032))
% 94.68/94.45 [5612]E(x56121,f2(a897))+~E(f129(a897,f317(f292(a897,x56122),x56121)),f103(a897))+P1(f317(f317(f224(a897),x56121),x56122))
% 94.68/94.45 [5622]~P76(x56221)+E(f317(f317(f6(x56221,x56221),f5(x56221)),f317(f162(x56221),x56222)),f317(f155(x56221),x56222))+~P1(f317(f127(x56221),x56222))
% 94.68/94.45 [5625]~P141(x56251)+E(f317(f90(x56251),f317(a95,x56252)),f317(f93(x56251),x56252))+~P1(f317(f317(f224(a1),f2(a1)),x56252))
% 94.68/94.45 [5652]E(x56521,x56522)+P1(f317(f317(f225(a897),x56521),x56522))+~P1(f317(f317(f224(a897),x56521),x56522))
% 94.68/94.45 [5653]E(x56531,x56532)+P1(f317(f317(f225(a1),x56531),x56532))+~P1(f317(f317(f224(a1),x56531),x56532))
% 94.68/94.45 [5656]E(x56561,f72(a1))+~E(f317(f317(f75(a1),x56562),x56561),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x56562))
% 94.68/94.45 [5657]E(x56571,f72(a1))+~E(f317(f317(f75(a1),x56571),x56572),f72(a1))+~P1(f317(f317(f225(a1),f2(a1)),x56571))
% 94.68/94.45 [5698]~P39(x56982)+P1(f317(f317(f224(a1),f2(a1)),x56981))+~P1(f317(f317(f319(a1),x56981),x56982))
% 94.68/94.45 [5717]~P57(x57171,x57172)+P36(x57171,x57172)+~P1(f317(f28(f903(x57171,x57171)),x57172))
% 94.68/94.45 [5719]~P57(x57191,x57192)+P43(x57191,x57192)+~P1(f317(f28(f903(x57191,x57191)),x57192))
% 94.68/94.45 [5761]E(x57611,f178(f904(x57612,a893)))+~P1(f317(f28(x57612),x57611))+P1(f317(f317(f225(a897),f2(a897)),f317(f29(x57612),x57611)))
% 94.68/94.45 [5788]~P1(f317(x57881,x57882))+P1(f317(x57881,f2(a897)))+P1(f317(f317(f225(a897),f612(x57882,x57881)),x57882))
% 94.68/94.45 [5811]E(x58111,f2(a897))+~E(f317(f155(a897),x58112),f2(a897))+~P1(f317(f317(f319(a897),x58111),f317(f162(a897),x58112)))
% 94.68/94.45 [5879]E(x58791,x58792)+~P1(f317(f317(f224(a897),x58792),x58791))+~P1(f317(f317(f224(a897),x58791),x58792))
% 94.68/94.45 [5880]E(x58801,x58802)+~P1(f317(f317(f224(a1),x58802),x58801))+~P1(f317(f317(f224(a1),x58801),x58802))
% 94.68/94.45 [5889]E(x58891,x58892)+~P1(f317(f317(f277(a897),x58892),x58891))+~P1(f317(f317(f277(a897),x58891),x58892))
% 94.68/94.45 [5891]E(f317(f29(x58911),x58912),f2(a897))+~P1(f317(f28(x58911),x58912))+P1(f317(f317(f319(x58911),f699(x58912,x58911)),x58912))
% 94.68/94.45 [5900]E(f45(x59001,x59002),f41(x59001,x59002))+P1(f317(f317(f224(a1),f2(a1)),x59001))+~P1(f317(f317(f225(a1),f2(a1)),x59002))
% 94.68/94.45 [5926]~P1(f317(x59261,f843(x59261)))+P1(f317(x59261,f317(a95,x59262)))+~P1(f317(f317(f224(a1),f2(a1)),x59262))
% 94.68/94.45 [5929]P1(f317(f317(f224(a897),x59291),f397(x59292)))+~P1(f317(f28(a897),x59292))+~P1(f317(f317(f319(a897),x59291),x59292))
% 94.68/94.45 [5930]P1(f317(f317(f225(a897),x59301),f518(x59302)))+~P1(f317(f28(a897),x59302))+~P1(f317(f317(f319(a897),x59301),x59302))
% 94.68/94.45 [5961]E(x59611,x59612)+~P1(f317(f317(f225(a897),x59611),f317(a102,x59612)))+P1(f317(f317(f225(a897),x59611),x59612))
% 94.68/94.45 [5998]E(x59981,f317(a102,x59982))+~P1(f317(f317(f224(a897),x59981),f317(a102,x59982)))+P1(f317(f317(f224(a897),x59981),x59982))
% 94.68/94.45 [6014]P1(f317(x60141,f844(x60141)))+~P1(f317(x60141,f317(a95,x60142)))+~P1(f317(f317(f224(a1),f2(a1)),x60142))
% 94.68/94.45 [6030]~P1(f317(x60301,x60302))+~P1(f317(f317(f224(a1),f2(a1)),x60302))+P1(f317(x60301,f317(f90(a1),f736(x60301))))
% 94.68/94.45 [6041]~P86(x60412)+~E(x60411,f2(x60412))+~P1(f317(f317(f225(x60412),f2(x60412)),f317(f70(x60412),x60411)))
% 94.68/94.45 [6066]~P57(x60661,x60662)+P36(x60661,f317(f276(x60661,x60661),x60662))+~P1(f317(f28(f903(x60661,x60661)),x60662))
% 94.68/94.45 [6075]~P94(x60751)+E(f317(f90(x60751),f317(f94(a897),x60752)),f317(f94(x60751),x60752))+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x60752)))
% 94.68/94.45 [6078]E(f317(a102,x60781),x60782)+~P1(f317(f317(f225(a897),x60781),x60782))+P1(f317(f317(f225(a897),f317(a102,x60781)),x60782))
% 94.68/94.45 [6094]E(f317(f317(f30(a1),x60941),x60942),f2(a1))+~P1(f317(f317(f224(a1),x60941),f2(a1)))+~P1(f317(f317(f225(a1),x60942),x60941))
% 94.68/94.45 [6106]E(f40(a1,x61061,x61062),x61061)+~P1(f317(f317(f224(a1),x61061),f2(a1)))+~P1(f317(f317(f225(a1),x61062),x61061))
% 94.68/94.45 [6120]E(f42(x61201,x61202),f41(x61201,x61202))+~P1(f317(f317(f224(a1),f2(a1)),x61201))+~P1(f317(f317(f224(a1),f2(a1)),x61202))
% 94.68/94.45 [6130]E(f317(f317(f30(a1),x61301),x61302),f2(a1))+~P1(f317(f317(f224(a1),f2(a1)),x61301))+~P1(f317(f317(f225(a1),x61301),x61302))
% 94.68/94.45 [6141]E(f40(a897,f317(f94(a897),x61411),f317(f94(a897),x61412)),f317(f94(a897),x61411))+P1(f317(a183,f317(f94(a1),x61411)))+~P1(f317(a183,f317(f94(a1),x61412)))
% 94.68/94.45 [6143]E(f40(a1,x61431,x61432),x61431)+~P1(f317(f317(f224(a1),f2(a1)),x61431))+~P1(f317(f317(f225(a1),x61431),x61432))
% 94.68/94.45 [6144]E(x61441,x61442)+~P1(f317(f317(f225(a897),x61441),f317(a102,x61442)))+~P1(f317(f317(f224(a897),x61442),x61441))
% 94.68/94.45 [6158]~P78(x61581)+~P1(f317(f317(f224(x61581),x61582),f2(x61581)))+P1(f317(f317(f224(x61581),x61582),f317(f73(x61581),x61582)))
% 94.68/94.45 [6159]~P111(x61591)+~P1(f317(f317(f225(x61591),x61592),f2(x61591)))+P1(f317(f317(f225(x61591),x61592),f317(f73(x61591),x61592)))
% 94.68/94.45 [6168]~P5(x61681)+E(f317(f317(f58(x61681,x61681,f92(x61681)),f232(x61681)),x61682),f32(x61681,x61682))+~P1(f317(f28(x61681),x61682))
% 94.68/94.45 [6169]~P5(x61691)+E(f317(f317(f58(x61691,x61691,f91(x61691)),f178(x61691)),x61692),f31(x61691,x61692))+~P1(f317(f28(x61691),x61692))
% 94.68/94.45 [6186]~P111(x61861)+~P1(f317(f317(f224(a1),f2(a1)),x61862))+P1(f317(f317(f224(x61861),f2(x61861)),f317(f93(x61861),x61862)))
% 94.68/94.45 [6187]~P110(x61871)+~P1(f317(f317(f225(a897),f2(a897)),x61872))+P1(f317(f317(f225(x61871),f2(x61871)),f317(f90(x61871),x61872)))
% 94.68/94.45 [6188]~P111(x61881)+~P1(f317(f317(f225(a1),f2(a1)),x61882))+P1(f317(f317(f225(x61881),f2(x61881)),f317(f93(x61881),x61882)))
% 94.68/94.45 [6191]~P6(x61912)+~P6(x61911)+E(f317(f300(a897,a1,f90(a1)),f293(a897,f317(a95,x61911),f317(a95,x61912))),f293(a1,x61911,x61912))
% 94.68/94.45 [6197]P1(f317(x61971,x61972))+~P1(f317(f317(f224(a1),f2(a1)),x61972))+~P1(f317(x61971,f317(f90(a1),f718(x61971))))
% 94.68/94.45 [6229]E(f317(f317(f74(a897),f317(f94(a897),x62291)),f317(f94(a897),x62292)),f317(f94(a897),x62291))+P1(f317(f317(f225(a1),x62291),a77))+~P1(f317(f317(f225(a1),x62292),a77))
% 94.68/94.45 [6233]~P111(x62331)+P1(f317(f317(f225(x62331),f2(x62331)),f76(x62331,x62332)))+~P1(f317(f317(f225(x62331),f2(x62331)),x62332))
% 94.68/94.45 [6247]~P67(x62471)+~P1(f317(f317(f224(x62471),x62472),f2(x62471)))+P1(f317(f317(f224(x62471),f2(x62471)),f317(f73(x62471),x62472)))
% 94.68/94.45 [6248]~P67(x62481)+~P1(f317(f317(f225(x62481),x62482),f2(x62481)))+P1(f317(f317(f225(x62481),f2(x62481)),f317(f73(x62481),x62482)))
% 94.68/94.45 [6251]E(x62511,f232(f904(x62512,a893)))+~E(f317(f29(x62512),x62511),f317(f29(x62512),f232(f904(x62512,a893))))+~P1(f317(f28(x62512),f232(f904(x62512,a893))))
% 94.68/94.45 [6277]~P1(f317(f317(f225(a897),f2(a897)),x62772))+~P1(f317(f317(f277(a897),x62771),x62772))+P1(f317(f317(f224(a897),x62771),x62772))
% 94.68/94.45 [6278]~P1(f317(f317(f225(a1),f2(a1)),x62782))+~P1(f317(f317(f277(a1),x62781),x62782))+P1(f317(f317(f224(a1),x62781),x62782))
% 94.68/94.45 [6285]~P78(x62851)+P1(f317(f317(f224(x62851),x62852),f2(x62851)))+~P1(f317(f317(f224(x62851),x62852),f317(f73(x62851),x62852)))
% 94.68/94.45 [6286]~P111(x62861)+P1(f317(f317(f225(x62861),x62862),f2(x62861)))+~P1(f317(f317(f225(x62861),x62862),f317(f73(x62861),x62862)))
% 94.68/94.45 [6295]~P94(x62951)+P1(f317(f317(f319(x62951),f317(f94(x62951),x62952)),f176(x62951)))+~P1(f317(f317(f224(a1),a77),x62952))
% 94.68/94.45 [6324]E(x63241,f2(a897))+~P1(f317(f317(f225(a897),x63241),f317(a102,x63242)))+P1(f317(f317(f225(a897),f560(x63242,x63241)),x63242))
% 94.68/94.45 [6327]~P149(x63272)+P150(x63271,f317(f317(f299(a892),f909(x63272)),f178(f904(a892,a893))))+P1(f317(f317(f319(a895),f851(x63271,x63272)),a905))
% 94.68/94.45 [6349]~P111(x63491)+~P1(f317(f317(f225(x63491),f2(x63491)),f76(x63491,x63492)))+P1(f317(f317(f225(x63491),f2(x63491)),x63492))
% 94.68/94.45 [6351]~E(f317(f94(a897),x63512),f317(f94(a897),x63511))+P1(f317(f317(f224(a1),f317(f94(a1),x63511)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x63512)))
% 94.68/94.45 [6381]E(f317(f241(a1,a1),f45(x63811,x63812)),f317(f317(f30(a1),x63811),x63812))+~P1(f317(f317(f225(a1),x63811),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x63812))
% 94.68/94.45 [6421]E(f317(f246(a1,a1),f45(x64211,x64212)),f40(a1,x64211,x64212))+~P1(f317(f317(f225(a1),x64211),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x64212))
% 94.68/94.45 [6424]~P111(x64242)+~P1(f317(f317(f224(x64242),f2(x64242)),f317(f93(x64242),x64241)))+P1(f317(f317(f224(a1),f2(a1)),x64241))
% 94.68/94.45 [6425]~P110(x64252)+~P1(f317(f317(f225(x64252),f2(x64252)),f317(f90(x64252),x64251)))+P1(f317(f317(f225(a897),f2(a897)),x64251))
% 94.68/94.45 [6426]~P111(x64262)+~P1(f317(f317(f225(x64262),f2(x64262)),f317(f93(x64262),x64261)))+P1(f317(f317(f225(a1),f2(a1)),x64261))
% 94.68/94.45 [6429]E(f317(f241(a1,a1),f42(x64291,x64292)),f317(f317(f30(a1),x64291),x64292))+~P1(f317(f317(f224(a1),f2(a1)),x64292))+~P1(f317(f317(f225(a1),f2(a1)),x64291))
% 94.68/94.45 [6443]E(f317(f246(a1,a1),f42(x64431,x64432)),f40(a1,x64431,x64432))+~P1(f317(f317(f224(a1),f2(a1)),x64432))+~P1(f317(f317(f225(a1),f2(a1)),x64431))
% 94.68/94.45 [6459]~P67(x64591)+P1(f317(f317(f224(x64591),x64592),f2(x64591)))+~P1(f317(f317(f224(x64591),f2(x64591)),f317(f73(x64591),x64592)))
% 94.68/94.45 [6460]~P67(x64601)+P1(f317(f317(f225(x64601),x64602),f2(x64601)))+~P1(f317(f317(f225(x64601),f2(x64601)),f317(f73(x64601),x64602)))
% 94.68/94.45 [6486]P1(f317(f44(x64861,x64862),f45(x64861,x64862)))+~P1(f317(f317(f225(a1),x64861),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x64862))
% 94.68/94.45 [6500]~P1(f317(f317(f225(a897),f2(a897)),x65001))+~P1(f317(f317(f277(a897),x65002),x65001))+~P1(f317(f317(f225(a897),x65001),x65002))
% 94.68/94.45 [6513]P1(f317(f44(x65131,x65132),f42(x65131,x65132)))+~P1(f317(f317(f224(a1),f2(a1)),x65131))+~P1(f317(f317(f225(a1),f2(a1)),x65132))
% 94.68/94.45 [6556]~P67(x65561)+P1(f317(f317(f224(x65561),f317(f73(x65561),x65562)),f2(x65561)))+~P1(f317(f317(f224(x65561),f2(x65561)),x65562))
% 94.68/94.45 [6557]~P67(x65571)+P1(f317(f317(f225(x65571),f317(f73(x65571),x65572)),f2(x65571)))+~P1(f317(f317(f225(x65571),f2(x65571)),x65572))
% 94.68/94.45 [6578]E(f317(f317(f23(a897),f317(a95,x65781)),f317(a95,x65782)),f317(a95,f184(x65781,x65782)))+~P1(f317(f317(f224(a1),f2(a1)),x65782))+~P1(f317(f317(f224(a1),f2(a1)),x65781))
% 94.68/94.45 [6596]P1(f317(f317(f224(a1),f2(a1)),f184(x65961,x65962)))+~P1(f317(f317(f224(a1),f2(a1)),x65962))+~P1(f317(f317(f224(a1),f2(a1)),x65961))
% 94.68/94.45 [6633]~P1(f317(x66331,x66332))+P1(f317(x66331,f2(a897)))+P1(f317(x66331,f317(f317(f74(a897),f612(x66332,x66331)),f72(a897))))
% 94.68/94.45 [6718]E(f317(f94(a897),x67181),f317(f94(a897),x67182))+~P1(f317(f317(f224(a1),f317(f94(a1),x67182)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x67181)))
% 94.68/94.45 [6732]~E(x67321,f2(a897))+~E(f652(x67322,x67321),f2(a897))+E(f317(f132(a897,a897,f74(a897),x67321),x67322),f2(a897))
% 94.68/94.45 [6756]~P1(f317(f28(x67561),f590(x67562,x67561)))+~P1(f317(f28(f904(x67561,a893)),x67562))+P1(f317(f28(x67561),f31(f904(x67561,a893),x67562)))
% 94.68/94.45 [6762]E(x67621,x67622)+P1(f317(f317(f225(a1),x67621),x67622))+~P1(f317(f317(f225(a1),x67621),f317(f317(f74(a1),x67622),f72(a1))))
% 94.68/94.45 [6763]P1(f317(f317(f224(a897),f317(a95,x67631)),f317(a95,x67632)))+~P1(f317(f317(f224(a1),f2(a1)),x67632))+~P1(f317(f317(f224(a1),x67631),x67632))
% 94.68/94.45 [6764]P1(f317(f317(f224(a897),f317(a95,x67641)),f317(a95,x67642)))+~P1(f317(f317(f225(a1),f2(a1)),x67641))+~P1(f317(f317(f224(a1),x67641),x67642))
% 94.68/94.45 [6766]P1(f317(f317(f225(a897),f317(a95,x67661)),f317(a95,x67662)))+~P1(f317(f317(f224(a1),f2(a1)),x67661))+~P1(f317(f317(f225(a1),x67661),x67662))
% 94.68/94.45 [6767]P1(f317(f317(f225(a897),f317(a95,x67671)),f317(a95,x67672)))+~P1(f317(f317(f225(a1),f2(a1)),x67672))+~P1(f317(f317(f225(a1),x67671),x67672))
% 94.68/94.45 [6778]E(f40(a897,f317(a95,x67781),f317(a95,x67782)),f317(a95,f40(a1,x67781,x67782)))+~P1(f317(f317(f224(a1),f2(a1)),x67782))+~P1(f317(f317(f224(a1),f2(a1)),x67781))
% 94.68/94.45 [6802]~P67(x68021)+~P1(f317(f317(f224(x68021),f317(f73(x68021),x68022)),f2(x68021)))+P1(f317(f317(f224(x68021),f2(x68021)),x68022))
% 94.68/94.45 [6803]~P67(x68031)+~P1(f317(f317(f225(x68031),f317(f73(x68031),x68032)),f2(x68031)))+P1(f317(f317(f225(x68031),f2(x68031)),x68032))
% 94.68/94.45 [6818]~P1(f317(f317(f225(a1),a77),x68182))+~P1(f317(f317(f225(a1),x68181),x68182))+P1(f317(f317(f225(a897),f317(f94(a897),x68181)),f317(f94(a897),x68182)))
% 94.68/94.45 [6912]~P1(f317(f317(f224(a1),f2(a1)),x69121))+P1(f317(f317(f225(a897),f317(a95,x69121)),x69122))+~P1(f317(f317(f225(a1),x69121),f317(f90(a1),x69122)))
% 94.68/94.45 [6917]P1(f317(x69171,x69172))+~P1(f317(x69171,f317(a20,f787(x69171,x69172))))+~P1(f317(f317(f319(a897),x69172),f232(f904(a897,a893))))
% 94.68/94.45 [6928]E(x69281,f2(a1))+E(f40(a1,x69282,x69281),f2(a1))+E(f317(f317(f23(a1),f317(f73(a1),f317(f317(f30(a1),x69282),x69281))),f72(a1)),f317(f317(f30(a1),x69282),f317(f73(a1),x69281)))
% 94.68/94.45 [6942]~P1(f317(f317(f224(a1),f2(a1)),x69421))+~P1(f317(f317(f225(a897),f317(a95,x69421)),x69422))+P1(f317(f317(f225(a1),x69421),f317(f90(a1),x69422)))
% 94.68/94.45 [6978]~P1(f317(f317(f224(a897),f317(a95,x69781)),f317(a95,x69782)))+~P1(f317(f317(f224(a1),f2(a1)),x69782))+P1(f317(f317(f224(a1),x69781),x69782))
% 94.68/94.45 [6979]~P1(f317(f317(f224(a897),f317(a95,x69791)),f317(a95,x69792)))+~P1(f317(f317(f225(a1),f2(a1)),x69791))+P1(f317(f317(f224(a1),x69791),x69792))
% 94.68/94.45 [7012]P1(f317(f317(f224(a1),x70121),x70122))+~P1(f317(f317(f224(a897),f317(f94(a897),x70121)),f317(f94(a897),x70122)))+P1(f317(f317(f224(a1),x70121),a77))
% 94.68/94.45 [7038]P1(f317(f317(f224(a1),f2(a1)),f40(a1,x70381,x70382)))+~P1(f317(f317(f224(a1),f2(a1)),x70382))+~P1(f317(f317(f224(a1),f2(a1)),x70381))
% 94.68/94.45 [7136]P1(f317(f317(f225(a1),a77),x71361))+~P1(f317(f317(f225(a1),x71362),x71361))+~P1(f317(f317(f225(a897),f317(f94(a897),x71362)),f317(f94(a897),x71361)))
% 94.68/94.45 [7190]E(f317(f317(f242(a1,a1),f317(f317(f30(a1),x71901),x71902)),f40(a1,x71901,x71902)),f45(x71901,x71902))+~P1(f317(f317(f225(a1),x71901),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x71902))
% 94.68/94.45 [7210]E(f317(f317(f242(a1,a1),f317(f317(f30(a1),x72101),x72102)),f40(a1,x72101,x72102)),f42(x72101,x72102))+~P1(f317(f317(f224(a1),f2(a1)),x72102))+~P1(f317(f317(f224(a1),f2(a1)),x72101))
% 94.68/94.45 [7264]~P98(x72642)+E(x72641,f103(x72642))+E(f317(f132(x72642,x72642,f75(x72642),f317(f131(x72642),x72641)),f317(f161(x72642),x72641)),f317(f57(x72642,f75(x72642)),f317(f162(x72642),x72641)))
% 94.68/94.45 [7379]~E(x73791,f2(a897))+E(f317(f132(a897,a897,f74(a897),x73791),x73792),f2(a897))+P1(f317(f317(f319(a897),f652(x73792,x73791)),f317(f162(a897),x73792)))
% 94.68/94.45 [7432]~P1(f317(f317(f224(a1),x74321),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x74321),x74322)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74322))
% 94.68/94.45 [7433]~P1(f317(f317(f225(a1),x74332),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x74331),x74332)),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x74331))
% 94.68/94.45 [7434]~P1(f317(f317(f225(a1),x74342),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f30(a1),x74341),x74342)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74341))
% 94.68/94.45 [7436]~P1(f317(f317(f225(a1),x74361),f2(a1)))+P1(f317(f317(f225(a1),f317(f317(f30(a1),x74361),x74362)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x74362))
% 94.68/94.45 [7443]P1(f317(f317(f319(f904(x74431,a893)),f590(x74432,x74431)),x74432))+~P1(f317(f28(f904(x74431,a893)),x74432))+P1(f317(f28(x74431),f31(f904(x74431,a893),x74432)))
% 94.68/94.45 [7533]P24(x75331,x75331,x75332,f232(f904(x75331,a893)))+~E(f317(f300(x75331,x75331,x75332),f232(f904(x75331,a893))),f232(f904(x75331,a893)))+~P1(f317(f28(x75331),f232(f904(x75331,a893))))
% 94.68/94.45 [7655]~P24(x76551,x76551,x76552,f232(f904(x76551,a893)))+E(f317(f300(x76551,x76551,x76552),f232(f904(x76551,a893))),f232(f904(x76551,a893)))+~P1(f317(f28(x76551),f232(f904(x76551,a893))))
% 94.68/94.45 [7795]E(f317(f317(f30(a1),x77951),x77952),f317(f94(a1),a87))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x77951),x77952)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x77951))
% 94.68/94.45 [7852]~P1(f317(f317(f225(a1),x78522),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f30(a1),x78521),x78522)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x78521))
% 94.68/94.45 [7857]E(f317(f317(f74(a1),x78571),x78572),f40(a1,x78571,x78572))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),x78571),x78572)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x78571))
% 94.68/94.45 [7860]P1(f317(f317(f225(a1),x78601),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f30(a1),x78601),x78602)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x78602))
% 94.68/94.45 [7876]~P149(x78762)+P150(x78761,f317(f317(f299(a892),f909(x78762)),f178(f904(a892,a893))))+~P150(x78761,f317(f317(f299(a892),f317(a908,f851(x78761,x78762))),f178(f904(a892,a893))))
% 94.68/94.45 [8557]~P66(x85571)+P13(x85571,x85572)+~P1(f317(f317(f224(x85571),f317(f317(f154(x85571),x85572),f686(x85572,x85571))),f317(f317(f154(x85571),x85572),f687(x85572,x85571))))
% 94.68/94.45 [8558]~P66(x85581)+P13(x85581,x85582)+~P1(f317(f317(f224(x85581),f317(f317(f154(x85581),x85582),f694(x85582,x85581))),f317(f317(f154(x85581),x85582),f698(x85582,x85581))))
% 94.68/94.45 [5754]E(x57541,f2(a1))+~E(f40(a1,x57542,x57541),f2(a1))+E(f317(f317(f30(a1),x57542),f317(f73(a1),x57541)),f317(f73(a1),f317(f317(f30(a1),x57542),x57541)))
% 94.68/94.45 [5772]~P39(x57722)+~P39(x57721)+P39(f317(f317(f91(f904(a1,a893)),x57721),x57722))
% 94.68/94.45 [5773]~P39(x57732)+~P39(x57731)+P39(f317(f317(f92(f904(a1,a893)),x57731),x57732))
% 94.68/94.45 [5791]~P94(x57911)+~P61(x57911)+E(f317(f73(x57911),f317(f317(f281(x57911),f72(x57911)),x57912)),f317(f317(f281(x57911),f317(f94(x57911),a87)),x57912))
% 94.68/94.45 [5918]E(x59181,f2(a1))+~E(f40(a1,x59182,x59181),f2(a1))+E(f317(f317(f30(a1),f317(f73(a1),x59182)),x59181),f317(f73(a1),f317(f317(f30(a1),x59182),x59181)))
% 94.68/94.45 [6060]~P66(x60601)+P13(x60601,x60602)+P1(f317(f317(f225(a897),f687(x60602,x60601)),f317(f179(f898(x60601)),x60602)))
% 94.68/94.45 [6061]~P66(x60611)+P13(x60611,x60612)+P1(f317(f317(f225(a897),f698(x60612,x60611)),f317(f179(f898(x60611)),x60612)))
% 94.68/94.45 [6223]~P94(x62231)+~E(f317(f94(x62231),x62232),f2(x62231))+P27(x62231,f317(f94(x62231),f317(f317(f74(a1),x62232),f317(f73(a1),a77))))
% 94.68/94.45 [6224]~P94(x62241)+~E(f317(f94(x62241),x62242),f2(x62241))+P27(x62241,f317(f94(x62241),f317(f317(f74(a1),a77),f317(f73(a1),x62242))))
% 94.68/94.45 [6226]E(f317(a46,f42(f317(f73(a1),x62261),f317(f73(a1),x62262))),f41(x62261,x62262))+P1(f317(f317(f224(a1),f2(a1)),x62261))+P1(f317(f317(f225(a1),f2(a1)),x62262))
% 94.68/94.45 [6357]~E(x63572,f2(a897))+~E(x63571,f2(a897))+P1(f317(f317(f224(a1),f317(f90(a1),x63571)),f317(f73(a1),f317(f90(a1),x63572))))
% 94.68/94.45 [6387]E(f317(f317(f74(a897),f317(f94(a897),x63871)),f317(f94(a897),x63872)),f317(f94(a897),f317(f317(f74(a1),x63871),x63872)))+P1(f317(f317(f225(a1),x63871),a77))+P1(f317(f317(f225(a1),x63872),a77))
% 94.68/94.45 [6522]~P78(x65221)+~P1(f317(f317(f224(x65221),f2(x65221)),x65222))+P1(f317(f317(f224(x65221),f317(f73(x65221),x65222)),x65222))
% 94.68/94.45 [6523]~P78(x65231)+~P1(f317(f317(f225(x65231),f2(x65231)),x65232))+P1(f317(f317(f225(x65231),f317(f73(x65231),x65232)),x65232))
% 94.68/94.45 [6704]E(f317(f317(f23(a897),f317(a95,x67041)),f317(a95,x67042)),f317(a95,f317(f317(f23(a1),x67041),x67042)))+~P1(f317(f317(f224(a1),f2(a1)),x67042))+~P1(f317(f317(f224(a1),x67042),x67041))
% 94.68/94.45 [6740]E(f317(a95,f40(a1,f317(f94(a1),x67401),f317(f94(a1),x67402))),f40(a897,f317(f94(a897),x67401),f317(f94(a897),x67402)))+P1(f317(a183,f317(f94(a1),x67401)))+P1(f317(a183,f317(f94(a1),x67402)))
% 94.68/94.45 [6757]~P78(x67571)+P1(f317(f317(f224(x67571),f2(x67571)),x67572))+~P1(f317(f317(f224(x67571),f317(f73(x67571),x67572)),x67572))
% 94.68/94.45 [6758]~P78(x67581)+P1(f317(f317(f225(x67581),f2(x67581)),x67582))+~P1(f317(f317(f225(x67581),f317(f73(x67581),x67582)),x67582))
% 94.68/94.45 [6770]~P78(x67701)+~P1(f317(f317(f224(x67701),f2(x67701)),x67702))+P1(f317(f317(f224(x67701),f2(x67701)),f317(f317(f74(x67701),x67702),x67702)))
% 94.68/94.45 [6772]~P78(x67721)+~P1(f317(f317(f225(x67721),f2(x67721)),x67722))+P1(f317(f317(f225(x67721),f2(x67721)),f317(f317(f74(x67721),x67722),x67722)))
% 94.68/94.45 [6783]E(f317(f317(f74(a897),f317(a95,x67831)),f317(a95,x67832)),f317(a95,f317(f317(f74(a1),x67831),x67832)))+~P1(f317(f317(f224(a1),f2(a1)),x67832))+~P1(f317(f317(f224(a1),f2(a1)),x67831))
% 94.68/94.45 [6795]E(x67951,f2(a897))+P1(f317(f317(f225(a897),f2(a897)),x67952))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f234(a897),x67952),x67951)))
% 94.68/94.45 [6830]~P94(x68301)+E(f317(f94(x68301),x68302),f2(x68301))+~P27(x68301,f317(f94(x68301),f317(f317(f74(a1),a77),f317(f73(a1),x68302))))
% 94.68/94.45 [6831]~P94(x68311)+E(f317(f94(x68311),x68312),f2(x68311))+~P27(x68311,f317(f94(x68311),f317(f317(f74(a1),x68312),f317(f73(a1),a77))))
% 94.68/94.45 [6890]~P1(f317(f28(x68901),x68902))+~P1(f317(f28(x68901),f232(f904(x68901,a893))))+P1(f317(f28(x68901),f317(f73(f904(x68901,a893)),x68902)))
% 94.68/94.45 [6913]~P1(f317(f317(f225(a1),f2(a1)),x69132))+~P1(f317(f317(f224(a1),x69132),x69131))+P1(f317(f317(f225(a1),f2(a1)),f317(f317(f30(a1),x69131),x69132)))
% 94.68/94.45 [6914]~P1(f317(f317(f224(a1),x69141),f2(a1)))+~P1(f317(f317(f225(a1),x69142),f2(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f30(a1),x69141),x69142)))
% 94.68/94.45 [6952]~P1(f317(f317(f224(a1),f2(a1)),x69522))+~P1(f317(f317(f224(a1),f2(a1)),x69521))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x69521),x69522)))
% 94.68/94.45 [6953]~P1(f317(f317(f224(a1),f2(a1)),x69532))+~P1(f317(f317(f224(a1),f2(a1)),x69531))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f75(a1),x69531),x69532)))
% 94.68/94.45 [6954]~P1(f317(f317(f224(a1),f2(a1)),x69542))+~P1(f317(f317(f224(a1),f2(a1)),x69541))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f30(a1),x69541),x69542)))
% 94.68/94.45 [6955]~P1(f317(f317(f224(a1),f2(a1)),x69551))+~P1(f317(f317(f225(a1),f2(a1)),x69552))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f30(a1),x69551),x69552)))
% 94.68/94.45 [6956]~P1(f317(f317(f225(a897),f2(a897)),x69562))+~P1(f317(f317(f225(a897),f2(a897)),x69561))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f75(a897),x69561),x69562)))
% 94.68/94.45 [7025]E(x70251,f2(a1))+E(f40(a1,x70252,x70251),f2(a1))+E(f317(f317(f23(a1),f317(f73(a1),f317(f317(f30(a1),x70252),x70251))),f72(a1)),f317(f317(f30(a1),f317(f73(a1),x70252)),x70251))
% 94.68/94.45 [7082]P1(f317(f317(f225(a897),f2(a897)),x70821))+P1(f317(f317(f225(a897),f2(a897)),x70822))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f74(a897),x70822),x70821)))
% 94.68/94.45 [7086]~P78(x70861)+P1(f317(f317(f224(x70861),f2(x70861)),x70862))+~P1(f317(f317(f224(x70861),f2(x70861)),f317(f317(f74(x70861),x70862),x70862)))
% 94.68/94.45 [7087]~P78(x70871)+P1(f317(f317(f225(x70871),f2(x70871)),x70872))+~P1(f317(f317(f225(x70871),f2(x70871)),f317(f317(f74(x70871),x70872),x70872)))
% 94.68/94.45 [7137]~P1(f317(f28(x71371),x71372))+P1(f317(f28(x71371),f232(f904(x71371,a893))))+~P1(f317(f28(x71371),f317(f73(f904(x71371,a893)),x71372)))
% 94.68/94.45 [7202]P1(f317(f317(f224(a1),x72021),f2(a1)))+~P1(f317(f317(f225(a1),x72022),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f30(a1),x72021),x72022)))
% 94.68/94.45 [7208]~P1(f317(f317(f225(a1),f2(a1)),x72081))+P1(f317(f317(f224(a1),x72081),x72082))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f30(a1),x72082),x72081)))
% 94.68/94.45 [7209]~P1(f317(f317(f224(a1),f2(a1)),x72092))+P1(f317(f317(f224(a1),x72091),x72092))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f30(a1),x72092),x72091)))
% 94.68/94.45 [7239]P1(f317(f317(f224(a1),f2(a1)),x72391))+~P1(f317(f317(f225(a1),f2(a1)),x72392))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f30(a1),x72391),x72392)))
% 94.68/94.45 [7240]P1(f317(f317(f225(a1),f2(a1)),x72401))+~P1(f317(f317(f224(a1),f2(a1)),x72402))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f30(a1),x72402),x72401)))
% 94.68/94.45 [7686]~P1(f317(f28(x76862),f232(f904(x76862,a893))))+~P1(f317(f28(x76861),f232(f904(x76861,a893))))+P1(f317(f28(f902(x76861,x76862)),f232(f904(f902(x76861,x76862),a893))))
% 94.68/94.45 [7687]~P1(f317(f28(x76872),f232(f904(x76872,a893))))+~P1(f317(f28(x76871),f232(f904(x76871,a893))))+P1(f317(f28(f903(x76871,x76872)),f232(f904(f903(x76871,x76872),a893))))
% 94.68/94.45 [7759]~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x77591))+~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x77592))+P1(f317(f317(f225(a897),x77591),f317(f317(f75(a897),x77592),x77591)))
% 94.68/94.45 [7760]~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x77601))+~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x77602))+P1(f317(f317(f225(a897),x77601),f317(f317(f75(a897),x77601),x77602)))
% 94.68/94.45 [7794]E(f317(f29(x77941),f232(f904(x77941,a893))),f317(a102,f2(a897)))+P1(f317(f28(x77942),f232(f904(x77942,a893))))+~P1(f317(f28(f904(x77942,x77941)),f232(f904(f904(x77942,x77941),a893))))
% 94.68/94.45 [7922]~P1(f317(f317(f224(a897),f317(a102,f2(a897))),x79221))+~P1(f317(f317(f224(a897),f317(a102,f2(a897))),x79222))+P1(f317(f317(f224(a897),f317(a102,f2(a897))),f317(f317(f75(a897),x79221),x79222)))
% 94.68/94.45 [7923]~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x79232))+~P1(f317(f317(f225(a897),f317(a102,f2(a897))),x79231))+P1(f317(f317(f225(a897),f317(a102,f2(a897))),f317(f317(f75(a897),x79231),x79232)))
% 94.68/94.45 [8604]E(x86041,f103(x86042))+~P1(f317(f127(x86042),x86041))+E(f167(x86042,f317(f317(f8(a893,a893,x86042),a312),f317(f317(f7(x86042,x86042,a893),a314),f134(x86042,x86041))),x86041),f104(x86042,x86041))
% 94.68/94.45 [8699]~P39(x86992)+~P39(x86991)+E(f317(f300(a897,a1,f90(a1)),f317(f317(f91(f904(a897,a893)),f317(f300(a1,a897,a95),x86991)),f317(f300(a1,a897,a95),x86992))),f317(f317(f91(f904(a1,a893)),x86991),x86992))
% 94.68/94.45 [8700]~P39(x87002)+~P39(x87001)+E(f317(f300(a897,a1,f90(a1)),f317(f317(f92(f904(a897,a893)),f317(f300(a1,a897,a95),x87001)),f317(f300(a1,a897,a95),x87002))),f317(f317(f92(f904(a1,a893)),x87001),x87002))
% 94.68/94.45 [9367]~P94(x93671)+~E(f317(f94(x93671),x93672),f72(x93671))+P27(x93671,f317(f94(x93671),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x93672))))
% 94.68/94.45 [9620]~P94(x96201)+E(f317(f94(x96201),x96202),f72(x96201))+~P27(x96201,f317(f94(x96201),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f73(a1),x96202))))
% 94.68/94.45 [10377]E(x103771,f2(a1))+E(x103772,f2(a1))+E(f317(f248(a1,a1,a1,a1,f25(a1),f317(f75(a1),f76(a1,x103772))),f317(f317(f317(f86(f903(a1,a1)),f317(f317(a314,f76(a1,x103771)),f76(a1,x103772))),f48(x103771,x103772)),f317(f317(f247(a1,a1,f903(a1,a1)),f317(f317(f18(a1,f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f904(f903(a1,a1),f903(a1,a1))),f904(f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),a1),f18(a1,f903(a1,a1),f903(a1,a1))),f317(f317(f8(f903(a1,a1),f904(a1,f904(f903(a1,a1),f903(a1,a1))),a1),f317(f7(a1,f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),f317(f317(f8(a893,f904(f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),a1),f86(f903(a1,a1))),f317(f317(f7(a1,a1,a893),a314),f2(a1))))),f317(f317(f7(a1,a1,f903(a1,a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f73(a1))),f2(a1))))),f317(f317(f7(a1,f904(a1,a1),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f903(a1,a1)),f904(f904(a1,a1),f904(a1,f903(a1,a1))),a1),f8(a1,f903(a1,a1),a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f904(a1,a1),a1),f23(a1)),f73(a1))),f72(a1))))),f317(f23(a1),f317(f70(a1),x103772))))),f48(x103771,x103772)))),f41(x103771,x103772))
% 94.68/94.45 [10378]E(x103781,f2(a1))+E(x103782,f2(a1))+E(f317(f248(a1,a1,a1,a1,f25(a1),f317(f75(a1),f76(a1,x103782))),f317(f317(f317(f86(f903(a1,a1)),f317(f317(a316,f317(f317(a315,f317(f317(f225(a1),f2(a1)),x103782)),f317(f317(f224(a1),f2(a1)),x103781))),f317(f317(a315,f317(f317(f225(a1),x103782),f2(a1))),f317(f317(f225(a1),x103781),f2(a1))))),f48(x103781,x103782)),f317(f317(f247(a1,a1,f903(a1,a1)),f317(f317(f18(a1,f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f904(f903(a1,a1),f903(a1,a1))),f904(f904(a1,f903(a1,a1)),f904(a1,f903(a1,a1))),a1),f18(a1,f903(a1,a1),f903(a1,a1))),f317(f317(f8(f903(a1,a1),f904(a1,f904(f903(a1,a1),f903(a1,a1))),a1),f317(f7(a1,f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),f317(f317(f8(a893,f904(f903(a1,a1),f904(f903(a1,a1),f903(a1,a1))),a1),f86(f903(a1,a1))),f317(f317(f7(a1,a1,a893),a314),f2(a1))))),f317(f317(f7(a1,a1,f903(a1,a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f73(a1))),f2(a1))))),f317(f317(f7(a1,f904(a1,a1),f904(a1,f903(a1,a1))),f317(f317(f8(f904(a1,f903(a1,a1)),f904(f904(a1,a1),f904(a1,f903(a1,a1))),a1),f8(a1,f903(a1,a1),a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f317(f317(f7(a1,a1,a1),f317(f317(f8(a1,f904(a1,a1),a1),f23(a1)),f73(a1))),f72(a1))))),f317(f23(a1),f317(f70(a1),x103782))))),f48(x103781,x103782)))),f41(x103781,x103782))
% 94.68/94.45 [5780]~P111(x57801)+~P94(x57801)+E(f317(f70(x57801),f317(f317(f234(x57801),f317(f94(x57801),a87)),x57802)),f72(x57801))
% 94.68/94.45 [6296]~P141(x62961)+~P1(f317(f317(f225(a1),x62962),f2(a1)))+E(f317(f73(x62961),f317(f90(x62961),f317(a95,f317(f73(a1),x62962)))),f317(f93(x62961),x62962))
% 94.68/94.45 [6506]P1(f317(f317(f224(a89),x65061),f72(a89)))+E(f317(f317(f74(a89),f72(a89)),f262(x65061,f317(f317(f30(a89),x65062),x65061))),f262(x65061,x65062))+P1(f317(f317(f225(a89),x65062),x65061))
% 94.68/94.45 [6993]~E(x69932,f72(a897))+~P1(f317(f317(f225(a897),f2(a897)),x69931))+P1(f317(f317(f277(a897),f317(f317(f75(a897),x69931),x69932)),x69931))
% 94.68/94.45 [6994]~E(x69941,f72(a897))+~P1(f317(f317(f225(a897),f2(a897)),x69942))+P1(f317(f317(f277(a897),f317(f317(f75(a897),x69941),x69942)),x69942))
% 94.68/94.45 [7127]~P93(x71271)+~P1(f317(f317(f319(x71271),x71272),f100(x71271)))+~E(f317(f317(f74(x71271),f317(f317(f74(x71271),f72(x71271)),x71272)),x71272),f2(x71271))
% 94.68/94.45 [7241]~P1(f317(f317(f224(a1),x72412),f2(a1)))+~P1(f317(f317(f225(a1),x72411),f2(a1)))+E(f317(f241(a1,a1),f317(a46,f42(f317(f73(a1),x72411),f317(f73(a1),x72412)))),f317(f317(f30(a1),x72411),x72412))
% 94.68/94.45 [7258]~P1(f317(f317(f224(a1),x72582),f2(a1)))+~P1(f317(f317(f225(a1),x72581),f2(a1)))+E(f317(f246(a1,a1),f317(a46,f42(f317(f73(a1),x72581),f317(f73(a1),x72582)))),f40(a1,x72581,x72582))
% 94.68/94.45 [7266]~P1(f317(f317(f225(a1),x72662),f2(a1)))+E(f317(f241(a1,a1),f317(a46,f45(f317(f73(a1),x72661),f317(f73(a1),x72662)))),f317(f317(f30(a1),x72661),x72662))+~P1(f317(f317(f225(a1),f2(a1)),x72661))
% 94.68/94.45 [7284]~P1(f317(f317(f225(a1),x72842),f2(a1)))+E(f317(f246(a1,a1),f317(a46,f45(f317(f73(a1),x72841),f317(f73(a1),x72842)))),f40(a1,x72841,x72842))+~P1(f317(f317(f225(a1),f2(a1)),x72841))
% 94.68/94.45 [7335]E(f317(f317(f30(a1),f317(f317(f234(a1),x73351),x73352)),x73351),f317(f317(f234(a1),x73351),f317(f317(f23(a897),x73352),f317(a102,f2(a897)))))+~P1(f317(f317(f225(a897),f2(a897)),x73352))+~P1(f317(f317(f225(a1),f2(a1)),x73351))
% 94.68/94.45 [7439]~P1(f317(f317(f225(a897),f2(a897)),x74391))+~P1(f317(f317(f225(a897),f2(a897)),x74392))+P1(f317(f317(f225(a897),f317(f317(f23(a897),x74391),x74392)),x74391))
% 94.68/94.45 [7440]~P1(f317(f317(f225(a897),f2(a897)),x74401))+~P1(f317(f317(f225(a897),f72(a897)),x74402))+P1(f317(f317(f225(a897),f317(f317(f30(a897),x74401),x74402)),x74401))
% 94.68/94.45 [7441]~P1(f317(f317(f225(a1),f2(a1)),x74411))+~P1(f317(f317(f225(a1),f72(a1)),x74412))+P1(f317(f317(f225(a1),f317(f317(f30(a1),x74411),x74412)),x74411))
% 94.68/94.45 [7578]E(x75781,f2(a897))+~E(x75782,f2(a1))+~P1(f317(f317(f225(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x75782)),x75781)))
% 94.68/94.45 [7619]E(x76191,f72(a897))+~P1(f317(f317(f225(a897),f2(a897)),x76192))+~P1(f317(f317(f277(a897),f317(f317(f75(a897),x76192),x76191)),x76192))
% 94.68/94.45 [7620]E(x76201,f72(a897))+~P1(f317(f317(f225(a897),f2(a897)),x76202))+~P1(f317(f317(f277(a897),f317(f317(f75(a897),x76201),x76202)),x76202))
% 94.68/94.45 [8001]~E(x80012,f103(f898(x80011)))+E(f317(f179(f898(f898(x80011))),f169(x80011,x80012)),f2(a897))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x80011),a897),f179(f898(x80011))),x80012)))
% 94.68/94.45 [8254]P1(f317(x82541,x82542))+~P1(f317(x82541,f317(a97,f485(x82541,x82542))))+~P1(f317(f317(f319(f904(f903(a897,a897),a893)),x82542),a88))
% 94.68/94.45 [8270]E(x82701,f103(f898(x82702)))+E(f317(f179(f898(x82702)),f317(f317(f154(f898(x82702)),x82701),f2(a897))),f317(f179(f898(f898(x82702))),f169(x82702,x82701)))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x82702),a897),f179(f898(x82702))),x82701)))
% 94.68/94.45 [8411]~P37(x84111,x84112)+~P38(x84111,x84112)+P37(x84111,f317(f317(f23(f904(f903(x84111,x84111),a893)),x84112),f297(x84111,f178(f904(f903(x84111,x84111),a893)))))
% 94.68/94.45 [8984]~P1(f317(f28(x89841),f317(f252(x89841),x89842)))+~P1(f317(f28(x89841),f232(f904(x89841,a893))))+P1(f317(f28(x89841),f317(f252(x89841),f317(f317(f8(a893,a893,x89841),a312),x89842))))
% 94.68/94.45 [9048]E(f317(f317(f242(a897,a897),f317(a102,f317(f317(f30(a897),f317(f317(f23(a897),x90481),x90482)),x90482))),f40(a897,f317(f317(f23(a897),x90481),x90482),x90482)),f79(f903(a897,a897),f43(x90481,x90482)))+~P1(f317(f317(f225(a897),f2(a897)),x90482))+~P1(f317(f317(f224(a897),x90482),x90481))
% 94.68/94.45 [9332]~P1(f317(f28(x93321),f317(f252(x93321),x93322)))+P1(f317(f28(x93321),f232(f904(x93321,a893))))+~P1(f317(f28(x93321),f317(f252(x93321),f317(f317(f8(a893,a893,x93321),a312),x93322))))
% 94.68/94.45 [10058]P26(x100581,x100582)+~P36(x100581,f317(f241(f904(f903(x100581,x100581),a893),f904(f903(x100581,x100581),a893)),x100582))+~P1(f317(f317(f224(f904(f903(x100581,x100581),a893)),f317(f317(f279(x100581,x100581,x100581),f317(f241(f904(f903(x100581,x100581),a893),f904(f903(x100581,x100581),a893)),x100582)),f317(f246(f904(f903(x100581,x100581),a893),f904(f903(x100581,x100581),a893)),x100582))),f317(f241(f904(f903(x100581,x100581),a893),f904(f903(x100581,x100581),a893)),x100582)))
% 94.68/94.45 [10155]~E(f287(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x101552,x101551),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x101552),x101551))+P1(f317(f317(f277(a897),x101551),x101552))
% 94.68/94.45 [10156]~E(f290(a897,f277(a897),f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x101562,x101561),f178(f904(a897,a893)))+~P1(f317(f317(f277(a897),x101562),x101561))+P1(f317(f317(f277(a897),x101561),x101562))
% 94.68/94.45 [7365]~P1(f317(f317(f225(a897),f2(a897)),x73652))+P1(f317(f317(f225(a897),x73651),x73652))+E(f317(a102,f317(f317(f30(a897),f317(f317(f23(a897),x73651),x73652)),x73652)),f317(f317(f30(a897),x73651),x73652))
% 94.68/94.45 [7506]~P1(f317(f317(f225(a897),f2(a897)),x75062))+~P1(f317(f317(f224(a897),x75062),x75061))+E(f317(a102,f317(f317(f30(a897),f317(f317(f23(a897),x75061),x75062)),x75062)),f317(f317(f30(a897),x75061),x75062))
% 94.68/94.45 [8475]~P94(x84751)+~P93(x84751)+~P27(x84751,f317(f94(x84751),f317(f317(f23(a1),f317(f317(f74(a1),x84752),x84752)),a87)))
% 94.68/94.45 [9238]E(x92381,f2(a897))+E(f317(f317(f247(a897,a897,f903(a897,a897)),f317(f317(f8(a897,f904(a897,f903(a897,a897)),a897),f242(a897,a897)),a102)),f79(f903(a897,a897),f43(f317(f317(f23(a897),x92382),x92381),x92381))),f79(f903(a897,a897),f43(x92382,x92381)))+P1(f317(f317(f225(a897),x92382),x92381))
% 94.68/94.45 [9422]~P37(x94221,x94222)+~P51(x94221,x94222)+P1(f317(f317(f224(f904(f903(x94221,x94221),a893)),f317(f317(f279(x94221,x94221,x94221),f317(f276(x94221,x94221),x94222)),x94222)),x94222))
% 94.68/94.45 [9684]P1(f317(x96842,f617(x96842,x96841)))+P1(f317(x96841,f617(x96842,x96841)))+E(f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96841)),f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96842)))
% 94.68/94.45 [9688]~P1(f317(x96882,f617(x96882,x96881)))+~P1(f317(x96881,f617(x96882,x96881)))+E(f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96881)),f317(f252(a1),f317(f317(f18(a1,a893,a893),f317(f317(f8(a893,f904(a893,a893),a1),a315),f317(f224(a1),f2(a1)))),x96882)))
% 94.68/94.45 [10238]~P1(f317(f317(f277(a897),x102382),x102381))+P1(f317(f317(f277(a897),x102381),x102382))+P1(f317(f317(f319(a897),x102381),f285(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102382)))
% 94.68/94.45 [10239]~P1(f317(f317(f277(a897),x102392),x102391))+P1(f317(f317(f277(a897),x102391),x102392))+P1(f317(f317(f319(a897),x102392),f288(a897,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x102391)))
% 94.68/94.45 [7717]~P94(x77171)+~P62(x77171)+E(f317(f317(f281(x77171),x77172),f317(f94(x77171),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))),x77172)
% 94.68/94.45 [9366]~P94(x93661)+~E(f317(f94(x93661),x93662),f72(x93661))+P27(x93661,f317(f94(x93661),f317(f317(f74(a1),x93662),f317(f73(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.45 [9554]~P143(x95541)+~E(x95542,f72(x95541))+E(f317(f317(f234(x95541),x95542),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95541))
% 94.68/94.45 [9555]~P143(x95551)+~E(x95552,f2(x95551))+E(f317(f317(f234(x95551),x95552),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f2(x95551))
% 94.68/94.45 [9570]~P143(x95701)+~E(x95702,f317(f73(x95701),f72(x95701)))+E(f317(f317(f234(x95701),x95702),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x95701))
% 94.68/94.45 [9621]~P94(x96211)+E(f317(f94(x96211),x96212),f72(x96211))+~P27(x96211,f317(f94(x96211),f317(f317(f74(a1),x96212),f317(f73(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.45 [10002]~P111(x100022)+E(x100021,f2(x100022))+P1(f317(f317(f225(x100022),f2(x100022)),f317(f317(f234(x100022),x100021),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.45 [10057]~P111(x100572)+~E(x100571,f2(x100572))+~P1(f317(f317(f225(x100572),f2(x100572)),f317(f317(f234(x100572),x100571),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.45 [10093]P1(f317(f317(f224(a1),x100931),f2(a1)))+P1(f317(f317(f225(a1),x100932),x100931))+E(f317(f38(x100931),f42(x100932,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100931))),f42(x100932,x100931))
% 94.68/94.45 [10094]~P1(f317(f317(f225(a1),f2(a1)),x100941))+P1(f317(f317(f225(a1),x100942),x100941))+E(f317(f38(x100941),f42(x100942,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100941))),f42(x100942,x100941))
% 94.68/94.45 [10095]P1(f317(f317(f224(a1),x100951),f2(a1)))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x100952),x100951)))+E(f317(f38(x100951),f45(x100952,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100951))),f45(x100952,x100951))
% 94.68/94.45 [10096]~P1(f317(f317(f225(a1),f2(a1)),x100961))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),x100962),x100961)))+E(f317(f38(x100961),f45(x100962,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100961))),f45(x100962,x100961))
% 94.68/94.45 [10097]~P144(x100971)+~P1(f317(f317(f224(a1),f2(a1)),x100972))+E(f317(f90(x100971),f317(a95,f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x100972))),f317(f317(f74(x100971),f317(f90(x100971),f317(a95,x100972))),f317(f90(x100971),f317(a95,x100972))))
% 94.68/94.45 [5114]~P147(x51141,x51143,x51142)+~E(x51143,f2(a1))+P1(f317(x51141,x51142))
% 94.68/94.45 [5238]~P66(x52381)+~P13(x52381,x52383)+P13(x52381,f160(x52381,x52382,x52383))
% 94.68/94.45 [5239]~P66(x52391)+~P13(x52391,x52393)+P13(x52391,f167(x52391,x52392,x52393))
% 94.68/94.45 [4802]~P75(x48022)+~E(x48023,f317(f73(x48022),x48021))+E(x48021,f317(f73(x48022),x48023))
% 94.68/94.45 [4804]~P75(x48041)+~E(f317(f73(x48041),x48043),x48042)+E(f317(f73(x48041),x48042),x48043)
% 94.68/94.45 [4883]~P96(x48833)+E(x48831,x48832)+~E(f317(f90(x48833),x48831),f317(f90(x48833),x48832))
% 94.68/94.45 [4884]~P75(x48843)+E(x48841,x48842)+~E(f317(f73(x48843),x48841),f317(f73(x48843),x48842))
% 94.68/94.45 [4885]~P97(x48853)+E(x48851,x48852)+~E(f317(f73(x48853),x48851),f317(f73(x48853),x48852))
% 94.68/94.45 [4886]~P93(x48863)+E(x48861,x48862)+~E(f317(f93(x48863),x48861),f317(f93(x48863),x48862))
% 94.68/94.45 [4887]~P66(x48873)+E(x48871,x48872)+~E(f317(f291(x48873),x48871),f317(f291(x48873),x48872))
% 94.68/94.45 [4888]~P66(x48883)+E(x48881,x48882)+~E(f317(f272(x48883),x48881),f317(f272(x48883),x48882))
% 94.68/94.45 [4889]~P66(x48893)+E(x48891,x48892)+~E(f317(f273(x48893),x48891),f317(f273(x48893),x48892))
% 94.68/94.45 [4890]~P66(x48903)+E(x48901,x48902)+~E(f317(f294(x48903),x48901),f317(f294(x48903),x48902))
% 94.68/94.45 [4992]~P60(x49921)+~P1(f317(x49922,x49923))+P1(f317(f51(x49921),x49922))
% 94.68/94.45 [5032]~P60(x50323)+P1(f317(x50321,x50322))+~P1(f317(f52(x50323),x50321))
% 94.68/94.45 [5134]~P148(x51341,x51342,x51343)+~E(x51342,f2(a1))+P1(f317(x51341,f2(a1)))
% 94.68/94.45 [5174]~E(x51741,f2(a897))+E(f533(x51741,x51742,x51743),f178(f904(x51743,a893)))+~E(f317(f29(x51743),x51742),f317(a102,x51741))
% 94.68/94.45 [5322]~E(x53222,f2(a897))+E(f317(f241(a897,a897),x53221),f2(a897))+~P1(f317(f43(x53223,x53222),x53221))
% 94.68/94.45 [5361]P1(f317(x53611,x53612))+~E(x53613,f317(f90(a1),x53612))+~P1(f317(x53611,f317(a95,x53613)))
% 94.68/94.45 [5844]~E(x58443,f2(a897))+~P1(f317(x58441,x58442))+P1(f317(x58441,f40(a897,x58442,x58443)))
% 94.68/94.45 [6089]~P106(x60892)+~P106(x60891)+E(f121(x60891,x60892,f122(x60891,x60893),f122(x60892,x60893)),f122(f903(x60891,x60892),x60893))
% 94.68/94.45 [6276]~E(x62763,f2(a897))+P1(f317(x62761,x62762))+~P1(f317(x62761,f40(a897,x62762,x62763)))
% 94.68/94.45 [6977]E(x69771,f2(a897))+~P1(f317(x69772,f856(x69771,x69773,x69772)))+P1(f317(x69772,f40(a897,x69773,x69771)))
% 94.68/94.45 [7092]~P5(x70921)+~P1(f317(f317(f224(x70921),x70922),f591(x70923,x70922,x70921)))+P1(f317(f317(f224(x70921),x70922),f32(x70921,x70923)))
% 94.68/94.45 [7094]~P1(f317(x70941,x70942))+~P1(f317(x70941,f856(x70943,x70942,x70941)))+P1(f317(x70941,f40(a897,x70942,x70943)))
% 94.68/94.45 [7196]E(x71961,f103(x71962))+E(f317(f317(f141(x71962),f667(x71963,x71961,x71962)),f671(x71963,x71961,x71962)),x71961)+~P1(f317(f317(f319(f898(x71962)),x71961),f151(x71962,x71963)))
% 94.68/94.45 [7228]~P141(x72281)+~P1(f317(f317(f319(x72281),x72282),f100(x72281)))+P1(f317(f317(f319(x72281),f317(f317(f234(x72281),x72282),x72283)),f100(x72281)))
% 94.68/94.45 [7551]P36(x75511,x75512)+~P1(f317(f317(f319(x75511),x75513),f611(x75512,x75511)))+P1(f317(f317(f319(x75511),f616(x75512,x75511,x75513)),f611(x75512,x75511)))
% 94.68/94.45 [7822]E(x78221,f103(x78222))+~P1(f317(f317(f319(f898(x78222)),x78221),f151(x78222,x78223)))+P1(f317(f317(f319(f898(x78222)),f671(x78223,x78221,x78222)),f151(x78222,x78223)))
% 94.68/94.45 [7874]E(x78741,f2(a897))+E(f317(f317(f74(a897),f317(f317(f75(a897),x78741),f857(x78741,x78742,x78743))),f856(x78741,x78742,x78743)),x78742)+P1(f317(x78743,f40(a897,x78742,x78741)))
% 94.68/94.45 [7917]~P1(f317(x79173,x79172))+E(f317(f317(f74(a897),f317(f317(f75(a897),x79171),f857(x79171,x79172,x79173))),f856(x79171,x79172,x79173)),x79172)+P1(f317(x79173,f40(a897,x79172,x79171)))
% 94.68/94.45 [8057]P1(f317(f317(f225(a1),x80571),f860(x80572,x80573,x80571)))+P1(f317(f317(x80573,f317(f317(f30(a1),x80572),x80571)),f40(a1,x80572,x80571)))+~P1(f317(f317(f225(a1),x80571),f2(a1)))
% 94.68/94.45 [8325]P1(f317(f317(x83252,f317(f317(f30(a1),x83251),x83253)),f40(a1,x83251,x83253)))+~P1(f317(f317(f225(a1),x83253),f2(a1)))+P1(f317(f317(f224(a1),f860(x83251,x83252,x83253)),f2(a1)))
% 94.68/94.45 [8509]E(f317(f317(f74(a1),f317(f317(f75(a1),x85091),f862(x85092,x85093,x85091))),f860(x85092,x85093,x85091)),x85092)+P1(f317(f317(x85093,f317(f317(f30(a1),x85092),x85091)),f40(a1,x85092,x85091)))+~P1(f317(f317(f225(a1),x85091),f2(a1)))
% 94.68/94.45 [8747]~P1(f317(f317(x87471,f862(x87472,x87471,x87473)),f860(x87472,x87471,x87473)))+P1(f317(f317(x87471,f317(f317(f30(a1),x87472),x87473)),f40(a1,x87472,x87473)))+~P1(f317(f317(f225(a1),x87473),f2(a1)))
% 94.68/94.45 [8997]~P66(x89971)+~P13(x89971,x89973)+P13(x89971,f139(x89971,x89971,f5(x89971),x89972,x89973))
% 94.68/94.45 [9499]~P125(x94992)+E(x94991,f2(x94992))+~P1(f317(f317(f224(x94992),f317(f317(f74(x94992),f317(f317(f75(x94992),x94993),x94993)),f317(f317(f75(x94992),x94991),x94991))),f2(x94992)))
% 94.68/94.45 [9500]~P125(x95002)+E(x95001,f2(x95002))+~P1(f317(f317(f224(x95002),f317(f317(f74(x95002),f317(f317(f75(x95002),x95001),x95001)),f317(f317(f75(x95002),x95003),x95003))),f2(x95002)))
% 94.68/94.45 [10312]~P111(x103121)+~P1(f317(f317(f225(x103121),x103122),f2(x103121)))+P1(f317(f317(f225(x103121),f317(f317(f234(x103121),x103122),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x103123)))),f2(x103121)))
% 94.68/94.45 [10321]~P111(x103212)+E(x103211,f2(x103212))+~P1(f317(f317(f224(x103212),f317(f317(f74(x103212),f317(f317(f234(x103212),x103213),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103212),x103211),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103212)))
% 94.68/94.45 [10322]~P111(x103222)+E(x103221,f2(x103222))+~P1(f317(f317(f224(x103222),f317(f317(f74(x103222),f317(f317(f234(x103222),x103221),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x103222),x103223),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x103222)))
% 94.68/94.45 [4838]~E(x48382,x48383)+~P69(x48381)+E(f317(f317(f23(x48381),x48382),x48383),f2(x48381))
% 94.68/94.45 [4839]~E(x48392,x48393)+~P75(x48391)+E(f317(f317(f23(x48391),x48392),x48393),f2(x48391))
% 94.68/94.45 [4852]~P146(x48521)+~E(x48523,f2(x48521))+E(f317(f317(f74(x48521),x48522),x48523),x48522)
% 94.68/94.45 [4870]~P142(x48701)+~E(x48703,f2(x48701))+E(f317(f317(f75(x48701),x48702),x48703),f2(x48701))
% 94.68/94.45 [4871]~P142(x48711)+~E(x48712,f2(x48711))+E(f317(f317(f75(x48711),x48712),x48713),f2(x48711))
% 94.68/94.45 [4892]~E(x48923,f103(x48921))+~E(x48922,f103(x48921))+E(f317(f317(f124(x48921),x48922),x48923),f103(x48921))
% 94.68/94.45 [4982]~P146(x49822)+E(x49821,f2(x49822))+~E(f317(f317(f74(x49822),x49823),x49821),x49823)
% 94.68/94.45 [4983]~P75(x49831)+~E(x49832,f317(f73(x49831),x49833))+E(f317(f317(f74(x49831),x49832),x49833),f2(x49831))
% 94.68/94.45 [4990]E(x49901,f103(x49902))+E(x49903,f2(a897))+~E(f317(f317(f165(x49902),x49903),x49901),f103(x49902))
% 94.68/94.45 [5000]~P69(x50003)+E(x50001,x50002)+~E(f317(f317(f23(x50003),x50001),x50002),f2(x50003))
% 94.68/94.45 [5001]~P75(x50013)+E(x50011,x50012)+~E(f317(f317(f23(x50013),x50011),x50012),f2(x50013))
% 94.68/94.45 [5014]~P143(x50142)+E(x50141,f2(x50142))+~E(f317(f317(f234(x50142),x50141),x50143),f2(x50142))
% 94.68/94.45 [5015]~P101(x50152)+E(x50151,f178(x50152))+~E(f317(f317(f91(x50152),x50153),x50151),f178(x50152))
% 94.68/94.45 [5016]~P101(x50162)+E(x50161,f178(x50162))+~E(f317(f317(f91(x50162),x50161),x50163),f178(x50162))
% 94.68/94.45 [5017]~P104(x50172)+E(x50171,f232(x50172))+~E(f317(f317(f92(x50172),x50173),x50171),f232(x50172))
% 94.68/94.45 [5018]~P104(x50182)+E(x50181,f232(x50182))+~E(f317(f317(f92(x50182),x50181),x50183),f232(x50182))
% 94.68/94.45 [5088]~P75(x50882)+E(x50881,f317(f73(x50882),x50883))+~E(f317(f317(f74(x50882),x50881),x50883),f2(x50882))
% 94.68/94.45 [5089]~P75(x50891)+E(f317(f73(x50891),x50892),x50893)+~E(f317(f317(f74(x50891),x50892),x50893),f2(x50891))
% 94.68/94.45 [5091]~E(x50912,x50913)+~P65(x50911)+P1(f317(f317(f224(x50911),x50912),x50913))
% 94.68/94.45 [5093]~E(x50932,x50933)+~P108(x50931)+P1(f317(f317(f224(x50931),x50932),x50933))
% 94.68/94.45 [5191]~P120(x51911)+~E(x51912,f317(f73(x51911),x51913))+E(f317(f317(f75(x51911),x51912),x51912),f317(f317(f75(x51911),x51913),x51913))
% 94.68/94.45 [5199]~P66(x51991)+~P13(x51991,x51993)+P13(x51991,f317(f317(f165(x51991),x51992),x51993))
% 94.68/94.45 [5200]~P66(x52001)+~P13(x52001,x52003)+P13(x52001,f317(f317(f128(x52001),x52002),x52003))
% 94.68/94.45 [5236]E(x52361,x52362)+E(x52363,f2(a897))+~E(f317(f317(f75(a897),x52363),x52361),f317(f317(f75(a897),x52363),x52362))
% 94.68/94.45 [5237]E(x52371,x52372)+E(x52373,f2(a897))+~E(f317(f317(f75(a897),x52371),x52373),f317(f317(f75(a897),x52372),x52373))
% 94.68/94.45 [5315]~E(x53152,x53153)+~P108(x53151)+E(f293(x53151,x53152,x53153),f317(f317(f299(x53151),x53152),f178(f904(x53151,a893))))
% 94.68/94.45 [5350]~P111(x53501)+~E(f317(f70(x53501),x53502),f317(f70(x53501),x53503))+P1(f317(f317(f277(x53501),x53502),x53503))
% 94.68/94.45 [5358]~E(x53581,x53582)+~P66(x53583)+~P1(f317(f317(f225(x53583),x53581),x53582))
% 94.68/94.45 [5359]~E(x53591,x53592)+~P108(x53593)+~P1(f317(f317(f225(x53593),x53591),x53592))
% 94.68/94.45 [5372]~P108(x53721)+E(f317(f292(x53721,x53722),x53723),f178(f904(x53721,a893)))+P1(f317(f317(f225(x53721),x53722),x53723))
% 94.68/94.45 [5421]~P108(x54211)+E(f295(x54211,x54212,x54213),f178(f904(x54211,a893)))+P1(f317(f317(f225(x54211),x54212),x54213))
% 94.68/94.45 [5422]~P108(x54221)+E(f293(x54221,x54222,x54223),f178(f904(x54221,a893)))+P1(f317(f317(f224(x54221),x54222),x54223))
% 94.68/94.45 [5423]~P108(x54231)+E(f178(f904(x54231,a893)),f295(x54231,x54232,x54233))+P1(f317(f317(f225(x54231),x54232),x54233))
% 94.68/94.45 [5424]~P108(x54241)+E(f178(f904(x54241,a893)),f293(x54241,x54242,x54243))+P1(f317(f317(f224(x54241),x54242),x54243))
% 94.68/94.45 [5432]~P66(x54321)+~E(f317(f317(f228(x54321),x54322),x54323),x54322)+P1(f317(f317(f224(x54321),x54322),x54323))
% 94.68/94.45 [5433]~P66(x54331)+~E(f317(f317(f223(x54331),x54332),x54333),x54333)+P1(f317(f317(f224(x54331),x54332),x54333))
% 94.68/94.45 [5434]~P99(x54341)+~E(f317(f317(f91(x54341),x54342),x54343),x54343)+P1(f317(f317(f224(x54341),x54342),x54343))
% 94.68/94.45 [5435]~P105(x54351)+~E(f317(f317(f92(x54351),x54352),x54353),x54352)+P1(f317(f317(f224(x54351),x54352),x54353))
% 94.68/94.45 [5454]~P66(x54541)+P13(x54541,x54542)+~P13(x54541,f317(f317(f141(x54541),x54543),x54542))
% 94.68/94.45 [5455]~P66(x54551)+P13(x54551,x54552)+~P13(x54551,f317(f317(f124(x54551),x54553),x54552))
% 94.68/94.45 [5456]~P66(x54561)+P13(x54561,x54562)+~P13(x54561,f317(f317(f124(x54561),x54562),x54563))
% 94.68/94.45 [5461]~P3(x54611)+~E(f40(x54611,x54613,x54612),f2(x54611))+P1(f317(f317(f277(x54611),x54612),x54613))
% 94.68/94.45 [5523]~P66(x55231)+P1(f317(f317(f224(x55231),x55233),x55232))+P1(f317(f317(f224(x55231),x55232),x55233))
% 94.68/94.45 [5528]~P66(x55281)+P1(f317(f317(f225(x55281),x55283),x55282))+P1(f317(f317(f224(x55281),x55282),x55283))
% 94.68/94.45 [5565]~P66(x55651)+E(f317(f317(f228(x55651),x55652),x55653),x55653)+~P1(f317(f317(f224(x55651),x55653),x55652))
% 94.68/94.45 [5567]~P66(x55671)+E(f317(f317(f228(x55671),x55672),x55673),x55672)+~P1(f317(f317(f224(x55671),x55672),x55673))
% 94.68/94.45 [5568]~P66(x55681)+E(f317(f317(f223(x55681),x55682),x55683),x55682)+~P1(f317(f317(f224(x55681),x55683),x55682))
% 94.68/94.45 [5570]~P66(x55701)+E(f317(f317(f223(x55701),x55702),x55703),x55703)+~P1(f317(f317(f224(x55701),x55702),x55703))
% 94.68/94.45 [5571]~P99(x55711)+E(f317(f317(f91(x55711),x55712),x55713),x55712)+~P1(f317(f317(f224(x55711),x55713),x55712))
% 94.68/94.45 [5573]~P99(x55731)+E(f317(f317(f91(x55731),x55732),x55733),x55733)+~P1(f317(f317(f224(x55731),x55732),x55733))
% 94.68/94.45 [5574]~P105(x55741)+E(f317(f317(f92(x55741),x55742),x55743),x55743)+~P1(f317(f317(f224(x55741),x55743),x55742))
% 94.68/94.45 [5576]~P105(x55761)+E(f317(f317(f92(x55761),x55762),x55763),x55762)+~P1(f317(f317(f224(x55761),x55762),x55763))
% 94.68/94.45 [5583]~P122(x55832)+E(x55831,f2(x55832))+E(f317(f317(f281(x55832),f317(f73(x55832),x55833)),f317(f73(x55832),x55831)),f317(f317(f281(x55832),x55833),x55831))
% 94.68/94.45 [5590]~P3(x55901)+E(f40(x55901,x55902,x55903),f2(x55901))+~P1(f317(f317(f277(x55901),x55903),x55902))
% 94.68/94.45 [5636]~P108(x56361)+E(f317(f292(x56361,x56362),x56363),f178(f904(x56361,a893)))+~P1(f317(f317(f224(x56361),x56363),x56362))
% 94.68/94.45 [5669]~P108(x56691)+E(f296(x56691,x56692,x56693),f178(f904(x56691,a893)))+~P1(f317(f317(f224(x56691),x56693),x56692))
% 94.68/94.45 [5670]~P108(x56701)+E(f295(x56701,x56702,x56703),f178(f904(x56701,a893)))+~P1(f317(f317(f224(x56701),x56703),x56702))
% 94.68/94.45 [5671]~P108(x56711)+E(f293(x56711,x56712,x56713),f178(f904(x56711,a893)))+~P1(f317(f317(f225(x56711),x56713),x56712))
% 94.68/94.45 [5723]~E(f317(f317(f23(a897),x57231),x57233),x57232)+E(x57231,f317(f317(f74(a897),x57232),x57233))+~P1(f317(f317(f224(a897),x57233),x57231))
% 94.68/94.45 [5724]~E(x57241,f317(f317(f74(a897),x57243),x57242))+E(f317(f317(f23(a897),x57241),x57242),x57243)+~P1(f317(f317(f224(a897),x57242),x57241))
% 94.68/94.45 [5769]~P1(f317(x57691,x57693))+P1(f317(x57691,f350(x57691,x57692)))+~P1(f317(f317(f224(a897),x57693),x57692))
% 94.68/94.45 [5770]~P1(f317(x57701,x57703))+P1(f317(x57701,f381(x57701,x57702)))+~P1(f317(f317(f225(a897),x57703),x57702))
% 94.68/94.45 [5778]~P108(x57781)+~E(f317(f292(x57781,x57782),x57783),f178(f904(x57781,a893)))+~P1(f317(f317(f225(x57781),x57782),x57783))
% 94.68/94.45 [5783]~P65(x57831)+~P1(f317(f317(f225(x57831),x57832),x57833))+P1(f317(f317(f224(x57831),x57832),x57833))
% 94.68/94.45 [5785]~P108(x57851)+~P1(f317(f317(f225(x57851),x57852),x57853))+P1(f317(f317(f224(x57851),x57852),x57853))
% 94.68/94.45 [5903]~P108(x59031)+~E(f295(x59031,x59032,x59033),f178(f904(x59031,a893)))+~P1(f317(f317(f225(x59031),x59032),x59033))
% 94.68/94.45 [5904]~P108(x59041)+~E(f293(x59041,x59042,x59043),f178(f904(x59041,a893)))+~P1(f317(f317(f224(x59041),x59042),x59043))
% 94.68/94.45 [5905]~P108(x59051)+~E(f178(f904(x59051,a893)),f295(x59051,x59052,x59053))+~P1(f317(f317(f225(x59051),x59052),x59053))
% 94.68/94.45 [5906]~P108(x59061)+~E(f178(f904(x59061,a893)),f293(x59061,x59062,x59063))+~P1(f317(f317(f224(x59061),x59062),x59063))
% 94.68/94.45 [5916]P1(f317(x59161,x59162))+~P1(f317(x59161,f352(x59161,x59163)))+~P1(f317(f317(f224(a897),x59162),x59163))
% 94.68/94.45 [5917]P1(f317(x59171,x59172))+~P1(f317(x59171,f393(x59171,x59173)))+~P1(f317(f317(f225(a897),x59172),x59173))
% 94.68/94.45 [5925]~E(x59251,f317(a102,x59253))+P1(f317(f317(f225(a897),x59251),f317(a102,x59252)))+~P1(f317(f317(f225(a897),x59253),x59252))
% 94.68/94.45 [5944]E(x59441,x59442)+~E(f317(f317(f75(a897),x59443),x59441),f317(f317(f75(a897),x59443),x59442))+~P1(f317(f317(f225(a897),f2(a897)),x59443))
% 94.68/94.45 [6005]E(f317(x60051,f398(x60051,x60052,x60053)),f72(a897))+~E(f317(f317(f6(x60053,a897),x60051),x60052),f72(a897))+~P1(f317(f28(x60053),x60052))
% 94.68/94.45 [6022]~P5(x60221)+P1(f317(f317(f224(x60221),x60222),f31(x60221,x60223)))+~P1(f317(f317(f319(x60221),x60222),x60223))
% 94.68/94.45 [6045]~P65(x60451)+~P1(f317(f317(f225(x60451),x60453),x60452))+~P1(f317(f317(f224(x60451),x60452),x60453))
% 94.68/94.45 [6049]~P65(x60491)+~P1(f317(f317(f225(x60491),x60493),x60492))+~P1(f317(f317(f225(x60491),x60492),x60493))
% 94.68/94.45 [6052]~P66(x60521)+~P1(f317(f317(f225(x60521),x60523),x60522))+~P1(f317(f317(f224(x60521),x60522),x60523))
% 94.68/94.45 [6053]~P66(x60531)+~P1(f317(f317(f225(x60531),x60533),x60532))+~P1(f317(f317(f225(x60531),x60532),x60533))
% 94.68/94.45 [6054]~P108(x60541)+~P1(f317(f317(f225(x60541),x60543),x60542))+~P1(f317(f317(f225(x60541),x60542),x60543))
% 94.68/94.45 [6074]~E(x60742,x60743)+~E(x60741,x60742)+E(f280(a897,f277(a897),x60741,x60742),f317(f317(f299(a897),x60743),f178(f904(a897,a893))))
% 94.68/94.45 [6081]~E(f317(x60812,f865(x60812,x60813,x60811)),f72(a897))+E(f317(f317(f9(x60811,a897),x60812),x60813),f72(a897))+~P1(f317(f28(x60811),x60813))
% 94.68/94.45 [6082]~E(f317(x60822,f399(x60822,x60823,x60821)),f2(a897))+E(f317(f317(f6(x60821,a897),x60822),x60823),f2(a897))+~P1(f317(f28(x60821),x60823))
% 94.68/94.45 [6098]~P109(x60981)+~P1(f317(f317(f224(x60981),x60983),x60982))+P1(f317(f317(f319(x60981),x60982),f317(f273(x60981),x60983)))
% 94.68/94.45 [6099]~P109(x60991)+~P1(f317(f317(f225(x60991),x60993),x60992))+P1(f317(f317(f319(x60991),x60992),f317(f294(x60991),x60993)))
% 94.68/94.45 [6100]~P109(x61001)+~P1(f317(f317(f224(x61001),x61002),x61003))+P1(f317(f317(f319(x61001),x61002),f317(f291(x61001),x61003)))
% 94.68/94.45 [6101]~P109(x61011)+~P1(f317(f317(f225(x61011),x61012),x61013))+P1(f317(f317(f319(x61011),x61012),f317(f272(x61011),x61013)))
% 94.68/94.45 [6102]~P114(x61021)+~P1(f317(f317(f277(x61021),x61022),x61023))+P1(f317(f317(f277(x61021),x61022),f317(f73(x61021),x61023)))
% 94.68/94.45 [6103]~P111(x61031)+~P1(f317(f317(f277(x61031),x61032),x61033))+P1(f317(f317(f277(x61031),x61032),f317(f70(x61031),x61033)))
% 94.68/94.45 [6115]E(f317(x61151,f409(x61151,x61152,x61153)),f317(a102,f2(a897)))+~E(f317(f317(f6(x61153,a897),x61151),x61152),f317(a102,f2(a897)))+~P1(f317(f28(x61153),x61152))
% 94.68/94.45 [6198]~P5(x61981)+~P1(f317(f317(f319(x61981),x61983),x61982))+P1(f317(f317(f224(x61981),f32(x61981,x61982)),x61983))
% 94.68/94.45 [6219]~P1(f317(f317(f224(a897),x62191),x62193))+P1(f317(f317(f224(a897),x62191),x62192))+~P1(f317(f317(f224(a897),x62193),x62192))
% 94.68/94.45 [6220]~P1(f317(f317(f224(a1),x62201),x62203))+P1(f317(f317(f224(a1),x62201),x62202))+~P1(f317(f317(f224(a1),x62203),x62202))
% 94.68/94.45 [6221]~P1(f317(f317(f277(a897),x62211),x62213))+P1(f317(f317(f277(a897),x62211),x62212))+~P1(f317(f317(f277(a897),x62213),x62212))
% 94.68/94.45 [6241]~P109(x62411)+~P1(f317(f317(f319(x62411),x62413),f317(f273(x62411),x62412)))+P1(f317(f317(f224(x62411),x62412),x62413))
% 94.68/94.45 [6242]~P109(x62421)+~P1(f317(f317(f319(x62421),x62422),f317(f291(x62421),x62423)))+P1(f317(f317(f224(x62421),x62422),x62423))
% 94.68/94.45 [6243]~P109(x62431)+~P1(f317(f317(f319(x62431),x62433),f317(f294(x62431),x62432)))+P1(f317(f317(f225(x62431),x62432),x62433))
% 94.68/94.45 [6244]~P109(x62441)+~P1(f317(f317(f319(x62441),x62442),f317(f272(x62441),x62443)))+P1(f317(f317(f225(x62441),x62442),x62443))
% 94.68/94.45 [6245]~P111(x62451)+~P1(f317(f317(f277(x62451),x62452),f317(f70(x62451),x62453)))+P1(f317(f317(f277(x62451),x62452),x62453))
% 94.68/94.45 [6246]~P114(x62461)+~P1(f317(f317(f277(x62461),x62462),f317(f73(x62461),x62463)))+P1(f317(f317(f277(x62461),x62462),x62463))
% 94.68/94.45 [6321]~P1(f317(x63211,x63212))+P1(f317(x63211,f767(x63211)))+~P1(f317(f317(f319(x63213),x63212),f232(f904(x63213,a893))))
% 94.68/94.45 [6469]~P63(x64691)+P1(f317(f317(f225(x64691),f2(x64691)),f422(x64693,x64692,x64691)))+P1(f317(f317(f224(x64691),x64692),x64693))
% 94.68/94.45 [6470]~P64(x64701)+P1(f317(f317(f225(x64701),f2(x64701)),f748(x64703,x64702,x64701)))+P1(f317(f317(f224(x64701),x64702),x64703))
% 94.68/94.45 [6539]~P67(x65391)+~P1(f317(f317(f224(x65391),x65393),f317(f73(x65391),x65392)))+P1(f317(f317(f224(x65391),x65392),f317(f73(x65391),x65393)))
% 94.68/94.45 [6541]~P67(x65411)+~P1(f317(f317(f225(x65411),x65413),f317(f73(x65411),x65412)))+P1(f317(f317(f225(x65411),x65412),f317(f73(x65411),x65413)))
% 94.68/94.45 [6553]~P1(f317(f317(f225(a897),x65531),x65533))+~P1(f317(f317(f225(a897),x65533),x65532))+P1(f317(f317(f225(a897),f317(a102,x65531)),x65532))
% 94.68/94.45 [6584]~P110(x65841)+P1(f317(f317(f224(x65841),f317(f90(x65841),x65842)),f317(f90(x65841),x65843)))+~P1(f317(f317(f224(a897),x65842),x65843))
% 94.68/94.45 [6585]~P111(x65851)+P1(f317(f317(f224(x65851),f317(f93(x65851),x65852)),f317(f93(x65851),x65853)))+~P1(f317(f317(f224(a1),x65852),x65853))
% 94.68/94.45 [6587]~P111(x65871)+P1(f317(f317(f225(x65871),f317(f93(x65871),x65872)),f317(f93(x65871),x65873)))+~P1(f317(f317(f225(a1),x65872),x65873))
% 94.68/94.45 [6588]~P110(x65881)+P1(f317(f317(f225(x65881),f317(f90(x65881),x65882)),f317(f90(x65881),x65883)))+~P1(f317(f317(f225(a897),x65882),x65883))
% 94.68/94.45 [6594]~P66(x65941)+E(f317(f317(f91(f904(x65941,a893)),f317(f272(x65941),x65942)),f317(f292(x65941,x65942),x65943)),f317(f272(x65941),x65943))+~P1(f317(f317(f224(x65941),x65942),x65943))
% 94.68/94.45 [6624]~P67(x66241)+~P1(f317(f317(f224(x66241),x66243),x66242))+P1(f317(f317(f224(x66241),f317(f73(x66241),x66242)),f317(f73(x66241),x66243)))
% 94.68/94.45 [6626]~P97(x66261)+~P1(f317(f317(f224(x66261),x66263),x66262))+P1(f317(f317(f224(x66261),f317(f73(x66261),x66262)),f317(f73(x66261),x66263)))
% 94.68/94.45 [6627]~P67(x66271)+~P1(f317(f317(f225(x66271),x66273),x66272))+P1(f317(f317(f225(x66271),f317(f73(x66271),x66272)),f317(f73(x66271),x66273)))
% 94.68/94.45 [6663]~P66(x66631)+E(f317(f317(f91(f904(x66631,a893)),f317(f291(x66631),x66632)),f296(x66631,x66632,x66633)),f317(f272(x66631),x66633))+~P1(f317(f317(f225(x66631),x66632),x66633))
% 94.68/94.45 [6664]~P66(x66641)+E(f317(f317(f91(f904(x66641,a893)),f317(f291(x66641),x66642)),f295(x66641,x66642,x66643)),f317(f291(x66641),x66643))+~P1(f317(f317(f224(x66641),x66642),x66643))
% 94.68/94.45 [6665]~P66(x66651)+E(f317(f317(f91(f904(x66651,a893)),f317(f272(x66651),x66652)),f293(x66651,x66652,x66653)),f317(f291(x66651),x66653))+~P1(f317(f317(f224(x66651),x66652),x66653))
% 94.68/94.45 [6699]~P66(x66991)+E(f317(f317(f91(f904(x66991,a893)),f317(f292(x66991,x66992),x66993)),f317(f273(x66991),x66993)),f317(f273(x66991),x66992))+~P1(f317(f317(f224(x66991),x66992),x66993))
% 94.68/94.45 [6860]~P66(x68601)+E(f317(f317(f91(f904(x68601,a893)),f296(x68601,x68602,x68603)),f317(f273(x68601),x68603)),f317(f294(x68601),x68602))+~P1(f317(f317(f225(x68601),x68602),x68603))
% 94.68/94.45 [6861]~P66(x68611)+E(f317(f317(f91(f904(x68611,a893)),f295(x68611,x68612,x68613)),f317(f294(x68611),x68613)),f317(f294(x68611),x68612))+~P1(f317(f317(f224(x68611),x68612),x68613))
% 94.68/94.45 [6862]~P66(x68621)+E(f317(f317(f91(f904(x68621,a893)),f293(x68621,x68622,x68623)),f317(f294(x68621),x68623)),f317(f273(x68621),x68622))+~P1(f317(f317(f224(x68621),x68622),x68623))
% 94.68/94.45 [6881]P1(f317(x68811,x68812))+~P1(f317(f317(f224(a897),x68812),x68813))+P1(f317(f317(f319(a897),f352(x68811,x68813)),f293(a897,f2(a897),x68813)))
% 94.68/94.45 [6915]E(x69151,x69152)+~E(f317(f317(f154(x69153),x69151),f614(x69153,x69152,x69151)),f317(f317(f154(x69153),x69152),f614(x69153,x69152,x69151)))+~E(f317(f179(f898(x69153)),x69151),f317(f179(f898(x69153)),x69152))
% 94.68/94.45 [6920]~E(x69203,f317(f317(f30(a897),x69201),x69202))+~P1(f317(f317(f225(a897),f2(a897)),x69202))+P1(f317(f317(f225(a897),x69201),f317(f317(f75(a897),x69202),f317(a102,x69203))))
% 94.68/94.45 [6936]~P1(f317(x69361,x69363))+~P1(f317(f317(f224(a897),x69363),x69362))+P1(f317(f317(f319(a897),f350(x69361,x69362)),f293(a897,f2(a897),x69362)))
% 94.68/94.45 [6975]~P1(f317(x69751,x69753))+P1(f317(x69751,f353(x69751,x69752)))+~P1(f317(f317(f319(a897),x69753),f293(a897,f2(a897),x69752)))
% 94.68/94.45 [6996]~P110(x69963)+~P1(f317(f317(f224(x69963),f317(f90(x69963),x69961)),f317(f90(x69963),x69962)))+P1(f317(f317(f224(a897),x69961),x69962))
% 94.68/94.45 [6997]~P111(x69973)+~P1(f317(f317(f224(x69973),f317(f93(x69973),x69971)),f317(f93(x69973),x69972)))+P1(f317(f317(f224(a1),x69971),x69972))
% 94.68/94.45 [6999]~P110(x69993)+~P1(f317(f317(f225(x69993),f317(f90(x69993),x69991)),f317(f90(x69993),x69992)))+P1(f317(f317(f225(a897),x69991),x69992))
% 94.68/94.45 [7000]~P111(x70003)+~P1(f317(f317(f225(x70003),f317(f93(x70003),x70001)),f317(f93(x70003),x70002)))+P1(f317(f317(f225(a1),x70001),x70002))
% 94.68/94.45 [7018]~P110(x70181)+~P1(f317(f317(f225(x70181),f72(x70181)),x70182))+P1(f317(f317(f225(x70181),f72(x70181)),f317(f317(f234(x70181),x70182),f317(a102,x70183))))
% 94.68/94.45 [7021]~P67(x70211)+~P1(f317(f317(f224(x70211),f317(f73(x70211),x70213)),f317(f73(x70211),x70212)))+P1(f317(f317(f224(x70211),x70212),x70213))
% 94.68/94.45 [7022]~P97(x70221)+~P1(f317(f317(f224(x70221),f317(f73(x70221),x70223)),f317(f73(x70221),x70222)))+P1(f317(f317(f224(x70221),x70222),x70223))
% 94.68/94.45 [7023]~P67(x70231)+~P1(f317(f317(f225(x70231),f317(f73(x70231),x70233)),f317(f73(x70231),x70232)))+P1(f317(f317(f225(x70231),x70232),x70233))
% 94.68/94.45 [7047]P1(f317(x70471,x70472))+~P1(f317(x70471,f354(x70471,x70473)))+~P1(f317(f317(f319(a897),x70472),f293(a897,f2(a897),x70473)))
% 94.68/94.45 [7069]~P63(x70691)+P1(f317(f317(f225(x70691),f422(x70693,x70692,x70691)),f72(x70691)))+P1(f317(f317(f224(x70691),x70692),x70693))
% 94.68/94.45 [7089]~E(f40(a897,x70893,x70892),f40(a897,x70891,x70892))+E(f317(f317(f74(a897),x70891),f317(f317(f75(a897),x70892),f529(x70891,x70892,x70893))),x70893)+~P1(f317(f317(f224(a897),x70891),x70893))
% 94.68/94.45 [7144]E(f317(f317(f9(x71441,a897),x71442),x71443),f72(a897))+~P1(f317(f28(x71441),x71443))+P1(f317(f317(f319(x71441),f865(x71442,x71443,x71441)),x71443))
% 94.68/94.45 [7145]E(f317(f317(f6(x71451,a897),x71452),x71453),f2(a897))+~P1(f317(f28(x71451),x71453))+P1(f317(f317(f319(x71451),f399(x71452,x71453,x71451)),x71453))
% 94.68/94.45 [7167]~P108(x71671)+~P1(f317(f317(f224(x71671),x71672),x71673))+P1(f317(f317(f224(f904(x71671,a893)),f317(f291(x71671),x71672)),f317(f291(x71671),x71673)))
% 94.68/94.45 [7168]~P66(x71681)+~P1(f317(f317(f224(x71681),x71682),x71683))+P1(f317(f317(f224(f904(x71681,a893)),f317(f272(x71681),x71682)),f317(f272(x71681),x71683)))
% 94.68/94.45 [7169]~P108(x71691)+~P1(f317(f317(f224(x71691),x71693),x71692))+P1(f317(f317(f224(f904(x71691,a893)),f317(f273(x71691),x71692)),f317(f273(x71691),x71693)))
% 94.68/94.45 [7170]~P66(x71701)+~P1(f317(f317(f224(x71701),x71703),x71702))+P1(f317(f317(f224(f904(x71701,a893)),f317(f294(x71701),x71702)),f317(f294(x71701),x71703)))
% 94.68/94.45 [7171]~P66(x71711)+~P1(f317(f317(f225(x71711),x71712),x71713))+P1(f317(f317(f225(f904(x71711,a893)),f317(f272(x71711),x71712)),f317(f272(x71711),x71713)))
% 94.68/94.45 [7182]~P5(x71821)+P1(f317(f317(f224(x71821),x71822),f32(x71821,x71823)))+P1(f317(f317(f319(x71821),f591(x71823,x71822,x71821)),x71823))
% 94.68/94.45 [7188]~P67(x71881)+P1(f317(f317(f224(x71881),f317(f317(f23(x71881),x71882),x71883)),f2(x71881)))+~P1(f317(f317(f224(x71881),x71882),x71883))
% 94.68/94.45 [7189]~P67(x71891)+P1(f317(f317(f225(x71891),f317(f317(f23(x71891),x71892),x71893)),f2(x71891)))+~P1(f317(f317(f225(x71891),x71892),x71893))
% 94.68/94.45 [7231]P1(f317(x72311,x72312))+P1(f317(f317(f224(a897),f354(x72311,x72313)),x72313))+~P1(f317(f317(f319(a897),x72312),f293(a897,f2(a897),x72313)))
% 94.68/94.45 [7273]~E(f317(f317(f6(x72731,a897),x72732),x72733),f72(a897))+~P1(f317(f28(x72731),x72733))+P1(f317(f317(f319(x72731),f398(x72732,x72733,x72731)),x72733))
% 94.68/94.45 [7274]~P1(f317(x72741,x72743))+P1(f317(f317(f224(a897),f353(x72741,x72742)),x72742))+~P1(f317(f317(f319(a897),x72743),f293(a897,f2(a897),x72742)))
% 94.68/94.45 [7312]~P5(x73121)+P1(f317(f317(f319(x73121),f593(x73123,x73122,x73121)),x73122))+P1(f317(f317(f224(x73121),f31(x73121,x73122)),x73123))
% 94.68/94.45 [7346]~E(f317(f317(f6(x73461,a897),x73462),x73463),f317(a102,f2(a897)))+~P1(f317(f28(x73461),x73463))+P1(f317(f317(f319(x73461),f409(x73462,x73463,x73461)),x73463))
% 94.68/94.45 [7357]E(x73571,f2(a897))+P1(f317(x73572,f40(a897,x73573,x73571)))+P1(f317(f317(f225(a897),f856(x73571,x73573,x73572)),x73571))
% 94.68/94.45 [7469]~P1(f317(x74691,x74692))+P1(f317(x74691,f40(a897,x74692,x74693)))+P1(f317(f317(f225(a897),f856(x74693,x74692,x74691)),x74693))
% 94.68/94.45 [7582]E(x75821,f103(x75822))+~P1(f317(f317(f319(f898(x75822)),x75821),f151(x75822,x75823)))+P1(f317(f317(f319(x75822),f667(x75823,x75821,x75822)),x75823))
% 94.68/94.45 [7605]~P66(x76051)+E(f317(f317(f91(f904(x76051,a893)),f317(f317(f299(x76051),x76052),f178(f904(x76051,a893)))),f296(x76051,x76052,x76053)),f317(f292(x76051,x76052),x76053))+~P1(f317(f317(f225(x76051),x76052),x76053))
% 94.68/94.45 [7628]~P66(x76281)+E(f317(f317(f91(f904(x76281,a893)),f317(f317(f299(x76281),x76282),f178(f904(x76281,a893)))),f295(x76281,x76282,x76283)),f293(x76281,x76282,x76283))+~P1(f317(f317(f224(x76281),x76282),x76283))
% 94.68/94.45 [7739]~P66(x77391)+P1(f317(f317(f224(x77391),x77392),x77393))+~P1(f317(f317(f224(f904(x77391,a893)),f317(f294(x77391),x77393)),f317(f294(x77391),x77392)))
% 94.68/94.45 [7740]~P108(x77401)+P1(f317(f317(f224(x77401),x77402),x77403))+~P1(f317(f317(f224(f904(x77401,a893)),f317(f273(x77401),x77403)),f317(f273(x77401),x77402)))
% 94.68/94.45 [7741]~P66(x77411)+P1(f317(f317(f224(x77411),x77412),x77413))+~P1(f317(f317(f224(f904(x77411,a893)),f317(f272(x77411),x77412)),f317(f272(x77411),x77413)))
% 94.68/94.45 [7742]~P108(x77421)+P1(f317(f317(f224(x77421),x77422),x77423))+~P1(f317(f317(f224(f904(x77421,a893)),f317(f291(x77421),x77422)),f317(f291(x77421),x77423)))
% 94.68/94.45 [7743]~P66(x77431)+P1(f317(f317(f225(x77431),x77432),x77433))+~P1(f317(f317(f225(f904(x77431,a893)),f317(f272(x77431),x77432)),f317(f272(x77431),x77433)))
% 94.68/94.45 [7766]~P67(x77661)+~P1(f317(f317(f224(x77661),f317(f317(f23(x77661),x77662),x77663)),f2(x77661)))+P1(f317(f317(f224(x77661),x77662),x77663))
% 94.68/94.45 [7767]~P67(x77671)+~P1(f317(f317(f225(x77671),f317(f317(f23(x77671),x77672),x77673)),f2(x77671)))+P1(f317(f317(f225(x77671),x77672),x77673))
% 94.68/94.45 [7924]E(x79241,f2(a897))+~E(f317(f132(a897,a897,f74(a897),x79242),x79243),f2(a897))+~P1(f317(f317(f319(a897),x79241),f317(f162(a897),x79243)))
% 94.68/94.45 [7928]~P5(x79281)+~P1(f317(f317(f224(x79281),f593(x79283,x79282,x79281)),x79283))+P1(f317(f317(f224(x79281),f31(x79281,x79282)),x79283))
% 94.68/94.45 [8082]P1(f317(f317(f224(a1),f2(a1)),f861(x80821,x80822,x80823)))+P1(f317(f317(x80822,f317(f317(f30(a1),x80821),x80823)),f40(a1,x80821,x80823)))+~P1(f317(f317(f225(a1),f2(a1)),x80823))
% 94.68/94.45 [8170]E(x81701,x81702)+~E(f317(f179(f898(x81703)),x81701),f317(f179(f898(x81703)),x81702))+~P1(f317(f317(f247(x81703,x81703,a893),a314),f641(x81703,x81701,x81702)))
% 94.68/94.45 [8241]~P36(x82412,x82413)+E(x82411,f178(f904(x82412,a893)))+~P1(f317(f317(f224(f904(x82412,a893)),x82411),f317(f275(x82412,x82412,x82413),x82411)))
% 94.68/94.45 [8272]~P64(x82721)+~P1(f317(f317(f224(x82721),x82722),f317(f317(f74(x82721),x82723),f748(x82723,x82722,x82721))))+P1(f317(f317(f224(x82721),x82722),x82723))
% 94.68/94.45 [8307]P52(x83071,x83072,x83073)+P1(f317(f317(f319(x83071),f510(x83073,x83072,x83071)),x83072))+P1(f317(f317(f319(f903(x83071,x83071)),f511(x83073,x83072,x83071)),x83073))
% 94.68/94.45 [8328]P1(f317(f317(x83282,f317(f317(f30(a1),x83281),x83283)),f40(a1,x83281,x83283)))+~P1(f317(f317(f225(a1),f2(a1)),x83283))+P1(f317(f317(f225(a1),f861(x83281,x83282,x83283)),x83283))
% 94.68/94.45 [8353]E(f317(f300(a897,a897,f317(f317(f7(a897,a897,a897),f23(a897)),x83531)),f317(f292(a897,x83532),x83533)),f178(f904(a897,a893)))+P1(f317(f317(f225(a897),x83531),x83533))+P1(f317(f317(f225(a897),x83532),x83533))
% 94.68/94.45 [8464]E(f317(f300(a897,a897,f317(f317(f7(a897,a897,a897),f23(a897)),x84641)),f317(f292(a897,x84642),x84643)),f317(f317(f299(a897),f2(a897)),f178(f904(a897,a893))))+P1(f317(f317(f225(a897),x84641),x84643))+~P1(f317(f317(f225(a897),x84642),x84643))
% 94.68/94.45 [8478]~P66(x84781)+E(f139(x84781,x84781,f5(x84781),x84782,x84783),x84783)+~P1(f317(f317(f319(x84781),x84782),f317(f162(x84781),x84783)))
% 94.68/94.45 [8491]P24(x84911,x84911,x84912,x84913)+~P1(f317(f28(x84911),x84913))+~P1(f317(f317(f224(f904(x84911,a893)),x84913),f317(f300(x84911,x84911,x84912),x84913)))
% 94.68/94.45 [8517]E(f317(f317(f74(a1),f317(f317(f75(a1),x85171),f859(x85172,x85173,x85171))),f861(x85172,x85173,x85171)),x85172)+P1(f317(f317(x85173,f317(f317(f30(a1),x85172),x85171)),f40(a1,x85172,x85171)))+~P1(f317(f317(f225(a1),f2(a1)),x85171))
% 94.68/94.45 [8754]~P1(f317(f317(x87541,f859(x87542,x87541,x87543)),f861(x87542,x87541,x87543)))+P1(f317(f317(x87541,f317(f317(f30(a1),x87542),x87543)),f40(a1,x87542,x87543)))+~P1(f317(f317(f225(a1),f2(a1)),x87543))
% 94.68/94.45 [9652]~P1(f317(f28(x96521),x96522))+~P1(f317(f317(f319(x96521),x96523),x96522))+P1(f317(f317(f225(a897),f317(f29(x96521),f317(f317(f23(f904(x96521,a893)),x96522),f317(f317(f299(x96521),x96523),f178(f904(x96521,a893)))))),f317(f29(x96521),x96522)))
% 94.68/94.45 [10252]P52(x102521,x102522,x102523)+~P1(f317(f317(f247(x102521,x102521,a893),f317(f317(f7(x102521,f904(x102521,a893),f904(x102521,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x102521,a893),f904(x102521,a893)),x102521),f8(a893,a893,x102521)),f317(f317(f8(a893,f904(a893,a893),x102521),a315),f317(f317(f7(x102521,f904(x102521,a893),a893),f319(x102521)),x102522)))),f317(f317(f7(x102521,f904(x102521,a893),a893),f319(x102521)),x102522))),f511(x102523,x102522,x102521)))+P1(f317(f317(f319(x102521),f510(x102523,x102522,x102521)),x102522))
% 94.68/94.45 [5545]~P122(x55452)+E(x55451,f2(x55452))+E(f317(f317(f281(x55452),x55453),f317(f73(x55452),x55451)),f317(f73(x55452),f317(f317(f281(x55452),x55453),x55451)))
% 94.68/94.45 [5685]~E(x56853,f178(f904(x56851,a893)))+~E(x56852,f178(f904(x56851,a893)))+E(f317(f317(f91(f904(x56851,a893)),x56852),x56853),f178(f904(x56851,a893)))
% 94.68/94.45 [5743]~E(x57433,f2(a897))+~P1(f317(x57431,f2(a897)))+P1(f317(x57431,f317(f317(f30(a897),x57432),x57433)))
% 94.68/94.45 [5895]~P64(x58952)+E(x58951,f2(x58952))+E(f317(f317(f281(x58952),f317(f70(x58952),x58953)),f317(f70(x58952),x58951)),f317(f70(x58952),f317(f317(f281(x58952),x58953),x58951)))
% 94.68/94.45 [5994]~P112(x59941)+~E(x59942,f72(x59941))+P1(f317(f317(f277(x59941),x59942),f317(f317(f234(x59941),x59942),x59943)))
% 94.68/94.45 [6015]~P3(x60151)+E(f317(f317(f75(x60151),x60152),f317(f317(f30(x60151),x60153),x60152)),x60153)+~P1(f317(f317(f277(x60151),x60152),x60153))
% 94.68/94.45 [6070]~P1(f317(f28(x60701),x60703))+E(f317(f29(x60701),f317(f317(f299(x60701),x60702),x60703)),f317(a102,f317(f29(x60701),x60703)))+P1(f317(f317(f319(x60701),x60702),x60703))
% 94.68/94.45 [6147]~E(x61472,f2(a897))+P1(f317(x61471,f2(a897)))+~P1(f317(x61471,f317(f317(f30(a897),x61473),x61472)))
% 94.68/94.45 [6164]~P1(f317(f28(x61641),x61643))+E(f317(f29(x61641),f317(f317(f299(x61641),x61642),x61643)),f317(f29(x61641),x61643))+~P1(f317(f317(f319(x61641),x61642),x61643))
% 94.68/94.45 [6200]~P1(f317(f28(x62001),x62003))+E(f317(f29(x62001),f317(f317(f299(x62001),x62002),x62003)),f317(f317(f74(a897),f72(a897)),f317(f29(x62001),x62003)))+P1(f317(f317(f319(x62001),x62002),x62003))
% 94.68/94.45 [6207]~P4(x62071)+E(f317(f317(f30(x62071),x62072),f317(f73(x62071),x62073)),f317(f73(x62071),f317(f317(f30(x62071),x62072),x62073)))+~P1(f317(f317(f277(x62071),x62073),x62072))
% 94.68/94.45 [6322]E(f317(f317(f74(a897),x63221),f567(x63221,x63222,x63223)),x63222)+~P1(f317(x63223,f2(a897)))+P1(f317(x63223,f317(f317(f23(a897),x63222),x63221)))
% 94.68/94.45 [6323]E(f317(f317(f74(a897),x63231),f578(x63231,x63232,x63233)),x63232)+~P1(f317(x63233,f2(a897)))+P1(f317(x63233,f317(f317(f23(a897),x63232),x63231)))
% 94.68/94.45 [6348]~P4(x63481)+E(f317(f317(f30(x63481),f317(f73(x63481),x63482)),x63483),f317(f73(x63481),f317(f317(f30(x63481),x63482),x63483)))+~P1(f317(f317(f277(x63481),x63483),x63482))
% 94.68/94.45 [6372]~P5(x63721)+~P1(f317(f28(x63721),x63723))+E(f317(f317(f58(x63721,x63721,f91(x63721)),x63722),x63723),f317(f317(f91(x63721),x63722),f31(x63721,x63723)))
% 94.68/94.45 [6373]~P5(x63731)+~P1(f317(f28(x63731),x63733))+E(f317(f317(f58(x63731,x63731,f92(x63731)),x63732),x63733),f317(f317(f92(x63731),x63732),f32(x63731,x63733)))
% 94.68/94.45 [6379]~P94(x63791)+~E(f317(f94(x63791),x63792),f317(f94(x63791),x63793))+P27(x63791,f317(f94(x63791),f317(f317(f74(a1),x63792),f317(f73(a1),x63793))))
% 94.68/94.45 [6389]~P141(x63891)+E(f317(f317(f23(x63891),f317(f90(x63891),x63892)),f317(f90(x63891),x63893)),f317(f90(x63891),f317(f317(f23(a897),x63892),x63893)))+~P1(f317(f317(f224(a897),x63893),x63892))
% 94.68/94.45 [6396]~P114(x63961)+~P1(f317(f317(f277(x63961),x63962),x63963))+P1(f317(f317(f277(x63961),f317(f73(x63961),x63962)),x63963))
% 94.68/94.45 [6397]~P111(x63971)+~P1(f317(f317(f277(x63971),x63972),x63973))+P1(f317(f317(f277(x63971),f317(f70(x63971),x63972)),x63973))
% 94.68/94.45 [6480]E(f317(f317(f74(a897),x64801),f567(x64801,x64802,x64803)),x64802)+P1(f317(f317(f225(a897),x64802),x64801))+P1(f317(x64803,f317(f317(f23(a897),x64802),x64801)))
% 94.68/94.45 [6481]E(f317(f317(f74(a897),x64811),f578(x64811,x64812,x64813)),x64812)+P1(f317(f317(f225(a897),x64812),x64811))+P1(f317(x64813,f317(f317(f23(a897),x64812),x64811)))
% 94.68/94.45 [6497]~P111(x64971)+E(f317(f317(f75(x64971),f317(f70(x64971),x64972)),x64973),f317(f70(x64971),f317(f317(f75(x64971),x64972),x64973)))+~P1(f317(f317(f224(x64971),f2(x64971)),x64973))
% 94.68/94.45 [6498]~P63(x64981)+E(f317(f317(f281(x64981),f317(f70(x64981),x64982)),x64983),f317(f70(x64981),f317(f317(f281(x64981),x64982),x64983)))+~P1(f317(f317(f225(x64981),f2(x64981)),x64983))
% 94.68/94.45 [6507]~P66(x65071)+~P1(f317(f28(x65071),x65073))+E(f317(f317(f58(x65071,x65071,f228(x65071)),x65072),x65073),f14(x65071,f317(f317(f299(x65071),x65072),x65073)))
% 94.68/94.45 [6508]~P66(x65081)+~P1(f317(f28(x65081),x65083))+E(f317(f317(f58(x65081,x65081,f223(x65081)),x65082),x65083),f15(x65081,f317(f317(f299(x65081),x65082),x65083)))
% 94.68/94.45 [6509]~P100(x65091)+~P1(f317(f28(x65091),x65093))+E(f317(f317(f58(x65091,x65091,f91(x65091)),x65092),x65093),f13(x65091,f317(f317(f299(x65091),x65092),x65093)))
% 94.68/94.45 [6510]~P100(x65101)+~P1(f317(f28(x65101),x65103))+E(f317(f317(f58(x65101,x65101,f92(x65101)),x65102),x65103),f10(x65101,f317(f317(f299(x65101),x65102),x65103)))
% 94.68/94.45 [6555]E(x65551,f103(x65552))+~E(f169(x65552,x65553),f103(f898(x65552)))+~P1(f317(f317(f319(f898(x65552)),x65551),f317(f162(f898(x65552)),x65553)))
% 94.68/94.45 [6574]~P112(x65741)+~P1(f317(f317(f225(a897),f2(a897)),x65743))+P1(f317(f317(f277(x65741),x65742),f317(f317(f234(x65741),x65742),x65743)))
% 94.68/94.45 [6602]~P1(f317(f127(x66021),x66023))+P1(f317(f317(f319(x66021),x66022),f317(f162(x66021),x66023)))+P1(f317(f127(x66021),f317(f317(f141(x66021),x66022),x66023)))
% 94.68/94.45 [6613]~P98(x66131)+~P1(f317(f28(x66131),x66133))+E(f317(f57(x66131,f75(x66131)),f317(f317(f299(x66131),x66132),x66133)),f317(f317(f58(x66131,x66131,f75(x66131)),x66132),x66133))
% 94.68/94.45 [6635]~P66(x66351)+~P1(f317(f28(x66351),x66353))+E(f11(x66351,f228(x66351),f317(f317(f299(x66351),x66352),x66353)),f317(f317(f58(x66351,x66351,f228(x66351)),x66352),x66353))
% 94.68/94.45 [6636]~P66(x66361)+~P1(f317(f28(x66361),x66363))+E(f12(x66361,f223(x66361),f317(f317(f299(x66361),x66362),x66363)),f317(f317(f58(x66361,x66361,f223(x66361)),x66362),x66363))
% 94.68/94.45 [6638]P1(f317(x66381,f2(a897)))+~P1(f317(f317(f225(a897),x66382),x66383))+~P1(f317(x66381,f317(f317(f23(a897),x66382),x66383)))
% 94.68/94.45 [6659]~P86(x66591)+P1(f317(f317(f224(x66591),x66592),x66593))+~P1(f317(f317(f224(x66591),f317(f70(x66591),x66592)),x66593))
% 94.68/94.45 [6660]~P111(x66601)+P1(f317(f317(f225(x66601),x66602),x66603))+~P1(f317(f317(f225(x66601),f317(f70(x66601),x66602)),x66603))
% 94.68/94.45 [6661]~P111(x66611)+P1(f317(f317(f277(x66611),x66612),x66613))+~P1(f317(f317(f277(x66611),f317(f70(x66611),x66612)),x66613))
% 94.68/94.45 [6662]~P114(x66621)+P1(f317(f317(f277(x66621),x66622),x66623))+~P1(f317(f317(f277(x66621),f317(f73(x66621),x66622)),x66623))
% 94.68/94.45 [6679]E(x66791,f103(x66792))+E(f317(f131(x66792),f317(f317(f128(x66792),x66793),x66791)),f317(f317(f154(x66792),x66791),x66793))+~P1(f317(f317(f225(a897),x66793),f317(f179(f898(x66792)),x66791)))
% 94.68/94.45 [6734]~P1(f317(x67341,x67343))+P1(f317(x67341,f394(x67341,x67342)))+~P1(f317(f317(f319(a897),x67343),f317(f292(a897,f2(a897)),x67342)))
% 94.68/94.45 [6754]P1(f317(x67541,x67542))+~P1(f317(f317(f225(a897),x67542),x67543))+P1(f317(f317(f319(a897),f393(x67541,x67543)),f317(f292(a897,f2(a897)),x67543)))
% 94.68/94.45 [6769]~P110(x67691)+~P1(f317(f317(f224(x67691),f72(x67691)),x67692))+P1(f317(f317(f224(x67691),f72(x67691)),f317(f317(f234(x67691),x67692),x67693)))
% 94.68/94.45 [6771]~P110(x67711)+~P1(f317(f317(f224(x67711),f2(x67711)),x67712))+P1(f317(f317(f224(x67711),f2(x67711)),f317(f317(f234(x67711),x67712),x67713)))
% 94.68/94.45 [6773]~P110(x67731)+~P1(f317(f317(f225(x67731),f2(x67731)),x67732))+P1(f317(f317(f225(x67731),f2(x67731)),f317(f317(f234(x67731),x67732),x67733)))
% 94.68/94.45 [6798]~P1(f317(x67981,x67983))+~P1(f317(f317(f225(a897),x67983),x67982))+P1(f317(f317(f319(a897),f381(x67981,x67982)),f317(f292(a897,f2(a897)),x67982)))
% 94.68/94.45 [6806]P1(f317(f28(x68061),x68062))+~P1(f317(f28(x68061),x68063))+~P1(f317(f317(f224(f904(x68061,a893)),x68062),x68063))
% 94.68/94.45 [6813]~P1(f317(f317(f277(a897),x68131),x68132))+~P1(f317(f317(f277(a897),x68131),x68133))+P1(f317(f317(f277(a897),x68131),f317(f317(f23(a897),x68132),x68133)))
% 94.68/94.45 [6814]P1(f317(x68141,x68142))+~P1(f317(x68141,f395(x68141,x68143)))+~P1(f317(f317(f319(a897),x68142),f317(f292(a897,f2(a897)),x68143)))
% 94.68/94.45 [6827]E(x68271,f2(a897))+P1(f317(x68272,f866(x68271,x68273,x68272)))+~P1(f317(x68272,f317(f317(f30(a897),x68273),x68271)))
% 94.68/94.45 [6835]~P125(x68352)+E(x68351,f2(x68352))+~E(f317(f317(f74(x68352),f317(f317(f75(x68352),x68353),x68353)),f317(f317(f75(x68352),x68351),x68351)),f2(x68352))
% 94.68/94.45 [6836]~P125(x68362)+E(x68361,f2(x68362))+~E(f317(f317(f74(x68362),f317(f317(f75(x68362),x68361),x68361)),f317(f317(f75(x68362),x68363),x68363)),f2(x68362))
% 94.68/94.45 [6882]E(x68821,f2(a897))+~P1(f317(x68822,f867(x68821,x68823,x68822)))+P1(f317(x68822,f317(f317(f30(a897),x68823),x68821)))
% 94.68/94.45 [6887]~P66(x68871)+~P13(x68871,x68873)+P13(x68871,f317(f317(f138(x68871,x68871,f5(x68871)),x68872),x68873))
% 94.68/94.45 [6929]P1(f317(x69291,f866(x69292,x69293,x69291)))+P1(f317(x69291,f2(a897)))+~P1(f317(x69291,f317(f317(f30(a897),x69293),x69292)))
% 94.68/94.45 [6935]~P94(x69351)+E(f317(f94(x69351),x69352),f317(f94(x69351),x69353))+~P27(x69351,f317(f94(x69351),f317(f317(f74(a1),x69352),f317(f73(a1),x69353))))
% 94.68/94.45 [7003]E(x70031,f2(a1))+E(x70032,f2(a1))+~P1(f317(f44(x70032,x70032),f317(f317(f242(a1,a1),x70033),x70031)))
% 94.68/94.45 [7004]E(x70041,f72(a1))+E(x70042,f2(a1))+~P1(f317(f44(x70042,x70042),f317(f317(f242(a1,a1),x70041),x70043)))
% 94.68/94.45 [7020]P1(f317(x70201,x70202))+P1(f317(f317(f225(a897),f395(x70201,x70203)),x70203))+~P1(f317(f317(f319(a897),x70202),f317(f292(a897,f2(a897)),x70203)))
% 94.68/94.45 [7043]~P1(f317(x70431,f567(x70433,x70432,x70431)))+~P1(f317(x70431,f2(a897)))+P1(f317(x70431,f317(f317(f23(a897),x70432),x70433)))
% 94.68/94.45 [7044]~P1(f317(x70441,f578(x70443,x70442,x70441)))+~P1(f317(x70441,f2(a897)))+P1(f317(x70441,f317(f317(f23(a897),x70442),x70443)))
% 94.68/94.45 [7045]~P1(f317(x70451,f867(x70453,x70452,x70451)))+~P1(f317(x70451,f2(a897)))+P1(f317(x70451,f317(f317(f30(a897),x70452),x70453)))
% 94.68/94.45 [7065]~P1(f317(x70651,x70653))+P1(f317(f317(f225(a897),f394(x70651,x70652)),x70652))+~P1(f317(f317(f319(a897),x70653),f317(f292(a897,f2(a897)),x70652)))
% 94.68/94.45 [7066]E(f317(f317(f23(a897),f317(f317(f23(a897),x70661),x70662)),f317(f317(f23(a897),x70663),x70662)),f317(f317(f23(a897),x70661),x70663))+~P1(f317(f317(f224(a897),x70662),x70661))+~P1(f317(f317(f224(a897),x70662),x70663))
% 94.68/94.45 [7102]~P67(x71021)+~P1(f317(f317(f224(x71021),f317(f73(x71021),x71023)),x71022))+P1(f317(f317(f224(x71021),f317(f73(x71021),x71022)),x71023))
% 94.68/94.45 [7104]~P86(x71041)+~P1(f317(f317(f224(x71041),f317(f70(x71041),x71042)),x71043))+P1(f317(f317(f224(x71041),f317(f73(x71041),x71042)),x71043))
% 94.68/94.45 [7106]~P67(x71061)+~P1(f317(f317(f225(x71061),f317(f73(x71061),x71063)),x71062))+P1(f317(f317(f225(x71061),f317(f73(x71061),x71062)),x71063))
% 94.68/94.45 [7107]~P111(x71071)+~P1(f317(f317(f225(x71071),f317(f70(x71071),x71072)),x71073))+P1(f317(f317(f225(x71071),f317(f73(x71071),x71072)),x71073))
% 94.68/94.45 [7139]~P1(f317(x71393,f567(x71392,x71391,x71393)))+P1(f317(f317(f225(a897),x71391),x71392))+P1(f317(x71393,f317(f317(f23(a897),x71391),x71392)))
% 94.68/94.45 [7140]~P1(f317(x71403,f578(x71402,x71401,x71403)))+P1(f317(f317(f225(a897),x71401),x71402))+P1(f317(x71403,f317(f317(f23(a897),x71401),x71402)))
% 94.68/94.45 [7192]~E(f598(x71923,x71922,x71921),f599(x71923,x71922,x71921))+E(f317(f317(f92(f904(x71921,a893)),x71922),f31(f904(x71921,a893),x71923)),f178(f904(x71921,a893)))+P1(f317(f317(f319(f904(x71921,a893)),x71922),x71923))
% 94.68/94.45 [7200]~P1(f317(f28(x72001),x72003))+P1(f317(f28(x72001),f32(f904(x72001,a893),x72002)))+~P1(f317(f317(f319(f904(x72001,a893)),x72003),x72002))
% 94.68/94.45 [7260]~P66(x72601)+E(f317(f317(f91(f904(x72601,a893)),f317(f292(x72601,x72602),x72603)),f317(f317(f299(x72601),x72603),f178(f904(x72601,a893)))),f293(x72601,x72602,x72603))+~P1(f317(f317(f224(x72601),x72602),x72603))
% 94.68/94.45 [7263]E(x72631,f2(a897))+P1(f317(f317(f225(a897),f868(x72631,x72633,x72632)),x72631))+P1(f317(x72632,f317(f317(f30(a897),x72633),x72631)))
% 94.68/94.45 [7292]P1(f317(f317(f225(a897),f317(f179(f898(x72921)),x72922)),f762(x72923,x72921)))+~P1(f317(f28(f898(x72921)),x72923))+~P1(f317(f317(f319(f898(x72921)),x72922),x72923))
% 94.68/94.45 [7298]E(x72981,x72982)+~P1(f317(f317(f224(f904(x72983,a893)),x72981),x72982))+P1(f317(f317(f225(f904(x72983,a893)),x72981),x72982))
% 94.68/94.45 [7309]E(x73091,x73092)+~E(f317(f179(f898(x73093)),x73091),f317(f179(f898(x73093)),x73092))+P1(f317(f317(f225(a897),f614(x73093,x73091,x73092)),f317(f179(f898(x73093)),x73092)))
% 94.68/94.45 [7358]P8(x73581,x73582,x73583)+~E(f317(f254(x73581,x73581),x73583),x73582)+~E(f317(f317(f279(x73581,x73581,x73581),f317(f276(x73581,x73581),x73583)),x73583),x73583)
% 94.68/94.45 [7438]~P1(f317(x74381,f2(a897)))+P1(f317(f317(f225(a897),f868(x74383,x74382,x74381)),x74383))+P1(f317(x74381,f317(f317(f30(a897),x74382),x74383)))
% 94.68/94.45 [7448]~P66(x74481)+E(f317(f317(f91(f904(x74481,a893)),f296(x74481,x74482,x74483)),f317(f317(f299(x74481),x74483),f178(f904(x74481,a893)))),f295(x74481,x74482,x74483))+~P1(f317(f317(f225(x74481),x74482),x74483))
% 94.68/94.45 [7540]~P1(f317(f28(x75401),x75403))+P1(f317(f317(f224(a897),f317(f29(x75401),x75402)),f317(f29(x75401),x75403)))+~P1(f317(f317(f224(f904(x75401,a893)),x75402),x75403))
% 94.68/94.45 [7541]~P1(f317(f28(x75411),x75413))+P1(f317(f317(f225(a897),f317(f29(x75411),x75412)),f317(f29(x75411),x75413)))+~P1(f317(f317(f225(f904(x75411,a893)),x75412),x75413))
% 94.68/94.45 [7674]E(x76741,x76742)+~P1(f317(f317(f224(f904(x76743,a893)),x76742),x76741))+~P1(f317(f317(f224(f904(x76743,a893)),x76741),x76742))
% 94.68/94.45 [7677]~P66(x76771)+P13(x76771,x76772)+~P13(x76771,f317(f317(f138(x76771,x76771,f5(x76771)),x76773),x76772))
% 94.68/94.45 [7748]~P1(f317(f317(f225(a897),x77483),x77482))+~P1(f317(f317(f225(a897),x77483),x77481))+P1(f317(f317(f225(a897),f317(f317(f23(a897),x77481),x77482)),f317(f317(f23(a897),x77481),x77483)))
% 94.68/94.45 [7749]~P1(f317(f317(f224(a897),x77492),x77491))+~P1(f317(f317(f225(a897),x77491),x77493))+P1(f317(f317(f225(a897),f317(f317(f23(a897),x77491),x77492)),f317(f317(f23(a897),x77493),x77492)))
% 94.68/94.45 [7764]~P1(f317(f317(f225(a1),x77642),f2(a1)))+~P1(f317(f317(f224(a1),x77643),x77641))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x77641),x77642)),f317(f317(f30(a1),x77643),x77642)))
% 94.68/94.45 [7781]~P1(f317(f317(f225(a897),f2(a897)),x77813))+~P1(f317(f317(f224(a897),x77813),x77812))+P1(f317(f317(f224(a897),f317(f317(f30(a897),x77811),x77812)),f317(f317(f30(a897),x77811),x77813)))
% 94.68/94.45 [7782]~P1(f317(f317(f225(a1),f2(a1)),x77822))+~P1(f317(f317(f224(a1),x77821),x77823))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x77821),x77822)),f317(f317(f30(a1),x77823),x77822)))
% 94.68/94.45 [7786]~P1(f317(f317(f225(a897),f2(a897)),x77862))+~P1(f317(f317(f225(a897),x77861),x77863))+P1(f317(f317(f225(a897),f317(f317(f75(a897),x77861),x77862)),f317(f317(f75(a897),x77863),x77862)))
% 94.68/94.45 [7787]~P1(f317(f317(f225(a897),f2(a897)),x77871))+~P1(f317(f317(f225(a897),x77872),x77873))+P1(f317(f317(f225(a897),f317(f317(f75(a897),x77871),x77872)),f317(f317(f75(a897),x77871),x77873)))
% 94.68/94.45 [7788]~P1(f317(f317(f225(a1),f2(a1)),x77881))+~P1(f317(f317(f225(a1),x77882),x77883))+P1(f317(f317(f225(a1),f317(f317(f75(a1),x77881),x77882)),f317(f317(f75(a1),x77881),x77883)))
% 94.68/94.45 [7837]E(x78371,f2(a897))+E(f317(f317(f74(a897),f317(f317(f75(a897),x78371),f867(x78371,x78372,x78373))),f868(x78371,x78372,x78373)),x78372)+P1(f317(x78373,f317(f317(f30(a897),x78372),x78371)))
% 94.68/94.45 [7897]E(f317(f317(f74(a897),f317(f317(f75(a897),x78971),f867(x78971,x78972,x78973))),f868(x78971,x78972,x78973)),x78972)+~P1(f317(x78973,f2(a897)))+P1(f317(x78973,f317(f317(f30(a897),x78972),x78971)))
% 94.68/94.45 [7915]~P1(f317(f28(x79151),x79153))+P1(f317(f317(f319(x79151),f874(x79152,x79153,x79151)),x79153))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f9(x79151,a897),x79152),x79153)))
% 94.68/94.45 [7916]~P1(f317(f28(x79161),x79163))+P1(f317(f317(f319(x79161),f479(x79162,x79163,x79161)),x79163))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f9(x79161,a897),x79162),x79163)))
% 94.68/94.45 [8016]E(x80161,f2(a897))+P1(f317(f317(f277(a897),x80162),x80163))+~P1(f317(f317(f277(a897),f317(f317(f75(a897),x80161),x80162)),f317(f317(f75(a897),x80161),x80163)))
% 94.68/94.45 [8206]E(x82061,f178(f904(x82062,a893)))+E(x82061,f317(f317(f299(x82062),x82063),f178(f904(x82062,a893))))+~P1(f317(f317(f224(f904(x82062,a893)),x82061),f317(f317(f299(x82062),x82063),f178(f904(x82062,a893)))))
% 94.68/94.45 [8242]~P1(f317(f317(f225(a897),f72(a897)),x82423))+P1(f317(f317(f224(a897),x82421),x82422))+~P1(f317(f317(f277(a897),f317(f317(f234(a897),x82423),x82421)),f317(f317(f234(a897),x82423),x82422)))
% 94.68/94.45 [8244]~P1(f317(f317(f225(a897),f2(a897)),x82443))+P1(f317(f317(f224(a897),x82441),x82442))+~P1(f317(f317(f224(a897),f317(f317(f75(a897),x82443),x82441)),f317(f317(f75(a897),x82443),x82442)))
% 94.68/94.45 [8245]~P1(f317(f317(f225(a897),f2(a897)),x82453))+P1(f317(f317(f224(a897),x82451),x82452))+~P1(f317(f317(f224(a897),f317(f317(f75(a897),x82451),x82453)),f317(f317(f75(a897),x82452),x82453)))
% 94.68/94.45 [8247]~P1(f317(f317(f225(a897),f2(a897)),x82473))+P1(f317(f317(f225(a897),x82471),x82472))+~P1(f317(f317(f225(a897),f317(f317(f234(a897),x82473),x82471)),f317(f317(f234(a897),x82473),x82472)))
% 94.68/94.45 [8249]~P1(f317(f317(f225(a897),f2(a897)),x82493))+P1(f317(f317(f277(a897),x82491),x82492))+~P1(f317(f317(f277(a897),f317(f317(f75(a897),x82493),x82491)),f317(f317(f75(a897),x82493),x82492)))
% 94.68/94.45 [8288]~E(f317(f317(f92(f904(x82881,a893)),f599(x82883,x82882,x82881)),f598(x82883,x82882,x82881)),f178(f904(x82881,a893)))+E(f317(f317(f92(f904(x82881,a893)),x82882),f31(f904(x82881,a893),x82883)),f178(f904(x82881,a893)))+P1(f317(f317(f319(f904(x82881,a893)),x82882),x82883))
% 94.68/94.45 [8302]E(x83021,f103(x83022))+~E(f317(f132(f898(x83022),f898(x83022),f124(x83022),f103(x83022)),x83023),f103(x83022))+~P1(f317(f317(f319(f898(x83022)),x83021),f317(f162(f898(x83022)),x83023)))
% 94.68/94.45 [8358]E(x83581,f178(f904(f904(x83582,a893),a893)))+P1(f317(f317(f319(f904(x83582,a893)),f602(x83583,x83581,x83582)),x83581))+P1(f317(f317(f224(f904(x83582,a893)),f32(f904(x83582,a893),x83581)),x83583))
% 94.68/94.45 [8364]~P76(x83641)+~P77(x83641)+E(f317(f317(f9(a1,x83641),f317(f317(f8(a897,x83641,a1),x83642),a95)),f317(f300(a897,a1,f90(a1)),x83643)),f317(f317(f9(a897,x83641),x83642),x83643))
% 94.68/94.45 [8365]~P76(x83651)+~P77(x83651)+E(f317(f317(f6(a1,x83651),f317(f317(f8(a897,x83651,a1),x83652),a95)),f317(f300(a897,a1,f90(a1)),x83653)),f317(f317(f6(a897,x83651),x83652),x83653))
% 94.68/94.45 [8407]~P1(f317(f28(x84071),x84073))+~P1(f317(f317(f225(a897),f2(a897)),f317(x84072,f874(x84072,x84073,x84071))))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f9(x84071,a897),x84072),x84073)))
% 94.68/94.45 [8408]~P1(f317(f28(x84081),x84083))+~P1(f317(f317(f225(a897),f2(a897)),f317(x84082,f479(x84082,x84083,x84081))))+P1(f317(f317(f225(a897),f2(a897)),f317(f317(f9(x84081,a897),x84082),x84083)))
% 94.68/94.45 [8444]~P62(x84442)+E(x84441,f72(x84442))+E(f317(f317(f281(x84442),f317(f317(f23(x84442),f317(f317(f234(x84442),x84441),x84443)),f72(x84442))),f317(f317(f23(x84442),x84441),f72(x84442))),f317(f317(f6(a897,x84442),f317(f234(x84442),x84441)),f317(f292(a897,f2(a897)),x84443)))
% 94.68/94.45 [8502]E(x85021,f2(a897))+~P1(f317(x85023,f317(f317(f30(a897),x85022),x85021)))+P1(f317(f317(f225(a897),x85022),f317(f317(f75(a897),x85021),f317(a102,f866(x85021,x85022,x85023)))))
% 94.68/94.45 [8521]P1(f317(x85211,f2(a897)))+~P1(f317(x85211,f317(f317(f30(a897),x85212),x85213)))+P1(f317(f317(f225(a897),x85212),f317(f317(f75(a897),x85213),f317(a102,f866(x85213,x85212,x85211)))))
% 94.68/94.45 [8559]E(x85591,f2(a897))+~P1(f317(x85593,f317(f317(f30(a897),x85592),x85591)))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x85591),f866(x85591,x85592,x85593))),x85592))
% 94.68/94.45 [8590]P1(f317(x85901,f2(a897)))+~P1(f317(x85901,f317(f317(f30(a897),x85903),x85902)))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x85902),f866(x85902,x85903,x85901))),x85903))
% 94.68/94.45 [8598]~P66(x85981)+E(f317(f317(f138(x85981,x85981,f5(x85981)),x85982),x85983),f139(x85981,x85981,f5(x85981),x85982,x85983))+P1(f317(f317(f319(x85981),x85982),f317(f162(x85981),x85983)))
% 94.68/94.45 [8633]~E(f317(x86333,f519(x86332,x86333,x86331)),f317(x86333,f522(x86332,x86333,x86331)))+~P59(x86331,f317(x86333,f520(x86332,x86333,x86331)))+P59(x86331,f317(f317(f34(x86332,f904(x86331,f904(x86331,a893))),f232(f904(x86332,a893))),x86333))
% 94.68/94.45 [8642]E(x86421,f178(f904(f904(x86422,a893),a893)))+~P1(f317(f317(f224(f904(x86422,a893)),f602(x86423,x86421,x86422)),x86423))+P1(f317(f317(f224(f904(x86422,a893)),f32(f904(x86422,a893),x86421)),x86423))
% 94.68/94.45 [8702]~P64(x87021)+~P1(f317(f317(f225(x87021),x87022),x87023))+P1(f317(f317(f225(x87021),x87022),f317(f317(f281(x87021),f317(f317(f74(x87021),x87022),x87023)),f317(f317(f74(x87021),f72(x87021)),f72(x87021)))))
% 94.68/94.45 [8760]~P1(f317(f317(x87601,f877(x87601,x87603,x87602)),f883(x87601,x87603,x87602)))+P1(f317(f317(x87601,x87602),x87603))+~P1(f317(f305(f903(a1,a1),a47),f317(f317(f242(a1,a1),x87602),x87603)))
% 94.68/94.45 [8761]~P1(f317(f317(x87611,f885(x87611,x87613,x87612)),f886(x87611,x87613,x87612)))+P1(f317(f317(x87611,x87612),x87613))+~P1(f317(f305(f903(a1,a1),a53),f317(f317(f242(a1,a1),x87612),x87613)))
% 94.68/94.45 [8762]~P1(f317(f317(x87621,f887(x87621,x87623,x87622)),f888(x87621,x87623,x87622)))+P1(f317(f317(x87621,x87622),x87623))+~P1(f317(f305(f903(a1,a1),a211),f317(f317(f242(a1,a1),x87622),x87623)))
% 94.68/94.45 [8763]~P1(f317(f317(x87631,f427(x87631,x87633,x87632)),f429(x87631,x87633,x87632)))+P1(f317(f317(x87631,x87632),x87633))+~P1(f317(f305(f903(a897,a897),a209),f317(f317(f242(a897,a897),x87632),x87633)))
% 94.68/94.45 [8764]~P1(f317(f317(x87641,f653(x87641,x87643,x87642)),f655(x87641,x87643,x87642)))+P1(f317(f317(x87641,x87642),x87643))+~P1(f317(f305(f903(a1,a1),a172),f317(f317(f242(a1,a1),x87642),x87643)))
% 94.68/94.45 [8765]~P1(f317(f317(x87651,f751(x87651,x87653,x87652)),f752(x87651,x87653,x87652)))+P1(f317(f317(x87651,x87652),x87653))+~P1(f317(f305(f903(a1,a1),a123),f317(f317(f242(a1,a1),x87652),x87653)))
% 94.68/94.45 [9038]P1(f317(f317(x90381,x90382),x90383))+P1(f317(f305(f903(a897,a897),a209),f317(f317(f242(a897,a897),f427(x90381,x90383,x90382)),f429(x90381,x90383,x90382))))+~P1(f317(f305(f903(a897,a897),a209),f317(f317(f242(a897,a897),x90382),x90383)))
% 94.68/94.45 [9039]P1(f317(f317(x90391,x90392),x90393))+P1(f317(f305(f903(a1,a1),a47),f317(f317(f242(a1,a1),f877(x90391,x90393,x90392)),f883(x90391,x90393,x90392))))+~P1(f317(f305(f903(a1,a1),a47),f317(f317(f242(a1,a1),x90392),x90393)))
% 94.68/94.45 [9040]P1(f317(f317(x90401,x90402),x90403))+P1(f317(f305(f903(a1,a1),a53),f317(f317(f242(a1,a1),f885(x90401,x90403,x90402)),f886(x90401,x90403,x90402))))+~P1(f317(f305(f903(a1,a1),a53),f317(f317(f242(a1,a1),x90402),x90403)))
% 94.68/94.45 [9041]P1(f317(f317(x90411,x90412),x90413))+P1(f317(f305(f903(a1,a1),a211),f317(f317(f242(a1,a1),f887(x90411,x90413,x90412)),f888(x90411,x90413,x90412))))+~P1(f317(f305(f903(a1,a1),a211),f317(f317(f242(a1,a1),x90412),x90413)))
% 94.68/94.45 [9042]P1(f317(f317(x90421,x90422),x90423))+P1(f317(f305(f903(a1,a1),a172),f317(f317(f242(a1,a1),f653(x90421,x90423,x90422)),f655(x90421,x90423,x90422))))+~P1(f317(f305(f903(a1,a1),a172),f317(f317(f242(a1,a1),x90422),x90423)))
% 94.68/94.45 [9043]P1(f317(f317(x90431,x90432),x90433))+P1(f317(f305(f903(a1,a1),a123),f317(f317(f242(a1,a1),f751(x90431,x90433,x90432)),f752(x90431,x90433,x90432))))+~P1(f317(f305(f903(a1,a1),a123),f317(f317(f242(a1,a1),x90432),x90433)))
% 94.68/94.45 [9380]~P1(f317(f28(x93801),x93803))+P1(f317(f317(f319(f903(f904(x93801,a893),f904(x93801,a893))),f317(f317(f242(f904(x93801,a893),f904(x93801,a893)),x93802),x93803)),f304(x93801)))+~P1(f317(f317(f225(f904(x93801,a893)),x93802),x93803))
% 94.68/94.45 [9455]~P59(x94551,f317(x94553,f520(x94552,x94553,x94551)))+P59(x94551,f317(f317(f34(x94552,f904(x94551,f904(x94551,a893))),f232(f904(x94552,a893))),x94553))+~E(f317(f317(f92(f904(x94551,a893)),f239(x94551,x94551,f317(x94553,f519(x94552,x94553,x94551)))),f240(x94551,x94551,f317(x94553,f522(x94552,x94553,x94551)))),f178(f904(x94551,a893)))
% 94.68/94.45 [9665]P52(x96651,x96652,x96653)+P1(f317(f317(f319(f903(x96651,x96651)),f511(x96653,x96652,x96651)),x96653))+~P1(f317(f317(f319(f903(x96651,x96651)),f317(f317(f242(x96651,x96651),f510(x96653,x96652,x96651)),f510(x96653,x96652,x96651))),x96653))
% 94.68/94.45 [10255]P52(x102551,x102552,x102553)+~P1(f317(f317(f247(x102551,x102551,a893),f317(f317(f7(x102551,f904(x102551,a893),f904(x102551,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x102551,a893),f904(x102551,a893)),x102551),f8(a893,a893,x102551)),f317(f317(f8(a893,f904(a893,a893),x102551),a315),f317(f317(f7(x102551,f904(x102551,a893),a893),f319(x102551)),x102552)))),f317(f317(f7(x102551,f904(x102551,a893),a893),f319(x102551)),x102552))),f511(x102553,x102552,x102551)))+~P1(f317(f317(f319(f903(x102551,x102551)),f317(f317(f242(x102551,x102551),f510(x102553,x102552,x102551)),f510(x102553,x102552,x102551))),x102553))
% 94.68/94.45 [5725]~P3(x57252)+E(x57251,f2(x57252))+E(f317(f317(f30(x57252),f317(f317(f75(x57252),x57253),x57251)),x57251),x57253)
% 94.68/94.45 [5726]~P3(x57262)+E(x57261,f2(x57262))+E(f317(f317(f30(x57262),f317(f317(f75(x57262),x57261),x57263)),x57261),x57263)
% 94.68/94.45 [6390]~P3(x63901)+E(f317(f317(f75(x63901),f317(f317(f30(x63901),x63902),x63903)),x63903),x63902)+~P1(f317(f317(f277(x63901),x63903),x63902))
% 94.68/94.45 [6554]~P76(x65541)+~E(f317(x65542,f2(a897)),f2(x65541))+E(f317(f317(f6(a897,x65541),x65542),f317(f292(a897,f317(a102,f2(a897))),x65543)),f317(f317(f6(a897,x65541),x65542),f317(f292(a897,f2(a897)),x65543)))
% 94.68/94.45 [6692]~P3(x66922)+E(x66921,f2(x66922))+E(f317(f317(f30(x66922),f317(f317(f74(x66922),x66923),x66921)),x66921),f317(f317(f74(x66922),f317(f317(f30(x66922),x66923),x66921)),f72(x66922)))
% 94.68/94.45 [6693]~P3(x66932)+E(x66931,f2(x66932))+E(f317(f317(f30(x66932),f317(f317(f74(x66932),x66931),x66933)),x66931),f317(f317(f74(x66932),f317(f317(f30(x66932),x66933),x66931)),f72(x66932)))
% 94.68/94.45 [6918]~P1(f317(x69183,f2(a1)))+P1(f317(f317(f224(a897),x69181),x69182))+P1(f317(x69183,f317(f90(a1),f317(f317(f23(a897),x69182),x69181))))
% 94.68/94.45 [7026]P1(f317(f317(f225(a897),x70262),x70261))+P1(f317(f317(f224(a897),x70261),x70262))+P1(f317(x70263,f317(f90(a1),f317(f317(f23(a897),x70262),x70261))))
% 94.68/94.45 [7100]E(f317(f317(f74(a897),f317(f94(a897),x71001)),f317(f317(f74(a897),f317(f94(a897),x71002)),x71003)),f317(f317(f74(a897),f317(f94(a897),x71001)),x71003))+P1(f317(a183,f317(f94(a1),x71001)))+~P1(f317(a183,f317(f94(a1),x71002)))
% 94.68/94.45 [7179]~E(x71792,f317(f317(f30(a897),x71793),x71791))+~P1(f317(f317(f225(a897),f2(a897)),x71791))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x71791),x71792)),x71793))
% 94.68/94.45 [7296]~P1(f317(f28(x72961),x72963))+~P1(f317(f28(x72961),x72962))+P1(f317(f28(x72961),f317(f317(f91(f904(x72961,a893)),x72962),x72963)))
% 94.68/94.45 [7343]~P37(x73431,x73433)+~P37(x73431,x73432)+P37(x73431,f317(f317(f92(f904(f903(x73431,x73431),a893)),x73432),x73433))
% 94.68/94.45 [7344]~P51(x73441,x73443)+~P51(x73441,x73442)+P51(x73441,f317(f317(f91(f904(f903(x73441,x73441),a893)),x73442),x73443))
% 94.68/94.45 [7345]~P51(x73451,x73453)+~P51(x73451,x73452)+P51(x73451,f317(f317(f92(f904(f903(x73451,x73451),a893)),x73452),x73453))
% 94.68/94.45 [7588]~P66(x75881)+~P1(f317(f28(x75881),x75882))+E(f129(x75881,f317(f317(f23(f904(x75881,a893)),x75882),f317(f317(f299(x75881),x75883),f178(f904(x75881,a893))))),f160(x75881,x75883,f129(x75881,x75882)))
% 94.68/94.45 [7653]P1(f317(x76531,f2(a1)))+~P1(f317(f317(f225(a897),x76532),x76533))+~P1(f317(x76531,f317(f90(a1),f317(f317(f23(a897),x76532),x76533))))
% 94.68/94.45 [7671]~P1(f317(f28(x76711),x76712))+E(f317(f29(x76711),f317(f317(f23(f904(x76711,a893)),x76712),f317(f317(f299(x76711),x76713),f178(f904(x76711,a893))))),f317(f29(x76711),x76712))+P1(f317(f317(f319(x76711),x76713),x76712))
% 94.68/94.45 [7804]~P110(x78041)+~P1(f317(f317(f225(x78041),f72(x78041)),x78042))+P1(f317(f317(f225(x78041),f72(x78041)),f317(f317(f75(x78041),x78042),f317(f317(f234(x78041),x78042),x78043))))
% 94.68/94.45 [7847]~P1(f317(f28(x78471),x78473))+E(f317(f317(f23(a897),f317(f29(x78471),x78472)),f317(f29(x78471),x78473)),f317(f29(x78471),f317(f317(f23(f904(x78471,a893)),x78472),x78473)))+~P1(f317(f317(f224(f904(x78471,a893)),x78473),x78472))
% 94.68/94.45 [7905]~P1(f317(f317(f224(a897),x79052),x79053))+~P1(f317(f317(f224(a897),x79051),f317(f317(f23(a897),x79053),x79052)))+P1(f317(f317(f224(a897),f317(f317(f74(a897),x79051),x79052)),x79053))
% 94.68/94.45 [7959]P1(f317(f28(x79591),x79592))+~P1(f317(f28(x79591),x79593))+~P1(f317(f28(x79591),f317(f317(f23(f904(x79591,a893)),x79592),x79593)))
% 94.68/94.45 [7965]~P1(f317(f28(x79651),x79652))+E(f317(f29(x79651),f317(f317(f23(f904(x79651,a893)),x79652),f317(f317(f299(x79651),x79653),f178(f904(x79651,a893))))),f317(f317(f23(a897),f317(f29(x79651),x79652)),f72(a897)))+~P1(f317(f317(f319(x79651),x79653),x79652))
% 94.68/94.45 [8041]P59(x80411,x80412)+~P59(x80411,x80413)+~P1(f317(f317(f224(f904(x80411,f904(x80411,a893))),x80412),x80413))
% 94.68/94.45 [8081]~P1(f317(f317(f224(a897),x80813),x80812))+P1(f317(f317(f224(a897),x80811),f317(f317(f23(a897),x80812),x80813)))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),x80811),x80813)),x80812))
% 94.68/94.45 [8099]P36(x80991,x80992)+~P36(x80991,x80993)+~P1(f317(f317(f224(f904(f903(x80991,x80991),a893)),x80992),x80993))
% 94.68/94.45 [8100]P57(x81001,x81002)+~P57(x81001,x81003)+~P1(f317(f317(f224(f904(f903(x81001,x81001),a893)),x81002),x81003))
% 94.68/94.45 [8101]P38(x81011,x81012)+~P38(x81011,x81013)+~P1(f317(f317(f224(f904(f903(x81011,x81011),a893)),x81012),x81013))
% 94.68/94.45 [8335]~P110(x83351)+~P1(f317(f317(f225(x83351),f72(x83351)),x83352))+P1(f317(f317(f225(x83351),f317(f317(f234(x83351),x83352),x83353)),f317(f317(f75(x83351),x83352),f317(f317(f234(x83351),x83352),x83353))))
% 94.68/94.45 [8426]~P1(f317(x84261,f2(a1)))+~P1(f317(x84261,f317(f317(f23(a1),f317(f90(a1),x84262)),f317(f90(a1),x84263))))+P1(f317(x84261,f317(f90(a1),f317(f317(f23(a897),x84262),x84263))))
% 94.68/94.45 [8441]~P1(f317(f317(f224(a897),x84413),x84412))+P1(f317(x84411,f317(f317(f23(a1),f317(f90(a1),x84412)),f317(f90(a1),x84413))))+~P1(f317(x84411,f317(f90(a1),f317(f317(f23(a897),x84412),x84413))))
% 94.68/94.45 [8461]P1(f317(f317(f225(a897),x84611),x84612))+~P1(f317(x84613,f317(f317(f23(a1),f317(f90(a1),x84611)),f317(f90(a1),x84612))))+P1(f317(x84613,f317(f90(a1),f317(f317(f23(a897),x84611),x84612))))
% 94.68/94.45 [8514]~P125(x85142)+E(x85141,f2(x85142))+P1(f317(f317(f225(x85142),f2(x85142)),f317(f317(f74(x85142),f317(f317(f75(x85142),x85143),x85143)),f317(f317(f75(x85142),x85141),x85141))))
% 94.68/94.45 [8515]~P125(x85152)+E(x85151,f2(x85152))+P1(f317(f317(f225(x85152),f2(x85152)),f317(f317(f74(x85152),f317(f317(f75(x85152),x85151),x85151)),f317(f317(f75(x85152),x85153),x85153))))
% 94.68/94.45 [8615]~P1(f317(f317(f225(a897),f2(a897)),x86151))+~P1(f317(f317(f225(a1),x86152),x86153))+P1(f317(f317(f225(a1),f317(f317(f75(a1),f317(f90(a1),x86151)),x86152)),f317(f317(f75(a1),f317(f90(a1),x86151)),x86153)))
% 94.68/94.45 [8671]E(f317(f317(f92(f904(x86711,a893)),x86712),f31(f904(x86711,a893),x86713)),f178(f904(x86711,a893)))+P1(f317(f317(f319(f904(x86711,a893)),x86712),x86713))+P1(f317(f317(f319(f904(x86711,a893)),f599(x86713,x86712,x86711)),f317(f317(f299(f904(x86711,a893)),x86712),x86713)))
% 94.68/94.45 [8672]E(f317(f317(f92(f904(x86721,a893)),x86722),f31(f904(x86721,a893),x86723)),f178(f904(x86721,a893)))+P1(f317(f317(f319(f904(x86721,a893)),x86722),x86723))+P1(f317(f317(f319(f904(x86721,a893)),f598(x86723,x86722,x86721)),f317(f317(f299(f904(x86721,a893)),x86722),x86723)))
% 94.68/94.45 [8701]E(x87011,x87012)+~E(f317(f179(f898(x87013)),x87011),f317(f179(f898(x87013)),x87012))+P1(f317(f317(f319(f903(x87013,x87013)),f641(x87013,x87011,x87012)),f317(f162(f903(x87013,x87013)),f317(f317(f171(x87013,x87013),x87012),x87011))))
% 94.68/94.45 [8951]E(f297(x89511,x89512),f297(x89511,x89513))+~P1(f317(f317(f224(f904(f903(x89511,x89511),a893)),x89513),f297(x89511,x89512)))+~P1(f317(f317(f224(f904(f903(x89511,x89511),a893)),x89512),x89513))
% 94.68/94.45 [9018]~P52(x90181,f232(f904(x90181,a893)),x90183)+P1(f317(f317(f224(f904(f903(f898(x90181),f898(x90181)),a893)),f147(x90181,x90182)),f148(x90181,x90183)))+~P1(f317(f317(f224(f904(f903(x90181,x90181),a893)),x90182),x90183))
% 94.68/94.45 [9214]P36(x92141,x92142)+~P1(f317(f317(f319(x92141),x92143),f611(x92142,x92141)))+P1(f317(f317(f319(f903(x92141,x92141)),f317(f317(f242(x92141,x92141),f616(x92142,x92141,x92143)),x92143)),x92142))
% 94.68/94.45 [9249]~P1(f317(f28(x92491),x92492))+P1(f317(f28(f904(x92491,a893)),f317(f317(f55(x92491),x92492),x92493)))+~P1(f317(f317(f224(f904(f903(x92491,x92491),a893)),x92493),f317(f317(f244(x92491,x92491),x92492),f317(f16(f904(x92491,a893),x92491),x92492))))
% 94.68/94.45 [9285]P52(x92851,x92852,x92853)+P1(f317(f317(f319(x92851),f480(x92853,x92852,x92851)),x92852))+~P1(f317(f317(f224(f904(f903(x92851,x92851),a893)),x92853),f317(f317(f244(x92851,x92851),x92852),f317(f16(f904(x92851,a893),x92851),x92852))))
% 94.68/94.45 [9286]P52(x92861,x92862,x92863)+P1(f317(f317(f319(x92861),f484(x92862,x92863,x92861)),x92862))+~P1(f317(f317(f224(f904(f903(x92861,x92861),a893)),x92863),f317(f317(f244(x92861,x92861),x92862),f317(f16(f904(x92861,a893),x92861),x92862))))
% 94.68/94.45 [9321]~P64(x93211)+~P1(f317(f317(f225(x93211),x93212),x93213))+P1(f317(f317(f225(x93211),f317(f317(f281(x93211),f317(f317(f74(x93211),x93212),x93213)),f317(f317(f74(x93211),f72(x93211)),f72(x93211)))),x93213))
% 94.68/94.45 [9352]~P63(x93521)+P1(f317(f317(f224(x93521),x93522),x93523))+~P1(f317(f317(f224(x93521),f317(f317(f75(x93521),f422(x93523,x93522,x93521)),x93522)),x93523))
% 94.68/94.45 [9490]E(f317(f179(f898(f898(x94901))),f317(f126(f898(x94901),f317(f317(f8(a897,a893,f898(x94901)),f317(f225(a897),x94902)),f179(f898(x94901)))),f169(x94901,x94903))),f317(f179(f898(x94901)),f317(f317(f154(f898(x94901)),x94903),x94902)))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x94901),a897),f179(f898(x94901))),x94903)))+~P1(f317(f317(f225(a897),x94902),f317(f179(f898(f898(x94901))),x94903)))
% 94.68/94.45 [9613]~P36(x96131,x96132)+P26(x96131,f317(f317(f242(f904(f903(x96131,x96131),a893),f904(f903(x96131,x96131),a893)),x96132),x96133))+~P1(f317(f317(f224(f904(f903(x96131,x96131),a893)),f317(f317(f279(x96131,x96131,x96131),x96132),x96133)),x96132))
% 94.68/94.45 [9618]E(f317(f317(f144(f898(x96181),x96181),f317(f317(f7(f898(x96181),a897,x96181),f154(x96181)),x96182)),f317(f126(f898(x96181),f317(f317(f8(a897,a893,f898(x96181)),f317(f225(a897),x96182)),f179(f898(x96181)))),f169(x96181,x96183))),f317(f317(f154(f898(x96181)),x96183),x96182))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x96181),a897),f179(f898(x96181))),x96183)))+~P1(f317(f317(f225(a897),x96182),f317(f179(f898(f898(x96181))),x96183)))
% 94.68/94.45 [9753]P52(x97531,x97532,x97533)+~P1(f317(f317(f319(f903(x97531,x97531)),f317(f317(f242(x97531,x97531),f480(x97533,x97532,x97531)),f480(x97533,x97532,x97531))),x97533))+~P1(f317(f317(f224(f904(f903(x97531,x97531),a893)),x97533),f317(f317(f244(x97531,x97531),x97532),f317(f16(f904(x97531,a893),x97531),x97532))))
% 94.68/94.45 [9754]P52(x97541,x97542,x97543)+~P1(f317(f317(f319(f903(x97541,x97541)),f317(f317(f242(x97541,x97541),f484(x97542,x97543,x97541)),f484(x97542,x97543,x97541))),x97543))+~P1(f317(f317(f224(f904(f903(x97541,x97541),a893)),x97543),f317(f317(f244(x97541,x97541),x97542),f317(f16(f904(x97541,a893),x97541),x97542))))
% 94.68/94.45 [9922]~P141(x99221)+~P124(x99221)+E(f317(f317(f281(x99221),f317(f93(x99221),f317(f317(f67(f903(a1,a1),a1,x99222,f241(a1,a1)),f202(x99222)),x99223))),f317(f93(x99221),f317(f317(f67(f903(a1,a1),a1,x99222,f246(a1,a1)),f202(x99222)),x99223))),f212(x99222,x99221,x99223))
% 94.68/94.45 [10125]~E(x101253,f2(a897))+~E(f317(f179(f898(x101251)),f317(f317(f154(f898(x101251)),x101252),f689(x101253,x101251,x101252))),x101253)+E(f317(f317(f144(a897,f898(x101251)),f317(f317(f7(a897,f898(a897),f898(x101251)),f317(f317(f8(f904(a897,x101251),f904(f898(a897),f898(x101251)),a897),f144(a897,x101251)),f317(f7(a897,a897,x101251),f317(f317(f8(f898(x101251),f904(a897,x101251),a897),f154(x101251)),f317(f154(f898(x101251)),x101252))))),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(f898(x101251))),x101252))))),f129(a897,f317(f292(a897,f2(a897)),x101253))),f169(x101251,x101252))
% 94.68/94.45 [10126]E(x101261,f103(f898(x101262)))+~E(f317(f179(f898(x101262)),f317(f317(f154(f898(x101262)),x101261),f689(x101263,x101262,x101261))),x101263)+E(f317(f317(f144(a897,f898(x101262)),f317(f317(f7(a897,f898(a897),f898(x101262)),f317(f317(f8(f904(a897,x101262),f904(f898(a897),f898(x101262)),a897),f144(a897,x101262)),f317(f7(a897,a897,x101262),f317(f317(f8(f898(x101262),f904(a897,x101262),a897),f154(x101262)),f317(f154(f898(x101262)),x101261))))),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(f898(x101262))),x101261))))),f129(a897,f317(f292(a897,f2(a897)),x101263))),f169(x101262,x101261))
% 94.68/94.45 [10127]~E(x101273,f2(a897))+E(f317(f317(f144(a897,f898(x101271)),f317(f317(f7(a897,f898(a897),f898(x101271)),f317(f317(f8(f904(a897,x101271),f904(f898(a897),f898(x101271)),a897),f144(a897,x101271)),f317(f7(a897,a897,x101271),f317(f317(f8(f898(x101271),f904(a897,x101271),a897),f154(x101271)),f317(f154(f898(x101271)),x101272))))),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(f898(x101271))),x101272))))),f129(a897,f317(f292(a897,f2(a897)),x101273))),f169(x101271,x101272))+P1(f317(f317(f225(a897),f689(x101273,x101271,x101272)),f317(f179(f898(f898(x101271))),x101272)))
% 94.68/94.45 [10128]E(x101281,f103(f898(x101282)))+E(f317(f317(f144(a897,f898(x101282)),f317(f317(f7(a897,f898(a897),f898(x101282)),f317(f317(f8(f904(a897,x101282),f904(f898(a897),f898(x101282)),a897),f144(a897,x101282)),f317(f7(a897,a897,x101282),f317(f317(f8(f898(x101282),f904(a897,x101282),a897),f154(x101282)),f317(f154(f898(x101282)),x101281))))),f129(a897,f317(f292(a897,f2(a897)),f317(f179(f898(f898(x101282))),x101281))))),f129(a897,f317(f292(a897,f2(a897)),x101283))),f169(x101282,x101281))+P1(f317(f317(f225(a897),f689(x101283,x101282,x101281)),f317(f179(f898(f898(x101282))),x101281)))
% 94.68/94.45 [7844]E(f317(f317(f74(a897),f317(f94(a897),x78441)),f317(f317(f74(a897),f317(f94(a897),x78442)),x78443)),f317(f317(f74(a897),f317(f94(a897),f317(f317(f74(a1),x78441),x78442))),x78443))+P1(f317(a183,f317(f94(a1),x78441)))+P1(f317(a183,f317(f94(a1),x78442)))
% 94.68/94.45 [8607]~P1(f317(f28(x86071),x86072))+~P1(f317(f317(f319(x86071),x86073),x86072))+E(f317(a102,f317(f29(x86071),f317(f317(f23(f904(x86071,a893)),x86072),f317(f317(f299(x86071),x86073),f178(f904(x86071,a893)))))),f317(f29(x86071),x86072))
% 94.68/94.45 [8623]~P1(f317(f28(x86231),x86232))+~P1(f317(f317(f319(x86231),x86233),x86232))+E(f317(f317(f74(a897),f72(a897)),f317(f29(x86231),f317(f317(f23(f904(x86231,a893)),x86232),f317(f317(f299(x86231),x86233),f178(f904(x86231,a893)))))),f317(f29(x86231),x86232))
% 94.68/94.45 [8710]~P66(x87101)+~P1(f317(f28(x87101),x87103))+E(f317(f317(f138(x87101,x87101,f5(x87101)),x87102),f129(x87101,f317(f317(f23(f904(x87101,a893)),x87103),f317(f317(f299(x87101),x87102),f178(f904(x87101,a893)))))),f129(x87101,f317(f317(f299(x87101),x87102),x87103)))
% 94.68/94.45 [8876]~P1(f317(f28(x88761),x88763))+~P1(f317(f28(x88761),x88762))+E(f317(f317(f74(a897),f317(f29(x88761),f317(f317(f91(f904(x88761,a893)),x88762),x88763))),f317(f29(x88761),f317(f317(f92(f904(x88761,a893)),x88762),x88763))),f317(f317(f74(a897),f317(f29(x88761),x88762)),f317(f29(x88761),x88763)))
% 94.68/94.45 [10074]~P24(x100741,f904(f904(x100741,a893),a893),f317(f317(f7(x100741,f904(f903(x100741,x100741),a893),f904(f904(x100741,a893),a893)),f317(f317(f8(f904(x100741,a893),f904(f904(f903(x100741,x100741),a893),f904(f904(x100741,a893),a893)),x100741),f55(x100741)),f317(f317(f7(x100741,f904(x100741,a893),f904(x100741,a893)),f299(x100741)),f178(f904(x100741,a893))))),x100743),x100742)+~P1(f317(f28(x100741),x100742))+E(f317(f29(f904(x100741,a893)),f317(f317(f55(x100741),x100742),x100743)),f317(f29(x100741),x100742))
% 94.68/94.45 [8113]~P94(x81131)+P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x81133)))+E(f317(f317(f234(x81131),x81132),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x81133),x81133)),a87))),f72(x81131))
% 94.68/94.45 [9595]~P94(x95951)+~P1(f317(f317(f224(a1),f2(a1)),f317(f94(a1),x95953)))+E(f317(f317(f234(x95951),x95952),f317(f94(a897),f317(f317(f23(a1),f317(f317(f74(a1),x95953),x95953)),a87))),f317(f317(f80(x95951,x95951),f317(f317(f234(x95951),x95952),f317(f94(a897),x95953))),f317(f317(f18(x95951,x95951,x95951),f317(f317(f8(x95951,f904(x95951,x95951),x95951),f75(x95951)),f317(f75(x95951),x95952))),f5(x95951))))
% 94.68/94.45 [9984]~P1(f317(f127(x99841),x99843))+~P1(f317(f317(f319(x99841),x99842),f317(f162(x99841),x99843)))+E(f317(f317(f128(x99841),f317(f179(f898(x99841)),f167(x99841,f317(f317(f8(a893,a893,x99841),a312),f317(f317(f7(x99841,x99841,a893),a314),x99842)),f317(f158(x99841),x99843)))),f317(f158(x99841),x99843)),f317(f317(f141(x99841),x99842),f317(f158(x99841),f167(x99841,f317(f317(f8(a893,a893,x99841),a312),f317(f317(f7(x99841,x99841,a893),a314),x99842)),x99843))))
% 94.68/94.45 [10044]P1(f317(f317(f224(f904(f903(x100441,x100441),a893)),f297(x100441,x100442)),x100443))+~P1(f317(f317(f224(f904(f903(x100441,x100441),a893)),f297(x100441,f178(f904(f903(x100441,x100441),a893)))),x100443))+~P1(f317(f317(f224(f904(f903(x100441,x100441),a893)),f317(f317(f279(x100441,x100441,x100441),f317(f317(f92(f904(f903(x100441,x100441),a893)),f297(x100441,x100442)),x100443)),x100442)),x100443))
% 94.68/94.45 [9902]~P1(f317(f28(x99021),f317(f252(x99021),x99023)))+~P1(f317(f28(x99021),f317(f252(x99021),x99022)))+P1(f317(f28(x99021),f317(f252(x99021),f317(f317(f18(x99021,a893,a893),f317(f317(f8(a893,f904(a893,a893),x99021),a316),x99022)),x99023))))
% 94.68/94.45 [10190]P1(f317(f317(f224(f904(f903(x101901,x101901),a893)),f317(f317(f279(x101901,x101901,x101901),x101902),f297(x101901,x101902))),x101903))+~P1(f317(f317(f224(f904(f903(x101901,x101901),a893)),x101902),x101903))+~P1(f317(f317(f224(f904(f903(x101901,x101901),a893)),f317(f317(f279(x101901,x101901,x101901),f317(f317(f92(f904(f903(x101901,x101901),a893)),f317(f317(f279(x101901,x101901,x101901),x101902),f297(x101901,x101902))),x101903)),x101902)),x101903))
% 94.68/94.45 [10141]~P111(x101412)+E(x101411,f2(x101412))+~E(f317(f317(f74(x101412),f317(f317(f234(x101412),x101413),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101412),x101411),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101412))
% 94.68/94.45 [10142]~P111(x101422)+E(x101421,f2(x101422))+~E(f317(f317(f74(x101422),f317(f317(f234(x101422),x101421),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x101422),x101423),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x101422))
% 94.68/94.45 [10147]~P1(f317(f127(x101471),x101473))+~P1(f317(f317(f319(x101471),x101472),f317(f162(x101471),x101473)))+E(f317(f158(x101471),f317(f161(x101471),f317(f317(f128(x101471),f317(f179(f898(x101471)),f167(x101471,f317(f317(f8(a893,a893,x101471),a312),f317(f317(f7(x101471,x101471,a893),a314),x101472)),x101473))),x101473))),f167(x101471,f317(f317(f8(a893,a893,x101471),a312),f317(f317(f7(x101471,x101471,a893),a314),x101472)),f317(f158(x101471),x101473)))
% 94.68/94.45 [10235]~P111(x102352)+E(x102351,f2(x102352))+P1(f317(f317(f225(x102352),f2(x102352)),f317(f317(f74(x102352),f317(f317(f234(x102352),x102353),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102352),x102351),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))))
% 94.68/94.45 [10236]~P111(x102362)+E(x102361,f2(x102362))+P1(f317(f317(f225(x102362),f2(x102362)),f317(f317(f74(x102362),f317(f317(f234(x102362),x102361),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102362),x102363),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))))
% 94.68/94.45 [10297]~P111(x102971)+P1(f317(f317(f224(x102971),f2(x102971)),x102972))+~P1(f317(f317(f224(x102971),f2(x102971)),f317(f317(f234(x102971),x102972),f317(a102,f317(f317(f75(a897),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),x102973)))))
% 94.68/94.45 [5024]~E(x50242,f84(x50243,x50241))+P1(f317(x50241,x50242))+~P1(f317(x50241,x50244))
% 94.68/94.45 [5270]E(f62(x52703,x52702,x52704),x52702)+E(x52701,f716(x52702,x52703,x52704))+~P1(f317(x52704,x52701))
% 94.68/94.45 [6614]E(f62(x66141,x66142,x66143),f79(x66141,x66143))+~E(f757(x66142,x66141,x66143,x66144),x66144)+~P1(f317(x66143,x66144))
% 94.68/94.45 [6828]~P36(x68282,x68284)+~P36(x68281,x68283)+P36(f903(x68281,x68282),f309(x68281,x68282,x68283,x68284))
% 94.68/94.45 [6829]~P37(x68292,x68294)+~P37(x68291,x68293)+P37(f903(x68291,x68292),f309(x68291,x68292,x68293,x68294))
% 94.68/94.45 [5210]~P7(x52104,x52101)+~E(f317(x52101,x52102),f317(x52101,x52103))+P1(f317(f317(x52101,x52102),x52103))
% 94.68/94.45 [5369]~P7(x53694,x53691)+E(f317(x53691,x53692),f317(x53691,x53693))+~P1(f317(f317(x53691,x53692),x53693))
% 94.68/94.45 [5370]~P15(x53704,x53701)+E(f317(x53701,x53702),f317(x53701,x53703))+~P1(f317(f317(x53701,x53702),x53703))
% 94.68/94.45 [5464]~P18(x54643,x54644,x54641)+E(f317(x54641,x54642),f317(f57(x54643,x54644),x54642))+~P1(f317(f28(x54643),x54642))
% 94.68/94.45 [5465]~P9(x54653,x54654,x54651)+E(f317(x54651,x54652),f317(f57(x54653,x54654),x54652))+~P1(f317(f28(x54653),x54652))
% 94.68/94.45 [5592]~P7(x55924,x55921)+~P1(f317(f317(x55921,x55923),x55922))+P1(f317(f317(x55921,x55922),x55923))
% 94.68/94.45 [5593]~P50(x55934,x55931)+~P1(f317(f317(x55931,x55933),x55932))+P1(f317(f317(x55931,x55932),x55933))
% 94.68/94.45 [5594]~P15(x55944,x55941)+~P1(f317(f317(x55941,x55943),x55942))+P1(f317(f317(x55941,x55942),x55943))
% 94.68/94.45 [5595]~P15(x55953,x55951)+P1(f317(f317(x55951,x55952),x55952))+~P1(f317(f317(x55951,x55954),x55952))
% 94.68/94.45 [5596]~P15(x55963,x55961)+P1(f317(f317(x55961,x55962),x55962))+~P1(f317(f317(x55961,x55962),x55964))
% 94.68/94.45 [5666]E(x56661,x56662)+~E(f317(f241(x56663,x56664),x56661),f317(f241(x56663,x56664),x56662))+~E(f317(f246(x56663,x56664),x56661),f317(f246(x56663,x56664),x56662))
% 94.68/94.45 [5694]E(x56941,x56942)+~P1(f317(f43(x56943,x56944),x56942))+~P1(f317(f43(x56943,x56944),x56941))
% 94.68/94.45 [5894]~P76(x58942)+E(f221(x58941,x58942,x58943,x58944),f2(x58942))+P1(f317(f28(x58941),x58944))
% 94.68/94.45 [5942]~P7(x59423,x59422)+~P1(f317(x59421,x59424))+P1(f317(x59421,f798(x59421,x59422,x59423)))
% 94.68/94.45 [6040]~P1(f317(f305(x60401,x60402),x60404))+P1(f317(f305(x60401,x60402),x60403))+~P1(f317(f317(x60402,x60403),x60404))
% 94.68/94.45 [6865]~P28(x68651,x68653,x68654)+P1(f317(x68651,x68652))+~P1(f317(f317(f319(a1),x68652),f293(a1,x68653,x68654)))
% 94.68/94.45 [7062]~P7(x70621,x70623)+~P1(f317(x70622,x70624))+P1(f317(f317(f319(x70621),f798(x70622,x70623,x70621)),f260(x70621,x70623)))
% 94.68/94.45 [7954]E(x79541,f2(a897))+~P1(f317(x79542,x79543))+P1(f317(x79542,f749(x79542,x79543,x79541,x79544)))
% 94.68/94.45 [8036]~P66(x80362)+~P1(f317(f127(x80361),x80364))+P1(f317(f127(x80361),f140(x80361,x80362,x80363,x80364)))
% 94.68/94.45 [8080]E(f62(x80801,x80802,x80803),f79(x80801,x80803))+~P1(f317(x80803,x80804))+P1(f317(x80803,f757(x80802,x80801,x80803,x80804)))
% 94.68/94.45 [8262]~P1(f317(f28(x82622),x82624))+~P1(f317(f28(x82621),x82623))+P1(f317(f28(f902(x82621,x82622)),f303(x82621,x82622,x82623,x82624)))
% 94.68/94.45 [8263]~P1(f317(f127(x82632),x82634))+~P1(f317(f127(x82631),x82633))+P1(f317(f127(f903(x82631,x82632)),f54(x82631,x82632,x82633,x82634)))
% 94.68/94.45 [8266]P1(f317(f317(f319(f898(x82661)),f317(f317(f124(x82661),x82662),x82663)),f151(x82661,x82664)))+~P1(f317(f317(f319(f898(x82661)),x82663),f151(x82661,x82664)))+~P1(f317(f317(f319(f898(x82661)),x82662),f151(x82661,x82664)))
% 94.68/94.45 [8545]E(x85451,f2(a897))+P1(f317(x85452,x85453))+~P1(f317(x85452,f750(x85452,x85453,x85451,x85454)))
% 94.68/94.45 [8582]~P66(x85823)+~P1(f317(f127(x85821),f140(x85821,x85823,x85824,x85822)))+P1(f317(f127(x85821),x85822))
% 94.68/94.45 [8865]~P1(f317(f317(f319(f903(x88651,x88651)),f317(f317(f242(x88651,x88651),x88652),x88654)),f297(x88651,x88653)))+P1(f317(f317(f319(x88651),x88652),f306(x88651,x88653)))+~P1(f317(f317(f319(x88651),x88654),f306(x88651,x88653)))
% 94.68/94.45 [5194]~P77(x51942)+E(f317(f317(f9(x51941,x51942),x51943),x51944),f72(x51942))+P1(f317(f28(x51941),x51944))
% 94.68/94.45 [5197]~P76(x51972)+E(f317(f317(f6(x51971,x51972),x51973),x51974),f2(x51972))+P1(f317(f28(x51971),x51974))
% 94.68/94.45 [5332]~P70(x53323)+E(x53321,x53322)+~E(f317(f317(f74(x53323),x53324),x53321),f317(f317(f74(x53323),x53324),x53322))
% 94.68/94.45 [5333]~P71(x53333)+E(x53331,x53332)+~E(f317(f317(f74(x53333),x53334),x53331),f317(f317(f74(x53333),x53334),x53332))
% 94.68/94.45 [5335]~P70(x53353)+E(x53351,x53352)+~E(f317(f317(f74(x53353),x53351),x53354),f317(f317(f74(x53353),x53352),x53354))
% 94.68/94.45 [5431]~P121(x54311)+~E(x54313,f317(f317(f75(x54311),x54312),x54314))+P1(f317(f317(f277(x54311),x54312),x54313))
% 94.68/94.45 [5459]~P5(x54593)+E(x54591,f178(f904(x54592,a893)))+E(f317(f317(f34(x54592,x54593),x54591),f317(f16(x54593,x54592),x54594)),x54594)
% 94.68/94.45 [5460]~P5(x54603)+E(x54601,f178(f904(x54602,a893)))+E(f317(f317(f35(x54602,x54603),x54601),f317(f16(x54603,x54602),x54604)),x54604)
% 94.68/94.45 [5680]~P108(x56803)+E(x56801,x56802)+~E(f293(x56803,x56804,x56801),f317(f317(f299(x56803),x56802),f178(f904(x56803,a893))))
% 94.68/94.45 [5681]~P108(x56813)+E(x56811,x56812)+~E(f293(x56813,x56811,x56812),f317(f317(f299(x56813),x56814),f178(f904(x56813,a893))))
% 94.68/94.45 [5741]~P34(x57413,x57411,x57414)+P34(x57413,x57411,f317(f317(f141(x57413),x57412),x57414))+P1(f317(x57411,x57412))
% 94.68/94.45 [5843]~P30(x58431,x58432,x58434)+~P1(f317(x58432,x58433))+P30(x58431,x58432,f317(f317(f141(x58431),x58433),x58434))
% 94.68/94.45 [5995]P1(f317(x59951,x59952))+~P1(f317(f238(x59953,x59951),x59954))+~P1(f317(f317(f319(x59953),x59952),x59954))
% 94.68/94.45 [6004]~P30(x60041,x60042,x60044)+~P30(x60041,x60042,x60043)+P30(x60041,x60042,f317(f317(f124(x60041),x60043),x60044))
% 94.68/94.45 [6019]P32(x60191,x60192,x60193)+~P32(x60191,x60192,f317(f317(f141(x60191),x60194),x60193))+P1(f317(x60192,x60194))
% 94.68/94.45 [6020]P34(x60201,x60202,x60203)+~P34(x60201,x60202,f317(f317(f141(x60201),x60204),x60203))+P1(f317(x60202,x60204))
% 94.68/94.45 [6095]P32(x60951,x60952,x60953)+P32(x60951,x60952,x60954)+~P32(x60951,x60952,f317(f317(f124(x60951),x60954),x60953))
% 94.68/94.45 [6116]~P76(x61161)+E(f317(f317(f6(a897,x61161),x61162),f317(f292(a897,x61163),f317(a102,x61164))),f2(x61161))+~P1(f317(f317(f225(a897),x61164),x61163))
% 94.68/94.45 [6121]~P4(x61211)+~E(f40(x61211,x61212,x61213),f40(x61211,x61214,x61213))+E(f40(x61211,f317(f73(x61211),x61212),x61213),f40(x61211,f317(f73(x61211),x61214),x61213))
% 94.68/94.45 [6189]P1(f317(x61891,x61892))+~E(f317(f126(x61893,x61891),x61894),x61894)+~P1(f317(f317(f319(x61893),x61892),f317(f162(x61893),x61894)))
% 94.68/94.45 [6209]~E(f317(f317(f74(a897),x62093),x62092),f317(f317(f74(a897),x62091),x62094))+~P1(f317(f317(f225(a897),x62093),x62094))+P1(f317(f317(f225(a897),x62091),x62092))
% 94.68/94.45 [6215]P32(x62151,x62152,x62153)+~P1(f317(x62152,x62154))+~P1(f317(f317(f319(x62151),x62154),f317(f162(x62151),x62153)))
% 94.68/94.45 [6218]~P3(x62181)+E(f40(x62181,f40(x62181,x62182,x62183),x62184),f40(x62181,x62182,x62184))+~P1(f317(f317(f277(x62181),x62184),x62183))
% 94.68/94.45 [6258]~P30(x62583,x62581,x62584)+P1(f317(x62581,x62582))+~P1(f317(f317(f319(x62583),x62582),f317(f162(x62583),x62584)))
% 94.68/94.45 [6260]~E(f317(f126(x62601,x62602),x62603),f103(x62601))+~P1(f317(x62602,x62604))+~P1(f317(f317(f319(x62601),x62604),f317(f162(x62601),x62603)))
% 94.68/94.45 [6261]~E(f167(x62613,x62611,x62614),x62614)+P1(f317(x62611,x62612))+~P1(f317(f317(f319(x62613),x62612),f317(f162(x62613),x62614)))
% 94.68/94.45 [6289]~E(x62894,f178(f904(x62892,a893)))+~E(x62893,f178(f904(x62891,a893)))+E(f303(x62891,x62892,x62893,x62894),f178(f904(f902(x62891,x62892),a893)))
% 94.68/94.45 [6441]P1(f317(x64411,x64412))+~P1(f317(f150(x64413,x64411),x64414))+~P1(f317(f317(f319(x64413),x64412),f317(f162(x64413),x64414)))
% 94.68/94.45 [6583]~P29(x65831,x65833,x65834)+P1(f317(x65831,x65832))+~P1(f317(f317(f319(a897),x65832),f317(f292(a897,x65833),x65834)))
% 94.68/94.45 [6722]~P76(x67221)+E(f317(f317(f6(a897,x67221),x67222),f293(a897,x67223,f317(a102,x67224))),f2(x67221))+~P1(f317(f317(f225(a897),f317(a102,x67224)),x67223))
% 94.68/94.45 [6868]~P66(x68681)+E(f317(f317(f23(f904(x68681,a893)),f317(f292(x68681,x68682),x68683)),f317(f292(x68681,x68682),x68684)),f317(f292(x68681,x68684),x68683))+~P1(f317(f317(f224(x68681),x68682),x68684))
% 94.68/94.45 [6939]~E(x69393,x69394)+E(x69391,f2(a897))+P1(f317(f317(f319(x69392),x69393),f317(f162(x69392),f159(x69392,x69391,x69394))))
% 94.68/94.45 [7225]~P1(f317(f317(f319(f898(x72251)),x72254),f151(x72251,x72253)))+P1(f317(f317(f319(x72251),x72252),x72253))+~P1(f317(f317(f319(x72251),x72252),f317(f162(x72251),x72254)))
% 94.68/94.45 [7232]~P36(x72321,x72322)+P1(f317(f317(f319(x72321),f600(x72322,x72321,x72323)),x72323))+~P1(f317(f317(f319(x72321),x72324),x72323))
% 94.68/94.45 [7289]~P77(x72891)+E(f317(f317(f317(f59(x72891,x72892,f75(x72891)),x72893),f72(x72891)),x72894),f317(f317(f9(x72892,x72891),x72893),x72894))+~P1(f317(f28(x72892),x72894))
% 94.68/94.45 [7291]~P76(x72911)+E(f317(f317(f317(f59(x72911,x72912,f74(x72911)),x72913),f2(x72911)),x72914),f317(f317(f6(x72912,x72911),x72913),x72914))+~P1(f317(f28(x72912),x72914))
% 94.68/94.45 [7318]P24(x73181,x73182,x73183,x73184)+~E(f317(f29(x73182),f317(f300(x73181,x73182,x73183),x73184)),f317(f29(x73181),x73184))+~P1(f317(f28(x73181),x73184))
% 94.68/94.45 [7512]~P76(x75121)+E(f317(f317(f74(x75121),f317(x75122,x75123)),f317(f317(f6(a897,x75121),x75122),f295(a897,x75123,x75124))),f317(f317(f6(a897,x75121),x75122),f293(a897,x75123,x75124)))+~P1(f317(f317(f224(a897),x75123),x75124))
% 94.68/94.45 [7521]~P77(x75211)+~P24(x75212,x75211,x75213,x75214)+E(f317(f317(f9(x75211,x75211),f25(x75211)),f317(f300(x75212,x75211,x75213),x75214)),f317(f317(f9(x75212,x75211),x75213),x75214))
% 94.68/94.45 [7522]~P76(x75221)+~P24(x75222,x75221,x75223,x75224)+E(f317(f317(f6(x75221,x75221),f25(x75221)),f317(f300(x75222,x75221,x75223),x75224)),f317(f317(f6(x75222,x75221),x75223),x75224))
% 94.68/94.45 [7570]E(f317(f29(f902(x75701,x75702)),f303(x75701,x75702,x75703,x75704)),f317(f317(f74(a897),f317(f29(x75701),x75703)),f317(f29(x75702),x75704)))+~P1(f317(f28(x75702),x75704))+~P1(f317(f28(x75701),x75703))
% 94.68/94.45 [7654]E(x76541,x76542)+P1(f317(f317(f319(x76543),x76541),f317(f162(x76543),f160(x76543,x76542,x76544))))+~P1(f317(f317(f319(x76543),x76541),f317(f162(x76543),x76544)))
% 94.68/94.45 [7884]~P76(x78841)+E(f317(f317(f74(x78841),f317(f317(f6(a897,x78841),x78842),f317(f292(a897,x78843),x78844))),f317(x78842,x78844)),f317(f317(f6(a897,x78841),x78842),f317(f292(a897,x78843),f317(a102,x78844))))+P1(f317(f317(f225(a897),x78844),x78843))
% 94.68/94.45 [7934]~P24(x79341,x79342,x79343,f232(f904(x79341,a893)))+~P1(f317(f28(x79342),x79344))+P1(f317(f28(x79341),f317(f301(x79341,x79342,x79343),x79344)))
% 94.68/94.45 [8051]P1(f317(f317(f319(f898(x80511)),f317(f317(f141(x80511),x80512),x80513)),f151(x80511,x80514)))+~P1(f317(f317(f319(f898(x80511)),x80513),f151(x80511,x80514)))+~P1(f317(f317(f319(x80511),x80512),x80514))
% 94.68/94.45 [8137]~E(f317(f300(x81373,x81371,x81374),f232(f904(x81373,a893))),f232(f904(x81371,a893)))+P1(f317(f28(x81371),x81372))+~P1(f317(f28(x81373),f317(f301(x81373,x81371,x81374),x81372)))
% 94.68/94.45 [8232]~P24(x82321,x82323,x82324,x82322)+P1(f317(f28(x82321),x82322))+~P1(f317(f28(x82323),f317(f300(x82321,x82323,x82324),x82322)))
% 94.68/94.45 [8256]~E(x82562,x82563)+P1(f317(f317(f319(f903(x82561,x82561)),f317(f317(f242(x82561,x82561),x82562),x82563)),f253(x82561,x82564)))+~P1(f317(f317(f319(x82561),x82562),x82564))
% 94.68/94.45 [8289]~P76(x82891)+E(f317(f317(f74(x82891),f317(f317(f6(a897,x82891),x82892),f293(a897,x82893,x82894))),f317(x82892,f317(a102,x82894))),f317(f317(f6(a897,x82891),x82892),f293(a897,x82893,f317(a102,x82894))))+P1(f317(f317(f225(a897),f317(a102,x82894)),x82893))
% 94.68/94.45 [8349]P1(f317(x83491,x83492))+~P1(f317(x83491,f317(f317(f154(x83493),x83494),f640(x83491,x83494,x83493))))+~P1(f317(f317(f319(x83493),x83492),f317(f162(x83493),x83494)))
% 94.68/94.45 [8490]~P1(f317(f317(f319(x84901),x84902),f306(x84901,x84904)))+P1(f317(f317(f319(f898(x84901)),f317(f317(f141(x84901),x84902),x84903)),f306(f898(x84901),f147(x84901,x84904))))+~P1(f317(f317(f319(f898(x84901)),x84903),f306(f898(x84901),f147(x84901,x84904))))
% 94.68/94.45 [8505]~P24(x85052,x85053,x85054,f603(x85054,x85053,x85052,x85051))+P24(x85052,x85053,x85054,f32(f904(x85052,a893),x85051))+E(x85051,f178(f904(f904(x85052,a893),a893)))
% 94.68/94.45 [8774]E(x87741,x87742)+~P1(f317(f317(f319(f903(x87743,x87743)),f317(f317(f242(x87743,x87743),x87741),x87742)),f297(x87743,x87744)))+P1(f317(f317(f319(x87743),x87741),f317(f254(x87743,x87743),x87744)))
% 94.68/94.45 [9052]E(x90521,f2(a897))+P1(f317(x90522,x90523))+P1(f317(f317(f319(x90524),f750(x90522,x90523,x90521,x90524)),f317(f162(x90524),f159(x90524,x90521,x90523))))
% 94.68/94.45 [9064]E(x90641,f2(a897))+~P1(f317(x90643,x90644))+P1(f317(f317(f319(x90642),f749(x90643,x90644,x90641,x90642)),f317(f162(x90642),f159(x90642,x90641,x90644))))
% 94.68/94.45 [9066]~P25(x90661,x90662,x90663,f232(f904(x90661,a893)),f232(f904(x90662,a893)))+~P1(f317(f28(x90662),x90664))+P1(f317(f28(x90661),f317(f301(x90661,x90662,x90663),x90664)))
% 94.68/94.45 [9069]P24(x90692,x90693,x90694,f32(f904(x90692,a893),x90691))+E(x90691,f178(f904(f904(x90692,a893),a893)))+P1(f317(f317(f319(f904(x90692,a893)),f603(x90694,x90693,x90692,x90691)),x90691))
% 94.68/94.45 [9185]~P25(x91853,x91851,x91854,f232(f904(x91853,a893)),f232(f904(x91851,a893)))+P1(f317(f28(x91851),x91852))+~P1(f317(f28(x91853),f317(f301(x91853,x91851,x91854),x91852)))
% 94.68/94.45 [9202]P1(f317(f28(x92021),x92022))+~P1(f317(f28(x92024),f317(f300(x92021,x92024,x92023),x92022)))+P1(f317(f317(f319(x92021),f500(x92023,x92024,x92022,x92021)),x92022))
% 94.68/94.45 [9297]~P5(x92972)+E(f317(f317(f58(x92971,x92972,f317(f317(f8(x92972,f904(x92972,x92972),x92971),f91(x92972)),x92973)),f178(x92972)),x92974),f317(f317(f34(x92971,x92972),x92974),x92973))+~P1(f317(f28(x92971),x92974))
% 94.68/94.45 [9298]~P5(x92982)+E(f317(f317(f58(x92981,x92982,f317(f317(f8(x92982,f904(x92982,x92982),x92981),f92(x92982)),x92983)),f232(x92982)),x92984),f317(f317(f35(x92981,x92982),x92984),x92983))+~P1(f317(f28(x92981),x92984))
% 94.68/94.45 [9328]~P1(f317(f317(f277(a897),x93283),x93284))+P1(f317(f317(f277(a897),x93281),x93282))+P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x93281,x93282)),f280(a897,f277(a897),x93283,x93284)))
% 94.68/94.45 [9341]~P1(f317(f317(f277(a897),x93412),x93414))+~P1(f317(f317(f277(a897),x93413),x93411))+P1(f317(f317(f224(f904(a897,a893)),f280(a897,f277(a897),x93411,x93412)),f280(a897,f277(a897),x93413,x93414)))
% 94.68/94.45 [9385]P1(f317(x93851,x93852))+~P1(f317(x93851,f317(f317(f154(x93853),x93854),f676(x93852,x93851,x93854,x93853))))+~P1(f317(f317(f319(x93853),x93852),f317(f162(x93853),x93854)))
% 94.68/94.45 [9406]E(x94061,x94062)+~P1(f317(f317(f319(f903(x94063,x94063)),f317(f317(f242(x94063,x94063),x94061),x94062)),f297(x94063,x94064)))+P1(f317(f317(f319(f903(x94063,x94063)),f317(f317(f242(x94063,x94063),x94061),x94062)),f317(f317(f279(x94063,x94063,x94063),x94064),f297(x94063,x94064))))
% 94.68/94.45 [9456]~E(f317(f179(f898(x94561)),x94562),f317(f179(f898(x94561)),x94563))+~P1(f317(f317(f319(f903(f898(x94561),f898(x94561))),f317(f317(f242(f898(x94561),f898(x94561)),x94562),x94563)),f137(x94561,x94564)))+P1(f317(f317(f319(f903(f898(x94561),f898(x94561))),f317(f317(f242(f898(x94561),f898(x94561)),x94562),x94563)),f135(x94561,x94564)))
% 94.68/94.45 [9579]P1(f317(f317(f277(a897),x95791),x95792))+~P1(f317(f317(f277(a897),x95793),x95791))+~P1(f317(f317(f224(f904(a897,a893)),f280(a897,f277(a897),x95793,x95791)),f280(a897,f277(a897),x95794,x95792)))
% 94.68/94.45 [9580]P1(f317(f317(f277(a897),x95801),x95802))+~P1(f317(f317(f277(a897),x95803),x95801))+~P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x95803,x95801)),f280(a897,f277(a897),x95804,x95802)))
% 94.68/94.45 [9581]P1(f317(f317(f277(a897),x95811),x95812))+~P1(f317(f317(f277(a897),x95812),x95813))+~P1(f317(f317(f224(f904(a897,a893)),f280(a897,f277(a897),x95812,x95813)),f280(a897,f277(a897),x95811,x95814)))
% 94.68/94.45 [9582]P1(f317(f317(f277(a897),x95821),x95822))+~P1(f317(f317(f277(a897),x95822),x95823))+~P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x95822,x95823)),f280(a897,f277(a897),x95821,x95824)))
% 94.68/94.45 [9701]P30(x97011,f317(f317(f18(x97011,a893,a893),f317(f317(f8(a893,f904(a893,a893),x97011),a316),f317(f317(f8(a893,a893,x97011),a312),x97012))),f317(a314,x97013)),x97014)+~P1(f317(x97012,x97013))+~P34(x97011,x97012,f317(f317(f141(x97011),x97013),x97014))
% 94.68/94.45 [9866]~P30(x98661,f317(f317(f18(x98661,a893,a893),f317(f317(f8(a893,f904(a893,a893),x98661),a316),f317(f317(f8(a893,a893,x98661),a312),x98662))),f317(a314,x98663)),x98664)+~P1(f317(x98662,x98663))+P34(x98661,x98662,f317(f317(f141(x98661),x98663),x98664))
% 94.68/94.45 [9870]~P34(x98701,x98702,x98704)+~P30(x98701,f317(f317(f18(x98701,a893,a893),f317(f317(f8(a893,f904(a893,a893),x98701),a316),f317(f317(f8(a893,a893,x98701),a312),x98702))),f317(a314,x98703)),x98704)+P34(x98701,x98702,f317(f317(f141(x98701),x98703),x98704))
% 94.68/94.45 [9903]~P69(x99031)+E(f317(f317(f6(a897,x99031),f317(f317(f18(a897,x99031,x99031),f317(f317(f8(x99031,f904(x99031,x99031),a897),f23(x99031)),x99032)),f317(f317(f8(a897,x99031,a897),x99032),f317(f317(f7(a897,a897,a897),f74(a897)),f72(a897))))),f293(a897,x99033,x99034)),f2(x99031))+P1(f317(f317(f224(a897),x99033),x99034))
% 94.68/94.45 [10140]~P36(x101402,x101404)+~P24(x101402,x101401,x101403,f232(f904(x101402,a893)))+P36(x101401,f317(f300(f903(x101402,x101402),f903(x101401,x101401),f248(x101402,x101401,x101402,x101401,x101403,x101403)),x101404))
% 94.68/94.45 [10332]~E(f317(f179(f898(x103321)),x103323),f317(f179(f898(x103321)),x103322))+P1(f317(f317(f319(f903(f898(x103321),f898(x103321))),f317(f317(f242(f898(x103321),f898(x103321)),x103322),x103323)),f148(x103321,x103324)))+~P1(f317(f317(f247(x103321,x103321,a893),f317(f317(f7(x103321,f904(f903(x103321,x103321),a893),f904(x103321,a893)),f317(f317(f8(f904(x103321,f904(f904(f903(x103321,x103321),a893),a893)),f904(f904(f903(x103321,x103321),a893),f904(x103321,a893)),x103321),f7(x103321,f904(f903(x103321,x103321),a893),a893)),f317(f317(f8(f904(x103321,f903(x103321,x103321)),f904(x103321,f904(f904(f903(x103321,x103321),a893),a893)),x103321),f317(f8(f903(x103321,x103321),f904(f904(f903(x103321,x103321),a893),a893),x103321),f319(f903(x103321,x103321)))),f242(x103321,x103321)))),x103324)),f642(x103324,x103323,x103322,x103321)))
% 94.68/94.45 [6170]~P3(x61701)+~E(x61702,f2(x61701))+E(f317(f317(f30(x61701),f317(f317(f75(x61701),x61702),x61703)),f317(f317(f75(x61701),x61702),x61704)),f2(x61701))
% 94.68/94.45 [6212]E(x62121,f103(x62122))+E(x62123,f317(f317(f23(a897),f317(f179(f898(x62122)),x62121)),f72(a897)))+E(f134(x62122,f317(f317(f149(x62122,x62121),x62123),x62124)),f134(x62122,x62121))
% 94.68/94.45 [6249]E(x62491,x62492)+P1(f317(x62493,x62492))+~P1(f317(f317(f317(f299(x62494),x62491),x62493),x62492))
% 94.68/94.45 [6265]~P76(x62651)+~P1(f317(f127(x62652),x62654))+E(f317(f155(x62651),f317(f317(f144(x62652,x62651),x62653),x62654)),f317(f317(f6(x62652,x62651),x62653),f317(f162(x62652),x62654)))
% 94.68/94.45 [6282]~P77(x62822)+~P1(f317(f28(x62821),x62824))+E(f317(f317(f9(x62821,x62822),f317(f16(x62822,x62821),x62823)),x62824),f317(f317(f234(x62822),x62823),f317(f29(x62821),x62824)))
% 94.68/94.45 [6337]~P3(x63372)+E(x63371,f2(x63372))+E(f317(f317(f30(x63372),f317(f317(f75(x63372),x63373),x63371)),f317(f317(f75(x63372),x63374),x63371)),f317(f317(f30(x63372),x63373),x63374))
% 94.68/94.45 [6339]~P61(x63392)+E(x63391,f2(x63392))+E(f317(f317(f281(x63392),f317(f317(f75(x63392),x63393),x63391)),f317(f317(f75(x63392),x63394),x63391)),f317(f317(f281(x63392),x63393),x63394))
% 94.68/94.45 [6340]~P61(x63402)+E(x63401,f2(x63402))+E(f317(f317(f281(x63402),f317(f317(f75(x63402),x63401),x63403)),f317(f317(f75(x63402),x63401),x63404)),f317(f317(f281(x63402),x63403),x63404))
% 94.68/94.45 [6341]~P3(x63412)+E(x63411,f2(x63412))+E(f317(f317(f30(x63412),f317(f317(f75(x63412),x63411),x63413)),f317(f317(f75(x63412),x63411),x63414)),f317(f317(f30(x63412),x63413),x63414))
% 94.68/94.45 [6410]P1(f317(x64101,x64102))+~E(x64103,f317(f317(f74(a897),x64104),x64102))+~P1(f317(x64101,f317(f317(f23(a897),x64103),x64104)))
% 94.68/94.45 [6496]~P1(f317(x64962,x64963))+~P1(f317(f150(x64961,x64962),x64964))+P1(f317(f150(x64961,x64962),f317(f317(f141(x64961),x64963),x64964)))
% 94.68/94.45 [6537]E(x65371,f103(x65372))+~E(x65373,f317(f317(f23(a897),f317(f179(f898(x65372)),x65371)),f72(a897)))+E(f134(x65372,f317(f317(f149(x65372,x65371),x65373),x65374)),x65374)
% 94.68/94.45 [6561]~P66(x65611)+~P1(f317(f317(f224(x65611),x65612),x65614))+P1(f317(f317(f224(x65611),x65612),f317(f317(f223(x65611),x65613),x65614)))
% 94.68/94.45 [6563]~P66(x65631)+~P1(f317(f317(f224(x65631),x65632),x65633))+P1(f317(f317(f224(x65631),x65632),f317(f317(f223(x65631),x65633),x65634)))
% 94.68/94.45 [6564]~P99(x65641)+~P1(f317(f317(f224(x65641),x65642),x65644))+P1(f317(f317(f224(x65641),x65642),f317(f317(f91(x65641),x65643),x65644)))
% 94.68/94.45 [6565]~P99(x65651)+~P1(f317(f317(f224(x65651),x65652),x65653))+P1(f317(f317(f224(x65651),x65652),f317(f317(f91(x65651),x65653),x65654)))
% 94.68/94.45 [6567]~P66(x65671)+~P1(f317(f317(f225(x65671),x65672),x65674))+P1(f317(f317(f225(x65671),x65672),f317(f317(f223(x65671),x65673),x65674)))
% 94.68/94.45 [6569]~P66(x65691)+~P1(f317(f317(f225(x65691),x65692),x65693))+P1(f317(f317(f225(x65691),x65692),f317(f317(f223(x65691),x65693),x65694)))
% 94.68/94.45 [6570]~P99(x65701)+~P1(f317(f317(f225(x65701),x65702),x65704))+P1(f317(f317(f225(x65701),x65702),f317(f317(f91(x65701),x65703),x65704)))
% 94.68/94.45 [6571]~P99(x65711)+~P1(f317(f317(f225(x65711),x65712),x65713))+P1(f317(f317(f225(x65711),x65712),f317(f317(f91(x65711),x65713),x65714)))
% 94.68/94.45 [6572]~P112(x65721)+~P1(f317(f317(f277(x65721),x65722),x65724))+P1(f317(f317(f277(x65721),x65722),f317(f317(f75(x65721),x65723),x65724)))
% 94.68/94.45 [6573]~P112(x65731)+~P1(f317(f317(f277(x65731),x65732),x65733))+P1(f317(f317(f277(x65731),x65732),f317(f317(f75(x65731),x65733),x65734)))
% 94.68/94.45 [6666]~E(f317(f317(f154(x66661),x66662),x66663),x66664)+E(f317(f317(f149(x66661,x66662),x66663),x66664),x66662)+~P1(f317(f317(f225(a897),x66663),f317(f179(f898(x66661)),x66662)))
% 94.68/94.45 [6706]P1(f317(x67061,x67062))+~P1(f317(x67063,x67062))+~P1(f317(f317(f224(f904(x67064,a893)),x67063),x67061))
% 94.68/94.45 [6741]~E(f317(f317(f149(x67411,x67412),x67413),x67414),x67412)+E(f317(f317(f154(x67411),x67412),x67413),x67414)+~P1(f317(f317(f225(a897),x67413),f317(f179(f898(x67411)),x67412)))
% 94.68/94.45 [6755]~P1(f317(f150(x67551,x67552),x67554))+~P1(f317(f150(x67551,x67552),x67553))+P1(f317(f150(x67551,x67552),f317(f317(f124(x67551),x67553),x67554)))
% 94.68/94.45 [6864]E(x68641,f178(f904(x68642,a893)))+E(x68643,f178(f904(x68644,a893)))+~E(f317(f317(f244(x68644,x68642),x68643),f317(f16(f904(x68642,a893),x68644),x68641)),f178(f904(f903(x68644,x68642),a893)))
% 94.68/94.45 [6884]E(x68841,x68842)+P1(f317(f317(f319(x68843),x68841),x68844))+~P1(f317(f317(f319(x68843),x68841),f317(f317(f299(x68843),x68842),x68844)))
% 94.68/94.45 [6901]~P66(x69011)+P1(f317(f317(f224(x69011),x69012),x69013))+~P1(f317(f317(f224(x69011),x69012),f317(f317(f228(x69011),x69014),x69013)))
% 94.68/94.45 [6903]~P66(x69031)+P1(f317(f317(f224(x69031),x69032),x69033))+~P1(f317(f317(f224(x69031),x69032),f317(f317(f228(x69031),x69033),x69034)))
% 94.68/94.45 [6905]~P105(x69051)+P1(f317(f317(f224(x69051),x69052),x69053))+~P1(f317(f317(f224(x69051),x69052),f317(f317(f92(x69051),x69054),x69053)))
% 94.68/94.45 [6907]~P105(x69071)+P1(f317(f317(f224(x69071),x69072),x69073))+~P1(f317(f317(f224(x69071),x69072),f317(f317(f92(x69071),x69073),x69074)))
% 94.68/94.45 [6908]~P66(x69081)+P1(f317(f317(f225(x69081),x69082),x69083))+~P1(f317(f317(f225(x69081),x69082),f317(f317(f228(x69081),x69084),x69083)))
% 94.68/94.45 [6909]~P66(x69091)+P1(f317(f317(f225(x69091),x69092),x69093))+~P1(f317(f317(f225(x69091),x69092),f317(f317(f228(x69091),x69093),x69094)))
% 94.68/94.45 [6930]~E(f317(f317(f154(x69301),x69303),x69304),x69302)+P1(f317(f317(f319(x69301),x69302),f317(f162(x69301),x69303)))+~P1(f317(f317(f225(a897),x69304),f317(f179(f898(x69301)),x69303)))
% 94.68/94.45 [6940]~P66(x69401)+~P13(x69401,f317(f317(f141(x69401),x69402),f317(f317(f141(x69401),x69403),x69404)))+P1(f317(f317(f224(x69401),x69402),x69403))
% 94.68/94.45 [7090]~P30(x70902,x70901,x70903)+P1(f317(x70901,f317(f317(f154(x70902),x70903),x70904)))+~P1(f317(f317(f225(a897),x70904),f317(f179(f898(x70902)),x70903)))
% 94.68/94.45 [7108]E(x71081,f2(a1))+E(f317(f317(f30(a1),x71082),x71081),x71083)+~P1(f317(f44(x71082,x71081),f317(f317(f242(a1,a1),x71083),x71084)))
% 94.68/94.45 [7130]E(f40(a1,x71302,x71301),x71303)+E(x71301,f2(a1))+~P1(f317(f44(x71302,x71301),f317(f317(f242(a1,a1),x71304),x71303)))
% 94.68/94.45 [7249]P1(f317(f317(f319(x72491),x72492),x72493))+~P1(f317(f317(f319(x72491),x72492),x72494))+~P1(f317(f317(f225(f904(x72491,a893)),x72494),x72493))
% 94.68/94.45 [7250]P1(f317(f317(f319(x72501),x72502),x72503))+~P1(f317(f317(f319(x72501),x72502),x72504))+~P1(f317(f317(f224(f904(x72501,a893)),x72504),x72503))
% 94.68/94.45 [7261]~P120(x72611)+~E(x72613,f2(x72611))+P1(f317(f317(f277(x72611),f317(f317(f75(x72611),x72612),x72613)),f317(f317(f75(x72611),x72614),x72613)))
% 94.68/94.45 [7262]~P120(x72621)+~E(x72622,f2(x72621))+P1(f317(f317(f277(x72621),f317(f317(f75(x72621),x72622),x72623)),f317(f317(f75(x72621),x72622),x72624)))
% 94.68/94.45 [7362]P32(x73621,x73622,x73623)+~P1(f317(x73622,f317(f317(f154(x73621),x73623),x73624)))+~P1(f317(f317(f225(a897),x73624),f317(f179(f898(x73621)),x73623)))
% 94.68/94.45 [7477]~P109(x74772)+~P1(f317(f317(f225(f904(x74771,x74772)),x74773),x74774))+P1(f317(f317(f224(f904(x74771,x74772)),x74773),x74774))
% 94.68/94.45 [7601]~P1(f317(f317(f319(x76011),x76012),x76014))+P1(f317(f317(f319(x76011),x76012),f31(f904(x76011,a893),x76013)))+~P1(f317(f317(f319(f904(x76011,a893)),x76014),x76013))
% 94.68/94.45 [7603]~P112(x76031)+~P1(f317(f317(f224(a897),x76033),x76034))+P1(f317(f317(f277(x76031),f317(f317(f234(x76031),x76032),x76033)),f317(f317(f234(x76031),x76032),x76034)))
% 94.68/94.45 [7631]~P84(x76311)+~P1(f317(f317(f224(x76311),x76313),x76314))+P1(f317(f317(f224(x76311),f317(f317(f74(x76311),x76312),x76313)),f317(f317(f74(x76311),x76312),x76314)))
% 94.68/94.45 [7632]~P85(x76321)+~P1(f317(f317(f224(x76321),x76323),x76324))+P1(f317(f317(f224(x76321),f317(f317(f74(x76321),x76322),x76323)),f317(f317(f74(x76321),x76322),x76324)))
% 94.68/94.45 [7633]~P84(x76331)+~P1(f317(f317(f224(x76331),x76332),x76334))+P1(f317(f317(f224(x76331),f317(f317(f74(x76331),x76332),x76333)),f317(f317(f74(x76331),x76334),x76333)))
% 94.68/94.45 [7634]~P85(x76341)+~P1(f317(f317(f224(x76341),x76342),x76344))+P1(f317(f317(f224(x76341),f317(f317(f74(x76341),x76342),x76343)),f317(f317(f74(x76341),x76344),x76343)))
% 94.68/94.45 [7635]~P84(x76351)+~P1(f317(f317(f225(x76351),x76353),x76354))+P1(f317(f317(f225(x76351),f317(f317(f74(x76351),x76352),x76353)),f317(f317(f74(x76351),x76352),x76354)))
% 94.68/94.45 [7636]~P87(x76361)+~P1(f317(f317(f225(x76361),x76363),x76364))+P1(f317(f317(f225(x76361),f317(f317(f74(x76361),x76362),x76363)),f317(f317(f74(x76361),x76362),x76364)))
% 94.68/94.45 [7637]~P84(x76371)+~P1(f317(f317(f225(x76371),x76372),x76374))+P1(f317(f317(f225(x76371),f317(f317(f74(x76371),x76372),x76373)),f317(f317(f74(x76371),x76374),x76373)))
% 94.68/94.45 [7638]~P87(x76381)+~P1(f317(f317(f225(x76381),x76382),x76384))+P1(f317(f317(f225(x76381),f317(f317(f74(x76381),x76382),x76383)),f317(f317(f74(x76381),x76384),x76383)))
% 94.68/94.45 [7639]~P120(x76391)+~P1(f317(f317(f277(x76391),x76393),x76394))+P1(f317(f317(f277(x76391),f317(f317(f75(x76391),x76392),x76393)),f317(f317(f75(x76391),x76392),x76394)))
% 94.68/94.45 [7640]~P120(x76401)+~P1(f317(f317(f277(x76401),x76402),x76404))+P1(f317(f317(f277(x76401),f317(f317(f75(x76401),x76402),x76403)),f317(f317(f75(x76401),x76404),x76403)))
% 94.68/94.45 [7641]~P112(x76411)+~P1(f317(f317(f277(x76411),x76412),x76414))+P1(f317(f317(f277(x76411),f317(f317(f234(x76411),x76412),x76413)),f317(f317(f234(x76411),x76414),x76413)))
% 94.68/94.45 [7648]~P95(x76481)+~P131(x76481)+E(f317(f317(f23(x76481),f317(f317(f75(x76481),x76482),f317(f94(x76481),x76483))),f317(f317(f75(x76481),x76484),f317(f94(x76481),x76483))),f317(f317(f75(x76481),f317(f317(f23(x76481),x76482),x76484)),f317(f94(x76481),x76483)))
% 94.68/94.45 [7649]~P95(x76491)+~P140(x76491)+E(f317(f317(f74(x76491),f317(f317(f75(x76491),x76492),f317(f94(x76491),x76493))),f317(f317(f75(x76491),x76494),f317(f94(x76491),x76493))),f317(f317(f75(x76491),f317(f317(f74(x76491),x76492),x76494)),f317(f94(x76491),x76493)))
% 94.68/94.45 [7685]~P76(x76851)+E(f317(f317(f74(x76851),f317(x76852,x76853)),f317(f317(f6(a897,x76851),x76852),f293(a897,f317(a102,x76853),x76854))),f317(f317(f6(a897,x76851),x76852),f293(a897,x76853,x76854)))+~P1(f317(f317(f224(a897),x76853),x76854))
% 94.68/94.45 [7697]~P24(x76972,x76971,x76973,f317(f162(x76972),x76974))+~P1(f317(f127(x76972),x76974))+P1(f317(f127(x76971),f317(f317(f144(x76972,x76971),x76973),x76974)))
% 94.68/94.45 [7746]~P1(f317(f317(f224(a897),x77462),x77464))+~P1(f317(f317(f224(a897),x77461),x77463))+P1(f317(f317(f224(a897),f317(f317(f74(a897),x77461),x77462)),f317(f317(f74(a897),x77463),x77464)))
% 94.68/94.45 [7747]~P1(f317(f317(f224(a897),x77472),x77474))+~P1(f317(f317(f224(a897),x77471),x77473))+P1(f317(f317(f224(a897),f317(f317(f75(a897),x77471),x77472)),f317(f317(f75(a897),x77473),x77474)))
% 94.68/94.45 [7750]~P1(f317(f317(f225(a897),x77502),x77504))+~P1(f317(f317(f225(a897),x77501),x77503))+P1(f317(f317(f225(a897),f317(f317(f74(a897),x77501),x77502)),f317(f317(f74(a897),x77503),x77504)))
% 94.68/94.45 [7751]~P1(f317(f317(f224(a1),x77512),x77514))+~P1(f317(f317(f225(a1),x77511),x77513))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x77511),x77512)),f317(f317(f74(a1),x77513),x77514)))
% 94.68/94.45 [7799]P1(f317(f317(f319(x77991),x77992),x77993))+~P1(f317(f317(f319(x77991),x77992),f32(f904(x77991,a893),x77994)))+~P1(f317(f317(f319(f904(x77991,a893)),x77993),x77994))
% 94.68/94.45 [7816]~P1(f317(x78161,f638(x78161,x78163,x78162)))+P1(f317(x78161,f317(f317(f154(x78162),x78163),x78164)))+~P1(f317(f317(f225(a897),x78164),f317(f179(f898(x78162)),x78163)))
% 94.68/94.45 [7821]P1(f317(x78211,x78212))+~P1(f317(f317(f319(x78214),x78212),f317(f162(x78214),x78213)))+P1(f317(f317(f225(a897),f640(x78211,x78213,x78214)),f317(f179(f898(x78214)),x78213)))
% 94.68/94.45 [7868]~P109(x78681)+~P1(f317(f317(f225(f904(x78682,x78681)),x78684),x78683))+~P1(f317(f317(f224(f904(x78682,x78681)),x78683),x78684))
% 94.68/94.45 [7913]~P1(f317(x79134,x79132))+~P1(f317(f317(f319(x79131),x79132),x79133))+P1(f317(f317(f319(x79131),x79132),f317(f317(f92(f904(x79131,a893)),x79133),f317(f252(x79131),x79134))))
% 94.68/94.45 [8058]~P1(f317(f317(f319(x80581),x80583),x80584))+~P1(f317(f317(f225(f904(x80581,a893)),x80582),x80584))+P1(f317(f317(f225(f904(x80581,a893)),x80582),f317(f317(f299(x80581),x80583),x80584)))
% 94.68/94.45 [8060]E(f317(f317(f92(f904(x80601,a893)),x80602),x80603),f178(f904(x80601,a893)))+~E(f317(f317(f92(f904(x80601,a893)),f31(f904(x80601,a893),x80604)),x80603),f178(f904(x80601,a893)))+~P1(f317(f317(f319(f904(x80601,a893)),x80602),x80604))
% 94.68/94.45 [8133]P1(f317(f317(f319(x81331),x81332),x81333))+~P1(f317(f317(f224(f904(x81331,a893)),x81333),f317(f317(f299(x81331),x81332),x81334)))+P1(f317(f317(f224(f904(x81331,a893)),x81333),x81334))
% 94.68/94.45 [8150]P1(f317(f317(f319(x81502),f638(x81501,x81503,x81502)),f317(f162(x81502),x81503)))+P1(f317(x81501,f317(f317(f154(x81502),x81503),x81504)))+~P1(f317(f317(f225(a897),x81504),f317(f179(f898(x81502)),x81503)))
% 94.68/94.45 [8158]~P1(f317(f317(f224(f904(x81581,a893)),x81582),x81584))+P1(f317(f317(f224(f904(x81581,a893)),x81582),x81583))+~P1(f317(f317(f224(f904(x81581,a893)),x81584),x81583))
% 94.68/94.45 [8159]~P1(f317(f317(f225(f904(x81591,a893)),x81592),x81594))+~P1(f317(f317(f224(f904(x81591,a893)),x81594),x81593))+P1(f317(f317(f225(f904(x81591,a893)),x81592),x81593))
% 94.68/94.45 [8160]~P1(f317(f317(f224(f904(x81601,a893)),x81602),x81604))+~P1(f317(f317(f225(f904(x81601,a893)),x81604),x81603))+P1(f317(f317(f225(f904(x81601,a893)),x81602),x81603))
% 94.68/94.45 [8161]~P1(f317(f317(f225(f904(x81611,a893)),x81612),x81614))+P1(f317(f317(f225(f904(x81611,a893)),x81612),x81613))+~P1(f317(f317(f225(f904(x81611,a893)),x81614),x81613))
% 94.68/94.45 [8205]~P1(f317(f317(f319(x82051),x82054),x82053))+~P1(f317(f317(f225(f904(x82051,a893)),x82052),f317(f317(f299(x82051),x82054),x82053)))+P1(f317(f317(f225(f904(x82051,a893)),x82052),x82053))
% 94.68/94.45 [8216]~P84(x82161)+P1(f317(f317(f224(x82161),x82162),x82163))+~P1(f317(f317(f224(x82161),f317(f317(f74(x82161),x82164),x82162)),f317(f317(f74(x82161),x82164),x82163)))
% 94.68/94.45 [8218]~P84(x82181)+P1(f317(f317(f224(x82181),x82182),x82183))+~P1(f317(f317(f224(x82181),f317(f317(f74(x82181),x82182),x82184)),f317(f317(f74(x82181),x82183),x82184)))
% 94.68/94.45 [8220]~P84(x82201)+P1(f317(f317(f225(x82201),x82202),x82203))+~P1(f317(f317(f225(x82201),f317(f317(f74(x82201),x82204),x82202)),f317(f317(f74(x82201),x82204),x82203)))
% 94.68/94.45 [8222]~P84(x82221)+P1(f317(f317(f225(x82221),x82222),x82223))+~P1(f317(f317(f225(x82221),f317(f317(f74(x82221),x82222),x82224)),f317(f317(f74(x82221),x82223),x82224)))
% 94.68/94.45 [8273]P1(f317(x82731,x82732))+~E(f317(f317(f128(x82733),f317(f179(f898(x82733)),f167(x82733,x82731,x82734))),x82734),f103(x82733))+~P1(f317(f317(f319(x82733),x82732),f317(f162(x82733),x82734)))
% 94.68/94.45 [8392]P1(f317(x83921,x83922))+~P1(f317(f317(f319(x83923),x83922),f317(f162(x83923),x83924)))+P1(f317(f317(f225(a897),f317(f179(f898(x83923)),f317(f126(x83923,x83921),x83924))),f317(f179(f898(x83923)),x83924)))
% 94.68/94.45 [8881]~P1(f317(x88811,f731(x88811,x88813,x88812,x88814)))+P1(f317(x88811,f317(f317(f154(x88812),x88813),x88814)))+~P1(f317(f317(f225(a897),x88814),f317(f179(f898(x88812)),x88813)))
% 94.68/94.45 [8905]~P24(x89054,x89053,x89051,f232(f904(x89054,a893)))+E(f317(x89051,f453(x89052,x89051,x89053,x89054)),x89052)+~P1(f317(f317(f319(x89053),x89052),f317(f300(x89054,x89053,x89051),f232(f904(x89054,a893)))))
% 94.68/94.45 [8973]E(f167(x89731,x89732,x89733),f317(f317(f165(x89731),x89734),x89733))+P1(f317(f317(f225(a897),f701(x89732,x89733,x89731,x89734)),x89734))+P1(f317(f317(f225(a897),x89734),f317(f179(f898(x89731)),x89733)))
% 94.68/94.45 [8976]E(f167(x89761,x89762,x89763),f317(f317(f165(x89761),x89764),x89763))+P1(f317(f317(f225(a897),f701(x89762,x89763,x89761,x89764)),x89764))+P1(f317(x89762,f317(f317(f154(x89761),x89763),x89764)))
% 94.68/94.45 [9011]P1(f317(x90111,x90112))+~P1(f317(f317(f319(x90114),x90112),f317(f162(x90114),x90113)))+P1(f317(f317(f225(a897),f676(x90112,x90111,x90113,x90114)),f317(f179(f898(x90114)),x90113)))
% 94.68/94.45 [9013]E(f167(x90131,x90132,x90133),f317(f317(f165(x90131),x90134),x90133))+P1(f317(f317(f225(a897),x90134),f317(f179(f898(x90131)),x90133)))+P1(f317(f317(f225(a897),f701(x90132,x90133,x90131,x90134)),f317(f179(f898(x90131)),x90133)))
% 94.68/94.45 [9020]E(f167(x90201,x90202,x90203),f317(f317(f165(x90201),x90204),x90203))+P1(f317(x90202,f317(f317(f154(x90201),x90203),x90204)))+P1(f317(f317(f225(a897),f701(x90202,x90203,x90201,x90204)),f317(f179(f898(x90201)),x90203)))
% 94.68/94.45 [9045]~P110(x90454)+P1(f317(f317(f319(x90451),f621(x90452,x90453,x90451,x90454)),x90453))+P1(f317(f317(f225(x90454),f2(x90454)),f317(f317(f9(x90451,x90454),x90452),x90453)))
% 94.68/94.45 [9046]~P110(x90464)+P1(f317(f317(f319(x90461),f626(x90462,x90463,x90461,x90464)),x90463))+P1(f317(f317(f224(x90464),f2(x90464)),f317(f317(f9(x90461,x90464),x90462),x90463)))
% 94.68/94.45 [9071]~P1(f317(f28(x90711),x90714))+P1(f317(f317(f319(x90711),f472(x90712,x90713,x90714,x90711)),x90714))+P1(f317(f28(f903(x90711,x90713)),f317(f317(f244(x90711,x90713),x90714),x90712)))
% 94.68/94.45 [9103]P1(f317(f317(f319(x91032),f731(x91031,x91033,x91032,x91034)),f317(f162(x91032),x91033)))+P1(f317(x91031,f317(f317(f154(x91032),x91033),x91034)))+~P1(f317(f317(f225(a897),x91034),f317(f179(f898(x91032)),x91033)))
% 94.68/94.45 [9233]P1(f317(f317(f224(a897),x92334),f317(f179(f898(x92332)),f167(x92332,x92333,x92331))))+P1(f317(f317(f225(a897),f702(x92331,x92332,x92333,x92334)),x92334))+~P1(f317(f317(f224(a897),x92334),f317(f179(f898(x92332)),x92331)))
% 94.68/94.45 [9389]E(f167(x93891,x93892,x93893),f317(f317(f165(x93891),x93894),x93893))+~P1(f317(x93892,f317(f317(f154(x93891),x93893),f701(x93892,x93893,x93891,x93894))))+P1(f317(f317(f225(a897),x93894),f317(f179(f898(x93891)),x93893)))
% 94.68/94.45 [9396]E(f167(x93961,x93962,x93963),f317(f317(f165(x93961),x93964),x93963))+~P1(f317(x93962,f317(f317(f154(x93961),x93963),f701(x93962,x93963,x93961,x93964))))+P1(f317(x93962,f317(f317(f154(x93961),x93963),x93964)))
% 94.68/94.45 [9400]~P1(f317(f28(x94001),x94003))+~P1(f317(f28(x94002),f317(x94004,f472(x94004,x94002,x94003,x94001))))+P1(f317(f28(f903(x94001,x94002)),f317(f317(f244(x94001,x94002),x94003),x94004)))
% 94.68/94.45 [9408]~P110(x94081)+~P1(f317(f317(f224(x94081),f2(x94081)),f317(x94083,f626(x94083,x94084,x94082,x94081))))+P1(f317(f317(f224(x94081),f2(x94081)),f317(f317(f9(x94082,x94081),x94083),x94084)))
% 94.68/94.45 [9409]~P110(x94091)+~P1(f317(f317(f225(x94091),f2(x94091)),f317(x94093,f621(x94093,x94094,x94092,x94091))))+P1(f317(f317(f225(x94091),f2(x94091)),f317(f317(f9(x94092,x94091),x94093),x94094)))
% 94.68/94.45 [9417]~E(f317(f179(f898(x94174)),x94172),f317(f179(f898(x94174)),x94173))+P1(f317(f317(f319(f903(f898(x94174),f898(x94174))),f317(f317(f242(f898(x94174),f898(x94174)),x94173),x94172)),f148(x94174,x94171)))+P1(f317(f317(f225(a897),f627(x94171,x94172,x94173,x94174)),f317(f179(f898(x94174)),x94173)))
% 94.68/94.45 [9469]~P1(f317(x94693,f317(f317(f154(x94692),x94694),f702(x94694,x94692,x94693,x94691))))+P1(f317(f317(f224(a897),x94691),f317(f179(f898(x94692)),f167(x94692,x94693,x94694))))+~P1(f317(f317(f224(a897),x94691),f317(f179(f898(x94692)),x94694)))
% 94.68/94.45 [9550]E(f317(f317(f165(x95501),f639(x95502,x95503,x95504,x95501)),x95503),f317(f317(f165(x95501),f639(x95502,x95503,x95504,x95501)),x95504))+~P1(f317(f317(f319(f903(f898(x95501),f898(x95501))),f317(f317(f242(f898(x95501),f898(x95501)),x95504),x95503)),f137(x95501,x95502)))+P1(f317(f317(f225(a897),f317(f179(f898(x95501)),x95504)),f317(f179(f898(x95501)),x95503)))
% 94.68/94.45 [9615]~P1(f317(f317(f225(a897),f2(a897)),x96153))+~P1(f317(f317(f225(a897),x96154),x96151))+P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),x96151),f40(a897,x96152,x96153))),x96154)),f317(f317(f75(a897),x96151),x96153)))
% 94.68/94.45 [9806]~P109(x98062)+~P1(f317(f317(f224(x98062),f317(x98063,f769(x98064,x98063,x98061,x98062))),f317(x98064,f769(x98064,x98063,x98061,x98062))))+P1(f317(f317(f224(f904(x98061,x98062)),x98063),x98064))
% 94.68/94.45 [9908]~P69(x99081)+E(f317(f317(f6(a897,x99081),f317(f317(f18(a897,x99081,x99081),f317(f317(f8(x99081,f904(x99081,x99081),a897),f23(x99081)),x99082)),f317(f317(f8(a897,x99081,a897),x99082),f317(f317(f7(a897,a897,a897),f74(a897)),f72(a897))))),f293(a897,x99083,x99084)),f317(f317(f23(x99081),f317(x99082,x99083)),f317(x99082,f317(f317(f74(a897),x99084),f72(a897)))))+~P1(f317(f317(f224(a897),x99083),x99084))
% 94.68/94.45 [9983]~P36(x99833,f317(f317(f279(x99833,x99833,x99833),x99832),f297(x99833,x99832)))+~P1(f317(f317(f319(f903(x99833,x99833)),f317(f317(f242(x99833,x99833),f317(x99831,f317(a102,f816(x99832,x99831,x99833)))),f317(x99831,f816(x99832,x99831,x99833)))),f297(x99833,x99832)))+E(f317(x99831,f317(f317(f74(a897),f815(x99832,x99831,x99833)),x99834)),f317(x99831,f815(x99832,x99831,x99833)))
% 94.68/94.45 [6847]~P3(x68471)+E(f317(f317(f30(x68471),f317(f317(f75(x68471),x68472),x68473)),x68474),f317(f317(f75(x68471),x68472),f317(f317(f30(x68471),x68473),x68474)))+~P1(f317(f317(f277(x68471),x68474),x68473))
% 94.68/94.45 [6934]E(f317(f317(f124(x69341),x69342),x69343),x69344)+~E(x69343,f317(f317(f128(x69341),f317(f179(f898(x69341)),x69342)),x69344))+~E(f317(f317(f165(x69341),f317(f179(f898(x69341)),x69342)),x69344),x69342)
% 94.68/94.45 [6990]~P62(x69902)+E(x69901,f2(x69902))+E(f317(f317(f281(x69902),f317(f317(f234(x69902),x69903),x69904)),f317(f317(f234(x69902),x69901),x69904)),f317(f317(f234(x69902),f317(f317(f281(x69902),x69903),x69901)),x69904))
% 94.68/94.45 [7138]~P3(x71381)+E(f317(f317(f30(x71381),f317(f317(f75(x71381),x71382),x71383)),x71384),f317(f317(f75(x71381),f317(f317(f30(x71381),x71382),x71384)),x71383))+~P1(f317(f317(f277(x71381),x71384),x71382))
% 94.68/94.45 [7147]~P66(x71471)+~P1(f317(f317(f224(x71471),x71473),x71474))+P1(f317(f317(f224(x71471),f317(f317(f228(x71471),x71472),x71473)),x71474))
% 94.68/94.45 [7149]~P66(x71491)+~P1(f317(f317(f224(x71491),x71492),x71494))+P1(f317(f317(f224(x71491),f317(f317(f228(x71491),x71492),x71493)),x71494))
% 94.68/94.45 [7150]~P105(x71501)+~P1(f317(f317(f224(x71501),x71503),x71504))+P1(f317(f317(f224(x71501),f317(f317(f92(x71501),x71502),x71503)),x71504))
% 94.68/94.45 [7151]~P105(x71511)+~P1(f317(f317(f224(x71511),x71512),x71514))+P1(f317(f317(f224(x71511),f317(f317(f92(x71511),x71512),x71513)),x71514))
% 94.68/94.45 [7153]~P66(x71531)+~P1(f317(f317(f225(x71531),x71533),x71534))+P1(f317(f317(f225(x71531),f317(f317(f228(x71531),x71532),x71533)),x71534))
% 94.68/94.45 [7155]~P66(x71551)+~P1(f317(f317(f225(x71551),x71552),x71554))+P1(f317(f317(f225(x71551),f317(f317(f228(x71551),x71552),x71553)),x71554))
% 94.68/94.45 [7156]~P105(x71561)+~P1(f317(f317(f225(x71561),x71563),x71564))+P1(f317(f317(f225(x71561),f317(f317(f92(x71561),x71562),x71563)),x71564))
% 94.68/94.45 [7157]~P105(x71571)+~P1(f317(f317(f225(x71571),x71572),x71574))+P1(f317(f317(f225(x71571),f317(f317(f92(x71571),x71572),x71573)),x71574))
% 94.68/94.45 [7180]~P1(f317(x71803,x71804))+~P1(f317(x71802,x71804))+P1(f317(f317(f317(f92(f904(x71801,a893)),x71802),x71803),x71804))
% 94.68/94.45 [7442]~P3(x74421)+E(f317(f317(f30(x74421),f317(f317(f234(x74421),x74422),x74423)),f317(f317(f234(x74421),x74424),x74423)),f317(f317(f234(x74421),f317(f317(f30(x74421),x74422),x74424)),x74423))+~P1(f317(f317(f277(x74421),x74424),x74422))
% 94.68/94.45 [7675]~P76(x76751)+E(f317(f317(f74(x76751),f317(x76752,x76753)),f317(f317(f6(a897,x76751),x76752),f317(f292(a897,f317(a102,x76753)),x76754))),f317(f317(f6(a897,x76751),x76752),f317(f292(a897,x76753),x76754)))+~P1(f317(f317(f225(a897),x76753),x76754))
% 94.68/94.45 [7693]E(x76931,x76932)+P1(f317(f317(f162(x76933),x76934),x76932))+~P1(f317(f317(f162(x76933),f317(f317(f141(x76933),x76931),x76934)),x76932))
% 94.68/94.45 [7705]~P66(x77051)+P1(f317(f317(f224(x77051),x77052),x77053))+~P1(f317(f317(f224(x77051),f317(f317(f223(x77051),x77054),x77052)),x77053))
% 94.68/94.45 [7707]~P66(x77071)+P1(f317(f317(f224(x77071),x77072),x77073))+~P1(f317(f317(f224(x77071),f317(f317(f223(x77071),x77072),x77074)),x77073))
% 94.68/94.45 [7709]~P99(x77091)+P1(f317(f317(f224(x77091),x77092),x77093))+~P1(f317(f317(f224(x77091),f317(f317(f91(x77091),x77094),x77092)),x77093))
% 94.68/94.45 [7711]~P99(x77111)+P1(f317(f317(f224(x77111),x77112),x77113))+~P1(f317(f317(f224(x77111),f317(f317(f91(x77111),x77112),x77114)),x77113))
% 94.68/94.45 [7712]~P66(x77121)+P1(f317(f317(f225(x77121),x77122),x77123))+~P1(f317(f317(f225(x77121),f317(f317(f223(x77121),x77124),x77122)),x77123))
% 94.68/94.45 [7713]~P66(x77131)+P1(f317(f317(f225(x77131),x77132),x77133))+~P1(f317(f317(f225(x77131),f317(f317(f223(x77131),x77132),x77134)),x77133))
% 94.68/94.45 [7714]~P112(x77141)+P1(f317(f317(f277(x77141),x77142),x77143))+~P1(f317(f317(f277(x77141),f317(f317(f75(x77141),x77144),x77142)),x77143))
% 94.68/94.45 [7715]~P112(x77151)+P1(f317(f317(f277(x77151),x77152),x77153))+~P1(f317(f317(f277(x77151),f317(f317(f75(x77151),x77152),x77154)),x77153))
% 94.68/94.45 [7791]~P1(f317(f317(f319(x77911),x77912),x77914))+P1(f317(f317(f319(x77911),x77912),x77913))+P1(f317(f317(f319(x77911),x77912),f317(f317(f23(f904(x77911,a893)),x77914),x77913)))
% 94.68/94.45 [7875]P1(f317(x78751,x78752))+P1(f317(x78753,x78752))+~P1(f317(f317(f317(f91(f904(x78754,a893)),x78753),x78751),x78752))
% 94.68/94.45 [7887]~P1(f317(f317(f319(x78871),x78872),x78874))+~P1(f317(f317(f319(x78871),x78872),x78873))+P1(f317(f317(f319(x78871),x78872),f317(f317(f92(f904(x78871,a893)),x78873),x78874)))
% 94.68/94.45 [7935]~P66(x79351)+~P1(f317(f28(x79351),x79354))+E(f317(f317(f58(x79351,x79351,f228(x79351)),x79352),f317(f317(f299(x79351),x79353),x79354)),f317(f317(f228(x79351),x79353),f317(f317(f58(x79351,x79351,f228(x79351)),x79352),x79354)))
% 94.68/94.45 [7936]~P66(x79361)+~P1(f317(f28(x79361),x79364))+E(f317(f317(f58(x79361,x79361,f223(x79361)),x79362),f317(f317(f299(x79361),x79363),x79364)),f317(f317(f223(x79361),x79363),f317(f317(f58(x79361,x79361,f223(x79361)),x79362),x79364)))
% 94.68/94.45 [7937]~P99(x79371)+~P1(f317(f28(x79371),x79374))+E(f317(f317(f58(x79371,x79371,f91(x79371)),x79372),f317(f317(f299(x79371),x79373),x79374)),f317(f317(f91(x79371),x79373),f317(f317(f58(x79371,x79371,f91(x79371)),x79372),x79374)))
% 94.68/94.45 [7938]~P105(x79381)+~P1(f317(f28(x79381),x79384))+E(f317(f317(f58(x79381,x79381,f92(x79381)),x79382),f317(f317(f299(x79381),x79383),x79384)),f317(f317(f92(x79381),x79383),f317(f317(f58(x79381,x79381,f92(x79381)),x79382),x79384)))
% 94.68/94.45 [7940]~P95(x79401)+~P131(x79401)+E(f317(f317(f23(x79401),f317(f317(f75(x79401),f317(f94(x79401),x79402)),x79403)),f317(f317(f75(x79401),f317(f94(x79401),x79402)),x79404)),f317(f317(f75(x79401),f317(f94(x79401),x79402)),f317(f317(f23(x79401),x79403),x79404)))
% 94.68/94.45 [7941]~P95(x79411)+~P140(x79411)+E(f317(f317(f74(x79411),f317(f317(f75(x79411),f317(f94(x79411),x79412)),x79413)),f317(f317(f75(x79411),f317(f94(x79411),x79412)),x79414)),f317(f317(f75(x79411),f317(f94(x79411),x79412)),f317(f317(f74(x79411),x79413),x79414)))
% 94.68/94.45 [8056]E(x80561,x80562)+P1(f317(f317(f319(x80563),x80561),f317(f162(x80563),x80564)))+~P1(f317(f317(f319(x80563),x80561),f317(f162(x80563),f317(f317(f141(x80563),x80562),x80564))))
% 94.68/94.45 [8227]P54(x82271,x82272,x82273)+~P54(x82271,x82272,x82274)+~P1(f317(f317(f224(f904(f903(x82271,x82272),a893)),x82273),x82274))
% 94.68/94.45 [8275]P1(f317(f317(f319(x82751),x82752),x82753))+P1(f317(f317(f319(x82751),x82752),x82754))+~P1(f317(f317(f319(x82751),x82752),f317(f317(f91(f904(x82751,a893)),x82754),x82753)))
% 94.68/94.45 [8285]~P52(x82851,x82854,x82853)+~P1(f317(f317(f319(x82851),x82852),x82854))+P1(f317(f317(f319(f903(x82851,x82851)),f317(f317(f242(x82851,x82851),x82852),x82852)),x82853))
% 94.68/94.45 [8297]~P1(f317(f28(x82972),x82974))+~P1(f317(f28(x82971),x82973))+P1(f317(f28(f903(x82971,x82972)),f317(f317(f244(x82971,x82972),x82973),f317(f16(f904(x82972,a893),x82971),x82974))))
% 94.68/94.45 [8298]~P1(f317(f317(f319(x82981),x82982),x82984))+~P1(f317(f317(f224(f904(x82981,a893)),x82983),x82984))+P1(f317(f317(f224(f904(x82981,a893)),f317(f317(f299(x82981),x82982),x82983)),x82984))
% 94.68/94.45 [8305]~P77(x83052)+~P144(x83052)+E(f317(f317(f9(x83051,x83052),f317(f317(f8(a897,x83052,x83051),f90(x83052)),x83053)),x83054),f317(f90(x83052),f317(f317(f9(x83051,a897),x83053),x83054)))
% 94.68/94.45 [8306]~P141(x83062)+~P77(x83062)+E(f317(f317(f9(x83061,x83062),f317(f317(f8(a1,x83062,x83061),f93(x83062)),x83063)),x83064),f317(f93(x83062),f317(f317(f9(x83061,a1),x83063),x83064)))
% 94.68/94.45 [8330]E(f317(f317(f23(f904(x83301,a893)),x83302),f317(f317(f23(f904(x83301,a893)),x83303),x83304)),x83304)+~P1(f317(f317(f224(f904(x83301,a893)),x83302),x83303))+~P1(f317(f317(f224(f904(x83301,a893)),x83304),x83302))
% 94.68/94.45 [8427]~P1(f317(f28(x84271),x84274))+E(f317(f317(f23(a897),f317(f317(f6(x84271,a897),x84272),x84273)),f317(f317(f6(x84271,a897),x84272),x84274)),f317(f317(f6(x84271,a897),x84272),f317(f317(f23(f904(x84271,a893)),x84273),x84274)))+~P1(f317(f317(f224(f904(x84271,a893)),x84274),x84273))
% 94.68/94.45 [8579]~P8(x85791,x85794,x85793)+~P1(f317(f317(f319(x85791),x85792),x85794))+P1(f317(f317(f319(x85791),x85792),f317(f275(x85791,x85791,x85793),f317(f317(f299(x85791),x85792),f178(f904(x85791,a893))))))
% 94.68/94.45 [8640]~P1(f317(f317(f224(f904(x86401,a893)),x86402),x86403))+~P1(f317(f317(f224(f904(x86401,a893)),x86402),x86404))+P1(f317(f317(f224(f904(x86401,a893)),x86402),f317(f317(f92(f904(x86401,a893)),x86403),x86404)))
% 94.68/94.45 [8742]E(x87421,f178(f904(x87422,a893)))+P1(f317(f28(x87423),x87424))+~P1(f317(f28(f903(x87423,x87422)),f317(f317(f244(x87423,x87422),x87424),f317(f16(f904(x87422,a893),x87423),x87421))))
% 94.68/94.45 [8743]E(x87431,f178(f904(x87432,a893)))+P1(f317(f28(x87433),x87434))+~P1(f317(f28(f903(x87432,x87433)),f317(f317(f244(x87432,x87433),x87431),f317(f16(f904(x87433,a893),x87432),x87434))))
% 94.68/94.45 [8816]P1(f317(f317(f319(x88161),x88162),f306(x88161,x88163)))+~P1(f317(f317(f319(x88161),x88164),f306(x88161,x88163)))+~P1(f317(f317(f319(f903(x88161,x88161)),f317(f317(f242(x88161,x88161),x88162),x88164)),x88163))
% 94.68/94.45 [8873]~P36(x88731,x88734)+P1(f317(f317(f319(f903(x88731,x88731)),f317(f317(f242(x88731,x88731),x88733),x88732)),f297(x88731,x88734)))+P36(x88731,f317(f317(f299(f903(x88731,x88731)),f317(f317(f242(x88731,x88731),x88732),x88733)),x88734))
% 94.68/94.45 [8874]~P57(x88741,x88744)+P1(f317(f317(f319(f903(x88741,x88741)),f317(f317(f242(x88741,x88741),x88743),x88742)),f297(x88741,x88744)))+P57(x88741,f317(f317(f299(f903(x88741,x88741)),f317(f317(f242(x88741,x88741),x88742),x88743)),x88744))
% 94.68/94.45 [8956]~E(x89562,x89563)+~P1(f317(f317(f319(x89561),x89562),f317(f162(x89561),x89564)))+P1(f317(f317(f319(f903(x89561,x89561)),f317(f317(f242(x89561,x89561),x89562),x89563)),f317(f162(f903(x89561,x89561)),f317(f317(f171(x89561,x89561),x89564),x89564))))
% 94.68/94.45 [9044]~E(x90443,x90444)+P1(f317(f317(f247(x90441,x90441,a893),a314),x90442))+~P1(f317(f317(f319(f903(x90441,x90441)),x90442),f317(f162(f903(x90441,x90441)),f317(f317(f171(x90441,x90441),x90443),x90444))))
% 94.68/94.45 [9088]P1(f317(f317(f319(f903(f898(x90881),f898(x90881))),f317(f317(f242(f898(x90881),f898(x90881)),x90882),x90883)),f137(x90881,x90884)))+~E(f317(f317(f165(x90881),f317(f179(f898(x90881)),x90882)),x90883),x90882)+~P1(f317(f317(f225(a897),f317(f179(f898(x90881)),x90882)),f317(f179(f898(x90881)),x90883)))
% 94.68/94.45 [9091]~P51(x90911,x90914)+~P1(f317(f317(f319(f903(x90911,x90911)),f317(f317(f242(x90911,x90911),x90913),x90912)),x90914))+P1(f317(f317(f319(f903(x90911,x90911)),f317(f317(f242(x90911,x90911),x90912),x90913)),x90914))
% 94.68/94.45 [9183]~P1(f317(f28(x91831),x91834))+P1(f317(f317(f319(x91831),f431(x91832,x91833,x91834,x91831)),x91834))+P1(f317(f28(x91833),f317(f317(f34(x91831,f904(x91833,a893)),x91834),x91832)))
% 94.68/94.45 [9184]~P1(f317(f28(x91841),x91844))+P1(f317(f317(f319(x91841),f521(x91842,x91843,x91844,x91841)),x91844))+P1(f317(f28(x91843),f317(f317(f34(x91841,f904(x91843,a893)),x91844),x91842)))
% 94.68/94.45 [9269]P1(f317(f317(f319(f903(x92691,x92691)),x92692),f317(f317(f279(x92691,x92691,x92691),x92693),f297(x92691,x92693))))+~P1(f317(f317(f225(a897),f2(a897)),x92694))+~P1(f317(f317(f319(f903(x92691,x92691)),x92692),f317(f317(f173(f903(x92691,x92691),a893),x92694),x92693)))
% 94.68/94.45 [9277]~P36(x92771,x92772)+~P1(f317(f317(f319(f903(x92771,x92771)),f317(f317(f242(x92771,x92771),x92774),x92773)),x92772))+~P1(f317(f317(f319(f903(x92771,x92771)),f317(f317(f242(x92771,x92771),x92773),x92774)),x92772))
% 94.68/94.45 [9407]~P1(f317(f28(x94071),x94074))+E(f317(f317(f6(x94071,a897),f317(f317(f8(f904(x94072,a893),a897,x94071),f29(x94072)),x94073)),x94074),f317(f29(f903(x94071,x94072)),f317(f317(f244(x94071,x94072),x94074),x94073)))+P1(f317(f317(f319(x94071),f474(x94073,x94072,x94074,x94071)),x94074))
% 94.68/94.45 [9411]~P1(f317(f127(x94111),x94112))+P1(f317(f127(x94111),f317(f317(f149(x94111,x94112),x94113),x94114)))+P1(f317(f317(f319(x94111),x94114),f317(f317(f23(f904(x94111,a893)),f317(f162(x94111),x94112)),f317(f317(f299(x94111),f317(f317(f154(x94111),x94112),x94113)),f178(f904(x94111,a893))))))
% 94.68/94.45 [9428]~P1(f317(f28(x94282),x94283))+~P1(f317(f28(x94281),f317(x94284,f431(x94284,x94281,x94283,x94282))))+P1(f317(f28(x94281),f317(f317(f34(x94282,f904(x94281,a893)),x94283),x94284)))
% 94.68/94.45 [9429]~P1(f317(f28(x94292),x94293))+~P1(f317(f28(x94291),f317(x94294,f521(x94294,x94291,x94293,x94292))))+P1(f317(f28(x94291),f317(f317(f34(x94292,f904(x94291,a893)),x94293),x94294)))
% 94.68/94.45 [9507]~P1(f317(f317(f319(f903(x95071,x95071)),x95072),f317(f317(f279(x95071,x95071,x95071),x95074),f297(x95071,x95074))))+P1(f317(f317(f319(f903(x95071,x95071)),x95072),f317(f317(f279(x95071,x95071,x95071),x95073),f297(x95071,x95073))))+~P1(f317(f317(f224(f904(f903(x95071,x95071),a893)),x95074),x95073))
% 94.68/94.45 [9517]E(f317(f317(f165(x95171),f639(x95174,x95173,x95172,x95171)),x95173),f317(f317(f165(x95171),f639(x95174,x95173,x95172,x95171)),x95172))+~P1(f317(f317(f319(f903(f898(x95171),f898(x95171))),f317(f317(f242(f898(x95171),f898(x95171)),x95172),x95173)),f137(x95171,x95174)))+E(f317(f317(f165(x95171),f317(f179(f898(x95171)),x95172)),x95173),x95172)
% 94.68/94.45 [9533]~P1(f317(f28(x95331),x95334))+E(f317(f317(f6(x95331,a897),f317(f317(f8(f904(x95332,a893),a897,x95331),f29(x95332)),x95333)),x95334),f317(f29(f903(x95331,x95332)),f317(f317(f244(x95331,x95332),x95334),x95333)))+~P1(f317(f28(x95332),f317(x95333,f474(x95333,x95332,x95334,x95331))))
% 94.68/94.45 [9537]~E(f317(f179(f898(x95371)),x95373),f317(f179(f898(x95371)),x95372))+P1(f317(f317(f319(f903(f898(x95371),f898(x95371))),f317(f317(f242(f898(x95371),f898(x95371)),x95372),x95373)),f148(x95371,x95374)))+P1(f317(f317(f319(f903(x95371,x95371)),f642(x95374,x95373,x95372,x95371)),f317(f162(f903(x95371,x95371)),f317(f317(f171(x95371,x95371),x95372),x95373))))
% 94.68/94.45 [9626]~P1(f317(f317(f319(f903(f898(x96261),f898(x96261))),f317(f317(f242(f898(x96261),f898(x96261)),x96262),x96263)),f137(x96261,x96264)))+E(f317(f317(f165(x96261),f317(f179(f898(x96261)),x96262)),x96263),x96262)+P1(f317(f317(f225(a897),f639(x96264,x96263,x96262,x96261)),f317(f317(f228(a897),f317(f179(f898(x96261)),x96262)),f317(f179(f898(x96261)),x96263))))
% 94.68/94.45 [9650]~P1(f317(f317(f319(f903(f898(x96501),f898(x96501))),f317(f317(f242(f898(x96501),f898(x96501)),x96502),x96503)),f137(x96501,x96504)))+P1(f317(f317(f225(a897),f317(f179(f898(x96501)),x96502)),f317(f179(f898(x96501)),x96503)))+P1(f317(f317(f225(a897),f639(x96504,x96503,x96502,x96501)),f317(f317(f228(a897),f317(f179(f898(x96501)),x96502)),f317(f179(f898(x96501)),x96503))))
% 94.68/94.45 [10050]~P1(f317(f317(f319(f903(f898(x100501),f898(x100501))),f317(f317(f242(f898(x100501),f898(x100501)),x100502),x100503)),f137(x100501,x100504)))+E(f317(f317(f165(x100501),f317(f179(f898(x100501)),x100502)),x100503),x100502)+P1(f317(f317(f319(f903(x100501,x100501)),f317(f317(f242(x100501,x100501),f317(f317(f154(x100501),x100502),f639(x100504,x100503,x100502,x100501))),f317(f317(f154(x100501),x100503),f639(x100504,x100503,x100502,x100501)))),x100504))
% 94.68/94.45 [10051]~P1(f317(f317(f319(f903(f898(x100511),f898(x100511))),f317(f317(f242(f898(x100511),f898(x100511)),x100512),x100513)),f137(x100511,x100514)))+P1(f317(f317(f225(a897),f317(f179(f898(x100511)),x100512)),f317(f179(f898(x100511)),x100513)))+P1(f317(f317(f319(f903(x100511,x100511)),f317(f317(f242(x100511,x100511),f317(f317(f154(x100511),x100512),f639(x100514,x100513,x100512,x100511))),f317(f317(f154(x100511),x100513),f639(x100514,x100513,x100512,x100511)))),x100514))
% 94.68/94.45 [10118]~E(f317(f179(f898(x101181)),x101182),f317(f179(f898(x101181)),x101183))+P1(f317(f317(f319(f903(f898(x101181),f898(x101181))),f317(f317(f242(f898(x101181),f898(x101181)),x101182),x101183)),f148(x101181,x101184)))+~P1(f317(f317(f319(f903(x101181,x101181)),f317(f317(f242(x101181,x101181),f317(f317(f154(x101181),x101182),f627(x101184,x101183,x101182,x101181))),f317(f317(f154(x101181),x101183),f627(x101184,x101183,x101182,x101181)))),x101184))
% 94.68/94.45 [10266]~P76(x102661)+~P1(f317(f28(x102662),x102664))+E(f317(f155(x102661),f317(f317(f144(x102662,x102661),x102663),f84(f898(x102662),f317(f317(f18(f898(x102662),a893,a893),f317(f317(f8(a893,f904(a893,a893),f898(x102662)),a315),f317(f317(f7(f898(x102662),f904(x102662,a893),a893),f317(f317(f8(f904(x102662,a893),f904(f904(x102662,a893),a893),f898(x102662)),a314),f162(x102662))),x102664))),f127(x102662))))),f221(x102662,x102661,x102663,x102664))
% 94.68/94.45 [7523]~P61(x75232)+E(x75231,f2(x75232))+E(f317(f317(f281(x75232),f317(f317(f74(x75232),x75233),f317(f317(f75(x75232),x75234),x75231))),x75231),f317(f317(f74(x75232),x75234),f317(f317(f281(x75232),x75233),x75231)))
% 94.68/94.45 [7524]~P3(x75242)+E(x75241,f2(x75242))+E(f317(f317(f30(x75242),f317(f317(f74(x75242),x75243),f317(f317(f75(x75242),x75244),x75241))),x75241),f317(f317(f74(x75242),x75244),f317(f317(f30(x75242),x75243),x75241)))
% 94.68/94.45 [7525]~P3(x75252)+E(x75251,f2(x75252))+E(f317(f317(f30(x75252),f317(f317(f74(x75252),x75253),f317(f317(f75(x75252),x75251),x75254))),x75251),f317(f317(f74(x75252),x75254),f317(f317(f30(x75252),x75253),x75251)))
% 94.68/94.45 [7754]~P62(x77542)+E(x77541,f2(x77542))+E(f317(f317(f281(x77542),f317(f317(f23(x77542),x77543),f317(f317(f75(x77542),x77541),x77544))),x77541),f317(f317(f23(x77542),f317(f317(f281(x77542),x77543),x77541)),x77544))
% 94.68/94.45 [7755]~P61(x77552)+E(x77551,f2(x77552))+E(f317(f317(f281(x77552),f317(f317(f74(x77552),x77553),f317(f317(f75(x77552),x77554),x77551))),x77551),f317(f317(f74(x77552),f317(f317(f281(x77552),x77553),x77551)),x77554))
% 94.68/94.45 [7756]~P62(x77562)+E(x77561,f2(x77562))+E(f317(f317(f281(x77562),f317(f317(f74(x77562),x77563),f317(f317(f75(x77562),x77561),x77564))),x77561),f317(f317(f74(x77562),f317(f317(f281(x77562),x77563),x77561)),x77564))
% 94.68/94.45 [8459]~P1(f317(f150(x84591,x84593),x84594))+~P1(f317(f150(x84591,x84592),x84594))+P1(f317(f150(x84591,f317(f317(f92(f904(x84591,a893)),x84592),x84593)),x84594))
% 94.68/94.45 [8831]~E(f317(f317(f279(x88311,x88311,x88311),x88312),x88314),f178(f904(f903(x88311,x88311),a893)))+~E(f317(f317(f279(x88311,x88311,x88311),x88312),x88313),f178(f904(f903(x88311,x88311),a893)))+E(f317(f317(f279(x88311,x88311,x88311),x88312),f317(f317(f91(f904(f903(x88311,x88311),a893)),x88313),x88314)),f178(f904(f903(x88311,x88311),a893)))
% 94.68/94.45 [8957]~P1(f317(f317(f224(f904(x89571,a893)),x89573),x89574))+~P1(f317(f317(f224(f904(x89571,a893)),x89572),x89574))+P1(f317(f317(f224(f904(x89571,a893)),f317(f317(f91(f904(x89571,a893)),x89572),x89573)),x89574))
% 94.68/94.45 [9333]~P1(f317(f28(x93331),x93334))+~P1(f317(f28(x93331),x93333))+E(f317(f317(f23(a897),f317(f317(f74(a897),f317(f317(f6(x93331,a897),x93332),x93333)),f317(f317(f6(x93331,a897),x93332),x93334))),f317(f317(f6(x93331,a897),x93332),f317(f317(f92(f904(x93331,a893)),x93333),x93334))),f317(f317(f6(x93331,a897),x93332),f317(f317(f91(f904(x93331,a893)),x93333),x93334)))
% 94.68/94.45 [9425]~P1(f317(f317(f319(x94251),x94253),x94252))+~P1(f317(f317(f224(f904(x94251,a893)),x94252),f317(f317(f299(x94251),x94253),x94254)))+P1(f317(f317(f224(f904(x94251,a893)),f317(f317(f23(f904(x94251,a893)),x94252),f317(f317(f299(x94251),x94253),f178(f904(x94251,a893))))),x94254))
% 94.68/94.45 [9601]~P1(f317(f317(f319(x96011),x96013),x96012))+P1(f317(f317(f224(f904(x96011,a893)),x96012),f317(f317(f299(x96011),x96013),x96014)))+~P1(f317(f317(f224(f904(x96011,a893)),f317(f317(f23(f904(x96011,a893)),x96012),f317(f317(f299(x96011),x96013),f178(f904(x96011,a893))))),x96014))
% 94.68/94.45 [9690]~P1(f317(f317(f224(a897),x96901),x96903))+~P1(f317(f317(f225(a897),x96902),x96904))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x96901),x96902)),f317(f317(f242(a897,a897),x96903),x96904))),a26))
% 94.68/94.45 [9691]~P1(f317(f317(f224(a897),x96912),x96914))+~P1(f317(f317(f224(a897),x96911),x96913))+P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),f317(f317(f242(a897,a897),x96911),x96912)),f317(f317(f242(a897,a897),x96913),x96914))),a65))
% 94.68/94.45 [9981]~P1(f317(f317(f319(f898(x99811)),x99814),f151(x99811,x99813)))+~P1(f317(f317(f319(f898(x99811)),x99814),f151(x99811,x99812)))+P1(f317(f150(x99811,f317(f317(f92(f904(x99811,a893)),f317(f317(f7(x99811,f904(x99811,a893),a893),f319(x99811)),x99812)),f317(f317(f7(x99811,f904(x99811,a893),a893),f319(x99811)),x99813))),x99814))
% 94.68/94.45 [10084]~P24(x100841,f904(f904(x100841,a893),a893),f317(f317(f7(x100841,f904(f903(x100841,x100841),a893),f904(f904(x100841,a893),a893)),f317(f317(f8(f904(x100841,a893),f904(f904(f903(x100841,x100841),a893),f904(f904(x100841,a893),a893)),x100841),f55(x100841)),f317(f317(f7(x100841,f904(x100841,a893),f904(x100841,a893)),f299(x100841)),f178(f904(x100841,a893))))),x100843),x100842)+~P1(f317(f317(f319(x100841),x100844),x100842))+E(f317(f317(f23(f904(f904(x100841,a893),a893)),f317(f317(f55(x100841),x100842),x100843)),f317(f317(f55(x100841),f317(f317(f299(x100841),x100844),f178(f904(x100841,a893)))),x100843)),f317(f317(f55(x100841),f317(f317(f23(f904(x100841,a893)),x100842),f317(f317(f299(x100841),x100844),f178(f904(x100841,a893))))),x100843))
% 94.68/94.45 [10220]~P52(x102201,x102202,x102204)+~P1(f317(f317(f319(f903(x102201,x102201)),x102203),x102204))+P1(f317(f317(f247(x102201,x102201,a893),f317(f317(f7(x102201,f904(x102201,a893),f904(x102201,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x102201,a893),f904(x102201,a893)),x102201),f8(a893,a893,x102201)),f317(f317(f8(a893,f904(a893,a893),x102201),a315),f317(f317(f7(x102201,f904(x102201,a893),a893),f319(x102201)),x102202)))),f317(f317(f7(x102201,f904(x102201,a893),a893),f319(x102201)),x102202))),x102203))
% 94.68/94.45 [10232]P1(f317(f28(x102321),x102322))+~P1(f317(f28(x102323),f317(f300(x102321,x102323,x102324),x102322)))+~P1(f317(f28(x102321),f317(f252(x102321),f317(f317(f18(x102321,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102321),a315),f317(f317(f7(x102321,f904(x102321,a893),a893),f319(x102321)),x102322))),f317(f317(f7(x102321,x102323,a893),f317(f317(f8(x102323,f904(x102323,a893),x102321),a314),x102324)),f317(x102324,f500(x102324,x102323,x102322,x102321)))))))
% 94.68/94.45 [8211]~P62(x82112)+E(x82111,f2(x82112))+E(f317(f317(f281(x82112),f317(f317(f23(x82112),f317(f317(f75(x82112),x82111),x82113)),x82114)),x82111),f317(f317(f23(x82112),x82113),f317(f317(f281(x82112),x82114),x82111)))
% 94.68/94.45 [8212]~P62(x82122)+E(x82121,f2(x82122))+E(f317(f317(f281(x82122),f317(f317(f74(x82122),f317(f317(f75(x82122),x82121),x82123)),x82124)),x82121),f317(f317(f74(x82122),x82123),f317(f317(f281(x82122),x82124),x82121)))
% 94.68/94.45 [9117]~E(f317(f317(f279(x91171,x91171,x91171),x91173),x91174),f178(f904(f903(x91171,x91171),a893)))+~E(f317(f317(f279(x91171,x91171,x91171),x91172),x91174),f178(f904(f903(x91171,x91171),a893)))+E(f317(f317(f279(x91171,x91171,x91171),f317(f317(f91(f904(f903(x91171,x91171),a893)),x91172),x91173)),x91174),f178(f904(f903(x91171,x91171),a893)))
% 94.68/94.45 [9898]~P1(f317(f150(x98981,x98983),x98984))+~P1(f317(f150(x98981,x98982),x98984))+P1(f317(f150(x98981,f317(f317(f18(x98981,a893,a893),f317(f317(f8(a893,f904(a893,a893),x98981),a315),x98982)),x98983)),x98984))
% 94.68/94.45 [10158]P1(f317(x101581,f493(x101582,x101583,x101581,x101584)))+~P1(f317(f28(x101584),f317(f252(x101584),x101581)))+P1(f317(f28(x101583),f317(f252(x101583),f317(f317(f8(f904(x101584,a893),a893,x101583),f81(x101584)),f317(f317(f8(f904(x101584,a893),f904(x101584,a893),x101583),f317(f18(x101584,a893,a893),f317(f317(f8(a893,f904(a893,a893),x101584),a315),x101581))),x101582)))))
% 94.68/94.45 [10176]~P1(f317(f28(x101762),f317(f252(x101762),x101763)))+~P1(f317(f28(x101761),f317(f252(x101761),f317(f317(f7(x101761,x101762,a893),x101764),f493(x101764,x101761,x101763,x101762)))))+P1(f317(f28(x101761),f317(f252(x101761),f317(f317(f8(f904(x101762,a893),a893,x101761),f81(x101762)),f317(f317(f8(f904(x101762,a893),f904(x101762,a893),x101761),f317(f18(x101762,a893,a893),f317(f317(f8(a893,f904(a893,a893),x101762),a315),x101763))),x101764)))))
% 94.68/94.45 [10245]~P1(f317(f28(x102451),x102454))+P1(f317(f317(f319(x102451),f773(x102452,x102453,x102454,x102451)),x102454))+P1(f317(f28(x102453),f317(f252(x102453),f317(f317(f8(f904(x102451,a893),a893,x102453),f81(x102451)),f317(f317(f8(f904(x102451,a893),f904(x102451,a893),x102453),f317(f18(x102451,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102451),a315),f317(f317(f7(x102451,f904(x102451,a893),a893),f319(x102451)),x102454)))),x102452)))))
% 94.68/94.45 [10251]~P1(f317(f28(x102512),x102513))+~P1(f317(f28(x102511),f317(f252(x102511),f317(f317(f7(x102511,x102512,a893),x102514),f773(x102514,x102511,x102513,x102512)))))+P1(f317(f28(x102511),f317(f252(x102511),f317(f317(f8(f904(x102512,a893),a893,x102511),f81(x102512)),f317(f317(f8(f904(x102512,a893),f904(x102512,a893),x102511),f317(f18(x102512,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102512),a315),f317(f317(f7(x102512,f904(x102512,a893),a893),f319(x102512)),x102513)))),x102514)))))
% 94.68/94.45 [5102]~E(x51022,x51024)+E(f159(x51021,x51022,x51023),f159(x51021,x51024,x51025))+~E(x51022,f2(a897))
% 94.68/94.45 [5349]E(x53491,x53492)+~E(f159(x53494,x53493,x53491),f159(x53494,x53495,x53492))+E(x53493,f2(a897))
% 94.68/94.45 [6644]E(x66441,x66442)+~E(f317(x66443,x66441),f317(x66443,x66442))+~P24(x66444,x66445,x66443,f232(f904(x66444,a893)))
% 94.68/94.45 [7555]E(x75551,x75552)+~P24(x75553,x75554,x75555,f232(f904(x75553,a893)))+~E(f317(f300(x75553,x75554,x75555),x75551),f317(f300(x75553,x75554,x75555),x75552))
% 94.68/94.45 [7809]P24(x78092,x78093,f355(x78094,x78093,x78092,x78091),x78091)+~E(f317(f300(x78093,x78092,x78095),x78094),x78091)+E(x78091,f178(f904(x78092,a893)))
% 94.68/94.45 [8341]~P1(f317(f317(x83413,x83412),x83415))+~P1(f317(f317(x83413,x83414),x83412))+P1(f317(f317(f319(x83411),x83412),f280(x83411,x83413,x83414,x83415)))
% 94.68/94.45 [8342]~P1(f317(f317(x83423,x83422),x83425))+~P1(f317(f317(x83423,x83424),x83422))+P1(f317(f317(f319(x83421),x83422),f289(x83421,x83423,x83424,x83425)))
% 94.68/94.45 [8648]~P24(x86481,x86482,x86483,x86484)+P25(x86481,x86482,x86483,x86484,x86485)+~E(f317(f300(x86481,x86482,x86483),x86484),x86485)
% 94.68/94.45 [8781]~P25(x87811,x87813,x87814,x87812,x87815)+~P1(f317(f28(x87813),x87815))+P1(f317(f28(x87811),x87812))
% 94.68/94.45 [8782]~P25(x87823,x87821,x87824,x87825,x87822)+~P1(f317(f28(x87823),x87825))+P1(f317(f28(x87821),x87822))
% 94.68/94.45 [8914]~P24(x89141,x89143,x89145,f232(f904(x89141,a893)))+~P24(x89143,x89142,x89144,f232(f904(x89143,a893)))+P24(x89141,x89142,f317(f67(x89143,x89142,x89141,x89144),x89145),f232(f904(x89141,a893)))
% 94.68/94.45 [9484]P1(f317(f317(f319(f903(x94841,x94841)),f317(f317(f242(x94841,x94841),x94842),x94843)),f297(x94841,x94844)))+~P1(f317(f317(f319(f903(x94841,x94841)),f317(f317(f242(x94841,x94841),x94842),x94845)),f297(x94841,x94844)))+~P1(f317(f317(f319(f903(x94841,x94841)),f317(f317(f242(x94841,x94841),x94845),x94843)),f297(x94841,x94844)))
% 94.68/94.45 [9524]~P66(x95242)+~P1(f317(f127(x95241),x95245))+P1(f317(f127(x95241),f139(x95241,x95242,x95243,x95244,x95245)))
% 94.68/94.45 [5426]~E(x54262,f103(x54261))+E(f317(f317(f124(x54261),x54262),x54263),f317(f317(f141(x54261),x54264),x54265))+~E(x54263,f317(f317(f141(x54261),x54264),x54265))
% 94.68/94.45 [5427]~E(x54272,f103(x54271))+E(f317(f317(f124(x54271),x54272),x54273),f317(f317(f141(x54271),x54274),x54275))+~E(f317(f317(f141(x54271),x54274),x54275),x54273)
% 94.68/94.45 [6600]~E(f317(f179(f898(x66001)),x66005),f317(f179(f898(x66002)),x66004))+E(f317(f317(f144(f903(x66001,x66002),x66002),f246(x66001,x66002)),x66003),x66004)+~E(f317(f317(f171(x66001,x66002),x66005),x66004),x66003)
% 94.68/94.45 [6601]~E(f317(f179(f898(x66011)),x66014),f317(f179(f898(x66012)),x66015))+E(f317(f317(f144(f903(x66011,x66012),x66011),f241(x66011,x66012)),x66013),x66014)+~E(f317(f317(f171(x66011,x66012),x66014),x66015),x66013)
% 94.68/94.45 [7091]~P66(x70911)+~P13(x70911,f317(f317(f144(x70912,x70911),x70913),x70915))+P13(x70911,f317(f317(f144(x70912,x70911),x70913),f317(f126(x70912,x70914),x70915)))
% 94.68/94.45 [7233]~P66(x72331)+P13(x72331,f317(f317(f144(x72332,x72331),x72333),f160(x72332,x72334,x72335)))+~P13(x72331,f317(f317(f144(x72332,x72331),x72333),x72335))
% 94.68/94.45 [7256]~P54(x72563,x72562,x72565)+~P54(x72561,x72563,x72564)+P54(x72561,x72562,f317(f317(f279(x72561,x72563,x72562),x72564),x72565))
% 94.68/94.45 [7351]E(x73511,x73512)+~P24(x73513,x73514,x73515,f232(f904(x73513,a893)))+~E(f317(f317(f144(x73513,x73514),x73515),x73511),f317(f317(f144(x73513,x73514),x73515),x73512))
% 94.68/94.45 [7510]~P1(f317(f317(f224(a897),x75101),f317(x75103,x75105)))+P1(f317(f317(f224(a897),x75101),f145(x75102,x75103,x75104)))+~P1(f317(f317(f319(x75102),x75105),f317(f162(x75102),x75104)))
% 94.68/94.45 [7511]~P1(f317(f317(f225(a897),x75111),f317(x75113,x75115)))+P1(f317(f317(f225(a897),x75111),f145(x75112,x75113,x75114)))+~P1(f317(f317(f319(x75112),x75115),f317(f162(x75112),x75114)))
% 94.68/94.45 [7906]P1(f317(x79061,x79062))+~P1(f317(x79061,x79063))+~P1(f317(f317(f319(x79064),x79062),f317(f162(x79064),f159(x79064,x79065,x79063))))
% 94.68/94.45 [7907]P1(f317(x79071,x79072))+~P1(f317(x79071,x79073))+~P1(f317(f317(f319(x79074),x79073),f317(f162(x79074),f159(x79074,x79075,x79072))))
% 94.68/94.45 [7912]~P108(x79121)+P1(f317(f317(f224(f904(x79121,a893)),f293(x79121,x79122,x79123)),f293(x79121,x79124,x79125)))+P1(f317(f317(f224(x79121),x79122),x79123))
% 94.68/94.45 [7933]~P5(x79331)+P1(f317(f317(f224(x79331),f317(f317(f35(x79332,x79331),x79333),x79334)),f317(x79334,x79335)))+~P1(f317(f317(f319(x79332),x79335),x79333))
% 94.68/94.45 [8002]~P24(x80021,x80022,x80024,x80023)+E(f317(f71(x80021,x80022,x80023,x80024),f317(x80024,x80025)),x80025)+~P1(f317(f317(f319(x80021),x80025),x80023))
% 94.68/94.45 [8003]~P24(x80031,x80032,x80034,x80033)+E(f317(f85(x80031,x80032,x80033,x80034),f317(x80034,x80035)),x80035)+~P1(f317(f317(f319(x80031),x80035),x80033))
% 94.68/94.45 [8200]~P1(f317(x82001,x82005))+P1(f317(x82001,f325(x82001,x82002,x82003,x82004)))+~P1(f317(f317(f319(x82004),x82005),x82003))
% 94.68/94.45 [8201]~P1(f317(x82011,x82015))+P1(f317(x82011,f325(x82011,x82012,x82013,x82014)))+~P1(f317(f317(f319(x82014),x82015),x82012))
% 94.68/94.45 [8295]P1(f317(f28(x82951),x82952))+~P1(f317(f28(x82953),x82954))+~P1(f317(f317(f224(f904(x82951,a893)),x82952),f317(f300(x82953,x82951,x82955),x82954)))
% 94.68/94.45 [8463]E(x84631,x84632)+~P24(x84633,x84634,x84635,f317(f317(f91(f904(x84633,a893)),f317(f162(x84633),x84631)),f317(f162(x84633),x84632)))+~E(f317(f317(f144(x84633,x84634),x84635),x84631),f317(f317(f144(x84633,x84634),x84635),x84632))
% 94.68/94.45 [8516]~P108(x85161)+~P1(f317(f317(f225(f904(x85161,a893)),f293(x85161,x85164,x85165)),f293(x85161,x85162,x85163)))+P1(f317(f317(f224(x85161),x85162),x85163))
% 94.68/94.45 [8578]~P24(x85781,x85784,x85785,f232(f904(x85781,a893)))+~P1(f317(f317(f319(x85784),f317(x85785,x85782)),f317(f300(x85781,x85784,x85785),x85783)))+P1(f317(f317(f319(x85781),x85782),x85783))
% 94.68/94.45 [8654]P1(f317(x86541,x86542))+~P1(f317(x86541,f329(x86541,x86543,x86544,x86545)))+~P1(f317(f317(f319(x86545),x86542),x86544))
% 94.68/94.45 [8655]P1(f317(x86551,x86552))+~P1(f317(x86551,f329(x86551,x86553,x86554,x86555)))+~P1(f317(f317(f319(x86555),x86552),x86553))
% 94.68/94.45 [8954]~P24(x89542,x89543,x89541,x89544)+E(f317(x89541,f317(f71(x89542,x89543,x89544,x89541),x89545)),x89545)+~P1(f317(f317(f319(x89543),x89545),f317(f300(x89542,x89543,x89541),x89544)))
% 94.68/94.45 [9057]E(x90571,f103(x90572))+E(f317(f317(f141(x90572),x90573),f656(x90574,x90573,x90575,x90571,x90572)),x90571)+~E(f317(f317(f124(x90572),x90571),x90575),f317(f317(f141(x90572),x90573),x90574))
% 94.68/94.45 [9058]E(x90581,f103(x90582))+E(f317(f317(f141(x90582),x90583),f657(x90584,x90581,x90585,x90583,x90582)),x90581)+~E(f317(f317(f124(x90582),x90581),x90584),f317(f317(f141(x90582),x90583),x90585))
% 94.68/94.45 [9076]E(f317(f317(f141(x90762),x90763),f656(x90764,x90763,x90761,x90765,x90762)),x90765)+~E(f317(f317(f124(x90762),x90765),x90761),f317(f317(f141(x90762),x90763),x90764))+E(x90761,f317(f317(f141(x90762),x90763),x90764))
% 94.68/94.45 [9077]E(f317(f317(f141(x90771),x90772),f657(x90774,x90775,x90773,x90772,x90771)),x90775)+~E(f317(f317(f124(x90771),x90775),x90774),f317(f317(f141(x90771),x90772),x90773))+E(f317(f317(f141(x90771),x90772),x90773),x90774)
% 94.68/94.45 [9154]~E(f317(f300(x91543,x91542,x91544),f232(f904(x91543,a893))),f232(f904(x91542,a893)))+~E(f317(f300(x91541,x91543,x91545),f232(f904(x91541,a893))),f232(f904(x91543,a893)))+E(f317(f300(x91541,x91542,f317(f67(x91543,x91542,x91541,x91544),x91545)),f232(f904(x91541,a893))),f232(f904(x91542,a893)))
% 94.68/94.45 [9530]E(x95301,f103(x95302))+~E(f317(f317(f124(x95302),x95301),x95303),f317(f317(f141(x95302),x95305),x95304))+E(f317(f317(f124(x95302),f657(x95303,x95301,x95304,x95305,x95302)),x95303),x95304)
% 94.68/94.45 [9531]E(x95311,f103(x95312))+~E(f317(f317(f124(x95312),x95311),x95315),f317(f317(f141(x95312),x95314),x95313))+E(f317(f317(f124(x95312),f656(x95313,x95314,x95315,x95311,x95312)),x95315),x95313)
% 94.68/94.45 [9538]E(f317(f317(f124(x95382),f656(x95384,x95383,x95381,x95385,x95382)),x95381),x95384)+~E(f317(f317(f124(x95382),x95385),x95381),f317(f317(f141(x95382),x95383),x95384))+E(x95381,f317(f317(f141(x95382),x95383),x95384))
% 94.68/94.45 [9539]~E(f317(f317(f124(x95391),x95395),x95394),f317(f317(f141(x95391),x95392),x95393))+E(f317(f317(f124(x95391),f657(x95394,x95395,x95393,x95392,x95391)),x95394),x95393)+E(f317(f317(f141(x95391),x95392),x95393),x95394)
% 94.68/94.45 [9540]E(f317(f317(f124(x95401),x95405),f661(x95403,x95402,x95404,x95405,x95401)),x95402)+E(f317(f317(f124(x95401),x95402),f660(x95403,x95402,x95404,x95405,x95401)),x95405)+~E(f317(f317(f124(x95401),x95405),x95404),f317(f317(f124(x95401),x95402),x95403))
% 94.68/94.45 [9577]~P66(x95771)+P13(x95771,f317(f317(f144(x95772,x95771),x95773),f139(x95772,x95771,x95773,x95774,x95775)))+~P13(x95771,f317(f317(f144(x95772,x95771),x95773),x95775))
% 94.68/94.45 [9596]~P58(x95965,x95961,x95964,x95963)+P1(f317(f317(x95961,x95962),f464(x95963,x95964,x95961,x95965,x95962)))+~P1(f317(f317(f319(x95965),x95962),x95964))
% 94.68/94.45 [9597]~P58(x95975,x95971,x95974,x95973)+P1(f317(f317(x95971,x95972),f777(x95973,x95974,x95971,x95975,x95972)))+~P1(f317(f317(f319(x95975),x95972),x95974))
% 94.68/94.45 [9702]~P1(f317(f317(f319(f903(x97021,x97021)),f317(f317(f242(x97021,x97021),x97025),x97023)),f297(x97021,x97024)))+P1(f317(f317(f319(f903(x97021,x97021)),f317(f317(f242(x97021,x97021),x97022),x97023)),f317(f317(f279(x97021,x97021,x97021),x97024),f297(x97021,x97024))))+~P1(f317(f317(f319(f903(x97021,x97021)),f317(f317(f242(x97021,x97021),x97022),x97025)),f317(f317(f279(x97021,x97021,x97021),x97024),f297(x97021,x97024))))
% 94.68/94.45 [9703]~P1(f317(f317(f319(f903(x97031,x97031)),f317(f317(f242(x97031,x97031),x97032),x97035)),f297(x97031,x97034)))+P1(f317(f317(f319(f903(x97031,x97031)),f317(f317(f242(x97031,x97031),x97032),x97033)),f317(f317(f279(x97031,x97031,x97031),x97034),f297(x97031,x97034))))+~P1(f317(f317(f319(f903(x97031,x97031)),f317(f317(f242(x97031,x97031),x97035),x97033)),f317(f317(f279(x97031,x97031,x97031),x97034),f297(x97031,x97034))))
% 94.68/94.45 [9705]P1(f317(f317(f319(f903(f898(x97051),f898(x97051))),f317(f317(f242(f898(x97051),f898(x97051)),x97052),x97053)),f148(x97051,f297(x97051,x97054))))+~P1(f317(f317(f319(f903(f898(x97051),f898(x97051))),f317(f317(f242(f898(x97051),f898(x97051)),x97052),x97055)),f148(x97051,f297(x97051,x97054))))+~P1(f317(f317(f319(f903(f898(x97051),f898(x97051))),f317(f317(f242(f898(x97051),f898(x97051)),x97055),x97053)),f148(x97051,f297(x97051,x97054))))
% 94.68/94.45 [9709]E(f317(f317(f124(x97091),x97092),f660(x97093,x97092,x97094,x97095,x97091)),x97095)+E(f317(f317(f124(x97091),f661(x97093,x97092,x97094,x97095,x97091)),x97093),x97094)+~E(f317(f317(f124(x97091),x97092),x97093),f317(f317(f124(x97091),x97095),x97094))
% 94.68/94.45 [9710]E(f317(f317(f124(x97101),x97102),f661(x97103,x97104,x97105,x97102,x97101)),x97104)+E(f317(f317(f124(x97101),f660(x97103,x97104,x97105,x97102,x97101)),x97105),x97103)+~E(f317(f317(f124(x97101),x97102),x97105),f317(f317(f124(x97101),x97104),x97103))
% 94.68/94.45 [9764]P1(f317(f317(f319(f903(x97641,x97641)),f317(f317(f242(x97641,x97641),x97642),x97643)),f317(f317(f279(x97641,x97641,x97641),x97644),f297(x97641,x97644))))+~P1(f317(f317(f319(f903(x97641,x97641)),f317(f317(f242(x97641,x97641),x97642),x97645)),f317(f317(f279(x97641,x97641,x97641),x97644),f297(x97641,x97644))))+~P1(f317(f317(f319(f903(x97641,x97641)),f317(f317(f242(x97641,x97641),x97645),x97643)),f317(f317(f279(x97641,x97641,x97641),x97644),f297(x97641,x97644))))
% 94.68/94.45 [9791]P33(x97911,x97912,x97913,x97914,x97915)+~E(f317(f179(f898(x97911)),x97914),f317(f179(f898(x97912)),x97915))+~P1(f317(f317(f247(x97911,x97912,a893),x97913),f677(x97915,x97914,x97913,x97912,x97911)))
% 94.68/94.45 [9792]P33(x97921,x97922,x97923,x97924,x97925)+~E(f317(f179(f898(x97921)),x97924),f317(f179(f898(x97922)),x97925))+~P1(f317(f317(f247(x97921,x97922,a893),x97923),f678(x97923,x97925,x97924,x97922,x97921)))
% 94.68/94.45 [9797]E(f317(f317(f124(x97971),f660(x97972,x97973,x97974,x97975,x97971)),x97974),x97972)+~E(f317(f317(f124(x97971),x97973),x97972),f317(f317(f124(x97971),x97975),x97974))+E(f317(f317(f124(x97971),f661(x97972,x97973,x97974,x97975,x97971)),x97972),x97974)
% 94.68/94.45 [9812]~P66(x98122)+E(f317(f317(f138(x98121,x98122,x98123),x98124),x98125),f317(f317(f141(x98121),x98124),x98125))+P1(f317(f317(f319(x98121),f722(x98124,x98123,x98125,x98121,x98122)),f317(f162(x98121),x98125)))
% 94.68/94.45 [9816]~P58(x98161,x98164,x98163,x98162)+~P1(f317(f317(f319(x98161),x98165),x98163))+P1(f317(f317(f319(x98161),f464(x98162,x98163,x98164,x98161,x98165)),x98162))
% 94.68/94.45 [9817]~P58(x98171,x98174,x98173,x98172)+~P1(f317(f317(f319(x98171),x98175),x98173))+P1(f317(f317(f319(x98171),f777(x98172,x98173,x98174,x98171,x98175)),x98172))
% 94.68/94.45 [9931]~P1(f317(f317(f319(f903(f904(x99311,a893),f904(x99311,a893))),f317(f317(f242(f904(x99311,a893),f904(x99311,a893)),x99314),x99313)),f308(x99311,x99312)))+~P1(f317(f317(f319(x99311),x99315),x99314))+P1(f317(f317(f319(x99311),f543(x99312,x99313,x99314,x99311,x99315)),x99313))
% 94.68/94.45 [9941]~P66(x99412)+E(f317(f317(f138(x99411,x99412,x99413),x99414),x99415),f317(f317(f141(x99411),x99414),x99415))+~P1(f317(f317(f224(x99412),f317(x99413,x99414)),f317(x99413,f722(x99414,x99413,x99415,x99411,x99412))))
% 94.68/94.45 [9990]~P24(x99903,x99904,x99905,f232(f904(x99903,a893)))+P1(f317(x99901,x99902))+~P1(f317(x99901,f317(f85(x99903,x99904,f232(f904(x99903,a893)),x99905),f791(x99902,x99901,x99905,x99904,x99903))))
% 94.68/94.45 [10135]P33(x101351,x101352,x101353,x101354,x101355)+~E(f317(f179(f898(x101351)),x101354),f317(f179(f898(x101352)),x101355))+~P1(f317(f317(x101353,f317(f317(f154(x101351),x101354),f679(x101355,x101354,x101353,x101352,x101351))),f317(f317(f154(x101352),x101355),f679(x101355,x101354,x101353,x101352,x101351))))
% 94.68/94.45 [10136]P33(x101361,x101362,x101363,x101364,x101365)+~E(f317(f179(f898(x101361)),x101364),f317(f179(f898(x101362)),x101365))+~P1(f317(f317(x101363,f317(f317(f154(x101361),x101364),f714(x101363,x101365,x101362,x101364,x101361))),f317(f317(f154(x101362),x101365),f714(x101363,x101365,x101362,x101364,x101361))))
% 94.68/94.45 [6675]~P17(x66752,x66755,x66751)+~P1(f317(f28(x66752),x66754))+E(f317(x66751,f317(f317(f299(x66752),x66753),x66754)),f317(f317(f58(x66752,x66752,x66755),x66753),x66754))
% 94.68/94.45 [6676]~E(x66763,x66764)+~E(x66762,x66765)+E(f317(f317(f299(x66761),x66762),f317(f317(f299(x66761),x66763),f178(f904(x66761,a893)))),f317(f317(f299(x66761),x66764),f317(f317(f299(x66761),x66765),f178(f904(x66761,a893)))))
% 94.68/94.45 [6687]P1(f317(x66872,x66875))+E(f167(x66871,x66872,f317(f317(f124(x66871),x66873),x66874)),f167(x66871,x66872,x66873))+~P1(f317(f317(f319(x66871),x66875),f317(f162(x66871),x66873)))
% 94.68/94.45 [6725]E(f317(x67251,x67252),f178(f904(x67253,a893)))+~E(f317(f317(f34(x67254,f904(x67253,a893)),x67255),x67251),f178(f904(x67253,a893)))+~P1(f317(f317(f319(x67254),x67252),x67255))
% 94.68/94.45 [6726]E(f317(x67261,x67262),f232(f904(x67263,a893)))+~E(f317(f317(f35(x67264,f904(x67263,a893)),x67265),x67261),f232(f904(x67263,a893)))+~P1(f317(f317(f319(x67264),x67262),x67265))
% 94.68/94.45 [7243]~E(x72432,x72434)+~P146(x72431)+E(f317(f317(f74(x72431),f317(f317(f75(x72431),x72432),x72433)),f317(f317(f75(x72431),x72434),x72435)),f317(f317(f74(x72431),f317(f317(f75(x72431),x72432),x72435)),f317(f317(f75(x72431),x72434),x72433)))
% 94.68/94.45 [7305]~P5(x73051)+~P1(f317(f317(f319(x73054),x73053),x73055))+P1(f317(f317(f224(x73051),f317(x73052,x73053)),f317(f317(f34(x73054,x73051),x73055),x73052)))
% 94.68/94.45 [7356]~P109(x73561)+P1(f317(f317(f224(x73561),f317(x73562,x73563)),f317(x73564,x73563)))+~P1(f317(f317(f224(f904(x73565,x73561)),x73562),x73564))
% 94.68/94.45 [7479]E(x74791,x74792)+E(x74793,x74791)+~E(f317(f317(f299(x74794),x74791),f317(f317(f299(x74794),x74795),f178(f904(x74794,a893)))),f317(f317(f299(x74794),x74792),f317(f317(f299(x74794),x74793),f178(f904(x74794,a893)))))
% 94.68/94.45 [7480]E(x74801,x74802)+E(x74803,x74801)+~E(f317(f317(f299(x74804),x74803),f317(f317(f299(x74804),x74802),f178(f904(x74804,a893)))),f317(f317(f299(x74804),x74805),f317(f317(f299(x74804),x74801),f178(f904(x74804,a893)))))
% 94.68/94.45 [7481]E(x74811,x74812)+E(x74811,x74813)+~E(f317(f317(f299(x74814),x74813),f317(f317(f299(x74814),x74812),f178(f904(x74814,a893)))),f317(f317(f299(x74814),x74815),f317(f317(f299(x74814),x74811),f178(f904(x74814,a893)))))
% 94.68/94.45 [7482]E(x74821,x74822)+E(x74821,x74823)+~E(f317(f317(f299(x74824),x74821),f317(f317(f299(x74824),x74825),f178(f904(x74824,a893)))),f317(f317(f299(x74824),x74822),f317(f317(f299(x74824),x74823),f178(f904(x74824,a893)))))
% 94.68/94.45 [8012]P24(x80121,x80122,x80123,x80124)+~P24(x80121,x80122,x80123,x80125)+~P1(f317(f317(f224(f904(x80121,a893)),x80124),x80125))
% 94.68/94.45 [8042]~E(f317(x80423,x80425),x80424)+~P24(x80421,x80422,x80423,f232(f904(x80421,a893)))+E(f317(f85(x80421,x80422,f232(f904(x80421,a893)),x80423),x80424),x80425)
% 94.68/94.45 [8188]E(x81881,x81882)+~E(f317(f300(x81883,x81884,x81885),x81881),f317(f300(x81883,x81884,x81885),x81882))+~P24(x81883,x81884,x81885,f317(f317(f91(f904(x81883,a893)),x81881),x81882))
% 94.68/94.45 [8265]P1(f317(x82652,x82654))+E(f317(f317(f128(x82651),f317(f179(f898(x82651)),f167(x82651,x82652,x82653))),x82653),f317(f317(f141(x82651),x82654),x82655))+~E(f317(f317(f124(x82651),f167(x82651,x82652,x82653)),f317(f317(f141(x82651),x82654),x82655)),x82653)
% 94.68/94.45 [8293]~P24(x82931,x82932,x82933,x82935)+~P24(x82931,x82932,x82933,x82934)+P24(x82931,x82932,x82933,f317(f317(f92(f904(x82931,a893)),x82934),x82935))
% 94.68/94.45 [8401]~P76(x84011)+E(f317(f317(f74(x84011),f317(x84012,x84013)),f317(f155(x84011),f317(f317(f144(x84014,x84011),x84012),f160(x84014,x84013,x84015)))),f317(f155(x84011),f317(f317(f144(x84014,x84011),x84012),x84015)))+~P1(f317(f317(f319(x84014),x84013),f317(f162(x84014),x84015)))
% 94.68/94.45 [8489]~P66(x84891)+~P13(x84891,f317(f317(f144(x84892,x84891),x84893),x84895))+P13(x84891,f317(f317(f144(x84892,x84891),x84893),f317(f317(f138(x84892,x84891,x84893),x84894),x84895)))
% 94.68/94.45 [8574]~P5(x85741)+P1(f317(f317(f224(x85741),f317(f317(f34(x85742,x85741),x85743),x85744)),f317(f317(f34(x85742,x85741),x85745),x85744)))+~P1(f317(f317(f224(f904(x85742,a893)),x85743),x85745))
% 94.68/94.45 [8575]~P5(x85751)+P1(f317(f317(f224(x85751),f317(f317(f35(x85752,x85751),x85753),x85754)),f317(f317(f35(x85752,x85751),x85755),x85754)))+~P1(f317(f317(f224(f904(x85752,a893)),x85755),x85753))
% 94.68/94.45 [8608]~P66(x86083)+P1(f317(f127(x86081),x86082))+~P1(f317(f127(x86081),f317(f317(f138(x86081,x86083,x86084),x86085),x86082)))
% 94.68/94.45 [8753]~P66(x87531)+~P1(f317(f317(f319(x87532),x87533),f317(f162(x87532),x87534)))+~P1(f317(f127(x87532),f317(f317(f138(x87532,x87531,x87535),x87533),x87534)))
% 94.68/94.45 [8843]~P66(x88431)+P13(x88431,f317(f317(f144(x88432,x88431),x88433),x88434))+~P13(x88431,f317(f317(f144(x88432,x88431),x88433),f317(f317(f138(x88432,x88431,x88433),x88435),x88434)))
% 94.68/94.45 [8889]~P24(x88892,x88891,x88894,x88893)+E(f317(f300(x88891,x88892,f85(x88892,x88891,x88893,x88894)),f317(f300(x88892,x88891,x88894),x88895)),x88895)+~P1(f317(f317(f224(f904(x88892,a893)),x88895),x88893))
% 94.68/94.45 [8942]~P66(x89422)+E(f317(f317(f138(x89421,x89422,x89423),x89424),x89425),f139(x89421,x89422,x89423,x89424,x89425))+P1(f317(f317(f319(x89422),f317(x89423,x89424)),f317(f300(x89421,x89422,x89423),f317(f162(x89421),x89425))))
% 94.68/94.45 [9023]~P66(x90232)+E(f139(x90231,x90232,x90233,x90234,x90235),x90235)+~P1(f317(f317(f319(x90232),f317(x90233,x90234)),f317(f300(x90231,x90232,x90233),f317(f162(x90231),x90235))))
% 94.68/94.45 [9037]~P24(x90372,x90371,x90373,x90375)+P1(f317(f317(f225(f904(x90371,a893)),f317(f300(x90372,x90371,x90373),x90374)),f317(f300(x90372,x90371,x90373),x90375)))+~P1(f317(f317(f225(f904(x90372,a893)),x90374),x90375))
% 94.68/94.45 [9195]~P24(x91951,x91952,x91953,f232(f904(x91951,a893)))+~P1(f317(f317(f224(f904(x91952,a893)),x91954),f317(f300(x91951,x91952,x91953),x91955)))+P1(f317(f317(f224(f904(x91951,a893)),f317(f301(x91951,x91952,x91953),x91954)),x91955))
% 94.68/94.45 [9218]~E(f317(f300(x92183,x92181,x92184),f232(f904(x92183,a893))),f232(f904(x92181,a893)))+P1(f317(f317(f224(f904(x92181,a893)),x92182),f317(f300(x92183,x92181,x92184),x92185)))+~P1(f317(f317(f224(f904(x92183,a893)),f317(f301(x92183,x92181,x92184),x92182)),x92185))
% 94.68/94.45 [9325]~P24(x93251,x93254,x93255,f232(f904(x93251,a893)))+~P1(f317(f317(f224(f904(x93254,a893)),f317(f300(x93251,x93254,x93255),x93252)),f317(f300(x93251,x93254,x93255),x93253)))+P1(f317(f317(f224(f904(x93251,a893)),x93252),x93253))
% 94.68/94.45 [9452]~P81(x94521)+~E(f317(x94523,f697(x94523,x94524,x94525,x94522,x94521)),f2(x94521))+E(f317(f155(x94521),f317(f317(f144(x94522,x94521),x94523),f317(f126(x94522,x94524),x94525))),f317(f155(x94521),f317(f317(f144(x94522,x94521),x94523),x94525)))
% 94.68/94.45 [9479]~P25(x94791,x94792,x94793,f232(f904(x94791,a893)),f232(f904(x94792,a893)))+~P1(f317(f317(f224(f904(x94792,a893)),x94794),f317(f300(x94791,x94792,x94793),x94795)))+P1(f317(f317(f224(f904(x94791,a893)),f317(f301(x94791,x94792,x94793),x94794)),x94795))
% 94.68/94.45 [9508]~P25(x95083,x95081,x95084,f232(f904(x95083,a893)),f232(f904(x95081,a893)))+P1(f317(f317(f224(f904(x95081,a893)),x95082),f317(f300(x95083,x95081,x95084),x95085)))+~P1(f317(f317(f224(f904(x95083,a893)),f317(f301(x95083,x95081,x95084),x95082)),x95085))
% 94.68/94.45 [9643]~P16(x96431,x96432,x96433)+~P1(f317(f28(x96431),x96435))+P1(f317(f60(x96431,x96432,x96433,x96434,x96435),f317(f317(f58(x96431,x96432,x96433),x96434),x96435)))
% 94.68/94.45 [9722]~P25(x97222,x97221,x97224,f232(f904(x97222,a893)),f232(f904(x97221,a893)))+~P25(x97221,x97223,x97225,f232(f904(x97221,a893)),f232(f904(x97223,a893)))+E(f317(f67(x97221,x97222,x97223,f85(x97222,x97221,f232(f904(x97222,a893)),x97224)),f85(x97221,x97223,f232(f904(x97221,a893)),x97225)),f85(x97222,x97223,f232(f904(x97222,a893)),f317(f67(x97221,x97223,x97222,x97225),x97224)))
% 94.68/94.45 [9723]P1(f317(x97231,f618(x97232,x97231,x97233,x97234,x97235)))+~P1(f317(f317(f224(f904(x97235,a893)),x97234),x97233))+P1(f317(f317(f224(f904(x97235,a893)),f317(f317(f92(f904(x97235,a893)),x97234),f317(f252(x97235),x97231))),f317(f317(f92(f904(x97235,a893)),x97233),f317(f252(x97235),x97232))))
% 94.68/94.45 [9737]~P81(x97371)+~P1(f317(x97374,f697(x97373,x97374,x97375,x97372,x97371)))+E(f317(f155(x97371),f317(f317(f144(x97372,x97371),x97373),f317(f126(x97372,x97374),x97375))),f317(f155(x97371),f317(f317(f144(x97372,x97371),x97373),x97375)))
% 94.68/94.45 [9814]~P5(x98145)+P1(f317(f317(f319(x98141),f577(x98142,x98143,x98141,x98144,x98145)),x98143))+P1(f317(f317(f224(x98145),x98144),f317(f317(f35(x98141,x98145),x98143),x98142)))
% 94.68/94.45 [9818]~P81(x98181)+E(f317(f155(x98181),f317(f317(f144(x98182,x98181),x98183),f317(f126(x98182,x98184),x98185))),f317(f155(x98181),f317(f317(f144(x98182,x98181),x98183),x98185)))+P1(f317(f317(f319(x98182),f697(x98183,x98184,x98185,x98182,x98181)),f317(f162(x98182),x98185)))
% 94.68/94.45 [9828]~P1(f317(x98285,f618(x98285,x98283,x98284,x98282,x98281)))+~P1(f317(f317(f224(f904(x98281,a893)),x98282),x98284))+P1(f317(f317(f224(f904(x98281,a893)),f317(f317(f92(f904(x98281,a893)),x98282),f317(f252(x98281),x98283))),f317(f317(f92(f904(x98281,a893)),x98284),f317(f252(x98281),x98285))))
% 94.68/94.45 [9844]~P24(x98445,x98443,x98444,f232(f904(x98445,a893)))+P1(f317(x98441,x98442))+P1(f317(f317(f319(x98443),f791(x98442,x98441,x98444,x98443,x98445)),f317(f300(x98445,x98443,x98444),f232(f904(x98445,a893)))))
% 94.68/94.45 [9867]P33(x98671,x98672,x98673,x98674,x98675)+~E(f317(f179(f898(x98672)),x98675),f317(f179(f898(x98671)),x98674))+P1(f317(f317(f225(a897),f679(x98675,x98674,x98673,x98672,x98671)),f317(f179(f898(x98671)),x98674)))
% 94.68/94.45 [9868]P33(x98681,x98682,x98683,x98684,x98685)+~E(f317(f179(f898(x98682)),x98685),f317(f179(f898(x98681)),x98684))+P1(f317(f317(f225(a897),f714(x98683,x98685,x98682,x98684,x98681)),f317(f179(f898(x98681)),x98684)))
% 94.68/94.45 [9899]P1(f317(f317(f319(x98991),f618(x98992,x98993,x98994,x98995,x98991)),x98995))+~P1(f317(f317(f224(f904(x98991,a893)),x98995),x98994))+P1(f317(f317(f224(f904(x98991,a893)),f317(f317(f92(f904(x98991,a893)),x98995),f317(f252(x98991),x98993))),f317(f317(f92(f904(x98991,a893)),x98994),f317(f252(x98991),x98992))))
% 94.68/94.45 [9942]~P5(x99421)+~P1(f317(f317(f224(x99421),x99422),f317(x99425,f577(x99425,x99424,x99423,x99422,x99421))))+P1(f317(f317(f224(x99421),x99422),f317(f317(f35(x99423,x99421),x99424),x99425)))
% 94.68/94.45 [9979]~P77(x99791)+~P1(f317(f28(x99792),x99795))+E(f317(f317(f317(f59(x99791,x99792,f75(x99791)),f317(f317(f18(x99792,x99791,x99791),f317(f317(f8(x99791,f904(x99791,x99791),x99792),f75(x99791)),x99793)),x99794)),f72(x99791)),x99795),f317(f317(f75(x99791),f317(f317(f317(f59(x99791,x99792,f75(x99791)),x99793),f72(x99791)),x99795)),f317(f317(f317(f59(x99791,x99792,f75(x99791)),x99794),f72(x99791)),x99795)))
% 94.68/94.45 [10034]~P1(f317(f317(f319(f903(f904(x100341,a893),f904(x100341,a893))),f317(f317(f242(f904(x100341,a893),f904(x100341,a893)),x100345),x100344)),f308(x100341,x100343)))+~P1(f317(f317(f319(x100341),x100342),x100345))+P1(f317(f317(f319(f903(x100341,x100341)),f317(f317(f242(x100341,x100341),x100342),f543(x100343,x100344,x100345,x100341,x100342))),x100343))
% 94.68/94.45 [10173]~P1(f317(f317(f319(f903(f898(x101731),f898(x101731))),f317(f317(f242(f898(x101731),f898(x101731)),f317(f317(f124(x101731),x101735),x101732)),f317(f317(f124(x101731),x101735),x101733))),f137(x101731,x101734)))+P1(f317(f317(f319(f903(f898(x101731),f898(x101731))),f317(f317(f242(f898(x101731),f898(x101731)),x101732),x101733)),f137(x101731,x101734)))+P1(f317(f317(f319(f903(x101731,x101731)),f317(f317(f242(x101731,x101731),f666(x101734,x101733,x101732,x101735,x101731)),f666(x101734,x101733,x101732,x101735,x101731))),x101734))
% 94.68/94.45 [7359]~E(x73593,x73595)+E(f317(f317(f154(x73591),f317(f317(f149(x73591,x73592),x73593),x73594)),x73595),x73594)+~P1(f317(f317(f225(a897),x73593),f317(f179(f898(x73591)),x73592)))
% 94.68/94.45 [7475]~E(f317(f317(f124(x74751),x74752),x74754),f317(f317(f124(x74751),x74753),x74755))+E(f317(f317(f165(x74751),f317(f179(f898(x74751)),x74752)),x74753),x74752)+P1(f317(f317(f224(a897),f317(f179(f898(x74751)),x74753)),f317(f179(f898(x74751)),x74752)))
% 94.68/94.45 [7973]~E(f317(f317(f124(x79731),x79732),x79734),f317(f317(f124(x79731),x79733),x79735))+E(f317(f317(f165(x79731),f317(f179(f898(x79731)),x79732)),x79733),x79732)+~P1(f317(f317(f224(a897),f317(f179(f898(x79731)),x79732)),f317(f179(f898(x79731)),x79733)))
% 94.68/94.45 [7997]~P1(f317(f28(x79971),f317(x79974,x79975)))+~P1(f317(f317(f319(x79972),x79975),x79973))+P1(f317(f28(x79971),f317(f317(f35(x79972,f904(x79971,a893)),x79973),x79974)))
% 94.68/94.45 [8172]~P52(x81721,x81723,x81725)+~P52(x81721,x81722,x81724)+P52(x81721,f317(f317(f91(f904(x81721,a893)),x81722),x81723),f317(f317(f91(f904(f903(x81721,x81721),a893)),x81724),x81725))
% 94.68/94.45 [8173]~P52(x81731,x81733,x81735)+~P52(x81731,x81732,x81734)+P52(x81731,f317(f317(f92(f904(x81731,a893)),x81732),x81733),f317(f317(f92(f904(f903(x81731,x81731),a893)),x81734),x81735))
% 94.68/94.45 [8529]E(f317(f317(f242(x85291,x85292),f317(f317(f154(x85291),x85293),x85294)),f317(f317(f154(x85292),x85295),x85294)),f317(f317(f154(f903(x85291,x85292)),f317(f317(f171(x85291,x85292),x85293),x85295)),x85294))+~P1(f317(f317(f225(a897),x85294),f317(f179(f898(x85291)),x85293)))+~P1(f317(f317(f225(a897),x85294),f317(f179(f898(x85292)),x85295)))
% 94.68/94.45 [8682]~P52(x86821,x86823,x86824)+P1(f317(f317(f319(x86821),x86822),x86823))+~P1(f317(f317(f319(f903(x86821,x86821)),f317(f317(f242(x86821,x86821),x86825),x86822)),x86824))
% 94.68/94.45 [8683]~P52(x86831,x86833,x86834)+P1(f317(f317(f319(x86831),x86832),x86833))+~P1(f317(f317(f319(f903(x86831,x86831)),f317(f317(f242(x86831,x86831),x86832),x86835)),x86834))
% 94.68/94.45 [8684]~P8(x86841,x86843,x86844)+P1(f317(f317(f319(x86841),x86842),x86843))+~P1(f317(f317(f319(f903(x86841,x86841)),f317(f317(f242(x86841,x86841),x86845),x86842)),x86844))
% 94.68/94.45 [8685]~P8(x86851,x86853,x86854)+P1(f317(f317(f319(x86851),x86852),x86853))+~P1(f317(f317(f319(f903(x86851,x86851)),f317(f317(f242(x86851,x86851),x86852),x86855)),x86854))
% 94.68/94.45 [8966]~P8(x89661,x89665,x89662)+E(f317(f275(x89661,x89661,x89662),f317(f317(f299(x89661),x89663),f178(f904(x89661,a893)))),f317(f275(x89661,x89661,x89662),f317(f317(f299(x89661),x89664),f178(f904(x89661,a893)))))+~P1(f317(f317(f319(f903(x89661,x89661)),f317(f317(f242(x89661,x89661),x89663),x89664)),x89662))
% 94.68/94.45 [9151]P1(f317(x91511,x91512))+~P1(f317(f317(f319(x91513),x91512),x91515))+P1(f317(f317(f319(x91513),f329(x91511,x91514,x91515,x91513)),f317(f317(f91(f904(x91513,a893)),x91515),x91514)))
% 94.68/94.45 [9152]P1(f317(x91521,x91522))+~P1(f317(f317(f319(x91523),x91522),x91524))+P1(f317(f317(f319(x91523),f329(x91521,x91524,x91525,x91523)),f317(f317(f91(f904(x91523,a893)),x91525),x91524)))
% 94.68/94.45 [9160]~P1(f317(x91602,x91605))+~P1(f317(f317(f319(x91601),x91605),x91604))+P1(f317(f317(f319(x91601),f325(x91602,x91603,x91604,x91601)),f317(f317(f91(f904(x91601,a893)),x91604),x91603)))
% 94.68/94.45 [9161]~P1(f317(x91612,x91615))+~P1(f317(f317(f319(x91611),x91615),x91613))+P1(f317(f317(f319(x91611),f325(x91612,x91613,x91614,x91611)),f317(f317(f91(f904(x91611,a893)),x91614),x91613)))
% 94.68/94.45 [9176]~P1(f317(f317(f224(f904(x91761,a893)),x91765),x91763))+~P1(f317(f317(f224(f904(x91761,a893)),x91762),x91764))+P1(f317(f317(f224(f904(x91761,a893)),f317(f317(f23(f904(x91761,a893)),x91762),x91763)),f317(f317(f23(f904(x91761,a893)),x91764),x91765)))
% 94.68/94.45 [9177]~P1(f317(f317(f224(f904(x91771,a893)),x91773),x91775))+~P1(f317(f317(f224(f904(x91771,a893)),x91772),x91774))+P1(f317(f317(f224(f904(x91771,a893)),f317(f317(f91(f904(x91771,a893)),x91772),x91773)),f317(f317(f91(f904(x91771,a893)),x91774),x91775)))
% 94.68/94.45 [9178]~P1(f317(f317(f224(f904(x91781,a893)),x91783),x91785))+~P1(f317(f317(f224(f904(x91781,a893)),x91782),x91784))+P1(f317(f317(f224(f904(x91781,a893)),f317(f317(f92(f904(x91781,a893)),x91782),x91783)),f317(f317(f92(f904(x91781,a893)),x91784),x91785)))
% 94.68/94.45 [9272]P1(f317(f317(f319(f903(x92721,x92721)),f317(f317(f242(x92721,x92721),x92722),x92723)),f311(x92721,x92724,x92725)))+~P1(f317(f317(f224(a897),f317(x92724,x92722)),f317(x92724,x92723)))+~P1(f317(f317(f319(f903(x92721,x92721)),f317(f317(f242(x92721,x92721),x92722),x92723)),x92725))
% 94.68/94.45 [9462]P1(f317(f317(f319(f903(x94621,x94621)),f317(f317(f242(x94621,x94621),x94622),x94623)),f297(x94621,x94624)))+~P1(f317(f317(f319(f903(x94621,x94621)),f317(f317(f242(x94621,x94621),x94622),x94625)),f297(x94621,x94624)))+~P1(f317(f317(f319(f903(x94621,x94621)),f317(f317(f242(x94621,x94621),x94625),x94623)),x94624))
% 94.68/94.45 [9463]P1(f317(f317(f319(f903(x94631,x94631)),f317(f317(f242(x94631,x94631),x94632),x94633)),f297(x94631,x94634)))+~P1(f317(f317(f319(f903(x94631,x94631)),f317(f317(f242(x94631,x94631),x94635),x94633)),f297(x94631,x94634)))+~P1(f317(f317(f319(f903(x94631,x94631)),f317(f317(f242(x94631,x94631),x94632),x94635)),x94634))
% 94.68/94.45 [9564]E(x95641,x95642)+E(f317(a102,f562(x95643,x95644,x95641,x95642,x95645)),x95644)+~P1(f317(f317(f319(f903(x95645,x95645)),f317(f317(f242(x95645,x95645),x95642),x95641)),f317(f317(f173(f903(x95645,x95645),a893),x95644),x95643)))
% 94.68/94.45 [9565]E(x95651,x95652)+E(f317(a102,f564(x95653,x95654,x95651,x95652,x95655)),x95654)+~P1(f317(f317(f319(f903(x95655,x95655)),f317(f317(f242(x95655,x95655),x95652),x95651)),f317(f317(f173(f903(x95655,x95655),a893),x95654),x95653)))
% 94.68/94.45 [9566]E(x95661,f2(a897))+E(f317(a102,f562(x95662,x95661,x95663,x95664,x95665)),x95661)+~P1(f317(f317(f319(f903(x95665,x95665)),f317(f317(f242(x95665,x95665),x95664),x95663)),f317(f317(f173(f903(x95665,x95665),a893),x95661),x95662)))
% 94.68/94.45 [9567]E(x95671,f2(a897))+E(f317(a102,f564(x95672,x95671,x95673,x95674,x95675)),x95671)+~P1(f317(f317(f319(f903(x95675,x95675)),f317(f317(f242(x95675,x95675),x95674),x95673)),f317(f317(f173(f903(x95675,x95675),a893),x95671),x95672)))
% 94.68/94.45 [9592]P1(f317(f317(f319(f903(x95921,x95921)),f317(f317(f242(x95921,x95921),x95922),x95923)),f317(f317(f279(x95921,x95921,x95921),x95924),f297(x95921,x95924))))+~P1(f317(f317(f319(f903(x95921,x95921)),f317(f317(f242(x95921,x95921),x95922),x95925)),x95924))+~P1(f317(f317(f319(f903(x95921,x95921)),f317(f317(f242(x95921,x95921),x95925),x95923)),x95924))
% 94.68/94.45 [9602]~P1(f317(f317(f319(f903(x96021,x96021)),f317(f317(f242(x96021,x96021),x96022),x96025)),f297(x96021,x96024)))+P1(f317(f317(f319(f903(x96021,x96021)),f317(f317(f242(x96021,x96021),x96022),x96023)),f317(f317(f279(x96021,x96021,x96021),x96024),f297(x96021,x96024))))+~P1(f317(f317(f319(f903(x96021,x96021)),f317(f317(f242(x96021,x96021),x96025),x96023)),x96024))
% 94.68/94.45 [9637]~P8(x96371,x96375,x96372)+~P1(f317(f317(f319(f903(x96371,x96371)),f317(f317(f242(x96371,x96371),x96373),x96374)),x96372))+P1(f317(f317(f224(f904(x96371,a893)),f317(f275(x96371,x96371,x96372),f317(f317(f299(x96371),x96373),f178(f904(x96371,a893))))),f317(f275(x96371,x96371,x96372),f317(f317(f299(x96371),x96374),f178(f904(x96371,a893))))))
% 94.68/94.45 [9695]P1(f317(f317(f319(f903(x96951,x96951)),f317(f317(f242(x96951,x96951),x96952),x96953)),f317(f317(f279(x96951,x96951,x96951),x96954),f297(x96951,x96954))))+~P1(f317(f317(f319(f903(x96951,x96951)),f317(f317(f242(x96951,x96951),x96952),x96955)),f317(f317(f279(x96951,x96951,x96951),x96954),f297(x96951,x96954))))+~P1(f317(f317(f319(f903(x96951,x96951)),f317(f317(f242(x96951,x96951),x96955),x96953)),x96954))
% 94.68/94.45 [9696]P1(f317(f317(f319(f903(x96961,x96961)),f317(f317(f242(x96961,x96961),x96962),x96963)),f317(f317(f279(x96961,x96961,x96961),x96964),f297(x96961,x96964))))+~P1(f317(f317(f319(f903(x96961,x96961)),f317(f317(f242(x96961,x96961),x96965),x96963)),f317(f317(f279(x96961,x96961,x96961),x96964),f297(x96961,x96964))))+~P1(f317(f317(f319(f903(x96961,x96961)),f317(f317(f242(x96961,x96961),x96962),x96965)),x96964))
% 94.68/94.45 [9746]~P1(f317(f60(x97461,x97461,x97464,x97462,x97463),x97465))+P1(f317(f317(f319(x97461),x97462),x97463))+P1(f317(f56(x97461,x97464,f317(f317(f299(x97461),x97462),x97463)),x97465))
% 94.68/94.45 [9784]~E(f317(f300(x97843,x97842,x97845),x97844),x97841)+E(x97841,f178(f904(x97842,a893)))+P1(f317(f317(f224(f904(x97843,a893)),f317(f300(x97842,x97843,f355(x97844,x97843,x97842,x97841)),x97841)),x97844))
% 94.68/94.45 [9831]~P5(x98315)+P1(f317(f317(f319(x98311),f443(x98312,x98313,x98314,x98311,x98315)),x98314))+P1(f317(f317(f224(x98315),f317(f317(f34(x98311,x98315),x98314),x98313)),x98312))
% 94.68/94.45 [9886]P33(x98861,x98862,x98863,x98864,x98865)+~E(f317(f179(f898(x98861)),x98864),f317(f179(f898(x98862)),x98865))+P1(f317(f317(f319(f903(x98861,x98862)),f677(x98865,x98864,x98863,x98862,x98861)),f317(f162(f903(x98861,x98862)),f317(f317(f171(x98861,x98862),x98864),x98865))))
% 94.68/94.45 [9887]P33(x98871,x98872,x98873,x98874,x98875)+~E(f317(f179(f898(x98871)),x98874),f317(f179(f898(x98872)),x98875))+P1(f317(f317(f319(f903(x98871,x98872)),f678(x98873,x98875,x98874,x98872,x98871)),f317(f162(f903(x98871,x98872)),f317(f317(f171(x98871,x98872),x98874),x98875))))
% 94.68/94.45 [10013]E(x100131,x100132)+P1(f317(f317(f319(f903(x100133,x100133)),f317(f317(f242(x100133,x100133),x100131),f563(x100134,x100135,x100132,x100131,x100133))),x100134))+~P1(f317(f317(f319(f903(x100133,x100133)),f317(f317(f242(x100133,x100133),x100131),x100132)),f317(f317(f173(f903(x100133,x100133),a893),x100135),x100134)))
% 94.68/94.45 [10014]E(x100141,f2(a897))+P1(f317(f317(f319(f903(x100142,x100142)),f317(f317(f242(x100142,x100142),x100143),f563(x100144,x100141,x100145,x100143,x100142))),x100144))+~P1(f317(f317(f319(f903(x100142,x100142)),f317(f317(f242(x100142,x100142),x100143),x100145)),f317(f317(f173(f903(x100142,x100142),a893),x100141),x100144)))
% 94.68/94.45 [10053]~P5(x100531)+~P1(f317(f317(f224(x100531),f317(x100534,f443(x100535,x100534,x100533,x100532,x100531))),x100535))+P1(f317(f317(f224(x100531),f317(f317(f34(x100532,x100531),x100533),x100534)),x100535))
% 94.68/94.45 [10105]E(x101051,x101052)+P1(f317(f317(f319(f903(x101053,x101053)),f317(f317(f242(x101053,x101053),f565(x101054,x101055,x101051,x101052,x101053)),x101051)),x101054))+~P1(f317(f317(f319(f903(x101053,x101053)),f317(f317(f242(x101053,x101053),x101052),x101051)),f317(f317(f173(f903(x101053,x101053),a893),x101055),x101054)))
% 94.68/94.45 [10106]E(x101061,f2(a897))+P1(f317(f317(f319(f903(x101062,x101062)),f317(f317(f242(x101062,x101062),f565(x101063,x101061,x101064,x101065,x101062)),x101064)),x101063))+~P1(f317(f317(f319(f903(x101062,x101062)),f317(f317(f242(x101062,x101062),x101065),x101064)),f317(f317(f173(f903(x101062,x101062),a893),x101061),x101063)))
% 94.68/94.45 [10110]E(x101101,x101102)+P1(f317(f317(f319(f903(x101103,x101103)),f317(f317(f242(x101103,x101103),x101101),f565(x101104,x101105,x101102,x101101,x101103))),f317(f317(f173(f903(x101103,x101103),a893),f564(x101104,x101105,x101102,x101101,x101103)),x101104)))+~P1(f317(f317(f319(f903(x101103,x101103)),f317(f317(f242(x101103,x101103),x101101),x101102)),f317(f317(f173(f903(x101103,x101103),a893),x101105),x101104)))
% 94.68/94.45 [10111]E(x101111,f2(a897))+P1(f317(f317(f319(f903(x101112,x101112)),f317(f317(f242(x101112,x101112),x101113),f565(x101114,x101111,x101115,x101113,x101112))),f317(f317(f173(f903(x101112,x101112),a893),f564(x101114,x101111,x101115,x101113,x101112)),x101114)))+~P1(f317(f317(f319(f903(x101112,x101112)),f317(f317(f242(x101112,x101112),x101113),x101115)),f317(f317(f173(f903(x101112,x101112),a893),x101111),x101114)))
% 94.68/94.45 [10164]E(x101641,x101642)+P1(f317(f317(f319(f903(x101643,x101643)),f317(f317(f242(x101643,x101643),f563(x101644,x101645,x101641,x101642,x101643)),x101641)),f317(f317(f173(f903(x101643,x101643),a893),f562(x101644,x101645,x101641,x101642,x101643)),x101644)))+~P1(f317(f317(f319(f903(x101643,x101643)),f317(f317(f242(x101643,x101643),x101642),x101641)),f317(f317(f173(f903(x101643,x101643),a893),x101645),x101644)))
% 94.68/94.45 [10165]E(x101651,f2(a897))+P1(f317(f317(f319(f903(x101652,x101652)),f317(f317(f242(x101652,x101652),f563(x101653,x101651,x101654,x101655,x101652)),x101654)),f317(f317(f173(f903(x101652,x101652),a893),f562(x101653,x101651,x101654,x101655,x101652)),x101653)))+~P1(f317(f317(f319(f903(x101652,x101652)),f317(f317(f242(x101652,x101652),x101655),x101654)),f317(f317(f173(f903(x101652,x101652),a893),x101651),x101653)))
% 94.68/94.45 [10198]~P76(x101982)+~P1(f317(f28(x101981),x101985))+E(f317(f317(f6(x101981,x101982),f317(f317(f7(x101981,x101982,x101982),f317(f317(f18(x101981,x101982,f904(x101982,x101982)),f317(f317(f8(a893,f904(x101982,f904(x101982,x101982)),x101981),f86(x101982)),f317(f317(f7(x101981,f904(x101981,a893),a893),f319(x101981)),x101983))),x101984)),f2(x101982))),x101985),f317(f317(f6(x101981,x101982),x101984),f317(f317(f92(f904(x101981,a893)),x101985),x101983)))
% 94.68/94.45 [8750]~P77(x87501)+~P1(f317(f28(x87504),x87505))+E(f317(f317(f75(x87501),f317(x87502,x87503)),f317(f317(f9(x87504,x87501),x87502),f317(f317(f23(f904(x87504,a893)),x87505),f317(f317(f299(x87504),x87503),f178(f904(x87504,a893)))))),f317(f317(f9(x87504,x87501),x87502),f317(f317(f299(x87504),x87503),x87505)))
% 94.68/94.45 [8751]~P76(x87511)+~P1(f317(f28(x87514),x87515))+E(f317(f317(f74(x87511),f317(x87512,x87513)),f317(f317(f6(x87514,x87511),x87512),f317(f317(f23(f904(x87514,a893)),x87515),f317(f317(f299(x87514),x87513),f178(f904(x87514,a893)))))),f317(f317(f6(x87514,x87511),x87512),f317(f317(f299(x87514),x87513),x87515)))
% 94.68/94.45 [9083]~P66(x90832)+~P13(x90832,f317(f158(x90832),f317(f317(f144(x90831,x90832),x90834),x90835)))+E(f317(f126(x90831,f317(f317(f8(x90832,a893,x90831),f317(f225(x90832),x90833)),x90834)),x90835),f167(x90831,f317(f317(f8(x90832,a893,x90831),f317(f225(x90832),x90833)),x90834),x90835))
% 94.68/94.45 [9107]~P76(x91071)+E(f317(f317(f74(x91071),f317(f317(f6(a897,x91071),x91072),f293(a897,x91073,x91074))),f317(f317(f6(a897,x91071),x91072),f293(a897,f317(f317(f74(a897),x91074),f72(a897)),f317(f317(f74(a897),x91074),x91075)))),f317(f317(f6(a897,x91071),x91072),f293(a897,x91073,f317(f317(f74(a897),x91074),x91075))))+~P1(f317(f317(f224(a897),x91073),f317(f317(f74(a897),x91074),f72(a897))))
% 94.68/94.45 [9108]~P1(f317(f317(f319(x91081),x91084),x91085))+~P1(f317(f317(f224(f904(x91081,a893)),f317(f162(x91081),x91082)),x91085))+P1(f317(f317(f224(f904(x91081,a893)),f317(f162(x91081),f317(f317(f149(x91081,x91082),x91083),x91084))),x91085))
% 94.68/94.45 [9334]~P5(x93342)+~P1(f317(f28(x93341),x93345))+E(f317(f317(f58(x93341,x93342,f317(f317(f8(x93342,f904(x93342,x93342),x93341),f91(x93342)),x93343)),x93344),x93345),f317(f317(f91(x93342),x93344),f317(f317(f34(x93341,x93342),x93345),x93343)))
% 94.68/94.45 [9335]~P5(x93352)+~P1(f317(f28(x93351),x93355))+E(f317(f317(f58(x93351,x93352,f317(f317(f8(x93352,f904(x93352,x93352),x93351),f92(x93352)),x93353)),x93354),x93355),f317(f317(f92(x93352),x93354),f317(f317(f35(x93351,x93352),x93355),x93353)))
% 94.68/94.45 [9387]E(f317(x93871,x93872),f317(x93871,x93873))+P1(f317(f317(f225(a897),f317(x93871,x93872)),f317(x93871,x93873)))+~P1(f317(f317(f319(f903(x93874,x93874)),f317(f317(f242(x93874,x93874),x93872),x93873)),f143(x93874,f317(f317(f141(f904(x93874,a897)),x93871),x93875))))
% 94.68/94.45 [9420]~E(f317(x94204,x94202),f317(x94204,x94203))+~P1(f317(f317(f319(f903(x94201,x94201)),f317(f317(f242(x94201,x94201),x94202),x94203)),f143(x94201,x94205)))+P1(f317(f317(f319(f903(x94201,x94201)),f317(f317(f242(x94201,x94201),x94202),x94203)),f143(x94201,f317(f317(f141(f904(x94201,a897)),x94204),x94205))))
% 94.68/94.45 [9440]~P24(x94401,x94402,x94403,x94405)+P24(x94401,x94402,x94403,f317(f317(f299(x94401),x94404),x94405))+P1(f317(f317(f319(x94402),f317(x94403,x94404)),f317(f300(x94401,x94402,x94403),f317(f317(f23(f904(x94401,a893)),x94405),f317(f317(f299(x94401),x94404),f178(f904(x94401,a893)))))))
% 94.68/94.45 [9443]P1(f317(x94432,x94435))+~P1(f317(f317(f319(x94431),x94435),f317(f162(x94431),x94433)))+E(f317(f317(f128(x94431),f317(f179(f898(x94431)),f167(x94431,x94432,f317(f317(f124(x94431),x94433),x94434)))),f317(f317(f124(x94431),x94433),x94434)),f317(f317(f124(x94431),f317(f317(f128(x94431),f317(f179(f898(x94431)),f167(x94431,x94432,x94433))),x94433)),x94434))
% 94.68/94.45 [9448]~P1(f317(f317(f319(f903(x94481,x94481)),f317(f317(f242(x94481,x94481),x94482),x94483)),f143(x94481,x94485)))+~P1(f317(f317(f224(a897),f317(x94484,x94482)),f317(x94484,x94483)))+P1(f317(f317(f319(f903(x94481,x94481)),f317(f317(f242(x94481,x94481),x94482),x94483)),f143(x94481,f317(f317(f141(f904(x94481,a897)),x94484),x94485))))
% 94.68/94.45 [9515]P1(f317(f317(f319(f903(x95154,x95154)),f317(f317(f242(x95154,x95154),x95152),x95153)),f143(x95154,x95155)))+P1(f317(f317(f225(a897),f317(x95151,x95152)),f317(x95151,x95153)))+~P1(f317(f317(f319(f903(x95154,x95154)),f317(f317(f242(x95154,x95154),x95152),x95153)),f143(x95154,f317(f317(f141(f904(x95154,a897)),x95151),x95155))))
% 94.68/94.45 [9667]~P1(f317(f317(f319(f903(f898(x96671),f898(x96671))),f317(f317(f242(f898(x96671),f898(x96671)),x96672),x96674)),f148(x96671,x96675)))+~P1(f317(f317(f225(a897),x96673),f317(f179(f898(x96671)),x96672)))+P1(f317(f317(f319(f903(x96671,x96671)),f317(f317(f242(x96671,x96671),f317(f317(f154(x96671),x96672),x96673)),f317(f317(f154(x96671),x96674),x96673))),x96675))
% 94.68/94.45 [9909]E(x99091,f2(a1))+~P1(f317(f44(x99093,x99091),f317(f317(f242(a1,a1),x99094),x99095)))+P1(f317(f44(f317(f317(f75(a1),x99092),x99093),x99091),f317(f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f75(a1),x99092),x99094)),f317(f317(f30(a1),f317(f317(f75(a1),x99092),x99095)),x99091))),f40(a1,f317(f317(f75(a1),x99092),x99095),x99091))))
% 94.68/94.45 [9910]~P1(f317(f317(f225(a897),f2(a897)),x99103))+~P1(f317(f43(x99102,x99103),f317(f317(f242(a897,a897),x99104),x99105)))+P1(f317(f43(f317(f317(f75(a897),x99101),x99102),x99103),f317(f317(f242(a897,a897),f317(f317(f74(a897),f317(f317(f75(a897),x99101),x99104)),f317(f317(f30(a897),f317(f317(f75(a897),x99101),x99105)),x99103))),f40(a897,f317(f317(f75(a897),x99101),x99105),x99103))))
% 94.68/94.45 [10221]~P76(x102212)+~P1(f317(f28(x102211),x102214))+E(f317(f317(f6(x102211,x102212),x102213),f317(f252(x102211),f317(f317(f18(x102211,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102211),a315),f317(f317(f7(x102211,f904(x102211,a893),a893),f319(x102211)),x102214))),f317(f317(f7(x102211,f904(x102211,a893),a893),f319(x102211)),x102215)))),f317(f317(f6(x102211,x102212),f317(f317(f7(x102211,x102212,x102212),f317(f317(f18(x102211,x102212,f904(x102212,x102212)),f317(f317(f8(a893,f904(x102212,f904(x102212,x102212)),x102211),f86(x102212)),f317(f317(f7(x102211,f904(x102211,a893),a893),f319(x102211)),x102215))),x102213)),f2(x102212))),x102214))
% 94.68/94.45 [8380]~E(f317(f317(f124(x83801),x83802),x83805),f317(f317(f124(x83801),x83803),x83804))+E(f317(f317(f124(x83801),f317(f317(f128(x83801),f317(f179(f898(x83801)),x83802)),x83803)),x83804),x83805)+P1(f317(f317(f224(a897),f317(f179(f898(x83801)),x83803)),f317(f179(f898(x83801)),x83802)))
% 94.68/94.45 [8577]~E(f317(f317(f124(x85772),x85773),x85771),f317(f317(f124(x85772),x85774),x85775))+E(x85771,f317(f317(f124(x85772),f317(f317(f128(x85772),f317(f179(f898(x85772)),x85773)),x85774)),x85775))+~P1(f317(f317(f224(a897),f317(f179(f898(x85772)),x85773)),f317(f179(f898(x85772)),x85774)))
% 94.68/94.45 [8665]~E(f317(f317(f74(a897),f317(f317(f75(a897),x86653),x86654)),x86651),f317(f317(f74(a897),f317(f317(f75(a897),x86652),x86654)),x86655))+~P1(f317(f317(f224(a897),x86653),x86652))+E(x86651,f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x86652),x86653)),x86654)),x86655))
% 94.68/94.45 [8666]~E(f317(f317(f74(a897),f317(f317(f75(a897),x86661),x86663)),x86664),f317(f317(f74(a897),f317(f317(f75(a897),x86662),x86663)),x86665))+~P1(f317(f317(f224(a897),x86662),x86661))+E(f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x86661),x86662)),x86663)),x86664),x86665)
% 94.68/94.45 [8834]E(f317(f317(f74(a897),f317(f317(f75(a897),x88341),x88342)),x88343),f317(f317(f74(a897),f317(f317(f75(a897),x88344),x88342)),x88345))+~P1(f317(f317(f224(a897),x88344),x88341))+~E(x88345,f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x88341),x88344)),x88342)),x88343))
% 94.68/94.45 [8835]E(f317(f317(f74(a897),f317(f317(f75(a897),x88351),x88352)),x88353),f317(f317(f74(a897),f317(f317(f75(a897),x88354),x88352)),x88355))+~P1(f317(f317(f224(a897),x88354),x88351))+~E(f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x88351),x88354)),x88352)),x88353),x88355)
% 94.68/94.45 [9720]~P61(x97202)+~P1(f317(f28(x97201),x97205))+E(f317(f317(f9(x97201,x97202),f317(f317(f18(x97201,x97202,x97202),f317(f317(f8(x97202,f904(x97202,x97202),x97201),f281(x97202)),x97203)),x97204)),x97205),f317(f317(f281(x97202),f317(f317(f9(x97201,x97202),x97203),x97205)),f317(f317(f9(x97201,x97202),x97204),x97205)))
% 94.68/94.45 [9850]~E(f570(x98505,x98504,x98503,x98502,x98501),f566(x98505,x98504,x98503,x98502,x98501))+P1(f317(f317(f319(f903(x98501,x98501)),f317(f317(f242(x98501,x98501),x98502),x98503)),f297(x98501,x98504)))+~P1(f317(f317(f319(f903(x98501,x98501)),f317(f317(f242(x98501,x98501),x98502),x98503)),f297(x98501,f317(f317(f91(f904(f903(x98501,x98501),a893)),x98504),x98505))))
% 94.68/94.45 [9851]~E(f571(x98515,x98514,x98513,x98512,x98511),f572(x98515,x98514,x98513,x98512,x98511))+P1(f317(f317(f319(f903(x98511,x98511)),f317(f317(f242(x98511,x98511),x98512),x98513)),f297(x98511,x98514)))+~P1(f317(f317(f319(f903(x98511,x98511)),f317(f317(f242(x98511,x98511),x98512),x98513)),f297(x98511,f317(f317(f91(f904(f903(x98511,x98511),a893)),x98514),x98515))))
% 94.68/94.45 [10043]P1(f317(f317(f319(f903(x100431,x100431)),f317(f317(f242(x100431,x100431),x100432),f566(x100435,x100434,x100433,x100432,x100431))),f297(x100431,x100434)))+P1(f317(f317(f319(f903(x100431,x100431)),f317(f317(f242(x100431,x100431),x100432),x100433)),f297(x100431,x100434)))+~P1(f317(f317(f319(f903(x100431,x100431)),f317(f317(f242(x100431,x100431),x100432),x100433)),f297(x100431,f317(f317(f91(f904(f903(x100431,x100431),a893)),x100434),x100435))))
% 94.68/94.45 [10132]P1(f317(f317(f319(f903(x101321,x101321)),f317(f317(f242(x101321,x101321),f572(x101325,x101324,x101323,x101322,x101321)),x101323)),f297(x101321,x101324)))+P1(f317(f317(f319(f903(x101321,x101321)),f317(f317(f242(x101321,x101321),x101322),x101323)),f297(x101321,x101324)))+~P1(f317(f317(f319(f903(x101321,x101321)),f317(f317(f242(x101321,x101321),x101322),x101323)),f297(x101321,f317(f317(f91(f904(f903(x101321,x101321),a893)),x101324),x101325))))
% 94.68/94.45 [10171]P1(f317(f317(f319(f903(x101711,x101711)),f317(f317(f242(x101711,x101711),x101712),x101713)),f297(x101711,x101714)))+P1(f317(f317(f319(f903(x101711,x101711)),f317(f317(f242(x101711,x101711),f566(x101715,x101714,x101713,x101712,x101711)),f570(x101715,x101714,x101713,x101712,x101711))),x101715))+~P1(f317(f317(f319(f903(x101711,x101711)),f317(f317(f242(x101711,x101711),x101712),x101713)),f297(x101711,f317(f317(f91(f904(f903(x101711,x101711),a893)),x101714),x101715))))
% 94.68/94.45 [10172]P1(f317(f317(f319(f903(x101721,x101721)),f317(f317(f242(x101721,x101721),x101722),x101723)),f297(x101721,x101724)))+P1(f317(f317(f319(f903(x101721,x101721)),f317(f317(f242(x101721,x101721),f571(x101725,x101724,x101723,x101722,x101721)),f572(x101725,x101724,x101723,x101722,x101721))),x101725))+~P1(f317(f317(f319(f903(x101721,x101721)),f317(f317(f242(x101721,x101721),x101722),x101723)),f297(x101721,f317(f317(f91(f904(f903(x101721,x101721),a893)),x101724),x101725))))
% 94.68/94.45 [10319]~P1(f317(f317(f319(f903(f898(x103191),f898(x103191))),f317(f317(f242(f898(x103191),f898(x103191)),x103194),x103195)),f148(x103191,x103192)))+~P1(f317(f317(f319(f903(x103191,x103191)),x103193),f317(f162(f903(x103191,x103191)),f317(f317(f171(x103191,x103191),x103194),x103195))))+P1(f317(f317(f247(x103191,x103191,a893),f317(f317(f7(x103191,f904(f903(x103191,x103191),a893),f904(x103191,a893)),f317(f317(f8(f904(x103191,f904(f904(f903(x103191,x103191),a893),a893)),f904(f904(f903(x103191,x103191),a893),f904(x103191,a893)),x103191),f7(x103191,f904(f903(x103191,x103191),a893),a893)),f317(f317(f8(f904(x103191,f903(x103191,x103191)),f904(x103191,f904(f904(f903(x103191,x103191),a893),a893)),x103191),f317(f8(f903(x103191,x103191),f904(f904(f903(x103191,x103191),a893),a893),x103191),f319(f903(x103191,x103191)))),f242(x103191,x103191)))),x103192)),x103193))
% 94.68/94.45 [9750]~P1(f317(f317(f224(a897),x97503),x97502))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),x97503),x97504)),x97501)),f317(f317(f74(a897),f317(f317(f75(a897),x97502),x97504)),x97505)))+P1(f317(f317(f224(a897),x97501),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x97502),x97503)),x97504)),x97505)))
% 94.68/94.45 [9751]~P1(f317(f317(f224(a897),x97513),x97512))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),x97513),x97514)),x97511)),f317(f317(f74(a897),f317(f317(f75(a897),x97512),x97514)),x97515)))+P1(f317(f317(f225(a897),x97511),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x97512),x97513)),x97514)),x97515)))
% 94.68/94.45 [9768]~P1(f317(f317(f224(a897),x97681),x97684))+P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),x97681),x97682)),x97683)),f317(f317(f74(a897),f317(f317(f75(a897),x97684),x97682)),x97685)))+~P1(f317(f317(f224(a897),x97683),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x97684),x97681)),x97682)),x97685)))
% 94.68/94.45 [9769]~P1(f317(f317(f224(a897),x97691),x97694))+P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),x97691),x97692)),x97693)),f317(f317(f74(a897),f317(f317(f75(a897),x97694),x97692)),x97695)))+~P1(f317(f317(f225(a897),x97693),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x97694),x97691)),x97692)),x97695)))
% 94.68/94.45 [9884]~P1(f317(f317(f224(a897),x98842),x98841))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),x98841),x98843)),x98844)),f317(f317(f74(a897),f317(f317(f75(a897),x98842),x98843)),x98845)))+P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x98841),x98842)),x98843)),x98844)),x98845))
% 94.68/94.45 [9885]~P1(f317(f317(f224(a897),x98852),x98851))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),x98851),x98853)),x98854)),f317(f317(f74(a897),f317(f317(f75(a897),x98852),x98853)),x98855)))+P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x98851),x98852)),x98853)),x98854)),x98855))
% 94.68/94.45 [9928]~P1(f317(f317(f224(a897),x99284),x99281))+P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),x99281),x99282)),x99283)),f317(f317(f74(a897),f317(f317(f75(a897),x99284),x99282)),x99285)))+~P1(f317(f317(f224(a897),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x99281),x99284)),x99282)),x99283)),x99285))
% 94.68/94.45 [9929]~P1(f317(f317(f224(a897),x99294),x99291))+P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),x99291),x99292)),x99293)),f317(f317(f74(a897),f317(f317(f75(a897),x99294),x99292)),x99295)))+~P1(f317(f317(f225(a897),f317(f317(f74(a897),f317(f317(f75(a897),f317(f317(f23(a897),x99291),x99294)),x99292)),x99293)),x99295))
% 94.68/94.45 [10159]~P11(x101591,x101592,x101595,x101593)+~P1(f317(f317(f319(f903(x101591,x101591)),x101594),x101595))+P1(f317(f317(f247(x101591,x101591,a893),f317(f317(f7(x101591,f904(x101591,x101592),f904(x101591,a893)),f317(f317(f8(f904(x101592,a893),f904(f904(x101591,x101592),f904(x101591,a893)),x101591),f8(x101592,a893,x101591)),f317(f317(f8(x101592,f904(x101592,a893),x101591),a314),x101593))),x101593)),x101594))
% 94.68/94.45 [8541]~P19(x85416,x85411,x85412,x85414)+E(f317(f67(x85411,x85411,x85411,f317(x85412,x85413)),f317(x85414,x85415)),f317(f67(x85411,x85411,x85411,f317(x85414,x85415)),f317(x85412,x85413)))+~P1(f317(f28(x85416),x85415))
% 94.68/94.45 [8978]~P24(x89781,x89783,x89785,x89786)+~P24(x89783,x89782,x89784,f317(f300(x89781,x89783,x89785),x89786))+P24(x89781,x89782,f317(f67(x89783,x89782,x89781,x89784),x89785),x89786)
% 94.68/94.45 [9547]~P1(f317(f317(x95474,x95472),x95476))+~P1(f317(f317(x95473,x95475),x95472))+P1(f317(f317(f319(x95471),x95472),f287(x95471,x95473,x95474,x95475,x95476)))
% 94.68/94.45 [9548]~P1(f317(f317(x95483,x95482),x95486))+~P1(f317(f317(x95484,x95485),x95482))+P1(f317(f317(f319(x95481),x95482),f290(x95481,x95483,x95484,x95485,x95486)))
% 94.68/94.45 [9668]E(x96681,x96682)+E(x96683,x96684)+~P1(f317(f317(f319(f903(f898(x96685),f898(x96685))),f317(f317(f242(f898(x96685),f898(x96685)),f317(f317(f141(x96685),x96683),x96681)),f317(f317(f141(x96685),x96684),x96682))),f147(x96685,x96686)))
% 94.68/94.45 [9677]~E(x96772,x96774)+P1(f317(f317(f319(f903(f898(x96771),f898(x96771))),f317(f317(f242(f898(x96771),f898(x96771)),f317(f317(f141(x96771),x96772),x96773)),f317(f317(f141(x96771),x96774),x96775))),f135(x96771,x96776)))+~P1(f317(f317(f319(f903(f898(x96771),f898(x96771))),f317(f317(f242(f898(x96771),f898(x96771)),x96773),x96775)),f135(x96771,x96776)))
% 94.68/94.45 [9678]~E(x96782,x96784)+P1(f317(f317(f319(f903(f898(x96781),f898(x96781))),f317(f317(f242(f898(x96781),f898(x96781)),f317(f317(f141(x96781),x96782),x96783)),f317(f317(f141(x96781),x96784),x96785))),f137(x96781,x96786)))+~P1(f317(f317(f319(f903(f898(x96781),f898(x96781))),f317(f317(f242(f898(x96781),f898(x96781)),x96783),x96785)),f137(x96781,x96786)))
% 94.68/94.45 [9679]~E(x96792,x96794)+P1(f317(f317(f319(f903(f898(x96791),f898(x96791))),f317(f317(f242(f898(x96791),f898(x96791)),f317(f317(f141(x96791),x96792),x96793)),f317(f317(f141(x96791),x96794),x96795))),f147(x96791,x96796)))+~P1(f317(f317(f319(f903(f898(x96791),f898(x96791))),f317(f317(f242(f898(x96791),f898(x96791)),x96793),x96795)),f147(x96791,x96796)))
% 94.68/94.45 [9680]~E(x96802,x96804)+P1(f317(f317(f319(f903(f898(x96801),f898(x96801))),f317(f317(f242(f898(x96801),f898(x96801)),f317(f317(f124(x96801),x96802),x96803)),f317(f317(f124(x96801),x96804),x96805))),f147(x96801,x96806)))+~P1(f317(f317(f319(f903(f898(x96801),f898(x96801))),f317(f317(f242(f898(x96801),f898(x96801)),x96803),x96805)),f147(x96801,x96806)))
% 94.68/94.45 [9681]~E(x96813,x96815)+P1(f317(f317(f319(f903(f898(x96811),f898(x96811))),f317(f317(f242(f898(x96811),f898(x96811)),f317(f317(f124(x96811),x96812),x96813)),f317(f317(f124(x96811),x96814),x96815))),f147(x96811,x96816)))+~P1(f317(f317(f319(f903(f898(x96811),f898(x96811))),f317(f317(f242(f898(x96811),f898(x96811)),x96812),x96814)),f147(x96811,x96816)))
% 94.68/94.45 [9738]E(x97381,x97382)+P1(f317(f317(f319(f903(f898(x97383),f898(x97383))),f317(f317(f242(f898(x97383),f898(x97383)),x97381),x97382)),f147(x97383,x97384)))+~P1(f317(f317(f319(f903(f898(x97383),f898(x97383))),f317(f317(f242(f898(x97383),f898(x97383)),f317(f317(f141(x97383),x97385),x97381)),f317(f317(f141(x97383),x97386),x97382))),f147(x97383,x97384)))
% 94.68/94.45 [9888]~E(x98883,x98885)+P1(f317(f317(f319(f903(f898(x98881),f898(x98881))),f317(f317(f242(f898(x98881),f898(x98881)),f317(f317(f124(x98881),x98882),f317(f317(f141(x98881),x98883),f103(x98881)))),f317(f317(f124(x98881),x98884),f317(f317(f141(x98881),x98885),f103(x98881))))),f147(x98881,x98886)))+~P1(f317(f317(f319(f903(f898(x98881),f898(x98881))),f317(f317(f242(f898(x98881),f898(x98881)),x98882),x98884)),f147(x98881,x98886)))
% 94.68/94.45 [9932]E(x99321,x99322)+E(x99323,x99324)+~P1(f317(f317(f319(f903(f898(x99325),f898(x99325))),f317(f317(f242(f898(x99325),f898(x99325)),f317(f317(f124(x99325),x99323),f317(f317(f141(x99325),x99321),f103(x99325)))),f317(f317(f124(x99325),x99324),f317(f317(f141(x99325),x99322),f103(x99325))))),f147(x99325,x99326)))
% 94.68/94.45 [9958]E(x99581,x99582)+~P1(f317(f317(f319(f903(f898(x99583),f898(x99583))),f317(f317(f242(f898(x99583),f898(x99583)),f317(f317(f124(x99583),x99581),f317(f317(f141(x99583),x99585),f103(x99583)))),f317(f317(f124(x99583),x99582),f317(f317(f141(x99583),x99586),f103(x99583))))),f147(x99583,x99584)))+P1(f317(f317(f319(f903(f898(x99583),f898(x99583))),f317(f317(f242(f898(x99583),f898(x99583)),x99581),x99582)),f147(x99583,x99584)))
% 94.68/94.45 [9996]~P1(f317(f317(f319(f903(f904(x99961,a893),f904(x99961,a893))),f317(f317(f242(f904(x99961,a893),f904(x99961,a893)),x99962),x99964)),f308(x99961,x99966)))+~P1(f317(f317(f319(f903(f904(x99961,a893),f904(x99961,a893))),f317(f317(f242(f904(x99961,a893),f904(x99961,a893)),x99963),x99965)),f308(x99961,x99966)))+P1(f317(f317(f319(f903(f904(x99961,a893),f904(x99961,a893))),f317(f317(f242(f904(x99961,a893),f904(x99961,a893)),f317(f317(f91(f904(x99961,a893)),x99962),x99963)),f317(f317(f91(f904(x99961,a893)),x99964),x99965))),f308(x99961,x99966)))
% 94.68/94.45 [5733]~E(f317(f317(f124(x57331),x57336),x57333),x57335)+E(f317(f317(f124(x57331),x57332),x57333),f317(f317(f141(x57331),x57334),x57335))+~E(x57332,f317(f317(f141(x57331),x57334),x57336))
% 94.68/94.45 [5734]~E(f317(f317(f124(x57341),x57346),x57343),x57345)+E(f317(f317(f124(x57341),x57342),x57343),f317(f317(f124(x57341),x57344),x57345))+~E(x57342,f317(f317(f124(x57341),x57344),x57346))
% 94.68/94.45 [5736]E(f317(f317(f124(x57361),x57362),x57363),f317(f317(f141(x57361),x57364),x57365))+~E(f317(f317(f141(x57361),x57364),x57366),x57362)+~E(x57365,f317(f317(f124(x57361),x57366),x57363))
% 94.68/94.45 [5738]~E(f317(f317(f124(x57381),x57382),x57386),x57384)+E(f317(f317(f124(x57381),x57382),x57383),f317(f317(f124(x57381),x57384),x57385))+~E(x57383,f317(f317(f124(x57381),x57386),x57385))
% 94.68/94.45 [6916]E(f317(x69161,x69162),f317(x69163,x69162))+~E(f317(f317(f144(x69164,x69165),x69161),x69166),f317(f317(f144(x69164,x69165),x69163),x69166))+~P1(f317(f317(f319(x69164),x69162),f317(f162(x69164),x69166)))
% 94.68/94.45 [7306]~P19(x73064,x73065,x73066,x73061)+E(f317(f317(x73061,x73062),x73063),f317(f317(f58(x73064,x73065,x73066),x73063),x73062))+~P1(f317(f28(x73064),x73062))
% 94.68/94.45 [7377]~E(x73772,f317(x73774,x73776))+~P1(f317(f317(f319(x73773),x73776),x73775))+P1(f317(f317(f319(x73771),x73772),f317(f300(x73773,x73771,x73774),x73775)))
% 94.68/94.45 [7378]~E(f317(x73784,x73782),x73786)+~P1(f317(f317(f319(x73783),x73786),x73785))+P1(f317(f317(f319(x73781),x73782),f317(f301(x73781,x73783,x73784),x73785)))
% 94.68/94.45 [7830]~P31(x78301,x78302,x78304,x78306)+P31(x78301,x78302,f317(f317(f141(x78301),x78303),x78304),f317(f317(f141(x78301),x78305),x78306))+~P1(f317(f317(x78302,x78303),x78305))
% 94.68/94.45 [8844]~P56(x88444,x88445,x88441,x88442,x88446)+E(f317(x88441,f317(x88442,x88443)),x88443)+~P1(f317(f317(f319(x88445),x88443),x88446))
% 94.68/94.45 [9344]~P25(x93442,x93441,x93445,x93444,x93443)+E(f317(f85(x93441,x93442,x93443,f85(x93442,x93441,x93444,x93445)),x93446),f317(x93445,x93446))+~P1(f317(f317(f319(x93442),x93446),x93444))
% 94.68/94.45 [9355]~P24(x93551,x93552,x93553,x93556)+P24(x93551,x93552,f69(x93551,x93552,x93553,x93554,x93555),x93556)+P1(f317(f317(f319(x93552),x93555),f317(f300(x93551,x93552,x93553),x93556)))
% 94.68/94.45 [9670]E(x96701,x96702)+E(f317(f179(f898(x96703)),x96704),f317(f179(f898(x96703)),x96705))+~P1(f317(f317(f319(f903(f898(x96703),f898(x96703))),f317(f317(f242(f898(x96703),f898(x96703)),f317(f317(f141(x96703),x96701),x96704)),f317(f317(f141(x96703),x96702),x96705))),f135(x96703,x96706)))
% 94.68/94.45 [9733]~P16(x97331,x97332,x97333)+E(f317(f317(f58(x97331,x97332,x97333),x97334),x97335),x97336)+~P1(f317(f60(x97331,x97332,x97333,x97334,x97335),x97336))
% 94.68/94.45 [9741]E(f317(f179(f898(x97411)),x97412),f317(f179(f898(x97411)),x97413))+P1(f317(f317(f319(f903(f898(x97411),f898(x97411))),f317(f317(f242(f898(x97411),f898(x97411)),x97412),x97413)),f135(x97411,x97414)))+~P1(f317(f317(f319(f903(f898(x97411),f898(x97411))),f317(f317(f242(f898(x97411),f898(x97411)),f317(f317(f141(x97411),x97415),x97412)),f317(f317(f141(x97411),x97416),x97413))),f135(x97411,x97414)))
% 94.68/94.45 [9762]~P1(f317(f317(f319(f903(x97621,x97621)),f317(f317(f242(x97621,x97621),x97622),x97624)),f297(x97621,x97626)))+P1(f317(f317(f319(f903(f898(x97621),f898(x97621))),f317(f317(f242(f898(x97621),f898(x97621)),f317(f317(f141(x97621),x97622),x97623)),f317(f317(f141(x97621),x97624),x97625))),f297(f898(x97621),f147(x97621,x97626))))+~P1(f317(f317(f319(f903(f898(x97621),f898(x97621))),f317(f317(f242(f898(x97621),f898(x97621)),x97623),x97625)),f297(f898(x97621),f147(x97621,x97626))))
% 94.68/94.45 [9938]~P1(f317(x99382,x99386))+~E(f317(f126(x99381,x99382),x99383),f317(f317(f141(x99381),x99384),x99385))+~P1(f317(f317(f319(x99381),x99386),f317(f162(x99381),f723(x99385,x99384,x99383,x99382,x99381))))
% 94.68/94.45 [9939]~P1(f317(x99394,x99396))+~E(f317(f317(f141(x99391),x99392),x99393),f317(f126(x99391,x99394),x99395))+~P1(f317(f317(f319(x99391),x99396),f317(f162(x99391),f721(x99395,x99394,x99393,x99392,x99391))))
% 94.68/94.45 [10256]~P76(x102562)+E(f317(f317(f6(x102561,x102562),f317(f317(f8(f904(x102563,a893),x102562,x102561),f317(f6(x102563,x102562),x102564)),f317(f317(f8(f904(x102563,a893),f904(x102563,a893),x102561),f252(x102563)),f317(f317(f8(f904(x102563,a893),f904(x102563,a893),x102561),f317(f18(x102563,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102563),a315),f317(f317(f7(x102563,f904(x102563,a893),a893),f319(x102563)),x102565)))),f317(f7(x102563,x102561,a893),f317(f317(f8(x102561,f904(x102561,a893),x102563),a314),x102566)))))),f317(f300(x102563,x102561,x102566),x102565)),f317(f317(f6(x102563,x102562),x102564),x102565))+~P1(f317(f28(x102563),x102565))
% 94.68/94.45 [6974]~P66(x69743)+P1(f317(x69742,x69745))+E(f317(f126(x69741,x69742),f317(f317(f138(x69741,x69743,x69744),x69745),x69746)),f317(f126(x69741,x69742),x69746))
% 94.68/94.45 [6976]P1(f317(x69761,x69762))+~E(f156(x69763,x69761,x69764),f317(f317(f242(f898(x69763),f898(x69763)),x69765),x69766))+~P1(f317(f317(f319(x69763),x69762),f317(f162(x69763),x69765)))
% 94.68/94.45 [7024]~P1(f317(x70242,x70246))+~E(f156(x70241,x70242,x70243),f317(f317(f242(f898(x70241),f898(x70241)),x70244),x70245))+~P1(f317(f317(f319(x70241),x70246),f317(f162(x70241),x70245)))
% 94.68/94.45 [7692]~P14(x76921,x76922,x76923)+~P1(f317(f28(x76921),x76926))+E(f317(f317(f58(x76921,x76922,x76923),x76924),f317(f317(f299(x76921),x76925),x76926)),f317(f317(f58(x76921,x76922,x76923),f317(f317(x76923,x76925),x76924)),x76926))
% 94.68/94.45 [7745]~P66(x77452)+~P1(f317(f317(f224(x77452),f317(x77453,x77454)),f317(x77453,x77455)))+E(f317(f317(f138(x77451,x77452,x77453),x77454),f317(f317(f141(x77451),x77455),x77456)),f317(f317(f141(x77451),x77454),f317(f317(f141(x77451),x77455),x77456)))
% 94.68/94.45 [7858]E(x78581,x78582)+~E(f317(f317(f244(x78583,x78584),x78581),f317(f16(f904(x78584,a893),x78583),x78585)),f317(f317(f244(x78583,x78584),x78582),f317(f16(f904(x78584,a893),x78583),x78585)))+~P1(f317(f317(f319(x78584),x78586),x78585))
% 94.68/94.45 [7925]~P14(x79251,x79252,x79253)+~P1(f317(f28(x79251),x79256))+E(f317(f317(f58(x79251,x79252,x79253),x79254),f317(f317(f299(x79251),x79255),x79256)),f317(f317(x79253,x79255),f317(f317(f58(x79251,x79252,x79253),x79254),x79256)))
% 94.68/94.45 [8043]~P16(x80431,x80432,x80433)+~P1(f317(f28(x80431),x80436))+E(f317(f317(f58(x80431,x80432,x80433),f317(f317(x80433,x80434),x80435)),x80436),f317(f317(x80433,x80434),f317(f317(f58(x80431,x80432,x80433),x80435),x80436)))
% 94.68/94.45 [8111]~P20(x81112,x81115,x81116,x81111)+~P1(f317(f28(x81112),x81114))+E(f317(x81111,f317(f317(f299(x81112),x81113),x81114)),f317(f67(x81115,x81115,x81115,f317(x81111,x81114)),f317(x81116,x81113)))
% 94.68/94.45 [8143]~P66(x81432)+P1(f317(f317(f224(x81432),f317(x81433,x81434)),f317(x81433,x81435)))+E(f317(f317(f138(x81431,x81432,x81433),x81434),f317(f317(f141(x81431),x81435),x81436)),f317(f317(f141(x81431),x81435),f317(f317(f138(x81431,x81432,x81433),x81434),x81436)))
% 94.68/94.45 [8286]~E(f317(f179(f898(x82861)),x82865),f317(f179(f898(x82862)),x82866))+~E(f317(f179(f898(x82861)),x82863),f317(f179(f898(x82862)),x82864))+E(f317(f317(f124(f903(x82861,x82862)),f317(f317(f171(x82861,x82862),x82863),x82864)),f317(f317(f171(x82861,x82862),x82865),x82866)),f317(f317(f171(x82861,x82862),f317(f317(f124(x82861),x82863),x82865)),f317(f317(f124(x82862),x82864),x82866)))
% 94.68/94.45 [8398]~E(x83982,f317(f300(x83983,x83981,x83984),x83986))+P1(f317(f317(f224(f904(x83981,a893)),x83982),f317(f300(x83983,x83981,x83984),x83985)))+~P1(f317(f317(f224(f904(x83983,a893)),x83986),x83985))
% 94.68/94.45 [8500]~P66(x85005)+E(f317(x85001,x85002),f317(x85001,x85003))+E(f317(f317(f138(x85004,x85005,x85001),x85002),f317(f317(f138(x85004,x85005,x85001),x85003),x85006)),f317(f317(f138(x85004,x85005,x85001),x85003),f317(f317(f138(x85004,x85005,x85001),x85002),x85006)))
% 94.68/94.45 [8674]~P1(f317(f317(f319(x86742),x86744),f317(x86746,x86743)))+~P1(f317(f317(f319(x86741),x86743),x86745))+P1(f317(f317(f319(f903(x86741,x86742)),f317(f317(f242(x86741,x86742),x86743),x86744)),f317(f317(f244(x86741,x86742),x86745),x86746)))
% 94.68/94.45 [9149]~P77(x91492)+~P24(x91494,x91491,x91495,x91496)+E(f317(f317(f9(x91491,x91492),x91493),f317(f300(x91494,x91491,x91495),x91496)),f317(f317(f9(x91494,x91492),f317(f67(x91491,x91492,x91494,x91493),x91495)),x91496))
% 94.68/94.45 [9150]~P76(x91502)+~P24(x91504,x91501,x91505,x91506)+E(f317(f317(f6(x91501,x91502),x91503),f317(f300(x91504,x91501,x91505),x91506)),f317(f317(f6(x91504,x91502),f317(f67(x91501,x91502,x91504,x91503),x91505)),x91506))
% 94.68/94.45 [9197]~P33(x91972,x91975,x91971,x91973,x91976)+P1(f317(f317(x91971,f317(f317(f154(x91972),x91973),x91974)),f317(f317(f154(x91975),x91976),x91974)))+~P1(f317(f317(f225(a897),x91974),f317(f179(f898(x91975)),x91976)))
% 94.68/94.45 [9198]~P33(x91982,x91985,x91981,x91983,x91986)+P1(f317(f317(x91981,f317(f317(f154(x91982),x91983),x91984)),f317(f317(f154(x91985),x91986),x91984)))+~P1(f317(f317(f225(a897),x91984),f317(f179(f898(x91982)),x91983)))
% 94.68/94.45 [9209]~E(f317(f300(x92091,x92092,x92093),x92094),x92096)+E(f317(f300(x92091,x92092,x92093),f317(f300(x92092,x92091,f85(x92091,x92092,x92094,x92093)),x92095)),x92095)+~P1(f317(f317(f224(f904(x92092,a893)),x92095),x92096))
% 94.68/94.45 [9415]~P19(x94153,x94151,x94156,x94152)+~P1(f317(f28(x94153),x94154))+E(f317(f67(x94151,x94151,x94151,f317(x94152,f317(f317(f23(f904(x94153,a893)),x94154),f317(f317(f299(x94153),x94155),f178(f904(x94153,a893)))))),f317(x94156,x94155)),f317(x94152,f317(f317(f299(x94153),x94155),x94154)))
% 94.68/94.45 [10025]~E(f317(f300(x100252,x100254,x100256),f232(f904(x100252,a893))),f232(f904(x100254,a893)))+~E(f317(f300(x100251,x100253,x100255),f232(f904(x100251,a893))),f232(f904(x100253,a893)))+E(f317(f300(f903(x100251,x100252),f903(x100253,x100254),f248(x100251,x100253,x100252,x100254,x100255,x100256)),f232(f904(f903(x100251,x100252),a893))),f232(f904(f903(x100253,x100254),a893)))
% 94.68/94.45 [10082]~P24(x100823,x100824,x100825,f317(x100826,f606(x100826,x100825,x100824,x100823,x100822,x100821)))+P24(x100823,x100824,x100825,f317(f317(f35(x100822,f904(x100823,a893)),x100821),x100826))+E(x100821,f178(f904(x100822,a893)))
% 94.68/94.45 [10139]P24(x101396,x101395,x101394,f317(f317(f35(x101392,f904(x101396,a893)),x101391),x101393))+E(x101391,f178(f904(x101392,a893)))+P1(f317(f317(f319(x101392),f606(x101393,x101394,x101395,x101396,x101392,x101391)),x101391))
% 94.68/94.45 [10144]P1(f317(f317(f319(x101441),f540(x101442,x101443,x101444,x101445,x101446,x101441)),x101446))+P1(f317(f317(f224(f904(f903(x101441,x101444),a893)),f317(f317(f244(x101441,x101444),x101446),x101443)),f317(f317(f244(x101441,x101444),x101445),x101442)))+~P1(f317(f317(f224(f904(x101441,a893)),x101446),x101445))
% 94.68/94.45 [10274]~P1(f317(f317(f224(f904(x102742,a893)),f317(x102744,f540(x102746,x102744,x102742,x102745,x102743,x102741))),f317(x102746,f540(x102746,x102744,x102742,x102745,x102743,x102741))))+~P1(f317(f317(f224(f904(x102741,a893)),x102743),x102745))+P1(f317(f317(f224(f904(f903(x102741,x102742),a893)),f317(f317(f244(x102741,x102742),x102743),x102744)),f317(f317(f244(x102741,x102742),x102745),x102746)))
% 94.68/94.45 [7881]~P1(f317(x78811,x78815))+~P1(f317(x78816,x78814))+P1(f317(x78811,f317(f246(x78812,x78813),f317(f317(f242(x78812,x78813),x78814),x78815))))
% 94.68/94.45 [7882]~P1(f317(x78821,x78824))+~P1(f317(x78826,x78825))+P1(f317(x78821,f317(f241(x78822,x78823),f317(f317(f242(x78822,x78823),x78824),x78825))))
% 94.68/94.45 [7930]~P1(f317(f317(x79304,x79306),x79305))+~P1(f317(f317(f319(x79301),x79306),x79303))+P1(f317(f317(f317(f34(x79301,f904(x79302,a893)),x79303),x79304),x79305))
% 94.68/94.45 [8236]~P1(f317(f317(f319(x82361),x82362),f317(x82365,x82366)))+~P1(f317(f317(f319(x82363),x82366),x82364))+P1(f317(f317(f319(x82361),x82362),f317(f317(f34(x82363,f904(x82361,a893)),x82364),x82365)))
% 94.68/94.45 [8280]P1(f317(f317(x82801,x82802),x82803))+~P1(f317(f317(x82804,x82802),x82803))+~P1(f317(f317(f224(f904(x82805,f904(x82806,a893))),x82804),x82801))
% 94.68/94.45 [8421]P1(f317(f317(x84211,x84212),x84213))+~P1(f317(f317(f319(x84214),x84212),x84215))+~P1(f317(f317(f317(f35(x84214,f904(x84216,a893)),x84215),x84211),x84213))
% 94.68/94.45 [8556]P1(f317(f317(f319(x85561),x85562),f317(x85563,x85564)))+~P1(f317(f317(f319(x85565),x85564),x85566))+~P1(f317(f317(f319(x85561),x85562),f317(f317(f35(x85565,f904(x85561,a893)),x85566),x85563)))
% 94.68/94.45 [8823]~P11(x88234,x88235,x88236,x88231)+E(f317(x88231,x88232),f317(x88231,x88233))+~P1(f317(f317(f319(f903(x88234,x88234)),f317(f317(f242(x88234,x88234),x88232),x88233)),x88236))
% 94.68/94.45 [8858]P1(f317(f317(f224(f904(x88581,a893)),x88582),f317(x88583,x88584)))+~P1(f317(f317(f319(x88585),x88584),x88586))+~P1(f317(f317(f224(f904(x88581,a893)),x88582),f317(f317(f35(x88585,f904(x88581,a893)),x88586),x88583)))
% 94.68/94.45 [8891]~P54(x88913,x88914,f317(f276(x88914,x88913),x88915))+E(x88911,f178(f904(x88912,a893)))+E(f317(f317(f35(x88912,f904(x88913,a893)),x88911),f317(f317(f8(f904(x88914,a893),f904(x88913,a893),x88912),f275(x88914,x88913,x88915)),x88916)),f317(f275(x88914,x88913,x88915),f317(f317(f35(x88912,f904(x88914,a893)),x88911),x88916)))
% 94.68/94.45 [8969]P1(f317(f317(f319(x89691),x89692),f317(f275(x89693,x89691,x89694),x89695)))+~P1(f317(f317(f319(x89693),x89696),x89695))+~P1(f317(f317(f319(f903(x89693,x89691)),f317(f317(f242(x89693,x89691),x89696),x89692)),x89694))
% 94.68/94.45 [9274]P1(f317(f317(f224(f904(x92741,a893)),f317(f275(x92742,x92741,x92743),x92744)),f317(f275(x92742,x92741,x92745),x92746)))+~P1(f317(f317(f224(f904(x92742,a893)),x92744),x92746))+~P1(f317(f317(f224(f904(f903(x92742,x92741),a893)),x92743),x92745))
% 94.68/94.45 [9464]~P1(f317(f317(f319(x94642),x94646),x94644))+~P1(f317(f317(f224(f904(x94641,a893)),x94643),x94645))+P1(f317(f317(f224(f904(f903(x94641,x94642),a893)),f317(f317(f244(x94641,x94642),x94643),f317(f16(f904(x94642,a893),x94641),x94644))),f317(f317(f244(x94641,x94642),x94645),f317(f16(f904(x94642,a893),x94641),x94644))))
% 94.68/94.45 [9476]~P33(x94761,x94762,x94763,x94765,x94766)+P1(f317(f317(f247(x94761,x94762,a893),x94763),x94764))+~P1(f317(f317(f319(f903(x94761,x94762)),x94764),f317(f162(f903(x94761,x94762)),f317(f317(f171(x94761,x94762),x94765),x94766))))
% 94.68/94.45 [9624]~E(x96243,x96245)+P1(f317(f317(f319(f903(f898(x96241),f898(x96241))),f317(f317(f242(f898(x96241),f898(x96241)),f317(f317(f141(x96241),x96242),x96243)),f317(f317(f141(x96241),x96244),x96245))),f147(x96241,x96246)))+~P1(f317(f317(f319(f903(x96241,x96241)),f317(f317(f242(x96241,x96241),x96242),x96244)),x96246))
% 94.68/94.45 [9630]~E(f317(f179(f898(x96301)),x96303),f317(f179(f898(x96301)),x96305))+P1(f317(f317(f319(f903(f898(x96301),f898(x96301))),f317(f317(f242(f898(x96301),f898(x96301)),f317(f317(f141(x96301),x96302),x96303)),f317(f317(f141(x96301),x96304),x96305))),f135(x96301,x96306)))+~P1(f317(f317(f319(f903(x96301,x96301)),f317(f317(f242(x96301,x96301),x96302),x96304)),x96306))
% 94.68/94.45 [9662]P1(f317(f317(f319(f903(x96621,x96621)),f317(f317(f242(x96621,x96621),x96622),x96623)),f317(f317(f173(f903(x96621,x96621),a893),f317(a102,x96624)),x96625)))+~P1(f317(f317(f319(f903(x96621,x96621)),f317(f317(f242(x96621,x96621),x96626),x96623)),x96625))+~P1(f317(f317(f319(f903(x96621,x96621)),f317(f317(f242(x96621,x96621),x96622),x96626)),f317(f317(f173(f903(x96621,x96621),a893),x96624),x96625)))
% 94.68/94.45 [9663]P1(f317(f317(f319(f903(x96631,x96631)),f317(f317(f242(x96631,x96631),x96632),x96633)),f317(f317(f173(f903(x96631,x96631),a893),f317(a102,x96634)),x96635)))+~P1(f317(f317(f319(f903(x96631,x96631)),f317(f317(f242(x96631,x96631),x96632),x96636)),x96635))+~P1(f317(f317(f319(f903(x96631,x96631)),f317(f317(f242(x96631,x96631),x96636),x96633)),f317(f317(f173(f903(x96631,x96631),a893),x96634),x96635)))
% 94.68/94.45 [9666]~P1(f317(f317(f319(x96664),x96665),x96666))+P1(f317(f317(f224(f904(x96661,a893)),x96662),x96663))+~P1(f317(f317(f224(f904(f903(x96661,x96664),a893)),f317(f317(f244(x96661,x96664),x96662),f317(f16(f904(x96664,a893),x96661),x96666))),f317(f317(f244(x96661,x96664),x96663),f317(f16(f904(x96664,a893),x96661),x96666))))
% 94.68/94.45 [9711]E(x97111,x97112)+~P1(f317(f317(f319(f903(f898(x97113),f898(x97113))),f317(f317(f242(f898(x97113),f898(x97113)),f317(f317(f141(x97113),x97111),x97115)),f317(f317(f141(x97113),x97112),x97116))),f135(x97113,x97114)))+P1(f317(f317(f319(f903(x97113,x97113)),f317(f317(f242(x97113,x97113),x97111),x97112)),x97114))
% 94.68/94.45 [9712]E(x97121,x97122)+~P1(f317(f317(f319(f903(f898(x97123),f898(x97123))),f317(f317(f242(f898(x97123),f898(x97123)),f317(f317(f141(x97123),x97121),x97125)),f317(f317(f141(x97123),x97122),x97126))),f137(x97123,x97124)))+P1(f317(f317(f319(f903(x97123,x97123)),f317(f317(f242(x97123,x97123),x97121),x97122)),x97124))
% 94.68/94.45 [9713]E(x97131,x97132)+~P1(f317(f317(f319(f903(f898(x97133),f898(x97133))),f317(f317(f242(f898(x97133),f898(x97133)),f317(f317(f141(x97133),x97131),x97135)),f317(f317(f141(x97133),x97132),x97136))),f147(x97133,x97134)))+P1(f317(f317(f319(f903(x97133,x97133)),f317(f317(f242(x97133,x97133),x97131),x97132)),x97134))
% 94.68/94.45 [9749]P1(f317(f317(f319(f903(f898(x97491),f898(x97491))),f317(f317(f242(f898(x97491),f898(x97491)),f317(f317(f141(x97491),x97492),x97493)),f317(f317(f141(x97491),x97494),x97495))),f148(x97491,x97496)))+~P1(f317(f317(f319(f903(f898(x97491),f898(x97491))),f317(f317(f242(f898(x97491),f898(x97491)),x97493),x97495)),f148(x97491,x97496)))+~P1(f317(f317(f319(f903(x97491,x97491)),f317(f317(f242(x97491,x97491),x97492),x97494)),x97496))
% 94.68/94.45 [9766]P1(f317(x97661,x97662))+~P1(f317(x97661,f440(x97661,x97663,x97664,x97665,x97666)))+~P1(f317(f317(f319(x97666),x97662),f317(f317(f34(x97665,f904(x97666,a893)),x97664),x97663)))
% 94.68/94.45 [9771]~P1(f317(f317(f319(f903(f898(x97711),f898(x97711))),f317(f317(f242(f898(x97711),f898(x97711)),f317(f317(f141(x97711),x97712),x97715)),f317(f317(f141(x97711),x97713),x97716))),f135(x97711,x97714)))+P1(f317(f317(f319(f903(f898(x97711),f898(x97711))),f317(f317(f242(f898(x97711),f898(x97711)),x97715),x97716)),f135(x97711,x97714)))+P1(f317(f317(f319(f903(x97711,x97711)),f317(f317(f242(x97711,x97711),x97712),x97713)),x97714))
% 94.68/94.45 [9772]~P1(f317(f317(f319(f903(f898(x97721),f898(x97721))),f317(f317(f242(f898(x97721),f898(x97721)),f317(f317(f141(x97721),x97722),x97725)),f317(f317(f141(x97721),x97723),x97726))),f137(x97721,x97724)))+P1(f317(f317(f319(f903(f898(x97721),f898(x97721))),f317(f317(f242(f898(x97721),f898(x97721)),x97725),x97726)),f137(x97721,x97724)))+P1(f317(f317(f319(f903(x97721,x97721)),f317(f317(f242(x97721,x97721),x97722),x97723)),x97724))
% 94.68/94.45 [9773]~P1(f317(f317(f319(f903(f898(x97731),f898(x97731))),f317(f317(f242(f898(x97731),f898(x97731)),f317(f317(f141(x97731),x97732),x97735)),f317(f317(f141(x97731),x97733),x97736))),f147(x97731,x97734)))+P1(f317(f317(f319(f903(f898(x97731),f898(x97731))),f317(f317(f242(f898(x97731),f898(x97731)),x97735),x97736)),f147(x97731,x97734)))+P1(f317(f317(f319(f903(x97731,x97731)),f317(f317(f242(x97731,x97731),x97732),x97733)),x97734))
% 94.68/94.45 [9861]P1(f317(x98611,x98612))+P1(f317(f317(f319(x98613),f441(x98611,x98614,x98615,x98613,x98616)),x98615))+~P1(f317(f317(f319(x98616),x98612),f317(f317(f34(x98613,f904(x98616,a893)),x98615),x98614)))
% 94.68/94.45 [9872]~E(x98722,x98724)+P1(f317(f317(f319(f903(f898(x98721),f898(x98721))),f317(f317(f242(f898(x98721),f898(x98721)),f317(f317(f124(x98721),x98722),f317(f317(f141(x98721),x98723),f103(x98721)))),f317(f317(f124(x98721),x98724),f317(f317(f141(x98721),x98725),f103(x98721))))),f147(x98721,x98726)))+~P1(f317(f317(f319(f903(x98721,x98721)),f317(f317(f242(x98721,x98721),x98723),x98725)),x98726))
% 94.68/94.45 [9946]E(x99461,x99462)+~P1(f317(f317(f319(f903(f898(x99463),f898(x99463))),f317(f317(f242(f898(x99463),f898(x99463)),f317(f317(f124(x99463),x99465),f317(f317(f141(x99463),x99461),f103(x99463)))),f317(f317(f124(x99463),x99466),f317(f317(f141(x99463),x99462),f103(x99463))))),f147(x99463,x99464)))+P1(f317(f317(f319(f903(x99463,x99463)),f317(f317(f242(x99463,x99463),x99461),x99462)),x99464))
% 94.68/94.45 [9977]~P1(f317(f317(f319(f903(f898(x99771),f898(x99771))),f317(f317(f242(f898(x99771),f898(x99771)),f317(f317(f124(x99771),x99775),f317(f317(f141(x99771),x99772),f103(x99771)))),f317(f317(f124(x99771),x99776),f317(f317(f141(x99771),x99773),f103(x99771))))),f147(x99771,x99774)))+P1(f317(f317(f319(f903(f898(x99771),f898(x99771))),f317(f317(f242(f898(x99771),f898(x99771)),x99775),x99776)),f147(x99771,x99774)))+P1(f317(f317(f319(f903(x99771,x99771)),f317(f317(f242(x99771,x99771),x99772),x99773)),x99774))
% 94.68/94.45 [9997]P1(f317(x99971,x99972))+P1(f317(f317(f319(x99973),f440(x99971,x99974,x99975,x99976,x99973)),f317(x99974,f441(x99971,x99974,x99975,x99976,x99973))))+~P1(f317(f317(f319(x99973),x99972),f317(f317(f34(x99976,f904(x99973,a893)),x99975),x99974)))
% 94.68/94.45 [10148]P1(f317(f317(f319(x101481),f817(x101482,x101483,x101484,x101485,x101486,x101481)),x101485))+~P1(f317(f317(f224(f904(x101481,a893)),x101486),x101485))+P1(f317(f317(f224(f904(x101484,a893)),f317(f317(f35(x101481,f904(x101484,a893)),x101485),x101483)),f317(f317(f35(x101481,f904(x101484,a893)),x101485),x101482)))
% 94.68/94.45 [10275]~P1(f317(f317(f224(f904(x102751,a893)),f317(x102754,f817(x102755,x102754,x102751,x102753,x102756,x102752))),f317(x102755,f817(x102755,x102754,x102751,x102753,x102756,x102752))))+~P1(f317(f317(f224(f904(x102752,a893)),x102756),x102753))+P1(f317(f317(f224(f904(x102751,a893)),f317(f317(f35(x102752,f904(x102751,a893)),x102753),x102754)),f317(f317(f35(x102752,f904(x102751,a893)),x102753),x102755)))
% 94.68/94.45 [8989]~P16(x89893,x89894,x89891)+~P1(f317(f28(x89893),x89896))+E(f317(f317(x89891,x89892),f317(f317(f58(x89893,x89894,x89891),x89895),f317(f317(f23(f904(x89893,a893)),x89896),f317(f317(f299(x89893),x89892),f178(f904(x89893,a893)))))),f317(f317(f58(x89893,x89894,x89891),x89895),f317(f317(f299(x89893),x89892),x89896)))
% 94.68/94.45 [9283]~P1(f317(f317(f319(x92835),x92833),x92836))+P1(f317(f317(f224(f904(x92831,a893)),f317(x92832,x92833)),x92834))+~P1(f317(f317(f224(f904(x92831,a893)),f317(f317(f34(x92835,f904(x92831,a893)),x92836),x92832)),x92834))
% 94.68/94.45 [9921]~P8(x99211,x99215,x99214)+P1(f317(f317(f319(f903(x99211,x99211)),f317(f317(f242(x99211,x99211),x99212),x99213)),x99214))+~P1(f317(f317(f319(x99211),x99216),f317(f317(f92(f904(x99211,a893)),f317(f275(x99211,x99211,x99214),f317(f317(f299(x99211),x99212),f178(f904(x99211,a893))))),f317(f275(x99211,x99211,x99214),f317(f317(f299(x99211),x99213),f178(f904(x99211,a893)))))))
% 94.68/94.45 [8711]~P131(x87112)+~E(f317(f317(f74(x87112),f317(f317(f75(x87112),x87114),x87115)),x87111),f317(f317(f74(x87112),f317(f317(f75(x87112),x87113),x87115)),x87116))+E(x87111,f317(f317(f74(x87112),f317(f317(f75(x87112),f317(f317(f23(x87112),x87113),x87114)),x87115)),x87116))
% 94.68/94.45 [8712]~P131(x87121)+~E(f317(f317(f74(x87121),f317(f317(f75(x87121),x87122),x87124)),x87125),f317(f317(f74(x87121),f317(f317(f75(x87121),x87123),x87124)),x87126))+E(f317(f317(f74(x87121),f317(f317(f75(x87121),f317(f317(f23(x87121),x87122),x87123)),x87124)),x87125),x87126)
% 94.68/94.45 [8894]~P131(x88941)+E(f317(f317(f74(x88941),f317(f317(f75(x88941),x88942),x88943)),x88944),f317(f317(f74(x88941),f317(f317(f75(x88941),x88945),x88943)),x88946))+~E(x88946,f317(f317(f74(x88941),f317(f317(f75(x88941),f317(f317(f23(x88941),x88942),x88945)),x88943)),x88944))
% 94.68/94.45 [8895]~P131(x88951)+E(f317(f317(f74(x88951),f317(f317(f75(x88951),x88952),x88953)),x88954),f317(f317(f74(x88951),f317(f317(f75(x88951),x88955),x88953)),x88956))+~E(f317(f317(f74(x88951),f317(f317(f75(x88951),f317(f317(f23(x88951),x88952),x88955)),x88953)),x88954),x88956)
% 94.68/94.45 [9220]~P1(f317(f317(x92204,x92205),x92206))+~P1(f317(f317(x92203,x92205),x92206))+P1(f317(f317(f317(f317(f92(f904(x92201,f904(x92202,a893))),x92203),x92204),x92205),x92206))
% 94.68/94.45 [9485]P1(f317(f317(x94851,x94852),x94853))+P1(f317(f317(x94854,x94852),x94853))+~P1(f317(f317(f317(f317(f91(f904(x94855,f904(x94856,a893))),x94854),x94851),x94852),x94853))
% 94.68/94.45 [9786]~P136(x97861)+~P1(f317(f317(f224(x97861),f317(f317(f74(x97861),f317(f317(f75(x97861),x97864),x97865)),x97862)),f317(f317(f74(x97861),f317(f317(f75(x97861),x97863),x97865)),x97866)))+P1(f317(f317(f224(x97861),x97862),f317(f317(f74(x97861),f317(f317(f75(x97861),f317(f317(f23(x97861),x97863),x97864)),x97865)),x97866)))
% 94.68/94.45 [9787]~P136(x97871)+~P1(f317(f317(f225(x97871),f317(f317(f74(x97871),f317(f317(f75(x97871),x97874),x97875)),x97872)),f317(f317(f74(x97871),f317(f317(f75(x97871),x97873),x97875)),x97876)))+P1(f317(f317(f225(x97871),x97872),f317(f317(f74(x97871),f317(f317(f75(x97871),f317(f317(f23(x97871),x97873),x97874)),x97875)),x97876)))
% 94.68/94.45 [9810]~P136(x98101)+P1(f317(f317(f224(x98101),f317(f317(f74(x98101),f317(f317(f75(x98101),x98102),x98103)),x98104)),f317(f317(f74(x98101),f317(f317(f75(x98101),x98105),x98103)),x98106)))+~P1(f317(f317(f224(x98101),x98104),f317(f317(f74(x98101),f317(f317(f75(x98101),f317(f317(f23(x98101),x98105),x98102)),x98103)),x98106)))
% 94.68/94.45 [9811]~P136(x98111)+P1(f317(f317(f225(x98111),f317(f317(f74(x98111),f317(f317(f75(x98111),x98112),x98113)),x98114)),f317(f317(f74(x98111),f317(f317(f75(x98111),x98115),x98113)),x98116)))+~P1(f317(f317(f225(x98111),x98114),f317(f317(f74(x98111),f317(f317(f75(x98111),f317(f317(f23(x98111),x98115),x98112)),x98113)),x98116)))
% 94.68/94.45 [9913]~P136(x99131)+~P1(f317(f317(f224(x99131),f317(f317(f74(x99131),f317(f317(f75(x99131),x99132),x99134)),x99135)),f317(f317(f74(x99131),f317(f317(f75(x99131),x99133),x99134)),x99136)))+P1(f317(f317(f224(x99131),f317(f317(f74(x99131),f317(f317(f75(x99131),f317(f317(f23(x99131),x99132),x99133)),x99134)),x99135)),x99136))
% 94.68/94.45 [9914]~P136(x99141)+~P1(f317(f317(f225(x99141),f317(f317(f74(x99141),f317(f317(f75(x99141),x99142),x99144)),x99145)),f317(f317(f74(x99141),f317(f317(f75(x99141),x99143),x99144)),x99146)))+P1(f317(f317(f225(x99141),f317(f317(f74(x99141),f317(f317(f75(x99141),f317(f317(f23(x99141),x99142),x99143)),x99144)),x99145)),x99146))
% 94.68/94.45 [9960]~P136(x99601)+P1(f317(f317(f224(x99601),f317(f317(f74(x99601),f317(f317(f75(x99601),x99602),x99603)),x99604)),f317(f317(f74(x99601),f317(f317(f75(x99601),x99605),x99603)),x99606)))+~P1(f317(f317(f224(x99601),f317(f317(f74(x99601),f317(f317(f75(x99601),f317(f317(f23(x99601),x99602),x99605)),x99603)),x99604)),x99606))
% 94.68/94.45 [9961]~P136(x99611)+P1(f317(f317(f225(x99611),f317(f317(f74(x99611),f317(f317(f75(x99611),x99612),x99613)),x99614)),f317(f317(f74(x99611),f317(f317(f75(x99611),x99615),x99613)),x99616)))+~P1(f317(f317(f225(x99611),f317(f317(f74(x99611),f317(f317(f75(x99611),f317(f317(f23(x99611),x99612),x99615)),x99613)),x99614)),x99616))
% 94.68/94.45 [10133]~P76(x101332)+~P1(f317(f28(x101331),x101336))+E(f317(f317(f6(x101331,x101332),f317(f317(f18(x101331,x101332,x101332),f317(f317(f18(x101331,x101332,f904(x101332,x101332)),f317(f317(f8(a893,f904(x101332,f904(x101332,x101332)),x101331),f86(x101332)),x101333)),x101334)),x101335)),x101336),f317(f317(f74(x101332),f317(f317(f6(x101331,x101332),x101334),f317(f317(f92(f904(x101331,a893)),x101336),f317(f252(x101331),x101333)))),f317(f317(f6(x101331,x101332),x101335),f317(f317(f92(f904(x101331,a893)),x101336),f317(f73(f904(x101331,a893)),f317(f252(x101331),x101333))))))
% 94.68/94.45 [10194]P1(f317(f317(f319(x101942),x101944),x101946))+P1(f317(f317(f319(x101942),x101945),x101946))+E(f317(f301(x101941,x101942,f317(f317(f7(x101941,x101942,x101942),f317(f317(f7(x101941,x101942,f904(x101942,x101942)),f317(f317(f8(a893,f904(x101942,f904(x101942,x101942)),x101941),f86(x101942)),f317(f317(f7(x101941,f904(x101941,a893),a893),f319(x101941)),x101943))),x101944)),x101945)),x101946),f178(f904(x101941,a893)))
% 94.68/94.45 [10195]P1(f317(f317(f319(x101952),x101955),x101956))+~P1(f317(f317(f319(x101952),x101954),x101956))+E(f317(f301(x101951,x101952,f317(f317(f7(x101951,x101952,x101952),f317(f317(f7(x101951,x101952,f904(x101952,x101952)),f317(f317(f8(a893,f904(x101952,f904(x101952,x101952)),x101951),f86(x101952)),f317(f317(f7(x101951,f904(x101951,a893),a893),f319(x101951)),x101953))),x101954)),x101955)),x101956),x101953)
% 94.68/94.45 [10196]P1(f317(f317(f319(x101962),x101964),x101966))+~P1(f317(f317(f319(x101962),x101965),x101966))+E(f317(f301(x101961,x101962,f317(f317(f7(x101961,x101962,x101962),f317(f317(f7(x101961,x101962,f904(x101962,x101962)),f317(f317(f8(a893,f904(x101962,f904(x101962,x101962)),x101961),f86(x101962)),f317(f317(f7(x101961,f904(x101961,a893),a893),f319(x101961)),x101963))),x101964)),x101965)),x101966),f317(f73(f904(x101961,a893)),x101963))
% 94.68/94.45 [10197]~P1(f317(f317(f319(x101972),x101974),x101976))+~P1(f317(f317(f319(x101972),x101975),x101976))+E(f317(f301(x101971,x101972,f317(f317(f7(x101971,x101972,x101972),f317(f317(f7(x101971,x101972,f904(x101972,x101972)),f317(f317(f8(a893,f904(x101972,f904(x101972,x101972)),x101971),f86(x101972)),f317(f317(f7(x101971,f904(x101971,a893),a893),f319(x101971)),x101973))),x101974)),x101975)),x101976),f232(f904(x101971,a893)))
% 94.68/94.45 [8744]E(x87441,x87442)+~P56(x87444,x87445,x87443,x87446,x87447)+~E(f317(x87443,x87441),f317(x87443,x87442))
% 94.68/94.45 [8773]~P10(x87736,x87735,x87737,x87734,x87731)+E(f317(f317(x87731,x87732),x87733),x87734)+P1(f317(f28(x87735),x87733))
% 94.68/94.45 [9653]P41(x96531,x96532,x96533,x96534,x96535,f317(f317(x96533,x96536),x96537))+~E(f317(f317(x96533,x96536),x96537),x96534)+~E(x96535,f178(f904(x96531,a893)))
% 94.68/94.45 [9832]~P1(f317(x98326,x98323))+~P1(f317(f317(f319(f903(x98322,x98322)),f317(f317(f242(x98322,x98322),x98324),x98325)),f317(x98327,x98323)))+P1(f317(f317(f319(f903(f903(x98321,x98322),f903(x98321,x98322))),f317(f317(f242(f903(x98321,x98322),f903(x98321,x98322)),f317(f317(f242(x98321,x98322),x98323),x98324)),f317(f317(f242(x98321,x98322),x98323),x98325))),f270(x98321,x98322,x98326,x98327)))
% 94.68/94.45 [10259]~P41(x102592,x102597,x102593,x102596,x102591,f317(f317(x102593,x102595),x102594))+E(f317(f317(x102593,f624(x102594,x102595,x102591,x102596,x102593,x102597,x102592)),f635(x102594,x102595,x102591,x102596,x102593,x102597,x102592)),f317(f317(x102593,x102595),x102594))+E(x102591,f178(f904(x102592,a893)))
% 94.68/94.45 [10260]~P41(x102607,x102606,x102601,x102604,x102605,f317(f317(x102601,x102602),x102603))+E(f317(f317(x102601,f624(x102603,x102602,x102605,x102604,x102601,x102606,x102607)),f635(x102603,x102602,x102605,x102604,x102601,x102606,x102607)),f317(f317(x102601,x102602),x102603))+E(f317(f317(x102601,x102602),x102603),x102604)
% 94.68/94.45 [9317]~P33(x93171,x93172,x93173,x93175,x93177)+P33(x93171,x93172,x93173,f317(f317(f141(x93171),x93174),x93175),f317(f317(f141(x93172),x93176),x93177))+~P1(f317(f317(x93173,x93174),x93176))
% 94.68/94.45 [9336]P33(x93361,x93362,x93363,x93364,x93365)+~P33(x93361,x93362,x93363,f317(f317(f124(x93361),x93366),x93364),f317(f317(f124(x93362),x93367),x93365))+~E(f317(f179(f898(x93361)),x93366),f317(f179(f898(x93362)),x93367))
% 94.68/94.45 [9337]P33(x93371,x93372,x93373,x93374,x93375)+~P33(x93371,x93372,x93373,f317(f317(f124(x93371),x93374),x93376),f317(f317(f124(x93372),x93375),x93377))+~E(f317(f179(f898(x93371)),x93374),f317(f179(f898(x93372)),x93375))
% 94.68/94.45 [9552]~P33(x95521,x95522,x95523,x95525,x95527)+~P33(x95521,x95522,x95523,x95524,x95526)+P33(x95521,x95522,x95523,f317(f317(f124(x95521),x95524),x95525),f317(f317(f124(x95522),x95526),x95527))
% 94.68/94.45 [9906]~P1(f317(f60(x99061,x99064,x99065,x99066,x99063),x99067))+P1(f317(f60(x99061,x99064,x99065,x99066,f317(f317(f299(x99061),x99062),x99063)),f317(f317(x99065,x99062),x99067)))+P1(f317(f317(f319(x99061),x99062),x99063))
% 94.68/94.45 [10291]~P41(x102912,x102917,x102916,x102915,x102911,f317(f317(x102916,x102914),x102913))+E(x102911,f178(f904(x102912,a893)))+P1(f317(f317(f319(x102912),f624(x102913,x102914,x102911,x102915,x102916,x102917,x102912)),x102911))
% 94.68/94.45 [10292]~P41(x102925,x102927,x102921,x102924,x102926,f317(f317(x102921,x102922),x102923))+E(f317(f317(x102921,x102922),x102923),x102924)+P1(f317(f317(f319(x102925),f624(x102923,x102922,x102926,x102924,x102921,x102927,x102925)),x102926))
% 94.68/94.45 [10379]E(f317(f317(f242(x103791,x103792),x103793),x103794),f317(f317(f242(x103791,x103792),x103795),x103796))+P1(f317(f317(f319(f903(f903(x103791,x103792),f903(x103791,x103792))),f317(f317(f242(f903(x103791,x103792),f903(x103791,x103792)),f317(f317(f242(x103791,x103792),f822(x103797,x103794,x103793,x103796,x103795,x103792,x103791)),f823(x103797,x103794,x103793,x103796,x103795,x103792,x103791))),f317(f317(f242(x103791,x103792),x103793),x103794))),f297(f903(x103791,x103792),x103797)))+~P1(f317(f317(f319(f903(f903(x103791,x103792),f903(x103791,x103792))),f317(f317(f242(f903(x103791,x103792),f903(x103791,x103792)),f317(f317(f242(x103791,x103792),x103795),x103796)),f317(f317(f242(x103791,x103792),x103793),x103794))),f297(f903(x103791,x103792),x103797)))
% 94.68/94.45 [9014]~P21(x90144,x90145,x90146,x90147,x90141)+~P1(f317(f28(x90145),x90143))+E(f317(f317(x90141,x90142),x90143),f317(f317(f317(f59(x90144,x90145,x90146),x90142),x90147),x90143))
% 94.68/94.45 [9015]~P10(x90154,x90155,x90156,x90157,x90151)+~P1(f317(f28(x90155),x90153))+E(f317(f317(x90151,x90152),x90153),f317(f317(f317(f59(x90154,x90155,x90156),x90152),x90157),x90153))
% 94.68/94.45 [9805]~P23(x98053,x98054,x98055,x98057,x98056,x98051)+~P1(f317(f28(x98054),x98052))+E(f317(x98051,x98052),f317(f317(f317(f59(x98053,x98054,x98055),x98056),x98057),x98052))
% 94.68/94.45 [9955]P41(x99551,x99552,x99553,x99554,x99555,f317(f317(x99553,x99556),x99557))+~P41(x99551,x99552,x99553,x99554,f317(f317(f23(f904(x99551,a893)),x99555),f317(f317(f299(x99551),x99556),f178(f904(x99551,a893)))),x99557)+~P1(f317(f317(f319(x99551),x99556),x99555))
% 94.68/94.45 [10315]P1(f317(f317(x103157,f765(x103154,x103155,x103151,x103156,x103153,x103152,x103157)),f766(x103154,x103155,x103151,x103156,x103153,x103152,x103157)))+~P1(f317(f317(x103157,f317(f246(x103152,x103153),x103156)),f317(f241(x103152,x103153),x103156)))+P1(f317(x103151,f317(f317(f247(x103152,x103153,x103154),x103155),x103156)))
% 94.68/94.45 [10325]~P41(x103252,x103253,x103254,x103255,x103251,f317(f317(x103254,x103257),x103256))+P41(x103252,x103253,x103254,x103255,f317(f317(f23(f904(x103252,a893)),x103251),f317(f317(f299(x103252),f624(x103256,x103257,x103251,x103255,x103254,x103253,x103252)),f178(f904(x103252,a893)))),f635(x103256,x103257,x103251,x103255,x103254,x103253,x103252))+E(x103251,f178(f904(x103252,a893)))
% 94.68/94.45 [10326]~P41(x103265,x103266,x103261,x103264,x103267,f317(f317(x103261,x103262),x103263))+P41(x103265,x103266,x103261,x103264,f317(f317(f23(f904(x103265,a893)),x103267),f317(f317(f299(x103265),f624(x103263,x103262,x103267,x103264,x103261,x103266,x103265)),f178(f904(x103265,a893)))),f635(x103263,x103262,x103267,x103264,x103261,x103266,x103265))+E(f317(f317(x103261,x103262),x103263),x103264)
% 94.68/94.45 [10346]~P1(f317(x103461,f317(f317(x103465,f766(x103464,x103465,x103461,x103466,x103463,x103462,x103467)),f765(x103464,x103465,x103461,x103466,x103463,x103462,x103467))))+~P1(f317(f317(x103467,f317(f246(x103462,x103463),x103466)),f317(f241(x103462,x103463),x103466)))+P1(f317(x103461,f317(f317(f247(x103462,x103463,x103464),x103465),x103466)))
% 94.68/94.45 [9638]P1(f317(f317(f224(f904(f903(x96381,x96382),a893)),f317(f317(f279(x96381,x96383,x96382),x96384),x96385)),f317(f317(f279(x96381,x96383,x96382),x96386),x96387)))+~P1(f317(f317(f224(f904(f903(x96383,x96382),a893)),x96385),x96387))+~P1(f317(f317(f224(f904(f903(x96381,x96383),a893)),x96384),x96386))
% 94.68/94.45 [10373]E(f317(f317(f242(x103731,x103732),x103733),x103734),f317(f317(f242(x103731,x103732),x103735),x103736))+~P1(f317(f317(f319(f903(f903(x103731,x103732),f903(x103731,x103732))),f317(f317(f242(f903(x103731,x103732),f903(x103731,x103732)),f317(f317(f242(x103731,x103732),x103733),x103734)),f317(f317(f242(x103731,x103732),x103735),x103736))),f297(f903(x103731,x103732),x103737)))+P1(f317(f317(f319(f903(f903(x103731,x103732),f903(x103731,x103732))),f317(f317(f242(f903(x103731,x103732),f903(x103731,x103732)),f317(f317(f242(x103731,x103732),x103733),x103734)),f317(f317(f242(x103731,x103732),f822(x103737,x103736,x103735,x103734,x103733,x103732,x103731)),f823(x103737,x103736,x103735,x103734,x103733,x103732,x103731)))),x103737))
% 94.68/94.45 [9966]~P1(f317(f317(f319(x99661),x99666),x99665))+P1(f317(f60(x99661,x99662,x99663,x99664,x99665),f317(f317(x99663,x99666),x99667)))+~P1(f317(f60(x99661,x99662,x99663,x99664,f317(f317(f23(f904(x99661,a893)),x99665),f317(f317(f299(x99661),x99666),f178(f904(x99661,a893))))),x99667))
% 94.68/94.45 [10386]~P145(x103861)+~P24(f903(x103862,x103863),x103861,f317(f247(x103862,x103863,x103861),f317(f317(f7(x103862,f904(x103863,x103861),f904(x103863,x103861)),f317(f317(f8(f904(x103861,x103861),f904(f904(x103863,x103861),f904(x103863,x103861)),x103862),f8(x103861,x103861,x103863)),f317(f317(f8(x103861,f904(x103861,x103861),x103862),f75(x103861)),x103864))),x103865)),f317(f317(f244(x103862,x103863),x103866),f317(f16(f904(x103863,a893),x103862),x103867)))+E(f317(f317(f6(x103861,x103861),f25(x103861)),f317(f252(x103861),f317(f317(f8(f904(x103862,a893),a893,x103861),f81(x103862)),f317(f317(f8(f904(x103862,f904(x103863,a893)),f904(x103862,a893),x103861),f317(f8(f904(x103863,a893),a893,x103862),f81(x103863))),f317(f317(f7(x103861,f904(x103862,f904(x103863,a893)),f904(x103862,f904(x103863,a893))),f317(f317(f8(f904(x103862,f904(f904(x103863,a893),f904(x103863,a893))),f904(f904(x103862,f904(x103863,a893)),f904(x103862,f904(x103863,a893))),x103861),f18(x103862,f904(x103863,a893),f904(x103863,a893))),f317(f317(f8(f904(x103862,f904(x103863,f904(a893,a893))),f904(x103862,f904(f904(x103863,a893),f904(x103863,a893))),x103861),f317(f8(f904(x103863,f904(a893,a893)),f904(f904(x103863,a893),f904(x103863,a893)),x103862),f18(x103863,a893,a893))),f317(f317(f8(f904(x103862,f904(x103863,a893)),f904(x103862,f904(x103863,f904(a893,a893))),x103861),f317(f8(f904(x103863,a893),f904(x103863,f904(a893,a893)),x103862),f317(f8(a893,f904(a893,a893),x103863),a315))),f317(f317(f7(x103861,f904(x103862,f904(x103863,x103861)),f904(x103862,f904(x103863,a893))),f317(f317(f8(f904(f904(x103863,x103861),f904(x103863,a893)),f904(f904(x103862,f904(x103863,x103861)),f904(x103862,f904(x103863,a893))),x103861),f8(f904(x103863,x103861),f904(x103863,a893),x103862)),f317(f317(f8(f904(x103861,a893),f904(f904(x103863,x103861),f904(x103863,a893)),x103861),f8(x103861,a893,x103863)),a314))),f317(f317(f7(x103862,f904(x103863,x103861),f904(x103863,x103861)),f317(f317(f8(f904(x103861,x103861),f904(f904(x103863,x103861),f904(x103863,x103861)),x103862),f8(x103861,x103861,x103863)),f317(f317(f8(x103861,f904(x103861,x103861),x103862),f75(x103861)),x103864))),x103865)))))),f317(f317(f7(x103862,f904(x103863,a893),f904(x103863,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x103863,a893),f904(x103863,a893)),x103862),f8(a893,a893,x103863)),f317(f317(f8(a893,f904(a893,a893),x103862),a315),f317(f317(f7(x103862,f904(x103862,a893),a893),f319(x103862)),x103866)))),f317(f317(f7(x103863,f904(x103863,a893),a893),f319(x103863)),x103867))))))),f317(f317(f75(x103861),f317(f317(f6(x103862,x103861),x103864),x103866)),f317(f317(f6(x103863,x103861),x103865),x103867)))
% 94.68/94.45 [9642]~P25(x96421,x96423,x96425,x96426,x96428)+~P25(x96423,x96422,x96424,x96428,x96427)+P25(x96421,x96422,f317(f67(x96423,x96422,x96421,x96424),x96425),x96426,x96427)
% 94.68/94.45 [9671]P25(x96711,x96712,x96713,x96714,x96715)+~P25(x96716,x96711,x96717,x96718,x96714)+~P25(x96716,x96712,f317(f67(x96711,x96712,x96716,x96713),x96717),x96718,x96715)
% 94.68/94.45 [9803]~P1(f317(f317(x98034,x98036),x98038))+~P1(f317(f317(x98035,x98038),x98037))+P1(f317(f317(f243(x98031,x98032,x98033,x98034,x98035),x98036),x98037))
% 94.68/94.45 [9392]~P19(x93928,x93921,x93923,x93925)+~P1(f317(f28(x93928),x93926))+E(f317(f67(x93921,x93921,x93922,f317(x93923,x93924)),f317(f67(x93921,x93921,x93922,f317(x93925,x93926)),x93927)),f317(f67(x93921,x93921,x93922,f317(x93925,x93926)),f317(f67(x93921,x93921,x93922,f317(x93923,x93924)),x93927)))
% 94.68/94.45 [9793]~P22(x97937,x97932,x97935,x97938,x97936,x97931)+~P1(f317(f28(x97932),x97934))+E(f317(x97931,f317(f317(f299(x97932),x97933),x97934)),f317(f317(x97935,f317(x97936,x97933)),f317(x97931,x97934)))
% 94.68/94.45 [9911]~P24(x99112,x99114,x99116,x99118)+~P24(x99111,x99113,x99115,x99117)+P24(f903(x99111,x99112),f903(x99113,x99114),f248(x99111,x99113,x99112,x99114,x99115,x99116),f317(f317(f244(x99111,x99112),x99117),f317(f16(f904(x99112,a893),x99111),x99118)))
% 94.68/94.45 [9578]P1(f317(f317(f319(f903(x95781,x95782)),f317(f317(f242(x95781,x95782),x95783),x95784)),f317(f317(f279(x95781,x95785,x95782),x95786),x95787)))+~P1(f317(f317(f319(f903(x95781,x95785)),f317(f317(f242(x95781,x95785),x95783),x95788)),x95786))+~P1(f317(f317(f319(f903(x95785,x95782)),f317(f317(f242(x95785,x95782),x95788),x95784)),x95787))
% 94.68/94.45 [9774]~P1(f317(f317(f224(f904(f903(x97743,x97742),a893)),x97745),f317(f317(f244(x97743,x97742),x97748),f317(f16(f904(x97742,a893),x97743),x97747))))+~P1(f317(f317(f224(f904(f903(x97741,x97743),a893)),x97744),f317(f317(f244(x97741,x97743),x97746),f317(f16(f904(x97743,a893),x97741),x97748))))+P1(f317(f317(f224(f904(f903(x97741,x97742),a893)),f317(f317(f279(x97741,x97743,x97742),x97744),x97745)),f317(f317(f244(x97741,x97742),x97746),f317(f16(f904(x97742,a893),x97741),x97747))))
% 94.68/94.45 [9827]~E(x98273,x98275)+P1(f317(f317(f319(f903(f903(x98271,x98272),f903(x98271,x98272))),f317(f317(f242(f903(x98271,x98272),f903(x98271,x98272)),f317(f317(f242(x98271,x98272),x98273),x98274)),f317(f317(f242(x98271,x98272),x98275),x98276))),f309(x98271,x98272,x98277,x98278)))+~P1(f317(f317(f319(f903(x98272,x98272)),f317(f317(f242(x98272,x98272),x98274),x98276)),x98278))
% 94.68/94.45 [9930]E(x99301,x99302)+~P1(f317(f317(f319(f903(f903(x99303,x99305),f903(x99303,x99305))),f317(f317(f242(f903(x99303,x99305),f903(x99303,x99305)),f317(f317(f242(x99303,x99305),x99301),x99306)),f317(f317(f242(x99303,x99305),x99302),x99307))),f309(x99303,x99305,x99304,x99308)))+P1(f317(f317(f319(f903(x99303,x99303)),f317(f317(f242(x99303,x99303),x99301),x99302)),x99304))
% 94.68/94.45 [9945]~P1(f317(f317(f319(f903(f903(x99451,x99455),f903(x99451,x99455))),f317(f317(f242(f903(x99451,x99455),f903(x99451,x99455)),f317(f317(f242(x99451,x99455),x99452),x99456)),f317(f317(f242(x99451,x99455),x99453),x99457))),f309(x99451,x99455,x99454,x99458)))+P1(f317(f317(f319(f903(x99451,x99451)),f317(f317(f242(x99451,x99451),x99452),x99453)),x99454))+P1(f317(f317(f319(f903(x99455,x99455)),f317(f317(f242(x99455,x99455),x99456),x99457)),x99458))
% 94.68/94.45 [9862]~P23(x98627,x98625,x98621,x98628,x98622,x98624)+~P1(f317(f28(x98625),x98626))+E(f317(f317(x98621,f317(x98622,x98623)),f317(x98624,f317(f317(f23(f904(x98625,a893)),x98626),f317(f317(f299(x98625),x98623),f178(f904(x98625,a893)))))),f317(x98624,f317(f317(f299(x98625),x98623),x98626)))
% 94.68/94.45 [9343]~P1(f317(f317(f317(x93435,x93438),x93436),x93437))+~P1(f317(f317(f319(x93431),x93438),x93434))+P1(f317(f317(f317(f317(f34(x93431,f904(x93432,f904(x93433,a893))),x93434),x93435),x93436),x93437))
% 94.68/94.45 [9563]P1(f317(f317(f317(x95631,x95632),x95633),x95634))+~P1(f317(f317(f319(x95635),x95632),x95636))+~P1(f317(f317(f317(f317(f35(x95635,f904(x95637,f904(x95638,a893))),x95636),x95631),x95633),x95634))
% 94.68/94.45 [9767]~P21(x97673,x97672,x97674,x97678,x97671)+~P1(f317(f28(x97672),x97677))+E(f317(f317(x97671,f317(f317(f18(x97672,x97673,x97673),f317(f317(f8(x97673,f904(x97673,x97673),x97672),x97674),x97675)),x97676)),x97677),f317(f317(x97674,f317(f317(x97671,x97675),x97677)),f317(f317(x97671,x97676),x97677)))
% 94.68/94.45 [10031]~E(f317(f300(x100312,x100314,x100316),x100318),x1003110)+~E(f317(f300(x100311,x100313,x100315),x100317),x100319)+E(f317(f300(f903(x100311,x100312),f903(x100313,x100314),f248(x100311,x100313,x100312,x100314,x100315,x100316)),f317(f317(f244(x100311,x100312),x100317),f317(f16(f904(x100312,a893),x100311),x100318))),f317(f317(f244(x100313,x100314),x100319),f317(f16(f904(x100314,a893),x100313),x1003110)))
% 94.68/94.45 [4942]~P42(x49421,x49422)+~P49(x49421,x49422)+~P50(x49421,x49422)+P7(x49421,x49422)
% 94.68/94.45 [4898]~P66(x48982)+~P13(x48982,x48981)+P13(x48982,f104(x48982,x48981))+E(x48981,f103(x48982))
% 94.68/94.45 [4899]~P66(x48992)+~P13(x48992,x48991)+P13(x48992,f685(x48991,x48992))+E(x48991,f103(x48992))
% 94.68/94.45 [5146]~P5(x51462)+E(f10(x51462,x51461),f32(x51462,x51461))+E(x51461,f178(f904(x51462,a893)))+~P1(f317(f28(x51462),x51461))
% 94.68/94.45 [5147]~P5(x51472)+E(f13(x51472,x51471),f31(x51472,x51471))+E(x51471,f178(f904(x51472,a893)))+~P1(f317(f28(x51472),x51471))
% 94.68/94.45 [5304]~P66(x53042)+~P13(x53042,x53041)+E(x53041,f103(x53042))+E(f317(f317(f141(x53042),f705(x53041,x53042)),f685(x53041,x53042)),x53041)
% 94.68/94.45 [6127]~P100(x61272)+E(x61271,f178(f904(x61272,a893)))+P1(f317(f317(f224(x61272),f10(x61272,x61271)),f13(x61272,x61271)))+~P1(f317(f28(x61272),x61271))
% 94.68/94.45 [6138]~P39(x61382)+~P39(x61381)+E(x61381,x61382)+~E(f317(f300(a1,a897,a95),x61381),f317(f300(a1,a897,a95),x61382))
% 94.68/94.45 [9199]~P111(x91991)+~P1(f317(f317(f319(x91991),x91992),f100(x91991)))+P1(f317(f317(f225(x91991),f317(f317(f74(x91991),f317(f317(f74(x91991),f72(x91991)),x91992)),x91992)),f2(x91991)))+~P1(f317(f317(f225(x91991),x91992),f2(x91991)))
% 94.68/94.45 [9445]~P111(x94451)+~P1(f317(f317(f319(x94451),x94452),f100(x94451)))+~P1(f317(f317(f225(x94451),f317(f317(f74(x94451),f317(f317(f74(x94451),f72(x94451)),x94452)),x94452)),f2(x94451)))+P1(f317(f317(f225(x94451),x94452),f2(x94451)))
% 94.68/94.45 [4957]~P115(x49572)+~P145(x49572)+E(x49571,f2(a897))+E(f317(f317(f234(x49572),f2(x49572)),x49571),f2(x49572))
% 94.68/94.45 [4960]~P115(x49601)+~P145(x49601)+~E(x49602,f2(a897))+E(f317(f317(f234(x49601),f2(x49601)),x49602),f72(x49601))
% 94.68/94.45 [5132]~P143(x51322)+E(x51321,f72(x51322))+E(x51321,f317(f73(x51322),f72(x51322)))+~E(f317(f317(f75(x51322),x51321),x51321),f72(x51322))
% 94.68/94.45 [5381]~P91(x53812)+E(x53811,f2(x53812))+E(f76(x53812,x53811),f317(f73(x53812),f72(x53812)))+P1(f317(f317(f225(x53812),f2(x53812)),x53811))
% 94.68/94.45 [5623]~P91(x56232)+E(f76(x56232,x56231),f72(x56232))+E(x56231,f2(x56232))+~P1(f317(f317(f225(x56232),f2(x56232)),x56231))
% 94.68/94.45 [5632]E(x56321,x56322)+~E(f317(f94(a897),x56321),f317(f94(a897),x56322))+P1(f317(a183,f317(f94(a1),x56322)))+P1(f317(a183,f317(f94(a1),x56321)))
% 94.68/94.45 [5683]~P93(x56831)+~E(x56832,f2(x56831))+E(f317(f317(f74(x56831),x56832),x56832),f2(x56831))+~P1(f317(f317(f319(x56831),x56832),f100(x56831)))
% 94.68/94.45 [5722]E(x57221,f2(a1))+~E(f317(f317(f30(a1),x57222),x57221),f2(a1))+P1(f317(f317(f225(a1),x57221),x57222))+P1(f317(f317(f225(a1),x57222),x57221))
% 94.68/94.45 [5752]E(x57521,f2(a1))+~E(f317(f317(f30(a1),x57522),x57521),f2(a1))+P1(f317(f317(f224(a1),x57522),f2(a1)))+P1(f317(f317(f225(a1),x57522),x57521))
% 94.68/94.45 [5786]E(x57861,f2(a1))+~E(f317(f317(f30(a1),x57862),x57861),f2(a1))+P1(f317(f317(f224(a1),f2(a1)),x57862))+P1(f317(f317(f225(a1),x57861),x57862))
% 94.68/94.45 [5821]~P93(x58212)+E(x58211,f2(x58212))+~E(f317(f317(f74(x58212),x58211),x58211),f2(x58212))+~P1(f317(f317(f319(x58212),x58211),f100(x58212)))
% 94.68/94.45 [5892]E(f317(f94(a897),x58921),f317(f94(a897),x58922))+~E(f317(f94(a1),x58922),f2(a1))+P1(f317(a183,f317(f94(a1),x58922)))+~P1(f317(a183,f317(f94(a1),x58921)))
% 94.68/94.45 [5921]~E(f317(f94(a897),x59212),f317(f94(a897),x59211))+E(f317(f94(a1),x59211),f2(a1))+P1(f317(a183,f317(f94(a1),x59211)))+~P1(f317(a183,f317(f94(a1),x59212)))
% 94.68/94.45 [5931]~P66(x59312)+E(x59311,f178(f904(x59312,a893)))+~P1(f317(f28(x59312),x59311))+P1(f317(f317(f319(x59312),f14(x59312,x59311)),x59311))
% 94.68/94.45 [5932]~P66(x59322)+E(x59321,f178(f904(x59322,a893)))+~P1(f317(f28(x59322),x59321))+P1(f317(f317(f319(x59322),f15(x59322,x59321)),x59321))
% 94.68/94.45 [6104]~P111(x61041)+~P94(x61041)+P1(f317(f317(f224(x61041),f2(x61041)),f317(f94(x61041),x61042)))+~P1(f317(f317(f224(a1),a77),x61042))
% 94.68/94.45 [6105]~P111(x61051)+~P94(x61051)+P1(f317(f317(f225(x61051),f2(x61051)),f317(f94(x61051),x61052)))+~P1(f317(f317(f225(a1),a77),x61052))
% 94.68/94.45 [6126]~P111(x61261)+~P94(x61261)+E(f317(f70(x61261),f317(f94(x61261),x61262)),f317(f94(x61261),x61262))+P1(f317(f317(f225(x61261),f317(f94(x61261),x61262)),f2(x61261)))
% 94.68/94.45 [6162]E(x61621,x61622)+~E(f317(a95,x61621),f317(a95,x61622))+~P1(f317(f317(f224(a1),f2(a1)),x61622))+~P1(f317(f317(f224(a1),f2(a1)),x61621))
% 94.68/94.45 [6364]~P94(x63642)+~P111(x63642)+~P1(f317(f317(f224(x63642),f2(x63642)),f317(f94(x63642),x63641)))+P1(f317(f317(f224(a1),a77),x63641))
% 94.68/94.45 [6365]~P94(x63652)+~P111(x63652)+~P1(f317(f317(f225(x63652),f2(x63652)),f317(f94(x63652),x63651)))+P1(f317(f317(f225(a1),a77),x63651))
% 94.68/94.45 [6370]~P111(x63701)+~P94(x63701)+P1(f317(f317(f224(x63701),f317(f94(x63701),x63702)),f2(x63701)))+~P1(f317(f317(f224(a1),x63702),a77))
% 94.68/94.45 [6371]~P111(x63711)+~P94(x63711)+P1(f317(f317(f225(x63711),f317(f94(x63711),x63712)),f2(x63711)))+~P1(f317(f317(f225(a1),x63712),a77))
% 94.68/94.45 [6697]~P94(x66972)+~P111(x66972)+~P1(f317(f317(f224(x66972),f317(f94(x66972),x66971)),f2(x66972)))+P1(f317(f317(f224(a1),x66971),a77))
% 94.68/94.45 [6698]~P94(x66982)+~P111(x66982)+~P1(f317(f317(f225(x66982),f317(f94(x66982),x66981)),f2(x66982)))+P1(f317(f317(f225(a1),x66981),a77))
% 94.68/94.45 [6791]~P111(x67911)+~P94(x67911)+E(f317(f70(x67911),f317(f94(x67911),x67912)),f317(f73(x67911),f317(f94(x67911),x67912)))+~P1(f317(f317(f225(x67911),f317(f94(x67911),x67912)),f2(x67911)))
% 94.68/94.45 [6810]E(f317(f94(a897),x68101),f317(f94(a897),x68102))+~E(f317(f94(a1),x68102),f2(a1))+~P1(f317(f317(f224(a1),f317(f94(a1),x68101)),f2(a1)))+~P1(f317(a183,f317(f94(a1),x68101)))
% 94.68/94.45 [7699]~P66(x76992)+E(x76991,f178(f904(x76992,a893)))+~P1(f317(f28(x76992),x76991))+P1(f317(f317(f224(x76992),f11(x76992,f228(x76992),x76991)),f12(x76992,f223(x76992),x76991)))
% 94.68/94.45 [8019]~P39(x80192)+~P6(x80191)+P1(f317(f317(f319(a1),x80191),x80192))+~P1(f317(f317(f319(a897),f317(a95,x80191)),f317(f300(a1,a897,a95),x80192)))
% 94.68/94.45 [5927]~P141(x59272)+E(x59271,f2(a1))+E(f317(f73(x59272),f317(f93(x59272),f317(f73(a1),x59271))),f317(f93(x59272),x59271))+~P1(f317(f317(f225(a1),x59271),f2(a1)))
% 94.68/94.45 [6006]~P93(x60061)+~P94(x60061)+~P27(x60061,f317(f94(x60061),x60062))+P27(x60061,f317(f94(x60061),f317(f317(f74(a1),x60062),x60062)))
% 94.68/94.45 [6353]~P78(x63532)+E(x63531,f178(f904(x63532,a893)))+E(f15(x63532,f317(f300(x63532,x63532,f73(x63532)),x63531)),f317(f73(x63532),f14(x63532,x63531)))+~P1(f317(f28(x63532),x63531))
% 94.68/94.45 [6354]~P78(x63542)+E(x63541,f178(f904(x63542,a893)))+E(f14(x63542,f317(f300(x63542,x63542,f73(x63542)),x63541)),f317(f73(x63542),f15(x63542,x63541)))+~P1(f317(f28(x63542),x63541))
% 94.68/94.45 [6388]~P93(x63881)+~P94(x63881)+P27(x63881,f317(f94(x63881),x63882))+~P27(x63881,f317(f94(x63881),f317(f317(f74(a1),x63882),x63882)))
% 94.68/94.45 [6482]E(x64821,f2(a1))+E(f317(a46,f45(f317(f73(a1),x64821),f317(f73(a1),x64822))),f41(x64821,x64822))+P1(f317(f317(f224(a1),f2(a1)),x64822))+~P1(f317(f317(f224(a1),f2(a1)),x64821))
% 94.68/94.45 [8801]~P39(x88012)+~P39(x88011)+P1(f317(f317(f225(f904(a897,a893)),f317(f300(a1,a897,a95),x88011)),f317(f300(a1,a897,a95),x88012)))+~P1(f317(f317(f225(f904(a1,a893)),x88011),x88012))
% 94.68/94.45 [9032]~E(f707(x90322,x90321),f708(x90322,x90321))+~P1(f317(f127(x90321),f709(x90322,x90321)))+~P1(f317(f127(f898(x90321)),x90322))+P1(f317(f127(x90321),f317(f132(f898(x90321),f898(x90321),f124(x90321),f103(x90321)),x90322)))
% 94.68/94.45 [9118]~P39(x91182)+~P39(x91181)+~P1(f317(f317(f224(f904(a897,a893)),f317(f300(a1,a897,a95),x91181)),f317(f300(a1,a897,a95),x91182)))+P1(f317(f317(f224(f904(a1,a893)),x91181),x91182))
% 94.68/94.45 [9119]~P39(x91192)+~P39(x91191)+~P1(f317(f317(f225(f904(a897,a893)),f317(f300(a1,a897,a95),x91191)),f317(f300(a1,a897,a95),x91192)))+P1(f317(f317(f225(f904(a1,a893)),x91191),x91192))
% 94.68/94.45 [9126]~E(f707(x91262,x91261),f708(x91262,x91261))+~P1(f317(f127(f898(x91261)),x91262))+P1(f317(f127(x91261),f317(f132(f898(x91261),f898(x91261),f124(x91261),f103(x91261)),x91262)))+P1(f317(f317(f319(f898(x91261)),f709(x91262,x91261)),f317(f162(f898(x91261)),x91262)))
% 94.68/94.45 [9167]~P1(f317(f127(x91671),f709(x91672,x91671)))+~P1(f317(f127(f898(x91671)),x91672))+P1(f317(f127(x91671),f317(f132(f898(x91671),f898(x91671),f124(x91671),f103(x91671)),x91672)))+P1(f317(f317(f319(f898(x91671)),f708(x91672,x91671)),f317(f162(f898(x91671)),x91672)))
% 94.68/94.45 [9168]~P1(f317(f127(x91681),f709(x91682,x91681)))+~P1(f317(f127(f898(x91681)),x91682))+P1(f317(f127(x91681),f317(f132(f898(x91681),f898(x91681),f124(x91681),f103(x91681)),x91682)))+P1(f317(f317(f319(f898(x91681)),f707(x91682,x91681)),f317(f162(f898(x91681)),x91682)))
% 94.68/94.45 [9245]~P1(f317(f127(f898(x92451)),x92452))+P1(f317(f127(x92451),f317(f132(f898(x92451),f898(x92451),f124(x92451),f103(x92451)),x92452)))+P1(f317(f317(f319(f898(x92451)),f708(x92452,x92451)),f317(f162(f898(x92451)),x92452)))+P1(f317(f317(f319(f898(x92451)),f709(x92452,x92451)),f317(f162(f898(x92451)),x92452)))
% 94.68/94.45 [9246]~P1(f317(f127(f898(x92461)),x92462))+P1(f317(f127(x92461),f317(f132(f898(x92461),f898(x92461),f124(x92461),f103(x92461)),x92462)))+P1(f317(f317(f319(f898(x92461)),f707(x92462,x92461)),f317(f162(f898(x92461)),x92462)))+P1(f317(f317(f319(f898(x92461)),f709(x92462,x92461)),f317(f162(f898(x92461)),x92462)))
% 94.68/94.45 [9260]~E(f317(f317(f92(f904(x92601,a893)),f317(f162(x92601),f708(x92602,x92601))),f317(f162(x92601),f707(x92602,x92601))),f178(f904(x92601,a893)))+~P1(f317(f127(x92601),f709(x92602,x92601)))+~P1(f317(f127(f898(x92601)),x92602))+P1(f317(f127(x92601),f317(f132(f898(x92601),f898(x92601),f124(x92601),f103(x92601)),x92602)))
% 94.68/94.45 [9323]~E(f317(f317(f92(f904(x93231,a893)),f317(f162(x93231),f708(x93232,x93231))),f317(f162(x93231),f707(x93232,x93231))),f178(f904(x93231,a893)))+~P1(f317(f127(f898(x93231)),x93232))+P1(f317(f127(x93231),f317(f132(f898(x93231),f898(x93231),f124(x93231),f103(x93231)),x93232)))+P1(f317(f317(f319(f898(x93231)),f709(x93232,x93231)),f317(f162(f898(x93231)),x93232)))
% 94.68/94.45 [9611]E(x96111,f2(a1))+E(x96112,f2(a1))+E(f317(f317(f80(a1,f903(a1,a1)),f317(f317(a207,x96112),x96111)),f317(f317(f18(a1,a1,f903(a1,a1)),f317(f317(f8(a1,f904(a1,f903(a1,a1)),a1),f242(a1,a1)),f317(f30(a1),x96112))),f317(f30(a1),x96111))),f205(x96112,x96111))+P1(f317(f317(f225(a1),x96111),f2(a1)))
% 94.68/94.45 [8345]~P94(x83452)+~P111(x83452)+~P1(f317(f317(f224(x83452),f317(f94(x83452),x83451)),f72(x83452)))+P1(f317(f317(f224(a1),x83451),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))
% 94.68/94.45 [8346]~P94(x83462)+~P111(x83462)+~P1(f317(f317(f225(x83462),f317(f94(x83462),x83461)),f72(x83462)))+P1(f317(f317(f225(a1),x83461),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))
% 94.68/94.45 [8617]~P111(x86171)+~P94(x86171)+P1(f317(f317(f224(x86171),f317(f94(x86171),x86172)),f72(x86171)))+~P1(f317(f317(f224(a1),x86172),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))
% 94.68/94.45 [8618]~P111(x86181)+~P94(x86181)+P1(f317(f317(f225(x86181),f317(f94(x86181),x86182)),f72(x86181)))+~P1(f317(f317(f225(a1),x86182),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))
% 94.68/94.45 [8829]~P94(x88292)+~P111(x88292)+~P1(f317(f317(f224(x88292),f72(x88292)),f317(f94(x88292),x88291)))+P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),x88291))
% 94.68/94.45 [8830]~P94(x88302)+~P111(x88302)+~P1(f317(f317(f225(x88302),f72(x88302)),f317(f94(x88302),x88301)))+P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),x88301))
% 94.68/94.45 [9205]~P111(x92051)+~P94(x92051)+P1(f317(f317(f224(x92051),f72(x92051)),f317(f94(x92051),x92052)))+~P1(f317(f317(f224(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),x92052))
% 94.68/94.45 [9206]~P111(x92061)+~P94(x92061)+P1(f317(f317(f225(x92061),f72(x92061)),f317(f94(x92061),x92062)))+~P1(f317(f317(f225(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),x92062))
% 94.68/94.45 [9740]~P143(x97402)+E(x97401,f72(x97402))+E(x97401,f317(f73(x97402),f72(x97402)))+~E(f317(f317(f234(x97402),x97401),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f72(x97402))
% 94.68/94.45 [10007]~P94(x100071)+~P63(x100071)+~P1(f317(f317(f225(x100071),f2(x100071)),x100072))+P1(f317(f317(f225(x100071),f2(x100071)),f317(f317(f281(x100071),x100072),f317(f94(x100071),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.45 [10059]~P94(x100591)+~P63(x100591)+P1(f317(f317(f225(x100591),f2(x100591)),x100592))+~P1(f317(f317(f225(x100591),f2(x100591)),f317(f317(f281(x100591),x100592),f317(f94(x100591),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.45 [10353]~P141(x103532)+E(x103531,f2(a1))+P1(f317(f317(f225(a1),x103531),f2(a1)))+E(f317(f317(f247(a1,a1,x103532),f317(f317(f7(a1,f904(a1,f904(x103532,x103532)),f904(a1,x103532)),f317(f317(f8(f904(f904(x103532,x103532),x103532),f904(f904(a1,f904(x103532,x103532)),f904(a1,x103532)),a1),f8(f904(x103532,x103532),x103532,a1)),f317(f317(f8(x103532,f904(f904(x103532,x103532),x103532),a1),f80(x103532,x103532)),f93(x103532)))),f317(f317(f7(a1,f904(x103532,x103532),f904(x103532,x103532)),f317(f317(f8(f904(x103532,f904(x103532,x103532)),f904(f904(x103532,x103532),f904(x103532,x103532)),a1),f18(x103532,x103532,x103532)),f317(f317(f7(a1,f904(x103532,x103532),f904(x103532,f904(x103532,x103532))),f317(f317(f8(f904(x103532,f904(x103532,x103532)),f904(f904(x103532,x103532),f904(x103532,f904(x103532,x103532))),a1),f8(x103532,f904(x103532,x103532),x103532)),f317(f317(f8(a893,f904(x103532,f904(x103532,x103532)),a1),f86(x103532)),f317(f317(f7(a1,a1,a893),a314),f2(a1))))),f317(f317(f18(x103532,x103532,x103532),f74(x103532)),f5(x103532))))),f317(f317(f7(x103532,x103532,x103532),f317(f317(f8(x103532,f904(x103532,x103532),x103532),f74(x103532)),f317(f317(f18(x103532,x103532,x103532),f74(x103532)),f5(x103532)))),f72(x103532))))),f41(x103531,f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f93(x103532),x103531))
% 94.68/94.45 [5390]~P37(x53901,x53903)+~P51(x53901,x53903)+~P52(x53901,x53902,x53903)+P8(x53901,x53902,x53903)
% 94.68/94.45 [4926]~P93(x49263)+~P94(x49263)+E(x49261,x49262)+~E(f317(f94(x49263),x49261),f317(f94(x49263),x49262))
% 94.68/94.45 [5400]~P49(x54001,x54002)+~P50(x54001,x54002)+P15(x54001,x54002)+~P1(f317(f317(x54002,x54003),x54003))
% 94.68/94.45 [5907]P15(x59072,x59071)+E(f317(x59071,f784(x59071)),f317(x59071,f785(x59071)))+P1(f317(f317(x59071,f784(x59071)),f785(x59071)))+~P1(f317(f317(x59071,x59073),x59073))
% 94.68/94.45 [6114]~P1(f317(x61141,x61142))+~P1(f317(x61141,x61143))+~P1(f317(f317(f224(a897),x61143),f612(x61142,x61141)))+P1(f317(x61141,f2(a897)))
% 94.68/94.45 [6181]P15(x61811,x61812)+P1(f317(f317(x61812,f784(x61812)),f784(x61812)))+P1(f317(f317(x61812,f784(x61812)),f785(x61812)))+~P1(f317(f317(x61812,x61813),x61813))
% 94.68/94.45 [6182]P15(x61821,x61822)+P1(f317(f317(x61822,f784(x61822)),f785(x61822)))+P1(f317(f317(x61822,f785(x61822)),f785(x61822)))+~P1(f317(f317(x61822,x61823),x61823))
% 94.68/94.45 [6547]P147(x65472,x65471,x65473)+E(x65471,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f834(x65473,x65471,x65472)))+P1(f317(f317(f225(a1),x65471),f2(a1)))
% 94.68/94.45 [6548]P148(x65482,x65481,x65483)+E(x65481,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x65483,x65481,x65482)))+P1(f317(f317(f225(a1),x65481),f2(a1)))
% 94.68/94.45 [6677]P147(x66771,x66772,x66773)+~P1(f317(x66771,x66773))+P1(f317(f317(f224(a1),f2(a1)),f834(x66773,x66772,x66771)))+P1(f317(f317(f225(a1),x66772),f2(a1)))
% 94.68/94.45 [6703]P148(x67031,x67032,x67033)+P1(f317(f317(f224(a1),f2(a1)),f846(x67033,x67032,x67031)))+~P1(f317(x67031,f2(a1)))+P1(f317(f317(f225(a1),x67032),f2(a1)))
% 94.68/94.45 [6735]P147(x67352,x67351,x67353)+E(x67351,f2(a1))+~P1(f317(x67352,f834(x67353,x67351,x67352)))+P1(f317(f317(f225(a1),x67351),f2(a1)))
% 94.68/94.45 [6736]P148(x67362,x67361,x67363)+E(x67361,f2(a1))+~P1(f317(x67362,f841(x67363,x67361,x67362)))+P1(f317(f317(f225(a1),x67361),f2(a1)))
% 94.68/94.45 [6838]~P66(x68381)+~P5(x68381)+~P1(f317(f317(f225(x68381),x68382),f31(x68381,x68383)))+P1(f317(f317(f225(x68381),x68382),f579(x68383,x68382,x68381)))
% 94.68/94.45 [6848]P147(x68481,x68482,x68483)+~P1(f317(x68481,x68483))+~P1(f317(x68481,f834(x68483,x68482,x68481)))+P1(f317(f317(f225(a1),x68482),f2(a1)))
% 94.68/94.45 [6880]P148(x68801,x68802,x68803)+~P1(f317(x68801,f841(x68803,x68802,x68801)))+~P1(f317(x68801,f2(a1)))+P1(f317(f317(f225(a1),x68802),f2(a1)))
% 94.68/94.45 [7134]P147(x71342,x71341,x71343)+E(x71341,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f834(x71343,x71341,x71342)))+P1(f317(f317(f225(a1),x71341),f833(x71343,x71341,x71342)))
% 94.68/94.45 [7135]P148(x71352,x71351,x71353)+E(x71351,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x71353,x71351,x71352)))+P1(f317(f317(f225(a1),x71351),f845(x71353,x71351,x71352)))
% 94.68/94.45 [7255]P147(x72551,x72552,x72553)+~P1(f317(x72551,x72553))+P1(f317(f317(f224(a1),f2(a1)),f834(x72553,x72552,x72551)))+P1(f317(f317(f225(a1),x72552),f833(x72553,x72552,x72551)))
% 94.68/94.45 [7276]P148(x72761,x72762,x72763)+P1(f317(f317(f224(a1),f2(a1)),f846(x72763,x72762,x72761)))+P1(f317(f317(f225(a1),x72762),f845(x72763,x72762,x72761)))+~P1(f317(x72761,f2(a1)))
% 94.68/94.45 [7307]P147(x73072,x73071,x73073)+E(x73071,f2(a1))+~P1(f317(x73072,f834(x73073,x73071,x73072)))+P1(f317(f317(f225(a1),x73071),f833(x73073,x73071,x73072)))
% 94.68/94.45 [7308]P148(x73082,x73081,x73083)+E(x73081,f2(a1))+~P1(f317(x73082,f841(x73083,x73081,x73082)))+P1(f317(f317(f225(a1),x73081),f845(x73083,x73081,x73082)))
% 94.68/94.45 [7352]P147(x73522,x73521,x73523)+E(x73521,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f834(x73523,x73521,x73522)))+~P1(f317(x73522,f833(x73523,x73521,x73522)))
% 94.68/94.45 [7353]P148(x73532,x73531,x73533)+E(x73531,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x73533,x73531,x73532)))+~P1(f317(x73532,f847(x73533,x73531,x73532)))
% 94.68/94.45 [7450]P147(x74501,x74502,x74503)+~P1(f317(x74501,x74503))+~P1(f317(x74501,f834(x74503,x74502,x74501)))+P1(f317(f317(f225(a1),x74502),f833(x74503,x74502,x74501)))
% 94.68/94.45 [7465]P148(x74651,x74652,x74653)+~P1(f317(x74651,f841(x74653,x74652,x74651)))+P1(f317(f317(f225(a1),x74652),f845(x74653,x74652,x74651)))+~P1(f317(x74651,f2(a1)))
% 94.68/94.45 [7468]P147(x74681,x74682,x74683)+~P1(f317(x74681,x74683))+P1(f317(f317(f224(a1),f2(a1)),f834(x74683,x74682,x74681)))+~P1(f317(x74681,f833(x74683,x74682,x74681)))
% 94.68/94.45 [7485]P148(x74851,x74852,x74853)+P1(f317(f317(f224(a1),f2(a1)),f846(x74853,x74852,x74851)))+~P1(f317(x74851,f847(x74853,x74852,x74851)))+~P1(f317(x74851,f2(a1)))
% 94.68/94.45 [7508]P147(x75082,x75081,x75083)+E(x75081,f2(a1))+~P1(f317(x75082,f834(x75083,x75081,x75082)))+~P1(f317(x75082,f833(x75083,x75081,x75082)))
% 94.68/94.45 [7509]P148(x75092,x75091,x75093)+E(x75091,f2(a1))+~P1(f317(x75092,f841(x75093,x75091,x75092)))+~P1(f317(x75092,f847(x75093,x75091,x75092)))
% 94.68/94.45 [7593]P147(x75931,x75932,x75933)+~P1(f317(x75931,x75933))+~P1(f317(x75931,f834(x75933,x75932,x75931)))+~P1(f317(x75931,f833(x75933,x75932,x75931)))
% 94.68/94.45 [7611]P148(x76111,x76112,x76113)+~P1(f317(x76111,f841(x76113,x76112,x76111)))+~P1(f317(x76111,f847(x76113,x76112,x76111)))+~P1(f317(x76111,f2(a1)))
% 94.68/94.45 [7658]P147(x76582,x76581,x76583)+E(x76581,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f834(x76583,x76581,x76582)))+P1(f317(f317(f224(a1),f833(x76583,x76581,x76582)),f2(a1)))
% 94.68/94.45 [7659]P148(x76592,x76591,x76593)+E(x76591,f2(a1))+P1(f317(f317(f224(a1),f2(a1)),f846(x76593,x76591,x76592)))+P1(f317(f317(f224(a1),f845(x76593,x76591,x76592)),f2(a1)))
% 94.68/94.45 [7660]~P89(x76601)+~P1(f317(f317(f224(x76601),x76603),f2(x76601)))+~P1(f317(f317(f224(x76601),x76602),f2(x76601)))+P1(f317(f317(f224(x76601),f317(f317(f74(x76601),x76602),x76603)),f2(x76601)))
% 94.68/94.45 [7661]~P141(x76611)+~P1(f317(f317(f319(x76611),x76613),f100(x76611)))+~P1(f317(f317(f319(x76611),x76612),f100(x76611)))+P1(f317(f317(f319(x76611),f317(f317(f23(x76611),x76612),x76613)),f100(x76611)))
% 94.68/94.45 [7662]~P141(x76621)+~P1(f317(f317(f319(x76621),x76623),f100(x76621)))+~P1(f317(f317(f319(x76621),x76622),f100(x76621)))+P1(f317(f317(f319(x76621),f317(f317(f74(x76621),x76622),x76623)),f100(x76621)))
% 94.68/94.45 [7663]~P144(x76631)+~P1(f317(f317(f319(x76631),x76633),f176(x76631)))+~P1(f317(f317(f319(x76631),x76632),f176(x76631)))+P1(f317(f317(f319(x76631),f317(f317(f74(x76631),x76632),x76633)),f176(x76631)))
% 94.68/94.45 [7664]~P141(x76641)+~P1(f317(f317(f319(x76641),x76643),f100(x76641)))+~P1(f317(f317(f319(x76641),x76642),f100(x76641)))+P1(f317(f317(f319(x76641),f317(f317(f75(x76641),x76642),x76643)),f100(x76641)))
% 94.68/94.45 [7665]~P144(x76651)+~P1(f317(f317(f319(x76651),x76653),f176(x76651)))+~P1(f317(f317(f319(x76651),x76652),f176(x76651)))+P1(f317(f317(f319(x76651),f317(f317(f75(x76651),x76652),x76653)),f176(x76651)))
% 94.68/94.45 [7666]~P89(x76661)+~P1(f317(f317(f224(x76661),x76663),f2(x76661)))+~P1(f317(f317(f225(x76661),x76662),f2(x76661)))+P1(f317(f317(f225(x76661),f317(f317(f74(x76661),x76662),x76663)),f2(x76661)))
% 94.68/94.45 [7667]~P89(x76671)+~P1(f317(f317(f224(x76671),x76672),f2(x76671)))+~P1(f317(f317(f225(x76671),x76673),f2(x76671)))+P1(f317(f317(f225(x76671),f317(f317(f74(x76671),x76672),x76673)),f2(x76671)))
% 94.68/94.45 [7668]~P89(x76681)+~P1(f317(f317(f225(x76681),x76683),f2(x76681)))+~P1(f317(f317(f225(x76681),x76682),f2(x76681)))+P1(f317(f317(f225(x76681),f317(f317(f74(x76681),x76682),x76683)),f2(x76681)))
% 94.68/94.45 [7695]P147(x76953,x76951,x76952)+E(x76951,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x76951),f837(x76952,x76951,x76953))),f834(x76952,x76951,x76953)),x76952)+P1(f317(f317(f225(a1),x76951),f2(a1)))
% 94.68/94.45 [7696]P148(x76963,x76961,x76962)+E(x76961,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x76961),f841(x76962,x76961,x76963))),f846(x76962,x76961,x76963)),x76962)+P1(f317(f317(f225(a1),x76961),f2(a1)))
% 94.68/94.45 [7779]P147(x77791,x77792,x77793)+~P1(f317(x77791,x77793))+P1(f317(f317(f224(a1),f2(a1)),f834(x77793,x77792,x77791)))+P1(f317(f317(f224(a1),f833(x77793,x77792,x77791)),f2(a1)))
% 94.68/94.45 [7810]P148(x78101,x78102,x78103)+P1(f317(f317(f224(a1),f2(a1)),f846(x78103,x78102,x78101)))+~P1(f317(x78101,f2(a1)))+P1(f317(f317(f224(a1),f845(x78103,x78102,x78101)),f2(a1)))
% 94.68/94.45 [7819]P147(x78193,x78191,x78192)+~P1(f317(x78193,x78192))+E(f317(f317(f74(a1),f317(f317(f75(a1),x78191),f837(x78192,x78191,x78193))),f834(x78192,x78191,x78193)),x78192)+P1(f317(f317(f225(a1),x78191),f2(a1)))
% 94.68/94.45 [7825]P147(x78252,x78251,x78253)+E(x78251,f2(a1))+~P1(f317(x78252,f834(x78253,x78251,x78252)))+P1(f317(f317(f224(a1),f833(x78253,x78251,x78252)),f2(a1)))
% 94.68/94.45 [7826]P148(x78262,x78261,x78263)+E(x78261,f2(a1))+~P1(f317(x78262,f841(x78263,x78261,x78262)))+P1(f317(f317(f224(a1),f845(x78263,x78261,x78262)),f2(a1)))
% 94.68/94.45 [7831]P148(x78313,x78311,x78312)+E(f317(f317(f74(a1),f317(f317(f75(a1),x78311),f841(x78312,x78311,x78313))),f846(x78312,x78311,x78313)),x78312)+~P1(f317(x78313,f2(a1)))+P1(f317(f317(f225(a1),x78311),f2(a1)))
% 94.68/94.45 [7888]P147(x78881,x78882,x78883)+~P1(f317(x78881,x78883))+~P1(f317(x78881,f834(x78883,x78882,x78881)))+P1(f317(f317(f224(a1),f833(x78883,x78882,x78881)),f2(a1)))
% 94.68/94.45 [7892]P148(x78921,x78922,x78923)+~P1(f317(x78921,f841(x78923,x78922,x78921)))+~P1(f317(x78921,f2(a1)))+P1(f317(f317(f224(a1),f845(x78923,x78922,x78921)),f2(a1)))
% 94.68/94.45 [7960]~P125(x79601)+~P1(f317(f317(f224(x79601),f317(f317(f75(x79601),x79603),x79602)),f2(x79601)))+P1(f317(f317(f224(x79601),x79602),f2(x79601)))+P1(f317(f317(f224(x79601),x79603),f2(x79601)))
% 94.68/94.45 [7961]~P63(x79611)+~P1(f317(f317(f224(x79611),f317(f317(f281(x79611),x79613),x79612)),f2(x79611)))+P1(f317(f317(f224(x79611),x79612),f2(x79611)))+P1(f317(f317(f224(x79611),x79613),f2(x79611)))
% 94.68/94.45 [7962]~P63(x79621)+~P1(f317(f317(f225(x79621),f317(f317(f281(x79621),x79623),x79622)),f2(x79621)))+P1(f317(f317(f225(x79621),x79622),f2(x79621)))+P1(f317(f317(f225(x79621),x79623),f2(x79621)))
% 94.68/94.45 [8075]P147(x80753,x80751,x80752)+E(x80751,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80751),f837(x80752,x80751,x80753))),f834(x80752,x80751,x80753)),x80752)+P1(f317(f317(f225(a1),x80751),f833(x80752,x80751,x80753)))
% 94.68/94.45 [8076]P148(x80763,x80761,x80762)+E(x80761,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80761),f841(x80762,x80761,x80763))),f846(x80762,x80761,x80763)),x80762)+P1(f317(f317(f225(a1),x80761),f845(x80762,x80761,x80763)))
% 94.68/94.45 [8088]P147(x80883,x80881,x80882)+E(x80881,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80881),f840(x80882,x80881,x80883))),f833(x80882,x80881,x80883)),x80882)+P1(f317(f317(f224(a1),f2(a1)),f834(x80882,x80881,x80883)))
% 94.68/94.45 [8089]P148(x80893,x80891,x80892)+E(x80891,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x80891),f847(x80892,x80891,x80893))),f845(x80892,x80891,x80893)),x80892)+P1(f317(f317(f224(a1),f2(a1)),f846(x80892,x80891,x80893)))
% 94.68/94.45 [8131]P147(x81313,x81311,x81312)+~P1(f317(x81313,x81312))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81311),f837(x81312,x81311,x81313))),f834(x81312,x81311,x81313)),x81312)+P1(f317(f317(f225(a1),x81311),f833(x81312,x81311,x81313)))
% 94.68/94.45 [8140]P148(x81403,x81401,x81402)+E(f317(f317(f74(a1),f317(f317(f75(a1),x81401),f841(x81402,x81401,x81403))),f846(x81402,x81401,x81403)),x81402)+P1(f317(f317(f225(a1),x81401),f845(x81402,x81401,x81403)))+~P1(f317(x81403,f2(a1)))
% 94.68/94.45 [8146]P147(x81463,x81461,x81462)+~P1(f317(x81463,x81462))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81461),f840(x81462,x81461,x81463))),f833(x81462,x81461,x81463)),x81462)+P1(f317(f317(f224(a1),f2(a1)),f834(x81462,x81461,x81463)))
% 94.68/94.45 [8152]P148(x81523,x81521,x81522)+E(f317(f317(f74(a1),f317(f317(f75(a1),x81521),f847(x81522,x81521,x81523))),f845(x81522,x81521,x81523)),x81522)+P1(f317(f317(f224(a1),f2(a1)),f846(x81522,x81521,x81523)))+~P1(f317(x81523,f2(a1)))
% 94.68/94.45 [8163]P147(x81633,x81631,x81632)+E(x81631,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81631),f837(x81632,x81631,x81633))),f834(x81632,x81631,x81633)),x81632)+~P1(f317(x81633,f833(x81632,x81631,x81633)))
% 94.68/94.45 [8164]P148(x81643,x81641,x81642)+E(x81641,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81641),f841(x81642,x81641,x81643))),f846(x81642,x81641,x81643)),x81642)+~P1(f317(x81643,f847(x81642,x81641,x81643)))
% 94.68/94.45 [8165]P147(x81653,x81651,x81652)+E(x81651,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81651),f840(x81652,x81651,x81653))),f833(x81652,x81651,x81653)),x81652)+~P1(f317(x81653,f834(x81652,x81651,x81653)))
% 94.68/94.45 [8166]P148(x81663,x81661,x81662)+E(x81661,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x81661),f847(x81662,x81661,x81663))),f845(x81662,x81661,x81663)),x81662)+~P1(f317(x81663,f841(x81662,x81661,x81663)))
% 94.68/94.45 [8225]P147(x82253,x82251,x82252)+~P1(f317(x82253,x82252))+E(f317(f317(f74(a1),f317(f317(f75(a1),x82251),f837(x82252,x82251,x82253))),f834(x82252,x82251,x82253)),x82252)+~P1(f317(x82253,f833(x82252,x82251,x82253)))
% 94.68/94.45 [8226]P147(x82263,x82261,x82262)+~P1(f317(x82263,x82262))+E(f317(f317(f74(a1),f317(f317(f75(a1),x82261),f840(x82262,x82261,x82263))),f833(x82262,x82261,x82263)),x82262)+~P1(f317(x82263,f834(x82262,x82261,x82263)))
% 94.68/94.45 [8239]P148(x82393,x82391,x82392)+E(f317(f317(f74(a1),f317(f317(f75(a1),x82391),f841(x82392,x82391,x82393))),f846(x82392,x82391,x82393)),x82392)+~P1(f317(x82393,f847(x82392,x82391,x82393)))+~P1(f317(x82393,f2(a1)))
% 94.68/94.45 [8240]P148(x82403,x82401,x82402)+E(f317(f317(f74(a1),f317(f317(f75(a1),x82401),f847(x82402,x82401,x82403))),f845(x82402,x82401,x82403)),x82402)+~P1(f317(x82403,f841(x82402,x82401,x82403)))+~P1(f317(x82403,f2(a1)))
% 94.68/94.45 [8338]P147(x83383,x83381,x83382)+E(x83381,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83381),f837(x83382,x83381,x83383))),f834(x83382,x83381,x83383)),x83382)+P1(f317(f317(f224(a1),f833(x83382,x83381,x83383)),f2(a1)))
% 94.68/94.45 [8339]P148(x83393,x83391,x83392)+E(x83391,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83391),f841(x83392,x83391,x83393))),f846(x83392,x83391,x83393)),x83392)+P1(f317(f317(f224(a1),f845(x83392,x83391,x83393)),f2(a1)))
% 94.68/94.45 [8379]P147(x83793,x83791,x83792)+~P1(f317(x83793,x83792))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83791),f837(x83792,x83791,x83793))),f834(x83792,x83791,x83793)),x83792)+P1(f317(f317(f224(a1),f833(x83792,x83791,x83793)),f2(a1)))
% 94.68/94.45 [8384]P148(x83843,x83841,x83842)+E(f317(f317(f74(a1),f317(f317(f75(a1),x83841),f841(x83842,x83841,x83843))),f846(x83842,x83841,x83843)),x83842)+~P1(f317(x83843,f2(a1)))+P1(f317(f317(f224(a1),f845(x83842,x83841,x83843)),f2(a1)))
% 94.68/94.45 [8519]P147(x85193,x85191,x85192)+E(x85191,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85191),f840(x85192,x85191,x85193))),f833(x85192,x85191,x85193)),x85192)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85191),f837(x85192,x85191,x85193))),f834(x85192,x85191,x85193)),x85192)
% 94.68/94.45 [8520]P148(x85203,x85201,x85202)+E(x85201,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85201),f847(x85202,x85201,x85203))),f845(x85202,x85201,x85203)),x85202)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85201),f841(x85202,x85201,x85203))),f846(x85202,x85201,x85203)),x85202)
% 94.68/94.45 [8540]P147(x85403,x85401,x85402)+~P1(f317(x85403,x85402))+E(f317(f317(f74(a1),f317(f317(f75(a1),x85401),f840(x85402,x85401,x85403))),f833(x85402,x85401,x85403)),x85402)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85401),f837(x85402,x85401,x85403))),f834(x85402,x85401,x85403)),x85402)
% 94.68/94.45 [8551]P148(x85513,x85511,x85512)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85511),f847(x85512,x85511,x85513))),f845(x85512,x85511,x85513)),x85512)+E(f317(f317(f74(a1),f317(f317(f75(a1),x85511),f841(x85512,x85511,x85513))),f846(x85512,x85511,x85513)),x85512)+~P1(f317(x85513,f2(a1)))
% 94.68/94.45 [9213]~P125(x92131)+~E(x92133,f2(x92131))+~E(x92132,f2(x92131))+P1(f317(f317(f224(x92131),f317(f317(f74(x92131),f317(f317(f75(x92131),x92132),x92132)),f317(f317(f75(x92131),x92133),x92133))),f2(x92131)))
% 94.68/94.45 [10294]~P111(x102941)+~E(x102943,f2(x102941))+~E(x102942,f2(x102941))+P1(f317(f317(f224(x102941),f317(f317(f74(x102941),f317(f317(f234(x102941),x102942),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102941),x102943),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))),f2(x102941)))
% 94.68/94.45 [4874]~E(x48743,x48741)+~P122(x48742)+E(x48741,f2(x48742))+E(f317(f317(f281(x48742),x48743),x48741),f72(x48742))
% 94.68/94.45 [4927]~P101(x49271)+~E(x49273,f178(x49271))+~E(x49272,f178(x49271))+E(f317(f317(f91(x49271),x49272),x49273),f178(x49271))
% 94.68/94.45 [4928]~P104(x49281)+~E(x49283,f232(x49281))+~E(x49282,f232(x49281))+E(f317(f317(f92(x49281),x49282),x49283),f232(x49281))
% 94.68/94.45 [5025]~P122(x50253)+E(x50251,x50252)+E(x50252,f2(x50253))+~E(f317(f317(f281(x50253),x50251),x50252),f72(x50253))
% 94.68/94.45 [5042]~P142(x50422)+E(x50421,f2(x50422))+E(x50423,f2(x50422))+~E(f317(f317(f75(x50422),x50423),x50421),f2(x50422))
% 94.68/94.45 [5044]~P134(x50442)+E(x50441,f2(x50442))+E(x50443,f2(x50442))+~E(f317(f317(f75(x50442),x50443),x50441),f2(x50442))
% 94.68/94.45 [5419]~P120(x54193)+E(x54191,x54192)+E(x54191,f317(f73(x54193),x54192))+~E(f317(f317(f75(x54193),x54191),x54191),f317(f317(f75(x54193),x54192),x54192))
% 94.68/94.45 [5458]~P97(x54581)+E(f317(f73(x54581),x54582),x54583)+~E(f317(f317(f91(x54581),x54582),x54583),f232(x54581))+~E(f317(f317(f92(x54581),x54582),x54583),f178(x54581))
% 94.68/94.45 [5539]~P111(x55393)+E(x55391,x55392)+P1(f317(f317(f225(x55393),x55392),x55391))+P1(f317(f317(f225(x55393),x55391),x55392))
% 94.68/94.45 [5540]~P66(x55403)+E(x55401,x55402)+P1(f317(f317(f225(x55403),x55402),x55401))+P1(f317(f317(f225(x55403),x55401),x55402))
% 94.68/94.45 [5541]~E(x55412,x55413)+~P66(x55411)+P1(f317(f317(f225(x55411),x55412),x55413))+P1(f317(f317(f224(x55411),x55412),x55413))
% 94.68/94.45 [5802]~P108(x58023)+E(x58021,x58022)+~P1(f317(f317(f224(x58023),x58022),x58021))+P1(f317(f317(f225(x58023),x58022),x58021))
% 94.68/94.45 [5804]~P66(x58043)+E(x58041,x58042)+~P1(f317(f317(f224(x58043),x58041),x58042))+P1(f317(f317(f225(x58043),x58041),x58042))
% 94.68/94.45 [5810]~P108(x58103)+E(x58101,x58102)+~P1(f317(f317(f224(x58103),x58101),x58102))+P1(f317(f317(f225(x58103),x58101),x58102))
% 94.68/94.45 [5924]P147(x59241,x59242,x59243)+~P1(f317(x59241,x59243))+P1(f317(f317(f225(a1),x59242),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x59242))
% 94.68/94.45 [5978]P148(x59781,x59782,x59783)+~P1(f317(x59781,f2(a1)))+P1(f317(f317(f225(a1),x59782),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x59782))
% 94.68/94.45 [5983]~P100(x59831)+E(f317(f317(f91(x59831),x59832),f10(x59831,x59833)),x59832)+~P1(f317(f28(x59831),x59833))+~P1(f317(f317(f319(x59831),x59832),x59833))
% 94.68/94.45 [5984]~P100(x59841)+E(f317(f317(f92(x59841),x59842),f13(x59841,x59843)),x59842)+~P1(f317(f28(x59841),x59843))+~P1(f317(f317(f319(x59841),x59842),x59843))
% 94.68/94.45 [6023]~P66(x60231)+E(f317(f317(f228(x60231),x60232),f14(x60231,x60233)),f14(x60231,x60233))+~P1(f317(f28(x60231),x60233))+~P1(f317(f317(f319(x60231),x60232),x60233))
% 94.68/94.45 [6024]~P66(x60241)+E(f317(f317(f223(x60241),x60242),f15(x60241,x60243)),f15(x60241,x60243))+~P1(f317(f28(x60241),x60243))+~P1(f317(f317(f319(x60241),x60242),x60243))
% 94.68/94.45 [6025]~P100(x60251)+E(f317(f317(f91(x60251),x60252),f13(x60251,x60253)),f13(x60251,x60253))+~P1(f317(f28(x60251),x60253))+~P1(f317(f317(f319(x60251),x60252),x60253))
% 94.68/94.45 [6026]~P100(x60261)+E(f317(f317(f92(x60261),x60262),f10(x60261,x60263)),f10(x60261,x60263))+~P1(f317(f28(x60261),x60263))+~P1(f317(f317(f319(x60261),x60262),x60263))
% 94.68/94.45 [6065]E(x60651,x60652)+~P108(x60653)+~P1(f317(f317(f224(x60653),x60652),x60651))+~P1(f317(f317(f224(x60653),x60651),x60652))
% 94.68/94.45 [6210]~P65(x62101)+P1(f317(f317(f225(x62101),x62103),x62102))+~P1(f317(f317(f224(x62101),x62103),x62102))+P1(f317(f317(f224(x62101),x62102),x62103))
% 94.68/94.45 [6238]~P66(x62381)+~P1(f317(f28(x62381),x62383))+P1(f317(f317(f224(x62381),x62382),f15(x62381,x62383)))+~P1(f317(f317(f319(x62381),x62382),x62383))
% 94.68/94.45 [6287]~P66(x62871)+E(f317(f317(f228(x62871),x62872),f12(x62871,f223(x62871),x62873)),x62872)+~P1(f317(f28(x62871),x62873))+~P1(f317(f317(f319(x62871),x62872),x62873))
% 94.68/94.45 [6288]~P66(x62881)+E(f317(f317(f223(x62881),x62882),f11(x62881,f228(x62881),x62883)),x62882)+~P1(f317(f28(x62881),x62883))+~P1(f317(f317(f319(x62881),x62882),x62883))
% 94.68/94.45 [6434]E(x64341,x64342)+~E(f317(f317(f23(a897),x64341),x64343),f317(f317(f23(a897),x64342),x64343))+~P1(f317(f317(f224(a897),x64343),x64341))+~P1(f317(f317(f224(a897),x64343),x64342))
% 94.68/94.45 [6461]~P66(x64611)+~P1(f317(f28(x64611),x64612))+~P1(f317(f317(f319(x64611),x64613),x64612))+P1(f317(f317(f224(x64611),f14(x64611,x64612)),x64613))
% 94.68/94.45 [6526]P147(x65262,x65261,x65263)+E(x65261,f2(a1))+P1(f317(f317(f225(a1),x65261),f833(x65263,x65261,x65262)))+P1(f317(f317(f225(a1),f2(a1)),x65261))
% 94.68/94.45 [6527]P148(x65272,x65271,x65273)+E(x65271,f2(a1))+P1(f317(f317(f225(a1),x65271),f845(x65273,x65271,x65272)))+P1(f317(f317(f225(a1),f2(a1)),x65271))
% 94.68/94.45 [6528]~P66(x65281)+E(f317(f317(f228(x65281),x65282),f11(x65281,f228(x65281),x65283)),f11(x65281,f228(x65281),x65283))+~P1(f317(f28(x65281),x65283))+~P1(f317(f317(f319(x65281),x65282),x65283))
% 94.68/94.45 [6529]~P66(x65291)+E(f317(f317(f223(x65291),x65292),f12(x65291,f223(x65291),x65293)),f12(x65291,f223(x65291),x65293))+~P1(f317(f28(x65291),x65293))+~P1(f317(f317(f319(x65291),x65292),x65293))
% 94.68/94.45 [6534]~P1(f317(x65341,x65342))+P1(f317(x65341,f538(x65342,x65341,x65343)))+P1(f317(x65341,f2(a897)))+~P1(f317(f317(f225(a897),x65342),x65343))
% 94.68/94.45 [6595]~P1(f317(x65951,x65952))+~P1(f317(f28(x65953),x65952))+P1(f317(x65951,f471(x65951,x65952,x65953)))+P1(f317(x65951,f178(f904(x65953,a893))))
% 94.68/94.45 [6608]~P111(x66081)+~P94(x66081)+P1(f317(f317(f224(x66081),f317(f94(x66081),x66082)),f317(f94(x66081),x66083)))+~P1(f317(f317(f224(a1),x66082),x66083))
% 94.68/94.45 [6609]~P111(x66091)+~P94(x66091)+P1(f317(f317(f225(x66091),f317(f94(x66091),x66092)),f317(f94(x66091),x66093)))+~P1(f317(f317(f225(a1),x66092),x66093))
% 94.68/94.45 [6612]~P1(f317(x66121,x66123))+~P1(f317(f28(x66122),x66123))+P1(f317(f28(x66122),f471(x66121,x66123,x66122)))+P1(f317(x66121,f178(f904(x66122,a893))))
% 94.68/94.45 [6646]P147(x66461,x66462,x66463)+~P1(f317(x66461,x66463))+P1(f317(f317(f225(a1),x66462),f833(x66463,x66462,x66461)))+P1(f317(f317(f225(a1),f2(a1)),x66462))
% 94.68/94.45 [6684]P148(x66841,x66842,x66843)+P1(f317(f317(f225(a1),x66842),f845(x66843,x66842,x66841)))+~P1(f317(x66841,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x66842))
% 94.68/94.45 [6714]~P109(x67141)+~P95(x67141)+E(f317(f317(f228(x67141),f317(f94(x67141),x67142)),f317(f94(x67141),x67143)),f317(f94(x67141),x67143))+P1(f317(f317(f224(x67141),f317(f94(x67141),x67142)),f317(f94(x67141),x67143)))
% 94.68/94.45 [6715]~P109(x67151)+~P95(x67151)+E(f317(f317(f223(x67151),f317(f94(x67151),x67152)),f317(f94(x67151),x67153)),f317(f94(x67151),x67152))+P1(f317(f317(f224(x67151),f317(f94(x67151),x67152)),f317(f94(x67151),x67153)))
% 94.68/94.45 [6775]P147(x67752,x67751,x67753)+E(x67751,f2(a1))+~P1(f317(x67752,f833(x67753,x67751,x67752)))+P1(f317(f317(f225(a1),f2(a1)),x67751))
% 94.68/94.45 [6776]P148(x67762,x67761,x67763)+E(x67761,f2(a1))+~P1(f317(x67762,f847(x67763,x67761,x67762)))+P1(f317(f317(f225(a1),f2(a1)),x67761))
% 94.68/94.45 [6780]P1(f317(x67801,x67802))+~P1(f317(f28(x67803),x67802))+P1(f317(x67801,f509(x67801,x67802,x67803)))+~P1(f317(x67801,f178(f904(x67803,a893))))
% 94.68/94.45 [6801]P1(f317(x68011,x68012))+P1(f317(f28(x68013),f509(x68011,x68012,x68013)))+~P1(f317(f28(x68013),x68012))+~P1(f317(x68011,f178(f904(x68013,a893))))
% 94.68/94.45 [6869]P147(x68691,x68692,x68693)+~P1(f317(x68691,x68693))+~P1(f317(x68691,f833(x68693,x68692,x68691)))+P1(f317(f317(f225(a1),f2(a1)),x68692))
% 94.68/94.45 [6899]P148(x68991,x68992,x68993)+~P1(f317(x68991,f847(x68993,x68992,x68991)))+~P1(f317(x68991,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x68992))
% 94.68/94.45 [7010]~P94(x70103)+~P111(x70103)+~P1(f317(f317(f224(x70103),f317(f94(x70103),x70101)),f317(f94(x70103),x70102)))+P1(f317(f317(f224(a1),x70101),x70102))
% 94.68/94.45 [7011]~P94(x70113)+~P111(x70113)+~P1(f317(f317(f225(x70113),f317(f94(x70113),x70111)),f317(f94(x70113),x70112)))+P1(f317(f317(f225(a1),x70111),x70112))
% 94.68/94.45 [7039]~P66(x70391)+~P13(x70391,x70393)+P13(x70391,f317(f317(f141(x70391),x70392),x70393))+~P1(f317(f317(f224(x70391),x70392),f688(x70393,x70392,x70391)))
% 94.68/94.45 [7040]~P66(x70401)+~P13(x70401,x70403)+P13(x70401,f317(f317(f141(x70401),x70402),x70403))+~P1(f317(f317(f224(x70401),x70402),f690(x70403,x70402,x70401)))
% 94.68/94.45 [7041]~P66(x70411)+~P13(x70411,x70413)+P13(x70411,f317(f317(f141(x70411),x70412),x70413))+~P1(f317(f317(f224(x70411),x70412),f730(x70412,x70413,x70411)))
% 94.68/94.45 [7128]P147(x71282,x71281,x71283)+E(x71281,f2(a1))+P1(f317(f317(f225(a1),x71281),f2(a1)))+P1(f317(f317(f225(a1),f834(x71283,x71281,x71282)),x71281))
% 94.68/94.45 [7129]P148(x71292,x71291,x71293)+E(x71291,f2(a1))+P1(f317(f317(f225(a1),x71291),f2(a1)))+P1(f317(f317(f225(a1),f846(x71293,x71291,x71292)),x71291))
% 94.68/94.45 [7165]P147(x71652,x71651,x71653)+E(x71651,f2(a1))+P1(f317(f317(f224(a1),f833(x71653,x71651,x71652)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x71651))
% 94.68/94.45 [7166]P148(x71662,x71661,x71663)+E(x71661,f2(a1))+P1(f317(f317(f224(a1),f845(x71663,x71661,x71662)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x71661))
% 94.68/94.45 [7191]~P66(x71911)+~P13(x71911,x71913)+E(f317(f317(f138(x71911,x71911,f5(x71911)),x71912),f160(x71911,x71912,x71913)),x71913)+~P1(f317(f317(f319(x71911),x71912),f317(f162(x71911),x71913)))
% 94.68/94.45 [7238]P147(x72381,x72382,x72383)+~P1(f317(x72381,x72383))+P1(f317(f317(f225(a1),x72382),f2(a1)))+P1(f317(f317(f225(a1),f834(x72383,x72382,x72381)),x72382))
% 94.68/94.45 [7244]~P109(x72441)+~P95(x72441)+E(f317(f317(f228(x72441),f317(f94(x72441),x72442)),f317(f94(x72441),x72443)),f317(f94(x72441),x72442))+~P1(f317(f317(f224(x72441),f317(f94(x72441),x72442)),f317(f94(x72441),x72443)))
% 94.68/94.45 [7245]~P109(x72451)+~P95(x72451)+E(f317(f317(f223(x72451),f317(f94(x72451),x72452)),f317(f94(x72451),x72453)),f317(f94(x72451),x72453))+~P1(f317(f317(f224(x72451),f317(f94(x72451),x72452)),f317(f94(x72451),x72453)))
% 94.68/94.45 [7259]P148(x72591,x72592,x72593)+~P1(f317(x72591,f2(a1)))+P1(f317(f317(f225(a1),x72592),f2(a1)))+P1(f317(f317(f225(a1),f846(x72593,x72592,x72591)),x72592))
% 94.68/94.45 [7269]P147(x72691,x72692,x72693)+~P1(f317(x72691,x72693))+P1(f317(f317(f224(a1),f833(x72693,x72692,x72691)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x72692))
% 94.68/94.45 [7293]P148(x72931,x72932,x72933)+~P1(f317(x72931,f2(a1)))+P1(f317(f317(f224(a1),f845(x72933,x72932,x72931)),f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x72932))
% 94.68/94.45 [7319]~P1(f317(x73191,x73192))+P1(f317(x73191,f2(a897)))+~P1(f317(f317(f225(a897),x73192),x73193))+P1(f317(f317(f225(a897),f538(x73192,x73191,x73193)),x73193))
% 94.68/94.45 [7336]~P66(x73361)+~P13(x73361,x73363)+P13(x73361,f317(f317(f141(x73361),x73362),x73363))+P1(f317(f317(f319(x73361),f688(x73363,x73362,x73361)),f317(f162(x73361),x73363)))
% 94.68/94.45 [7337]~P66(x73371)+~P13(x73371,x73373)+P13(x73371,f317(f317(f141(x73371),x73372),x73373))+P1(f317(f317(f319(x73371),f690(x73373,x73372,x73371)),f317(f162(x73371),x73373)))
% 94.68/94.45 [7338]~P66(x73381)+~P13(x73381,x73383)+P13(x73381,f317(f317(f141(x73381),x73382),x73383))+P1(f317(f317(f319(x73381),f730(x73382,x73383,x73381)),f317(f162(x73381),x73383)))
% 94.68/94.45 [7454]~P66(x74541)+~P5(x74541)+~P1(f317(f317(f225(x74541),x74543),f31(x74541,x74542)))+P1(f317(f317(f319(x74541),f579(x74542,x74543,x74541)),x74542))
% 94.68/94.45 [7609]~P66(x76091)+~P5(x76091)+~P1(f317(f317(f225(x76091),f32(x76091,x76093)),x76092))+P1(f317(f317(f319(x76091),f592(x76092,x76093,x76091)),x76093))
% 94.68/94.45 [7610]~P66(x76101)+~P5(x76101)+~P1(f317(f317(f225(x76101),f32(x76101,x76103)),x76102))+P1(f317(f317(f225(x76101),f592(x76102,x76103,x76101)),x76102))
% 94.68/94.45 [7623]P147(x76232,x76231,x76233)+E(x76231,f2(a1))+P1(f317(f317(f225(a1),x76231),f833(x76233,x76231,x76232)))+P1(f317(f317(f225(a1),f834(x76233,x76231,x76232)),x76231))
% 94.68/94.45 [7624]P148(x76242,x76241,x76243)+E(x76241,f2(a1))+P1(f317(f317(f225(a1),x76241),f845(x76243,x76241,x76242)))+P1(f317(f317(f225(a1),f846(x76243,x76241,x76242)),x76241))
% 94.68/94.45 [7718]P147(x77183,x77181,x77182)+E(x77181,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x77181),f840(x77182,x77181,x77183))),f833(x77182,x77181,x77183)),x77182)+P1(f317(f317(f225(a1),f2(a1)),x77181))
% 94.68/94.45 [7719]P148(x77193,x77191,x77192)+E(x77191,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x77191),f847(x77192,x77191,x77193))),f845(x77192,x77191,x77193)),x77192)+P1(f317(f317(f225(a1),f2(a1)),x77191))
% 94.68/94.45 [7722]~P135(x77221)+~P1(f317(f317(f224(x77221),x77223),f2(x77221)))+P1(f317(f317(f224(x77221),f317(f317(f75(x77221),x77222),x77223)),f2(x77221)))+~P1(f317(f317(f224(x77221),f2(x77221)),x77222))
% 94.68/94.45 [7724]~P135(x77241)+~P1(f317(f317(f224(x77241),x77242),f2(x77241)))+P1(f317(f317(f224(x77241),f317(f317(f75(x77241),x77242),x77243)),f2(x77241)))+~P1(f317(f317(f224(x77241),f2(x77241)),x77243))
% 94.68/94.45 [7725]~P125(x77251)+~P1(f317(f317(f224(x77251),x77253),f2(x77251)))+P1(f317(f317(f224(x77251),f317(f317(f75(x77251),x77252),x77253)),f2(x77251)))+~P1(f317(f317(f224(x77251),f2(x77251)),x77252))
% 94.68/94.45 [7726]~P125(x77261)+~P1(f317(f317(f224(x77261),x77262),f2(x77261)))+P1(f317(f317(f224(x77261),f317(f317(f75(x77261),x77262),x77263)),f2(x77261)))+~P1(f317(f317(f224(x77261),f2(x77261)),x77263))
% 94.68/94.45 [7727]~P63(x77271)+~P1(f317(f317(f224(x77271),x77273),f2(x77271)))+P1(f317(f317(f224(x77271),f317(f317(f281(x77271),x77272),x77273)),f2(x77271)))+~P1(f317(f317(f224(x77271),f2(x77271)),x77272))
% 94.68/94.45 [7728]~P63(x77281)+~P1(f317(f317(f224(x77281),x77282),f2(x77281)))+P1(f317(f317(f224(x77281),f317(f317(f281(x77281),x77282),x77283)),f2(x77281)))+~P1(f317(f317(f224(x77281),f2(x77281)),x77283))
% 94.68/94.45 [7729]~P64(x77291)+~P1(f317(f317(f224(x77291),x77292),f2(x77291)))+P1(f317(f317(f224(x77291),f317(f317(f281(x77291),x77292),x77293)),f2(x77291)))+~P1(f317(f317(f225(x77291),f2(x77291)),x77293))
% 94.68/94.45 [7730]~P64(x77301)+~P1(f317(f317(f225(x77301),x77303),f2(x77301)))+P1(f317(f317(f224(x77301),f317(f317(f281(x77301),x77302),x77303)),f2(x77301)))+~P1(f317(f317(f224(x77301),f2(x77301)),x77302))
% 94.68/94.45 [7732]~P133(x77321)+~P1(f317(f317(f225(x77321),x77323),f2(x77321)))+P1(f317(f317(f225(x77321),f317(f317(f75(x77321),x77322),x77323)),f2(x77321)))+~P1(f317(f317(f225(x77321),f2(x77321)),x77322))
% 94.68/94.45 [7733]~P133(x77331)+~P1(f317(f317(f225(x77331),x77332),f2(x77331)))+P1(f317(f317(f225(x77331),f317(f317(f75(x77331),x77332),x77333)),f2(x77331)))+~P1(f317(f317(f225(x77331),f2(x77331)),x77333))
% 94.68/94.45 [7734]~P63(x77341)+~P1(f317(f317(f225(x77341),x77343),f2(x77341)))+P1(f317(f317(f225(x77341),f317(f317(f281(x77341),x77342),x77343)),f2(x77341)))+~P1(f317(f317(f225(x77341),f2(x77341)),x77342))
% 94.68/94.45 [7735]~P63(x77351)+~P1(f317(f317(f225(x77351),x77352),f2(x77351)))+P1(f317(f317(f225(x77351),f317(f317(f281(x77351),x77352),x77353)),f2(x77351)))+~P1(f317(f317(f225(x77351),f2(x77351)),x77353))
% 94.68/94.45 [7736]~P64(x77361)+~P1(f317(f317(f225(x77361),x77363),f2(x77361)))+P1(f317(f317(f225(x77361),f317(f317(f281(x77361),x77362),x77363)),f2(x77361)))+~P1(f317(f317(f225(x77361),f2(x77361)),x77362))
% 94.68/94.45 [7737]~P64(x77371)+~P1(f317(f317(f225(x77371),x77372),f2(x77371)))+P1(f317(f317(f225(x77371),f317(f317(f281(x77371),x77372),x77373)),f2(x77371)))+~P1(f317(f317(f225(x77371),f2(x77371)),x77373))
% 94.68/94.45 [7752]P147(x77521,x77522,x77523)+~P1(f317(x77521,x77523))+P1(f317(f317(f225(a1),x77522),f833(x77523,x77522,x77521)))+P1(f317(f317(f225(a1),f834(x77523,x77522,x77521)),x77522))
% 94.68/94.45 [7765]P148(x77651,x77652,x77653)+P1(f317(f317(f225(a1),x77652),f845(x77653,x77652,x77651)))+~P1(f317(x77651,f2(a1)))+P1(f317(f317(f225(a1),f846(x77653,x77652,x77651)),x77652))
% 94.68/94.45 [7817]P147(x78172,x78171,x78173)+E(x78171,f2(a1))+~P1(f317(x78172,f833(x78173,x78171,x78172)))+P1(f317(f317(f225(a1),f834(x78173,x78171,x78172)),x78171))
% 94.68/94.45 [7818]P148(x78182,x78181,x78183)+E(x78181,f2(a1))+~P1(f317(x78182,f847(x78183,x78181,x78182)))+P1(f317(f317(f225(a1),f846(x78183,x78181,x78182)),x78181))
% 94.68/94.45 [7828]P147(x78283,x78281,x78282)+~P1(f317(x78283,x78282))+E(f317(f317(f74(a1),f317(f317(f75(a1),x78281),f840(x78282,x78281,x78283))),f833(x78282,x78281,x78283)),x78282)+P1(f317(f317(f225(a1),f2(a1)),x78281))
% 94.68/94.45 [7843]P148(x78433,x78431,x78432)+E(f317(f317(f74(a1),f317(f317(f75(a1),x78431),f847(x78432,x78431,x78433))),f845(x78432,x78431,x78433)),x78432)+~P1(f317(x78433,f2(a1)))+P1(f317(f317(f225(a1),f2(a1)),x78431))
% 94.68/94.45 [7871]~P1(f317(x78711,x78713))+~P1(f317(f28(x78712),x78713))+P1(f317(f317(f319(x78712),f460(x78711,x78713,x78712)),f471(x78711,x78713,x78712)))+P1(f317(x78711,f178(f904(x78712,a893))))
% 94.68/94.45 [7883]P147(x78831,x78832,x78833)+~P1(f317(x78831,x78833))+~P1(f317(x78831,f833(x78833,x78832,x78831)))+P1(f317(f317(f225(a1),f834(x78833,x78832,x78831)),x78832))
% 94.68/94.45 [7889]P148(x78891,x78892,x78893)+~P1(f317(x78891,f847(x78893,x78892,x78891)))+~P1(f317(x78891,f2(a1)))+P1(f317(f317(f225(a1),f846(x78893,x78892,x78891)),x78892))
% 94.68/94.45 [7991]~P125(x79911)+~P1(f317(f317(f224(x79911),f317(f317(f75(x79911),x79913),x79912)),f2(x79911)))+P1(f317(f317(f224(x79911),x79912),f2(x79911)))+P1(f317(f317(f224(x79911),f2(x79911)),x79912))
% 94.68/94.45 [7992]~P125(x79921)+~P1(f317(f317(f224(x79921),f317(f317(f75(x79921),x79922),x79923)),f2(x79921)))+P1(f317(f317(f224(x79921),x79922),f2(x79921)))+P1(f317(f317(f224(x79921),f2(x79921)),x79922))
% 94.68/94.45 [7993]~P63(x79931)+~P1(f317(f317(f224(x79931),f317(f317(f281(x79931),x79933),x79932)),f2(x79931)))+P1(f317(f317(f224(x79931),x79932),f2(x79931)))+P1(f317(f317(f224(x79931),f2(x79931)),x79932))
% 94.68/94.45 [7994]~P63(x79941)+~P1(f317(f317(f224(x79941),f317(f317(f281(x79941),x79942),x79943)),f2(x79941)))+P1(f317(f317(f224(x79941),x79942),f2(x79941)))+P1(f317(f317(f224(x79941),f2(x79941)),x79942))
% 94.68/94.45 [7995]~P63(x79951)+~P1(f317(f317(f225(x79951),f317(f317(f281(x79951),x79953),x79952)),f2(x79951)))+P1(f317(f317(f225(x79951),x79952),f2(x79951)))+P1(f317(f317(f225(x79951),f2(x79951)),x79952))
% 94.68/94.45 [7996]~P63(x79961)+~P1(f317(f317(f225(x79961),f317(f317(f281(x79961),x79962),x79963)),f2(x79961)))+P1(f317(f317(f225(x79961),x79962),f2(x79961)))+P1(f317(f317(f225(x79961),f2(x79961)),x79962))
% 94.68/94.45 [8020]~P125(x80201)+~P1(f317(f317(f224(x80201),f317(f317(f75(x80201),x80202),x80203)),f2(x80201)))+P1(f317(f317(f224(x80201),f2(x80201)),x80202))+P1(f317(f317(f224(x80201),f2(x80201)),x80203))
% 94.68/94.45 [8021]~P63(x80211)+~P1(f317(f317(f224(x80211),f317(f317(f281(x80211),x80212),x80213)),f2(x80211)))+P1(f317(f317(f224(x80211),f2(x80211)),x80212))+P1(f317(f317(f224(x80211),f2(x80211)),x80213))
% 94.68/94.45 [8022]~P63(x80221)+~P1(f317(f317(f225(x80221),f317(f317(f281(x80221),x80222),x80223)),f2(x80221)))+P1(f317(f317(f225(x80221),f2(x80221)),x80222))+P1(f317(f317(f225(x80221),f2(x80221)),x80223))
% 94.68/94.45 [8044]P147(x80442,x80441,x80443)+E(x80441,f2(a1))+P1(f317(f317(f224(a1),f833(x80443,x80441,x80442)),f2(a1)))+P1(f317(f317(f225(a1),f834(x80443,x80441,x80442)),x80441))
% 94.68/94.45 [8045]P148(x80452,x80451,x80453)+E(x80451,f2(a1))+P1(f317(f317(f224(a1),f845(x80453,x80451,x80452)),f2(a1)))+P1(f317(f317(f225(a1),f846(x80453,x80451,x80452)),x80451))
% 94.68/94.45 [8052]~P110(x80521)+~P1(f317(f317(f225(x80521),x80522),f72(x80521)))+P1(f317(f317(f225(x80521),f317(f317(f234(x80521),x80522),f317(a102,x80523))),f72(x80521)))+~P1(f317(f317(f225(x80521),f2(x80521)),x80522))
% 94.68/94.45 [8105]~P66(x81051)+~E(x81053,f103(x81051))+~P13(x81051,f317(f158(x81051),x81053))+E(f317(f132(x81051,x81051,f317(f7(x81051,x81051,x81051),f223(x81051)),x81052),f317(f158(x81051),x81053)),x81052)
% 94.68/94.45 [8108]P147(x81081,x81082,x81083)+~P1(f317(x81081,x81083))+P1(f317(f317(f224(a1),f833(x81083,x81082,x81081)),f2(a1)))+P1(f317(f317(f225(a1),f834(x81083,x81082,x81081)),x81082))
% 94.68/94.45 [8115]P148(x81151,x81152,x81153)+~P1(f317(x81151,f2(a1)))+P1(f317(f317(f224(a1),f845(x81153,x81152,x81151)),f2(a1)))+P1(f317(f317(f225(a1),f846(x81153,x81152,x81151)),x81152))
% 94.68/94.45 [8333]P147(x83333,x83331,x83332)+E(x83331,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83331),f840(x83332,x83331,x83333))),f833(x83332,x83331,x83333)),x83332)+P1(f317(f317(f225(a1),f834(x83332,x83331,x83333)),x83331))
% 94.68/94.45 [8334]P148(x83343,x83341,x83342)+E(x83341,f2(a1))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83341),f847(x83342,x83341,x83343))),f845(x83342,x83341,x83343)),x83342)+P1(f317(f317(f225(a1),f846(x83342,x83341,x83343)),x83341))
% 94.68/94.45 [8370]P147(x83703,x83701,x83702)+~P1(f317(x83703,x83702))+E(f317(f317(f74(a1),f317(f317(f75(a1),x83701),f840(x83702,x83701,x83703))),f833(x83702,x83701,x83703)),x83702)+P1(f317(f317(f225(a1),f834(x83702,x83701,x83703)),x83701))
% 94.68/94.45 [8371]~P76(x83711)+~P77(x83711)+~P39(x83713)+E(f317(f317(f9(a897,x83711),f317(f317(f8(a1,x83711,a897),x83712),f90(a1))),f317(f300(a1,a897,a95),x83713)),f317(f317(f9(a1,x83711),x83712),x83713))
% 94.68/94.45 [8372]~P76(x83721)+~P77(x83721)+~P39(x83723)+E(f317(f317(f6(a897,x83721),f317(f317(f8(a1,x83721,a897),x83722),f90(a1))),f317(f300(a1,a897,a95),x83723)),f317(f317(f6(a1,x83721),x83722),x83723))
% 94.68/94.45 [8381]P148(x83813,x83811,x83812)+E(f317(f317(f74(a1),f317(f317(f75(a1),x83811),f847(x83812,x83811,x83813))),f845(x83812,x83811,x83813)),x83812)+~P1(f317(x83813,f2(a1)))+P1(f317(f317(f225(a1),f846(x83812,x83811,x83813)),x83811))
% 94.68/94.45 [8403]~E(x84032,f2(a897))+~E(f317(f241(a897,a897),x84033),f2(a897))+~E(x84031,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x84033)),x84032)),f317(f246(a897,a897),x84033)))+P1(f317(f43(x84031,x84032),x84033))
% 94.68/94.45 [8460]P1(f317(x84601,x84602))+~P1(f317(f317(f319(x84603),f499(x84601,x84602,x84603)),f509(x84601,x84602,x84603)))+~P1(f317(f28(x84603),x84602))+~P1(f317(x84601,f178(f904(x84603,a893))))
% 94.68/94.45 [9084]P1(f317(x90841,x90842))+~P1(f317(f28(x90843),x90842))+~P1(f317(x90841,f317(f317(f299(x90843),f499(x90841,x90842,x90843)),f509(x90841,x90842,x90843))))+~P1(f317(x90841,f178(f904(x90843,a893))))
% 94.68/94.45 [9316]P1(f317(f317(f224(a1),x93161),f2(a1)))+~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x93163),x93161)),x93162)),f2(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x93162))+~P1(f317(f317(f225(a1),f2(a1)),x93163))
% 94.68/94.45 [5872]~P66(x58722)+E(x58721,f178(f904(x58722,a893)))+~P1(f317(f28(x58722),x58721))+E(f14(x58722,f317(f317(f299(x58722),x58723),x58721)),f317(f317(f228(x58722),x58723),f14(x58722,x58721)))
% 94.68/94.45 [5873]~P66(x58732)+E(x58731,f178(f904(x58732,a893)))+~P1(f317(f28(x58732),x58731))+E(f15(x58732,f317(f317(f299(x58732),x58733),x58731)),f317(f317(f223(x58732),x58733),f15(x58732,x58731)))
% 94.68/94.45 [5874]~P100(x58742)+E(x58741,f178(f904(x58742,a893)))+~P1(f317(f28(x58742),x58741))+E(f13(x58742,f317(f317(f299(x58742),x58743),x58741)),f317(f317(f91(x58742),x58743),f13(x58742,x58741)))
% 94.68/94.45 [5875]~P100(x58752)+E(x58751,f178(f904(x58752,a893)))+~P1(f317(f28(x58752),x58751))+E(f10(x58752,f317(f317(f299(x58752),x58753),x58751)),f317(f317(f92(x58752),x58753),f10(x58752,x58751)))
% 94.68/94.45 [6206]~P125(x62061)+~E(x62063,f2(x62061))+~E(x62062,f2(x62061))+E(f317(f317(f74(x62061),f317(f317(f75(x62061),x62062),x62062)),f317(f317(f75(x62061),x62063),x62063)),f2(x62061))
% 94.68/94.45 [6280]~P98(x62802)+E(x62801,f178(f904(x62802,a893)))+~P1(f317(f28(x62802),x62801))+E(f317(f57(x62802,f75(x62802)),f317(f317(f299(x62802),x62803),x62801)),f317(f317(f75(x62802),x62803),f317(f57(x62802,f75(x62802)),x62801)))
% 94.68/94.45 [6411]~P66(x64112)+E(x64111,f178(f904(x64112,a893)))+~P1(f317(f28(x64112),x64111))+E(f11(x64112,f228(x64112),f317(f317(f299(x64112),x64113),x64111)),f317(f317(f228(x64112),x64113),f11(x64112,f228(x64112),x64111)))
% 94.68/94.45 [6412]~P66(x64122)+E(x64121,f178(f904(x64122,a893)))+~P1(f317(f28(x64122),x64121))+E(f12(x64122,f223(x64122),f317(f317(f299(x64122),x64123),x64121)),f317(f317(f223(x64122),x64123),f12(x64122,f223(x64122),x64121)))
% 94.68/94.45 [6933]~P73(x69331)+~P1(f317(f28(x69331),x69333))+E(f317(f57(x69331,f75(x69331)),f317(f317(f299(x69331),x69332),x69333)),f317(f317(f58(x69331,x69331,f75(x69331)),x69332),x69333))+P1(f317(f317(f319(x69331),x69332),x69333))
% 94.68/94.45 [7017]~E(f317(f317(f74(a1),x70172),f317(f317(f75(a1),x70173),x70171)),x70173)+~P1(f317(f317(f225(a1),f2(a1)),x70173))+P1(f317(f317(f224(a1),f72(a1)),x70171))+~P1(f317(f317(f225(a1),x70172),x70173))
% 94.68/94.45 [7046]~E(f317(f317(f74(a1),x70462),f317(f317(f75(a1),x70463),x70461)),x70463)+P1(f317(f317(f224(a1),x70461),f72(a1)))+~P1(f317(f317(f224(a1),f2(a1)),x70462))+~P1(f317(f317(f225(a1),f2(a1)),x70463))
% 94.68/94.45 [7064]E(x70641,f2(a897))+~P1(f317(f43(x70643,x70641),x70642))+~P1(f317(f317(f225(a897),f2(a897)),x70641))+P1(f317(f317(f225(a897),f317(f246(a897,a897),x70642)),x70641))
% 94.68/94.45 [7095]~P139(x70951)+~P1(f317(f317(f224(x70951),x70952),f2(x70951)))+~P1(f317(f317(f224(x70951),x70953),f2(x70951)))+E(f317(f317(f75(x70951),f317(f70(x70951),x70952)),f317(f70(x70951),x70953)),f317(f70(x70951),f317(f317(f75(x70951),x70952),x70953)))
% 94.68/94.45 [7142]~P139(x71421)+~P1(f317(f317(f224(x71421),x71422),f2(x71421)))+E(f317(f317(f75(x71421),f317(f70(x71421),x71422)),f317(f70(x71421),x71423)),f317(f70(x71421),f317(f317(f75(x71421),x71422),x71423)))+~P1(f317(f317(f224(x71421),f2(x71421)),x71423))
% 94.68/94.45 [7143]~P139(x71431)+~P1(f317(f317(f224(x71431),x71433),f2(x71431)))+E(f317(f317(f75(x71431),f317(f70(x71431),x71432)),f317(f70(x71431),x71433)),f317(f70(x71431),f317(f317(f75(x71431),x71432),x71433)))+~P1(f317(f317(f224(x71431),f2(x71431)),x71432))
% 94.68/94.45 [7199]~P139(x71991)+E(f317(f317(f75(x71991),f317(f70(x71991),x71992)),f317(f70(x71991),x71993)),f317(f70(x71991),f317(f317(f75(x71991),x71992),x71993)))+~P1(f317(f317(f224(x71991),f2(x71991)),x71992))+~P1(f317(f317(f224(x71991),f2(x71991)),x71993))
% 94.68/94.45 [7216]~P136(x72161)+~P1(f317(f317(f224(x72161),x72163),f2(x72161)))+~P1(f317(f317(f224(x72161),x72162),f2(x72161)))+P1(f317(f317(f224(x72161),f2(x72161)),f317(f317(f75(x72161),x72162),x72163)))
% 94.68/94.45 [7217]~P125(x72171)+~P1(f317(f317(f224(x72171),x72173),f2(x72171)))+~P1(f317(f317(f224(x72171),x72172),f2(x72171)))+P1(f317(f317(f224(x72171),f2(x72171)),f317(f317(f75(x72171),x72172),x72173)))
% 94.68/94.45 [7218]~P63(x72181)+~P1(f317(f317(f224(x72181),x72183),f2(x72181)))+~P1(f317(f317(f224(x72181),x72182),f2(x72181)))+P1(f317(f317(f224(x72181),f2(x72181)),f317(f317(f281(x72181),x72182),x72183)))
% 94.68/94.45 [7219]~P64(x72191)+~P1(f317(f317(f225(x72191),x72193),f2(x72191)))+~P1(f317(f317(f224(x72191),x72192),f2(x72191)))+P1(f317(f317(f224(x72191),f2(x72191)),f317(f317(f281(x72191),x72192),x72193)))
% 94.68/94.45 [7220]~P125(x72201)+~P1(f317(f317(f225(x72201),x72203),f2(x72201)))+~P1(f317(f317(f225(x72201),x72202),f2(x72201)))+P1(f317(f317(f225(x72201),f2(x72201)),f317(f317(f75(x72201),x72202),x72203)))
% 94.68/94.45 [7221]~P63(x72211)+~P1(f317(f317(f225(x72211),x72213),f2(x72211)))+~P1(f317(f317(f225(x72211),x72212),f2(x72211)))+P1(f317(f317(f225(x72211),f2(x72211)),f317(f317(f281(x72211),x72212),x72213)))
% 94.68/94.45 [7222]~P64(x72221)+~P1(f317(f317(f225(x72221),x72223),f2(x72221)))+~P1(f317(f317(f225(x72221),x72222),f2(x72221)))+P1(f317(f317(f225(x72221),f2(x72221)),f317(f317(f281(x72221),x72222),x72223)))
% 94.68/94.45 [7223]~P110(x72231)+~P1(f317(f317(f225(a897),f2(a897)),x72233))+~P1(f317(f317(f225(x72231),f72(x72231)),x72232))+P1(f317(f317(f225(x72231),f72(x72231)),f317(f317(f234(x72231),x72232),x72233)))
% 94.68/94.45 [7321]~P135(x73211)+~P1(f317(f317(f224(x73211),f2(x73211)),x73213))+~P1(f317(f317(f224(x73211),f2(x73211)),x73212))+P1(f317(f317(f224(x73211),f2(x73211)),f317(f317(f75(x73211),x73212),x73213)))
% 94.68/94.45 [7322]~P136(x73221)+~P1(f317(f317(f224(x73221),f2(x73221)),x73223))+~P1(f317(f317(f224(x73221),f2(x73221)),x73222))+P1(f317(f317(f224(x73221),f2(x73221)),f317(f317(f75(x73221),x73222),x73223)))
% 94.68/94.45 [7323]~P125(x73231)+~P1(f317(f317(f224(x73231),f2(x73231)),x73233))+~P1(f317(f317(f224(x73231),f2(x73231)),x73232))+P1(f317(f317(f224(x73231),f2(x73231)),f317(f317(f75(x73231),x73232),x73233)))
% 94.68/94.45 [7324]~P63(x73241)+~P1(f317(f317(f224(x73241),f2(x73241)),x73243))+~P1(f317(f317(f224(x73241),f2(x73241)),x73242))+P1(f317(f317(f224(x73241),f2(x73241)),f317(f317(f281(x73241),x73242),x73243)))
% 94.68/94.45 [7325]~P64(x73251)+~P1(f317(f317(f225(x73251),f2(x73251)),x73253))+~P1(f317(f317(f224(x73251),f2(x73251)),x73252))+P1(f317(f317(f224(x73251),f2(x73251)),f317(f317(f281(x73251),x73252),x73253)))
% 94.68/94.45 [7326]~P110(x73261)+~P1(f317(f317(f225(x73261),f72(x73261)),x73263))+~P1(f317(f317(f225(x73261),f72(x73261)),x73262))+P1(f317(f317(f225(x73261),f72(x73261)),f317(f317(f75(x73261),x73262),x73263)))
% 94.68/94.45 [7329]~P89(x73291)+~P1(f317(f317(f225(x73291),f2(x73291)),x73293))+~P1(f317(f317(f225(x73291),f2(x73291)),x73292))+P1(f317(f317(f225(x73291),f2(x73291)),f317(f317(f74(x73291),x73292),x73293)))
% 94.68/94.45 [7330]~P133(x73301)+~P1(f317(f317(f225(x73301),f2(x73301)),x73303))+~P1(f317(f317(f225(x73301),f2(x73301)),x73302))+P1(f317(f317(f225(x73301),f2(x73301)),f317(f317(f75(x73301),x73302),x73303)))
% 94.68/94.45 [7331]~P63(x73311)+~P1(f317(f317(f225(x73311),f2(x73311)),x73313))+~P1(f317(f317(f225(x73311),f2(x73311)),x73312))+P1(f317(f317(f225(x73311),f2(x73311)),f317(f317(f281(x73311),x73312),x73313)))
% 94.68/94.45 [7332]~P64(x73321)+~P1(f317(f317(f225(x73321),f2(x73321)),x73323))+~P1(f317(f317(f225(x73321),f2(x73321)),x73322))+P1(f317(f317(f225(x73321),f2(x73321)),f317(f317(f281(x73321),x73322),x73323)))
% 94.68/94.45 [7411]~P66(x74111)+~P1(f317(f28(x74111),x74113))+E(f14(x74111,f317(f317(f299(x74111),x74112),x74113)),x74112)+~E(f317(f317(f23(f904(x74111,a893)),x74113),f317(f317(f299(x74111),x74112),f178(f904(x74111,a893)))),f178(f904(x74111,a893)))
% 94.68/94.45 [7412]~P66(x74121)+~P1(f317(f28(x74121),x74123))+E(f15(x74121,f317(f317(f299(x74121),x74122),x74123)),x74122)+~E(f317(f317(f23(f904(x74121,a893)),x74123),f317(f317(f299(x74121),x74122),f178(f904(x74121,a893)))),f178(f904(x74121,a893)))
% 94.68/94.45 [7413]~P100(x74131)+~P1(f317(f28(x74131),x74133))+E(f13(x74131,f317(f317(f299(x74131),x74132),x74133)),x74132)+~E(f317(f317(f23(f904(x74131,a893)),x74133),f317(f317(f299(x74131),x74132),f178(f904(x74131,a893)))),f178(f904(x74131,a893)))
% 94.68/94.45 [7414]~P100(x74141)+~P1(f317(f28(x74141),x74143))+E(f10(x74141,f317(f317(f299(x74141),x74142),x74143)),x74142)+~E(f317(f317(f23(f904(x74141,a893)),x74143),f317(f317(f299(x74141),x74142),f178(f904(x74141,a893)))),f178(f904(x74141,a893)))
% 94.68/94.45 [7416]~P125(x74161)+P1(f317(f317(f224(x74161),x74162),f2(x74161)))+P1(f317(f317(f224(x74161),f2(x74161)),x74163))+~P1(f317(f317(f224(x74161),f2(x74161)),f317(f317(f75(x74161),x74163),x74162)))
% 94.68/94.45 [7417]~P125(x74171)+P1(f317(f317(f224(x74171),x74172),f2(x74171)))+P1(f317(f317(f224(x74171),f2(x74171)),x74173))+~P1(f317(f317(f224(x74171),f2(x74171)),f317(f317(f75(x74171),x74172),x74173)))
% 94.68/94.45 [7418]~P63(x74181)+P1(f317(f317(f224(x74181),x74182),f2(x74181)))+P1(f317(f317(f224(x74181),f2(x74181)),x74183))+~P1(f317(f317(f224(x74181),f2(x74181)),f317(f317(f281(x74181),x74183),x74182)))
% 94.68/94.45 [7419]~P63(x74191)+P1(f317(f317(f224(x74191),x74192),f2(x74191)))+P1(f317(f317(f224(x74191),f2(x74191)),x74193))+~P1(f317(f317(f224(x74191),f2(x74191)),f317(f317(f281(x74191),x74192),x74193)))
% 94.68/94.45 [7420]~P125(x74201)+P1(f317(f317(f224(x74201),x74202),f2(x74201)))+P1(f317(f317(f224(x74201),f2(x74201)),x74202))+~P1(f317(f317(f224(x74201),f2(x74201)),f317(f317(f75(x74201),x74203),x74202)))
% 94.68/94.45 [7421]~P125(x74211)+P1(f317(f317(f224(x74211),x74212),f2(x74211)))+P1(f317(f317(f224(x74211),f2(x74211)),x74212))+~P1(f317(f317(f224(x74211),f2(x74211)),f317(f317(f75(x74211),x74212),x74213)))
% 94.68/94.45 [7422]~P63(x74221)+P1(f317(f317(f224(x74221),x74222),f2(x74221)))+P1(f317(f317(f224(x74221),f2(x74221)),x74222))+~P1(f317(f317(f224(x74221),f2(x74221)),f317(f317(f281(x74221),x74223),x74222)))
% 94.68/94.45 [7423]~P63(x74231)+P1(f317(f317(f224(x74231),x74232),f2(x74231)))+P1(f317(f317(f224(x74231),f2(x74231)),x74232))+~P1(f317(f317(f224(x74231),f2(x74231)),f317(f317(f281(x74231),x74232),x74233)))
% 94.68/94.45 [7424]~P63(x74241)+P1(f317(f317(f225(x74241),x74242),f2(x74241)))+P1(f317(f317(f225(x74241),f2(x74241)),x74243))+~P1(f317(f317(f225(x74241),f2(x74241)),f317(f317(f281(x74241),x74243),x74242)))
% 94.68/94.45 [7425]~P63(x74251)+P1(f317(f317(f225(x74251),x74252),f2(x74251)))+P1(f317(f317(f225(x74251),f2(x74251)),x74253))+~P1(f317(f317(f225(x74251),f2(x74251)),f317(f317(f281(x74251),x74252),x74253)))
% 94.68/94.45 [7426]~P63(x74261)+P1(f317(f317(f225(x74261),x74262),f2(x74261)))+P1(f317(f317(f225(x74261),f2(x74261)),x74262))+~P1(f317(f317(f225(x74261),f2(x74261)),f317(f317(f281(x74261),x74263),x74262)))
% 94.68/94.45 [7427]~P63(x74271)+P1(f317(f317(f225(x74271),x74272),f2(x74271)))+P1(f317(f317(f225(x74271),f2(x74271)),x74272))+~P1(f317(f317(f225(x74271),f2(x74271)),f317(f317(f281(x74271),x74272),x74273)))
% 94.68/94.45 [7500]~P1(f317(f317(f277(a897),x75001),x75003))+P1(f317(f317(f277(a897),x75001),x75002))+~P1(f317(f317(f224(a897),x75002),x75003))+~P1(f317(f317(f277(a897),x75001),f317(f317(f23(a897),x75003),x75002)))
% 94.68/94.45 [7501]~P1(f317(f317(f277(a897),x75011),x75013))+P1(f317(f317(f277(a897),x75011),x75012))+~P1(f317(f317(f224(a897),x75013),x75012))+~P1(f317(f317(f277(a897),x75011),f317(f317(f23(a897),x75012),x75013)))
% 94.68/94.45 [7516]~E(f317(f317(f92(f904(x75161,a893)),f317(f162(x75161),x75162)),f317(f162(x75161),x75163)),f178(f904(x75161,a893)))+~P1(f317(f127(x75161),x75163))+~P1(f317(f127(x75161),x75162))+P1(f317(f127(x75161),f317(f317(f124(x75161),x75162),x75163)))
% 94.68/94.45 [7517]~P66(x75171)+~P1(f317(f28(x75171),x75173))+E(f11(x75171,f228(x75171),f317(f317(f299(x75171),x75172),x75173)),x75172)+~E(f317(f317(f23(f904(x75171,a893)),x75173),f317(f317(f299(x75171),x75172),f178(f904(x75171,a893)))),f178(f904(x75171,a893)))
% 94.68/94.45 [7518]~P66(x75181)+~P1(f317(f28(x75181),x75183))+E(f12(x75181,f223(x75181),f317(f317(f299(x75181),x75182),x75183)),x75182)+~E(f317(f317(f23(f904(x75181,a893)),x75183),f317(f317(f299(x75181),x75182),f178(f904(x75181,a893)))),f178(f904(x75181,a893)))
% 94.68/94.45 [7531]~P86(x75311)+~P1(f317(f317(f224(x75311),x75312),x75313))+~P1(f317(f317(f224(x75311),f317(f73(x75311),x75312)),x75313))+P1(f317(f317(f224(x75311),f317(f70(x75311),x75312)),x75313))
% 94.68/94.45 [7532]~P111(x75321)+~P1(f317(f317(f225(x75321),x75322),x75323))+~P1(f317(f317(f225(x75321),f317(f73(x75321),x75322)),x75323))+P1(f317(f317(f225(x75321),f317(f70(x75321),x75322)),x75323))
% 94.68/94.45 [7598]~P133(x75981)+P1(f317(f317(f225(x75981),f2(x75981)),x75982))+~P1(f317(f317(f225(x75981),f2(x75981)),x75983))+~P1(f317(f317(f225(x75981),f2(x75981)),f317(f317(f75(x75981),x75983),x75982)))
% 94.68/94.45 [7599]~P133(x75991)+P1(f317(f317(f225(x75991),f2(x75991)),x75992))+~P1(f317(f317(f225(x75991),f2(x75991)),x75993))+~P1(f317(f317(f225(x75991),f2(x75991)),f317(f317(f75(x75991),x75992),x75993)))
% 94.68/94.45 [7903]E(x79031,x79032)+~P1(f317(f28(x79033),x79031))+~P1(f317(f317(f224(a897),f317(f29(x79033),x79031)),f317(f29(x79033),x79032)))+~P1(f317(f317(f224(f904(x79033,a893)),x79032),x79031))
% 94.68/94.45 [8049]~P1(f317(f317(f225(a1),x80491),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x80492))+~P1(f317(f317(f224(a1),x80492),x80493))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x80491),x80492)),f317(f317(f30(a1),x80491),x80493)))
% 94.68/94.45 [8059]~P1(f317(f317(f224(a1),f2(a1)),x80591))+~P1(f317(f317(f225(a1),f2(a1)),x80593))+~P1(f317(f317(f224(a1),x80593),x80592))+P1(f317(f317(f224(a1),f317(f317(f30(a1),x80591),x80592)),f317(f317(f30(a1),x80591),x80593)))
% 94.68/94.45 [8193]E(f317(x81931,f466(x81932,x81931,x81933)),x81932)+~P1(f317(f317(f224(a1),x81932),f317(x81931,x81933)))+P1(f317(f317(f225(a897),f462(x81932,x81931,x81933)),x81933))+~P1(f317(f317(f224(a1),f317(x81931,f2(a897))),x81932))
% 94.68/94.45 [8194]E(f317(x81941,f467(x81942,x81941,x81943)),x81942)+~P1(f317(f317(f224(a1),x81942),f317(x81941,x81943)))+P1(f317(f317(f225(a897),f468(x81942,x81941,x81943)),x81943))+~P1(f317(f317(f224(a1),f317(x81941,f2(a897))),x81942))
% 94.68/94.45 [8296]~P1(f317(f28(x82961),x82963))+~P1(f317(f317(f225(a897),f317(f29(x82961),x82962)),f317(f29(x82961),x82963)))+~P1(f317(f317(f224(f904(x82961,a893)),x82962),x82963))+P1(f317(f317(f225(f904(x82961,a893)),x82962),x82963))
% 94.68/94.45 [8323]E(f317(f317(f74(a1),f356(x83233,x83231,x83232)),f357(x83233,x83231,x83232)),x83231)+E(f317(f317(f23(a1),x83231),x83232),x83231)+~P1(f317(f317(f225(a1),f2(a1)),x83232))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x83231),f72(a1))),x83233))
% 94.68/94.45 [8324]E(f317(f317(f23(a1),f362(x83243,x83241,x83242)),f363(x83243,x83241,x83242)),x83241)+E(f317(f317(f74(a1),x83241),x83242),x83241)+~P1(f317(f317(f225(a1),f2(a1)),x83242))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x83241),f72(a1))),x83243))
% 94.68/94.45 [8376]~P1(f317(f317(f224(a897),x83763),x83761))+P1(f317(f317(f224(a897),x83761),x83762))+~P1(f317(f317(f224(a897),x83763),x83762))+~P1(f317(f317(f224(a897),f317(f317(f23(a897),x83761),x83763)),f317(f317(f23(a897),x83762),x83763)))
% 94.68/94.45 [8377]~P1(f317(f317(f224(a897),x83773),x83771))+P1(f317(f317(f225(a897),x83771),x83772))+~P1(f317(f317(f224(a897),x83773),x83772))+~P1(f317(f317(f225(a897),f317(f317(f23(a897),x83771),x83773)),f317(f317(f23(a897),x83772),x83773)))
% 94.68/94.45 [8396]~P66(x83962)+E(x83961,f103(x83962))+~P13(x83962,f317(f158(x83962),x83961))+E(f317(f132(x83962,x83962,f317(f7(x83962,x83962,x83962),f223(x83962)),x83963),f317(f158(x83962),x83961)),f317(f317(f223(x83962),f317(f317(f154(x83962),x83961),f2(a897))),x83963))
% 94.68/94.45 [8465]E(f317(f317(f23(a1),x84651),x84652),x84651)+~P1(f317(f317(f225(a1),f2(a1)),x84652))+P1(f317(f317(f319(a1),f356(x84653,x84651,x84652)),x84653))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x84651),f72(a1))),x84653))
% 94.68/94.45 [8466]E(f317(f317(f74(a1),x84661),x84662),x84661)+~P1(f317(f317(f225(a1),f2(a1)),x84662))+P1(f317(f317(f319(a1),f362(x84663,x84661,x84662)),x84663))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x84661),f72(a1))),x84663))
% 94.68/94.45 [8538]~P1(f317(f317(f224(a1),x85381),f317(x85382,x85383)))+P1(f317(f317(f225(a897),f462(x85381,x85382,x85383)),x85383))+P1(f317(f317(f224(a897),f466(x85381,x85382,x85383)),x85383))+~P1(f317(f317(f224(a1),f317(x85382,f2(a897))),x85381))
% 94.68/94.45 [8539]~P1(f317(f317(f224(a1),x85391),f317(x85392,x85393)))+P1(f317(f317(f225(a897),f468(x85391,x85392,x85393)),x85393))+P1(f317(f317(f224(a897),f467(x85391,x85392,x85393)),x85393))+~P1(f317(f317(f224(a1),f317(x85392,f2(a897))),x85391))
% 94.68/94.45 [8611]E(f317(f317(f23(a1),x86111),x86112),x86111)+~P1(f317(f317(f225(a1),f2(a1)),x86112))+P1(f317(f317(f319(a1),f357(x86113,x86111,x86112)),f293(a1,f72(a1),x86112)))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x86111),f72(a1))),x86113))
% 94.68/94.45 [8612]E(f317(f317(f74(a1),x86121),x86122),x86121)+~P1(f317(f317(f225(a1),f2(a1)),x86122))+P1(f317(f317(f319(a1),f363(x86123,x86121,x86122)),f293(a1,f72(a1),x86122)))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x86121),f72(a1))),x86123))
% 94.68/94.45 [8745]~P110(x87451)+~P1(f317(f317(f225(x87451),x87452),f72(x87451)))+~P1(f317(f317(f225(x87451),f2(x87451)),x87452))+P1(f317(f317(f225(x87451),f317(f317(f75(x87451),x87452),f317(f317(f234(x87451),x87452),x87453))),f317(f317(f234(x87451),x87452),x87453)))
% 94.68/94.45 [8838]~P1(f317(x88381,x88382))+P1(f317(x88381,f2(a897)))+~P1(f317(f317(f225(a897),x88382),x88383))+~P1(f317(x88381,f40(a897,f317(a102,f538(x88382,x88381,x88383)),x88383)))
% 94.68/94.45 [8990]E(f429(x89901,x89902,x89903),f2(a897))+P1(f317(f317(x89901,x89903),x89902))+P1(f317(f317(x89901,f429(x89901,x89902,x89903)),f40(a897,f427(x89901,x89902,x89903),f429(x89901,x89902,x89903))))+~P1(f317(f305(f903(a897,a897),a209),f317(f317(f242(a897,a897),x89903),x89902)))
% 94.68/94.45 [9026]~P24(x90261,x90261,x90262,x90263)+E(f317(f300(x90261,x90261,x90262),x90263),x90263)+~P1(f317(f28(x90261),x90263))+~P1(f317(f317(f224(f904(x90261,a893)),f317(f300(x90261,x90261,x90262),x90263)),x90263))
% 94.68/94.45 [9242]P1(f317(f317(x92421,x92422),x92423))+P1(f317(f317(f225(a1),f751(x92421,x92423,x92422)),f752(x92421,x92423,x92422)))+P1(f317(f317(x92421,f751(x92421,x92423,x92422)),f317(f317(f74(a1),f752(x92421,x92423,x92422)),f72(a1))))+~P1(f317(f305(f903(a1,a1),a123),f317(f317(f242(a1,a1),x92422),x92423)))
% 94.68/94.45 [9259]P1(f317(f317(x92591,x92592),x92593))+~P1(f317(f317(f225(a1),f888(x92591,x92593,x92592)),f2(a1)))+P1(f317(f317(x92591,f317(f73(a1),f887(x92591,x92593,x92592))),f317(f73(a1),f888(x92591,x92593,x92592))))+~P1(f317(f305(f903(a1,a1),a211),f317(f317(f242(a1,a1),x92592),x92593)))
% 94.68/94.45 [9451]P1(f317(f317(x94511,x94512),x94513))+P1(f317(f317(x94511,f317(f317(f74(a1),f653(x94511,x94513,x94512)),f72(a1))),f655(x94511,x94513,x94512)))+~P1(f317(f317(f224(a1),f653(x94511,x94513,x94512)),f655(x94511,x94513,x94512)))+~P1(f317(f305(f903(a1,a1),a172),f317(f317(f242(a1,a1),x94512),x94513)))
% 94.68/94.45 [9893]~P60(x98932)+~P60(x98931)+~P1(f317(f51(f903(x98931,x98932)),x98933))+P1(f317(f51(x98931),f317(f317(f8(f904(x98932,a893),a893,x98931),f51(x98932)),f317(f317(f8(f904(x98932,f903(x98931,x98932)),f904(x98932,a893),x98931),f317(f8(f903(x98931,x98932),a893,x98932),x98933)),f242(x98931,x98932)))))
% 94.68/94.45 [9894]~P60(x98942)+~P60(x98941)+~P1(f317(f52(f903(x98941,x98942)),x98943))+P1(f317(f52(x98941),f317(f317(f8(f904(x98942,a893),a893,x98941),f52(x98942)),f317(f317(f8(f904(x98942,f903(x98941,x98942)),f904(x98942,a893),x98941),f317(f8(f903(x98941,x98942),a893,x98942),x98943)),f242(x98941,x98942)))))
% 94.68/94.45 [9988]~P60(x99882)+~P60(x99881)+P1(f317(f51(f903(x99881,x99882)),x99883))+~P1(f317(f51(x99881),f317(f317(f8(f904(x99882,a893),a893,x99881),f51(x99882)),f317(f317(f8(f904(x99882,f903(x99881,x99882)),f904(x99882,a893),x99881),f317(f8(f903(x99881,x99882),a893,x99882),x99883)),f242(x99881,x99882)))))
% 94.68/94.45 [9989]~P60(x99892)+~P60(x99891)+P1(f317(f52(f903(x99891,x99892)),x99893))+~P1(f317(f52(x99891),f317(f317(f8(f904(x99892,a893),a893,x99891),f52(x99892)),f317(f317(f8(f904(x99892,f903(x99891,x99892)),f904(x99892,a893),x99891),f317(f8(f903(x99891,x99892),a893,x99892),x99893)),f242(x99891,x99892)))))
% 94.68/94.45 [10162]E(f317(x101621,f466(x101622,x101621,x101623)),x101622)+~P1(f317(f317(f224(a1),x101622),f317(x101621,x101623)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x101621,f317(f317(f74(a897),f462(x101622,x101621,x101623)),f72(a897)))),f317(x101621,f462(x101622,x101621,x101623))))),f72(a1)))+~P1(f317(f317(f224(a1),f317(x101621,f2(a897))),x101622))
% 94.68/94.45 [10163]E(f317(x101631,f467(x101632,x101631,x101633)),x101632)+~P1(f317(f317(f224(a1),x101632),f317(x101631,x101633)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x101631,f317(f317(f74(a897),f468(x101632,x101631,x101633)),f72(a897)))),f317(x101631,f468(x101632,x101631,x101633))))),f72(a1)))+~P1(f317(f317(f224(a1),f317(x101631,f2(a897))),x101632))
% 94.68/94.45 [10166]~P1(f317(f317(f224(a1),x101661),f317(x101662,x101663)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x101662,f317(f317(f74(a897),f462(x101661,x101662,x101663)),f72(a897)))),f317(x101662,f462(x101661,x101662,x101663))))),f72(a1)))+P1(f317(f317(f224(a897),f466(x101661,x101662,x101663)),x101663))+~P1(f317(f317(f224(a1),f317(x101662,f2(a897))),x101661))
% 94.68/94.45 [10167]~P1(f317(f317(f224(a1),x101671),f317(x101672,x101673)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x101672,f317(f317(f74(a897),f468(x101671,x101672,x101673)),f72(a897)))),f317(x101672,f468(x101671,x101672,x101673))))),f72(a1)))+P1(f317(f317(f224(a897),f467(x101671,x101672,x101673)),x101673))+~P1(f317(f317(f224(a1),f317(x101672,f2(a897))),x101671))
% 94.68/94.45 [10224]E(x102241,x102242)+~E(f317(f132(f898(x102243),f898(x102243),f124(x102243),f103(x102243)),x102241),f317(f132(f898(x102243),f898(x102243),f124(x102243),f103(x102243)),x102242))+~E(f317(f179(f898(f898(x102243))),x102241),f317(f179(f898(f898(x102243))),x102242))+~P1(f317(f317(f247(f898(x102243),f898(x102243),a893),f317(f317(f7(f898(x102243),f904(f898(x102243),a897),f904(f898(x102243),a893)),f317(f317(f8(f904(a897,a893),f904(f904(f898(x102243),a897),f904(f898(x102243),a893)),f898(x102243)),f8(a897,a893,f898(x102243))),f317(f317(f8(a897,f904(a897,a893),f898(x102243)),a314),f179(f898(x102243))))),f179(f898(x102243)))),f681(x102242,x102241,x102243)))
% 94.68/94.45 [10225]E(x102251,x102252)+~E(f317(f132(f898(x102253),f898(x102253),f124(x102253),f103(x102253)),x102251),f317(f132(f898(x102253),f898(x102253),f124(x102253),f103(x102253)),x102252))+~E(f317(f179(f898(f898(x102253))),x102251),f317(f179(f898(f898(x102253))),x102252))+~P1(f317(f317(f247(f898(x102253),f898(x102253),a893),f317(f317(f7(f898(x102253),f904(f898(x102253),a897),f904(f898(x102253),a893)),f317(f317(f8(f904(a897,a893),f904(f904(f898(x102253),a897),f904(f898(x102253),a893)),f898(x102253)),f8(a897,a893,f898(x102253))),f317(f317(f8(a897,f904(a897,a893),f898(x102253)),a314),f179(f898(x102253))))),f179(f898(x102253)))),f682(x102251,x102252,x102253)))
% 94.68/94.45 [6921]~E(f72(a897),f2(a897))+~P1(f317(f28(x69211),x69213))+~P1(f317(f28(x69211),x69212))+E(f317(f317(f74(a897),f317(f29(x69211),x69212)),f317(f29(x69211),x69213)),f317(f29(x69211),f317(f317(f91(f904(x69211,a893)),x69212),x69213)))
% 94.68/94.45 [7339]~P66(x73391)+~P1(f317(f28(x73391),x73392))+~P1(f317(f317(f319(x73391),x73393),x73392))+P1(f317(f317(f224(x73391),f317(f57(x73391,f228(x73391)),x73392)),x73393))
% 94.68/94.45 [7340]~P105(x73401)+~P1(f317(f28(x73401),x73402))+~P1(f317(f317(f319(x73401),x73403),x73402))+P1(f317(f317(f224(x73401),f317(f57(x73401,f92(x73401)),x73402)),x73403))
% 94.68/94.45 [7592]~P1(f317(f28(x75921),x75923))+~P1(f317(f28(x75921),x75922))+~E(f317(f317(f92(f904(x75921,a893)),x75922),x75923),f178(f904(x75921,a893)))+E(f317(f317(f74(a897),f317(f29(x75921),x75922)),f317(f29(x75921),x75923)),f317(f29(x75921),f317(f317(f91(f904(x75921,a893)),x75922),x75923)))
% 94.68/94.45 [8382]~P36(x83821,x83823)+~P36(x83821,x83822)+~E(f317(f317(f92(f904(x83821,a893)),f317(f254(x83821,x83821),x83822)),f317(f274(x83821,x83821),x83823)),f178(f904(x83821,a893)))+P36(x83821,f317(f317(f91(f904(f903(x83821,x83821),a893)),x83822),x83823))
% 94.68/94.45 [8477]E(x84771,f317(f317(f30(a897),x84772),x84773))+~P1(f317(f317(f225(a897),f2(a897)),x84773))+~P1(f317(f317(f225(a897),x84772),f317(f317(f75(a897),x84773),f317(a102,x84771))))+~P1(f317(f317(f224(a897),f317(f317(f75(a897),x84773),x84771)),x84772))
% 94.68/94.45 [8609]~P1(f317(f28(x86091),x86092))+~P1(f317(f28(x86091),x86093))+E(f317(f317(f74(a897),f317(f29(x86091),x86092)),f317(f29(x86091),x86093)),f317(f29(x86091),f317(f317(f91(f904(x86091,a893)),x86092),x86093)))+P1(f317(f317(f319(x86091),f401(x86093,x86092,x86091)),f317(f317(f92(f904(x86091,a893)),x86092),x86093)))
% 94.68/94.45 [9002]~P125(x90022)+~E(x90021,f2(x90022))+~E(x90023,f2(x90022))+~P1(f317(f317(f225(x90022),f2(x90022)),f317(f317(f74(x90022),f317(f317(f75(x90022),x90023),x90023)),f317(f317(f75(x90022),x90021),x90021))))
% 94.68/94.45 [9532]~P36(x95321,x95323)+~P36(x95321,x95322)+P36(x95321,f317(f317(f91(f904(f903(x95321,x95321),a893)),x95322),x95323))+~P1(f317(f317(f224(f904(f903(x95321,x95321),a893)),f317(f317(f279(x95321,x95321,x95321),x95322),x95323)),x95322))
% 94.68/94.45 [9669]~P1(f317(x96691,x96693))+~P1(f317(f28(x96692),x96693))+P1(f317(x96691,f178(f904(x96692,a893))))+~P1(f317(x96691,f317(f317(f23(f904(x96692,a893)),f471(x96691,x96693,x96692)),f317(f317(f299(x96692),f460(x96691,x96693,x96692)),f178(f904(x96692,a893))))))
% 94.68/94.45 [8785]~P1(f317(f317(f225(a1),f2(a1)),x87853))+P1(f317(f317(f224(a1),f2(a1)),x87851))+~P1(f317(f317(f225(a1),x87852),x87853))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x87853),x87851)),x87852)))
% 94.68/94.45 [8809]~P66(x88091)+~P1(f317(f28(x88091),x88092))+E(f317(f317(f23(f904(x88091,a893)),x88092),f317(f317(f299(x88091),x88093),f178(f904(x88091,a893)))),f178(f904(x88091,a893)))+E(f317(f317(f228(x88091),x88093),f14(x88091,f317(f317(f23(f904(x88091,a893)),x88092),f317(f317(f299(x88091),x88093),f178(f904(x88091,a893)))))),f14(x88091,f317(f317(f299(x88091),x88093),x88092)))
% 94.68/94.45 [8810]~P66(x88101)+~P1(f317(f28(x88101),x88102))+E(f317(f317(f23(f904(x88101,a893)),x88102),f317(f317(f299(x88101),x88103),f178(f904(x88101,a893)))),f178(f904(x88101,a893)))+E(f317(f317(f223(x88101),x88103),f15(x88101,f317(f317(f23(f904(x88101,a893)),x88102),f317(f317(f299(x88101),x88103),f178(f904(x88101,a893)))))),f15(x88101,f317(f317(f299(x88101),x88103),x88102)))
% 94.68/94.45 [8811]~P100(x88111)+~P1(f317(f28(x88111),x88112))+E(f317(f317(f23(f904(x88111,a893)),x88112),f317(f317(f299(x88111),x88113),f178(f904(x88111,a893)))),f178(f904(x88111,a893)))+E(f317(f317(f91(x88111),x88113),f13(x88111,f317(f317(f23(f904(x88111,a893)),x88112),f317(f317(f299(x88111),x88113),f178(f904(x88111,a893)))))),f13(x88111,f317(f317(f299(x88111),x88113),x88112)))
% 94.68/94.45 [8812]~P100(x88121)+~P1(f317(f28(x88121),x88122))+E(f317(f317(f23(f904(x88121,a893)),x88122),f317(f317(f299(x88121),x88123),f178(f904(x88121,a893)))),f178(f904(x88121,a893)))+E(f317(f317(f92(x88121),x88123),f10(x88121,f317(f317(f23(f904(x88121,a893)),x88122),f317(f317(f299(x88121),x88123),f178(f904(x88121,a893)))))),f10(x88121,f317(f317(f299(x88121),x88123),x88122)))
% 94.68/94.45 [8884]~P66(x88841)+~P1(f317(f28(x88841),x88842))+E(f317(f317(f23(f904(x88841,a893)),x88842),f317(f317(f299(x88841),x88843),f178(f904(x88841,a893)))),f178(f904(x88841,a893)))+E(f317(f317(f228(x88841),x88843),f11(x88841,f228(x88841),f317(f317(f23(f904(x88841,a893)),x88842),f317(f317(f299(x88841),x88843),f178(f904(x88841,a893)))))),f11(x88841,f228(x88841),f317(f317(f299(x88841),x88843),x88842)))
% 94.68/94.45 [8885]~P66(x88851)+~P1(f317(f28(x88851),x88852))+E(f317(f317(f23(f904(x88851,a893)),x88852),f317(f317(f299(x88851),x88853),f178(f904(x88851,a893)))),f178(f904(x88851,a893)))+E(f317(f317(f223(x88851),x88853),f12(x88851,f223(x88851),f317(f317(f23(f904(x88851,a893)),x88852),f317(f317(f299(x88851),x88853),f178(f904(x88851,a893)))))),f12(x88851,f223(x88851),f317(f317(f299(x88851),x88853),x88852)))
% 94.68/94.45 [9470]E(x94701,x94702)+~E(f317(f132(f898(x94703),f898(x94703),f124(x94703),f103(x94703)),x94701),f317(f132(f898(x94703),f898(x94703),f124(x94703),f103(x94703)),x94702))+~E(f317(f179(f898(f898(x94703))),x94701),f317(f179(f898(f898(x94703))),x94702))+P1(f317(f317(f319(f903(f898(x94703),f898(x94703))),f681(x94702,x94701,x94703)),f317(f162(f903(f898(x94703),f898(x94703))),f317(f317(f171(f898(x94703),f898(x94703)),x94701),x94702))))
% 94.68/94.45 [9471]E(x94711,x94712)+~E(f317(f132(f898(x94713),f898(x94713),f124(x94713),f103(x94713)),x94711),f317(f132(f898(x94713),f898(x94713),f124(x94713),f103(x94713)),x94712))+~E(f317(f179(f898(f898(x94713))),x94711),f317(f179(f898(f898(x94713))),x94712))+P1(f317(f317(f319(f903(f898(x94713),f898(x94713))),f682(x94711,x94712,x94713)),f317(f162(f903(f898(x94713),f898(x94713))),f317(f317(f171(f898(x94713),f898(x94713)),x94712),x94711))))
% 94.68/94.45 [10333]~P79(x103332)+E(x103331,f178(f904(x103332,a893)))+~P1(f317(f28(x103332),x103331))+E(f14(x103332,f317(f252(x103332),f317(f317(f8(f904(x103332,a893),a893,x103332),f81(x103332)),f317(f317(f7(x103332,f904(x103332,a893),f904(x103332,a893)),f317(f317(f8(f904(x103332,f904(a893,a893)),f904(f904(x103332,a893),f904(x103332,a893)),x103332),f18(x103332,a893,a893)),f317(f317(f8(f904(x103332,a893),f904(x103332,f904(a893,a893)),x103332),f317(f8(a893,f904(a893,a893),x103332),a315)),f317(f317(f7(x103332,f904(x103332,x103332),f904(x103332,a893)),f317(f317(f8(f904(x103332,a893),f904(f904(x103332,x103332),f904(x103332,a893)),x103332),f8(x103332,a893,x103332)),a314)),f317(f74(x103332),x103333))))),f317(f317(f7(x103332,f904(x103332,a893),a893),f319(x103332)),x103331))))),f317(f317(f74(x103332),x103333),f14(x103332,x103331)))
% 94.68/94.45 [10334]~P79(x103342)+E(x103341,f178(f904(x103342,a893)))+~P1(f317(f28(x103342),x103341))+E(f15(x103342,f317(f252(x103342),f317(f317(f8(f904(x103342,a893),a893,x103342),f81(x103342)),f317(f317(f7(x103342,f904(x103342,a893),f904(x103342,a893)),f317(f317(f8(f904(x103342,f904(a893,a893)),f904(f904(x103342,a893),f904(x103342,a893)),x103342),f18(x103342,a893,a893)),f317(f317(f8(f904(x103342,a893),f904(x103342,f904(a893,a893)),x103342),f317(f8(a893,f904(a893,a893),x103342),a315)),f317(f317(f7(x103342,f904(x103342,x103342),f904(x103342,a893)),f317(f317(f8(f904(x103342,a893),f904(f904(x103342,x103342),f904(x103342,a893)),x103342),f8(x103342,a893,x103342)),a314)),f317(f74(x103342),x103343))))),f317(f317(f7(x103342,f904(x103342,a893),a893),f319(x103342)),x103341))))),f317(f317(f74(x103342),x103343),f15(x103342,x103341)))
% 94.68/94.45 [10335]~P103(x103352)+E(x103351,f178(f904(x103352,a893)))+~P1(f317(f28(x103352),x103351))+E(f10(x103352,f317(f252(x103352),f317(f317(f8(f904(x103352,a893),a893,x103352),f81(x103352)),f317(f317(f7(x103352,f904(x103352,a893),f904(x103352,a893)),f317(f317(f8(f904(x103352,f904(a893,a893)),f904(f904(x103352,a893),f904(x103352,a893)),x103352),f18(x103352,a893,a893)),f317(f317(f8(f904(x103352,a893),f904(x103352,f904(a893,a893)),x103352),f317(f8(a893,f904(a893,a893),x103352),a315)),f317(f317(f7(x103352,f904(x103352,x103352),f904(x103352,a893)),f317(f317(f8(f904(x103352,a893),f904(f904(x103352,x103352),f904(x103352,a893)),x103352),f8(x103352,a893,x103352)),a314)),f317(f91(x103352),x103353))))),f317(f317(f7(x103352,f904(x103352,a893),a893),f319(x103352)),x103351))))),f317(f317(f91(x103352),x103353),f10(x103352,x103351)))
% 94.68/94.45 [10336]~P103(x103362)+E(x103361,f178(f904(x103362,a893)))+~P1(f317(f28(x103362),x103361))+E(f13(x103362,f317(f252(x103362),f317(f317(f8(f904(x103362,a893),a893,x103362),f81(x103362)),f317(f317(f7(x103362,f904(x103362,a893),f904(x103362,a893)),f317(f317(f8(f904(x103362,f904(a893,a893)),f904(f904(x103362,a893),f904(x103362,a893)),x103362),f18(x103362,a893,a893)),f317(f317(f8(f904(x103362,a893),f904(x103362,f904(a893,a893)),x103362),f317(f8(a893,f904(a893,a893),x103362),a315)),f317(f317(f7(x103362,f904(x103362,x103362),f904(x103362,a893)),f317(f317(f8(f904(x103362,a893),f904(f904(x103362,x103362),f904(x103362,a893)),x103362),f8(x103362,a893,x103362)),a314)),f317(f92(x103362),x103363))))),f317(f317(f7(x103362,f904(x103362,a893),a893),f319(x103362)),x103361))))),f317(f317(f92(x103362),x103363),f13(x103362,x103361)))
% 94.68/94.45 [10337]~P66(x103372)+E(x103371,f178(f904(x103372,a893)))+~P1(f317(f28(x103372),x103371))+E(f12(x103372,f223(x103372),f317(f252(x103372),f317(f317(f8(f904(x103372,a893),a893,x103372),f81(x103372)),f317(f317(f7(x103372,f904(x103372,a893),f904(x103372,a893)),f317(f317(f8(f904(x103372,f904(a893,a893)),f904(f904(x103372,a893),f904(x103372,a893)),x103372),f18(x103372,a893,a893)),f317(f317(f8(f904(x103372,a893),f904(x103372,f904(a893,a893)),x103372),f317(f8(a893,f904(a893,a893),x103372),a315)),f317(f317(f7(x103372,f904(x103372,x103372),f904(x103372,a893)),f317(f317(f8(f904(x103372,a893),f904(f904(x103372,x103372),f904(x103372,a893)),x103372),f8(x103372,a893,x103372)),a314)),f317(f228(x103372),x103373))))),f317(f317(f7(x103372,f904(x103372,a893),a893),f319(x103372)),x103371))))),f317(f317(f228(x103372),x103373),f12(x103372,f223(x103372),x103371)))
% 94.68/94.45 [10338]~P66(x103382)+E(x103381,f178(f904(x103382,a893)))+~P1(f317(f28(x103382),x103381))+E(f11(x103382,f228(x103382),f317(f252(x103382),f317(f317(f8(f904(x103382,a893),a893,x103382),f81(x103382)),f317(f317(f7(x103382,f904(x103382,a893),f904(x103382,a893)),f317(f317(f8(f904(x103382,f904(a893,a893)),f904(f904(x103382,a893),f904(x103382,a893)),x103382),f18(x103382,a893,a893)),f317(f317(f8(f904(x103382,a893),f904(x103382,f904(a893,a893)),x103382),f317(f8(a893,f904(a893,a893),x103382),a315)),f317(f317(f7(x103382,f904(x103382,x103382),f904(x103382,a893)),f317(f317(f8(f904(x103382,a893),f904(f904(x103382,x103382),f904(x103382,a893)),x103382),f8(x103382,a893,x103382)),a314)),f317(f223(x103382),x103383))))),f317(f317(f7(x103382,f904(x103382,a893),a893),f319(x103382)),x103381))))),f317(f317(f223(x103382),x103383),f11(x103382,f228(x103382),x103381)))
% 94.68/94.45 [10052]~P111(x100521)+~E(x100523,f2(x100521))+~E(x100522,f2(x100521))+E(f317(f317(f74(x100521),f317(f317(f234(x100521),x100522),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x100521),x100523),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f2(x100521))
% 94.68/94.45 [10205]~P110(x102051)+~P1(f317(f317(f224(x102051),f2(x102051)),x102053))+P1(f317(f317(f224(x102051),x102052),x102053))+~P1(f317(f317(f224(x102051),f317(f317(f234(x102051),x102052),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102051),x102053),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))))
% 94.68/94.45 [10262]~P111(x102622)+~E(x102621,f2(x102622))+~E(x102623,f2(x102622))+~P1(f317(f317(f225(x102622),f2(x102622)),f317(f317(f74(x102622),f317(f317(f234(x102622),x102623),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87))))),f317(f317(f234(x102622),x102621),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))))
% 94.68/94.45 [6799]~P7(x67993,x67992)+~P1(f317(x67991,x67994))+~P1(f317(f317(f319(x67993),x67994),f260(x67993,x67992)))+P1(f317(x67991,f799(x67991,x67992,x67993)))
% 94.68/94.45 [8720]P25(x87201,x87202,f803(x87203,x87202,x87204,x87201),x87204,x87203)+~E(f317(f29(x87201),x87204),f317(f29(x87202),x87203))+~P1(f317(f28(x87202),x87203))+~P1(f317(f28(x87201),x87204))
% 94.68/94.45 [9433]E(x94331,x94332)+~E(f628(x94331,x94332,x94334,x94333),f630(x94331,x94332,x94334,x94333))+P1(f317(f317(f319(f903(f898(x94333),f898(x94333))),f317(f317(f242(f898(x94333),f898(x94333)),x94332),x94331)),f137(x94333,x94334)))+P1(f317(f317(f319(f903(f898(x94333),f898(x94333))),f317(f317(f242(f898(x94333),f898(x94333)),x94331),x94332)),f137(x94333,x94334)))
% 94.68/94.45 [4912]~P61(x49122)+~E(x49124,f2(x49122))+~E(x49121,f2(x49122))+E(x49121,f317(f317(f281(x49122),x49123),x49124))
% 94.68/94.45 [4913]~P61(x49131)+~E(x49133,f2(x49131))+~E(x49134,f2(x49131))+E(f317(f317(f281(x49131),x49132),x49133),x49134)
% 94.68/94.45 [5033]~P61(x50332)+E(x50331,f2(x50332))+~E(x50333,f2(x50332))+~E(x50331,f317(f317(f281(x50332),x50334),x50333))
% 94.68/94.45 [5034]~P61(x50342)+E(x50341,f2(x50342))+~E(x50343,f2(x50342))+~E(f317(f317(f281(x50342),x50344),x50343),x50341)
% 94.68/94.45 [5217]~P122(x52172)+E(x52171,f2(x52172))+~E(f317(f317(f281(x52172),x52173),x52171),x52174)+E(x52173,f317(f317(f75(x52172),x52174),x52171))
% 94.68/94.45 [5219]~P122(x52192)+E(x52191,f2(x52192))+~E(f317(f317(f75(x52192),x52193),x52191),x52194)+E(x52193,f317(f317(f281(x52192),x52194),x52191))
% 94.68/94.45 [5220]~P61(x52202)+E(x52201,f2(x52202))+~E(f317(f317(f281(x52202),x52203),x52201),x52204)+E(x52203,f317(f317(f75(x52202),x52204),x52201))
% 94.68/94.45 [5221]~P61(x52212)+E(x52211,f2(x52212))+~E(f317(f317(f75(x52212),x52213),x52211),x52214)+E(x52213,f317(f317(f281(x52212),x52214),x52211))
% 94.68/94.45 [5222]~P122(x52222)+E(x52221,f2(x52222))+~E(x52223,f317(f317(f281(x52222),x52224),x52221))+E(f317(f317(f75(x52222),x52223),x52221),x52224)
% 94.68/94.45 [5224]~P122(x52242)+E(x52241,f2(x52242))+~E(x52243,f317(f317(f75(x52242),x52244),x52241))+E(f317(f317(f281(x52242),x52243),x52241),x52244)
% 94.68/94.45 [5225]~P61(x52252)+E(x52251,f2(x52252))+~E(x52253,f317(f317(f281(x52252),x52254),x52251))+E(f317(f317(f75(x52252),x52253),x52251),x52254)
% 94.68/94.45 [5226]~P61(x52262)+E(x52261,f2(x52262))+~E(x52263,f317(f317(f75(x52262),x52264),x52261))+E(f317(f317(f281(x52262),x52263),x52261),x52264)
% 94.68/94.45 [5250]~P61(x52502)+~E(x52501,f2(x52502))+~E(f317(f317(f75(x52502),x52501),x52504),x52503)+E(x52501,f317(f317(f281(x52502),x52503),x52504))
% 94.68/94.45 [5251]~P61(x52511)+~E(x52514,f2(x52511))+~E(x52512,f317(f317(f75(x52511),x52514),x52513))+E(f317(f317(f281(x52511),x52512),x52513),x52514)
% 94.68/94.45 [5325]~E(x53253,x53254)+~E(x53252,x53253)+~P108(x53251)+E(f293(x53251,x53252,x53253),f317(f317(f299(x53251),x53254),f178(f904(x53251,a893))))
% 94.68/94.45 [5529]~E(f104(x55292,x55291),x55293)+~E(f134(x55292,x55291),x55294)+E(x55291,f103(x55292))+E(f317(f317(f124(x55292),x55293),f317(f317(f141(x55292),x55294),f103(x55292))),x55291)
% 94.68/94.45 [6172]~P110(x61723)+E(x61721,x61722)+~E(f317(f317(f234(x61723),x61724),x61721),f317(f317(f234(x61723),x61724),x61722))+~P1(f317(f317(f225(x61723),f72(x61723)),x61724))
% 94.68/94.45 [6173]E(x61731,x61732)+~E(f317(f317(f299(x61733),x61734),x61731),f317(f317(f299(x61733),x61734),x61732))+P1(f317(f317(f319(x61733),x61734),x61732))+P1(f317(f317(f319(x61733),x61734),x61731))
% 94.68/94.45 [6216]E(f317(x62161,x62162),f72(a897))+~E(f317(f317(f9(x62163,a897),x62161),x62164),f72(a897))+~P1(f317(f28(x62163),x62164))+~P1(f317(f317(f319(x62163),x62162),x62164))
% 94.68/94.45 [6217]E(f317(x62171,x62172),f2(a897))+~E(f317(f317(f6(x62173,a897),x62171),x62174),f2(a897))+~P1(f317(f28(x62173),x62174))+~P1(f317(f317(f319(x62173),x62172),x62174))
% 94.68/94.45 [6445]~P108(x64451)+~P1(f317(f317(f224(x64451),x64454),x64453))+P1(f317(f317(f224(x64451),x64452),x64453))+~P1(f317(f317(f224(x64451),x64452),x64454))
% 94.68/94.45 [6446]~P65(x64461)+~P1(f317(f317(f224(x64461),x64462),x64464))+P1(f317(f317(f224(x64461),x64462),x64463))+~P1(f317(f317(f224(x64461),x64464),x64463))
% 94.68/94.45 [6447]~P108(x64471)+~P1(f317(f317(f225(x64471),x64474),x64473))+P1(f317(f317(f225(x64471),x64472),x64473))+~P1(f317(f317(f224(x64471),x64472),x64474))
% 94.68/94.45 [6448]~P108(x64481)+~P1(f317(f317(f225(x64481),x64482),x64484))+P1(f317(f317(f225(x64481),x64482),x64483))+~P1(f317(f317(f224(x64481),x64484),x64483))
% 94.68/94.45 [6449]~P108(x64491)+~P1(f317(f317(f225(x64491),x64494),x64493))+P1(f317(f317(f225(x64491),x64492),x64493))+~P1(f317(f317(f225(x64491),x64492),x64494))
% 94.68/94.45 [6450]~P65(x64501)+~P1(f317(f317(f225(x64501),x64502),x64504))+P1(f317(f317(f225(x64501),x64502),x64503))+~P1(f317(f317(f224(x64501),x64504),x64503))
% 94.68/94.45 [6451]~P65(x64511)+~P1(f317(f317(f225(x64511),x64514),x64513))+P1(f317(f317(f225(x64511),x64512),x64513))+~P1(f317(f317(f224(x64511),x64512),x64514))
% 94.68/94.45 [6452]~P65(x64521)+~P1(f317(f317(f225(x64521),x64522),x64524))+P1(f317(f317(f225(x64521),x64522),x64523))+~P1(f317(f317(f225(x64521),x64524),x64523))
% 94.68/94.45 [6453]~P112(x64531)+~P1(f317(f317(f277(x64531),x64532),x64534))+P1(f317(f317(f277(x64531),x64532),x64533))+~P1(f317(f317(f277(x64531),x64534),x64533))
% 94.68/94.45 [6535]~P34(x65354,x65353,x65352)+E(x65351,f735(x65352,x65353,x65354))+~P1(f317(x65353,x65351))+~P1(f317(f317(f319(x65354),x65351),f317(f162(x65354),x65352)))
% 94.68/94.45 [6536]~P34(x65364,x65363,x65362)+E(x65361,f747(x65362,x65363,x65364))+~P1(f317(x65363,x65361))+~P1(f317(f317(f319(x65364),x65361),f317(f162(x65364),x65362)))
% 94.68/94.45 [6690]~P5(x66901)+~P1(f317(f317(f224(x66901),x66902),f32(x66901,x66904)))+P1(f317(f317(f224(x66901),x66902),x66903))+~P1(f317(f317(f319(x66901),x66903),x66904))
% 94.68/94.45 [6841]~P66(x68411)+~P13(x68411,f317(f317(f141(x68411),x68412),x68414))+~P1(f317(f317(f319(x68411),x68413),f317(f162(x68411),x68414)))+P1(f317(f317(f224(x68411),x68412),x68413))
% 94.68/94.45 [6931]~P5(x69311)+~P1(f317(f317(f224(x69311),f31(x69311,x69314)),x69313))+P1(f317(f317(f224(x69311),x69312),x69313))+~P1(f317(f317(f319(x69311),x69312),x69314))
% 94.68/94.45 [7078]~P3(x70781)+P1(f317(f317(f277(x70781),x70782),f40(x70781,x70783,x70784)))+~P1(f317(f317(f277(x70781),x70782),x70784))+~P1(f317(f317(f277(x70781),x70782),x70783))
% 94.68/94.45 [7342]~P66(x73421)+E(f317(f317(f91(f904(x73421,a893)),f317(f292(x73421,x73422),x73423)),f317(f292(x73421,x73423),x73424)),f317(f292(x73421,x73422),x73424))+~P1(f317(f317(f224(x73421),x73423),x73424))+~P1(f317(f317(f224(x73421),x73422),x73423))
% 94.68/94.45 [7386]P34(x73861,x73862,x73863)+~E(f745(x73863,x73862,x73861,x73864),x73864)+~P1(f317(x73862,x73864))+~P1(f317(f317(f319(x73861),x73864),f317(f162(x73861),x73863)))
% 94.68/94.45 [7387]P34(x73871,x73872,x73873)+~E(f754(x73873,x73872,x73871,x73874),x73874)+~P1(f317(x73872,x73874))+~P1(f317(f317(f319(x73871),x73874),f317(f162(x73871),x73873)))
% 94.68/94.45 [7430]~P3(x74301)+~P1(f317(f317(f277(x74301),x74302),f40(x74301,x74303,x74304)))+P1(f317(f317(f277(x74301),x74302),x74303))+~P1(f317(f317(f277(x74301),x74302),x74304))
% 94.68/94.45 [7464]~P66(x74641)+E(f317(f317(f91(f904(x74641,a893)),f317(f292(x74641,x74642),x74643)),f293(x74641,x74643,x74644)),f293(x74641,x74642,x74644))+~P1(f317(f317(f224(x74641),x74643),x74644))+~P1(f317(f317(f224(x74641),x74642),x74643))
% 94.68/94.45 [7526]~P66(x75261)+E(f317(f317(f91(f904(x75261,a893)),f296(x75261,x75262,x75263)),f317(f292(x75261,x75263),x75264)),f296(x75261,x75262,x75264))+~P1(f317(f317(f224(x75261),x75263),x75264))+~P1(f317(f317(f225(x75261),x75262),x75263))
% 94.68/94.45 [7543]~P66(x75431)+E(f317(f317(f91(f904(x75431,a893)),f293(x75431,x75432,x75433)),f296(x75431,x75433,x75434)),f317(f292(x75431,x75432),x75434))+~P1(f317(f317(f224(x75431),x75432),x75433))+~P1(f317(f317(f225(x75431),x75433),x75434))
% 94.68/94.45 [7573]~P66(x75731)+E(f317(f317(f91(f904(x75731,a893)),f296(x75731,x75732,x75733)),f293(x75731,x75733,x75734)),f295(x75731,x75732,x75734))+~P1(f317(f317(f224(x75731),x75733),x75734))+~P1(f317(f317(f225(x75731),x75732),x75733))
% 94.68/94.45 [7574]~P66(x75741)+E(f317(f317(f91(f904(x75741,a893)),f295(x75741,x75742,x75743)),f296(x75741,x75743,x75744)),f296(x75741,x75742,x75744))+~P1(f317(f317(f224(x75741),x75742),x75743))+~P1(f317(f317(f225(x75741),x75743),x75744))
% 94.68/94.45 [7575]~P66(x75751)+E(f317(f317(f91(f904(x75751,a893)),f295(x75751,x75752,x75753)),f295(x75751,x75753,x75754)),f295(x75751,x75752,x75754))+~P1(f317(f317(f224(x75751),x75753),x75754))+~P1(f317(f317(f224(x75751),x75752),x75753))
% 94.68/94.45 [7576]~P66(x75761)+E(f317(f317(f91(f904(x75761,a893)),f293(x75761,x75762,x75763)),f295(x75761,x75763,x75764)),f293(x75761,x75762,x75764))+~P1(f317(f317(f224(x75761),x75763),x75764))+~P1(f317(f317(f224(x75761),x75762),x75763))
% 94.68/94.45 [8366]P24(x83661,x83662,f327(x83663,x83662,x83664,x83661),x83664)+~P1(f317(f28(x83662),x83663))+~P1(f317(f28(x83661),x83664))+~P1(f317(f317(f224(a897),f317(f29(x83661),x83664)),f317(f29(x83662),x83663)))
% 94.68/94.45 [8387]P34(x83871,x83872,x83873)+~P1(f317(x83872,x83874))+P1(f317(x83872,f745(x83873,x83872,x83871,x83874)))+~P1(f317(f317(f319(x83871),x83874),f317(f162(x83871),x83873)))
% 94.68/94.45 [8388]P34(x83881,x83882,x83883)+~P1(f317(x83882,x83884))+P1(f317(x83882,f754(x83883,x83882,x83881,x83884)))+~P1(f317(f317(f319(x83881),x83884),f317(f162(x83881),x83883)))
% 94.68/94.45 [8442]~P77(x84421)+~E(f317(x84423,f775(x84423,x84424,x84422,x84421)),f72(x84421))+E(f317(f317(f317(f59(x84421,x84422,f75(x84421)),x84423),f72(x84421)),x84424),f72(x84421))+~P1(f317(f28(x84422),x84424))
% 94.68/94.45 [8709]~P110(x87091)+~P1(f317(f317(f224(x87091),f2(x87091)),x87093))+P1(f317(f317(f224(x87091),x87092),x87093))+~P1(f317(f317(f224(x87091),f317(f317(f234(x87091),x87092),f317(a102,x87094))),f317(f317(f234(x87091),x87093),f317(a102,x87094))))
% 94.68/94.45 [9027]P34(x90271,x90272,x90273)+~P1(f317(x90272,x90274))+~P1(f317(f317(f319(x90271),x90274),f317(f162(x90271),x90273)))+P1(f317(f317(f319(x90271),f745(x90273,x90272,x90271,x90274)),f317(f162(x90271),x90273)))
% 94.68/94.45 [9028]P34(x90281,x90282,x90283)+~P1(f317(x90282,x90284))+~P1(f317(f317(f319(x90281),x90284),f317(f162(x90281),x90283)))+P1(f317(f317(f319(x90281),f754(x90283,x90282,x90281,x90284)),f317(f162(x90281),x90283)))
% 94.68/94.45 [9104]~P77(x91041)+E(f317(f317(f317(f59(x91041,x91042,f75(x91041)),x91043),f72(x91041)),x91044),f72(x91041))+~P1(f317(f28(x91042),x91044))+P1(f317(f317(f319(x91042),f775(x91043,x91044,x91042,x91041)),x91044))
% 94.68/94.45 [9368]~P8(x93682,x93683,x93684)+~P1(f317(f28(x93682),x93683))+~P1(f317(f317(f277(a897),x93681),f317(f29(x93682),f839(x93681,x93684,x93683,x93682))))+P1(f317(f317(f277(a897),x93681),f317(f29(x93682),x93683)))
% 94.68/94.45 [9607]~P1(f317(f317(f277(a897),x96071),x96073))+~P1(f317(f317(f277(a897),x96071),x96072))+~P1(f317(f317(f277(a897),x96074),x96073))+~P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x96071,x96073)),f280(a897,f277(a897),x96072,x96074)))
% 94.68/94.45 [9612]~P1(f317(f317(f224(a1),x96124),f2(a1)))+P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x96121),f40(a1,x96122,x96123))),x96124)),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x96123))+~P1(f317(f317(f225(a1),x96121),x96124))
% 94.68/94.45 [10045]~P1(f317(f28(x100451),x100452))+~P1(f317(f317(f319(x100451),x100454),x100452))+~P1(f317(f317(f319(x100451),x100453),x100452))+P1(f317(f317(f225(a897),f317(f29(x100451),f317(f317(f23(f904(x100451,a893)),f317(f317(f23(f904(x100451,a893)),x100452),f317(f317(f299(x100451),x100453),f178(f904(x100451,a893))))),f317(f317(f299(x100451),x100454),f178(f904(x100451,a893)))))),f317(f29(x100451),x100452)))
% 94.68/94.45 [6989]~P145(x69893)+~P121(x69893)+P1(f317(x69891,f835(x69892,x69891,x69893)))+~P1(f317(x69891,f317(f317(f75(x69893),x69892),x69894)))
% 94.68/94.45 [7050]~P66(x70501)+~P1(f317(f317(f224(x70501),x70502),x70504))+~P1(f317(f317(f224(x70501),x70502),x70503))+P1(f317(f317(f224(x70501),x70502),f317(f317(f228(x70501),x70503),x70504)))
% 94.68/94.45 [7053]~P105(x70531)+~P1(f317(f317(f224(x70531),x70532),x70534))+~P1(f317(f317(f224(x70531),x70532),x70533))+P1(f317(f317(f224(x70531),x70532),f317(f317(f92(x70531),x70533),x70534)))
% 94.68/94.45 [7054]~P66(x70541)+~P1(f317(f317(f225(x70541),x70542),x70544))+~P1(f317(f317(f225(x70541),x70542),x70543))+P1(f317(f317(f225(x70541),x70542),f317(f317(f228(x70541),x70543),x70544)))
% 94.68/94.45 [7055]~P114(x70551)+~P1(f317(f317(f277(x70551),x70552),x70554))+~P1(f317(f317(f277(x70551),x70552),x70553))+P1(f317(f317(f277(x70551),x70552),f317(f317(f23(x70551),x70553),x70554)))
% 94.68/94.45 [7056]~P112(x70561)+~P1(f317(f317(f277(x70561),x70562),x70564))+~P1(f317(f317(f277(x70561),x70562),x70563))+P1(f317(f317(f277(x70561),x70562),f317(f317(f74(x70561),x70563),x70564)))
% 94.68/94.45 [7076]~P62(x70762)+E(x70761,f2(x70762))+E(f317(f317(f281(x70762),f317(f317(f234(x70762),x70761),x70763)),f317(f317(f234(x70762),x70761),x70764)),f317(f317(f234(x70762),x70761),f317(f317(f23(a897),x70763),x70764)))+~P1(f317(f317(f224(a897),x70764),x70763))
% 94.68/94.45 [7122]~P66(x71221)+~P13(x71221,f317(f317(f141(x71221),x71223),x71224))+P13(x71221,f317(f317(f141(x71221),x71222),f317(f317(f141(x71221),x71223),x71224)))+~P1(f317(f317(f224(x71221),x71222),x71223))
% 94.68/94.45 [7158]~P89(x71581)+~P1(f317(f317(f224(x71581),f2(x71581)),x71584))+~P1(f317(f317(f224(x71581),x71582),x71583))+P1(f317(f317(f224(x71581),x71582),f317(f317(f74(x71581),x71583),x71584)))
% 94.68/94.45 [7159]~P89(x71591)+~P1(f317(f317(f224(x71591),f2(x71591)),x71593))+~P1(f317(f317(f224(x71591),x71592),x71594))+P1(f317(f317(f224(x71591),x71592),f317(f317(f74(x71591),x71593),x71594)))
% 94.68/94.45 [7160]~P110(x71601)+~P1(f317(f317(f225(x71601),f2(x71601)),x71603))+~P1(f317(f317(f225(x71601),x71602),x71604))+P1(f317(f317(f225(x71601),x71602),f317(f317(f74(x71601),x71603),x71604)))
% 94.68/94.45 [7161]~P89(x71611)+~P1(f317(f317(f224(x71611),x71612),x71614))+~P1(f317(f317(f225(x71611),f2(x71611)),x71613))+P1(f317(f317(f225(x71611),x71612),f317(f317(f74(x71611),x71613),x71614)))
% 94.68/94.45 [7162]~P89(x71621)+~P1(f317(f317(f224(x71621),f2(x71621)),x71623))+~P1(f317(f317(f225(x71621),x71622),x71624))+P1(f317(f317(f225(x71621),x71622),f317(f317(f74(x71621),x71623),x71624)))
% 94.68/94.45 [7203]~P66(x72031)+P1(f317(f317(f224(x72031),x72032),x72033))+P1(f317(f317(f224(x72031),x72032),x72034))+~P1(f317(f317(f224(x72031),x72032),f317(f317(f223(x72031),x72034),x72033)))
% 94.68/94.45 [7204]~P66(x72041)+P1(f317(f317(f225(x72041),x72042),x72043))+P1(f317(f317(f225(x72041),x72042),x72044))+~P1(f317(f317(f225(x72041),x72042),f317(f317(f223(x72041),x72044),x72043)))
% 94.68/94.45 [7498]~P108(x74982)+~P60(x74981)+~P1(f317(f317(f225(f904(x74981,x74982)),x74983),x74984))+P1(f317(f317(f224(f904(x74981,x74982)),x74983),x74984))
% 94.68/94.45 [7864]~P64(x78641)+~P1(f317(f317(f225(x78641),x78644),f2(x78641)))+~P1(f317(f317(f224(x78641),x78643),f317(f317(f281(x78641),x78642),x78644)))+P1(f317(f317(f224(x78641),x78642),f317(f317(f75(x78641),x78643),x78644)))
% 94.68/94.45 [7865]~P64(x78651)+~P1(f317(f317(f225(x78651),x78654),f2(x78651)))+~P1(f317(f317(f224(x78651),x78653),f317(f317(f75(x78651),x78652),x78654)))+P1(f317(f317(f224(x78651),x78652),f317(f317(f281(x78651),x78653),x78654)))
% 94.68/94.45 [7866]~P64(x78661)+~P1(f317(f317(f225(x78661),x78664),f2(x78661)))+~P1(f317(f317(f225(x78661),x78663),f317(f317(f281(x78661),x78662),x78664)))+P1(f317(f317(f225(x78661),x78662),f317(f317(f75(x78661),x78663),x78664)))
% 94.68/94.45 [7867]~P64(x78671)+~P1(f317(f317(f225(x78671),x78674),f2(x78671)))+~P1(f317(f317(f225(x78671),x78673),f317(f317(f75(x78671),x78672),x78674)))+P1(f317(f317(f225(x78671),x78672),f317(f317(f281(x78671),x78673),x78674)))
% 94.68/94.45 [7974]~P136(x79741)+~P1(f317(f317(f224(x79741),x79742),f2(x79741)))+~P1(f317(f317(f224(x79741),x79744),x79743))+P1(f317(f317(f224(x79741),f317(f317(f75(x79741),x79742),x79743)),f317(f317(f75(x79741),x79742),x79744)))
% 94.68/94.45 [7975]~P125(x79751)+~P1(f317(f317(f225(x79751),x79752),f2(x79751)))+~P1(f317(f317(f224(x79751),x79754),x79753))+P1(f317(f317(f224(x79751),f317(f317(f75(x79751),x79752),x79753)),f317(f317(f75(x79751),x79752),x79754)))
% 94.68/94.45 [7976]~P136(x79761)+~P1(f317(f317(f224(x79761),x79763),f2(x79761)))+~P1(f317(f317(f224(x79761),x79764),x79762))+P1(f317(f317(f224(x79761),f317(f317(f75(x79761),x79762),x79763)),f317(f317(f75(x79761),x79764),x79763)))
% 94.68/94.45 [7977]~P63(x79771)+~P1(f317(f317(f224(x79771),x79773),f2(x79771)))+~P1(f317(f317(f224(x79771),x79774),x79772))+P1(f317(f317(f224(x79771),f317(f317(f281(x79771),x79772),x79773)),f317(f317(f281(x79771),x79774),x79773)))
% 94.68/94.45 [7981]~P125(x79811)+~P1(f317(f317(f225(x79811),x79813),f2(x79811)))+~P1(f317(f317(f225(x79811),x79814),x79812))+P1(f317(f317(f225(x79811),f317(f317(f75(x79811),x79812),x79813)),f317(f317(f75(x79811),x79814),x79813)))
% 94.68/94.45 [7982]~P125(x79821)+~P1(f317(f317(f225(x79821),x79822),f2(x79821)))+~P1(f317(f317(f225(x79821),x79824),x79823))+P1(f317(f317(f225(x79821),f317(f317(f75(x79821),x79822),x79823)),f317(f317(f75(x79821),x79822),x79824)))
% 94.68/94.45 [7983]~P64(x79831)+~P1(f317(f317(f225(x79831),x79833),f2(x79831)))+~P1(f317(f317(f225(x79831),x79834),x79832))+P1(f317(f317(f225(x79831),f317(f317(f281(x79831),x79832),x79833)),f317(f317(f281(x79831),x79834),x79833)))
% 94.68/94.45 [7984]~P110(x79841)+~P1(f317(f317(f225(x79841),f72(x79841)),x79842))+~P1(f317(f317(f224(a897),x79843),x79844))+P1(f317(f317(f224(x79841),f317(f317(f234(x79841),x79842),x79843)),f317(f317(f234(x79841),x79842),x79844)))
% 94.68/94.45 [7985]~P110(x79851)+~P1(f317(f317(f224(x79851),f72(x79851)),x79852))+~P1(f317(f317(f224(a897),x79853),x79854))+P1(f317(f317(f224(x79851),f317(f317(f234(x79851),x79852),x79853)),f317(f317(f234(x79851),x79852),x79854)))
% 94.68/94.45 [7987]~P110(x79871)+~P1(f317(f317(f225(x79871),f72(x79871)),x79872))+~P1(f317(f317(f225(a897),x79873),x79874))+P1(f317(f317(f225(x79871),f317(f317(f234(x79871),x79872),x79873)),f317(f317(f234(x79871),x79872),x79874)))
% 94.68/94.45 [8014]P1(f317(f317(f225(a897),f2(a897)),f317(x80141,x80142)))+~P1(f317(f28(x80143),x80144))+~P1(f317(f317(f319(x80143),x80142),x80144))+~P1(f317(f317(f225(a897),f2(a897)),f317(f317(f9(x80143,a897),x80141),x80144)))
% 94.68/94.45 [8023]~P138(x80231)+~P1(f317(f317(f224(x80231),x80233),x80234))+~P1(f317(f317(f224(x80231),f2(x80231)),x80232))+P1(f317(f317(f224(x80231),f317(f317(f75(x80231),x80232),x80233)),f317(f317(f75(x80231),x80232),x80234)))
% 94.68/94.45 [8024]~P137(x80241)+~P1(f317(f317(f224(x80241),x80243),x80244))+~P1(f317(f317(f224(x80241),f2(x80241)),x80242))+P1(f317(f317(f224(x80241),f317(f317(f75(x80241),x80242),x80243)),f317(f317(f75(x80241),x80242),x80244)))
% 94.68/94.45 [8025]~P125(x80251)+~P1(f317(f317(f225(x80251),f2(x80251)),x80252))+~P1(f317(f317(f224(x80251),x80253),x80254))+P1(f317(f317(f224(x80251),f317(f317(f75(x80251),x80252),x80253)),f317(f317(f75(x80251),x80252),x80254)))
% 94.68/94.45 [8026]~P138(x80261)+~P1(f317(f317(f224(x80261),x80262),x80264))+~P1(f317(f317(f224(x80261),f2(x80261)),x80263))+P1(f317(f317(f224(x80261),f317(f317(f75(x80261),x80262),x80263)),f317(f317(f75(x80261),x80264),x80263)))
% 94.68/94.45 [8027]~P110(x80271)+~P1(f317(f317(f224(x80271),x80272),x80274))+~P1(f317(f317(f224(x80271),f2(x80271)),x80272))+P1(f317(f317(f224(x80271),f317(f317(f234(x80271),x80272),x80273)),f317(f317(f234(x80271),x80274),x80273)))
% 94.68/94.45 [8028]~P63(x80281)+~P1(f317(f317(f224(x80281),x80282),x80284))+~P1(f317(f317(f224(x80281),f2(x80281)),x80283))+P1(f317(f317(f224(x80281),f317(f317(f281(x80281),x80282),x80283)),f317(f317(f281(x80281),x80284),x80283)))
% 94.68/94.45 [8030]~P119(x80301)+~P1(f317(f317(f225(x80301),x80303),x80304))+~P1(f317(f317(f225(x80301),f2(x80301)),x80302))+P1(f317(f317(f225(x80301),f317(f317(f75(x80301),x80302),x80303)),f317(f317(f75(x80301),x80302),x80304)))
% 94.68/94.45 [8031]~P133(x80311)+~P1(f317(f317(f225(x80311),x80313),x80314))+~P1(f317(f317(f225(x80311),f2(x80311)),x80312))+P1(f317(f317(f225(x80311),f317(f317(f75(x80311),x80312),x80313)),f317(f317(f75(x80311),x80312),x80314)))
% 94.68/94.45 [8032]~P125(x80321)+~P1(f317(f317(f225(x80321),x80322),x80324))+~P1(f317(f317(f225(x80321),f2(x80321)),x80323))+P1(f317(f317(f225(x80321),f317(f317(f75(x80321),x80322),x80323)),f317(f317(f75(x80321),x80324),x80323)))
% 94.68/94.45 [8033]~P133(x80331)+~P1(f317(f317(f225(x80331),x80332),x80334))+~P1(f317(f317(f225(x80331),f2(x80331)),x80333))+P1(f317(f317(f225(x80331),f317(f317(f75(x80331),x80332),x80333)),f317(f317(f75(x80331),x80334),x80333)))
% 94.68/94.45 [8034]~P125(x80341)+~P1(f317(f317(f225(x80341),x80343),x80344))+~P1(f317(f317(f225(x80341),f2(x80341)),x80342))+P1(f317(f317(f225(x80341),f317(f317(f75(x80341),x80342),x80343)),f317(f317(f75(x80341),x80342),x80344)))
% 94.68/94.45 [8035]~P64(x80351)+~P1(f317(f317(f225(x80351),x80352),x80354))+~P1(f317(f317(f225(x80351),f2(x80351)),x80353))+P1(f317(f317(f225(x80351),f317(f317(f281(x80351),x80352),x80353)),f317(f317(f281(x80351),x80354),x80353)))
% 94.68/94.45 [8077]~P109(x80772)+P1(f317(f317(f225(f904(x80771,x80772)),x80774),x80773))+~P1(f317(f317(f224(f904(x80771,x80772)),x80774),x80773))+P1(f317(f317(f224(f904(x80771,x80772)),x80773),x80774))
% 94.68/94.45 [8117]P1(f317(f317(f319(x81171),x81172),x81173))+P1(f317(f317(f319(x81171),x81172),x81174))+~P1(f317(f317(f224(f904(x81171,a893)),x81174),x81173))+P1(f317(f317(f225(f904(x81171,a893)),x81174),f317(f317(f299(x81171),x81172),x81173)))
% 94.68/94.45 [8228]~P120(x82282)+E(x82281,f2(x82282))+P1(f317(f317(f277(x82282),x82283),x82284))+~P1(f317(f317(f277(x82282),f317(f317(f75(x82282),x82283),x82281)),f317(f317(f75(x82282),x82284),x82281)))
% 94.68/94.45 [8229]~P120(x82292)+E(x82291,f2(x82292))+P1(f317(f317(f277(x82292),x82293),x82294))+~P1(f317(f317(f277(x82292),f317(f317(f75(x82292),x82291),x82293)),f317(f317(f75(x82292),x82291),x82294)))
% 94.68/94.45 [8278]P1(f317(f317(f319(x82781),x82782),x82783))+P1(f317(f317(f319(x82781),x82782),x82784))+~P1(f317(f317(f225(f904(x82781,a893)),x82784),f317(f317(f299(x82781),x82782),x82783)))+P1(f317(f317(f224(f904(x82781,a893)),x82784),x82783))
% 94.68/94.45 [8343]~P125(x83431)+P1(f317(f317(f225(x83431),x83433),x83432))+P1(f317(f317(f225(x83431),x83432),x83433))+~P1(f317(f317(f225(x83431),f317(f317(f75(x83431),x83434),x83432)),f317(f317(f75(x83431),x83434),x83433)))
% 94.68/94.45 [8344]~P125(x83441)+P1(f317(f317(f225(x83441),x83443),x83442))+P1(f317(f317(f225(x83441),x83442),x83443))+~P1(f317(f317(f225(x83441),f317(f317(f75(x83441),x83442),x83444)),f317(f317(f75(x83441),x83443),x83444)))
% 94.68/94.45 [8356]~P125(x83561)+P1(f317(f317(f225(x83561),x83564),f2(x83561)))+P1(f317(f317(f225(x83561),x83562),x83563))+~P1(f317(f317(f225(x83561),f317(f317(f75(x83561),x83562),x83564)),f317(f317(f75(x83561),x83563),x83564)))
% 94.68/94.45 [8357]~P125(x83571)+P1(f317(f317(f225(x83571),x83574),f2(x83571)))+P1(f317(f317(f225(x83571),x83572),x83573))+~P1(f317(f317(f225(x83571),f317(f317(f75(x83571),x83574),x83572)),f317(f317(f75(x83571),x83574),x83573)))
% 94.68/94.45 [8360]~P125(x83601)+P1(f317(f317(f225(x83601),x83602),x83603))+P1(f317(f317(f225(x83601),f2(x83601)),x83604))+~P1(f317(f317(f225(x83601),f317(f317(f75(x83601),x83604),x83603)),f317(f317(f75(x83601),x83604),x83602)))
% 94.68/94.45 [8361]~P125(x83611)+P1(f317(f317(f225(x83611),x83612),x83613))+P1(f317(f317(f225(x83611),f2(x83611)),x83614))+~P1(f317(f317(f225(x83611),f317(f317(f75(x83611),x83613),x83614)),f317(f317(f75(x83611),x83612),x83614)))
% 94.68/94.45 [8374]~P125(x83741)+P1(f317(f317(f225(x83741),x83742),f2(x83741)))+P1(f317(f317(f225(x83741),f2(x83741)),x83742))+~P1(f317(f317(f225(x83741),f317(f317(f75(x83741),x83743),x83742)),f317(f317(f75(x83741),x83744),x83742)))
% 94.68/94.45 [8375]~P125(x83751)+P1(f317(f317(f225(x83751),x83752),f2(x83751)))+P1(f317(f317(f225(x83751),f2(x83751)),x83752))+~P1(f317(f317(f225(x83751),f317(f317(f75(x83751),x83752),x83753)),f317(f317(f75(x83751),x83752),x83754)))
% 94.68/94.45 [8404]~P125(x84041)+~P1(f317(f317(f225(x84041),x84044),f2(x84041)))+P1(f317(f317(f224(x84041),x84042),x84043))+~P1(f317(f317(f224(x84041),f317(f317(f75(x84041),x84044),x84043)),f317(f317(f75(x84041),x84044),x84042)))
% 94.68/94.45 [8405]~P125(x84051)+~P1(f317(f317(f225(x84051),x84054),f2(x84051)))+P1(f317(f317(f225(x84051),x84052),x84053))+~P1(f317(f317(f225(x84051),f317(f317(f75(x84051),x84054),x84053)),f317(f317(f75(x84051),x84054),x84052)))
% 94.68/94.45 [8416]~P110(x84163)+~P1(f317(f317(f225(x84163),f72(x84163)),x84164))+P1(f317(f317(f224(a897),x84161),x84162))+~P1(f317(f317(f224(x84163),f317(f317(f234(x84163),x84164),x84161)),f317(f317(f234(x84163),x84164),x84162)))
% 94.68/94.45 [8418]~P110(x84183)+~P1(f317(f317(f225(x84183),f72(x84183)),x84184))+P1(f317(f317(f225(a897),x84181),x84182))+~P1(f317(f317(f225(x84183),f317(f317(f234(x84183),x84184),x84181)),f317(f317(f234(x84183),x84184),x84182)))
% 94.68/94.45 [8428]~P125(x84281)+P1(f317(f317(f224(x84281),x84282),x84283))+~P1(f317(f317(f225(x84281),f2(x84281)),x84284))+~P1(f317(f317(f224(x84281),f317(f317(f75(x84281),x84284),x84282)),f317(f317(f75(x84281),x84284),x84283)))
% 94.68/94.45 [8429]~P133(x84291)+P1(f317(f317(f224(x84291),x84292),x84293))+~P1(f317(f317(f225(x84291),f2(x84291)),x84294))+~P1(f317(f317(f224(x84291),f317(f317(f75(x84291),x84294),x84292)),f317(f317(f75(x84291),x84294),x84293)))
% 94.68/94.45 [8430]~P133(x84301)+P1(f317(f317(f224(x84301),x84302),x84303))+~P1(f317(f317(f225(x84301),f2(x84301)),x84304))+~P1(f317(f317(f224(x84301),f317(f317(f75(x84301),x84302),x84304)),f317(f317(f75(x84301),x84303),x84304)))
% 94.68/94.45 [8431]~P125(x84311)+P1(f317(f317(f225(x84311),x84312),x84313))+~P1(f317(f317(f225(x84311),f2(x84311)),x84314))+~P1(f317(f317(f225(x84311),f317(f317(f75(x84311),x84314),x84312)),f317(f317(f75(x84311),x84314),x84313)))
% 94.68/94.45 [8432]~P133(x84321)+P1(f317(f317(f225(x84321),x84322),x84323))+~P1(f317(f317(f224(x84321),f2(x84321)),x84324))+~P1(f317(f317(f225(x84321),f317(f317(f75(x84321),x84324),x84322)),f317(f317(f75(x84321),x84324),x84323)))
% 94.68/94.45 [8433]~P129(x84331)+P1(f317(f317(f225(x84331),x84332),x84333))+~P1(f317(f317(f224(x84331),f2(x84331)),x84334))+~P1(f317(f317(f225(x84331),f317(f317(f75(x84331),x84334),x84332)),f317(f317(f75(x84331),x84334),x84333)))
% 94.68/94.45 [8434]~P110(x84341)+~P1(f317(f317(f224(x84341),f2(x84341)),x84343))+P1(f317(f317(f225(x84341),x84342),x84343))+~P1(f317(f317(f225(x84341),f317(f317(f234(x84341),x84342),x84344)),f317(f317(f234(x84341),x84343),x84344)))
% 94.68/94.45 [8435]~P133(x84351)+P1(f317(f317(f225(x84351),x84352),x84353))+~P1(f317(f317(f224(x84351),f2(x84351)),x84354))+~P1(f317(f317(f225(x84351),f317(f317(f75(x84351),x84352),x84354)),f317(f317(f75(x84351),x84353),x84354)))
% 94.68/94.45 [8436]~P129(x84361)+P1(f317(f317(f225(x84361),x84362),x84363))+~P1(f317(f317(f224(x84361),f2(x84361)),x84364))+~P1(f317(f317(f225(x84361),f317(f317(f75(x84361),x84362),x84364)),f317(f317(f75(x84361),x84363),x84364)))
% 94.68/94.45 [8480]P1(f317(f317(f319(x84801),x84802),x84803))+~P1(f317(f317(f224(f904(x84801,a893)),x84803),x84804))+~P1(f317(f317(f225(f904(x84801,a893)),x84803),x84804))+P1(f317(f317(f225(f904(x84801,a893)),x84803),f317(f317(f299(x84801),x84802),x84804)))
% 94.68/94.45 [8512]~P145(x85121)+~P121(x85121)+P1(f317(f317(f277(x85121),x85122),f317(f317(f74(x85121),f835(x85122,x85123,x85121)),f2(x85121))))+~P1(f317(x85123,f317(f317(f75(x85121),x85122),x85124)))
% 94.68/94.45 [8859]E(f317(f317(f23(a1),f372(x88591,x88592,x88593,x88594)),f373(x88591,x88592,x88593,x88594)),x88594)+~P1(f317(f317(f225(a1),f2(a1)),x88593))+~P1(f317(f317(f224(a1),x88591),x88594))+P1(f317(f317(f224(a1),x88591),f317(f317(f74(a1),x88594),x88593)))
% 94.68/94.45 [8860]E(f317(f317(f23(a1),f386(x88601,x88602,x88603,x88604)),f387(x88601,x88602,x88603,x88604)),x88604)+~P1(f317(f317(f225(a1),f2(a1)),x88603))+~P1(f317(f317(f225(a1),x88601),x88604))+P1(f317(f317(f225(a1),x88601),f317(f317(f74(a1),x88604),x88603)))
% 94.68/94.45 [9010]~E(f317(f317(f154(x90101),x90103),f654(x90104,x90103,x90101,x90102)),f317(f317(f154(x90101),x90104),f654(x90104,x90103,x90101,x90102)))+E(f317(f317(f165(x90101),x90102),x90103),f317(f317(f165(x90101),x90102),x90104))+~P1(f317(f317(f224(a897),x90102),f317(f179(f898(x90101)),x90103)))+~P1(f317(f317(f224(a897),x90102),f317(f179(f898(x90101)),x90104)))
% 94.68/94.45 [9072]~P1(f317(f317(f225(a1),f2(a1)),x90723))+~P1(f317(f317(f224(a1),x90721),x90724))+P1(f317(f317(f319(a1),f372(x90721,x90722,x90723,x90724)),x90722))+P1(f317(f317(f224(a1),x90721),f317(f317(f74(a1),x90724),x90723)))
% 94.68/94.45 [9073]~P1(f317(f317(f225(a1),f2(a1)),x90733))+~P1(f317(f317(f225(a1),x90731),x90734))+P1(f317(f317(f319(a1),f386(x90731,x90732,x90733,x90734)),x90732))+P1(f317(f317(f225(a1),x90731),f317(f317(f74(a1),x90734),x90733)))
% 94.68/94.45 [9113]~P66(x91131)+~P1(f317(f28(x91131),x91133))+~P1(f317(f317(f319(x91131),x91134),x91133))+P1(f317(f317(f224(x91131),f317(f317(f58(x91131,x91131,f228(x91131)),x91132),x91133)),f317(f317(f228(x91131),x91134),x91132)))
% 94.68/94.45 [9114]~P105(x91141)+~P1(f317(f28(x91141),x91143))+~P1(f317(f317(f319(x91141),x91144),x91143))+P1(f317(f317(f224(x91141),f317(f317(f58(x91141,x91141,f92(x91141)),x91142),x91143)),f317(f317(f92(x91141),x91144),x91142)))
% 94.68/94.45 [9121]~P8(x91212,x91213,x91214)+~P1(f317(f28(x91212),x91213))+P1(f317(f317(f277(a897),x91211),f317(f29(x91212),x91213)))+P1(f317(f317(f319(f904(x91212,a893)),f839(x91211,x91214,x91213,x91212)),f317(f317(f55(x91212),x91213),x91214)))
% 94.68/94.45 [9159]E(f317(f317(f165(x91591),x91592),x91593),f317(f317(f165(x91591),x91592),x91594))+P1(f317(f317(f225(a897),f654(x91593,x91594,x91591,x91592)),x91592))+~P1(f317(f317(f224(a897),x91592),f317(f179(f898(x91591)),x91593)))+~P1(f317(f317(f224(a897),x91592),f317(f179(f898(x91591)),x91594)))
% 94.68/94.45 [9164]~P1(f317(f317(f225(a1),f2(a1)),x91643))+~P1(f317(f317(f224(a1),x91641),x91642))+P1(f317(f317(f319(a1),f373(x91641,x91644,x91643,x91642)),f293(a1,f72(a1),x91643)))+P1(f317(f317(f224(a1),x91641),f317(f317(f74(a1),x91642),x91643)))
% 94.68/94.45 [9165]~P1(f317(f317(f225(a1),f2(a1)),x91653))+~P1(f317(f317(f225(a1),x91651),x91652))+P1(f317(f317(f319(a1),f387(x91651,x91654,x91653,x91652)),f293(a1,f72(a1),x91653)))+P1(f317(f317(f225(a1),x91651),f317(f317(f74(a1),x91652),x91653)))
% 94.68/94.45 [9491]~P66(x94911)+~P1(f317(f28(x94911),x94914))+P1(f317(f317(f319(x94911),f605(x94912,x94913,x94914,x94911)),x94914))+P1(f317(f317(f224(x94911),f317(f317(f58(x94911,x94911,f223(x94911)),x94912),x94914)),f317(f317(f223(x94911),x94913),x94912)))
% 94.68/94.45 [9492]~P99(x94921)+~P1(f317(f28(x94921),x94924))+P1(f317(f317(f319(x94921),f609(x94922,x94923,x94924,x94921)),x94924))+P1(f317(f317(f224(x94921),f317(f317(f58(x94921,x94921,f91(x94921)),x94922),x94924)),f317(f317(f91(x94921),x94923),x94922)))
% 94.68/94.45 [9628]~P66(x96281)+~P1(f317(f28(x96281),x96283))+~P1(f317(f317(f224(x96281),f605(x96282,x96284,x96283,x96281)),x96284))+P1(f317(f317(f224(x96281),f317(f317(f58(x96281,x96281,f223(x96281)),x96282),x96283)),f317(f317(f223(x96281),x96284),x96282)))
% 94.68/94.45 [9629]~P99(x96291)+~P1(f317(f28(x96291),x96293))+~P1(f317(f317(f224(x96291),f609(x96292,x96294,x96293,x96291)),x96294))+P1(f317(f317(f224(x96291),f317(f317(f58(x96291,x96291,f91(x96291)),x96292),x96293)),f317(f317(f91(x96291),x96294),x96292)))
% 94.68/94.45 [9631]~P1(f317(f317(f224(a1),f2(a1)),x96314))+~P1(f317(f317(f225(a1),f2(a1)),x96313))+~P1(f317(f317(f225(a1),x96314),x96311))+P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x96311),f40(a1,x96312,x96313))),x96314)),f317(f317(f75(a1),x96311),x96313)))
% 94.68/94.45 [10017]E(x100171,x100172)+P1(f317(f317(f319(f903(f898(x100173),f898(x100173))),f317(f317(f242(f898(x100173),f898(x100173)),x100172),x100171)),f137(x100173,x100174)))+P1(f317(f317(f319(f903(f898(x100173),f898(x100173))),f317(f317(f242(f898(x100173),f898(x100173)),x100171),x100172)),f137(x100173,x100174)))+~P1(f317(f317(f319(f903(x100173,x100173)),f317(f317(f242(x100173,x100173),f628(x100171,x100172,x100174,x100173)),f630(x100171,x100172,x100174,x100173))),x100174))
% 94.68/94.45 [10018]E(x100181,x100182)+P1(f317(f317(f319(f903(f898(x100183),f898(x100183))),f317(f317(f242(f898(x100183),f898(x100183)),x100182),x100181)),f137(x100183,x100184)))+P1(f317(f317(f319(f903(f898(x100183),f898(x100183))),f317(f317(f242(f898(x100183),f898(x100183)),x100181),x100182)),f137(x100183,x100184)))+~P1(f317(f317(f319(f903(x100183,x100183)),f317(f317(f242(x100183,x100183),f630(x100181,x100182,x100184,x100183)),f628(x100181,x100182,x100184,x100183))),x100184))
% 94.68/94.45 [7564]~P66(x75641)+~P1(f317(f317(f224(x75641),x75643),x75644))+~P1(f317(f317(f224(x75641),x75642),x75644))+P1(f317(f317(f224(x75641),f317(f317(f223(x75641),x75642),x75643)),x75644))
% 94.68/94.45 [7567]~P99(x75671)+~P1(f317(f317(f224(x75671),x75673),x75674))+~P1(f317(f317(f224(x75671),x75672),x75674))+P1(f317(f317(f224(x75671),f317(f317(f91(x75671),x75672),x75673)),x75674))
% 94.68/94.45 [7568]~P66(x75681)+~P1(f317(f317(f225(x75681),x75683),x75684))+~P1(f317(f317(f225(x75681),x75682),x75684))+P1(f317(f317(f225(x75681),f317(f317(f223(x75681),x75682),x75683)),x75684))
% 94.68/94.45 [7807]~P3(x78071)+E(f317(f317(f74(x78071),f317(f317(f30(x78071),x78072),x78073)),f317(f317(f30(x78071),x78074),x78073)),f317(f317(f30(x78071),f317(f317(f74(x78071),x78072),x78074)),x78073))+~P1(f317(f317(f277(x78071),x78073),x78074))+~P1(f317(f317(f277(x78071),x78073),x78072))
% 94.68/94.45 [7890]~E(x78901,x78903)+E(f129(a897,f317(f292(a897,x78901),x78902)),f317(f317(f141(a897),x78903),x78904))+~E(f129(a897,f317(f292(a897,f317(f317(f74(a897),x78901),f72(a897))),x78902)),x78904)+~P1(f317(f317(f225(a897),x78901),x78902))
% 94.68/94.45 [7898]~P66(x78981)+P1(f317(f317(f224(x78981),x78982),x78983))+P1(f317(f317(f224(x78981),x78984),x78983))+~P1(f317(f317(f224(x78981),f317(f317(f228(x78981),x78984),x78982)),x78983))
% 94.68/94.45 [7899]~P66(x78991)+P1(f317(f317(f225(x78991),x78992),x78993))+P1(f317(f317(f225(x78991),x78994),x78993))+~P1(f317(f317(f225(x78991),f317(f317(f228(x78991),x78994),x78992)),x78993))
% 94.68/94.45 [8175]~P63(x81751)+~P1(f317(f317(f225(x81751),f2(x81751)),x81753))+~P1(f317(f317(f224(x81751),x81752),f317(f317(f281(x81751),x81754),x81753)))+P1(f317(f317(f224(x81751),f317(f317(f75(x81751),x81752),x81753)),x81754))
% 94.68/94.45 [8176]~P64(x81761)+~P1(f317(f317(f225(x81761),f2(x81761)),x81763))+~P1(f317(f317(f224(x81761),x81762),f317(f317(f281(x81761),x81764),x81763)))+P1(f317(f317(f224(x81761),f317(f317(f75(x81761),x81762),x81763)),x81764))
% 94.68/94.45 [8177]~P63(x81771)+~P1(f317(f317(f225(x81771),f2(x81771)),x81773))+~P1(f317(f317(f224(x81771),x81772),f317(f317(f75(x81771),x81774),x81773)))+P1(f317(f317(f224(x81771),f317(f317(f281(x81771),x81772),x81773)),x81774))
% 94.68/94.45 [8179]~P64(x81791)+~P1(f317(f317(f225(x81791),f2(x81791)),x81793))+~P1(f317(f317(f224(x81791),x81792),f317(f317(f75(x81791),x81794),x81793)))+P1(f317(f317(f224(x81791),f317(f317(f281(x81791),x81792),x81793)),x81794))
% 94.68/94.45 [8180]~P63(x81801)+~P1(f317(f317(f225(x81801),f2(x81801)),x81803))+~P1(f317(f317(f225(x81801),x81802),f317(f317(f281(x81801),x81804),x81803)))+P1(f317(f317(f225(x81801),f317(f317(f75(x81801),x81802),x81803)),x81804))
% 94.68/94.45 [8181]~P64(x81811)+~P1(f317(f317(f225(x81811),f2(x81811)),x81813))+~P1(f317(f317(f225(x81811),x81812),f317(f317(f281(x81811),x81814),x81813)))+P1(f317(f317(f225(x81811),f317(f317(f75(x81811),x81812),x81813)),x81814))
% 94.68/94.45 [8182]~P63(x81821)+~P1(f317(f317(f225(x81821),f2(x81821)),x81823))+~P1(f317(f317(f225(x81821),x81822),f317(f317(f75(x81821),x81824),x81823)))+P1(f317(f317(f225(x81821),f317(f317(f281(x81821),x81822),x81823)),x81824))
% 94.68/94.45 [8184]~P64(x81841)+~P1(f317(f317(f225(x81841),f2(x81841)),x81843))+~P1(f317(f317(f225(x81841),x81842),f317(f317(f75(x81841),x81844),x81843)))+P1(f317(f317(f225(x81841),f317(f317(f281(x81841),x81842),x81843)),x81844))
% 94.68/94.45 [8313]~P63(x83131)+~P1(f317(f317(f225(x83131),f2(x83131)),x83134))+P1(f317(f317(f224(x83131),x83132),f317(f317(f75(x83131),x83133),x83134)))+~P1(f317(f317(f224(x83131),f317(f317(f281(x83131),x83132),x83134)),x83133))
% 94.68/94.45 [8314]~P63(x83141)+~P1(f317(f317(f225(x83141),f2(x83141)),x83144))+P1(f317(f317(f224(x83141),x83142),f317(f317(f281(x83141),x83143),x83144)))+~P1(f317(f317(f224(x83141),f317(f317(f75(x83141),x83142),x83144)),x83143))
% 94.68/94.45 [8316]~P64(x83161)+~P1(f317(f317(f225(x83161),f2(x83161)),x83164))+P1(f317(f317(f224(x83161),x83162),f317(f317(f75(x83161),x83163),x83164)))+~P1(f317(f317(f224(x83161),f317(f317(f281(x83161),x83162),x83164)),x83163))
% 94.68/94.45 [8317]~P64(x83171)+~P1(f317(f317(f225(x83171),f2(x83171)),x83174))+P1(f317(f317(f224(x83171),x83172),f317(f317(f281(x83171),x83173),x83174)))+~P1(f317(f317(f224(x83171),f317(f317(f75(x83171),x83172),x83174)),x83173))
% 94.68/94.45 [8318]~P63(x83181)+~P1(f317(f317(f225(x83181),f2(x83181)),x83184))+P1(f317(f317(f225(x83181),x83182),f317(f317(f75(x83181),x83183),x83184)))+~P1(f317(f317(f225(x83181),f317(f317(f281(x83181),x83182),x83184)),x83183))
% 94.68/94.45 [8319]~P63(x83191)+~P1(f317(f317(f225(x83191),f2(x83191)),x83194))+P1(f317(f317(f225(x83191),x83192),f317(f317(f281(x83191),x83193),x83194)))+~P1(f317(f317(f225(x83191),f317(f317(f75(x83191),x83192),x83194)),x83193))
% 94.68/94.45 [8321]~P64(x83211)+~P1(f317(f317(f225(x83211),f2(x83211)),x83214))+P1(f317(f317(f225(x83211),x83212),f317(f317(f75(x83211),x83213),x83214)))+~P1(f317(f317(f225(x83211),f317(f317(f281(x83211),x83212),x83214)),x83213))
% 94.68/94.45 [8322]~P64(x83221)+~P1(f317(f317(f225(x83221),f2(x83221)),x83224))+P1(f317(f317(f225(x83221),x83222),f317(f317(f281(x83221),x83223),x83224)))+~P1(f317(f317(f225(x83221),f317(f317(f75(x83221),x83222),x83224)),x83223))
% 94.68/94.45 [8483]~P64(x84831)+~P1(f317(f317(f225(x84831),x84833),f2(x84831)))+~P1(f317(f317(f224(x84831),f317(f317(f281(x84831),x84834),x84833)),x84832))+P1(f317(f317(f224(x84831),f317(f317(f75(x84831),x84832),x84833)),x84834))
% 94.68/94.45 [8484]~P64(x84841)+~P1(f317(f317(f225(x84841),x84843),f2(x84841)))+~P1(f317(f317(f224(x84841),f317(f317(f75(x84841),x84844),x84843)),x84842))+P1(f317(f317(f224(x84841),f317(f317(f281(x84841),x84842),x84843)),x84844))
% 94.68/94.45 [8485]~P64(x84851)+~P1(f317(f317(f225(x84851),x84853),f2(x84851)))+~P1(f317(f317(f225(x84851),f317(f317(f281(x84851),x84854),x84853)),x84852))+P1(f317(f317(f225(x84851),f317(f317(f75(x84851),x84852),x84853)),x84854))
% 94.68/94.45 [8486]~P64(x84861)+~P1(f317(f317(f225(x84861),x84863),f2(x84861)))+~P1(f317(f317(f225(x84861),f317(f317(f75(x84861),x84864),x84863)),x84862))+P1(f317(f317(f225(x84861),f317(f317(f281(x84861),x84862),x84863)),x84864))
% 94.68/94.45 [8498]~P1(f317(x84981,x84984))+~P1(f317(f317(f225(a897),x84982),f317(f317(f75(a897),x84983),f317(a102,x84984))))+P1(f317(x84981,f317(f317(f30(a897),x84982),x84983)))+~P1(f317(f317(f224(a897),f317(f317(f75(a897),x84983),x84984)),x84982))
% 94.68/94.45 [8707]~P66(x87071)+~P1(f317(f28(x87071),x87074))+~P1(f317(f317(f319(x87071),x87072),x87074))+P1(f317(f317(f224(x87071),f317(f317(f223(x87071),x87072),x87073)),f317(f317(f58(x87071,x87071,f223(x87071)),x87073),x87074)))
% 94.68/94.45 [8708]~P99(x87081)+~P1(f317(f28(x87081),x87084))+~P1(f317(f317(f319(x87081),x87082),x87084))+P1(f317(f317(f224(x87081),f317(f317(f91(x87081),x87082),x87083)),f317(f317(f58(x87081,x87081,f91(x87081)),x87083),x87084)))
% 94.68/94.45 [8861]~P1(f317(f28(x88611),x88612))+E(f317(f29(x88611),f317(f317(f23(f904(x88611,a893)),x88612),f317(f317(f299(x88611),x88613),x88614))),f317(f317(f23(a897),f317(f29(x88611),f317(f317(f23(f904(x88611,a893)),x88612),x88614))),f72(a897)))+P1(f317(f317(f319(x88611),x88613),x88614))+~P1(f317(f317(f319(x88611),x88613),x88612))
% 94.68/94.45 [8938]E(f317(f317(f74(a1),f376(x89381,x89382,x89383,x89384)),f377(x89381,x89382,x89383,x89384)),x89384)+~P1(f317(f317(f225(a1),f2(a1)),x89383))+~P1(f317(f317(f224(a1),x89384),x89381))+P1(f317(f317(f224(a1),f317(f317(f23(a1),x89384),x89383)),x89381))
% 94.68/94.45 [8939]E(f317(f317(f74(a1),f388(x89391,x89392,x89393,x89394)),f389(x89391,x89392,x89393,x89394)),x89394)+~P1(f317(f317(f225(a1),f2(a1)),x89393))+~P1(f317(f317(f225(a1),x89394),x89391))+P1(f317(f317(f225(a1),f317(f317(f23(a1),x89394),x89393)),x89391))
% 94.68/94.45 [9144]~P1(f317(f317(f225(a1),f2(a1)),x91443))+~P1(f317(f317(f224(a1),x91444),x91441))+P1(f317(f317(f319(a1),f376(x91441,x91442,x91443,x91444)),x91442))+P1(f317(f317(f224(a1),f317(f317(f23(a1),x91444),x91443)),x91441))
% 94.68/94.45 [9145]~P1(f317(f317(f225(a1),f2(a1)),x91453))+~P1(f317(f317(f225(a1),x91454),x91451))+P1(f317(f317(f319(a1),f388(x91451,x91452,x91453,x91454)),x91452))+P1(f317(f317(f225(a1),f317(f317(f23(a1),x91454),x91453)),x91451))
% 94.68/94.45 [9231]~P1(f317(f317(f225(a1),f2(a1)),x92312))+~P1(f317(f317(f224(a1),x92311),x92313))+P1(f317(f317(f319(a1),f377(x92313,x92314,x92312,x92311)),f293(a1,f72(a1),x92312)))+P1(f317(f317(f224(a1),f317(f317(f23(a1),x92311),x92312)),x92313))
% 94.68/94.45 [9232]~P1(f317(f317(f225(a1),f2(a1)),x92322))+~P1(f317(f317(f225(a1),x92321),x92323))+P1(f317(f317(f319(a1),f389(x92323,x92324,x92322,x92321)),f293(a1,f72(a1),x92322)))+P1(f317(f317(f225(a1),f317(f317(f23(a1),x92321),x92322)),x92323))
% 94.68/94.45 [9250]~P1(f317(f317(f224(a1),f2(a1)),x92504))+~P1(f317(f317(f225(a1),f2(a1)),x92503))+~P1(f317(f317(f225(a1),x92504),x92501))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x92501),f40(a1,x92502,x92503))),x92504)))
% 94.68/94.45 [9279]E(x92791,x92792)+~P38(x92793,x92794)+~P1(f317(f317(f319(f903(x92793,x92793)),f317(f317(f242(x92793,x92793),x92792),x92791)),x92794))+~P1(f317(f317(f319(f903(x92793,x92793)),f317(f317(f242(x92793,x92793),x92791),x92792)),x92794))
% 94.68/94.45 [9312]~P66(x93121)+~P1(f317(f28(x93121),x93124))+~P1(f317(f317(f224(x93121),x93122),f604(x93123,x93122,x93124,x93121)))+P1(f317(f317(f224(x93121),f317(f317(f228(x93121),x93122),x93123)),f317(f317(f58(x93121,x93121,f228(x93121)),x93123),x93124)))
% 94.68/94.45 [9313]~P105(x93131)+~P1(f317(f28(x93131),x93134))+~P1(f317(f317(f224(x93131),x93132),f608(x93133,x93132,x93134,x93131)))+P1(f317(f317(f224(x93131),f317(f317(f92(x93131),x93132),x93133)),f317(f317(f58(x93131,x93131,f92(x93131)),x93133),x93134)))
% 94.68/94.45 [9330]~P1(f317(f317(f224(a1),x93304),f2(a1)))+~P1(f317(f317(f225(a1),f2(a1)),x93302))+~P1(f317(f317(f225(a1),x93301),x93304))+P1(f317(f317(f225(a1),f317(f317(f75(a1),x93301),x93302)),f317(f317(f74(a1),f317(f317(f75(a1),x93301),f40(a1,x93303,x93302))),x93304)))
% 94.68/94.45 [9356]P1(f317(f28(x93561),x93562))+~P1(f317(f28(x93561),x93563))+~P1(f317(f317(f319(f904(x93561,a893)),x93562),f317(f317(f55(x93561),x93563),x93564)))+~P1(f317(f317(f224(f904(f903(x93561,x93561),a893)),x93564),f317(f317(f244(x93561,x93561),x93563),f317(f16(f904(x93561,a893),x93561),x93563))))
% 94.68/94.45 [9381]~P66(x93811)+~P1(f317(f28(x93811),x93814))+P1(f317(f317(f319(x93811),f604(x93812,x93813,x93814,x93811)),x93814))+P1(f317(f317(f224(x93811),f317(f317(f228(x93811),x93813),x93812)),f317(f317(f58(x93811,x93811,f228(x93811)),x93812),x93814)))
% 94.68/94.45 [9382]~P105(x93821)+~P1(f317(f28(x93821),x93824))+P1(f317(f317(f319(x93821),f608(x93822,x93823,x93824,x93821)),x93824))+P1(f317(f317(f224(x93821),f317(f317(f92(x93821),x93823),x93822)),f317(f317(f58(x93821,x93821,f92(x93821)),x93822),x93824)))
% 94.68/94.45 [9795]~P1(f317(f28(x97952),x97954))+~P1(f317(f28(x97951),x97953))+~P1(f317(f317(f224(a897),f317(f29(x97952),x97954)),f317(f29(x97951),x97953)))+P1(f317(f317(f224(f904(x97951,a893)),f317(f300(x97952,x97951,f327(x97953,x97951,x97954,x97952)),x97954)),x97953))
% 94.68/94.45 [9432]~P1(f317(f317(f319(x94321),x94322),x94324))+P1(f317(f317(f319(x94321),x94322),x94323))+~P1(f317(f317(f225(f904(x94321,a893)),x94324),f317(f317(f299(x94321),x94322),x94323)))+P1(f317(f317(f225(f904(x94321,a893)),f317(f317(f23(f904(x94321,a893)),x94324),f317(f317(f299(x94321),x94322),f178(f904(x94321,a893))))),x94323))
% 94.68/94.45 [9609]~P1(f317(f317(f319(x96091),x96092),x96094))+P1(f317(f317(f319(x96091),x96092),x96093))+P1(f317(f317(f225(f904(x96091,a893)),x96094),f317(f317(f299(x96091),x96092),x96093)))+~P1(f317(f317(f225(f904(x96091,a893)),f317(f317(f23(f904(x96091,a893)),x96094),f317(f317(f299(x96091),x96092),f178(f904(x96091,a893))))),x96093))
% 94.68/94.45 [9634]P1(f317(f317(f319(x96341),x96342),x96343))+~P1(f317(f317(f224(f904(x96341,a893)),x96344),x96343))+P1(f317(f317(f225(f904(x96341,a893)),x96344),f317(f317(f299(x96341),x96342),x96343)))+~P1(f317(f317(f225(f904(x96341,a893)),f317(f317(f23(f904(x96341,a893)),x96344),f317(f317(f299(x96341),x96342),f178(f904(x96341,a893))))),x96343))
% 94.68/94.45 [9639]~P1(f317(f317(f319(x96391),x96393),x96392))+~P1(f317(f317(f225(f904(x96391,a893)),x96392),x96394))+P1(f317(f317(f225(f904(x96391,a893)),x96392),f317(f317(f299(x96391),x96393),x96394)))+~P1(f317(f317(f225(f904(x96391,a893)),f317(f317(f23(f904(x96391,a893)),x96392),f317(f317(f299(x96391),x96393),f178(f904(x96391,a893))))),x96394))
% 94.68/94.45 [9655]~P1(f317(f317(f224(f904(x96551,a893)),x96552),x96554))+~P1(f317(f317(f225(f904(x96551,a893)),x96552),x96554))+P1(f317(f317(f225(f904(x96551,a893)),x96552),f317(f317(f299(x96551),x96553),x96554)))+~P1(f317(f317(f225(f904(x96551,a893)),f317(f317(f23(f904(x96551,a893)),x96552),f317(f317(f299(x96551),x96553),f178(f904(x96551,a893))))),x96554))
% 94.68/94.45 [9700]~P108(x97002)+~P60(x97001)+~P1(f317(f317(f224(f904(x97001,x97002)),x97003),x97004))+P1(f317(f52(x97001),f317(f317(f18(x97001,x97002,a893),f317(f317(f8(x97002,f904(x97002,a893),x97001),f224(x97002)),x97003)),x97004)))
% 94.68/94.45 [9843]~P108(x98432)+~P60(x98431)+P1(f317(f317(f224(f904(x98431,x98432)),x98433),x98434))+~P1(f317(f52(x98431),f317(f317(f18(x98431,x98432,a893),f317(f317(f8(x98432,f904(x98432,a893),x98431),f224(x98432)),x98433)),x98434)))
% 94.68/94.45 [10008]E(f317(f317(f154(x100081),f317(f317(f154(f898(x100081)),f169(x100081,x100082)),x100083)),x100084),f317(f317(f154(x100081),f317(f317(f154(f898(x100081)),x100082),x100084)),x100083))+~P1(f317(f317(f225(a897),x100083),f317(f179(f898(f898(x100081))),f169(x100081,x100082))))+~P13(a897,f317(f158(a897),f317(f317(f144(f898(x100081),a897),f179(f898(x100081))),x100082)))+~P1(f317(f317(f225(a897),x100084),f317(f179(f898(f898(x100081))),f317(f126(f898(x100081),f317(f317(f8(a897,a893,f898(x100081)),f317(f225(a897),x100083)),f179(f898(x100081)))),x100082))))
% 94.68/94.45 [10029]~P1(f317(f317(f319(f903(a897,a897)),x100294),x100291))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x100294),x100292)),a26))+~P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100291),x100293)),a63))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100291),f317(f317(f299(f903(a897,a897)),x100292),x100293))),a63))
% 94.68/94.45 [10030]~P1(f317(f317(f319(f903(a897,a897)),x100304),x100301))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x100304),x100302)),a65))+~P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100301),x100303)),a66))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100301),f317(f317(f299(f903(a897,a897)),x100302),x100303))),a66))
% 94.68/94.45 [9920]~P108(x99202)+~P60(x99201)+~P1(f317(f317(f225(f904(x99201,x99202)),x99203),x99204))+P1(f317(f51(x99201),f317(f317(f8(a893,a893,x99201),a312),f317(f317(f18(x99201,x99202,a893),f317(f317(f8(x99202,f904(x99202,a893),x99201),a314),x99203)),x99204))))
% 94.68/94.45 [10041]~P1(f317(f317(f319(f903(a897,a897)),x100414),x100413))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x100411),x100414)),a26))+~P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100412),x100413)),a27))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f317(f317(f299(f903(a897,a897)),x100411),x100412)),x100413)),a27))
% 94.68/94.45 [10042]~P1(f317(f317(f319(f903(a897,a897)),x100424),x100423))+~P1(f317(f317(f319(f903(f903(a897,a897),f903(a897,a897))),f317(f317(f242(f903(a897,a897),f903(a897,a897)),x100421),x100424)),a65))+~P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),x100422),x100423)),a64))+P1(f317(f317(f319(f903(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893))),f317(f317(f242(f904(f903(a897,a897),a893),f904(f903(a897,a897),a893)),f317(f317(f299(f903(a897,a897)),x100421),x100422)),x100423)),a64))
% 94.68/94.45 [6123]~P7(x61234,x61231)+~P1(f317(f317(x61231,x61232),x61235))+P1(f317(f317(x61231,x61232),x61233))+~P1(f317(f317(x61231,x61235),x61233))
% 94.68/94.45 [6124]~P49(x61244,x61241)+~P1(f317(f317(x61241,x61242),x61245))+P1(f317(f317(x61241,x61242),x61243))+~P1(f317(f317(x61241,x61245),x61243))
% 94.68/94.45 [6125]~P15(x61254,x61251)+~P1(f317(f317(x61251,x61252),x61255))+P1(f317(f317(x61251,x61252),x61253))+~P1(f317(f317(x61251,x61255),x61253))
% 94.68/94.45 [8846]~P7(x88464,x88463)+~P1(f317(x88461,x88465))+P1(f317(x88462,f810(x88462,x88461,x88463,x88464)))+P1(f317(x88461,f809(x88462,x88461,x88463,x88464)))
% 94.68/94.45 [9080]~P7(x90804,x90803)+~P1(f317(x90802,x90805))+~P1(f317(x90801,f809(x90801,x90802,x90803,x90804)))+P1(f317(x90801,f810(x90801,x90802,x90803,x90804)))
% 94.68/94.45 [9263]~P7(x92634,x92633)+~P1(f317(x92631,x92635))+P1(f317(f317(f319(x92634),f810(x92632,x92631,x92633,x92634)),f260(x92634,x92633)))+P1(f317(x92631,f809(x92632,x92631,x92633,x92634)))
% 94.68/94.45 [9390]~P7(x93901,x93904)+~P1(f317(x93903,x93905))+~P1(f317(x93902,f809(x93902,x93903,x93904,x93901)))+P1(f317(f317(f319(x93901),f810(x93902,x93903,x93904,x93901)),f260(x93901,x93904)))
% 94.68/94.45 [9689]~P37(x96891,x96894)+P1(f317(f317(f319(f903(f898(x96891),f898(x96891))),f317(f317(f242(f898(x96891),f898(x96891)),x96892),x96893)),f137(x96891,x96894)))+~P1(f317(f317(f319(f903(f898(x96891),f898(x96891))),f317(f317(f242(f898(x96891),f898(x96891)),x96892),x96895)),f137(x96891,x96894)))+~P1(f317(f317(f319(f903(f898(x96891),f898(x96891))),f317(f317(f242(f898(x96891),f898(x96891)),x96895),x96893)),f137(x96891,x96894)))
% 94.68/94.45 [5348]~P69(x53485)+E(x53481,x53482)+~E(x53483,x53484)+~E(f317(f317(f23(x53485),x53483),x53484),f317(f317(f23(x53485),x53481),x53482))
% 94.68/94.45 [6239]~P17(x62395,x62391,x62393)+E(f317(f317(x62391,x62392),f317(x62393,x62394)),f317(x62393,x62394))+~P1(f317(f28(x62395),x62394))+~P1(f317(f317(f319(x62395),x62392),x62394))
% 94.68/94.45 [6436]~P67(x64361)+~E(f317(f317(f23(x64361),x64364),x64365),f317(f317(f23(x64361),x64362),x64363))+~P1(f317(f317(f224(x64361),x64364),x64365))+P1(f317(f317(f224(x64361),x64362),x64363))
% 94.68/94.45 [6438]~P67(x64381)+~E(f317(f317(f23(x64381),x64384),x64385),f317(f317(f23(x64381),x64382),x64383))+~P1(f317(f317(f225(x64381),x64384),x64385))+P1(f317(f317(f225(x64381),x64382),x64383))
% 94.68/94.45 [7431]~E(x74312,f317(f317(f141(x74311),x74314),x74315))+P1(f317(f317(f319(f898(x74311)),x74312),f151(x74311,x74313)))+~P1(f317(f317(f319(f898(x74311)),x74315),f151(x74311,x74313)))+~P1(f317(f317(f319(x74311),x74314),x74313))
% 94.68/94.45 [7838]~E(f317(f179(f898(x78381)),x78383),f317(f179(f898(x78382)),x78384))+~E(f317(f317(f144(f903(x78381,x78382),x78382),f246(x78381,x78382)),x78385),x78384)+~E(f317(f317(f144(f903(x78381,x78382),x78381),f241(x78381,x78382)),x78385),x78383)+E(f317(f317(f171(x78381,x78382),x78383),x78384),x78385)
% 94.68/94.45 [8171]~P108(x81711)+P1(f317(f317(f225(f904(x81711,a893)),f293(x81711,x81712,x81713)),f293(x81711,x81714,x81715)))+~P1(f317(f317(f224(x81711),x81714),x81715))+P1(f317(f317(f224(x81711),x81712),x81713))
% 94.68/94.45 [8271]~P108(x82711)+P1(f317(f317(f224(f904(x82711,a893)),f293(x82711,x82712,x82713)),f293(x82711,x82714,x82715)))+~P1(f317(f317(f224(x82711),x82713),x82715))+~P1(f317(f317(f224(x82711),x82714),x82712))
% 94.68/94.45 [8390]~P66(x83901)+P1(f317(f317(f224(x83901),x83902),x83903))+P1(f317(f317(f224(x83901),x83904),x83903))+~P1(f317(f317(f224(f904(x83901,a893)),f317(f292(x83901,x83903),x83902)),f317(f292(x83901,x83904),x83905)))
% 94.68/94.45 [8391]~P66(x83911)+P1(f317(f317(f224(x83911),x83912),x83913))+P1(f317(f317(f224(x83911),x83912),x83914))+~P1(f317(f317(f224(f904(x83911,a893)),f317(f292(x83911,x83913),x83912)),f317(f292(x83911,x83915),x83914)))
% 94.68/94.45 [8624]~P108(x86241)+~P1(f317(f317(f224(f904(x86241,a893)),f293(x86241,x86244,x86242)),f293(x86241,x86245,x86243)))+P1(f317(f317(f224(x86241),x86242),x86243))+~P1(f317(f317(f224(x86241),x86244),x86242))
% 94.68/94.45 [8625]~P108(x86251)+~P1(f317(f317(f225(f904(x86251,a893)),f293(x86251,x86254,x86252)),f293(x86251,x86255,x86253)))+P1(f317(f317(f224(x86251),x86252),x86253))+~P1(f317(f317(f224(x86251),x86254),x86252))
% 94.68/94.45 [8626]~P108(x86261)+~P1(f317(f317(f224(f904(x86261,a893)),f293(x86261,x86263,x86264)),f293(x86261,x86262,x86265)))+P1(f317(f317(f224(x86261),x86262),x86263))+~P1(f317(f317(f224(x86261),x86263),x86264))
% 94.68/94.45 [8627]~P108(x86271)+~P1(f317(f317(f225(f904(x86271,a893)),f293(x86271,x86273,x86274)),f293(x86271,x86272,x86275)))+P1(f317(f317(f224(x86271),x86272),x86273))+~P1(f317(f317(f224(x86271),x86273),x86274))
% 94.68/94.45 [6122]~P17(x61222,x61225,x61223)+E(x61221,f178(f904(x61222,a893)))+~P1(f317(f28(x61222),x61221))+E(f317(x61223,f317(f317(f299(x61222),x61224),x61221)),f317(f317(x61225,x61224),f317(x61223,x61221)))
% 94.68/94.45 [6919]~E(x69191,x69192)+~E(f317(f317(f92(f904(x69193,a893)),x69194),x69195),f178(f904(x69193,a893)))+~P1(f317(f317(f319(x69193),x69192),x69195))+~P1(f317(f317(f319(x69193),x69191),x69194))
% 94.68/94.45 [7002]~P18(x70022,x70025,x70021)+~P1(f317(f28(x70022),x70024))+E(f317(x70021,f317(f317(f299(x70022),x70023),x70024)),f317(f317(f58(x70022,x70022,x70025),x70023),x70024))+P1(f317(f317(f319(x70022),x70023),x70024))
% 94.68/94.45 [7072]~P77(x70722)+~P1(f317(f28(x70721),x70725))+E(f317(f317(f9(x70721,x70722),x70723),f317(f317(f299(x70721),x70724),x70725)),f317(f317(f75(x70722),f317(x70723,x70724)),f317(f317(f9(x70721,x70722),x70723),x70725)))+P1(f317(f317(f319(x70721),x70724),x70725))
% 94.68/94.45 [7074]~P76(x70742)+~P1(f317(f28(x70741),x70745))+E(f317(f317(f6(x70741,x70742),x70743),f317(f317(f299(x70741),x70744),x70745)),f317(f317(f74(x70742),f317(x70743,x70744)),f317(f317(f6(x70741,x70742),x70743),x70745)))+P1(f317(f317(f319(x70741),x70744),x70745))
% 94.68/94.45 [7478]~P112(x74781)+~P1(f317(f28(x74784),x74785))+~P1(f317(f317(f319(x74784),x74783),x74785))+P1(f317(f317(f277(x74781),f317(x74782,x74783)),f317(f317(f9(x74784,x74781),x74782),x74785)))
% 94.68/94.45 [7577]~P18(x75772,x75775,x75771)+~P1(f317(f28(x75772),x75774))+E(f317(x75771,f317(f317(f299(x75772),x75773),x75774)),x75773)+~E(f317(f317(f23(f904(x75772,a893)),x75774),f317(f317(f299(x75772),x75773),f178(f904(x75772,a893)))),f178(f904(x75772,a893)))
% 94.68/94.45 [7911]~P112(x79111)+~P1(f317(f317(f277(x79111),x79112),x79114))+~P1(f317(f317(f224(a897),x79113),x79115))+P1(f317(f317(f277(x79111),f317(f317(f234(x79111),x79112),x79113)),f317(f317(f234(x79111),x79114),x79115)))
% 94.68/94.45 [7939]~P3(x79391)+E(f317(f317(f30(x79391),f317(f317(f75(x79391),x79392),x79393)),f317(f317(f75(x79391),x79394),x79395)),f317(f317(f75(x79391),f317(f317(f30(x79391),x79392),x79394)),f317(f317(f30(x79391),x79393),x79395)))+~P1(f317(f317(f277(x79391),x79395),x79393))+~P1(f317(f317(f277(x79391),x79394),x79392))
% 94.68/94.45 [7943]~P85(x79431)+~P1(f317(f317(f224(x79431),x79433),x79435))+~P1(f317(f317(f224(x79431),x79432),x79434))+P1(f317(f317(f224(x79431),f317(f317(f74(x79431),x79432),x79433)),f317(f317(f74(x79431),x79434),x79435)))
% 94.68/94.45 [7944]~P66(x79441)+~P1(f317(f317(f224(x79441),x79443),x79445))+~P1(f317(f317(f224(x79441),x79442),x79444))+P1(f317(f317(f224(x79441),f317(f317(f228(x79441),x79442),x79443)),f317(f317(f228(x79441),x79444),x79445)))
% 94.68/94.45 [7945]~P66(x79451)+~P1(f317(f317(f224(x79451),x79453),x79455))+~P1(f317(f317(f224(x79451),x79452),x79454))+P1(f317(f317(f224(x79451),f317(f317(f223(x79451),x79452),x79453)),f317(f317(f223(x79451),x79454),x79455)))
% 94.68/94.45 [7946]~P99(x79461)+~P1(f317(f317(f224(x79461),x79463),x79465))+~P1(f317(f317(f224(x79461),x79462),x79464))+P1(f317(f317(f224(x79461),f317(f317(f91(x79461),x79462),x79463)),f317(f317(f91(x79461),x79464),x79465)))
% 94.68/94.45 [7947]~P105(x79471)+~P1(f317(f317(f224(x79471),x79473),x79475))+~P1(f317(f317(f224(x79471),x79472),x79474))+P1(f317(f317(f224(x79471),f317(f317(f92(x79471),x79472),x79473)),f317(f317(f92(x79471),x79474),x79475)))
% 94.68/94.45 [7948]~P87(x79481)+~P1(f317(f317(f224(x79481),x79483),x79485))+~P1(f317(f317(f225(x79481),x79482),x79484))+P1(f317(f317(f225(x79481),f317(f317(f74(x79481),x79482),x79483)),f317(f317(f74(x79481),x79484),x79485)))
% 94.68/94.45 [7949]~P87(x79491)+~P1(f317(f317(f224(x79491),x79492),x79494))+~P1(f317(f317(f225(x79491),x79493),x79495))+P1(f317(f317(f225(x79491),f317(f317(f74(x79491),x79492),x79493)),f317(f317(f74(x79491),x79494),x79495)))
% 94.68/94.45 [7950]~P87(x79501)+~P1(f317(f317(f225(x79501),x79503),x79505))+~P1(f317(f317(f225(x79501),x79502),x79504))+P1(f317(f317(f225(x79501),f317(f317(f74(x79501),x79502),x79503)),f317(f317(f74(x79501),x79504),x79505)))
% 94.68/94.45 [7951]~P112(x79511)+~P1(f317(f317(f277(x79511),x79513),x79515))+~P1(f317(f317(f277(x79511),x79512),x79514))+P1(f317(f317(f277(x79511),f317(f317(f75(x79511),x79512),x79513)),f317(f317(f75(x79511),x79514),x79515)))
% 94.68/94.45 [8087]~P146(x80875)+E(x80871,x80872)+E(x80873,x80874)+~E(f317(f317(f74(x80875),f317(f317(f75(x80875),x80873),x80871)),f317(f317(f75(x80875),x80874),x80872)),f317(f317(f74(x80875),f317(f317(f75(x80875),x80873),x80872)),f317(f317(f75(x80875),x80874),x80871)))
% 94.68/94.45 [8291]~P66(x82914)+~P1(f317(f127(x82911),x82913))+P1(f317(f317(f319(x82911),x82912),f317(f162(x82911),x82913)))+P1(f317(f127(x82911),f317(f317(f138(x82911,x82914,x82915),x82912),x82913)))
% 94.68/94.45 [8437]~P69(x84371)+E(f317(f317(f23(x84371),f317(f317(f6(a897,x84371),x84372),f317(f292(a897,x84373),x84374))),f317(f317(f6(a897,x84371),x84372),f317(f292(a897,x84373),x84375))),f317(f317(f6(a897,x84371),x84372),f317(f292(a897,x84375),x84374)))+~P1(f317(f317(f224(a897),x84375),x84374))+~P1(f317(f317(f224(a897),x84373),x84375))
% 94.68/94.45 [8438]~P76(x84381)+E(f317(f317(f74(x84381),f317(f317(f6(a897,x84381),x84382),f317(f292(a897,x84383),x84384))),f317(f317(f6(a897,x84381),x84382),f317(f292(a897,x84384),x84385))),f317(f317(f6(a897,x84381),x84382),f317(f292(a897,x84383),x84385)))+~P1(f317(f317(f224(a897),x84384),x84385))+~P1(f317(f317(f224(a897),x84383),x84384))
% 94.68/94.45 [8767]~P62(x87672)+E(x87671,f2(x87672))+E(x87673,f2(x87672))+E(f317(f317(f281(x87672),f317(f317(f23(x87672),f317(f317(f75(x87672),x87674),x87671)),f317(f317(f75(x87672),x87675),x87673))),f317(f317(f75(x87672),x87673),x87671)),f317(f317(f23(x87672),f317(f317(f281(x87672),x87674),x87673)),f317(f317(f281(x87672),x87675),x87671)))
% 94.68/94.45 [8768]~P62(x87682)+E(x87681,f2(x87682))+E(x87683,f2(x87682))+E(f317(f317(f281(x87682),f317(f317(f74(x87682),f317(f317(f75(x87682),x87684),x87681)),f317(f317(f75(x87682),x87685),x87683))),f317(f317(f75(x87682),x87683),x87681)),f317(f317(f74(x87682),f317(f317(f281(x87682),x87684),x87683)),f317(f317(f281(x87682),x87685),x87681)))
% 94.68/94.45 [8777]~E(x87772,f317(x87773,x87771))+E(x87771,f453(x87772,x87773,x87774,x87775))+~P24(x87775,x87774,x87773,f232(f904(x87775,a893)))+~P1(f317(f317(f319(x87774),x87772),f317(f300(x87775,x87774,x87773),f232(f904(x87775,a893)))))
% 94.68/94.45 [8994]~P111(x89941)+~P1(f317(f317(f225(x89941),f317(f70(x89941),x89942)),x89944))+P1(f317(f317(f225(x89941),f317(f317(f75(x89941),f317(f70(x89941),x89942)),f317(f70(x89941),x89943))),f317(f317(f75(x89941),x89944),x89945)))+~P1(f317(f317(f225(x89941),f317(f70(x89941),x89943)),x89945))
% 94.68/94.45 [9105]~P24(x91051,x91053,x91055,x91052)+~P1(f317(f28(x91053),x91054))+P1(f317(f317(f224(a897),f317(f29(x91051),x91052)),f317(f29(x91053),x91054)))+~P1(f317(f317(f224(f904(x91053,a893)),f317(f300(x91051,x91053,x91055),x91052)),x91054))
% 94.68/94.45 [9173]~P77(x91732)+~P24(x91731,x91731,x91734,x91735)+~P1(f317(f28(x91731),x91735))+E(f317(f317(f9(x91731,x91732),f317(f67(x91731,x91732,x91731,x91733),x91734)),x91735),f317(f317(f9(x91731,x91732),x91733),f317(f300(x91731,x91731,x91734),x91735)))
% 94.68/94.45 [9174]~P76(x91742)+~P24(x91741,x91741,x91744,x91745)+~P1(f317(f28(x91741),x91745))+E(f317(f317(f6(x91741,x91742),f317(f67(x91741,x91742,x91741,x91743),x91744)),x91745),f317(f317(f6(x91741,x91742),x91743),f317(f300(x91741,x91741,x91744),x91745)))
% 94.68/94.45 [9292]~P36(x92921,x92922)+~P1(f317(f317(f319(x92921),x92923),x92924))+~P1(f317(f317(f319(x92921),x92925),x92924))+~P1(f317(f317(f319(f903(x92921,x92921)),f317(f317(f242(x92921,x92921),x92925),f600(x92922,x92921,x92924))),x92922))
% 94.68/94.45 [9329]~P24(x93292,x93293,x93295,x93291)+E(x93291,f178(f904(x93292,a893)))+E(f317(f300(x93293,x93292,f346(x93294,x93293,x93292,x93291)),x93294),x93291)+~P1(f317(f317(f224(f904(x93293,a893)),f317(f300(x93292,x93293,x93295),x93291)),x93294))
% 94.68/94.45 [9824]~P66(x98245)+~P5(x98245)+P1(f317(f317(f319(x98241),f442(x98242,x98243,x98241,x98244,x98245)),x98243))+~P1(f317(f317(f225(x98245),x98244),f317(f317(f34(x98241,x98245),x98243),x98242)))
% 94.68/94.45 [9829]~P66(x98291)+~P5(x98291)+P1(f317(f317(f225(x98291),x98292),f317(x98293,f442(x98293,x98294,x98295,x98292,x98291))))+~P1(f317(f317(f225(x98291),x98292),f317(f317(f34(x98295,x98291),x98294),x98293)))
% 94.68/94.45 [9907]~P73(x99071)+~P1(f317(f60(x99071,x99071,f75(x99071),x99072,x99073),x99075))+P1(f317(f317(f319(x99071),x99072),x99073))+P1(f317(f60(x99071,x99071,f75(x99071),x99074,f317(f317(f299(x99071),x99072),x99073)),f317(f317(f75(x99071),x99074),x99075)))
% 94.68/94.45 [10119]~P77(x101192)+~P1(f317(f28(x101191),x101195))+E(f317(f317(f9(x101191,x101192),f317(f317(f7(x101191,x101192,x101192),f317(f317(f18(x101191,x101192,f904(x101192,x101192)),f317(f317(f8(a893,f904(x101192,f904(x101192,x101192)),x101191),f86(x101192)),f317(a314,x101193))),x101194)),f72(x101192))),x101195),f72(x101192))+P1(f317(f317(f319(x101191),x101193),x101195))
% 94.68/94.45 [10120]~P76(x101202)+~P1(f317(f28(x101201),x101205))+E(f317(f317(f6(x101201,x101202),f317(f317(f7(x101201,x101202,x101202),f317(f317(f18(x101201,x101202,f904(x101202,x101202)),f317(f317(f8(a893,f904(x101202,f904(x101202,x101202)),x101201),f86(x101202)),f317(a314,x101203))),x101204)),f2(x101202))),x101205),f2(x101202))+P1(f317(f317(f319(x101201),x101203),x101205))
% 94.68/94.45 [10121]~P77(x101212)+~P1(f317(f28(x101211),x101215))+E(f317(f317(f9(x101211,x101212),f317(f317(f7(x101211,x101212,x101212),f317(f317(f18(x101211,x101212,f904(x101212,x101212)),f317(f317(f8(a893,f904(x101212,f904(x101212,x101212)),x101211),f86(x101212)),f317(a314,x101213))),x101214)),f72(x101212))),x101215),f317(x101214,x101213))+~P1(f317(f317(f319(x101211),x101213),x101215))
% 94.68/94.45 [10122]~P76(x101222)+~P1(f317(f28(x101221),x101225))+E(f317(f317(f6(x101221,x101222),f317(f317(f7(x101221,x101222,x101222),f317(f317(f18(x101221,x101222,f904(x101222,x101222)),f317(f317(f8(a893,f904(x101222,f904(x101222,x101222)),x101221),f86(x101222)),f317(a314,x101223))),x101224)),f2(x101222))),x101225),f317(x101224,x101223))+~P1(f317(f317(f319(x101221),x101223),x101225))
% 94.68/94.45 [10180]~P77(x101802)+~P1(f317(f28(x101801),x101805))+E(f317(f317(f9(x101801,x101802),f317(f317(f7(x101801,x101802,x101802),f317(f317(f18(x101801,x101802,f904(x101802,x101802)),f317(f317(f8(a893,f904(x101802,f904(x101802,x101802)),x101801),f86(x101802)),f317(f317(f7(x101801,x101801,a893),a314),x101803))),x101804)),f72(x101802))),x101805),f72(x101802))+P1(f317(f317(f319(x101801),x101803),x101805))
% 94.68/94.45 [10181]~P76(x101812)+~P1(f317(f28(x101811),x101815))+E(f317(f317(f6(x101811,x101812),f317(f317(f7(x101811,x101812,x101812),f317(f317(f18(x101811,x101812,f904(x101812,x101812)),f317(f317(f8(a893,f904(x101812,f904(x101812,x101812)),x101811),f86(x101812)),f317(f317(f7(x101811,x101811,a893),a314),x101813))),x101814)),f2(x101812))),x101815),f2(x101812))+P1(f317(f317(f319(x101811),x101813),x101815))
% 94.68/94.45 [10183]~P77(x101832)+~P1(f317(f28(x101831),x101835))+E(f317(f317(f9(x101831,x101832),f317(f317(f7(x101831,x101832,x101832),f317(f317(f18(x101831,x101832,f904(x101832,x101832)),f317(f317(f8(a893,f904(x101832,f904(x101832,x101832)),x101831),f86(x101832)),f317(f317(f7(x101831,x101831,a893),a314),x101833))),x101834)),f72(x101832))),x101835),f317(x101834,x101833))+~P1(f317(f317(f319(x101831),x101833),x101835))
% 94.68/94.45 [10184]~P76(x101842)+~P1(f317(f28(x101841),x101845))+E(f317(f317(f6(x101841,x101842),f317(f317(f7(x101841,x101842,x101842),f317(f317(f18(x101841,x101842,f904(x101842,x101842)),f317(f317(f8(a893,f904(x101842,f904(x101842,x101842)),x101841),f86(x101842)),f317(f317(f7(x101841,x101841,a893),a314),x101843))),x101844)),f2(x101842))),x101845),f317(x101844,x101843))+~P1(f317(f317(f319(x101841),x101843),x101845))
% 94.68/94.45 [7942]~P69(x79422)+~P1(f317(f28(x79421),x79424))+E(f317(f317(f6(x79421,x79422),x79423),f317(f317(f23(f904(x79421,a893)),x79424),f317(f317(f299(x79421),x79425),f178(f904(x79421,a893))))),f317(f317(f6(x79421,x79422),x79423),x79424))+P1(f317(f317(f319(x79421),x79425),x79424))
% 94.68/94.45 [8445]~P131(x84452)+~P1(f317(f28(x84451),x84454))+E(f317(f317(f6(x84451,x84452),x84453),f317(f317(f23(f904(x84451,a893)),x84454),f317(f317(f299(x84451),x84455),f178(f904(x84451,a893))))),f317(f317(f23(x84452),f317(f317(f6(x84451,x84452),x84453),x84454)),f317(x84453,x84455)))+~P1(f317(f317(f319(x84451),x84455),x84454))
% 94.68/94.46 [8446]~P69(x84462)+~P1(f317(f28(x84461),x84464))+E(f317(f317(f6(x84461,x84462),x84463),f317(f317(f23(f904(x84461,a893)),x84464),f317(f317(f299(x84461),x84465),f178(f904(x84461,a893))))),f317(f317(f23(x84462),f317(f317(f6(x84461,x84462),x84463),x84464)),f317(x84463,x84465)))+~P1(f317(f317(f319(x84461),x84465),x84464))
% 94.68/94.46 [8458]~P112(x84581)+~P1(f317(f317(f224(a897),x84583),x84585))+~P1(f317(f317(f277(x84581),f317(f317(f234(x84581),x84582),x84585)),x84584))+P1(f317(f317(f277(x84581),f317(f317(f234(x84581),x84582),x84583)),x84584))
% 94.68/94.46 [8476]~P69(x84761)+~P1(f317(f28(x84762),x84764))+E(f317(f317(f23(x84761),f317(f317(f6(x84762,x84761),x84763),x84764)),f317(f317(f6(x84762,x84761),x84763),x84765)),f317(f317(f6(x84762,x84761),x84763),f317(f317(f23(f904(x84762,a893)),x84764),x84765)))+~P1(f317(f317(f224(f904(x84762,a893)),x84765),x84764))
% 94.68/94.46 [8495]P1(f317(f28(x84951),f317(x84952,x84953)))+~P1(f317(f28(x84954),x84955))+~P1(f317(f317(f319(x84954),x84953),x84955))+~P1(f317(f28(x84951),f317(f317(f34(x84954,f904(x84951,a893)),x84955),x84952)))
% 94.68/94.46 [8950]~P8(x89501,x89505,x89504)+~E(f317(f275(x89501,x89501,x89504),f317(f317(f299(x89501),x89502),f178(f904(x89501,a893)))),f317(f275(x89501,x89501,x89504),f317(f317(f299(x89501),x89503),f178(f904(x89501,a893)))))+~P1(f317(f317(f319(x89501),x89503),x89505))+P1(f317(f317(f319(f903(x89501,x89501)),f317(f317(f242(x89501,x89501),x89502),x89503)),x89504))
% 94.68/94.46 [9248]~P1(f317(x92481,x92485))+P1(f317(x92481,f326(x92481,x92482,x92483,x92484)))+P1(f317(x92481,f889(x92481,x92482,x92483,x92484)))+~P1(f317(f317(f319(x92484),x92485),f317(f317(f91(f904(x92484,a893)),x92483),x92482)))
% 94.68/94.46 [9437]~P1(f317(x94371,x94375))+P1(f317(x94371,f889(x94371,x94372,x94373,x94374)))+P1(f317(f317(f319(x94374),f326(x94371,x94372,x94373,x94374)),x94372))+~P1(f317(f317(f319(x94374),x94375),f317(f317(f91(f904(x94374,a893)),x94373),x94372)))
% 94.68/94.46 [9438]~P1(f317(x94381,x94385))+P1(f317(x94381,f326(x94381,x94382,x94383,x94384)))+P1(f317(f317(f319(x94384),f889(x94381,x94382,x94383,x94384)),x94383))+~P1(f317(f317(f319(x94384),x94385),f317(f317(f91(f904(x94384,a893)),x94383),x94382)))
% 94.68/94.46 [9442]P1(f317(x94421,x94422))+~P1(f317(x94421,f331(x94421,x94423,x94424,x94425)))+~P1(f317(x94421,f330(x94421,x94423,x94424,x94425)))+~P1(f317(f317(f319(x94425),x94422),f317(f317(f91(f904(x94425,a893)),x94424),x94423)))
% 94.68/94.46 [9447]~P37(x94471,x94474)+~P1(f317(f317(f319(f903(x94471,x94471)),f317(f317(f242(x94471,x94471),x94472),x94475)),x94474))+P1(f317(f317(f319(f903(x94471,x94471)),f317(f317(f242(x94471,x94471),x94472),x94473)),x94474))+~P1(f317(f317(f319(f903(x94471,x94471)),f317(f317(f242(x94471,x94471),x94475),x94473)),x94474))
% 94.68/94.46 [9486]E(x94861,x94862)+~P1(f317(f317(f319(f903(x94863,x94863)),f317(f317(f242(x94863,x94863),x94861),x94862)),f297(x94863,x94865)))+P1(f317(f317(f319(x94863),x94861),x94864))+~P1(f317(f317(f224(f904(f903(x94863,x94863),a893)),x94865),f317(f317(f244(x94863,x94863),x94864),f317(f16(f904(x94863,a893),x94863),x94864))))
% 94.68/94.46 [9504]P1(f317(x95041,x95042))+~P1(f317(x95041,f330(x95041,x95044,x95045,x95043)))+P1(f317(f317(f319(x95043),f331(x95041,x95044,x95045,x95043)),x95044))+~P1(f317(f317(f319(x95043),x95042),f317(f317(f91(f904(x95043,a893)),x95045),x95044)))
% 94.68/94.46 [9505]P1(f317(x95051,x95052))+~P1(f317(x95051,f331(x95051,x95054,x95055,x95053)))+P1(f317(f317(f319(x95053),f330(x95051,x95054,x95055,x95053)),x95055))+~P1(f317(f317(f319(x95053),x95052),f317(f317(f91(f904(x95053,a893)),x95055),x95054)))
% 94.68/94.46 [9573]P1(f317(x95731,x95732))+P1(f317(f317(f319(x95733),f331(x95731,x95734,x95735,x95733)),x95734))+P1(f317(f317(f319(x95733),f330(x95731,x95734,x95735,x95733)),x95735))+~P1(f317(f317(f319(x95733),x95732),f317(f317(f91(f904(x95733,a893)),x95735),x95734)))
% 94.68/94.46 [9575]~P1(f317(x95752,x95755))+P1(f317(f317(f319(x95751),f326(x95752,x95753,x95754,x95751)),x95753))+P1(f317(f317(f319(x95751),f889(x95752,x95753,x95754,x95751)),x95754))+~P1(f317(f317(f319(x95751),x95755),f317(f317(f91(f904(x95751,a893)),x95754),x95753)))
% 94.68/94.46 [9731]~P8(x97311,x97315,x97314)+~P1(f317(f317(f319(x97311),x97313),x97315))+P1(f317(f317(f319(f903(x97311,x97311)),f317(f317(f242(x97311,x97311),x97312),x97313)),x97314))+~P1(f317(f317(f224(f904(x97311,a893)),f317(f275(x97311,x97311,x97314),f317(f317(f299(x97311),x97313),f178(f904(x97311,a893))))),f317(f275(x97311,x97311,x97314),f317(f317(f299(x97311),x97312),f178(f904(x97311,a893))))))
% 94.68/94.46 [9858]~P66(x98585)+~P5(x98585)+P1(f317(f317(f319(x98581),f584(x98582,x98583,x98584,x98581,x98585)),x98584))+~P1(f317(f317(f225(x98585),f317(f317(f35(x98581,x98585),x98584),x98583)),x98582))
% 94.68/94.46 [9890]~P85(x98905)+~P81(x98905)+P1(f317(f317(f319(x98901),f673(x98902,x98903,x98904,x98901,x98905)),f317(f162(x98901),x98904)))+P1(f317(f317(f224(x98905),f317(f155(x98905),f317(f317(f144(x98901,x98905),x98903),x98904))),f317(f155(x98905),f317(f317(f144(x98901,x98905),x98902),x98904))))
% 94.68/94.46 [9998]~P66(x99981)+~P5(x99981)+P1(f317(f317(f225(x99981),f317(x99982,f584(x99983,x99982,x99984,x99985,x99981))),x99983))+~P1(f317(f317(f225(x99981),f317(f317(f35(x99985,x99981),x99984),x99982)),x99983))
% 94.68/94.46 [10137]~P85(x101371)+~P81(x101371)+~P1(f317(f317(f224(x101371),f317(x101373,f673(x101375,x101373,x101374,x101372,x101371))),f317(x101375,f673(x101375,x101373,x101374,x101372,x101371))))+P1(f317(f317(f224(x101371),f317(f155(x101371),f317(f317(f144(x101372,x101371),x101373),x101374))),f317(f155(x101371),f317(f317(f144(x101372,x101371),x101375),x101374))))
% 94.68/94.46 [8789]~P77(x87891)+~P1(f317(f28(x87894),x87895))+~P1(f317(f317(f319(x87894),x87893),x87895))+E(f317(f317(f75(x87891),f317(x87892,x87893)),f317(f317(f9(x87894,x87891),x87892),f317(f317(f23(f904(x87894,a893)),x87895),f317(f317(f299(x87894),x87893),f178(f904(x87894,a893)))))),f317(f317(f9(x87894,x87891),x87892),x87895))
% 94.68/94.46 [8791]~P76(x87911)+~P1(f317(f28(x87914),x87915))+~P1(f317(f317(f319(x87914),x87913),x87915))+E(f317(f317(f74(x87911),f317(x87912,x87913)),f317(f317(f6(x87914,x87911),x87912),f317(f317(f23(f904(x87914,a893)),x87915),f317(f317(f299(x87914),x87913),f178(f904(x87914,a893)))))),f317(f317(f6(x87914,x87911),x87912),x87915))
% 94.68/94.46 [8851]~P18(x88511,x88514,x88515)+~P1(f317(f28(x88511),x88512))+E(f317(f317(f23(f904(x88511,a893)),x88512),f317(f317(f299(x88511),x88513),f178(f904(x88511,a893)))),f178(f904(x88511,a893)))+E(f317(f317(x88514,x88513),f317(x88515,f317(f317(f23(f904(x88511,a893)),x88512),f317(f317(f299(x88511),x88513),f178(f904(x88511,a893)))))),f317(x88515,f317(f317(f299(x88511),x88513),x88512)))
% 94.68/94.46 [9226]~P76(x92261)+~P1(f317(f28(x92262),x92265))+~P1(f317(f28(x92262),x92264))+E(f317(f317(f74(x92261),f317(f317(f6(x92262,x92261),x92263),f317(f317(f91(f904(x92262,a893)),x92264),x92265))),f317(f317(f6(x92262,x92261),x92263),f317(f317(f92(f904(x92262,a893)),x92264),x92265))),f317(f317(f74(x92261),f317(f317(f6(x92262,x92261),x92263),x92264)),f317(f317(f6(x92262,x92261),x92263),x92265)))
% 94.68/94.46 [9228]~P77(x92281)+~P1(f317(f28(x92282),x92285))+~P1(f317(f28(x92282),x92284))+E(f317(f317(f75(x92281),f317(f317(f9(x92282,x92281),x92283),f317(f317(f91(f904(x92282,a893)),x92284),x92285))),f317(f317(f9(x92282,x92281),x92283),f317(f317(f92(f904(x92282,a893)),x92284),x92285))),f317(f317(f75(x92281),f317(f317(f9(x92282,x92281),x92283),x92284)),f317(f317(f9(x92282,x92281),x92283),x92285)))
% 94.68/94.46 [9370]~P69(x93701)+~P1(f317(f28(x93702),x93705))+~P1(f317(f28(x93702),x93704))+E(f317(f317(f23(x93701),f317(f317(f74(x93701),f317(f317(f6(x93702,x93701),x93703),x93704)),f317(f317(f6(x93702,x93701),x93703),x93705))),f317(f317(f6(x93702,x93701),x93703),f317(f317(f92(f904(x93702,a893)),x93704),x93705))),f317(f317(f6(x93702,x93701),x93703),f317(f317(f91(f904(x93702,a893)),x93704),x93705)))
% 94.68/94.46 [9589]~P24(x95891,x95892,x95893,x95895)+~P24(x95891,x95892,x95893,x95894)+P24(x95891,x95892,x95893,f317(f317(f91(f904(x95891,a893)),x95894),x95895))+~E(f317(f317(f92(f904(x95892,a893)),f317(f300(x95891,x95892,x95893),f317(f317(f23(f904(x95891,a893)),x95894),x95895))),f317(f300(x95891,x95892,x95893),f317(f317(f23(f904(x95891,a893)),x95895),x95894))),f178(f904(x95892,a893)))
% 94.68/94.46 [9706]E(x97061,f2(a1))+~P1(f317(f317(f225(a1),f2(a1)),x97063))+~P1(f317(f44(x97062,x97061),f317(f317(f242(a1,a1),x97064),x97065)))+P1(f317(f44(x97062,f317(f317(f75(a1),x97061),x97063)),f317(f317(f242(a1,a1),f317(f317(f30(a1),x97064),x97063)),f317(f317(f74(a1),f317(f317(f75(a1),x97061),f40(a1,x97064,x97063))),x97065))))
% 94.68/94.46 [9714]~P1(f317(f317(f225(a897),f2(a897)),x97143))+~P1(f317(f317(f225(a897),f2(a897)),x97142))+~P1(f317(f43(x97141,x97142),f317(f317(f242(a897,a897),x97144),x97145)))+P1(f317(f43(x97141,f317(f317(f75(a897),x97142),x97143)),f317(f317(f242(a897,a897),f317(f317(f30(a897),x97144),x97143)),f317(f317(f74(a897),f317(f317(f75(a897),x97142),f40(a897,x97144,x97143))),x97145))))
% 94.68/94.46 [9763]~P77(x97631)+~P1(f317(f28(x97632),x97635))+~P1(f317(f28(x97632),x97634))+E(f317(f317(f75(x97631),f317(f317(f317(f59(x97631,x97632,f75(x97631)),x97633),f72(x97631)),f317(f317(f91(f904(x97632,a893)),x97634),x97635))),f317(f317(f317(f59(x97631,x97632,f75(x97631)),x97633),f72(x97631)),f317(f317(f92(f904(x97632,a893)),x97634),x97635))),f317(f317(f75(x97631),f317(f317(f317(f59(x97631,x97632,f75(x97631)),x97633),f72(x97631)),x97634)),f317(f317(f317(f59(x97631,x97632,f75(x97631)),x97633),f72(x97631)),x97635)))
% 94.68/94.46 [9765]~E(f317(f317(f165(x97651),x97655),x97652),f317(f317(f165(x97651),x97655),x97653))+P1(f317(f317(f319(f903(f898(x97651),f898(x97651))),f317(f317(f242(f898(x97651),f898(x97651)),x97652),x97653)),f137(x97651,x97654)))+~P1(f317(f317(f225(a897),x97655),f317(f317(f228(a897),f317(f179(f898(x97651)),x97652)),f317(f179(f898(x97651)),x97653))))+~P1(f317(f317(f319(f903(x97651,x97651)),f317(f317(f242(x97651,x97651),f317(f317(f154(x97651),x97652),x97655)),f317(f317(f154(x97651),x97653),x97655))),x97654))
% 94.68/94.46 [9879]~P85(x98795)+~P144(x98795)+P1(f317(f317(f319(x98791),f408(x98792,x98793,x98794,x98791,x98795)),x98794))+P1(f317(f317(f224(x98795),f317(f317(f6(x98791,x98795),x98793),x98794)),f317(f317(f75(x98795),f317(f90(x98795),f317(f29(x98791),x98794))),x98792)))
% 94.68/94.46 [10055]~P85(x100551)+~P144(x100551)+~P1(f317(f317(f224(x100551),f317(x100553,f408(x100555,x100553,x100554,x100552,x100551))),x100555))+P1(f317(f317(f224(x100551),f317(f317(f6(x100552,x100551),x100553),x100554)),f317(f317(f75(x100551),f317(f90(x100551),f317(f29(x100552),x100554))),x100555)))
% 94.68/94.46 [8819]E(f317(f317(f124(x88191),x88192),x88193),f317(f317(f124(x88191),x88194),x88195))+~E(f317(f317(f165(x88191),f317(f179(f898(x88191)),x88192)),x88194),x88192)+~E(f317(f317(f124(x88191),f317(f317(f128(x88191),f317(f179(f898(x88191)),x88192)),x88194)),x88195),x88193)+P1(f317(f317(f224(a897),f317(f179(f898(x88191)),x88194)),f317(f179(f898(x88191)),x88192)))
% 94.68/94.46 [8949]E(f317(f317(f124(x89491),x89492),x89493),f317(f317(f124(x89491),x89494),x89495))+~E(f317(f317(f165(x89491),f317(f179(f898(x89491)),x89492)),x89494),x89492)+~E(x89493,f317(f317(f124(x89491),f317(f317(f128(x89491),f317(f179(f898(x89491)),x89492)),x89494)),x89495))+~P1(f317(f317(f224(a897),f317(f179(f898(x89491)),x89492)),f317(f179(f898(x89491)),x89494)))
% 94.68/94.46 [10201]~P1(f317(x102015,x102014))+~P1(f317(f28(x102012),f317(f252(x102012),x102015)))+P1(f317(f28(x102011),f317(f252(x102011),f317(f317(f7(x102011,x102012,a893),x102013),x102014))))+~P1(f317(f28(x102011),f317(f252(x102011),f317(f317(f8(f904(x102012,a893),a893,x102011),f81(x102012)),f317(f317(f8(f904(x102012,a893),f904(x102012,a893),x102011),f317(f18(x102012,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102012),a315),x102015))),x102013)))))
% 94.68/94.46 [10277]~P1(f317(f28(x102772),x102775))+~P1(f317(f317(f319(x102772),x102774),x102775))+P1(f317(f28(x102771),f317(f252(x102771),f317(f317(f7(x102771,x102772,a893),x102773),x102774))))+~P1(f317(f28(x102771),f317(f252(x102771),f317(f317(f8(f904(x102772,a893),a893,x102771),f81(x102772)),f317(f317(f8(f904(x102772,a893),f904(x102772,a893),x102771),f317(f18(x102772,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102772),a315),f317(f317(f7(x102772,f904(x102772,a893),a893),f319(x102772)),x102775)))),x102773)))))
% 94.68/94.46 [8605]~P19(x86055,x86051,x86056,x86052)+E(f317(f67(x86051,x86051,x86051,f317(x86052,x86053)),f317(x86052,x86054)),f317(f67(x86051,x86051,x86051,f317(x86052,x86054)),f317(x86052,x86053)))+~P1(f317(f28(x86055),x86054))+~P1(f317(f28(x86055),x86053))
% 94.68/94.46 [7998]~P24(x79981,x79982,x79984,x79983)+~E(f317(x79984,x79986),x79985)+E(f317(f71(x79981,x79982,x79983,x79984),x79985),x79986)+~P1(f317(f317(f319(x79981),x79986),x79983))
% 94.68/94.46 [7999]~P24(x79991,x79992,x79994,x79993)+~E(f317(x79994,x79996),x79995)+E(f317(f85(x79991,x79992,x79993,x79994),x79995),x79996)+~P1(f317(f317(f319(x79991),x79996),x79993))
% 94.68/94.46 [8192]~P20(x81926,x81921,x81924,x81922)+E(f317(f67(x81921,x81921,x81921,f317(x81922,x81923)),f317(x81924,x81925)),f317(x81922,x81923))+~P1(f317(f28(x81926),x81923))+~P1(f317(f317(f319(x81926),x81925),x81923))
% 94.68/94.46 [9320]E(x93201,x93202)+~E(f317(f85(x93203,x93204,x93205,x93206),x93201),f317(f85(x93203,x93204,x93205,x93206),x93202))+~P1(f317(f317(f319(x93204),x93202),f317(f300(x93203,x93204,x93206),x93205)))+~P1(f317(f317(f319(x93204),x93201),f317(f300(x93203,x93204,x93206),x93205)))
% 94.68/94.46 [9421]~P19(x94213,x94211,x94216,x94212)+E(f317(f67(x94211,x94211,x94211,f317(x94212,f317(f317(f23(f904(x94213,a893)),x94214),f317(f317(f299(x94213),x94215),f178(f904(x94213,a893)))))),f317(x94216,x94215)),f317(x94212,x94214))+~P1(f317(f28(x94213),x94214))+~P1(f317(f317(f319(x94213),x94215),x94214))
% 94.68/94.46 [7079]~P4(x70791)+~E(f40(x70791,x70793,x70794),f40(x70791,x70796,x70794))+~E(f40(x70791,x70792,x70794),f40(x70791,x70795,x70794))+E(f40(x70791,f317(f317(f23(x70791),x70792),x70793),x70794),f40(x70791,f317(f317(f23(x70791),x70795),x70796),x70794))
% 94.68/94.46 [7080]~P3(x70801)+~E(f40(x70801,x70803,x70804),f40(x70801,x70806,x70804))+~E(f40(x70801,x70802,x70804),f40(x70801,x70805,x70804))+E(f40(x70801,f317(f317(f74(x70801),x70802),x70803),x70804),f40(x70801,f317(f317(f74(x70801),x70805),x70806),x70804))
% 94.68/94.46 [7081]~P3(x70811)+~E(f40(x70811,x70813,x70814),f40(x70811,x70816,x70814))+~E(f40(x70811,x70812,x70814),f40(x70811,x70815,x70814))+E(f40(x70811,f317(f317(f75(x70811),x70812),x70813),x70814),f40(x70811,f317(f317(f75(x70811),x70815),x70816),x70814))
% 94.68/94.46 [7893]~P16(x78931,x78932,x78933)+~P1(f317(f28(x78931),x78936))+E(f317(f317(f58(x78931,x78932,x78933),x78934),f317(f317(f299(x78931),x78935),x78936)),f317(f317(f58(x78931,x78932,x78933),f317(f317(x78933,x78935),x78934)),x78936))+P1(f317(f317(f319(x78931),x78935),x78936))
% 94.68/94.46 [7957]~P5(x79571)+P1(f317(f317(f224(x79571),x79572),f317(x79573,x79574)))+~P1(f317(f317(f319(x79575),x79574),x79576))+~P1(f317(f317(f224(x79571),x79572),f317(f317(f35(x79575,x79571),x79576),x79573)))
% 94.68/94.46 [8114]~P16(x81141,x81142,x81143)+~P1(f317(f28(x81141),x81146))+E(f317(f317(f58(x81141,x81142,x81143),x81144),f317(f317(f299(x81141),x81145),x81146)),f317(f317(x81143,x81145),f317(f317(f58(x81141,x81142,x81143),x81144),x81146)))+P1(f317(f317(f319(x81141),x81145),x81146))
% 94.68/94.46 [8210]~P66(x82103)+~P1(f317(x82102,x82105))+~P13(x82103,f317(f317(f144(x82101,x82103),x82104),x82106))+E(f317(f126(x82101,x82102),f317(f317(f138(x82101,x82103,x82104),x82105),x82106)),f317(f317(f138(x82101,x82103,x82104),x82105),f317(f126(x82101,x82102),x82106)))
% 94.68/94.46 [8233]E(x82331,x82332)+E(x82333,f2(a1))+~P1(f317(f44(x82334,x82333),f317(f317(f242(a1,a1),x82335),x82332)))+~P1(f317(f44(x82334,x82333),f317(f317(f242(a1,a1),x82336),x82331)))
% 94.68/94.46 [8234]E(x82341,x82342)+E(x82343,f2(a1))+~P1(f317(f44(x82344,x82343),f317(f317(f242(a1,a1),x82342),x82345)))+~P1(f317(f44(x82344,x82343),f317(f317(f242(a1,a1),x82341),x82346)))
% 94.68/94.46 [8257]~P19(x82572,x82575,x82576,x82571)+~P1(f317(f28(x82572),x82574))+E(f317(x82571,f317(f317(f299(x82572),x82573),x82574)),f317(f67(x82575,x82575,x82575,f317(x82571,x82574)),f317(x82576,x82573)))+P1(f317(f317(f319(x82572),x82573),x82574))
% 94.68/94.46 [8479]~P20(x84795,x84791,x84796,x84792)+E(f317(f67(x84791,x84791,x84791,f317(x84792,x84793)),f317(x84792,x84794)),f317(x84792,x84793))+~P1(f317(f28(x84795),x84793))+~P1(f317(f317(f224(f904(x84795,a893)),x84794),x84793))
% 94.68/94.46 [9636]~P24(x96361,x96362,x96364,x96363)+~P1(f317(f317(f319(x96362),x96365),f317(f300(x96361,x96362,x96364),x96363)))+P1(f317(f317(f319(x96361),f317(f71(x96361,x96362,x96363,x96364),x96365)),x96366))+~P1(f317(f317(f224(f904(x96361,a893)),x96363),x96366))
% 94.68/94.46 [10009]~P76(x100092)+~E(f530(x100091,x100093,x100095,x100096,x100094,x100092),f531(x100091,x100093,x100095,x100096,x100094,x100092))+~P1(f317(f28(x100094),x100096))+E(f317(f317(f6(x100091,x100092),x100093),f317(f300(x100094,x100091,x100095),x100096)),f317(f317(f6(x100094,x100092),f317(f67(x100091,x100092,x100094,x100093),x100095)),x100096))
% 94.68/94.46 [10037]~P76(x100376)+E(f317(x100371,f530(x100372,x100373,x100371,x100374,x100375,x100376)),f317(x100371,f531(x100372,x100373,x100371,x100374,x100375,x100376)))+E(f317(f317(f6(x100372,x100376),x100373),f317(f300(x100375,x100372,x100371),x100374)),f317(f317(f6(x100375,x100376),f317(f67(x100372,x100376,x100375,x100373),x100371)),x100374))+~P1(f317(f28(x100375),x100374))
% 94.68/94.46 [10087]~P76(x100872)+~E(f317(x100873,f317(x100875,f531(x100871,x100873,x100875,x100876,x100874,x100872))),f2(x100872))+~P1(f317(f28(x100874),x100876))+E(f317(f317(f6(x100871,x100872),x100873),f317(f300(x100874,x100871,x100875),x100876)),f317(f317(f6(x100874,x100872),f317(f67(x100871,x100872,x100874,x100873),x100875)),x100876))
% 94.68/94.46 [10145]~P76(x101452)+~P1(f317(f28(x101454),x101456))+E(f317(f317(f6(x101451,x101452),x101453),f317(f300(x101454,x101451,x101455),x101456)),f317(f317(f6(x101454,x101452),f317(f67(x101451,x101452,x101454,x101453),x101455)),x101456))+P1(f317(f317(f319(x101454),f531(x101451,x101453,x101455,x101456,x101454,x101452)),x101456))
% 94.68/94.46 [10146]~P76(x101462)+~P1(f317(f28(x101464),x101466))+E(f317(f317(f6(x101461,x101462),x101463),f317(f300(x101464,x101461,x101465),x101466)),f317(f317(f6(x101464,x101462),f317(f67(x101461,x101462,x101464,x101463),x101465)),x101466))+P1(f317(f317(f319(x101464),f530(x101461,x101463,x101465,x101466,x101464,x101462)),x101466))
% 94.68/94.46 [10276]~P77(x102761)+~P1(f317(f28(x102762),x102766))+E(f317(f317(f317(f59(x102761,x102762,f75(x102761)),f317(f317(f18(x102762,f904(x102763,a893),x102761),f317(f317(f7(x102762,x102761,f904(f904(x102763,a893),x102761)),f317(f317(f8(f904(x102763,x102761),f904(x102761,f904(f904(x102763,a893),x102761)),x102762),f59(x102761,x102763,f75(x102761))),x102764)),f72(x102761))),x102765)),f72(x102761)),x102766),f317(f317(f317(f59(x102761,f903(x102762,x102763),f75(x102761)),f317(f247(x102762,x102763,x102761),x102764)),f72(x102761)),f317(f317(f244(x102762,x102763),x102766),x102765)))+P1(f317(f317(f319(x102762),f473(x102764,x102765,x102763,x102766,x102762,x102761)),x102766))
% 94.68/94.46 [10298]~P77(x102981)+~P1(f317(f28(x102982),x102986))+E(f317(f317(f317(f59(x102981,x102982,f75(x102981)),f317(f317(f18(x102982,f904(x102983,a893),x102981),f317(f317(f7(x102982,x102981,f904(f904(x102983,a893),x102981)),f317(f317(f8(f904(x102983,x102981),f904(x102981,f904(f904(x102983,a893),x102981)),x102982),f59(x102981,x102983,f75(x102981))),x102984)),f72(x102981))),x102985)),f72(x102981)),x102986),f317(f317(f317(f59(x102981,f903(x102982,x102983),f75(x102981)),f317(f247(x102982,x102983,x102981),x102984)),f72(x102981)),f317(f317(f244(x102982,x102983),x102986),x102985)))+~P1(f317(f28(x102983),f317(x102985,f473(x102984,x102985,x102983,x102986,x102982,x102981))))
% 94.68/94.46 [8389]~P20(x83892,x83895,x83896,x83891)+~P1(f317(f28(x83892),x83894))+~P1(f317(f28(x83892),x83893))+E(f317(x83891,f317(f317(f91(f904(x83892,a893)),x83893),x83894)),f317(f67(x83895,x83895,x83895,f317(x83891,x83893)),f317(x83891,x83894)))
% 94.68/94.46 [8606]~P5(x86061)+P1(f317(f317(f224(x86061),f317(x86062,x86063)),x86064))+~P1(f317(f317(f319(x86065),x86063),x86066))+~P1(f317(f317(f224(x86061),f317(f317(f34(x86065,x86061),x86066),x86062)),x86064))
% 94.68/94.46 [9035]~P24(x90352,x90351,x90353,x90356)+E(f317(f317(f23(f904(x90351,a893)),f317(f300(x90352,x90351,x90353),x90354)),f317(f300(x90352,x90351,x90353),x90355)),f317(f300(x90352,x90351,x90353),f317(f317(f23(f904(x90352,a893)),x90354),x90355)))+~P1(f317(f317(f224(f904(x90352,a893)),x90355),x90356))+~P1(f317(f317(f224(f904(x90352,a893)),x90354),x90356))
% 94.68/94.46 [9036]~P24(x90362,x90361,x90363,x90366)+E(f317(f317(f92(f904(x90361,a893)),f317(f300(x90362,x90361,x90363),x90364)),f317(f300(x90362,x90361,x90363),x90365)),f317(f300(x90362,x90361,x90363),f317(f317(f92(f904(x90362,a893)),x90364),x90365)))+~P1(f317(f317(f224(f904(x90362,a893)),x90365),x90366))+~P1(f317(f317(f224(f904(x90362,a893)),x90364),x90366))
% 94.68/94.46 [9294]E(x92941,x92942)+~P54(x92943,x92944,x92945)+~P1(f317(f317(f319(f903(x92943,x92944)),f317(f317(f242(x92943,x92944),x92946),x92942)),x92945))+~P1(f317(f317(f319(f903(x92943,x92944)),f317(f317(f242(x92943,x92944),x92946),x92941)),x92945))
% 94.68/94.46 [10083]~P73(x100831)+~E(f317(x100833,f546(x100834,x100836,x100833,x100835,x100832,x100831)),f317(x100836,f546(x100834,x100836,x100833,x100835,x100832,x100831)))+~P1(f317(f28(x100832),x100835))+E(f317(f317(f317(f59(x100831,x100832,f75(x100831)),x100833),x100834),x100835),f317(f317(f317(f59(x100831,x100832,f75(x100831)),x100836),x100834),x100835))
% 94.68/94.46 [10143]~P73(x101431)+~P1(f317(f28(x101432),x101435))+E(f317(f317(f317(f59(x101431,x101432,f75(x101431)),x101433),x101434),x101435),f317(f317(f317(f59(x101431,x101432,f75(x101431)),x101436),x101434),x101435))+P1(f317(f317(f319(x101432),f546(x101434,x101433,x101436,x101435,x101432,x101431)),x101435))
% 94.68/94.46 [8833]~P73(x88331)+~P1(f317(f28(x88332),x88336))+P1(f317(f317(f319(x88332),x88335),x88336))+E(f317(f317(f317(f59(x88331,x88332,f75(x88331)),x88333),x88334),f317(f317(f299(x88332),x88335),x88336)),f317(f317(f75(x88331),f317(x88333,x88335)),f317(f317(f317(f59(x88331,x88332,f75(x88331)),x88333),x88334),x88336)))
% 94.68/94.46 [8886]~P8(x88861,x88866,x88863)+~P11(x88861,f904(x88862,a893),x88863,x88865)+~P1(f317(f317(f319(x88861),x88864),x88866))+E(f317(f317(f34(x88861,f904(x88862,a893)),f317(f275(x88861,x88861,x88863),f317(f317(f299(x88861),x88864),f178(f904(x88861,a893))))),x88865),f317(x88865,x88864))
% 94.68/94.46 [9012]~P16(x90123,x90124,x90121)+~P1(f317(f28(x90123),x90126))+~P1(f317(f317(f319(x90123),x90122),x90126))+E(f317(f317(x90121,x90122),f317(f317(f58(x90123,x90124,x90121),x90125),f317(f317(f23(f904(x90123,a893)),x90126),f317(f317(f299(x90123),x90122),f178(f904(x90123,a893)))))),f317(f317(f58(x90123,x90124,x90121),x90125),x90126))
% 94.68/94.46 [9304]~P19(x93043,x93041,x93046,x93042)+~P1(f317(f28(x93043),x93045))+~P1(f317(f28(x93043),x93044))+E(f317(f67(x93041,x93041,x93041,f317(x93042,f317(f317(f91(f904(x93043,a893)),x93044),x93045))),f317(x93042,f317(f317(f92(f904(x93043,a893)),x93044),x93045))),f317(f67(x93041,x93041,x93041,f317(x93042,x93044)),f317(x93042,x93045)))
% 94.68/94.46 [9659]~E(x96593,f317(f317(f149(x96591,x96592),x96595),x96596))+P1(f317(f317(f319(f903(f898(x96591),f898(x96591))),f317(f317(f242(f898(x96591),f898(x96591)),x96592),x96593)),f147(x96591,x96594)))+~P1(f317(f317(f225(a897),x96595),f317(f179(f898(x96591)),x96592)))+~P1(f317(f317(f319(f903(x96591,x96591)),f317(f317(f242(x96591,x96591),f317(f317(f154(x96591),x96592),x96595)),x96596)),x96594))
% 94.68/94.46 [10160]~P77(x101602)+~P1(f317(f28(x101601),x101606))+P1(f317(f317(f319(x101601),f475(x101604,x101605,x101603,x101606,x101601,x101602)),x101606))+E(f317(f317(f9(x101601,x101602),f317(f317(f18(x101601,f904(x101603,a893),x101602),f317(f317(f8(f904(x101603,x101602),f904(f904(x101603,a893),x101602),x101601),f9(x101603,x101602)),x101604)),x101605)),x101606),f317(f317(f9(f903(x101601,x101603),x101602),f317(f247(x101601,x101603,x101602),x101604)),f317(f317(f244(x101601,x101603),x101606),x101605)))
% 94.68/94.46 [10161]~P76(x101612)+~P1(f317(f28(x101611),x101616))+P1(f317(f317(f319(x101611),f476(x101614,x101615,x101613,x101616,x101611,x101612)),x101616))+E(f317(f317(f6(x101611,x101612),f317(f317(f18(x101611,f904(x101613,a893),x101612),f317(f317(f8(f904(x101613,x101612),f904(f904(x101613,a893),x101612),x101611),f6(x101613,x101612)),x101614)),x101615)),x101616),f317(f317(f6(f903(x101611,x101613),x101612),f317(f247(x101611,x101613,x101612),x101614)),f317(f317(f244(x101611,x101613),x101616),x101615)))
% 94.68/94.46 [10199]~P77(x101992)+~P1(f317(f28(x101991),x101996))+~P1(f317(f28(x101993),f317(x101995,f475(x101994,x101995,x101993,x101996,x101991,x101992))))+E(f317(f317(f9(x101991,x101992),f317(f317(f18(x101991,f904(x101993,a893),x101992),f317(f317(f8(f904(x101993,x101992),f904(f904(x101993,a893),x101992),x101991),f9(x101993,x101992)),x101994)),x101995)),x101996),f317(f317(f9(f903(x101991,x101993),x101992),f317(f247(x101991,x101993,x101992),x101994)),f317(f317(f244(x101991,x101993),x101996),x101995)))
% 94.68/94.46 [10200]~P76(x102002)+~P1(f317(f28(x102001),x102006))+~P1(f317(f28(x102003),f317(x102005,f476(x102004,x102005,x102003,x102006,x102001,x102002))))+E(f317(f317(f6(x102001,x102002),f317(f317(f18(x102001,f904(x102003,a893),x102002),f317(f317(f8(f904(x102003,x102002),f904(f904(x102003,a893),x102002),x102001),f6(x102003,x102002)),x102004)),x102005)),x102006),f317(f317(f6(f903(x102001,x102003),x102002),f317(f247(x102001,x102003,x102002),x102004)),f317(f317(f244(x102001,x102003),x102006),x102005)))
% 94.68/94.46 [10182]~P77(x101822)+~P1(f317(f28(x101821),x101826))+P1(f317(f317(f319(x101821),x101823),x101826))+E(f317(f317(f9(x101821,x101822),f317(f317(f7(x101821,x101822,x101822),f317(f317(f18(x101821,x101822,f904(x101822,x101822)),f317(f317(f8(a893,f904(x101822,f904(x101822,x101822)),x101821),f86(x101822)),f317(f317(f7(x101821,x101821,a893),a314),x101823))),x101824)),x101825)),x101826),f317(f317(f234(x101822),x101825),f317(f29(x101821),x101826)))
% 94.68/94.46 [10185]~P77(x101852)+~P1(f317(f28(x101851),x101856))+~P1(f317(f317(f319(x101851),x101853),x101856))+E(f317(f317(f9(x101851,x101852),f317(f317(f7(x101851,x101852,x101852),f317(f317(f18(x101851,x101852,f904(x101852,x101852)),f317(f317(f8(a893,f904(x101852,f904(x101852,x101852)),x101851),f86(x101852)),f317(f317(f7(x101851,x101851,a893),a314),x101853))),x101854)),x101855)),x101856),f317(f317(f75(x101852),f317(x101854,x101853)),f317(f317(f234(x101852),x101855),f317(f317(f23(a897),f317(f29(x101851),x101856)),f72(a897)))))
% 94.68/94.46 [10263]~P1(f317(f28(x102631),x102635))+~P1(f317(f28(x102632),x102633))+P1(f317(f317(f319(x102632),f494(x102636,x102634,x102633,x102632,x102635,x102631)),x102633))+E(f317(f317(f6(x102631,a897),f317(f317(f8(f904(x102632,a893),a897,x102631),f29(x102632)),f317(f317(f8(f904(x102632,a893),f904(x102632,a893),x102631),f252(x102632)),f317(f317(f8(f904(x102632,a893),f904(x102632,a893),x102631),f317(f18(x102632,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102632),a315),f317(f317(f7(x102632,f904(x102632,a893),a893),f319(x102632)),x102633)))),x102634)))),x102635),f317(f317(f75(a897),x102636),f317(f29(x102632),x102633)))
% 94.68/94.46 [10264]~P1(f317(f28(x102641),x102645))+~P1(f317(f28(x102642),x102643))+P1(f317(f317(f319(x102642),f495(x102646,x102644,x102643,x102642,x102645,x102641)),x102643))+E(f317(f317(f6(x102641,a897),f317(f317(f8(f904(x102642,a893),a897,x102641),f29(x102642)),f317(f317(f8(f904(x102642,a893),f904(x102642,a893),x102641),f252(x102642)),f317(f317(f8(f904(x102642,a893),f904(x102642,a893),x102641),f317(f18(x102642,a893,a893),f317(f317(f8(a893,f904(a893,a893),x102642),a315),f317(f317(f7(x102642,f904(x102642,a893),a893),f319(x102642)),x102643)))),x102644)))),x102645),f317(f317(f6(x102642,a897),x102646),x102643))
% 94.68/94.46 [10311]~P1(f317(f28(x103112),x103113))+~P1(f317(f28(x103111),x103115))+~E(f317(f29(x103111),f317(f252(x103111),f317(f317(f18(x103111,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103111),a315),f317(f317(f7(x103111,f904(x103111,a893),a893),f319(x103111)),x103115))),f317(f317(f7(x103111,x103112,a893),x103114),f494(x103116,x103114,x103113,x103112,x103115,x103111))))),x103116)+E(f317(f317(f6(x103111,a897),f317(f317(f8(f904(x103112,a893),a897,x103111),f29(x103112)),f317(f317(f8(f904(x103112,a893),f904(x103112,a893),x103111),f252(x103112)),f317(f317(f8(f904(x103112,a893),f904(x103112,a893),x103111),f317(f18(x103112,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103112),a315),f317(f317(f7(x103112,f904(x103112,a893),a893),f319(x103112)),x103113)))),x103114)))),x103115),f317(f317(f75(a897),x103116),f317(f29(x103112),x103113)))
% 94.68/94.46 [10313]~P1(f317(f28(x103132),x103133))+~P1(f317(f28(x103131),x103135))+~E(f317(f29(x103131),f317(f252(x103131),f317(f317(f18(x103131,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103131),a315),f317(f317(f7(x103131,f904(x103131,a893),a893),f319(x103131)),x103135))),f317(f317(f7(x103131,x103132,a893),x103134),f495(x103136,x103134,x103133,x103132,x103135,x103131))))),f317(x103136,f495(x103136,x103134,x103133,x103132,x103135,x103131)))+E(f317(f317(f6(x103131,a897),f317(f317(f8(f904(x103132,a893),a897,x103131),f29(x103132)),f317(f317(f8(f904(x103132,a893),f904(x103132,a893),x103131),f252(x103132)),f317(f317(f8(f904(x103132,a893),f904(x103132,a893),x103131),f317(f18(x103132,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103132),a315),f317(f317(f7(x103132,f904(x103132,a893),a893),f319(x103132)),x103133)))),x103134)))),x103135),f317(f317(f6(x103132,a897),x103136),x103133))
% 94.68/94.46 [9935]E(x99351,x99352)+~P16(x99353,x99354,x99355)+~P1(f317(f60(x99353,x99354,x99355,x99356,x99357),x99352))+~P1(f317(f60(x99353,x99354,x99355,x99356,x99357),x99351))
% 94.68/94.46 [9735]P1(f317(x97351,x97352))+~P1(f317(f317(f319(x97357),x97352),f317(x97356,x97354)))+~P1(f317(x97351,f438(x97351,x97356,x97355,x97353,x97357)))+~P1(f317(f317(f319(x97353),x97354),x97355))
% 94.68/94.46 [10174]~P16(x101747,x101746,x101741)+E(f317(f317(x101741,x101742),f587(x101742,x101743,x101744,x101745,x101741,x101746,x101747)),x101743)+~P1(f317(f60(x101747,x101746,x101741,x101745,x101744),x101743))+~P1(f317(f317(f319(x101747),x101742),x101744))
% 94.68/94.46 [10241]~P16(x102411,x102412,x102413)+~P1(f317(f60(x102411,x102412,x102413,x102414,x102415),x102417))+P1(f317(f60(x102411,x102412,x102413,x102414,f317(f317(f23(f904(x102411,a893)),x102415),f317(f317(f299(x102411),x102416),f178(f904(x102411,a893))))),f587(x102416,x102417,x102415,x102414,x102413,x102412,x102411)))+~P1(f317(f317(f319(x102411),x102416),x102415))
% 94.68/94.46 [9377]P25(x93771,x93772,x93773,x93774,x93775)+~P25(x93771,x93772,x93773,x93776,x93777)+~E(f317(f300(x93771,x93772,x93773),x93774),x93775)+~P1(f317(f317(f224(f904(x93771,a893)),x93774),x93776))
% 94.68/94.46 [9627]~P25(x96271,x96272,x96273,x96275,x96277)+~P25(x96271,x96272,x96273,x96274,x96276)+P25(x96271,x96272,x96273,f317(f317(f91(f904(x96271,a893)),x96274),x96275),f317(f317(f91(f904(x96272,a893)),x96276),x96277))+~E(f317(f317(f92(f904(x96272,a893)),x96276),x96277),f178(f904(x96272,a893)))
% 94.68/94.46 [9632]~P73(x96321)+~P24(x96325,x96322,x96326,x96327)+~P1(f317(f28(x96325),x96327))+E(f317(f317(f317(f59(x96321,x96322,f75(x96321)),x96323),x96324),f317(f300(x96325,x96322,x96326),x96327)),f317(f317(f317(f59(x96321,x96325,f75(x96321)),f317(f67(x96322,x96321,x96325,x96323),x96326)),x96324),x96327))
% 94.68/94.46 [9758]~E(f317(f317(f299(x97581),x97585),x97586),f317(f317(f299(x97581),x97582),x97583))+~P1(f317(f60(x97581,x97581,x97584,x97582,x97583),x97587))+P1(f317(f317(f319(x97581),x97582),x97583))+P1(f317(f56(x97581,x97584,f317(f317(f299(x97581),x97585),x97586)),x97587))
% 94.68/94.46 [9842]P1(f317(x98421,x98422))+~P1(f317(f317(f319(x98423),x98422),f317(x98424,x98427)))+~P1(f317(f317(f319(x98426),x98427),x98425))+P1(f317(f317(f319(x98423),f438(x98421,x98424,x98425,x98426,x98423)),f317(f317(f34(x98426,f904(x98423,a893)),x98425),x98424)))
% 94.68/94.46 [9859]~P24(x98592,x98591,x98595,x98594)+~P24(x98591,x98593,x98596,f317(f300(x98592,x98591,x98595),x98594))+E(f317(f317(f67(x98591,x98592,x98593,f71(x98592,x98591,x98594,x98595)),f71(x98591,x98593,f317(f300(x98592,x98591,x98595),x98594),x98596)),x98597),f317(f71(x98592,x98593,x98594,f317(f67(x98591,x98593,x98592,x98596),x98595)),x98597))+~P1(f317(f317(f319(x98593),x98597),f317(f300(x98591,x98593,x98596),f317(f300(x98592,x98591,x98595),x98594))))
% 94.68/94.46 [9860]~P24(x98602,x98601,x98605,x98604)+~P24(x98601,x98603,x98606,f317(f300(x98602,x98601,x98605),x98604))+E(f317(f317(f67(x98601,x98602,x98603,f85(x98602,x98601,x98604,x98605)),f85(x98601,x98603,f317(f300(x98602,x98601,x98605),x98604),x98606)),x98607),f317(f85(x98602,x98603,x98604,f317(f67(x98601,x98603,x98602,x98606),x98605)),x98607))+~P1(f317(f317(f319(x98603),x98607),f317(f300(x98601,x98603,x98606),f317(f300(x98602,x98601,x98605),x98604))))
% 94.68/94.46 [10175]~P16(x101757,x101756,x101751)+E(f317(f317(x101751,x101752),f607(x101753,x101754,x101752,x101755,x101751,x101756,x101757)),x101753)+P1(f317(f317(f319(x101757),x101752),x101754))+~P1(f317(f60(x101757,x101756,x101751,x101755,f317(f317(f299(x101757),x101752),x101754)),x101753))
% 94.68/94.46 [10240]~P16(x102401,x102404,x102405)+P1(f317(f60(x102401,x102404,x102405,x102406,x102403),f607(x102407,x102403,x102402,x102406,x102405,x102404,x102401)))+P1(f317(f317(f319(x102401),x102402),x102403))+~P1(f317(f60(x102401,x102404,x102405,x102406,f317(f317(f299(x102401),x102402),x102403)),x102407))
% 94.68/94.46 [9917]E(x99171,f2(a1))+~P1(f317(f44(x99173,x99171),f317(f317(f242(a1,a1),x99175),x99177)))+~P1(f317(f44(x99172,x99171),f317(f317(f242(a1,a1),x99174),x99176)))+P1(f317(f44(f317(f317(f74(a1),x99172),x99173),x99171),f317(f317(f242(a1,a1),f317(f317(f74(a1),f317(f317(f74(a1),x99174),x99175)),f317(f317(f30(a1),f317(f317(f74(a1),x99176),x99177)),x99171))),f40(a1,f317(f317(f74(a1),x99176),x99177),x99171))))
% 94.68/94.46 [9919]~P1(f317(f317(f225(a897),f2(a897)),x99193))+~P1(f317(f43(x99192,x99193),f317(f317(f242(a897,a897),x99195),x99197)))+~P1(f317(f43(x99191,x99193),f317(f317(f242(a897,a897),x99194),x99196)))+P1(f317(f43(f317(f317(f74(a897),x99191),x99192),x99193),f317(f317(f242(a897,a897),f317(f317(f74(a897),f317(f317(f74(a897),x99194),x99195)),f317(f317(f30(a897),f317(f317(f74(a897),x99196),x99197)),x99193))),f40(a897,f317(f317(f74(a897),x99196),x99197),x99193))))
% 94.68/94.46 [10310]~P76(x103102)+~P1(f317(f28(x103103),x103105))+~P1(f317(f28(x103101),x103107))+E(f317(f317(f6(x103101,x103102),f317(f317(f18(x103101,f904(x103103,a893),x103102),f317(f317(f8(f904(x103103,x103102),f904(f904(x103103,a893),x103102),x103101),f6(x103103,x103102)),x103104)),f317(f317(f8(f904(x103103,a893),f904(x103103,a893),x103101),f252(x103103)),f317(f317(f8(f904(x103103,a893),f904(x103103,a893),x103101),f317(f18(x103103,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103103),a315),f317(f317(f7(x103103,f904(x103103,a893),a893),f319(x103103)),x103105)))),x103106)))),x103107),f317(f317(f6(x103103,x103102),f317(f317(f18(x103103,f904(x103101,a893),x103102),f317(f317(f8(f904(x103101,x103102),f904(f904(x103101,a893),x103102),x103103),f6(x103101,x103102)),f317(f7(x103101,x103103,x103102),x103104))),f317(f317(f8(f904(x103101,a893),f904(x103101,a893),x103103),f252(x103101)),f317(f317(f8(f904(x103101,a893),f904(x103101,a893),x103103),f317(f18(x103101,a893,a893),f317(f317(f8(a893,f904(a893,a893),x103101),a315),f317(f317(f7(x103101,f904(x103101,a893),a893),f319(x103101)),x103107)))),f317(f7(x103101,x103103,a893),x103106))))),x103105))
% 94.68/94.46 [10261]~P21(x102618,x102617,x102616,x102615,x102611)+~E(f317(x102612,f836(x102614,x102612,x102613,x102611,x102615,x102616,x102617)),f317(x102614,f836(x102614,x102612,x102613,x102611,x102615,x102616,x102617)))+E(f317(f317(x102611,x102612),x102613),f317(f317(x102611,x102614),x102613))+~P1(f317(f28(x102617),x102613))
% 94.68/94.46 [9794]~P22(x97947,x97946,x97941,x97948,x97942,x97944)+E(f317(f317(x97941,f317(x97942,x97943)),f317(x97944,x97945)),f317(x97944,x97945))+~P1(f317(f28(x97946),x97945))+~P1(f317(f317(f319(x97946),x97943),x97945))
% 94.68/94.46 [9798]~P12(x97986,x97981,x97982,x97988,x97983,x97984)+~P8(x97986,x97987,x97988)+P11(x97981,x97982,x97983,f317(x97984,x97985))+~P1(f317(f317(f319(x97986),x97985),x97987))
% 94.68/94.46 [10283]~P21(x102838,x102835,x102837,x102836,x102831)+E(f317(f317(x102831,x102832),x102833),f317(f317(x102831,x102834),x102833))+~P1(f317(f28(x102835),x102833))+P1(f317(f317(f319(x102835),f836(x102832,x102834,x102833,x102831,x102836,x102837,x102835)),x102833))
% 94.68/94.46 [10360]~P1(f317(f317(x103601,x103606),x103605))+P1(f317(f317(x103601,f826(x103601,x103604,x103605,x103606,x103603,x103602,x103607,x103608)),f829(x103601,x103604,x103605,x103606,x103603,x103602,x103607,x103608)))+P1(f317(f317(x103601,x103602),x103603))+~P1(f317(f317(f319(f903(f903(x103608,x103607),f903(x103608,x103607))),f317(f317(f242(f903(x103608,x103607),f903(x103608,x103607)),f317(f317(f242(x103608,x103607),x103602),x103603)),f317(f317(f242(x103608,x103607),x103606),x103605))),f297(f903(x103608,x103607),x103604)))
% 94.68/94.46 [10361]~P1(f317(f317(x103611,x103616),x103615))+P1(f317(f317(x103611,f818(x103611,x103614,x103613,x103612,x103615,x103616,x103617,x103618)),f819(x103611,x103614,x103613,x103612,x103615,x103616,x103617,x103618)))+P1(f317(f317(x103611,x103612),x103613))+~P1(f317(f317(f319(f903(f903(x103618,x103617),f903(x103618,x103617))),f317(f317(f242(f903(x103618,x103617),f903(x103618,x103617)),f317(f317(f242(x103618,x103617),x103616),x103615)),f317(f317(f242(x103618,x103617),x103612),x103613))),f297(f903(x103618,x103617),x103614)))
% 94.68/94.46 [10371]~P1(f317(f317(x103711,f827(x103711,x103716,x103715,x103714,x103713,x103712,x103717,x103718)),f828(x103711,x103716,x103715,x103714,x103713,x103712,x103717,x103718)))+P1(f317(f317(x103711,x103712),x103713))+~P1(f317(f317(x103711,x103714),x103715))+~P1(f317(f317(f319(f903(f903(x103718,x103717),f903(x103718,x103717))),f317(f317(f242(f903(x103718,x103717),f903(x103718,x103717)),f317(f317(f242(x103718,x103717),x103712),x103713)),f317(f317(f242(x103718,x103717),x103714),x103715))),f297(f903(x103718,x103717),x103716)))
% 94.68/94.46 [10372]~P1(f317(f317(x103721,f820(x103721,x103726,x103723,x103722,x103725,x103724,x103727,x103728)),f821(x103721,x103726,x103723,x103722,x103725,x103724,x103727,x103728)))+P1(f317(f317(x103721,x103722),x103723))+~P1(f317(f317(x103721,x103724),x103725))+~P1(f317(f317(f319(f903(f903(x103728,x103727),f903(x103728,x103727))),f317(f317(f242(f903(x103728,x103727),f903(x103728,x103727)),f317(f317(f242(x103728,x103727),x103724),x103725)),f317(f317(f242(x103728,x103727),x103722),x103723))),f297(f903(x103728,x103727),x103726)))
% 94.68/94.46 [10385]~P1(f317(f317(x103851,x103856),x103857))+P1(f317(f317(x103851,x103852),x103853))+P1(f317(f317(f319(f903(f903(x103854,x103855),f903(x103854,x103855))),f317(f317(f242(f903(x103854,x103855),f903(x103854,x103855)),f317(f317(f242(x103854,x103855),x103856),x103857)),f317(f317(f242(x103854,x103855),f818(x103851,x103858,x103853,x103852,x103857,x103856,x103855,x103854)),f819(x103851,x103858,x103853,x103852,x103857,x103856,x103855,x103854)))),f297(f903(x103854,x103855),x103858)))+~P1(f317(f317(f319(f903(f903(x103854,x103855),f903(x103854,x103855))),f317(f317(f242(f903(x103854,x103855),f903(x103854,x103855)),f317(f317(f242(x103854,x103855),x103856),x103857)),f317(f317(f242(x103854,x103855),x103852),x103853))),f297(f903(x103854,x103855),x103858)))
% 94.68/94.46 [10387]~P1(f317(f317(x103871,x103878),x103877))+P1(f317(f317(x103871,x103872),x103873))+P1(f317(f317(f319(f903(f903(x103874,x103875),f903(x103874,x103875))),f317(f317(f242(f903(x103874,x103875),f903(x103874,x103875)),f317(f317(f242(x103874,x103875),f826(x103871,x103876,x103877,x103878,x103873,x103872,x103875,x103874)),f829(x103871,x103876,x103877,x103878,x103873,x103872,x103875,x103874))),f317(f317(f242(x103874,x103875),x103878),x103877))),f297(f903(x103874,x103875),x103876)))+~P1(f317(f317(f319(f903(f903(x103874,x103875),f903(x103874,x103875))),f317(f317(f242(f903(x103874,x103875),f903(x103874,x103875)),f317(f317(f242(x103874,x103875),x103872),x103873)),f317(f317(f242(x103874,x103875),x103878),x103877))),f297(f903(x103874,x103875),x103876)))
% 94.68/94.46 [9404]~P19(x94047,x94041,x94048,x94043)+~P1(f317(f28(x94047),x94045))+~P1(f317(f28(x94047),x94044))+E(f317(f67(x94041,x94041,x94042,f317(x94043,x94044)),f317(f67(x94041,x94041,x94042,f317(x94043,x94045)),x94046)),f317(f67(x94041,x94041,x94042,f317(x94043,x94045)),f317(f67(x94041,x94041,x94042,f317(x94043,x94044)),x94046)))
% 94.68/94.46 [9413]~P33(x94131,x94132,x94133,x94134,x94137)+P33(x94131,x94132,x94133,f317(f317(f149(x94131,x94134),x94135),x94136),f317(f317(f149(x94132,x94137),x94135),x94138))+~P1(f317(f317(x94133,x94136),x94138))+~P1(f317(f317(f225(a897),x94135),f317(f179(f898(x94131)),x94134)))
% 94.68/94.46 [9414]~P33(x94141,x94142,x94143,x94144,x94147)+P33(x94141,x94142,x94143,f317(f317(f149(x94141,x94144),x94145),x94146),f317(f317(f149(x94142,x94147),x94145),x94148))+~P1(f317(f317(x94143,x94146),x94148))+~P1(f317(f317(f225(a897),x94145),f317(f179(f898(x94142)),x94147)))
% 94.68/94.46 [9493]~P24(x94932,x94932,x94935,x94936)+~P21(x94933,x94932,x94937,x94938,x94931)+~P1(f317(f28(x94932),x94936))+E(f317(f317(x94931,f317(f67(x94932,x94933,x94932,x94934),x94935)),x94936),f317(f317(x94931,x94934),f317(f300(x94932,x94932,x94935),x94936)))
% 94.68/94.46 [9759]P25(x97591,x97592,x97593,x97594,x97595)+~P25(x97592,x97596,x97597,x97595,x97598)+~P25(x97591,x97596,f317(f67(x97592,x97596,x97591,x97597),x97593),x97594,x97598)+~P1(f317(f317(f224(f904(x97592,a893)),f317(f300(x97591,x97592,x97593),x97594)),x97595))
% 94.68/94.46 [9796]~P23(x97967,x97962,x97965,x97968,x97966,x97961)+~P1(f317(f28(x97962),x97964))+E(f317(x97961,f317(f317(f299(x97962),x97963),x97964)),f317(f317(x97965,f317(x97966,x97963)),f317(x97961,x97964)))+P1(f317(f317(f319(x97962),x97963),x97964))
% 94.68/94.46 [9807]~P22(x98076,x98075,x98071,x98077,x98078,x98072)+E(f317(f317(x98071,f317(x98072,x98073)),f317(x98072,x98074)),f317(x98072,x98074))+~P1(f317(f28(x98075),x98074))+~P1(f317(f317(f224(f904(x98075,a893)),x98073),x98074))
% 94.68/94.46 [9391]P1(f317(f317(f319(f903(f898(x93911),f898(x93911))),f317(f317(f242(f898(x93911),f898(x93911)),x93912),x93913)),f147(x93911,x93914)))+~E(x93913,f317(f317(f124(x93911),x93915),f317(f317(f141(x93911),x93916),x93917)))+~E(x93912,f317(f317(f124(x93911),x93915),f317(f317(f141(x93911),x93918),x93917)))+~P1(f317(f317(f319(f903(x93911,x93911)),f317(f317(f242(x93911,x93911),x93918),x93916)),x93914))
% 94.68/94.46 [9801]~P22(x98016,x98012,x98015,x98017,x98018,x98011)+~P1(f317(f28(x98012),x98014))+~P1(f317(f28(x98012),x98013))+E(f317(x98011,f317(f317(f91(f904(x98012,a893)),x98013),x98014)),f317(f317(x98015,f317(x98011,x98013)),f317(x98011,x98014)))
% 94.68/94.46 [10350]~P24(x103504,x103502,x103505,x103508)+E(f317(f317(f35(x103501,f904(x103502,a893)),x103503),f317(f317(f8(f904(x103504,a893),f904(x103502,a893),x103501),f300(x103504,x103502,x103505)),x103506)),f317(f300(x103504,x103502,x103505),f317(f317(f35(x103501,f904(x103504,a893)),x103503),x103506)))+~P1(f317(f317(f319(x103501),x103507),x103503))+P1(f317(f317(f319(x103501),f597(x103507,x103506,x103503,x103501,x103508,x103505,x103502,x103504)),x103503))
% 94.68/94.46 [10376]~P24(x103764,x103762,x103765,x103767)+E(f317(f317(f35(x103761,f904(x103762,a893)),x103763),f317(f317(f8(f904(x103764,a893),f904(x103762,a893),x103761),f300(x103764,x103762,x103765)),x103766)),f317(f300(x103764,x103762,x103765),f317(f317(f35(x103761,f904(x103764,a893)),x103763),x103766)))+~P1(f317(f317(f319(x103761),x103768),x103763))+~P1(f317(f317(f224(f904(x103764,a893)),f317(x103766,f597(x103768,x103766,x103763,x103761,x103767,x103765,x103762,x103764))),x103767))
% 94.68/94.46 [10388]~P1(f317(f317(x103881,x103888),x103887))+P1(f317(f317(x103881,x103882),x103883))+~P1(f317(f317(f319(f903(f903(x103884,x103885),f903(x103884,x103885))),f317(f317(f242(f903(x103884,x103885),f903(x103884,x103885)),f317(f317(f242(x103884,x103885),x103882),x103883)),f317(f317(f242(x103884,x103885),x103888),x103887))),f297(f903(x103884,x103885),x103886)))+P1(f317(f317(f319(f903(f903(x103884,x103885),f903(x103884,x103885))),f317(f317(f242(f903(x103884,x103885),f903(x103884,x103885)),f317(f317(f242(x103884,x103885),f827(x103881,x103886,x103887,x103888,x103883,x103882,x103885,x103884)),f828(x103881,x103886,x103887,x103888,x103883,x103882,x103885,x103884))),f317(f317(f242(x103884,x103885),f826(x103881,x103886,x103887,x103888,x103883,x103882,x103885,x103884)),f829(x103881,x103886,x103887,x103888,x103883,x103882,x103885,x103884)))),x103886))
% 94.68/94.46 [10389]~P1(f317(f317(x103891,x103898),x103897))+P1(f317(f317(x103891,x103892),x103893))+~P1(f317(f317(f319(f903(f903(x103894,x103895),f903(x103894,x103895))),f317(f317(f242(f903(x103894,x103895),f903(x103894,x103895)),f317(f317(f242(x103894,x103895),x103898),x103897)),f317(f317(f242(x103894,x103895),x103892),x103893))),f297(f903(x103894,x103895),x103896)))+P1(f317(f317(f319(f903(f903(x103894,x103895),f903(x103894,x103895))),f317(f317(f242(f903(x103894,x103895),f903(x103894,x103895)),f317(f317(f242(x103894,x103895),f818(x103891,x103896,x103893,x103892,x103897,x103898,x103895,x103894)),f819(x103891,x103896,x103893,x103892,x103897,x103898,x103895,x103894))),f317(f317(f242(x103894,x103895),f820(x103891,x103896,x103893,x103892,x103897,x103898,x103895,x103894)),f821(x103891,x103896,x103893,x103892,x103897,x103898,x103895,x103894)))),x103896))
% 94.68/94.46 [9869]~P23(x98697,x98695,x98691,x98698,x98692,x98694)+~P1(f317(f28(x98695),x98696))+~P1(f317(f317(f319(x98695),x98693),x98696))+E(f317(f317(x98691,f317(x98692,x98693)),f317(x98694,f317(f317(f23(f904(x98695,a893)),x98696),f317(f317(f299(x98695),x98693),f178(f904(x98695,a893)))))),f317(x98694,x98696))
% 94.68/94.46 [9877]~P23(x98776,x98773,x98771,x98777,x98778,x98772)+~P1(f317(f28(x98773),x98775))+~P1(f317(f28(x98773),x98774))+E(f317(f317(x98771,f317(x98772,f317(f317(f91(f904(x98773,a893)),x98774),x98775))),f317(x98772,f317(f317(f92(f904(x98773,a893)),x98774),x98775))),f317(f317(x98771,f317(x98772,x98774)),f317(x98772,x98775)))
% 94.68/94.46 [9959]P41(x99591,x99592,x99593,x99594,x99595,f317(f317(x99593,x99596),x99597))+~P41(x99591,x99592,x99593,x99594,f317(f317(f23(f904(x99591,a893)),x99595),f317(f317(f299(x99591),x99598),f178(f904(x99591,a893)))),x99599)+~E(f317(f317(x99593,x99596),x99597),f317(f317(x99593,x99598),x99599))+~P1(f317(f317(f319(x99591),x99598),x99595))
% 94.68/94.46 [9901]~P12(x99016,x99017,x99018,x99019,x990110,x99011)+E(f317(f317(x99011,x99012),x99013),f317(f317(x99011,x99014),x99015))+~P1(f317(f317(f319(f903(x99017,x99017)),f317(f317(f242(x99017,x99017),x99013),x99015)),x990110))+~P1(f317(f317(f319(f903(x99016,x99016)),f317(f317(f242(x99016,x99016),x99012),x99014)),x99019))
% 94.68/94.46 [7009]E(x70091,x70092)+~P1(f317(f317(f224(a1),f2(a1)),x70092))+~P1(f317(f317(f224(a1),f2(a1)),x70091))+~P1(f317(f317(f277(a1),x70092),x70091))+~P1(f317(f317(f277(a1),x70091),x70092))
% 94.68/94.46 [9497]~P100(x94972)+E(x94971,f178(f904(x94972,a893)))+~P1(f317(f28(x94972),x94971))+P1(f317(f317(f319(x94972),f13(x94972,x94971)),x94971))+~P1(f317(f317(f319(x94972),f317(f317(f91(x94972),f334(x94971,x94972)),f335(x94971,x94972))),f317(f317(f299(x94972),f334(x94971,x94972)),f317(f317(f299(x94972),f335(x94971,x94972)),f178(f904(x94972,a893))))))
% 94.68/94.46 [9498]~P100(x94982)+E(x94981,f178(f904(x94982,a893)))+~P1(f317(f28(x94982),x94981))+P1(f317(f317(f319(x94982),f10(x94982,x94981)),x94981))+~P1(f317(f317(f319(x94982),f317(f317(f92(x94982),f414(x94981,x94982)),f421(x94981,x94982))),f317(f317(f299(x94982),f414(x94981,x94982)),f317(f317(f299(x94982),f421(x94981,x94982)),f178(f904(x94982,a893))))))
% 94.68/94.46 [9529]~P73(x95292)+E(x95291,f178(f904(x95292,a893)))+~P1(f317(f28(x95292),x95291))+P1(f317(f317(f319(x95292),f317(f57(x95292,f75(x95292)),x95291)),x95291))+~P1(f317(f317(f319(x95292),f317(f317(f75(x95292),f789(x95291,x95292)),f804(x95291,x95292))),f317(f317(f299(x95292),f789(x95291,x95292)),f317(f317(f299(x95292),f804(x95291,x95292)),f178(f904(x95292,a893))))))
% 94.68/94.46 [9534]~P66(x95342)+E(x95341,f178(f904(x95342,a893)))+~P1(f317(f28(x95342),x95341))+P1(f317(f317(f319(x95342),f11(x95342,f228(x95342),x95341)),x95341))+~P1(f317(f317(f319(x95342),f317(f317(f228(x95342),f875(x95341,x95342)),f876(x95341,x95342))),f317(f317(f299(x95342),f875(x95341,x95342)),f317(f317(f299(x95342),f876(x95341,x95342)),f178(f904(x95342,a893))))))
% 94.68/94.46 [9535]~P66(x95352)+E(x95351,f178(f904(x95352,a893)))+~P1(f317(f28(x95352),x95351))+P1(f317(f317(f319(x95352),f12(x95352,f223(x95352),x95351)),x95351))+~P1(f317(f317(f319(x95352),f317(f317(f223(x95352),f332(x95351,x95352)),f333(x95351,x95352))),f317(f317(f299(x95352),f332(x95351,x95352)),f317(f317(f299(x95352),f333(x95351,x95352)),f178(f904(x95352,a893))))))
% 94.68/94.46 [6631]~P89(x66312)+E(x66311,f2(x66312))+~E(f317(f317(f74(x66312),x66313),x66311),f2(x66312))+~P1(f317(f317(f224(x66312),f2(x66312)),x66313))+~P1(f317(f317(f224(x66312),f2(x66312)),x66311))
% 94.68/94.46 [6632]~P89(x66322)+E(x66321,f2(x66322))+~E(f317(f317(f74(x66322),x66321),x66323),f2(x66322))+~P1(f317(f317(f224(x66322),f2(x66322)),x66323))+~P1(f317(f317(f224(x66322),f2(x66322)),x66321))
% 94.68/94.46 [7178]~P66(x71782)+~P13(x71782,x71781)+E(x71781,f103(x71782))+~P1(f317(f317(f319(x71782),x71783),f317(f162(x71782),f685(x71781,x71782))))+P1(f317(f317(f224(x71782),f705(x71781,x71782)),x71783))
% 94.68/94.46 [7347]~P66(x73471)+E(f14(x73471,x73472),x73473)+~P1(f317(f28(x73471),x73472))+~P1(f317(f317(f224(x73471),x73473),f544(x73473,x73472,x73471)))+~P1(f317(f317(f319(x73471),x73473),x73472))
% 94.68/94.46 [7380]~P66(x73801)+~P13(x73801,x73802)+~P13(x73801,x73803)+P13(x73801,f317(f317(f124(x73801),x73802),x73803))+P1(f317(f317(f319(x73801),f691(x73803,x73802,x73801)),f317(f162(x73801),x73802)))
% 94.68/94.46 [7381]~P66(x73811)+~P13(x73811,x73812)+~P13(x73811,x73813)+P13(x73811,f317(f317(f124(x73811),x73812),x73813))+P1(f317(f317(f319(x73811),f692(x73813,x73812,x73811)),f317(f162(x73811),x73813)))
% 94.68/94.46 [7444]~P66(x74441)+E(f14(x74441,x74442),x74443)+~P1(f317(f28(x74441),x74442))+P1(f317(f317(f319(x74441),f544(x74443,x74442,x74441)),x74442))+~P1(f317(f317(f319(x74441),x74443),x74442))
% 94.68/94.46 [7445]~P66(x74451)+E(f15(x74451,x74452),x74453)+~P1(f317(f28(x74451),x74452))+P1(f317(f317(f319(x74451),f545(x74453,x74452,x74451)),x74452))+~P1(f317(f317(f319(x74451),x74453),x74452))
% 94.68/94.46 [8018]~P66(x80181)+E(f15(x80181,x80182),x80183)+~P1(f317(f28(x80181),x80182))+~P1(f317(f317(f319(x80181),x80183),x80182))+~P1(f317(f317(f224(x80181),f545(x80183,x80182,x80181)),x80183))
% 94.68/94.46 [8336]~P66(x83361)+~P13(x83361,x83362)+~P13(x83361,x83363)+P13(x83361,f317(f317(f124(x83361),x83362),x83363))+~P1(f317(f317(f224(x83361),f691(x83363,x83362,x83361)),f692(x83363,x83362,x83361)))
% 94.68/94.46 [9129]~P66(x91292)+E(x91291,f178(f904(x91292,a893)))+~E(f317(f317(f228(x91292),f317(x91293,f336(x91291,x91293,x91292))),f317(x91293,f343(x91291,x91293,x91292))),f317(x91293,f317(f317(f228(x91292),f336(x91291,x91293,x91292)),f343(x91291,x91293,x91292))))+E(f14(x91292,f317(f300(x91292,x91292,x91293),x91291)),f317(x91293,f14(x91292,x91291)))+~P1(f317(f28(x91292),x91291))
% 94.68/94.46 [9130]~P66(x91302)+E(x91301,f178(f904(x91302,a893)))+~E(f317(f317(f223(x91302),f317(x91303,f337(x91301,x91303,x91302))),f317(x91303,f342(x91301,x91303,x91302))),f317(x91303,f317(f317(f223(x91302),f337(x91301,x91303,x91302)),f342(x91301,x91303,x91302))))+E(f15(x91302,f317(f300(x91302,x91302,x91303),x91301)),f317(x91303,f15(x91302,x91301)))+~P1(f317(f28(x91302),x91301))
% 94.68/94.46 [9131]~P100(x91312)+E(x91311,f178(f904(x91312,a893)))+~E(f317(f317(f91(x91312),f317(x91313,f344(x91311,x91313,x91312))),f317(x91313,f345(x91311,x91313,x91312))),f317(x91313,f317(f317(f91(x91312),f344(x91311,x91313,x91312)),f345(x91311,x91313,x91312))))+E(f13(x91312,f317(f300(x91312,x91312,x91313),x91311)),f317(x91313,f13(x91312,x91311)))+~P1(f317(f28(x91312),x91311))
% 94.68/94.46 [9132]~P100(x91322)+E(x91321,f178(f904(x91322,a893)))+~E(f317(f317(f92(x91322),f317(x91323,f413(x91321,x91323,x91322))),f317(x91323,f423(x91321,x91323,x91322))),f317(x91323,f317(f317(f92(x91322),f413(x91321,x91323,x91322)),f423(x91321,x91323,x91322))))+E(f10(x91322,f317(f300(x91322,x91322,x91323),x91321)),f317(x91323,f10(x91322,x91321)))+~P1(f317(f28(x91322),x91321))
% 94.68/94.46 [9200]~P66(x92002)+E(x92001,f178(f904(x92002,a893)))+~E(f317(f317(f228(x92002),f317(x92003,f338(x92001,x92003,x92002))),f317(x92003,f341(x92001,x92003,x92002))),f317(x92003,f317(f317(f228(x92002),f338(x92001,x92003,x92002)),f341(x92001,x92003,x92002))))+E(f11(x92002,f228(x92002),f317(f300(x92002,x92002,x92003),x92001)),f317(x92003,f11(x92002,f228(x92002),x92001)))+~P1(f317(f28(x92002),x92001))
% 94.68/94.46 [9201]~P66(x92012)+E(x92011,f178(f904(x92012,a893)))+~E(f317(f317(f223(x92012),f317(x92013,f339(x92011,x92013,x92012))),f317(x92013,f340(x92011,x92013,x92012))),f317(x92013,f317(f317(f223(x92012),f339(x92011,x92013,x92012)),f340(x92011,x92013,x92012))))+E(f12(x92012,f223(x92012),f317(f300(x92012,x92012,x92013),x92011)),f317(x92013,f12(x92012,f223(x92012),x92011)))+~P1(f317(f28(x92012),x92011))
% 94.68/94.46 [6648]~P73(x66482)+E(x66481,f178(f904(x66482,a893)))+~P1(f317(f28(x66482),x66481))+E(f317(f57(x66482,f75(x66482)),f317(f317(f299(x66482),x66483),x66481)),f317(f317(f75(x66482),x66483),f317(f57(x66482,f75(x66482)),x66481)))+P1(f317(f317(f319(x66482),x66483),x66481))
% 94.68/94.46 [7184]~P66(x71842)+E(f317(f317(f228(x71842),f14(x71842,x71841)),f14(x71842,x71843)),f14(x71842,x71843))+E(x71841,f178(f904(x71842,a893)))+~P1(f317(f28(x71842),x71843))+~P1(f317(f317(f224(f904(x71842,a893)),x71841),x71843))
% 94.68/94.46 [7185]~P66(x71852)+E(f317(f317(f223(x71852),f15(x71852,x71851)),f15(x71852,x71853)),f15(x71852,x71853))+E(x71851,f178(f904(x71852,a893)))+~P1(f317(f28(x71852),x71853))+~P1(f317(f317(f224(f904(x71852,a893)),x71851),x71853))
% 94.68/94.46 [7186]~P100(x71862)+E(f317(f317(f91(x71862),f13(x71862,x71861)),f13(x71862,x71863)),f13(x71862,x71863))+E(x71861,f178(f904(x71862,a893)))+~P1(f317(f28(x71862),x71863))+~P1(f317(f317(f224(f904(x71862,a893)),x71861),x71863))
% 94.68/94.46 [7187]~P100(x71872)+E(f317(f317(f92(x71872),f10(x71872,x71871)),f10(x71872,x71873)),f10(x71872,x71873))+E(x71871,f178(f904(x71872,a893)))+~P1(f317(f28(x71872),x71873))+~P1(f317(f317(f224(f904(x71872,a893)),x71871),x71873))
% 94.68/94.46 [7492]~P66(x74922)+E(x74921,f178(f904(x74922,a893)))+~P1(f317(f28(x74922),x74923))+P1(f317(f317(f224(x74922),f14(x74922,x74923)),f14(x74922,x74921)))+~P1(f317(f317(f224(f904(x74922,a893)),x74921),x74923))
% 94.68/94.46 [7493]~P66(x74932)+E(x74931,f178(f904(x74932,a893)))+~P1(f317(f28(x74932),x74933))+P1(f317(f317(f224(x74932),f15(x74932,x74931)),f15(x74932,x74933)))+~P1(f317(f317(f224(f904(x74932,a893)),x74931),x74933))
% 94.68/94.46 [7547]~P66(x75471)+E(f14(x75471,x75472),x75473)+~P1(f317(f28(x75471),x75472))+~E(f317(f317(f23(f904(x75471,a893)),x75472),f317(f317(f299(x75471),x75473),f178(f904(x75471,a893)))),f178(f904(x75471,a893)))+~P1(f317(f317(f319(x75471),x75473),x75472))
% 94.68/94.46 [7548]~P66(x75481)+E(f15(x75481,x75482),x75483)+~P1(f317(f28(x75481),x75482))+~E(f317(f317(f23(f904(x75481,a893)),x75482),f317(f317(f299(x75481),x75483),f178(f904(x75481,a893)))),f178(f904(x75481,a893)))+~P1(f317(f317(f319(x75481),x75483),x75482))
% 94.68/94.46 [7549]~P100(x75491)+E(f13(x75491,x75492),x75493)+~P1(f317(f28(x75491),x75492))+~E(f317(f317(f23(f904(x75491,a893)),x75492),f317(f317(f299(x75491),x75493),f178(f904(x75491,a893)))),f178(f904(x75491,a893)))+~P1(f317(f317(f319(x75491),x75493),x75492))
% 94.68/94.46 [7550]~P100(x75501)+E(f10(x75501,x75502),x75503)+~P1(f317(f28(x75501),x75502))+~E(f317(f317(f23(f904(x75501,a893)),x75502),f317(f317(f299(x75501),x75503),f178(f904(x75501,a893)))),f178(f904(x75501,a893)))+~P1(f317(f317(f319(x75501),x75503),x75502))
% 94.68/94.46 [7646]~P66(x76461)+E(f11(x76461,f228(x76461),x76462),x76463)+~P1(f317(f28(x76461),x76462))+~E(f317(f317(f23(f904(x76461,a893)),x76462),f317(f317(f299(x76461),x76463),f178(f904(x76461,a893)))),f178(f904(x76461,a893)))+~P1(f317(f317(f319(x76461),x76463),x76462))
% 94.68/94.46 [7647]~P66(x76471)+E(f12(x76471,f223(x76471),x76472),x76473)+~P1(f317(f28(x76471),x76472))+~E(f317(f317(f23(f904(x76471,a893)),x76472),f317(f317(f299(x76471),x76473),f178(f904(x76471,a893)))),f178(f904(x76471,a893)))+~P1(f317(f317(f319(x76471),x76473),x76472))
% 94.68/94.46 [7682]~P66(x76822)+E(x76821,f178(f904(x76822,a893)))+~P1(f317(f28(x76822),x76821))+~P1(f317(f317(f224(x76822),x76823),f852(x76823,x76821,x76822)))+P1(f317(f317(f224(x76822),x76823),f317(f57(x76822,f228(x76822)),x76821)))
% 94.68/94.46 [7683]~P105(x76832)+E(x76831,f178(f904(x76832,a893)))+~P1(f317(f28(x76832),x76831))+~P1(f317(f317(f224(x76832),x76833),f400(x76833,x76831,x76832)))+P1(f317(f317(f224(x76832),x76833),f317(f57(x76832,f92(x76832)),x76831)))
% 94.68/94.46 [7684]~P66(x76842)+E(x76841,f178(f904(x76842,a893)))+~P1(f317(f28(x76842),x76841))+~P1(f317(f317(f225(x76842),x76843),f853(x76843,x76841,x76842)))+P1(f317(f317(f225(x76842),x76843),f317(f57(x76842,f228(x76842)),x76841)))
% 94.68/94.46 [7771]~P66(x77712)+E(x77711,f178(f904(x77712,a893)))+~P1(f317(f28(x77712),x77711))+P1(f317(f317(f319(x77712),f853(x77713,x77711,x77712)),x77711))+P1(f317(f317(f225(x77712),x77713),f317(f57(x77712,f228(x77712)),x77711)))
% 94.68/94.46 [7772]~P66(x77722)+E(x77721,f178(f904(x77722,a893)))+~P1(f317(f28(x77722),x77721))+P1(f317(f317(f319(x77722),f852(x77723,x77721,x77722)),x77721))+P1(f317(f317(f224(x77722),x77723),f317(f57(x77722,f228(x77722)),x77721)))
% 94.68/94.46 [7773]~P105(x77732)+E(x77731,f178(f904(x77732,a893)))+~P1(f317(f28(x77732),x77731))+P1(f317(f317(f319(x77732),f400(x77733,x77731,x77732)),x77731))+P1(f317(f317(f224(x77732),x77733),f317(f57(x77732,f92(x77732)),x77731)))
% 94.68/94.46 [7895]~P66(x78952)+E(x78951,f178(f904(x78952,a893)))+E(f317(f317(f228(x78952),f11(x78952,f228(x78952),x78951)),f11(x78952,f228(x78952),x78953)),f11(x78952,f228(x78952),x78953))+~P1(f317(f28(x78952),x78953))+~P1(f317(f317(f224(f904(x78952,a893)),x78951),x78953))
% 94.68/94.46 [7896]~P66(x78962)+E(x78961,f178(f904(x78962,a893)))+E(f317(f317(f223(x78962),f12(x78962,f223(x78962),x78961)),f12(x78962,f223(x78962),x78963)),f12(x78962,f223(x78962),x78963))+~P1(f317(f28(x78962),x78963))+~P1(f317(f317(f224(f904(x78962,a893)),x78961),x78963))
% 94.68/94.46 [8095]~E(f594(x80951,x80953,x80952),f595(x80951,x80953,x80952))+~E(f317(f29(x80952),f596(x80951,x80953,x80952)),x80951)+E(f317(f317(f75(a897),x80951),f317(f29(f904(x80952,a893)),x80953)),f317(f29(x80952),f31(f904(x80952,a893),x80953)))+~P1(f317(f28(x80952),f31(f904(x80952,a893),x80953)))+~P1(f317(f28(f904(x80952,a893)),x80953))
% 94.68/94.46 [8276]~P66(x82762)+E(x82761,f178(f904(x82762,a893)))+~P1(f317(f28(x82762),x82763))+P1(f317(f317(f224(x82762),f317(f57(x82762,f228(x82762)),x82763)),f317(f57(x82762,f228(x82762)),x82761)))+~P1(f317(f317(f224(f904(x82762,a893)),x82761),x82763))
% 94.68/94.46 [8576]~E(f594(x85761,x85763,x85762),f595(x85761,x85763,x85762))+E(f317(f317(f75(a897),x85761),f317(f29(f904(x85762,a893)),x85763)),f317(f29(x85762),f31(f904(x85762,a893),x85763)))+P1(f317(f317(f319(f904(x85762,a893)),f596(x85761,x85763,x85762)),x85763))+~P1(f317(f28(x85762),f31(f904(x85762,a893),x85763)))+~P1(f317(f28(f904(x85762,a893)),x85763))
% 94.68/94.46 [8602]~E(f317(f29(x86022),f596(x86021,x86023,x86022)),x86021)+E(f317(f317(f75(a897),x86021),f317(f29(f904(x86022,a893)),x86023)),f317(f29(x86022),f31(f904(x86022,a893),x86023)))+P1(f317(f317(f319(f904(x86022,a893)),f595(x86021,x86023,x86022)),x86023))+~P1(f317(f28(x86022),f31(f904(x86022,a893),x86023)))+~P1(f317(f28(f904(x86022,a893)),x86023))
% 94.68/94.46 [8603]~E(f317(f29(x86032),f596(x86031,x86033,x86032)),x86031)+E(f317(f317(f75(a897),x86031),f317(f29(f904(x86032,a893)),x86033)),f317(f29(x86032),f31(f904(x86032,a893),x86033)))+P1(f317(f317(f319(f904(x86032,a893)),f594(x86031,x86033,x86032)),x86033))+~P1(f317(f28(x86032),f31(f904(x86032,a893),x86033)))+~P1(f317(f28(f904(x86032,a893)),x86033))
% 94.68/94.46 [8628]~E(f317(f29(x86282),f596(x86281,x86283,x86282)),x86281)+~E(f317(f317(f92(f904(x86282,a893)),f595(x86281,x86283,x86282)),f594(x86281,x86283,x86282)),f178(f904(x86282,a893)))+E(f317(f317(f75(a897),x86281),f317(f29(f904(x86282,a893)),x86283)),f317(f29(x86282),f31(f904(x86282,a893),x86283)))+~P1(f317(f28(f904(x86282,a893)),x86283))+~P1(f317(f28(x86282),f31(f904(x86282,a893),x86283)))
% 94.68/94.46 [8892]E(f317(f317(f75(a897),x88921),f317(f29(f904(x88922,a893)),x88923)),f317(f29(x88922),f31(f904(x88922,a893),x88923)))+P1(f317(f317(f319(f904(x88922,a893)),f596(x88921,x88923,x88922)),x88923))+P1(f317(f317(f319(f904(x88922,a893)),f595(x88921,x88923,x88922)),x88923))+~P1(f317(f28(f904(x88922,a893)),x88923))+~P1(f317(f28(x88922),f31(f904(x88922,a893),x88923)))
% 94.68/94.46 [8893]E(f317(f317(f75(a897),x88931),f317(f29(f904(x88932,a893)),x88933)),f317(f29(x88932),f31(f904(x88932,a893),x88933)))+P1(f317(f317(f319(f904(x88932,a893)),f596(x88931,x88933,x88932)),x88933))+P1(f317(f317(f319(f904(x88932,a893)),f594(x88931,x88933,x88932)),x88933))+~P1(f317(f28(f904(x88932,a893)),x88933))+~P1(f317(f28(x88932),f31(f904(x88932,a893),x88933)))
% 94.68/94.46 [8919]~E(f317(f317(f92(f904(x89192,a893)),f595(x89191,x89193,x89192)),f594(x89191,x89193,x89192)),f178(f904(x89192,a893)))+E(f317(f317(f75(a897),x89191),f317(f29(f904(x89192,a893)),x89193)),f317(f29(x89192),f31(f904(x89192,a893),x89193)))+~P1(f317(f28(f904(x89192,a893)),x89193))+P1(f317(f317(f319(f904(x89192,a893)),f596(x89191,x89193,x89192)),x89193))+~P1(f317(f28(x89192),f31(f904(x89192,a893),x89193)))
% 94.68/94.46 [9175]~P98(x91752)+E(x91751,f178(f904(x91752,a893)))+~E(f317(f317(f75(x91752),f317(x91753,f813(x91751,x91753,x91752))),f317(x91753,f832(x91751,x91753,x91752))),f317(x91753,f317(f317(f75(x91752),f813(x91751,x91753,x91752)),f832(x91751,x91753,x91752))))+~P1(f317(f28(x91752),x91751))+E(f317(f57(x91752,f75(x91752)),f317(f300(x91752,x91752,x91753),x91751)),f317(x91753,f317(f57(x91752,f75(x91752)),x91751)))
% 94.68/94.46 [10117]P1(f317(f317(x101171,x101172),x101173))+P1(f317(f317(f225(a1),f885(x101171,x101173,x101172)),f886(x101171,x101173,x101172)))+P1(f317(f317(f224(a1),f886(x101171,x101173,x101172)),f2(a1)))+P1(f317(f317(x101171,f885(x101171,x101173,x101172)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f886(x101171,x101173,x101172))))+~P1(f317(f305(f903(a1,a1),a53),f317(f317(f242(a1,a1),x101172),x101173)))
% 94.68/94.46 [10123]P1(f317(f317(x101231,x101232),x101233))+P1(f317(f317(f224(a1),f883(x101231,x101233,x101232)),f2(a1)))+P1(f317(f317(x101231,f877(x101231,x101233,x101232)),f317(f317(f75(a1),f317(f94(a1),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f883(x101231,x101233,x101232))))+P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f877(x101231,x101233,x101232)),f883(x101231,x101233,x101232))))+~P1(f317(f305(f903(a1,a1),a47),f317(f317(f242(a1,a1),x101232),x101233)))
% 94.68/94.46 [8067]~P111(x80671)+~P1(f317(f317(f224(x80671),x80672),f72(x80671)))+~P1(f317(f317(f224(x80671),f2(x80671)),x80672))+~P1(f317(f317(f224(x80671),f2(x80671)),x80673))+P1(f317(f317(f224(x80671),f317(f317(f75(x80671),x80672),x80673)),x80673))
% 94.68/94.46 [8068]~P111(x80681)+~P1(f317(f317(f224(x80681),x80683),f72(x80681)))+~P1(f317(f317(f224(x80681),f2(x80681)),x80683))+~P1(f317(f317(f224(x80681),f2(x80681)),x80682))+P1(f317(f317(f224(x80681),f317(f317(f75(x80681),x80682),x80683)),x80682))
% 94.68/94.46 [8422]~P66(x84222)+E(x84221,f178(f904(x84222,a893)))+~P1(f317(f28(x84222),x84221))+P1(f317(f317(f224(x84222),f855(x84223,x84221,x84222)),x84223))+~P1(f317(f317(f224(x84222),f317(f57(x84222,f228(x84222)),x84221)),x84223))
% 94.68/94.46 [8423]~P66(x84232)+E(x84231,f178(f904(x84232,a893)))+~P1(f317(f28(x84232),x84231))+P1(f317(f317(f319(x84232),f854(x84233,x84231,x84232)),x84231))+~P1(f317(f317(f225(x84232),f317(f57(x84232,f228(x84232)),x84231)),x84233))
% 94.68/94.46 [8424]~P66(x84242)+E(x84241,f178(f904(x84242,a893)))+~P1(f317(f28(x84242),x84241))+P1(f317(f317(f319(x84242),f855(x84243,x84241,x84242)),x84241))+~P1(f317(f317(f224(x84242),f317(f57(x84242,f228(x84242)),x84241)),x84243))
% 94.68/94.46 [8425]~P66(x84252)+E(x84251,f178(f904(x84252,a893)))+~P1(f317(f28(x84252),x84251))+P1(f317(f317(f225(x84252),f854(x84253,x84251,x84252)),x84253))+~P1(f317(f317(f225(x84252),f317(f57(x84252,f228(x84252)),x84251)),x84253))
% 94.68/94.46 [8511]~P1(f317(x85111,x85113))+P1(f317(x85111,f383(x85111,x85112)))+P1(f317(x85111,f382(x85111,x85112)))+~P1(f317(f317(f225(a1),f2(a1)),x85112))+P1(f317(x85111,f317(f317(f23(a1),f382(x85111,x85112)),f317(f317(f75(a1),f384(x85111,x85112)),x85112))))
% 94.68/94.46 [8729]~P1(f317(x87291,x87293))+P1(f317(x87291,f382(x87291,x87292)))+~P1(f317(f317(f225(a1),f2(a1)),x87292))+P1(f317(f317(f319(a1),f383(x87291,x87292)),f293(a1,f72(a1),x87292)))+P1(f317(x87291,f317(f317(f23(a1),f382(x87291,x87292)),f317(f317(f75(a1),f384(x87291,x87292)),x87292))))
% 94.68/94.46 [8941]~P1(f317(x89411,x89413))+~P1(f317(x89411,f382(x89411,x89412)))+P1(f317(x89411,f383(x89411,x89412)))+~P1(f317(f317(f225(a1),f2(a1)),x89412))+~P1(f317(x89411,f317(f317(f23(a1),f382(x89411,x89412)),f317(f317(f75(a1),f384(x89411,x89412)),x89412))))
% 94.68/94.46 [9065]~P1(f317(x90651,x90653))+~P1(f317(x90651,f382(x90651,x90652)))+~P1(f317(f317(f225(a1),f2(a1)),x90652))+P1(f317(f317(f319(a1),f383(x90651,x90652)),f293(a1,f72(a1),x90652)))+~P1(f317(x90651,f317(f317(f23(a1),f382(x90651,x90652)),f317(f317(f75(a1),f384(x90651,x90652)),x90652))))
% 94.68/94.46 [8847]~P66(x88471)+~P1(f317(f28(x88471),x88472))+E(f317(f317(f23(f904(x88471,a893)),x88472),f317(f317(f299(x88471),x88473),f178(f904(x88471,a893)))),f178(f904(x88471,a893)))+~P1(f317(f317(f319(x88471),x88473),x88472))+E(f317(f317(f228(x88471),x88473),f14(x88471,f317(f317(f23(f904(x88471,a893)),x88472),f317(f317(f299(x88471),x88473),f178(f904(x88471,a893)))))),f14(x88471,x88472))
% 94.68/94.46 [8848]~P66(x88481)+~P1(f317(f28(x88481),x88482))+E(f317(f317(f23(f904(x88481,a893)),x88482),f317(f317(f299(x88481),x88483),f178(f904(x88481,a893)))),f178(f904(x88481,a893)))+~P1(f317(f317(f319(x88481),x88483),x88482))+E(f317(f317(f223(x88481),x88483),f15(x88481,f317(f317(f23(f904(x88481,a893)),x88482),f317(f317(f299(x88481),x88483),f178(f904(x88481,a893)))))),f15(x88481,x88482))
% 94.68/94.46 [8849]~P100(x88491)+~P1(f317(f28(x88491),x88492))+E(f317(f317(f23(f904(x88491,a893)),x88492),f317(f317(f299(x88491),x88493),f178(f904(x88491,a893)))),f178(f904(x88491,a893)))+~P1(f317(f317(f319(x88491),x88493),x88492))+E(f317(f317(f91(x88491),x88493),f13(x88491,f317(f317(f23(f904(x88491,a893)),x88492),f317(f317(f299(x88491),x88493),f178(f904(x88491,a893)))))),f13(x88491,x88492))
% 94.68/94.46 [8850]~P100(x88501)+~P1(f317(f28(x88501),x88502))+E(f317(f317(f23(f904(x88501,a893)),x88502),f317(f317(f299(x88501),x88503),f178(f904(x88501,a893)))),f178(f904(x88501,a893)))+~P1(f317(f317(f319(x88501),x88503),x88502))+E(f317(f317(f92(x88501),x88503),f10(x88501,f317(f317(f23(f904(x88501,a893)),x88502),f317(f317(f299(x88501),x88503),f178(f904(x88501,a893)))))),f10(x88501,x88502))
% 94.68/94.46 [8912]~P66(x89121)+~P1(f317(f28(x89121),x89122))+E(f317(f317(f23(f904(x89121,a893)),x89122),f317(f317(f299(x89121),x89123),f178(f904(x89121,a893)))),f178(f904(x89121,a893)))+~P1(f317(f317(f319(x89121),x89123),x89122))+E(f317(f317(f228(x89121),x89123),f11(x89121,f228(x89121),f317(f317(f23(f904(x89121,a893)),x89122),f317(f317(f299(x89121),x89123),f178(f904(x89121,a893)))))),f11(x89121,f228(x89121),x89122))
% 94.68/94.46 [8913]~P66(x89131)+~P1(f317(f28(x89131),x89132))+E(f317(f317(f23(f904(x89131,a893)),x89132),f317(f317(f299(x89131),x89133),f178(f904(x89131,a893)))),f178(f904(x89131,a893)))+~P1(f317(f317(f319(x89131),x89133),x89132))+E(f317(f317(f223(x89131),x89133),f12(x89131,f223(x89131),f317(f317(f23(f904(x89131,a893)),x89132),f317(f317(f299(x89131),x89133),f178(f904(x89131,a893)))))),f12(x89131,f223(x89131),x89132))
% 94.68/94.46 [8928]~P66(x89281)+~P1(f317(f28(x89281),x89283))+~P1(f317(f28(x89281),x89282))+E(f317(f317(f92(f904(x89281,a893)),x89282),x89283),f178(f904(x89281,a893)))+E(f317(f317(f228(x89281),f14(x89281,f317(f317(f91(f904(x89281,a893)),x89282),x89283))),f14(x89281,f317(f317(f92(f904(x89281,a893)),x89282),x89283))),f317(f317(f228(x89281),f14(x89281,x89282)),f14(x89281,x89283)))
% 94.68/94.46 [8929]~P66(x89291)+~P1(f317(f28(x89291),x89293))+~P1(f317(f28(x89291),x89292))+E(f317(f317(f92(f904(x89291,a893)),x89292),x89293),f178(f904(x89291,a893)))+E(f317(f317(f223(x89291),f15(x89291,f317(f317(f91(f904(x89291,a893)),x89292),x89293))),f15(x89291,f317(f317(f92(f904(x89291,a893)),x89292),x89293))),f317(f317(f223(x89291),f15(x89291,x89292)),f15(x89291,x89293)))
% 94.68/94.46 [8930]~P100(x89301)+~P1(f317(f28(x89301),x89303))+~P1(f317(f28(x89301),x89302))+E(f317(f317(f92(f904(x89301,a893)),x89302),x89303),f178(f904(x89301,a893)))+E(f317(f317(f91(x89301),f13(x89301,f317(f317(f91(f904(x89301,a893)),x89302),x89303))),f13(x89301,f317(f317(f92(f904(x89301,a893)),x89302),x89303))),f317(f317(f91(x89301),f13(x89301,x89302)),f13(x89301,x89303)))
% 94.68/94.46 [8931]~P100(x89311)+~P1(f317(f28(x89311),x89313))+~P1(f317(f28(x89311),x89312))+E(f317(f317(f92(f904(x89311,a893)),x89312),x89313),f178(f904(x89311,a893)))+E(f317(f317(f92(x89311),f10(x89311,f317(f317(f91(f904(x89311,a893)),x89312),x89313))),f10(x89311,f317(f317(f92(f904(x89311,a893)),x89312),x89313))),f317(f317(f92(x89311),f10(x89311,x89312)),f10(x89311,x89313)))
% 94.68/94.46 [9147]~P66(x91471)+~P1(f317(f28(x91471),x91473))+~P1(f317(f28(x91471),x91472))+E(f317(f317(f92(f904(x91471,a893)),x91472),x91473),f178(f904(x91471,a893)))+E(f317(f317(f228(x91471),f11(x91471,f228(x91471),f317(f317(f91(f904(x91471,a893)),x91472),x91473))),f11(x91471,f228(x91471),f317(f317(f92(f904(x91471,a893)),x91472),x91473))),f317(f317(f228(x91471),f11(x91471,f228(x91471),x91472)),f11(x91471,f228(x91471),x91473)))
% 94.68/94.46 [9148]~P66(x91481)+~P1(f317(f28(x91481),x91483))+~P1(f317(f28(x91481),x91482))+E(f317(f317(f92(f904(x91481,a893)),x91482),x91483),f178(f904(x91481,a893)))+E(f317(f317(f223(x91481),f12(x91481,f223(x91481),f317(f317(f91(f904(x91481,a893)),x91482),x91483))),f12(x91481,f223(x91481),f317(f317(f92(f904(x91481,a893)),x91482),x91483))),f317(f317(f223(x91481),f12(x91481,f223(x91481),x91482)),f12(x91481,f223(x91481),x91483)))
% 94.68/94.46 [9956]~P110(x99563)+E(x99561,x99562)+~P1(f317(f317(f224(x99563),f2(x99563)),x99562))+~P1(f317(f317(f224(x99563),f2(x99563)),x99561))+~E(f317(f317(f234(x99563),x99561),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))),f317(f317(f234(x99563),x99562),f317(f94(a897),f317(f317(f74(a1),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)),f317(f317(f23(a1),f317(f317(f74(a1),a77),a77)),a87)))))
% 94.68/94.46 [5962]~P3(x59622)+E(x59621,f2(x59622))+~E(f317(f317(f30(x59622),x59623),x59621),x59624)+E(x59623,f317(f317(f75(x59622),x59624),x59621))+~P1(f317(f317(f277(x59622),x59621),x59623))
% 94.68/94.46 [5963]~P3(x59632)+E(x59631,f2(x59632))+~E(x59633,f317(f317(f75(x59632),x59634),x59631))+E(f317(f317(f30(x59632),x59633),x59631),x59634)+~P1(f317(f317(f277(x59632),x59631),x59633))
% 94.68/94.46 [6440]E(f398(x64401,x64402,x64403),x64404)+E(f317(x64401,x64404),f2(a897))+~E(f317(f317(f6(x64403,a897),x64401),x64402),f72(a897))+~P1(f317(f28(x64403),x64402))+~P1(f317(f317(f319(x64403),x64404),x64402))
% 94.68/94.46 [6505]E(f409(x65051,x65052,x65053),x65054)+E(f317(x65051,x65054),f2(a897))+~E(f317(f317(f6(x65053,a897),x65051),x65052),f317(a102,f2(a897)))+~P1(f317(f28(x65053),x65052))+~P1(f317(f317(f319(x65053),x65054),x65052))
% 94.68/94.46 [6617]~P66(x66171)+~P5(x66171)+P1(f317(f317(f225(x66171),x66172),f31(x66171,x66173)))+~P1(f317(f317(f225(x66171),x66172),x66174))+~P1(f317(f317(f319(x66171),x66174),x66173))
% 94.68/94.46 [6794]~P66(x67941)+~P5(x67941)+~P1(f317(f317(f225(x67941),x67944),x67943))+P1(f317(f317(f225(x67941),f32(x67941,x67942)),x67943))+~P1(f317(f317(f319(x67941),x67944),x67942))
% 94.68/94.46 [7063]~P110(x70633)+E(x70631,x70632)+~E(f317(f317(f234(x70633),x70631),f317(a102,x70634)),f317(f317(f234(x70633),x70632),f317(a102,x70634)))+~P1(f317(f317(f224(x70633),f2(x70633)),x70632))+~P1(f317(f317(f224(x70633),f2(x70633)),x70631))
% 94.68/94.46 [7275]~E(f411(x72752,x72753,x72751,x72754),x72754)+~E(f317(x72752,x72754),f72(a897))+E(f317(f317(f6(x72751,a897),x72752),x72753),f72(a897))+~P1(f317(f28(x72751),x72753))+~P1(f317(f317(f319(x72751),x72754),x72753))
% 94.68/94.46 [7282]~P112(x72824)+~P134(x72824)+E(f317(x72821,f869(x72821,x72822,x72823,x72824)),f2(x72824))+~E(f317(f317(f9(x72823,x72824),x72821),x72822),f2(x72824))+~P1(f317(f28(x72823),x72822))
% 94.68/94.46 [7370]~E(f410(x73702,x73703,x73701,x73704),x73704)+~E(f317(x73702,x73704),f317(a102,f2(a897)))+E(f317(f317(f6(x73701,a897),x73702),x73703),f317(a102,f2(a897)))+~P1(f317(f28(x73701),x73703))+~P1(f317(f317(f319(x73701),x73704),x73703))
% 94.68/94.46 [8107]~E(f317(x81072,x81074),f72(a897))+~E(f317(x81072,f411(x81072,x81073,x81071,x81074)),f2(a897))+E(f317(f317(f6(x81071,a897),x81072),x81073),f72(a897))+~P1(f317(f28(x81071),x81073))+~P1(f317(f317(f319(x81071),x81074),x81073))
% 94.68/94.46 [8145]~E(f317(x81452,x81454),f317(a102,f2(a897)))+~E(f317(x81452,f410(x81452,x81453,x81451,x81454)),f2(a897))+E(f317(f317(f6(x81451,a897),x81452),x81453),f317(a102,f2(a897)))+~P1(f317(f28(x81451),x81453))+~P1(f317(f317(f319(x81451),x81454),x81453))
% 94.68/94.46 [8231]~P145(x82312)+~P121(x82312)+~P1(f317(x82311,x82314))+~P1(f317(f317(f277(x82312),x82313),f317(f317(f74(x82312),x82314),f2(x82312))))+P1(f317(x82311,f317(f317(f75(x82312),x82313),f838(x82313,x82311,x82312))))
% 94.68/94.46 [8696]~P66(x86961)+~P13(x86961,x86964)+P13(x86961,x86962)+~E(x86962,f317(f317(f141(x86961),x86963),x86964))+~P1(f317(f317(f224(x86961),x86963),f706(x86962,x86961,x86964,x86963)))
% 94.68/94.46 [8733]E(x87331,x87332)+E(f317(f317(f23(a1),f365(x87333,x87332,x87334,x87331)),f366(x87333,x87332,x87334,x87331)),x87331)+~E(f317(f317(f74(a1),x87331),x87334),x87332)+~P1(f317(f317(f225(a1),f2(a1)),x87334))+~P1(f317(f317(f319(a1),x87332),x87333))
% 94.68/94.46 [8734]E(x87341,x87342)+E(f317(f317(f74(a1),f370(x87343,x87342,x87344,x87341)),f371(x87343,x87342,x87344,x87341)),x87341)+~E(f317(f317(f23(a1),x87341),x87344),x87342)+~P1(f317(f317(f225(a1),f2(a1)),x87344))+~P1(f317(f317(f319(a1),x87342),x87343))
% 94.68/94.46 [8926]E(f317(x89261,f548(x89262,x89261,x89263,x89264)),x89262)+P1(f317(f317(f224(a897),x89264),f549(x89262,x89261,x89263,x89264)))+~P1(f317(f317(f224(a1),x89262),f317(x89261,x89263)))+~P1(f317(f317(f225(a897),x89264),x89263))+~P1(f317(f317(f224(a1),f317(x89261,x89264)),x89262))
% 94.68/94.46 [8927]~P66(x89271)+~P13(x89271,x89273)+P13(x89271,x89272)+~E(x89272,f317(f317(f141(x89271),x89274),x89273))+P1(f317(f317(f319(x89271),f706(x89272,x89271,x89273,x89274)),f317(f162(x89271),x89273)))
% 94.68/94.46 [8945]~P112(x89454)+~P134(x89454)+~E(f317(f317(f9(x89451,x89454),x89452),x89453),f2(x89454))+~P1(f317(f28(x89451),x89453))+P1(f317(f317(f319(x89451),f869(x89452,x89453,x89451,x89454)),x89453))
% 94.68/94.46 [8983]~E(f317(x89832,x89834),f72(a897))+E(f317(f317(f6(x89831,a897),x89832),x89833),f72(a897))+~P1(f317(f28(x89831),x89833))+~P1(f317(f317(f319(x89831),x89834),x89833))+P1(f317(f317(f319(x89831),f411(x89832,x89833,x89831,x89834)),x89833))
% 94.68/94.46 [8995]E(x89951,x89952)+~E(f317(f317(f74(a1),x89952),x89954),x89951)+~P1(f317(f317(f225(a1),f2(a1)),x89954))+~P1(f317(f317(f319(a1),x89951),x89953))+P1(f317(f317(f319(a1),f365(x89953,x89951,x89954,x89952)),x89953))
% 94.68/94.46 [8996]E(x89961,x89962)+~E(f317(f317(f23(a1),x89962),x89964),x89961)+~P1(f317(f317(f225(a1),f2(a1)),x89964))+~P1(f317(f317(f319(a1),x89961),x89963))+P1(f317(f317(f319(a1),f370(x89963,x89961,x89964,x89962)),x89963))
% 94.68/94.46 [8998]~E(f317(x89982,x89984),f317(a102,f2(a897)))+E(f317(f317(f6(x89981,a897),x89982),x89983),f317(a102,f2(a897)))+~P1(f317(f28(x89981),x89983))+~P1(f317(f317(f319(x89981),x89984),x89983))+P1(f317(f317(f319(x89981),f410(x89982,x89983,x89981,x89984)),x89983))
% 94.68/94.46 [9003]P58(x90032,x90033,x90034,x90031)+E(x90031,f178(f904(x90032,a893)))+~P1(f317(f28(x90032),x90034))+~P1(f317(f28(x90032),x90031))+P1(f317(f317(f319(x90032),f776(x90033,x90031,x90034,x90032)),x90034))
% 94.68/94.46 [9004]P58(x90042,x90043,x90044,x90041)+E(x90041,f178(f904(x90042,a893)))+~P1(f317(f28(x90042),x90044))+~P1(f317(f28(x90042),x90041))+P1(f317(f317(f319(x90042),f463(x90041,x90044,x90043,x90042)),x90044))
% 94.68/94.46 [9005]P58(x90052,x90053,x90054,x90051)+E(x90051,f178(f904(x90052,a893)))+~P1(f317(f28(x90052),x90054))+~P1(f317(f28(x90052),x90051))+P1(f317(f317(f319(x90052),f778(x90051,x90054,x90053,x90052)),x90054))
% 94.68/94.46 [9078]E(x90781,x90782)+~E(f317(f317(f74(a1),x90782),x90784),x90781)+~P1(f317(f317(f225(a1),f2(a1)),x90784))+~P1(f317(f317(f319(a1),x90781),x90783))+P1(f317(f317(f319(a1),f366(x90783,x90781,x90784,x90782)),f293(a1,f72(a1),x90784)))
% 94.68/94.46 [9079]E(x90791,x90792)+~E(f317(f317(f23(a1),x90792),x90794),x90791)+~P1(f317(f317(f225(a1),f2(a1)),x90794))+~P1(f317(f317(f319(a1),x90791),x90793))+P1(f317(f317(f319(a1),f371(x90793,x90791,x90794,x90792)),f293(a1,f72(a1),x90794)))
% 94.68/94.46 [9153]P1(f317(f317(f224(a897),x91531),f548(x91532,x91533,x91534,x91531)))+~P1(f317(f317(f224(a1),x91532),f317(x91533,x91534)))+P1(f317(f317(f224(a897),x91531),f549(x91532,x91533,x91534,x91531)))+~P1(f317(f317(f225(a897),x91531),x91534))+~P1(f317(f317(f224(a1),f317(x91533,x91531)),x91532))
% 94.68/94.46 [9267]E(f317(x92671,f548(x92672,x92671,x92673,x92674)),x92672)+~P1(f317(f317(f224(a1),x92672),f317(x92671,x92673)))+P1(f317(f317(f225(a897),f549(x92672,x92671,x92673,x92674)),x92673))+~P1(f317(f317(f225(a897),x92674),x92673))+~P1(f317(f317(f224(a1),f317(x92671,x92674)),x92672))
% 94.68/94.46 [9383]~P1(f317(f317(f277(a897),x93834),x93831))+~P1(f317(f317(f277(a897),x93834),x93833))+~P1(f317(f317(f277(a897),x93832),x93831))+P1(f317(f317(f277(a897),x93831),x93832))+P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x93833,x93832)),f280(a897,f277(a897),x93834,x93831)))
% 94.68/94.46 [9384]~P1(f317(f317(f277(a897),x93842),x93841))+~P1(f317(f317(f277(a897),x93843),x93844))+~P1(f317(f317(f277(a897),x93842),x93844))+P1(f317(f317(f277(a897),x93841),x93842))+P1(f317(f317(f225(f904(a897,a893)),f280(a897,f277(a897),x93841,x93843)),f280(a897,f277(a897),x93842,x93844)))
% 94.68/94.46 [9401]~P1(f317(f317(f224(a1),x94012),f317(x94013,x94014)))+P1(f317(f317(f224(a897),x94011),f549(x94012,x94013,x94014,x94011)))+P1(f317(f317(f224(a897),f548(x94012,x94013,x94014,x94011)),x94014))+~P1(f317(f317(f225(a897),x94011),x94014))+~P1(f317(f317(f224(a1),f317(x94013,x94011)),x94012))
% 94.68/94.46 [9402]~P1(f317(f317(f224(a1),x94022),f317(x94023,x94024)))+P1(f317(f317(f224(a897),x94021),f548(x94022,x94023,x94024,x94021)))+P1(f317(f317(f225(a897),f549(x94022,x94023,x94024,x94021)),x94024))+~P1(f317(f317(f225(a897),x94021),x94024))+~P1(f317(f317(f224(a1),f317(x94023,x94021)),x94022))
% 94.68/94.46 [9510]~P1(f317(f317(f224(a1),x95101),f317(x95102,x95103)))+P1(f317(f317(f225(a897),f549(x95101,x95102,x95103,x95104)),x95103))+~P1(f317(f317(f225(a897),x95104),x95103))+~P1(f317(f317(f224(a1),f317(x95102,x95104)),x95101))+P1(f317(f317(f224(a897),f548(x95101,x95102,x95103,x95104)),x95103))
% 94.68/94.46 [9604]E(x96041,f178(f904(x96042,a893)))+~P1(f317(f28(x96042),x96044))+~P1(f317(f28(x96042),x96041))+P1(f317(f317(f319(f903(f904(x96042,a893),f904(x96042,a893))),f317(f317(f242(f904(x96042,a893),f904(x96042,a893)),x96044),x96041)),f308(x96042,x96043)))+P1(f317(f317(f319(x96042),f465(x96043,x96041,x96044,x96042)),x96044))
% 94.68/94.46 [9605]E(x96051,f178(f904(x96052,a893)))+~P1(f317(f28(x96052),x96054))+~P1(f317(f28(x96052),x96051))+P1(f317(f317(f319(f903(f904(x96052,a893),f904(x96052,a893))),f317(f317(f242(f904(x96052,a893),f904(x96052,a893)),x96054),x96051)),f308(x96052,x96053)))+P1(f317(f317(f319(x96052),f542(x96053,x96051,x96054,x96052)),x96054))
% 94.68/94.46 [10278]E(f317(x102781,f548(x102782,x102781,x102783,x102784)),x102782)+~P1(f317(f317(f224(a1),x102782),f317(x102781,x102783)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x102781,f317(f317(f74(a897),f549(x102782,x102781,x102783,x102784)),f72(a897)))),f317(x102781,f549(x102782,x102781,x102783,x102784))))),f72(a1)))+~P1(f317(f317(f225(a897),x102784),x102783))+~P1(f317(f317(f224(a1),f317(x102781,x102784)),x102782))
% 94.68/94.46 [10279]~P1(f317(f317(f224(a1),x102792),f317(x102793,x102794)))+P1(f317(f317(f224(a897),x102791),f548(x102792,x102793,x102794,x102791)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x102793,f317(f317(f74(a897),f549(x102792,x102793,x102794,x102791)),f72(a897)))),f317(x102793,f549(x102792,x102793,x102794,x102791))))),f72(a1)))+~P1(f317(f317(f225(a897),x102791),x102794))+~P1(f317(f317(f224(a1),f317(x102793,x102791)),x102792))
% 94.68/94.46 [10280]~P1(f317(f317(f224(a1),x102801),f317(x102802,x102803)))+~P1(f317(f317(f224(a1),f317(f70(a1),f317(f317(f23(a1),f317(x102802,f317(f317(f74(a897),f549(x102801,x102802,x102803,x102804)),f72(a897)))),f317(x102802,f549(x102801,x102802,x102803,x102804))))),f72(a1)))+~P1(f317(f317(f225(a897),x102804),x102803))+~P1(f317(f317(f224(a1),f317(x102802,x102804)),x102801))+P1(f317(f317(f224(a897),f548(x102801,x102802,x102803,x102804)),x102803))
% 94.68/94.46 [7333]~P63(x73331)+P1(f317(f317(f225(x73331),x73332),f2(x73331)))+~P1(f317(f317(f224(x73331),x73333),f2(x73331)))+P1(f317(f317(f225(x73331),f2(x73331)),x73332))+P1(f317(f317(f224(x73331),x73333),f317(f317(f281(x73331),x73334),x73332)))
% 94.68/94.46 [7334]~P63(x73341)+P1(f317(f317(f225(x73341),x73342),f2(x73341)))+~P1(f317(f317(f225(x73341),x73343),f2(x73341)))+P1(f317(f317(f225(x73341),f2(x73341)),x73342))+P1(f317(f317(f225(x73341),x73343),f317(f317(f281(x73341),x73344),x73342)))
% 94.68/94.46 [7583]~P63(x75831)+P1(f317(f317(f224(x75831),x75832),f2(x75831)))+P1(f317(f317(f225(x75831),x75833),f2(x75831)))+P1(f317(f317(f225(x75831),f2(x75831)),x75833))+~P1(f317(f317(f224(x75831),x75832),f317(f317(f281(x75831),x75834),x75833)))
% 94.68/94.46 [7584]~P63(x75841)+P1(f317(f317(f225(x75841),x75842),f2(x75841)))+P1(f317(f317(f225(x75841),x75843),f2(x75841)))+P1(f317(f317(f225(x75841),f2(x75841)),x75843))+~P1(f317(f317(f225(x75841),x75842),f317(f317(f281(x75841),x75844),x75843)))
% 94.68/94.46 [7703]E(x77031,x77032)+~E(f317(f317(f154(x77033),x77034),x77031),f317(f317(f154(x77033),x77034),x77032))+~P1(f317(f127(x77033),x77034))+~P1(f317(f317(f225(a897),x77032),f317(f179(f898(x77033)),x77034)))+~P1(f317(f317(f225(a897),x77031),f317(f179(f898(x77033)),x77034)))
% 94.68/94.46 [8069]~P63(x80691)+~P1(f317(f317(f224(x80691),x80693),f2(x80691)))+P1(f317(f317(f225(x80691),f2(x80691)),x80692))+~P1(f317(f317(f224(x80691),x80694),f317(f317(f75(x80691),x80693),x80692)))+P1(f317(f317(f224(x80691),x80693),f317(f317(f281(x80691),x80694),x80692)))
% 94.68/94.46 [8070]~P63(x80701)+~P1(f317(f317(f225(x80701),x80703),f2(x80701)))+P1(f317(f317(f225(x80701),f2(x80701)),x80702))+~P1(f317(f317(f225(x80701),x80704),f317(f317(f75(x80701),x80703),x80702)))+P1(f317(f317(f225(x80701),x80703),f317(f317(f281(x80701),x80704),x80702)))
% 94.68/94.46 [8071]~P63(x80711)+~P1(f317(f317(f225(x80711),x80712),f2(x80711)))+P1(f317(f317(f225(x80711),f2(x80711)),x80712))+~P1(f317(f317(f224(x80711),x80714),f317(f317(f75(x80711),x80713),x80712)))+P1(f317(f317(f224(x80711),x80713),f317(f317(f281(x80711),x80714),x80712)))
% 94.68/94.46 [8072]~P63(x80721)+~P1(f317(f317(f225(x80721),x80722),f2(x80721)))+P1(f317(f317(f225(x80721),f2(x80721)),x80722))+~P1(f317(f317(f224(x80721),x80724),f317(f317(f281(x80721),x80723),x80722)))+P1(f317(f317(f224(x80721),x80723),f317(f317(f75(x80721),x80724),x80722)))
% 94.68/94.46 [8073]~P63(x80731)+~P1(f317(f317(f225(x80731),x80732),f2(x80731)))+P1(f317(f317(f225(x80731),f2(x80731)),x80732))+~P1(f317(f317(f225(x80731),x80734),f317(f317(f75(x80731),x80733),x80732)))+P1(f317(f317(f225(x80731),x80733),f317(f317(f281(x80731),x80734),x80732)))
% 94.68/94.46 [8074]~P63(x80741)+~P1(f317(f317(f225(x80741),x80742),f2(x80741)))+P1(f317(f317(f225(x80741),f2(x80741)),x80742))+~P1(f317(f317(f225(x80741),x80744),f317(f317(f281(x80741),x80743),x80742)))+P1(f317(f317(f225(x80741),x80743),f317(f317(f75(x80741),x80744),x80742)))
% 94.68/94.46 [8199]~P3(x81991)+~P1(f317(f317(f277(x81991),x81993),x81994))+~P1(f317(f317(f277(x81991),x81993),x81992))+~P1(f317(f317(f277(x81991),x81992),x81994))+P1(f317(f317(f277(x81991),f317(f317(f30(x81991),x81992),x81993)),f317(f317(f30(x81991),x81994),x81993)))
% 94.68/94.46 [8214]~P66(x82141)+~P13(x82141,x82142)+~P1(f317(f317(f224(a897),x82143),x82144))+P1(f317(f317(f224(x82141),f317(f317(f154(x82141),x82142),x82143)),f317(f317(f154(x82141),x82142),x82144)))+~P1(f317(f317(f225(a897),x82144),f317(f179(f898(x82141)),x82142)))
% 94.68/94.46 [8267]~P110(x82671)+~P1(f317(f317(f224(x82671),x82672),f72(x82671)))+~P1(f317(f317(f224(x82671),f2(x82671)),x82672))+~P1(f317(f317(f224(a897),x82674),x82673))+P1(f317(f317(f224(x82671),f317(f317(f234(x82671),x82672),x82673)),f317(f317(f234(x82671),x82672),x82674)))
% 94.68/94.46 [8268]~P110(x82681)+~P1(f317(f317(f225(x82681),x82682),f72(x82681)))+~P1(f317(f317(f225(x82681),f2(x82681)),x82682))+~P1(f317(f317(f225(a897),x82684),x82683))+P1(f317(f317(f225(x82681),f317(f317(f234(x82681),x82682),x82683)),f317(f317(f234(x82681),x82682),x82684)))
% 94.68/94.46 [8269]~P110(x82691)+~P1(f317(f317(f224(x82691),f2(x82691)),x82692))+~P1(f317(f317(f225(a897),f2(a897)),x82693))+~P1(f317(f317(f225(x82691),x82692),x82694))+P1(f317(f317(f225(x82691),f317(f317(f234(x82691),x82692),x82693)),f317(f317(f234(x82691),x82694),x82693)))
% 94.68/94.46 [8287]~P66(x82871)+~P13(x82871,f317(f158(x82871),x82872))+~P1(f317(f317(f224(a897),x82874),x82873))+P1(f317(f317(f224(x82871),f317(f317(f154(x82871),x82872),x82873)),f317(f317(f154(x82871),x82872),x82874)))+~P1(f317(f317(f225(a897),x82873),f317(f179(f898(x82871)),x82872)))
% 94.68/94.46 [8518]~P3(x85181)+P1(f317(f317(f277(x85181),x85182),x85183))+~P1(f317(f317(f277(x85181),x85184),x85183))+~P1(f317(f317(f277(x85181),x85184),x85182))+~P1(f317(f317(f277(x85181),f317(f317(f30(x85181),x85182),x85184)),f317(f317(f30(x85181),x85183),x85184)))
% 94.68/94.46 [8533]~P63(x85331)+~P1(f317(f317(f224(x85331),x85332),f2(x85331)))+~P1(f317(f317(f224(x85331),x85333),x85334))+~P1(f317(f317(f225(x85331),f2(x85331)),f317(f317(f75(x85331),x85333),x85334)))+P1(f317(f317(f224(x85331),f317(f317(f281(x85331),x85332),x85333)),f317(f317(f281(x85331),x85332),x85334)))
% 94.68/94.46 [8534]~P64(x85341)+~P1(f317(f317(f225(x85341),x85342),f2(x85341)))+~P1(f317(f317(f225(x85341),x85343),x85344))+~P1(f317(f317(f225(x85341),f2(x85341)),f317(f317(f75(x85341),x85343),x85344)))+P1(f317(f317(f225(x85341),f317(f317(f281(x85341),x85342),x85343)),f317(f317(f281(x85341),x85342),x85344)))
% 94.68/94.46 [8543]~P64(x85431)+~P1(f317(f317(f224(x85431),x85434),x85433))+~P1(f317(f317(f224(x85431),f2(x85431)),x85432))+~P1(f317(f317(f225(x85431),f2(x85431)),f317(f317(f75(x85431),x85433),x85434)))+P1(f317(f317(f224(x85431),f317(f317(f281(x85431),x85432),x85433)),f317(f317(f281(x85431),x85432),x85434)))
% 94.68/94.46 [8544]~P64(x85441)+~P1(f317(f317(f225(x85441),x85444),x85443))+~P1(f317(f317(f225(x85441),f2(x85441)),x85442))+~P1(f317(f317(f225(x85441),f2(x85441)),f317(f317(f75(x85441),x85443),x85444)))+P1(f317(f317(f225(x85441),f317(f317(f281(x85441),x85442),x85443)),f317(f317(f281(x85441),x85442),x85444)))
% 94.68/94.46 [8644]P1(f317(x86441,x86442))+~P1(f317(f28(x86444),x86442))+P1(f317(x86441,f364(x86441,x86443,x86442,x86444)))+~P1(f317(x86441,f178(f904(x86444,a893))))+~P1(f317(f317(f224(f904(x86444,a893)),x86442),x86443))
% 94.68/94.46 [8653]P1(f317(x86531,x86532))+P1(f317(f28(x86533),f364(x86531,x86534,x86532,x86533)))+~P1(f317(f28(x86533),x86532))+~P1(f317(x86531,f178(f904(x86533,a893))))+~P1(f317(f317(f224(f904(x86533,a893)),x86532),x86534))
% 94.68/94.46 [8921]E(f317(f317(f74(a1),f374(x89211,x89212,x89213,x89214)),f375(x89211,x89212,x89213,x89214)),x89214)+~P1(f317(f317(f225(a1),f2(a1)),x89213))+~P1(f317(f317(f225(a1),x89212),x89214))+~P1(f317(f317(f319(a1),x89212),x89211))+P1(f317(f317(f225(a1),x89212),f317(f317(f23(a1),x89214),x89213)))
% 94.68/94.46 [9135]~P1(f317(f317(f225(a1),f2(a1)),x91353))+~P1(f317(f317(f225(a1),x91352),x91354))+~P1(f317(f317(f319(a1),x91352),x91351))+P1(f317(f317(f319(a1),f374(x91351,x91352,x91353,x91354)),x91351))+P1(f317(f317(f225(a1),x91352),f317(f317(f23(a1),x91354),x91353)))
% 94.68/94.46 [9146]P1(f317(x91461,x91462))+~P1(f317(f28(x91463),x91462))+P1(f317(f317(f319(x91463),f369(x91461,x91464,x91462,x91463)),x91464))+~P1(f317(x91461,f178(f904(x91463,a893))))+~P1(f317(f317(f224(f904(x91463,a893)),x91462),x91464))
% 94.68/94.46 [9163]E(f317(f317(f74(a1),f358(x91631,x91632,x91633,x91634)),f359(x91631,x91632,x91633,x91634)),x91634)+~P1(f317(f317(f225(a1),f2(a1)),x91633))+~P1(f317(f317(f224(a1),x91632),x91634))+P1(f317(f317(f224(a1),x91632),f317(f317(f23(a1),x91634),x91633)))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x91632),f72(a1))),x91631))
% 94.68/94.46 [9217]~P1(f317(f317(f225(a1),f2(a1)),x92173))+~P1(f317(f317(f225(a1),x92171),x92172))+~P1(f317(f317(f319(a1),x92171),x92174))+P1(f317(f317(f319(a1),f375(x92174,x92171,x92173,x92172)),f293(a1,f72(a1),x92173)))+P1(f317(f317(f225(a1),x92171),f317(f317(f23(a1),x92172),x92173)))
% 94.68/94.46 [9243]~P76(x92432)+~E(f758(x92433,x92434,x92431,x92432),f755(x92433,x92434,x92431,x92432))+~P1(f317(f28(x92431),f756(x92433,x92434,x92431,x92432)))+E(f317(f317(f6(f904(x92431,a893),x92432),f317(f6(x92431,x92432),x92433)),x92434),f317(f317(f6(x92431,x92432),x92433),f31(f904(x92431,a893),x92434)))+~P1(f317(f28(f904(x92431,a893)),x92434))
% 94.68/94.46 [9247]~P76(x92472)+~E(f317(x92473,f759(x92473,x92474,x92471,x92472)),f2(x92472))+~P1(f317(f28(x92471),f756(x92473,x92474,x92471,x92472)))+E(f317(f317(f6(f904(x92471,a893),x92472),f317(f6(x92471,x92472),x92473)),x92474),f317(f317(f6(x92471,x92472),x92473),f31(f904(x92471,a893),x92474)))+~P1(f317(f28(f904(x92471,a893)),x92474))
% 94.68/94.46 [9311]~P1(f317(f317(f225(a1),f2(a1)),x93113))+~P1(f317(f317(f224(a1),x93112),x93114))+P1(f317(f317(f319(a1),f358(x93111,x93112,x93113,x93114)),x93111))+P1(f317(f317(f224(a1),x93112),f317(f317(f23(a1),x93114),x93113)))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x93112),f72(a1))),x93111))
% 94.68/94.46 [9357]~P1(f317(f317(f225(a1),f2(a1)),x93573))+~P1(f317(f317(f224(a1),x93571),x93572))+P1(f317(f317(f319(a1),f359(x93574,x93571,x93573,x93572)),f293(a1,f72(a1),x93573)))+P1(f317(f317(f224(a1),x93571),f317(f317(f23(a1),x93572),x93573)))+~P1(f317(f317(f319(a1),f317(f317(f23(a1),x93571),f72(a1))),x93574))
% 94.68/94.46 [9379]~P76(x93792)+~E(f758(x93793,x93794,x93791,x93792),f755(x93793,x93794,x93791,x93792))+E(f317(f317(f6(f904(x93791,a893),x93792),f317(f6(x93791,x93792),x93793)),x93794),f317(f317(f6(x93791,x93792),x93793),f31(f904(x93791,a893),x93794)))+P1(f317(f317(f319(f904(x93791,a893)),f756(x93793,x93794,x93791,x93792)),x93794))+~P1(f317(f28(f904(x93791,a893)),x93794))
% 94.68/94.46 [9386]~P76(x93862)+~E(f317(x93863,f759(x93863,x93864,x93861,x93862)),f2(x93862))+E(f317(f317(f6(f904(x93861,a893),x93862),f317(f6(x93861,x93862),x93863)),x93864),f317(f317(f6(x93861,x93862),x93863),f31(f904(x93861,a893),x93864)))+P1(f317(f317(f319(f904(x93861,a893)),f756(x93863,x93864,x93861,x93862)),x93864))+~P1(f317(f28(f904(x93861,a893)),x93864))
% 94.68/94.46 [9487]~P76(x94872)+~P1(f317(f28(x94871),f756(x94873,x94874,x94871,x94872)))+E(f317(f317(f6(f904(x94871,a893),x94872),f317(f6(x94871,x94872),x94873)),x94874),f317(f317(f6(x94871,x94872),x94873),f31(f904(x94871,a893),x94874)))+P1(f317(f317(f319(f904(x94871,a893)),f755(x94873,x94874,x94871,x94872)),x94874))+~P1(f317(f28(f904(x94871,a893)),x94874))
% 94.68/94.46 [9488]~P76(x94882)+~P1(f317(f28(x94881),f756(x94883,x94884,x94881,x94882)))+E(f317(f317(f6(f904(x94881,a893),x94882),f317(f6(x94881,x94882),x94883)),x94884),f317(f317(f6(x94881,x94882),x94883),f31(f904(x94881,a893),x94884)))+P1(f317(f317(f319(f904(x94881,a893)),f758(x94883,x94884,x94881,x94882)),x94884))+~P1(f317(f28(f904(x94881,a893)),x94884))
% 94.68/94.46 [9568]~P76(x95682)+E(f317(f317(f6(f904(x95681,a893),x95682),f317(f6(x95681,x95682),x95683)),x95684),f317(f317(f6(x95681,x95682),x95683),f31(f904(x95681,a893),x95684)))+P1(f317(f317(f319(f904(x95681,a893)),f756(x95683,x95684,x95681,x95682)),x95684))+P1(f317(f317(f319(f904(x95681,a893)),f755(x95683,x95684,x95681,x95682)),x95684))+~P1(f317(f28(f904(x95681,a893)),x95684))
% 94.68/94.46 [9569]~P76(x95692)+E(f317(f317(f6(f904(x95691,a893),x95692),f317(f6(x95691,x95692),x95693)),x95694),f317(f317(f6(x95691,x95692),x95693),f31(f904(x95691,a893),x95694)))+P1(f317(f317(f319(f904(x95691,a893)),f756(x95693,x95694,x95691,x95692)),x95694))+P1(f317(f317(f319(f904(x95691,a893)),f758(x95693,x95694,x95691,x95692)),x95694))+~P1(f317(f28(f904(x95691,a893)),x95694))
% 94.68/94.46 [9590]~P76(x95902)+P1(f317(f317(f319(x95901),f759(x95903,x95904,x95901,x95902)),f755(x95903,x95904,x95901,x95902)))+~P1(f317(f28(x95901),f756(x95903,x95904,x95901,x95902)))+E(f317(f317(f6(f904(x95901,a893),x95902),f317(f6(x95901,x95902),x95903)),x95904),f317(f317(f6(x95901,x95902),x95903),f31(f904(x95901,a893),x95904)))+~P1(f317(f28(f904(x95901,a893)),x95904))
% 94.68/94.46 [9591]~P76(x95912)+P1(f317(f317(f319(x95911),f759(x95913,x95914,x95911,x95912)),f758(x95913,x95914,x95911,x95912)))+~P1(f317(f28(x95911),f756(x95913,x95914,x95911,x95912)))+E(f317(f317(f6(f904(x95911,a893),x95912),f317(f6(x95911,x95912),x95913)),x95914),f317(f317(f6(x95911,x95912),x95913),f31(f904(x95911,a893),x95914)))+~P1(f317(f28(f904(x95911,a893)),x95914))
% 94.68/94.46 [9608]P1(f317(x96081,x96082))+~P1(f317(f317(f319(x96083),f369(x96081,x96084,x96082,x96083)),f364(x96081,x96084,x96082,x96083)))+~P1(f317(f28(x96083),x96082))+~P1(f317(x96081,f178(f904(x96083,a893))))+~P1(f317(f317(f224(f904(x96083,a893)),x96082),x96084))
% 94.68/94.46 [9645]~P76(x96452)+P1(f317(f317(f319(x96451),f759(x96453,x96454,x96451,x96452)),f755(x96453,x96454,x96451,x96452)))+E(f317(f317(f6(f904(x96451,a893),x96452),f317(f6(x96451,x96452),x96453)),x96454),f317(f317(f6(x96451,x96452),x96453),f31(f904(x96451,a893),x96454)))+P1(f317(f317(f319(f904(x96451,a893)),f756(x96453,x96454,x96451,x96452)),x96454))+~P1(f317(f28(f904(x96451,a893)),x96454))
% 94.68/94.46 [9646]~P76(x96462)+P1(f317(f317(f319(x96461),f759(x96463,x96464,x96461,x96462)),f758(x96463,x96464,x96461,x96462)))+E(f317(f317(f6(f904(x96461,a893),x96462),f317(f6(x96461,x96462),x96463)),x96464),f317(f317(f6(x96461,x96462),x96463),f31(f904(x96461,a893),x96464)))+P1(f317(f317(f319(f904(x96461,a893)),f756(x96463,x96464,x96461,x96462)),x96464))+~P1(f317(f28(f904(x96461,a893)),x96464))
% 94.68/94.46 [9821]P1(f317(x98211,x98212))+~P1(f317(f28(x98213),x98212))+~P1(f317(x98211,f317(f317(f299(x98213),f369(x98211,x98214,x98212,x98213)),f364(x98211,x98214,x98212,x98213))))+~P1(f317(x98211,f178(f904(x98213,a893))))+~P1(f317(f317(f224(f904(x98213,a893)),x98212),x98214))
% 94.68/94.46 [10152]~P108(x101523)+~P48(a897,x101523,f317(f317(f18(a897,f904(a897,a893),f904(a897,a893)),f317(f317(f8(f904(a897,f904(a893,a893)),f904(f904(a897,a893),f904(a897,a893)),a897),f18(a897,a893,a893)),f317(f317(f8(f904(a897,a893),f904(a897,f904(a893,a893)),a897),f317(f8(a893,f904(a893,a893),a897),a315)),f277(a897)))),f317(f317(f8(f904(a897,a893),f904(a897,a893),a897),f317(f8(a893,a893,a897),a312)),f317(f7(a897,a897,a893),f277(a897)))),x101524)+P1(f317(f317(f225(x101523),f317(x101524,x101522)),f317(x101524,x101521)))+~P1(f317(f317(f277(a897),x101522),x101521))+P1(f317(f317(f277(a897),x101521),x101522))
% 94.68/94.46 [7839]~P63(x78391)+P1(f317(f317(f225(x78391),x78392),f2(x78391)))+~P1(f317(f317(f224(x78391),f2(x78391)),x78394))+P1(f317(f317(f225(x78391),f2(x78391)),x78392))+P1(f317(f317(f224(x78391),f317(f317(f281(x78391),x78393),x78392)),x78394))
% 94.68/94.46 [7840]~P63(x78401)+P1(f317(f317(f225(x78401),x78402),f2(x78401)))+P1(f317(f317(f225(x78401),f2(x78401)),x78402))+~P1(f317(f317(f225(x78401),f2(x78401)),x78404))+P1(f317(f317(f225(x78401),f317(f317(f281(x78401),x78403),x78402)),x78404))
% 94.68/94.46 [8120]~P1(f317(f317(f224(a1),x81204),f2(a1)))+~E(x81202,f317(f317(f74(a1),f317(f317(f75(a1),x81201),x81203)),x81204))+P1(f317(f317(f225(a1),f2(a1)),x81201))+~P1(f317(f317(f225(a1),x81201),x81204))+P1(f317(f44(x81202,x81201),f317(f317(f242(a1,a1),x81203),x81204)))
% 94.68/94.46 [8154]~P1(f317(x81541,x81544))+P1(f317(x81541,f808(x81542,x81541,x81543)))+~P1(f317(f317(f224(a1),f2(a1)),x81542))+~P1(f317(f317(f225(a1),f2(a1)),x81543))+P1(f317(x81541,f317(f317(f23(a1),x81544),f317(f317(f75(a1),x81542),x81543))))
% 94.68/94.46 [8155]~P1(f317(x81551,x81554))+P1(f317(x81551,f347(x81552,x81551,x81553)))+~P1(f317(f317(f224(a1),f2(a1)),x81552))+~P1(f317(f317(f225(a1),f2(a1)),x81553))+P1(f317(x81551,f317(f317(f74(a1),x81554),f317(f317(f75(a1),x81552),x81553))))
% 94.68/94.46 [8156]~P63(x81561)+P1(f317(f317(f225(x81561),x81562),f2(x81561)))+P1(f317(f317(f225(x81561),f2(x81561)),x81562))+P1(f317(f317(f224(x81561),f2(x81561)),x81563))+~P1(f317(f317(f224(x81561),f317(f317(f281(x81561),x81564),x81562)),x81563))
% 94.68/94.46 [8157]~P63(x81571)+P1(f317(f317(f225(x81571),x81572),f2(x81571)))+P1(f317(f317(f225(x81571),f2(x81571)),x81572))+P1(f317(f317(f225(x81571),f2(x81571)),x81573))+~P1(f317(f317(f225(x81571),f317(f317(f281(x81571),x81574),x81572)),x81573))
% 94.68/94.46 [8209]~E(x82091,f317(f317(f74(a1),f317(f317(f75(a1),x82092),x82093)),x82094))+~P1(f317(f317(f224(a1),f2(a1)),x82094))+~P1(f317(f317(f225(a1),f2(a1)),x82092))+~P1(f317(f317(f225(a1),x82094),x82092))+P1(f317(f44(x82091,x82092),f317(f317(f242(a1,a1),x82093),x82094)))
% 94.68/94.46 [8326]~P63(x83261)+P1(f317(f317(f225(x83261),x83262),f2(x83261)))+~P1(f317(f317(f224(x83261),f2(x83261)),x83264))+~P1(f317(f317(f224(x83261),x83263),f317(f317(f75(x83261),x83264),x83262)))+P1(f317(f317(f224(x83261),f317(f317(f281(x83261),x83263),x83262)),x83264))
% 94.68/94.46 [8327]~P63(x83271)+P1(f317(f317(f225(x83271),x83272),f2(x83271)))+~P1(f317(f317(f225(x83271),f2(x83271)),x83274))+~P1(f317(f317(f225(x83271),x83273),f317(f317(f75(x83271),x83274),x83272)))+P1(f317(f317(f225(x83271),f317(f317(f281(x83271),x83273),x83272)),x83274))
% 94.68/94.46 [8412]~P63(x84121)+P1(f317(f317(f225(x84121),x84122),f2(x84121)))+~P1(f317(f317(f224(x84121),x84123),f2(x84121)))+P1(f317(f317(f224(x84121),x84123),f317(f317(f281(x84121),x84124),x84122)))+~P1(f317(f317(f224(x84121),f317(f317(f75(x84121),x84123),x84122)),x84124))
% 94.68/94.46 [8413]~P63(x84131)+P1(f317(f317(f225(x84131),x84132),f2(x84131)))+~P1(f317(f317(f225(x84131),x84133),f2(x84131)))+P1(f317(f317(f225(x84131),x84133),f317(f317(f281(x84131),x84134),x84132)))+~P1(f317(f317(f225(x84131),f317(f317(f75(x84131),x84133),x84132)),x84134))
% 94.68/94.46 [8565]~P63(x85651)+~P1(f317(f317(f225(x85651),x85652),f2(x85651)))+P1(f317(f317(f225(x85651),f2(x85651)),x85652))+~P1(f317(f317(f224(x85651),f317(f317(f281(x85651),x85654),x85652)),x85653))+P1(f317(f317(f224(x85651),f317(f317(f75(x85651),x85653),x85652)),x85654))
% 94.68/94.46 [8566]~P63(x85661)+~P1(f317(f317(f225(x85661),x85662),f2(x85661)))+P1(f317(f317(f225(x85661),f2(x85661)),x85662))+~P1(f317(f317(f224(x85661),f317(f317(f75(x85661),x85664),x85662)),x85663))+P1(f317(f317(f224(x85661),f317(f317(f281(x85661),x85663),x85662)),x85664))
% 94.68/94.46 [8567]~P63(x85671)+~P1(f317(f317(f225(x85671),x85672),f2(x85671)))+P1(f317(f317(f225(x85671),f2(x85671)),x85672))+~P1(f317(f317(f225(x85671),f317(f317(f281(x85671),x85674),x85672)),x85673))+P1(f317(f317(f225(x85671),f317(f317(f75(x85671),x85673),x85672)),x85674))
% 94.68/94.46 [8568]~P63(x85681)+~P1(f317(f317(f225(x85681),x85682),f2(x85681)))+P1(f317(f317(f225(x85681),f2(x85681)),x85682))+~P1(f317(f317(f225(x85681),f317(f317(f75(x85681),x85684),x85682)),x85683))+P1(f317(f317(f225(x85681),f317(f317(f281(x85681),x85683),x85682)),x85684))
% 94.68/94.46 [8584]~P63(x85841)+~P1(f317(f317(f224(x85841),f2(x85841)),x85844))+P1(f317(f317(f225(x85841),f2(x85841)),x85842))+~P1(f317(f317(f224(x85841),f317(f317(f75(x85841),x85844),x85842)),x85843))+P1(f317(f317(f224(x85841),f317(f317(f281(x85841),x85843),x85842)),x85844))
% 94.68/94.46 [8585]~P63(x85851)+~P1(f317(f317(f225(x85851),f2(x85851)),x85854))+P1(f317(f317(f225(x85851),f2(x85851)),x85852))+~P1(f317(f317(f225(x85851),f317(f317(f75(x85851),x85854),x85852)),x85853))+P1(f317(f317(f225(x85851),f317(f317(f281(x85851),x85853),x85852)),x85854))
% 94.68/94.46 [8661]~P63(x86611)+~P1(f317(f317(f225(x86611),x86614),f2(x86611)))+~P1(f317(f317(f224(x86611),x86613),f317(f317(f75(x86611),x86612),x86614)))+P1(f317(f317(f224(x86611),x86612),f317(f317(f281(x86611),x86613),x86614)))+~P1(f317(f317(f224(x86611),f317(f317(f75(x86611),x86612),x86614)),x86613))
% 94.68/94.46 [8662]~P63(x86621)+~P1(f317(f317(f224(x86621),x86622),f2(x86621)))+~P1(f317(f317(f224(x86621),x86623),f317(f317(f75(x86621),x86622),x86624)))+P1(f317(f317(f224(x86621),x86622),f317(f317(f281(x86621),x86623),x86624)))+~P1(f317(f317(f224(x86621),f317(f317(f75(x86621),x86622),x86624)),x86623))
% 94.68/94.46 [8663]~P63(x86631)+~P1(f317(f317(f225(x86631),x86634),f2(x86631)))+~P1(f317(f317(f225(x86631),x86633),f317(f317(f75(x86631),x86632),x86634)))+P1(f317(f317(f225(x86631),x86632),f317(f317(f281(x86631),x86633),x86634)))+~P1(f317(f317(f225(x86631),f317(f317(f75(x86631),x86632),x86634)),x86633))
% 94.68/94.46 [8664]~P63(x86641)+~P1(f317(f317(f225(x86641),x86642),f2(x86641)))+~P1(f317(f317(f225(x86641),x86643),f317(f317(f75(x86641),x86642),x86644)))+P1(f317(f317(f225(x86641),x86642),f317(f317(f281(x86641),x86643),x86644)))+~P1(f317(f317(f225(x86641),f317(f317(f75(x86641),x86642),x86644)),x86643))
% 94.68/94.46 [8786]~P63(x87861)+~P1(f317(f317(f225(x87861),x87863),f2(x87861)))+~P1(f317(f317(f224(x87861),x87862),f317(f317(f75(x87861),x87864),x87863)))+~P1(f317(f317(f224(x87861),f317(f317(f75(x87861),x87864),x87863)),x87862))+P1(f317(f317(f224(x87861),f317(f317(f281(x87861),x87862),x87863)),x87864))
% 94.68/94.46 [8787]~P63(x87871)+~P1(f317(f317(f225(x87871),x87873),f2(x87871)))+~P1(f317(f317(f225(x87871),x87872),f317(f317(f75(x87871),x87874),x87873)))+~P1(f317(f317(f225(x87871),f317(f317(f75(x87871),x87874),x87873)),x87872))+P1(f317(f317(f225(x87871),f317(f317(f281(x87871),x87872),x87873)),x87874))
% 94.68/94.46 [8804]~P63(x88041)+~P1(f317(f317(f224(x88041),f2(x88041)),x88044))+~P1(f317(f317(f224(x88041),x88042),f317(f317(f75(x88041),x88044),x88043)))+~P1(f317(f317(f224(x88041),f317(f317(f75(x88041),x88044),x88043)),x88042))+P1(f317(f317(f224(x88041),f317(f317(f281(x88041),x88042),x88043)),x88044))
% 94.68/94.46 [8805]~P63(x88051)+~P1(f317(f317(f225(x88051),f2(x88051)),x88054))+~P1(f317(f317(f225(x88051),x88052),f317(f317(f75(x88051),x88054),x88053)))+~P1(f317(f317(f225(x88051),f317(f317(f75(x88051),x88054),x88053)),x88052))+P1(f317(f317(f225(x88051),f317(f317(f281(x88051),x88052),x88053)),x88054))
% 94.68/94.46 [8988]E(f317(f317(f23(a1),f367(x89881,x89882,x89883,x89884)),f368(x89881,x89882,x89883,x89884)),x89884)+~P1(f317(f317(f225(a1),f2(a1)),x89883))+~P1(f317(f317(f319(a1),x89882),x89881))+~P1(f317(f317(f225(a1),x89884),x89882))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x89884),x89883)),x89882))
% 94.68/94.46 [9059]~P1(f317(x90591,x90592))+~P1(f317(f317(f224(a1),f2(a1)),x90593))+~P1(f317(f317(f225(a1),f2(a1)),x90594))+~P1(f317(x90591,f317(f317(f23(a1),f808(x90593,x90591,x90594)),x90594)))+P1(f317(x90591,f317(f317(f23(a1),x90592),f317(f317(f75(a1),x90593),x90594))))
% 94.68/94.46 [9060]~P1(f317(x90601,x90602))+~P1(f317(f317(f224(a1),f2(a1)),x90603))+~P1(f317(f317(f225(a1),f2(a1)),x90604))+~P1(f317(x90601,f317(f317(f74(a1),f347(x90603,x90601,x90604)),x90604)))+P1(f317(x90601,f317(f317(f74(a1),x90602),f317(f317(f75(a1),x90603),x90604))))
% 94.68/94.46 [9211]~P1(f317(f317(f225(a1),f2(a1)),x92113))+~P1(f317(f317(f319(a1),x92112),x92111))+~P1(f317(f317(f225(a1),x92114),x92112))+P1(f317(f317(f319(a1),f367(x92111,x92112,x92113,x92114)),x92111))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x92114),x92113)),x92112))
% 94.68/94.46 [9230]E(f317(f317(f23(a1),f360(x92301,x92302,x92303,x92304)),f361(x92301,x92302,x92303,x92304)),x92304)+~P1(f317(f317(f225(a1),f2(a1)),x92303))+~P1(f317(f317(f224(a1),x92304),x92302))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x92302),f72(a1))),x92301))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x92304),x92303)),x92302))
% 94.68/94.46 [9258]~P1(f317(f317(f225(a1),f2(a1)),x92582))+~P1(f317(f317(f319(a1),x92583),x92584))+~P1(f317(f317(f225(a1),x92581),x92583))+P1(f317(f317(f319(a1),f368(x92584,x92583,x92582,x92581)),f293(a1,f72(a1),x92582)))+P1(f317(f317(f225(a1),f317(f317(f74(a1),x92581),x92582)),x92583))
% 94.68/94.46 [9349]~P1(f317(f317(f225(a1),f2(a1)),x93493))+~P1(f317(f317(f224(a1),x93494),x93492))+P1(f317(f317(f319(a1),f360(x93491,x93492,x93493,x93494)),x93491))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x93492),f72(a1))),x93491))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x93494),x93493)),x93492))
% 94.68/94.46 [9397]~P1(f317(f317(f225(a1),f2(a1)),x93972))+~P1(f317(f317(f224(a1),x93971),x93973))+P1(f317(f317(f319(a1),f361(x93974,x93973,x93972,x93971)),f293(a1,f72(a1),x93972)))+~P1(f317(f317(f319(a1),f317(f317(f74(a1),x93973),f72(a1))),x93974))+P1(f317(f317(f224(a1),f317(f317(f74(a1),x93971),x93972)),x93973))
% 94.68/94.46 [9699]~P36(x96991,x96993)+~P26(x96991,x96994)+P36(x96991,f317(f317(f91(f904(f903(x96991,x96991),a893)),x96992),x96993))+~P1(f317(f317(f224(f904(f903(x96991,x96991),a893)),x96992),f317(f241(f904(f903(x96991,x96991),a893),f904(f903(x96991,x96991),a893)),x96994)))+~P1(f317(f317(f224(f904(f903(x96991,x96991),a893)),x96993),f317(f246(f904(f903(x96991,x96991),a893),f904(f903(x96991,x96991),a893)),x96994)))
% 94.68/94.46 [10086]~P18(x100862,x100864,x100863)+E(x100861,f178(f904(x100862,a893)))+~P1(f317(f28(x100862),x100861))+P1(f317(f317(f319(x100862),f317(x100863,x100861)),x100861))+~P1(f317(f317(f319(x100862),f317(f317(x100864,f432(x100861,x100863,x100864,x100862)),f446(x100861,x100863,x100864,x100862))),f317(f317(f299(x100862),f432(x100861,x100863,x100864,x100862)),f317(f317(f299(x100862),f446(x100861,x100863,x100864,x100862)),f178(f904(x100862,a893))))))
% 94.68/94.46 [10011]~P108(x100112)+~P60(x100111)+~P1(f317(f317(f224(f904(x100111,x100112)),x100113),x100114))+P1(f317(f317(f225(f904(x100111,x100112)),x100113),x100114))+~P1(f317(f51(x100111),f317(f317(f8(a893,a893,x100111),a312),f317(f317(f18(x100111,x100112,a893),f317(f317(f8(x100112,f904(x100112,a893),x100111),a314),x100113)),x100114))))
% 94.68/94.46 [9614]~P54(x96141,x96141,x96144)+P1(f317(f317(f319(f903(x96141,x96141)),f317(f317(f242(x96141,x96141),x96142),x96143)),f297(x96141,x96144)))+P1(f317(f317(f319(f903(x96141,x96141)),f317(f317(f242(x96141,x96141),x96143),x96142)),f297(x96141,x96144)))+~P1(f317(f317(f319(f903(x96141,x96141)),f317(f317(f242(x96141,x96141),x96145),x96142)),f297(x96141,x96144)))+~P1(f317(f317(f319(f903(x96141,x96141)),f317(f317(f242(x96141,x96141),x96145),x96143)),f297(x96141,x96144)))
% 94.68/94.46 [5692]E(x56921,f2(a897))+~E(f317(f29(x56922),x56925),x56921)+E(f317(f29(x56922),x56923),f317(a102,x56921))+~E(x56923,f317(f317(f299(x56922),x56924),x56925))+P1(f317(f317(f319(x56922),x56924),x56925))
% 94.68/94.46 [5814]~P62(x58142)+E(x58141,f2(x58142))+E(x58143,f2(x58142))+~E(f317(f317(f281(x58142),x58144),x58143),f317(f317(f281(x58142),x58145),x58141))+E(f317(f317(f75(x58142),x58144),x58141),f317(f317(f75(x58142),x58145),x58143))
% 94.68/94.46 [5815]~P62(x58152)+E(x58151,f2(x58152))+E(x58153,f2(x58152))+~E(f317(f317(f75(x58152),x58154),x58153),f317(f317(f75(x58152),x58155),x58151))+E(f317(f317(f281(x58152),x58154),x58151),f317(f317(f281(x58152),x58155),x58153))
% 94.68/94.46 [5893]~E(f317(f29(x58931),x58935),x58933)+~E(x58935,f178(f904(x58931,a893)))+E(f317(f29(x58931),x58932),f317(a102,x58933))+~E(x58932,f317(f317(f299(x58931),x58934),x58935))+P1(f317(f317(f319(x58931),x58934),x58935))
% 94.68/94.46 [6134]~P112(x61342)+~E(f317(x61343,x61345),f2(x61342))+E(f317(f317(f9(x61341,x61342),x61343),x61344),f2(x61342))+~P1(f317(f28(x61341),x61344))+~P1(f317(f317(f319(x61341),x61345),x61344))
% 94.68/94.46 [6518]~P66(x65183)+E(x65181,x65182)+~E(f317(f292(x65183,x65184),x65181),f317(f292(x65183,x65185),x65182))+~P1(f317(f317(f225(x65183),x65185),x65182))+~P1(f317(f317(f225(x65183),x65184),x65181))
% 94.68/94.46 [6519]~P66(x65193)+E(x65191,x65192)+~E(f317(f292(x65193,x65191),x65194),f317(f292(x65193,x65192),x65195))+~P1(f317(f317(f225(x65193),x65192),x65195))+~P1(f317(f317(f225(x65193),x65191),x65194))
% 94.68/94.46 [7600]~P66(x76001)+~P13(x76001,f317(f317(f124(x76001),x76004),x76005))+~P1(f317(f317(f319(x76001),x76003),f317(f162(x76001),x76005)))+~P1(f317(f317(f319(x76001),x76002),f317(f162(x76001),x76004)))+P1(f317(f317(f224(x76001),x76002),x76003))
% 94.68/94.46 [8698]~P108(x86981)+~P1(f317(f317(f225(f904(x86981,a893)),f293(x86981,x86985,x86982)),f293(x86981,x86984,x86983)))+~P1(f317(f317(f224(x86981),x86985),x86982))+P1(f317(f317(f225(x86981),x86982),x86983))+P1(f317(f317(f225(x86981),x86984),x86985))
% 94.68/94.46 [10129]~P17(x101292,x101295,x101293)+E(x101291,f178(f904(x101292,a893)))+~E(f317(f317(x101295,f317(x101294,f391(x101291,x101294,x101293,x101295,x101292))),f317(x101294,f405(x101291,x101294,x101293,x101295,x101292))),f317(x101294,f317(f317(x101295,f391(x101291,x101294,x101293,x101295,x101292)),f405(x101291,x101294,x101293,x101295,x101292))))+E(f317(x101293,f317(f300(x101292,x101292,x101294),x101291)),f317(x101294,f317(x101293,x101291)))+~P1(f317(f28(x101292),x101291))
% 94.68/94.46 [6515]~P18(x65152,x65155,x65153)+E(x65151,f178(f904(x65152,a893)))+~P1(f317(f28(x65152),x65151))+E(f317(x65153,f317(f317(f299(x65152),x65154),x65151)),f317(f317(x65155,x65154),f317(x65153,x65151)))+P1(f317(f317(f319(x65152),x65154),x65151))
% 94.68/94.46 [7361]~P17(x73612,x73613,x73614)+E(f317(f317(x73613,f317(x73614,x73611)),f317(x73614,x73615)),f317(x73614,x73615))+E(x73611,f178(f904(x73612,a893)))+~P1(f317(f28(x73612),x73615))+~P1(f317(f317(f224(f904(x73612,a893)),x73611),x73615))
% 94.68/94.46 [7738]~P18(x77384,x77385,x77381)+E(f317(x77381,x77382),x77383)+~P1(f317(f28(x77384),x77382))+~E(f317(f317(f23(f904(x77384,a893)),x77382),f317(f317(f299(x77384),x77383),f178(f904(x77384,a893)))),f178(f904(x77384,a893)))+~P1(f317(f317(f319(x77384),x77383),x77382))
% 94.68/94.46 [8619]~P77(x86191)+~P121(x86191)+~P1(f317(f28(x86192),x86195))+P1(f317(f317(f277(x86191),f317(f317(f9(x86192,x86191),x86193),x86194)),f317(f317(f9(x86192,x86191),x86193),x86195)))+~P1(f317(f317(f224(f904(x86192,a893)),x86194),x86195))
% 94.68/94.46 [8668]E(x86681,x86682)+~P8(x86683,x86684,x86685)+E(f317(f317(f92(f904(x86683,a893)),x86681),x86682),f178(f904(x86683,a893)))+~P1(f317(f317(f319(f904(x86683,a893)),x86682),f317(f317(f55(x86683),x86684),x86685)))+~P1(f317(f317(f319(f904(x86683,a893)),x86681),f317(f317(f55(x86683),x86684),x86685)))
% 94.68/94.46 [9480]~P77(x94802)+~E(f317(x94803,f348(x94803,x94804,x94805,x94801,x94802)),f72(x94802))+E(f317(f317(f9(x94801,x94802),x94803),x94804),f317(f317(f9(x94801,x94802),x94803),x94805))+~P1(f317(f28(x94801),x94805))+~P1(f317(f317(f224(f904(x94801,a893)),x94804),x94805))
% 94.68/94.46 [9481]~P77(x94812)+~E(f317(x94813,f349(x94813,x94814,x94815,x94811,x94812)),f72(x94812))+E(f317(f317(f9(x94811,x94812),x94813),x94814),f317(f317(f9(x94811,x94812),x94813),x94815))+~P1(f317(f28(x94811),x94815))+~P1(f317(f317(f224(f904(x94811,a893)),x94814),x94815))
% 94.68/94.46 [9482]~P76(x94822)+~E(f317(x94823,f424(x94823,x94824,x94825,x94821,x94822)),f2(x94822))+E(f317(f317(f6(x94821,x94822),x94823),x94824),f317(f317(f6(x94821,x94822),x94823),x94825))+~P1(f317(f28(x94821),x94825))+~P1(f317(f317(f224(f904(x94821,a893)),x94824),x94825))
% 94.68/94.46 [9483]~P76(x94832)+~E(f317(x94833,f425(x94833,x94834,x94835,x94831,x94832)),f2(x94832))+E(f317(f317(f6(x94831,x94832),x94833),x94834),f317(f317(f6(x94831,x94832),x94833),x94835))+~P1(f317(f28(x94831),x94835))+~P1(f317(f317(f224(f904(x94831,a893)),x94834),x94835))
% 94.68/94.46 [9964]~P89(x99641)+~P1(f317(f28(x99642),x99645))+~P1(f317(f317(f224(x99641),f2(x99641)),f317(x99643,f406(x99643,x99644,x99645,x99642,x99641))))+P1(f317(f317(f224(x99641),f317(f317(f6(x99642,x99641),x99643),x99644)),f317(f317(f6(x99642,x99641),x99643),x99645)))+~P1(f317(f317(f224(f904(x99642,a893)),x99644),x99645))
% 94.68/94.46 [7597]E(x75971,f2(a897))+P1(f317(x75972,x75973))+~E(x75974,f317(f317(f74(a897),f317(f317(f75(a897),x75971),x75973)),x75975))+~P1(f317(f317(f225(a897),x75975),x75971))+~P1(f317(x75972,f317(f317(f30(a897),x75974),x75971)))
% 94.68/94.46 [7676]E(x76761,f2(a897))+P1(f317(x76762,x76763))+~P1(f317(x76762,f40(a897,x76764,x76761)))+~E(x76764,f317(f317(f74(a897),f317(f317(f75(a897),x76761),x76765)),x76763))+~P1(f317(f317(f225(a897),x76763),x76761))
% 94.68/94.46 [7970]~P62(x79703)+E(f317(x79701,x79702),f2(x79703))+~P1(f317(f28(x79704),x79705))+E(f317(f317(f9(x79704,x79703),x79701),f317(f317(f23(f904(x79704,a893)),x79705),f317(f317(f299(x79704),x79702),f178(f904(x79704,a893))))),f317(f317(f9(x79704,x79703),x79701),x79705))+P1(f317(f317(f319(x79704),x79702),x79705))
% 94.68/94.46 [8368]~P77(x83681)+~P1(f317(f28(x83682),x83685))+~P1(f317(f28(x83682),x83684))+~E(f317(f317(f92(f904(x83682,a893)),x83684),x83685),f178(f904(x83682,a893)))+E(f317(f317(f75(x83681),f317(f317(f9(x83682,x83681),x83683),x83684)),f317(f317(f9(x83682,x83681),x83683),x83685)),f317(f317(f9(x83682,x83681),x83683),f317(f317(f91(f904(x83682,a893)),x83684),x83685)))
% 94.68/94.46 [8369]~P76(x83691)+~P1(f317(f28(x83692),x83695))+~P1(f317(f28(x83692),x83694))+~E(f317(f317(f92(f904(x83692,a893)),x83694),x83695),f178(f904(x83692,a893)))+E(f317(f317(f74(x83691),f317(f317(f6(x83692,x83691),x83693),x83694)),f317(f317(f6(x83692,x83691),x83693),x83695)),f317(f317(f6(x83692,x83691),x83693),f317(f317(f91(f904(x83692,a893)),x83694),x83695)))
% 94.68/94.46 [8468]~P62(x84683)+E(f317(x84681,x84682),f2(x84683))+~P1(f317(f28(x84684),x84685))+E(f317(f317(f9(x84684,x84683),x84681),f317(f317(f23(f904(x84684,a893)),x84685),f317(f317(f299(x84684),x84682),f178(f904(x84684,a893))))),f317(f317(f281(x84683),f317(f317(f9(x84684,x84683),x84681),x84685)),f317(x84681,x84682)))+~P1(f317(f317(f319(x84684),x84682),x84685))
% 94.68/94.46 [9188]~P8(x91881,x91885,x91884)+~E(f317(f317(f55(x91881),f317(f317(f299(x91881),x91882),f178(f904(x91881,a893)))),x91884),f317(f317(f55(x91881),f317(f317(f299(x91881),x91883),f178(f904(x91881,a893)))),x91884))+~P1(f317(f317(f319(x91881),x91883),x91885))+~P1(f317(f317(f319(x91881),x91882),x91885))+P1(f317(f317(f319(f903(x91881,x91881)),f317(f317(f242(x91881,x91881),x91882),x91883)),x91884))
% 94.68/94.46 [9210]~P8(x92101,x92105,x92103)+E(f317(f317(f55(x92101),f317(f317(f299(x92101),x92102),f178(f904(x92101,a893)))),x92103),f317(f317(f55(x92101),f317(f317(f299(x92101),x92104),f178(f904(x92101,a893)))),x92103))+~P1(f317(f317(f319(x92101),x92104),x92105))+~P1(f317(f317(f319(x92101),x92102),x92105))+~P1(f317(f317(f319(f903(x92101,x92101)),f317(f317(f242(x92101,x92101),x92102),x92104)),x92103))
% 94.68/94.46 [9509]~P77(x95091)+~P1(f317(f28(x95092),x95095))+~P1(f317(f28(x95092),x95094))+~E(f317(f317(f92(f904(x95092,a893)),x95094),x95095),f178(f904(x95092,a893)))+E(f317(f317(f75(x95091),f317(f317(f317(f59(x95091,x95092,f75(x95091)),x95093),f72(x95091)),x95094)),f317(f317(f317(f59(x95091,x95092,f75(x95091)),x95093),f72(x95091)),x95095)),f317(f317(f317(f59(x95091,x95092,f75(x95091)),x95093),f72(x95091)),f317(f317(f91(f904(x95092,a893)),x95094),x95095)))
% 94.68/94.46 [9520]~P77(x95201)+~E(f317(x95203,f402(x95203,x95205,x95204,x95202,x95201)),f72(x95201))+~P1(f317(f28(x95202),x95204))+~P1(f317(f28(x95202),x95205))+E(f317(f317(f75(x95201),f317(f317(f9(x95202,x95201),x95203),x95204)),f317(f317(f9(x95202,x95201),x95203),x95205)),f317(f317(f9(x95202,x95201),x95203),f317(f317(f91(f904(x95202,a893)),x95204),x95205)))
% 94.68/94.46 [9521]~P77(x95211)+~E(f317(x95213,f407(x95213,x95215,x95214,x95212,x95211)),f72(x95211))+~P1(f317(f28(x95212),x95214))+~P1(f317(f28(x95212),x95215))+E(f317(f317(f75(x95211),f317(f317(f9(x95212,x95211),x95213),x95214)),f317(f317(f9(x95212,x95211),x95213),x95215)),f317(f317(f9(x95212,x95211),x95213),f317(f317(f91(f904(x95212,a893)),x95214),x95215)))
% 94.68/94.46 [9522]~P76(x95221)+~E(f317(x95223,f415(x95223,x95225,x95224,x95222,x95221)),f2(x95221))+~P1(f317(f28(x95222),x95224))+~P1(f317(f28(x95222),x95225))+E(f317(f317(f74(x95221),f317(f317(f6(x95222,x95221),x95223),x95224)),f317(f317(f6(x95222,x95221),x95223),x95225)),f317(f317(f6(x95222,x95221),x95223),f317(f317(f91(f904(x95222,a893)),x95224),x95225)))
% 94.68/94.46 [9523]~P76(x95231)+~E(f317(x95233,f416(x95233,x95235,x95234,x95232,x95231)),f2(x95231))+~P1(f317(f28(x95232),x95234))+~P1(f317(f28(x95232),x95235))+E(f317(f317(f74(x95231),f317(f317(f6(x95232,x95231),x95233),x95234)),f317(f317(f6(x95232,x95231),x95233),x95235)),f317(f317(f6(x95232,x95231),x95233),f317(f317(f91(f904(x95232,a893)),x95234),x95235)))
% 94.68/94.46 [9742]~P77(x97421)+~E(f317(x97423,f404(x97423,x97425,x97424,x97422,x97421)),f72(x97421))+~P1(f317(f28(x97422),x97424))+~P1(f317(f28(x97422),x97425))+E(f317(f317(f75(x97421),f317(f317(f317(f59(x97421,x97422,f75(x97421)),x97423),f72(x97421)),x97424)),f317(f317(f317(f59(x97421,x97422,f75(x97421)),x97423),f72(x97421)),x97425)),f317(f317(f317(f59(x97421,x97422,f75(x97421)),x97423),f72(x97421)),f317(f317(f91(f904(x97422,a893)),x97424),x97425)))
% 94.68/94.46 [9852]~P77(x98522)+E(f317(f317(f9(x98521,x98522),x98523),x98524),f317(f317(f9(x98521,x98522),x98523),x98525))+~P1(f317(f28(x98521),x98525))+~P1(f317(f317(f224(f904(x98521,a893)),x98524),x98525))+P1(f317(f317(f319(x98521),f348(x98523,x98524,x98525,x98521,x98522)),f317(f317(f23(f904(x98521,a893)),x98525),x98524)))
% 94.68/94.46 [9853]~P77(x98532)+E(f317(f317(f9(x98531,x98532),x98533),x98534),f317(f317(f9(x98531,x98532),x98533),x98535))+~P1(f317(f28(x98531),x98535))+~P1(f317(f317(f224(f904(x98531,a893)),x98534),x98535))+P1(f317(f317(f319(x98531),f349(x98533,x98534,x98535,x98531,x98532)),f317(f317(f23(f904(x98531,a893)),x98535),x98534)))
% 94.68/94.46 [9854]~P76(x98542)+E(f317(f317(f6(x98541,x98542),x98543),x98544),f317(f317(f6(x98541,x98542),x98543),x98545))+~P1(f317(f28(x98541),x98545))+~P1(f317(f317(f224(f904(x98541,a893)),x98544),x98545))+P1(f317(f317(f319(x98541),f424(x98543,x98544,x98545,x98541,x98542)),f317(f317(f23(f904(x98541,a893)),x98545),x98544)))
% 94.68/94.46 [9855]~P76(x98552)+E(f317(f317(f6(x98551,x98552),x98553),x98554),f317(f317(f6(x98551,x98552),x98553),x98555))+~P1(f317(f28(x98551),x98555))+~P1(f317(f317(f224(f904(x98551,a893)),x98554),x98555))+P1(f317(f317(f319(x98551),f425(x98553,x98554,x98555,x98551,x98552)),f317(f317(f23(f904(x98551,a893)),x98555),x98554)))
% 94.68/94.46 [9873]~P77(x98731)+~P1(f317(f28(x98732),x98734))+~P1(f317(f28(x98732),x98735))+E(f317(f317(f75(x98731),f317(f317(f9(x98732,x98731),x98733),x98734)),f317(f317(f9(x98732,x98731),x98733),x98735)),f317(f317(f9(x98732,x98731),x98733),f317(f317(f91(f904(x98732,a893)),x98734),x98735)))+P1(f317(f317(f319(x98732),f402(x98733,x98735,x98734,x98732,x98731)),f317(f317(f92(f904(x98732,a893)),x98734),x98735)))
% 94.68/94.46 [9874]~P77(x98741)+~P1(f317(f28(x98742),x98744))+~P1(f317(f28(x98742),x98745))+E(f317(f317(f75(x98741),f317(f317(f9(x98742,x98741),x98743),x98744)),f317(f317(f9(x98742,x98741),x98743),x98745)),f317(f317(f9(x98742,x98741),x98743),f317(f317(f91(f904(x98742,a893)),x98744),x98745)))+P1(f317(f317(f319(x98742),f407(x98743,x98745,x98744,x98742,x98741)),f317(f317(f92(f904(x98742,a893)),x98744),x98745)))
% 94.68/94.46 [9875]~P76(x98751)+~P1(f317(f28(x98752),x98754))+~P1(f317(f28(x98752),x98755))+E(f317(f317(f74(x98751),f317(f317(f6(x98752,x98751),x98753),x98754)),f317(f317(f6(x98752,x98751),x98753),x98755)),f317(f317(f6(x98752,x98751),x98753),f317(f317(f91(f904(x98752,a893)),x98754),x98755)))+P1(f317(f317(f319(x98752),f415(x98753,x98755,x98754,x98752,x98751)),f317(f317(f92(f904(x98752,a893)),x98754),x98755)))
% 94.68/94.46 [9876]~P76(x98761)+~P1(f317(f28(x98762),x98764))+~P1(f317(f28(x98762),x98765))+E(f317(f317(f74(x98761),f317(f317(f6(x98762,x98761),x98763),x98764)),f317(f317(f6(x98762,x98761),x98763),x98765)),f317(f317(f6(x98762,x98761),x98763),f317(f317(f91(f904(x98762,a893)),x98764),x98765)))+P1(f317(f317(f319(x98762),f416(x98763,x98765,x98764,x98762,x98761)),f317(f317(f92(f904(x98762,a893)),x98764),x98765)))
% 94.68/94.46 [9882]~P89(x98825)+~P1(f317(f28(x98821),x98824))+P1(f317(f317(f224(x98825),f317(f317(f6(x98821,x98825),x98822),x98823)),f317(f317(f6(x98821,x98825),x98822),x98824)))+~P1(f317(f317(f224(f904(x98821,a893)),x98823),x98824))+P1(f317(f317(f319(x98821),f406(x98822,x98823,x98824,x98821,x98825)),f317(f317(f23(f904(x98821,a893)),x98824),x98823)))
% 94.68/94.46 [9926]~P77(x99261)+~P1(f317(f28(x99262),x99264))+~P1(f317(f28(x99262),x99265))+E(f317(f317(f75(x99261),f317(f317(f317(f59(x99261,x99262,f75(x99261)),x99263),f72(x99261)),x99264)),f317(f317(f317(f59(x99261,x99262,f75(x99261)),x99263),f72(x99261)),x99265)),f317(f317(f317(f59(x99261,x99262,f75(x99261)),x99263),f72(x99261)),f317(f317(f91(f904(x99262,a893)),x99264),x99265)))+P1(f317(f317(f319(x99262),f404(x99263,x99265,x99264,x99262,x99261)),f317(f317(f92(f904(x99262,a893)),x99264),x99265)))
% 94.68/94.46 [8877]~P18(x88771,x88774,x88775)+~P1(f317(f28(x88771),x88772))+E(f317(f317(f23(f904(x88771,a893)),x88772),f317(f317(f299(x88771),x88773),f178(f904(x88771,a893)))),f178(f904(x88771,a893)))+~P1(f317(f317(f319(x88771),x88773),x88772))+E(f317(f317(x88774,x88773),f317(x88775,f317(f317(f23(f904(x88771,a893)),x88772),f317(f317(f299(x88771),x88773),f178(f904(x88771,a893)))))),f317(x88775,x88772))
% 94.68/94.46 [8955]~P18(x89551,x89554,x89555)+~P1(f317(f28(x89551),x89553))+~P1(f317(f28(x89551),x89552))+E(f317(f317(f92(f904(x89551,a893)),x89552),x89553),f178(f904(x89551,a893)))+E(f317(f317(x89554,f317(x89555,f317(f317(f91(f904(x89551,a893)),x89552),x89553))),f317(x89555,f317(f317(f92(f904(x89551,a893)),x89552),x89553))),f317(f317(x89554,f317(x89555,x89552)),f317(x89555,x89553)))
% 94.68/94.46 [9525]~P1(f317(f317(f224(a1),x95254),f2(a1)))+~P1(f317(f317(f225(a1),x95253),x95255))+P1(f317(f317(f224(a1),x95251),x95252))+~P1(f317(f317(f225(a1),x95253),x95254))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x95253),x95252)),x95255)),f317(f317(f74(a1),f317(f317(f75(a1),x95253),x95251)),x95254)))
% 94.68/94.46 [9527]~P1(f317(f317(f224(a1),f2(a1)),x95275))+P1(f317(f317(f224(a1),x95271),x95272))+~P1(f317(f317(f225(a1),x95273),x95274))+~P1(f317(f317(f225(a1),x95275),x95274))+~P1(f317(f317(f224(a1),f317(f317(f74(a1),f317(f317(f75(a1),x95274),x95271)),x95275)),f317(f317(f74(a1),f317(f317(f75(a1),x95274),x95272)),x95273)))
% 94.68/94.46 [9651]~P62(x96515)+E(f317(x96511,f403(x96511,x96512,x96513,x96514,x96515)),f2(x96515))+~P1(f317(f28(x96514),x96513))+~P1(f317(f28(x96514),x96512))+E(f317(f317(f281(x96515),f317(f317(f75(x96515),f317(f317(f9(x96514,x96515),x96511),x96513)),f317(f317(f9(x96514,x96515),x96511),x96512))),f317(f317(f9(x96514,x96515),x96511),f317(f317(f92(f904(x96514,a893)),x96513),x96512))),f317(f317(f9(x96514,x96515),x96511),f317(f317(f91(f904(x96514,a893)),x96513),x96512)))
% 94.68/94.46 [9918]~P62(x99181)+~P1(f317(f28(x99182),x99184))+~P1(f317(f28(x99182),x99185))+E(f317(f317(f281(x99181),f317(f317(f75(x99181),f317(f317(f9(x99182,x99181),x99183),x99184)),f317(f317(f9(x99182,x99181),x99183),x99185))),f317(f317(f9(x99182,x99181),x99183),f317(f317(f92(f904(x99182,a893)),x99184),x99185))),f317(f317(f9(x99182,x99181),x99183),f317(f317(f91(f904(x99182,a893)),x99184),x99185)))+P1(f317(f317(f319(x99182),f403(x99183,x99185,x99184,x99182,x99181)),f317(f317(f92(f904(x99182,a893)),x99184),x99185)))
% 94.68/94.46 [9229]E(f317(f317(f124(x92291),x92292),x92293),f317(f317(f124(x92291),x92294),x92295))+~E(f317(f317(f165(x92291),f317(f179(f898(x92291)),x92294)),x92292),x92294)+~E(f317(f317(f165(x92291),f317(f179(f898(x92291)),x92292)),x92294),x92292)+~E(x92295,f317(f317(f124(x92291),f317(f317(f128(x92291),f317(f179(f898(x92291)),x92294)),x92292)),x92293))+~E(f317(f317(f124(x92291),f317(f317(f128(x92291),f317(f179(f898(x92291)),x92292)),x92294)),x92295),x92293)
% 94.68/94.46 [9649]~P66(x96492)+E(f317(f317(f138(x96491,x96492,x96493),x96494),f160(x96491,x96494,x96495)),x96495)+~P13(x96492,f317(f317(f144(x96491,x96492),x96493),x96495))+~P1(f317(f317(f319(x96491),x96494),f317(f162(x96491),x96495)))+~E(f317(f131(x96491),f317(f126(x96491,f317(f317(f8(x96492,a893,x96491),f317(a314,f317(x96493,x96494))),x96493)),x96495)),x96494)
% 94.68/94.46 [9982]~P73(x99821)+~P1(f317(f60(x99821,x99821,f75(x99821),x99822,x99823),x99825))+~P1(f317(f317(f319(x99821),x99824),x99823))+P1(f317(f317(f319(x99821),x99822),x99823))+P1(f317(f60(x99821,x99821,f75(x99821),x99824,f317(f317(f299(x99821),x99822),f317(f317(f23(f904(x99821,a893)),x99823),f317(f317(f299(x99821),x99824),f178(f904(x99821,a893)))))),x99825))
% 94.68/94.46 [7369]E(x73691,x73692)+~P24(x73694,x73695,x73693,x73696)+~E(f317(x73693,x73691),f317(x73693,x73692))+~P1(f317(f317(f319(x73694),x73692),x73696))+~P1(f317(f317(f319(x73694),x73691),x73696))
% 94.68/94.46 [6611]~P146(x66114)+E(x66111,x66112)+~E(x66115,x66116)+E(x66113,f2(x66114))+~E(f317(f317(f74(x66114),x66115),f317(f317(f75(x66114),x66113),x66111)),f317(f317(f74(x66114),x66116),f317(f317(f75(x66114),x66113),x66112)))
% 94.68/94.46 [7656]~P66(x76561)+~P5(x76561)+~P1(f317(f317(f225(x76561),x76562),f317(x76565,x76566)))+~P1(f317(f317(f319(x76563),x76566),x76564))+P1(f317(f317(f225(x76561),x76562),f317(f317(f34(x76563,x76561),x76564),x76565)))
% 94.68/94.46 [9978]~P24(x99782,x99781,x99783,x99784)+~P24(x99781,x99782,x99786,x99785)+P25(x99781,x99782,f805(x99783,x99784,x99785,x99786,x99782,x99781),x99785,x99784)+~P1(f317(f317(f224(f904(x99782,a893)),f317(f300(x99781,x99782,x99786),x99785)),x99784))+~P1(f317(f317(f224(f904(x99781,a893)),f317(f300(x99782,x99781,x99783),x99784)),x99785))
% 94.68/94.46 [8337]~P66(x83371)+~P5(x83371)+~P1(f317(f317(f225(x83371),f317(x83374,x83376)),x83375))+~P1(f317(f317(f319(x83372),x83376),x83373))+P1(f317(f317(f225(x83371),f317(f317(f35(x83372,x83371),x83373),x83374)),x83375))
% 94.68/94.46 [8591]~P19(x85912,x85915,x85916,x85911)+~P1(f317(f28(x85912),x85914))+~P1(f317(f28(x85912),x85913))+~E(f317(f317(f92(f904(x85912,a893)),x85913),x85914),f178(f904(x85912,a893)))+E(f317(x85911,f317(f317(f91(f904(x85912,a893)),x85913),x85914)),f317(f67(x85915,x85915,x85915,f317(x85911,x85913)),f317(x85911,x85914)))
% 94.68/94.46 [10189]~P77(x101891)+~E(f793(x101894,x101895,x101893,x101896,x101892,x101891),f794(x101894,x101895,x101893,x101896,x101892,x101891))+~P1(f317(f28(x101892),x101896))+E(f317(f317(f317(f59(x101891,x101892,f75(x101891)),f317(f317(f8(f904(x101893,a893),x101891,x101892),f317(f317(f59(x101891,x101893,f75(x101891)),x101894),f72(x101891))),x101895)),f72(x101891)),x101896),f317(f317(f317(f59(x101891,x101893,f75(x101891)),x101894),f72(x101891)),f317(f317(f34(x101892,f904(x101893,a893)),x101896),x101895)))+P1(f317(f317(f319(x101892),f792(x101894,x101895,x101893,x101896,x101892,x101891)),x101896))
% 94.68/94.46 [10219]~P77(x102191)+~E(f793(x102194,x102195,x102193,x102196,x102192,x102191),f794(x102194,x102195,x102193,x102196,x102192,x102191))+~P1(f317(f28(x102192),x102196))+E(f317(f317(f317(f59(x102191,x102192,f75(x102191)),f317(f317(f8(f904(x102193,a893),x102191,x102192),f317(f317(f59(x102191,x102193,f75(x102191)),x102194),f72(x102191))),x102195)),f72(x102191)),x102196),f317(f317(f317(f59(x102191,x102193,f75(x102191)),x102194),f72(x102191)),f317(f317(f34(x102192,f904(x102193,a893)),x102196),x102195)))+~P1(f317(f28(x102193),f317(x102195,f792(x102194,x102195,x102193,x102196,x102192,x102191))))
% 94.68/94.46 [10222]~P77(x102221)+~P1(f317(f28(x102222),x102226))+E(f317(f317(f317(f59(x102221,x102222,f75(x102221)),f317(f317(f8(f904(x102223,a893),x102221,x102222),f317(f317(f59(x102221,x102223,f75(x102221)),x102224),f72(x102221))),x102225)),f72(x102221)),x102226),f317(f317(f317(f59(x102221,x102223,f75(x102221)),x102224),f72(x102221)),f317(f317(f34(x102222,f904(x102223,a893)),x102226),x102225)))+P1(f317(f317(f319(x102222),f792(x102224,x102225,x102223,x102226,x102222,x102221)),x102226))+P1(f317(f317(f319(x102222),f794(x102224,x102225,x102223,x102226,x102222,x102221)),x102226))
% 94.68/94.46 [10223]~P77(x102231)+~P1(f317(f28(x102232),x102236))+E(f317(f317(f317(f59(x102231,x102232,f75(x102231)),f317(f317(f8(f904(x102233,a893),x102231,x102232),f317(f317(f59(x102231,x102233,f75(x102231)),x102234),f72(x102231))),x102235)),f72(x102231)),x102236),f317(f317(f317(f59(x102231,x102233,f75(x102231)),x102234),f72(x102231)),f317(f317(f34(x102232,f904(x102233,a893)),x102236),x102235)))+P1(f317(f317(f319(x102232),f792(x102234,x102235,x102233,x102236,x102232,x102231)),x102236))+P1(f317(f317(f319(x102232),f793(x102234,x102235,x102233,x102236,x102232,x102231)),x102236))
% 94.68/94.46 [10242]~P77(x102421)+~P1(f317(f28(x102422),x102426))+E(f317(f317(f317(f59(x102421,x102422,f75(x102421)),f317(f317(f8(f904(x102423,a893),x102421,x102422),f317(f317(f59(x102421,x102423,f75(x102421)),x102424),f72(x102421))),x102425)),f72(x102421)),x102426),f317(f317(f317(f59(x102421,x102423,f75(x102421)),x102424),f72(x102421)),f317(f317(f34(x102422,f904(x102423,a893)),x102426),x102425)))+P1(f317(f317(f319(x102422),f794(x102424,x102425,x102423,x102426,x102422,x102421)),x102426))+~P1(f317(f28(x102423),f317(x102425,f792(x102424,x102425,x102423,x102426,x102422,x102421))))
% 94.68/94.46 [10243]~P77(x102431)+~P1(f317(f28(x102432),x102436))+E(f317(f317(f317(f59(x102431,x102432,f75(x102431)),f317(f317(f8(f904(x102433,a893),x102431,x102432),f317(f317(f59(x102431,x102433,f75(x102431)),x102434),f72(x102431))),x102435)),f72(x102431)),x102436),f317(f317(f317(f59(x102431,x102433,f75(x102431)),x102434),f72(x102431)),f317(f317(f34(x102432,f904(x102433,a893)),x102436),x102435)))+P1(f317(f317(f319(x102432),f793(x102434,x102435,x102433,x102436,x102432,x102431)),x102436))+~P1(f317(f28(x102433),f317(x102435,f792(x102434,x102435,x102433,x102436,x102432,x102431))))
% 94.68/94.46 [10254]~P77(x102541)+~E(f317(f317(f92(f904(x102543,a893)),f317(x102545,f794(x102544,x102545,x102543,x102546,x102542,x102541))),f317(x102545,f793(x102544,x102545,x102543,x102546,x102542,x102541))),f178(f904(x102543,a893)))+~P1(f317(f28(x102542),x102546))+E(f317(f317(f317(f59(x102541,x102542,f75(x102541)),f317(f317(f8(f904(x102543,a893),x102541,x102542),f317(f317(f59(x102541,x102543,f75(x102541)),x102544),f72(x102541))),x102545)),f72(x102541)),x102546),f317(f317(f317(f59(x102541,x102543,f75(x102541)),x102544),f72(x102541)),f317(f317(f34(x102542,f904(x102543,a893)),x102546),x102545)))+P1(f317(f317(f319(x102542),f792(x102544,x102545,x102543,x102546,x102542,x102541)),x102546))
% 94.68/94.46 [10265]~P77(x102651)+~E(f317(f317(f92(f904(x102653,a893)),f317(x102655,f794(x102654,x102655,x102653,x102656,x102652,x102651))),f317(x102655,f793(x102654,x102655,x102653,x102656,x102652,x102651))),f178(f904(x102653,a893)))+~P1(f317(f28(x102652),x102656))+E(f317(f317(f317(f59(x102651,x102652,f75(x102651)),f317(f317(f8(f904(x102653,a893),x102651,x102652),f317(f317(f59(x102651,x102653,f75(x102651)),x102654),f72(x102651))),x102655)),f72(x102651)),x102656),f317(f317(f317(f59(x102651,x102653,f75(x102651)),x102654),f72(x102651)),f317(f317(f34(x102652,f904(x102653,a893)),x102656),x102655)))+~P1(f317(f28(x102653),f317(x102655,f792(x102654,x102655,x102653,x102656,x102652,x102651))))
% 94.68/94.46 [9319]~P121(x93191)+~P118(x93191)+~P1(f317(f317(f277(x93191),x93192),x93195))+~P1(f317(f317(f277(x93191),x93192),f317(f317(f74(x93191),x93193),x93196)))+P1(f317(f317(f277(x93191),x93192),f317(f317(f74(x93191),f317(f317(f23(x93191),x93193),f317(f317(f75(x93191),x93194),x93195))),x93196)))
% 94.68/94.46 [9514]~P121(x95141)+~P118(x95141)+~P1(f317(f317(f277(x95141),x95142),x95145))+P1(f317(f317(f277(x95141),x95142),f317(f317(f74(x95141),x95143),x95144)))+~P1(f317(f317(f277(x95141),x95142),f317(f317(f74(x95141),f317(f317(f23(x95141),x95143),f317(f317(f75(x95141),x95146),x95145))),x95144)))
% 94.68/94.46 [8925]E(x89251,x89252)+~P56(x89254,x89255,x89256,x89253,x89257)+~E(f317(x89253,x89251),f317(x89253,x89252))+~P1(f317(f317(f319(x89255),x89252),x89257))+~P1(f317(f317(f319(x89255),x89251),x89257))
% 94.68/94.46 [10230]~P1(f317(x102302,x102304))+~E(x102305,f317(f126(x102301,x102302),x102307))+E(f317(f126(x102301,x102302),x102303),f317(f317(f141(x102301),x102304),x102305))+~E(x102303,f317(f317(f124(x102301),x102306),f317(f317(f141(x102301),x102304),x102307)))+P1(f317(x102302,f726(x102305,x102304,x102303,x102302,x102301,x102306,x102307)))
% 94.68/94.46 [10231]~P1(f317(x102314,x102312))+~E(x102313,f317(f126(x102311,x102314),x102317))+E(f317(f317(f141(x102311),x102312),x102313),f317(f126(x102311,x102314),x102315))+~E(x102315,f317(f317(f124(x102311),x102316),f317(f317(f141(x102311),x102312),x102317)))+P1(f317(x102314,f724(x102315,x102314,x102313,x102312,x102311,x102316,x102317)))
% 94.68/94.46 [10281]~P1(f317(x102812,x102814))+~E(x102815,f317(f126(x102811,x102812),x102817))+E(f317(f126(x102811,x102812),x102813),f317(f317(f141(x102811),x102814),x102815))+~E(x102813,f317(f317(f124(x102811),x102816),f317(f317(f141(x102811),x102814),x102817)))+P1(f317(f317(f319(x102811),f726(x102815,x102814,x102813,x102812,x102811,x102816,x102817)),f317(f162(x102811),x102816)))
% 94.68/94.46 [10282]~P1(f317(x102824,x102822))+~E(x102823,f317(f126(x102821,x102824),x102827))+E(f317(f317(f141(x102821),x102822),x102823),f317(f126(x102821,x102824),x102825))+~E(x102825,f317(f317(f124(x102821),x102826),f317(f317(f141(x102821),x102822),x102827)))+P1(f317(f317(f319(x102821),f724(x102825,x102824,x102823,x102822,x102821,x102826,x102827)),f317(f162(x102821),x102826)))
% 94.68/94.46 [10286]~P8(x102861,x102867,x102866)+~P11(x102861,f904(x102865,a893),x102866,x102864)+P1(f317(f317(f319(x102861),f449(x102862,x102863,x102864,x102865,x102866,x102867,x102861)),x102867))+~P1(f317(f317(f319(f904(x102861,a893)),x102863),f317(f317(f55(x102861),x102867),x102866)))+P1(f317(f317(f319(f904(x102865,a893)),f317(f317(f34(x102861,f904(x102865,a893)),x102863),x102864)),x102862))
% 94.68/94.46 [10341]~P8(x103412,x103416,x103417)+~P11(x103412,f904(x103411,a893),x103417,x103414)+~P1(f317(f317(f319(f904(x103412,a893)),x103413),f317(f317(f55(x103412),x103416),x103417)))+~P1(f317(f317(f319(f904(x103411,a893)),f317(x103414,f449(x103415,x103413,x103414,x103411,x103417,x103416,x103412))),x103415))+P1(f317(f317(f319(f904(x103411,a893)),f317(f317(f34(x103412,f904(x103411,a893)),x103413),x103414)),x103415))
% 94.68/94.46 [8510]~P77(x85102)+~P24(x85101,x85105,x85108,x85104)+~E(x85103,f317(f67(x85105,x85102,x85101,x85106),x85108))+~E(x85107,f317(f300(x85101,x85105,x85108),x85104))+E(f317(f317(f9(x85101,x85102),x85103),x85104),f317(f317(f9(x85105,x85102),x85106),x85107))
% 94.68/94.46 [10345]~P77(x103452)+~P24(x103455,x103451,x103458,x103457)+~E(f317(x103456,f532(x103453,x103456,x103454,x103457,x103458,x103451,x103455,x103452)),f317(f317(f67(x103451,x103452,x103455,x103453),x103458),f532(x103453,x103456,x103454,x103457,x103458,x103451,x103455,x103452)))+~E(x103454,f317(f300(x103455,x103451,x103458),x103457))+E(f317(f317(f9(x103451,x103452),x103453),x103454),f317(f317(f9(x103455,x103452),x103456),x103457))
% 94.68/94.46 [10348]~P77(x103482)+~P24(x103481,x103485,x103488,x103484)+~E(x103487,f317(f300(x103481,x103485,x103488),x103484))+E(f317(f317(f9(x103481,x103482),x103483),x103484),f317(f317(f9(x103485,x103482),x103486),x103487))+P1(f317(f317(f319(x103481),f532(x103486,x103483,x103487,x103484,x103488,x103485,x103481,x103482)),x103484))
% 94.68/94.46 [10349]~P76(x103492)+~P24(x103491,x103495,x103498,x103494)+~E(x103497,f317(f300(x103491,x103495,x103498),x103494))+E(f317(f317(f6(x103491,x103492),x103493),x103494),f317(f317(f6(x103495,x103492),x103496),x103497))+P1(f317(f317(f319(x103491),f552(x103496,x103493,x103497,x103494,x103498,x103495,x103491,x103492)),x103494))
% 94.68/94.46 [10354]~P76(x103542)+~P24(x103545,x103541,x103548,x103547)+~E(x103544,f317(f300(x103545,x103541,x103548),x103547))+~E(f317(x103546,f552(x103543,x103546,x103544,x103547,x103548,x103541,x103545,x103542)),f317(x103543,f317(x103548,f552(x103543,x103546,x103544,x103547,x103548,x103541,x103545,x103542))))+E(f317(f317(f6(x103541,x103542),x103543),x103544),f317(f317(f6(x103545,x103542),x103546),x103547))
% 94.68/94.46 [9815]~P23(x98156,x98152,x98155,x98157,x98158,x98151)+~P1(f317(f28(x98152),x98154))+~P1(f317(f28(x98152),x98153))+~E(f317(f317(f92(f904(x98152,a893)),x98153),x98154),f178(f904(x98152,a893)))+E(f317(x98151,f317(f317(f91(f904(x98152,a893)),x98153),x98154)),f317(f317(x98155,f317(x98151,x98153)),f317(x98151,x98154)))
% 94.68/94.46 [10216]~P23(x102168,x102162,x102165,x102167,x102166,x102161)+~E(f317(x102166,f486(x102164,x102163,x102161,x102166,x102167,x102165,x102162)),x102167)+~P1(f317(f28(x102162),x102163))+~P1(f317(f28(x102162),x102164))+E(f317(x102161,f317(f317(f91(f904(x102162,a893)),x102163),x102164)),f317(f317(x102165,f317(x102161,x102163)),f317(x102161,x102164)))
% 94.68/94.46 [10293]~P23(x102938,x102932,x102935,x102937,x102936,x102931)+~P1(f317(f28(x102932),x102933))+~P1(f317(f28(x102932),x102934))+E(f317(x102931,f317(f317(f91(f904(x102932,a893)),x102933),x102934)),f317(f317(x102935,f317(x102931,x102933)),f317(x102931,x102934)))+P1(f317(f317(f319(x102932),f486(x102934,x102933,x102931,x102936,x102937,x102935,x102932)),f317(f317(f92(f904(x102932,a893)),x102933),x102934)))
% 94.68/94.46 [9969]~P8(x99694,x99698,x99695)+~P8(x99691,x99699,x99693)+~P12(x99691,x99694,f904(x99692,a893),x99693,x99695,x99697)+P11(x99691,f904(x99692,a893),x99693,f317(f317(f8(f904(x99694,f904(x99692,a893)),f904(x99692,a893),x99691),f317(f34(x99694,f904(x99692,a893)),f317(f275(x99694,x99694,x99695),f317(f317(f299(x99694),x99696),f178(f904(x99694,a893)))))),x99697))+~P1(f317(f317(f319(x99694),x99696),x99698))
% 94.68/94.46 [5489]~P66(x54893)+~P13(x54893,x54891)+E(x54891,f703(x54892,x54893))+~E(f317(f162(x54893),x54891),x54892)+~P1(f317(f28(x54893),x54892))+~P1(f317(f127(x54893),x54891))
% 94.68/94.46 [7360]P15(x73601,x73602)+~E(f317(x73602,f784(x73602)),f317(x73602,f785(x73602)))+~P1(f317(f317(x73602,f784(x73602)),f784(x73602)))+~P1(f317(f317(x73602,f784(x73602)),f785(x73602)))+~P1(f317(f317(x73602,f785(x73602)),f785(x73602)))+~P1(f317(f317(x73602,x73603),x73603))
% 94.68/94.46 [5115]~P127(x51152)+~P132(x51152)+~P134(x51152)+~P115(x51152)+E(x51151,f2(x51152))+~E(f317(f317(f234(x51152),x51151),x51153),f2(x51152))
% 94.68/94.46 [5116]~P127(x51162)+~P132(x51162)+~P134(x51162)+~P115(x51162)+~E(x51161,f2(a897))+~E(f317(f317(f234(x51162),x51163),x51161),f2(x51162))
% 94.68/94.46 [6593]~P89(x65931)+~E(x65933,f2(x65931))+~E(x65932,f2(x65931))+E(f317(f317(f74(x65931),x65932),x65933),f2(x65931))+~P1(f317(f317(f224(x65931),f2(x65931)),x65933))+~P1(f317(f317(f224(x65931),f2(x65931)),x65932))
% 94.68/94.46 [8993]~E(f317(f241(a897,a897),x89933),f2(a897))+~E(x89931,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x89933)),x89932)),f317(f246(a897,a897),x89933)))+P1(f317(f43(x89931,x89932),x89933))+~P1(f317(f317(f224(a897),f317(f246(a897,a897),x89933)),f2(a897)))+P1(f317(f317(f225(a897),f2(a897)),x89932))+~P1(f317(f317(f225(a897),x89932),f317(f246(a897,a897),x89933)))
% 94.68/94.46 [9001]E(x90011,f2(a897))+~E(x90012,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x90013)),x90011)),f317(f246(a897,a897),x90013)))+P1(f317(f43(x90012,x90011),x90013))+~P1(f317(f317(f225(a897),f2(a897)),x90011))+~P1(f317(f317(f224(a897),f2(a897)),f317(f246(a897,a897),x90013)))+~P1(f317(f317(f225(a897),f317(f246(a897,a897),x90013)),x90011))
% 94.68/94.46 [9019]~E(f317(f241(a897,a897),x90193),f2(a897))+~E(x90191,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x90193)),x90192)),f317(f246(a897,a897),x90193)))+P1(f317(f43(x90191,x90192),x90193))+~P1(f317(f317(f225(a897),f2(a897)),x90192))+~P1(f317(f317(f224(a897),f2(a897)),f317(f246(a897,a897),x90193)))+~P1(f317(f317(f225(a897),f317(f246(a897,a897),x90193)),x90192))
% 94.68/94.46 [6983]~P66(x69832)+E(x69831,f178(f904(x69832,a893)))+E(x69833,f178(f904(x69832,a893)))+~P1(f317(f28(x69832),x69831))+~P1(f317(f28(x69832),x69833))+E(f14(x69832,f317(f317(f91(f904(x69832,a893)),x69833),x69831)),f317(f317(f228(x69832),f14(x69832,x69833)),f14(x69832,x69831)))
% 94.68/94.46 [6984]~P66(x69842)+E(x69841,f178(f904(x69842,a893)))+E(x69843,f178(f904(x69842,a893)))+~P1(f317(f28(x69842),x69841))+~P1(f317(f28(x69842),x69843))+E(f15(x69842,f317(f317(f91(f904(x69842,a893)),x69843),x69841)),f317(f317(f223(x69842),f15(x69842,x69843)),f15(x69842,x69841)))
% 94.68/94.46 [6985]~P100(x69852)+E(x69851,f178(f904(x69852,a893)))+E(x69853,f178(f904(x69852,a893)))+~P1(f317(f28(x69852),x69851))+~P1(f317(f28(x69852),x69853))+E(f13(x69852,f317(f317(f91(f904(x69852,a893)),x69853),x69851)),f317(f317(f91(x69852),f13(x69852,x69853)),f13(x69852,x69851)))
% 94.68/94.46 [6986]~P100(x69862)+E(x69861,f178(f904(x69862,a893)))+E(x69863,f178(f904(x69862,a893)))+~P1(f317(f28(x69862),x69861))+~P1(f317(f28(x69862),x69863))+E(f10(x69862,f317(f317(f91(f904(x69862,a893)),x69863),x69861)),f317(f317(f92(x69862),f10(x69862,x69863)),f10(x69862,x69861)))
% 94.68/94.46 [7630]~P98(x76302)+E(x76301,f178(f904(x76302,a893)))+E(x76303,f178(f904(x76302,a893)))+~P1(f317(f28(x76302),x76301))+~P1(f317(f28(x76302),x76303))+E(f317(f317(f75(x76302),f317(f57(x76302,f75(x76302)),x76303)),f317(f57(x76302,f75(x76302)),x76301)),f317(f57(x76302,f75(x76302)),f317(f317(f91(f904(x76302,a893)),x76303),x76301)))
% 94.68/94.46 [7792]~P66(x77922)+E(x77921,f178(f904(x77922,a893)))+E(x77923,f178(f904(x77922,a893)))+~P1(f317(f28(x77922),x77921))+~P1(f317(f28(x77922),x77923))+E(f317(f317(f228(x77922),f11(x77922,f228(x77922),x77923)),f11(x77922,f228(x77922),x77921)),f11(x77922,f228(x77922),f317(f317(f91(f904(x77922,a893)),x77923),x77921)))
% 94.68/94.46 [7793]~P66(x77932)+E(x77931,f178(f904(x77932,a893)))+E(x77933,f178(f904(x77932,a893)))+~P1(f317(f28(x77932),x77931))+~P1(f317(f28(x77932),x77933))+E(f317(f317(f223(x77932),f12(x77932,f223(x77932),x77933)),f12(x77932,f223(x77932),x77931)),f12(x77932,f223(x77932),f317(f317(f91(f904(x77932,a893)),x77933),x77931)))
% 94.68/94.46 [8826]~P1(f317(x88261,x88263))+P1(f317(x88261,f385(x88261,x88262)))+P1(f317(x88261,f382(x88261,x88262)))+~P1(f317(f317(f225(a1),f2(a1)),x88262))+~P1(f317(f317(f319(a1),x88263),f293(a1,f72(a1),x88262)))+P1(f317(x88261,f317(f317(f23(a1),f382(x88261,x88262)),f317(f317(f75(a1),f384(x88261,x88262)),x88262))))
% 94.68/94.46 [9128]~P1(f317(x91281,x91283))+~P1(f317(x91281,f382(x91281,x91282)))+P1(f317(x91281,f385(x91281,x91282)))+~P1(f317(f317(f225(a1),f2(a1)),x91282))+~P1(f317(f317(f319(a1),x91283),f293(a1,f72(a1),x91282)))+~P1(f317(x91281,f317(f317(f23(a1),f382(x91281,x91282)),f317(f317(f75(a1),f384(x91281,x91282)),x91282))))
% 94.68/94.46 [10381]~P103(x103812)+E(x103811,f178(f904(x103812,a893)))+E(x103813,f178(f904(x103812,a893)))+~P1(f317(f28(x103812),x103811))+~P1(f317(f28(x103812),x103813))+E(f10(x103812,f317(f252(x103812),f317(f317(f8(f904(x103812,a893),a893,x103812),f81(x103812)),f317(f317(f8(f904(x103812,f904(x103812,a893)),f904(x103812,a893),x103812),f317(f8(f904(x103812,a893),a893,x103812),f81(x103812))),f317(f317(f7(x103812,f904(x103812,f904(x103812,a893)),f904(x103812,f904(x103812,a893))),f317(f317(f8(f904(x103812,f904(f904(x103812,a893),f904(x103812,a893))),f904(f904(x103812,f904(x103812,a893)),f904(x103812,f904(x103812,a893))),x103812),f18(x103812,f904(x103812,a893),f904(x103812,a893))),f317(f317(f8(f904(x103812,f904(x103812,f904(a893,a893))),f904(x103812,f904(f904(x103812,a893),f904(x103812,a893))),x103812),f317(f8(f904(x103812,f904(a893,a893)),f904(f904(x103812,a893),f904(x103812,a893)),x103812),f18(x103812,a893,a893))),f317(f317(f8(f904(x103812,f904(x103812,a893)),f904(x103812,f904(x103812,f904(a893,a893))),x103812),f317(f8(f904(x103812,a893),f904(x103812,f904(a893,a893)),x103812),f317(f8(a893,f904(a893,a893),x103812),a315))),f317(f317(f7(x103812,f904(x103812,f904(x103812,x103812)),f904(x103812,f904(x103812,a893))),f317(f317(f8(f904(f904(x103812,x103812),f904(x103812,a893)),f904(f904(x103812,f904(x103812,x103812)),f904(x103812,f904(x103812,a893))),x103812),f8(f904(x103812,x103812),f904(x103812,a893),x103812)),f317(f317(f8(f904(x103812,a893),f904(f904(x103812,x103812),f904(x103812,a893)),x103812),f8(x103812,a893,x103812)),a314))),f91(x103812)))))),f317(f317(f7(x103812,f904(x103812,a893),f904(x103812,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x103812,a893),f904(x103812,a893)),x103812),f8(a893,a893,x103812)),f317(f317(f8(a893,f904(a893,a893),x103812),a315),f317(f317(f7(x103812,f904(x103812,a893),a893),f319(x103812)),x103813)))),f317(f317(f7(x103812,f904(x103812,a893),a893),f319(x103812)),x103811))))))),f317(f317(f91(x103812),f10(x103812,x103813)),f10(x103812,x103811)))
% 94.68/94.46 [10382]~P103(x103822)+E(x103821,f178(f904(x103822,a893)))+E(x103823,f178(f904(x103822,a893)))+~P1(f317(f28(x103822),x103821))+~P1(f317(f28(x103822),x103823))+E(f13(x103822,f317(f252(x103822),f317(f317(f8(f904(x103822,a893),a893,x103822),f81(x103822)),f317(f317(f8(f904(x103822,f904(x103822,a893)),f904(x103822,a893),x103822),f317(f8(f904(x103822,a893),a893,x103822),f81(x103822))),f317(f317(f7(x103822,f904(x103822,f904(x103822,a893)),f904(x103822,f904(x103822,a893))),f317(f317(f8(f904(x103822,f904(f904(x103822,a893),f904(x103822,a893))),f904(f904(x103822,f904(x103822,a893)),f904(x103822,f904(x103822,a893))),x103822),f18(x103822,f904(x103822,a893),f904(x103822,a893))),f317(f317(f8(f904(x103822,f904(x103822,f904(a893,a893))),f904(x103822,f904(f904(x103822,a893),f904(x103822,a893))),x103822),f317(f8(f904(x103822,f904(a893,a893)),f904(f904(x103822,a893),f904(x103822,a893)),x103822),f18(x103822,a893,a893))),f317(f317(f8(f904(x103822,f904(x103822,a893)),f904(x103822,f904(x103822,f904(a893,a893))),x103822),f317(f8(f904(x103822,a893),f904(x103822,f904(a893,a893)),x103822),f317(f8(a893,f904(a893,a893),x103822),a315))),f317(f317(f7(x103822,f904(x103822,f904(x103822,x103822)),f904(x103822,f904(x103822,a893))),f317(f317(f8(f904(f904(x103822,x103822),f904(x103822,a893)),f904(f904(x103822,f904(x103822,x103822)),f904(x103822,f904(x103822,a893))),x103822),f8(f904(x103822,x103822),f904(x103822,a893),x103822)),f317(f317(f8(f904(x103822,a893),f904(f904(x103822,x103822),f904(x103822,a893)),x103822),f8(x103822,a893,x103822)),a314))),f92(x103822)))))),f317(f317(f7(x103822,f904(x103822,a893),f904(x103822,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x103822,a893),f904(x103822,a893)),x103822),f8(a893,a893,x103822)),f317(f317(f8(a893,f904(a893,a893),x103822),a315),f317(f317(f7(x103822,f904(x103822,a893),a893),f319(x103822)),x103823)))),f317(f317(f7(x103822,f904(x103822,a893),a893),f319(x103822)),x103821))))))),f317(f317(f92(x103822),f13(x103822,x103823)),f13(x103822,x103821)))
% 94.68/94.46 [10383]~P66(x103832)+E(x103831,f178(f904(x103832,a893)))+E(x103833,f178(f904(x103832,a893)))+~P1(f317(f28(x103832),x103831))+~P1(f317(f28(x103832),x103833))+E(f12(x103832,f223(x103832),f317(f252(x103832),f317(f317(f8(f904(x103832,a893),a893,x103832),f81(x103832)),f317(f317(f8(f904(x103832,f904(x103832,a893)),f904(x103832,a893),x103832),f317(f8(f904(x103832,a893),a893,x103832),f81(x103832))),f317(f317(f7(x103832,f904(x103832,f904(x103832,a893)),f904(x103832,f904(x103832,a893))),f317(f317(f8(f904(x103832,f904(f904(x103832,a893),f904(x103832,a893))),f904(f904(x103832,f904(x103832,a893)),f904(x103832,f904(x103832,a893))),x103832),f18(x103832,f904(x103832,a893),f904(x103832,a893))),f317(f317(f8(f904(x103832,f904(x103832,f904(a893,a893))),f904(x103832,f904(f904(x103832,a893),f904(x103832,a893))),x103832),f317(f8(f904(x103832,f904(a893,a893)),f904(f904(x103832,a893),f904(x103832,a893)),x103832),f18(x103832,a893,a893))),f317(f317(f8(f904(x103832,f904(x103832,a893)),f904(x103832,f904(x103832,f904(a893,a893))),x103832),f317(f8(f904(x103832,a893),f904(x103832,f904(a893,a893)),x103832),f317(f8(a893,f904(a893,a893),x103832),a315))),f317(f317(f7(x103832,f904(x103832,f904(x103832,x103832)),f904(x103832,f904(x103832,a893))),f317(f317(f8(f904(f904(x103832,x103832),f904(x103832,a893)),f904(f904(x103832,f904(x103832,x103832)),f904(x103832,f904(x103832,a893))),x103832),f8(f904(x103832,x103832),f904(x103832,a893),x103832)),f317(f317(f8(f904(x103832,a893),f904(f904(x103832,x103832),f904(x103832,a893)),x103832),f8(x103832,a893,x103832)),a314))),f228(x103832)))))),f317(f317(f7(x103832,f904(x103832,a893),f904(x103832,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x103832,a893),f904(x103832,a893)),x103832),f8(a893,a893,x103832)),f317(f317(f8(a893,f904(a893,a893),x103832),a315),f317(f317(f7(x103832,f904(x103832,a893),a893),f319(x103832)),x103833)))),f317(f317(f7(x103832,f904(x103832,a893),a893),f319(x103832)),x103831))))))),f317(f317(f228(x103832),f12(x103832,f223(x103832),x103833)),f12(x103832,f223(x103832),x103831)))
% 94.68/94.46 [10384]~P66(x103842)+E(x103841,f178(f904(x103842,a893)))+E(x103843,f178(f904(x103842,a893)))+~P1(f317(f28(x103842),x103841))+~P1(f317(f28(x103842),x103843))+E(f11(x103842,f228(x103842),f317(f252(x103842),f317(f317(f8(f904(x103842,a893),a893,x103842),f81(x103842)),f317(f317(f8(f904(x103842,f904(x103842,a893)),f904(x103842,a893),x103842),f317(f8(f904(x103842,a893),a893,x103842),f81(x103842))),f317(f317(f7(x103842,f904(x103842,f904(x103842,a893)),f904(x103842,f904(x103842,a893))),f317(f317(f8(f904(x103842,f904(f904(x103842,a893),f904(x103842,a893))),f904(f904(x103842,f904(x103842,a893)),f904(x103842,f904(x103842,a893))),x103842),f18(x103842,f904(x103842,a893),f904(x103842,a893))),f317(f317(f8(f904(x103842,f904(x103842,f904(a893,a893))),f904(x103842,f904(f904(x103842,a893),f904(x103842,a893))),x103842),f317(f8(f904(x103842,f904(a893,a893)),f904(f904(x103842,a893),f904(x103842,a893)),x103842),f18(x103842,a893,a893))),f317(f317(f8(f904(x103842,f904(x103842,a893)),f904(x103842,f904(x103842,f904(a893,a893))),x103842),f317(f8(f904(x103842,a893),f904(x103842,f904(a893,a893)),x103842),f317(f8(a893,f904(a893,a893),x103842),a315))),f317(f317(f7(x103842,f904(x103842,f904(x103842,x103842)),f904(x103842,f904(x103842,a893))),f317(f317(f8(f904(f904(x103842,x103842),f904(x103842,a893)),f904(f904(x103842,f904(x103842,x103842)),f904(x103842,f904(x103842,a893))),x103842),f8(f904(x103842,x103842),f904(x103842,a893),x103842)),f317(f317(f8(f904(x103842,a893),f904(f904(x103842,x103842),f904(x103842,a893)),x103842),f8(x103842,a893,x103842)),a314))),f223(x103842)))))),f317(f317(f7(x103842,f904(x103842,a893),f904(x103842,a893)),f317(f317(f8(f904(a893,a893),f904(f904(x103842,a893),f904(x103842,a893)),x103842),f8(a893,a893,x103842)),f317(f317(f8(a893,f904(a893,a893),x103842),a315),f317(f317(f7(x103842,f904(x103842,a893),a893),f319(x103842)),x103843)))),f317(f317(f7(x103842,f904(x103842,a893),a893),f319(x103842)),x103841))))))),f317(f317(f223(x103842),f11(x103842,f228(x103842),x103843)),f11(x103842,f228(x103842),x103841)))
% 94.68/94.46 [7316]~P110(x73163)+E(x73161,x73162)+~E(f317(f317(f234(x73163),x73161),x73164),f317(f317(f234(x73163),x73162),x73164))+~P1(f317(f317(f224(x73163),f2(x73163)),x73162))+~P1(f317(f317(f224(x73163),f2(x73163)),x73161))+~P1(f317(f317(f225(a897),f2(a897)),x73164))
% 94.68/94.46 [7589]~P66(x75892)+E(x75891,f178(f904(x75892,a893)))+~P1(f317(f28(x75892),x75891))+~P1(f317(f317(f319(x75892),x75894),x75891))+P1(f317(f317(f224(x75892),x75893),x75894))+~P1(f317(f317(f224(x75892),x75893),f317(f57(x75892,f228(x75892)),x75891)))
% 94.68/94.46 [7590]~P105(x75902)+E(x75901,f178(f904(x75902,a893)))+~P1(f317(f28(x75902),x75901))+~P1(f317(f317(f319(x75902),x75904),x75901))+P1(f317(f317(f224(x75902),x75903),x75904))+~P1(f317(f317(f224(x75902),x75903),f317(f57(x75902,f92(x75902)),x75901)))
% 94.68/94.46 [7591]~P66(x75912)+E(x75911,f178(f904(x75912,a893)))+~P1(f317(f28(x75912),x75911))+~P1(f317(f317(f319(x75912),x75914),x75911))+P1(f317(f317(f225(x75912),x75913),x75914))+~P1(f317(f317(f225(x75912),x75913),f317(f57(x75912,f228(x75912)),x75911)))
% 94.68/94.46 [7496]E(x74961,f2(a1))+E(f317(f317(f30(a1),x74962),x74961),x74963)+~P1(f317(f317(f224(a1),x74964),f2(a1)))+~E(x74962,f317(f317(f74(a1),f317(f317(f75(a1),x74961),x74963)),x74964))+P1(f317(f317(f225(a1),f2(a1)),x74961))+~P1(f317(f317(f225(a1),x74961),x74964))
% 94.68/94.46 [7513]E(f40(a1,x75132,x75131),x75133)+E(x75131,f2(a1))+~P1(f317(f317(f224(a1),x75133),f2(a1)))+~E(x75132,f317(f317(f74(a1),f317(f317(f75(a1),x75131),x75134)),x75133))+P1(f317(f317(f225(a1),f2(a1)),x75131))+~P1(f317(f317(f225(a1),x75131),x75133))
% 94.68/94.46 [7629]E(x76291,f2(a1))+E(f317(f317(f30(a1),x76292),x76291),x76293)+~E(x76292,f317(f317(f74(a1),f317(f317(f75(a1),x76291),x76293)),x76294))+~P1(f317(f317(f224(a1),f2(a1)),x76294))+~P1(f317(f317(f225(a1),f2(a1)),x76291))+~P1(f317(f317(f225(a1),x76294),x76291))
% 94.68/94.46 [7652]E(f40(a1,x76522,x76521),x76523)+E(x76521,f2(a1))+~E(x76522,f317(f317(f74(a1),f317(f317(f75(a1),x76521),x76524)),x76523))+~P1(f317(f317(f224(a1),f2(a1)),x76523))+~P1(f317(f317(f225(a1),f2(a1)),x76521))+~P1(f317(f317(f225(a1),x76523),x76521))
% 94.68/94.46 [7796]~P66(x77962)+E(x77961,f178(f904(x77962,a893)))+~P1(f317(f28(x77962),x77961))+~P1(f317(f317(f319(x77962),x77964),x77961))+~P1(f317(f317(f224(x77962),x77964),x77963))+P1(f317(f317(f224(x77962),f317(f57(x77962,f228(x77962)),x77961)),x77963))
% 94.68/94.46 [7797]~P66(x77972)+E(x77971,f178(f904(x77972,a893)))+~P1(f317(f28(x77972),x77971))+~P1(f317(f317(f225(x77972),x77974),x77973))+~P1(f317(f317(f319(x77972),x77974),x77971))+P1(f317(f317(f225(x77972),f317(f57(x77972,f228(x77972)),x77971)),x77973))
% 94.68/94.46 [8362]~P1(f317(f317(f224(a1),x83624),f2(a1)))+~E(x83621,f317(f317(f74(a1),f317(f317(f75(a1),x83622),x83623)),x83624))+~P1(f317(f317(f224(a1),f2(a1)),x83624))+~P1(f317(f317(f225(a1),x83624),x83622))+~P1(f317(f317(f225(a1),x83622),x83624))+P1(f317(f44(x83621,x83622),f317(f317(f242(a1,a1),x83623),x83624)))
% 94.68/94.46 [8530]~P108(x85301)+P1(f317(f317(f225(f904(x85301,a893)),f293(x85301,x85302,x85303)),f293(x85301,x85304,x85305)))+~P1(f317(f317(f224(x85301),x85304),x85302))+~P1(f317(f317(f224(x85301),x85304),x85305))+~P1(f317(f317(f224(x85301),x85303),x85305))+~P1(f317(f317(f225(x85301),x85303),x85305))
% 94.68/94.46 [8531]~P108(x85311)+P1(f317(f317(f225(f904(x85311,a893)),f293(x85311,x85312,x85313)),f293(x85311,x85314,x85315)))+~P1(f317(f317(f224(x85311),x85313),x85315))+~P1(f317(f317(f224(x85311),x85314),x85315))+~P1(f317(f317(f224(x85311),x85314),x85312))+~P1(f317(f317(f225(x85311),x85314),x85312))
% 94.68/94.46 [9393]P58(x93932,x93933,x93934,x93931)+E(x93931,f178(f904(x93932,a893)))+~P1(f317(f28(x93932),x93934))+~P1(f317(f28(x93932),x93931))+~P1(f317(f317(x93933,f463(x93931,x93934,x93933,x93932)),x93935))+~P1(f317(f317(f319(x93932),x93935),x93931))
% 94.68/94.46 [9394]P58(x93942,x93943,x93944,x93941)+E(x93941,f178(f904(x93942,a893)))+~P1(f317(f28(x93942),x93944))+~P1(f317(f28(x93942),x93941))+~P1(f317(f317(x93943,f776(x93943,x93941,x93944,x93942)),x93945))+~P1(f317(f317(f319(x93942),x93945),x93941))
% 94.68/94.46 [9395]P58(x93952,x93953,x93954,x93951)+E(x93951,f178(f904(x93952,a893)))+~P1(f317(f28(x93952),x93954))+~P1(f317(f28(x93952),x93951))+~P1(f317(f317(x93953,f778(x93951,x93954,x93953,x93952)),x93955))+~P1(f317(f317(f319(x93952),x93955),x93951))
% 94.68/94.46 [9543]~E(x95433,x95435)+~P76(x95431)+~P77(x95431)+~P39(x95433)+E(f317(f317(f9(a1,x95431),x95432),x95433),f317(f317(f9(a1,x95431),x95434),x95435))+P1(f317(f317(f224(a1),f2(a1)),f428(x95432,x95434,x95433,x95435,x95431)))
% 94.68/94.46 [9544]~E(x95443,x95445)+~P76(x95441)+~P77(x95441)+~P39(x95443)+E(f317(f317(f6(a1,x95441),x95442),x95443),f317(f317(f6(a1,x95441),x95444),x95445))+P1(f317(f317(f224(a1),f2(a1)),f454(x95442,x95444,x95443,x95445,x95441)))
% 94.68/94.46 [9725]~E(x97255,x97253)+~P76(x97251)+~P77(x97251)+~P39(x97255)+~E(f317(x97252,f428(x97254,x97252,x97255,x97253,x97251)),f317(x97254,f428(x97254,x97252,x97255,x97253,x97251)))+E(f317(f317(f9(a1,x97251),x97252),x97253),f317(f317(f9(a1,x97251),x97254),x97255))
% 94.68/94.46 [9726]~E(x97265,x97263)+~P76(x97261)+~P77(x97261)+~P39(x97265)+~E(f317(x97262,f454(x97264,x97262,x97265,x97263,x97261)),f317(x97264,f454(x97264,x97262,x97265,x97263,x97261)))+E(f317(f317(f6(a1,x97261),x97262),x97263),f317(f317(f6(a1,x97261),x97264),x97265))
% 94.68/94.46 [9813]~P67(x98133)+E(f317(x98131,x98132),f2(x98133))+~E(f317(f317(f6(x98134,x98133),x98131),x98135),f2(x98133))+~P1(f317(f28(x98134),x98135))+P1(f317(f317(f319(x98134),f418(x98132,x98131,x98135,x98134,x98133)),x98135))+~P1(f317(f317(f319(x98134),x98132),x98135))
% 94.68/94.46 [9940]~P67(x99403)+E(f317(x99401,x99402),f2(x99403))+~E(f317(f317(f6(x99404,x99403),x99401),x99405),f2(x99403))+~P1(f317(f28(x99404),x99405))+~P1(f317(f317(f319(x99404),x99402),x99405))+~P1(f317(f317(f224(x99403),f2(x99403)),f317(x99401,f418(x99402,x99401,x99405,x99404,x99403))))
% 94.68/94.46 [8447]~P138(x84471)+~P1(f317(f317(f224(x84471),x84473),x84475))+~P1(f317(f317(f224(x84471),x84472),x84474))+~P1(f317(f317(f224(x84471),f2(x84471)),x84473))+~P1(f317(f317(f224(x84471),f2(x84471)),x84474))+P1(f317(f317(f224(x84471),f317(f317(f75(x84471),x84472),x84473)),f317(f317(f75(x84471),x84474),x84475)))
% 94.68/94.46 [8448]~P138(x84481)+~P1(f317(f317(f224(x84481),x84483),x84485))+~P1(f317(f317(f224(x84481),x84482),x84484))+~P1(f317(f317(f224(x84481),f2(x84481)),x84483))+~P1(f317(f317(f224(x84481),f2(x84481)),x84482))+P1(f317(f317(f224(x84481),f317(f317(f75(x84481),x84482),x84483)),f317(f317(f75(x84481),x84484),x84485)))
% 94.68/94.46 [8449]~P64(x84491)+~P1(f317(f317(f225(x84491),f2(x84491)),x84495))+~P1(f317(f317(f224(x84491),x84495),x84493))+~P1(f317(f317(f224(x84491),x84492),x84494))+~P1(f317(f317(f224(x84491),f2(x84491)),x84492))+P1(f317(f317(f224(x84491),f317(f317(f281(x84491),x84492),x84493)),f317(f317(f281(x84491),x84494),x84495)))
% 94.68/94.46 [8450]~P133(x84501)+~P1(f317(f317(f224(x84501),x84503),x84505))+~P1(f317(f317(f224(x84501),f2(x84501)),x84502))+~P1(f317(f317(f225(x84501),x84502),x84504))+~P1(f317(f317(f225(x84501),f2(x84501)),x84503))+P1(f317(f317(f225(x84501),f317(f317(f75(x84501),x84502),x84503)),f317(f317(f75(x84501),x84504),x84505)))
% 94.68/94.46 [8451]~P133(x84511)+~P1(f317(f317(f224(x84511),x84512),x84514))+~P1(f317(f317(f224(x84511),f2(x84511)),x84513))+~P1(f317(f317(f225(x84511),x84513),x84515))+~P1(f317(f317(f225(x84511),f2(x84511)),x84512))+P1(f317(f317(f225(x84511),f317(f317(f75(x84511),x84512),x84513)),f317(f317(f75(x84511),x84514),x84515)))
% 94.68/94.46 [8452]~P133(x84521)+~P1(f317(f317(f224(x84521),f2(x84521)),x84523))+~P1(f317(f317(f224(x84521),f2(x84521)),x84522))+~P1(f317(f317(f225(x84521),x84523),x84525))+~P1(f317(f317(f225(x84521),x84522),x84524))+P1(f317(f317(f225(x84521),f317(f317(f75(x84521),x84522),x84523)),f317(f317(f75(x84521),x84524),x84525)))
% 94.68/94.46 [8453]~P133(x84531)+~P1(f317(f317(f224(x84531),f2(x84531)),x84533))+~P1(f317(f317(f225(x84531),x84533),x84535))+~P1(f317(f317(f225(x84531),x84532),x84534))+~P1(f317(f317(f225(x84531),f2(x84531)),x84534))+P1(f317(f317(f225(x84531),f317(f317(f75(x84531),x84532),x84533)),f317(f317(f75(x84531),x84534),x84535)))
% 94.68/94.46 [8454]~P64(x84541)+~P1(f317(f317(f224(x84541),x84545),x84543))+~P1(f317(f317(f224(x84541),f2(x84541)),x84542))+~P1(f317(f317(f225(x84541),x84542),x84544))+~P1(f317(f317(f225(x84541),f2(x84541)),x84545))+P1(f317(f317(f225(x84541),f317(f317(f281(x84541),x84542),x84543)),f317(f317(f281(x84541),x84544),x84545)))
% 94.68/94.46 [8455]~P64(x84551)+~P1(f317(f317(f224(x84551),x84552),x84554))+~P1(f317(f317(f225(x84551),x84555),x84553))+~P1(f317(f317(f225(x84551),f2(x84551)),x84555))+~P1(f317(f317(f225(x84551),f2(x84551)),x84552))+P1(f317(f317(f225(x84551),f317(f317(f281(x84551),x84552),x84553)),f317(f317(f281(x84551),x84554),x84555)))
% 94.68/94.46 [9856]~P87(x98565)+~P76(x98565)+E(x98561,f178(f904(x98562,a893)))+~P1(f317(f28(x98562),x98561))+P1(f317(f317(f319(x98562),f426(x98563,x98564,x98561,x98562,x98565)),x98561))+P1(f317(f317(f225(x98565),f317(f317(f6(x98562,x98565),x98564),x98561)),f317(f317(f6(x98562,x98565),x98563),x98561)))
% 94.68/94.46 [9965]~P85(x99651)+~P76(x99651)+~P1(f317(f28(x99652),x99655))+~P1(f317(f317(f224(x99651),f2(x99651)),f317(x99653,f419(x99653,x99654,x99655,x99652,x99651))))+P1(f317(f317(f224(x99651),f317(f317(f6(x99652,x99651),x99653),x99654)),f317(f317(f6(x99652,x99651),x99653),x99655)))+~P1(f317(f317(f224(f904(x99652,a893)),x99654),x99655))
% 94.68/94.46 [10134]~P87(x101343)+~P76(x101343)+E(x101341,f178(f904(x101342,a893)))+~P1(f317(f28(x101342),x101341))+~P1(f317(f317(f225(x101343),f317(x101344,f426(x101345,x101344,x101341,x101342,x101343))),f317(x101345,f426(x101345,x101344,x101341,x101342,x101343))))+P1(f317(f317(f225(x101343),f317(f317(f6(x101342,x101343),x101344),x101341)),f317(f317(f6(x101342,x101343),x101345),x101341)))
% 94.68/94.46 [7172]~P17(x71722,x71725,x71724)+E(x71721,f178(f904(x71722,a893)))+E(x71723,f178(f904(x71722,a893)))+~P1(f317(f28(x71722),x71721))+~P1(f317(f28(x71722),x71723))+E(f317(x71724,f317(f317(f91(f904(x71722,a893)),x71723),x71721)),f317(f317(x71725,f317(x71724,x71723)),f317(x71724,x71721)))
% 94.68/94.46 [7762]~P148(x77621,x77624,x77623)+P1(f317(x77621,x77622))+~P1(f317(f317(f225(a1),x77624),f2(a1)))+~P1(f317(f317(f224(a1),x77625),f2(a1)))+~E(x77623,f317(f317(f74(a1),f317(f317(f75(a1),x77624),x77622)),x77625))+~P1(f317(f317(f225(a1),x77624),x77625))
% 94.68/94.46 [7763]~P147(x77631,x77634,x77633)+P1(f317(x77631,x77632))+~P1(f317(f317(f225(a1),x77634),f2(a1)))+~P1(f317(f317(f224(a1),x77632),f2(a1)))+~E(x77633,f317(f317(f74(a1),f317(f317(f75(a1),x77634),x77635)),x77632))+~P1(f317(f317(f225(a1),x77634),x77632))
% 94.68/94.46 [7805]~P148(x78051,x78054,x78053)+P1(f317(x78051,x78052))+~E(x78053,f317(f317(f74(a1),f317(f317(f75(a1),x78054),x78052)),x78055))+~P1(f317(f317(f224(a1),f2(a1)),x78055))+~P1(f317(f317(f225(a1),f2(a1)),x78054))+~P1(f317(f317(f225(a1),x78055),x78054))
% 94.68/94.46 [7806]~P147(x78061,x78064,x78063)+P1(f317(x78061,x78062))+~E(x78063,f317(f317(f74(a1),f317(f317(f75(a1),x78064),x78065)),x78062))+~P1(f317(f317(f224(a1),f2(a1)),x78062))+~P1(f317(f317(f225(a1),f2(a1)),x78064))+~P1(f317(f317(f225(a1),x78062),x78064))
% 94.68/94.46 [8739]P1(f317(f317(x87391,x87392),x87393))+~P1(f317(f317(x87391,f317(f317(f30(a1),x87394),x87395)),f40(a1,x87394,x87395)))+~P1(f317(f317(f225(a1),x87395),f2(a1)))+~P1(f317(f317(f224(a1),x87393),f2(a1)))+~E(x87394,f317(f317(f74(a1),f317(f317(f75(a1),x87395),x87392)),x87393))+~P1(f317(f317(f225(a1),x87395),x87393))
% 94.68/94.46 [8748]P1(f317(f317(x87481,x87482),x87483))+~P1(f317(f317(x87481,f317(f317(f30(a1),x87484),x87485)),f40(a1,x87484,x87485)))+~E(x87484,f317(f317(f74(a1),f317(f317(f75(a1),x87485),x87482)),x87483))+~P1(f317(f317(f224(a1),f2(a1)),x87483))+~P1(f317(f317(f225(a1),f2(a1)),x87485))+~P1(f317(f317(f225(a1),x87483),x87485))
% 94.68/94.46 [9009]E(x90091,x90092)+~P55(x90093,x90095,x90094)+~P1(f317(f317(f319(x90093),x90092),x90095))+~P1(f317(f317(f319(x90093),x90091),x90095))+P1(f317(f317(f319(f903(x90093,x90093)),f317(f317(f242(x90093,x90093),x90091),x90092)),x90094))+P1(f317(f317(f319(f903(x90093,x90093)),f317(f317(f242(x90093,x90093),x90092),x90091)),x90094))
% 94.68/94.46 [9883]~P85(x98835)+~P76(x98835)+~P1(f317(f28(x98831),x98834))+P1(f317(f317(f224(x98835),f317(f317(f6(x98831,x98835),x98832),x98833)),f317(f317(f6(x98831,x98835),x98832),x98834)))+~P1(f317(f317(f224(f904(x98831,a893)),x98833),x98834))+P1(f317(f317(f319(x98831),f419(x98832,x98833,x98834,x98831,x98835)),f317(f317(f23(f904(x98831,a893)),x98834),x98833)))
% 94.68/94.46 [9973]E(x99731,f178(f904(x99732,a893)))+~P1(f317(f28(x99732),x99733))+~P1(f317(f28(x99732),x99731))+P1(f317(f317(f319(f903(f904(x99732,a893),f904(x99732,a893))),f317(f317(f242(f904(x99732,a893),f904(x99732,a893)),x99733),x99731)),f308(x99732,x99734)))+~P1(f317(f317(f319(x99732),x99735),x99731))+~P1(f317(f317(f319(f903(x99732,x99732)),f317(f317(f242(x99732,x99732),f465(x99734,x99731,x99733,x99732)),x99735)),x99734))
% 94.68/94.46 [9974]E(x99741,f178(f904(x99742,a893)))+~P1(f317(f28(x99742),x99743))+~P1(f317(f28(x99742),x99741))+P1(f317(f317(f319(f903(f904(x99742,a893),f904(x99742,a893))),f317(f317(f242(f904(x99742,a893),f904(x99742,a893)),x99743),x99741)),f308(x99742,x99744)))+~P1(f317(f317(f319(x99742),x99745),x99741))+~P1(f317(f317(f319(f903(x99742,x99742)),f317(f317(f242(x99742,x99742),f542(x99744,x99741,x99743,x99742)),x99745)),x99744))
% 94.68/94.46 [10138]~P67(x101381)+~E(f317(f317(f6(x101385,x101381),x101382),x101386),x101384)+~P1(f317(f28(x101385),x101386))+P1(f317(f317(f319(x101385),f420(x101383,x101384,x101382,x101386,x101385,x101381)),x101386))+P1(f317(f317(f224(x101381),f317(x101382,x101383)),x101384))+~P1(f317(f317(f319(x101385),x101383),x101386))
% 94.68/94.46 [10186]~P67(x101861)+~E(f317(f317(f6(x101865,x101861),x101862),x101866),x101864)+~P1(f317(f28(x101865),x101866))+~P1(f317(f317(f319(x101865),x101863),x101866))+~P1(f317(f317(f224(x101861),f2(x101861)),f317(x101862,f420(x101863,x101864,x101862,x101866,x101865,x101861))))+P1(f317(f317(f224(x101861),f317(x101862,x101863)),x101864))
% 94.68/94.46 [10328]~E(x103285,x103288)+~E(x103284,x103287)+~P109(x103281)+~P76(x103282)+E(f317(f317(f6(x103281,x103282),x103283),f317(f292(x103281,x103284),x103285)),f317(f317(f6(x103281,x103282),x103286),f317(f292(x103281,x103287),x103288)))+P1(f317(f317(f224(x103281),x103284),f551(x103283,x103286,x103285,x103288,x103284,x103287,x103281,x103282)))
% 94.68/94.46 [10344]~E(x103447,x103444)+~E(x103448,x103445)+~P109(x103441)+~P76(x103442)+~E(f317(x103443,f551(x103446,x103443,x103448,x103445,x103447,x103444,x103441,x103442)),f317(x103446,f551(x103446,x103443,x103448,x103445,x103447,x103444,x103441,x103442)))+E(f317(f317(f6(x103441,x103442),x103443),f317(f292(x103441,x103444),x103445)),f317(f317(f6(x103441,x103442),x103446),f317(f292(x103441,x103447),x103448)))
% 94.68/94.46 [10347]~E(x103474,x103477)+~E(x103475,x103478)+~P109(x103471)+~P76(x103472)+E(f317(f317(f6(x103471,x103472),x103473),f317(f292(x103471,x103474),x103475)),f317(f317(f6(x103471,x103472),x103476),f317(f292(x103471,x103477),x103478)))+P1(f317(f317(f225(x103471),f551(x103473,x103476,x103475,x103478,x103474,x103477,x103471,x103472)),x103475))
% 94.68/94.46 [9980]~P8(x99805,x99809,x99806)+~P8(x99801,x998010,x99803)+~P12(x99801,x99805,f904(x99802,a893),x99803,x99806,x99808)+~P1(f317(f317(f319(x99805),x99807),x99809))+~P1(f317(f317(f319(x99801),x99804),x998010))+E(f317(f317(f34(x99801,f904(x99802,a893)),f317(f275(x99801,x99801,x99803),f317(f317(f299(x99801),x99804),f178(f904(x99801,a893))))),f317(f317(f8(f904(x99805,f904(x99802,a893)),f904(x99802,a893),x99801),f317(f34(x99805,f904(x99802,a893)),f317(f275(x99805,x99805,x99806),f317(f317(f299(x99805),x99807),f178(f904(x99805,a893)))))),x99808)),f317(f317(x99808,x99804),x99807))
% 94.68/94.46 [5662]~P66(x56623)+~P13(x56623,x56622)+~P13(x56623,x56621)+E(x56621,x56622)+~E(f317(f162(x56623),x56621),f317(f162(x56623),x56622))+~P1(f317(f127(x56623),x56622))+~P1(f317(f127(x56623),x56621))
% 94.68/94.46 [4989]~P127(x49892)+~P132(x49892)+~P134(x49892)+~P115(x49892)+~E(x49893,f2(x49892))+E(x49891,f2(a897))+E(f317(f317(f234(x49892),x49893),x49891),f2(x49892))
% 94.68/94.46 [9265]E(x92651,f2(a897))+~E(x92652,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x92653)),x92651)),f317(f246(a897,a897),x92653)))+P1(f317(f43(x92652,x92651),x92653))+~P1(f317(f317(f224(a897),f317(f246(a897,a897),x92653)),f2(a897)))+~P1(f317(f317(f224(a897),f2(a897)),f317(f246(a897,a897),x92653)))+~P1(f317(f317(f225(a897),x92651),f317(f246(a897,a897),x92653)))+~P1(f317(f317(f225(a897),f317(f246(a897,a897),x92653)),x92651))
% 94.68/94.46 [9273]~E(f317(f241(a897,a897),x92733),f2(a897))+~E(x92731,f317(f317(f74(a897),f317(f317(f75(a897),f317(f241(a897,a897),x92733)),x92732)),f317(f246(a897,a897),x92733)))+P1(f317(f43(x92731,x92732),x92733))+~P1(f317(f317(f224(a897),f317(f246(a897,a897),x92733)),f2(a897)))+~P1(f317(f317(f224(a897),f2(a897)),f317(f246(a897,a897),x92733)))+~P1(f317(f317(f225(a897),x92732),f317(f246(a897,a897),x92733)))+~P1(f317(f317(f225(a897),f317(f246(a897,a897),x92733)),x92732))
% 94.68/94.46 [8116]~P73(x81162)+E(x81161,f178(f904(x81162,a893)))+E(x81163,f178(f904(x81162,a893)))+~P1(f317(f28(x81162),x81161))+~P1(f317(f28(x81162),x81163))+~E(f317(f317(f92(f904(x81162,a893)),x81163),x81161),f178(f904(x81162,a893)))+E(f317(f317(f75(x81162),f317(f57(x81162,f75(x81162)),x81163)),f317(f57(x81162,f75(x81162)),x81161)),f317(f57(x81162,f75(x81162)),f317(f317(f91(f904(x81162,a893)),x81163),x81161)))
% 94.68/94.46 [7901]E(x79011,f2(a1))+E(f317(f317(f30(a1),x79012),x79011),x79013)+~P1(f317(f317(f224(a1),x79014),f2(a1)))+~E(x79012,f317(f317(f74(a1),f317(f317(f75(a1),x79011),x79013)),x79014))+~P1(f317(f317(f224(a1),f2(a1)),x79014))+~P1(f317(f317(f225(a1),x79014),x79011))+~P1(f317(f317(f225(a1),x79011),x79014))
% 94.68/94.46 [7909]E(f40(a1,x79092,x79091),x79093)+E(x79091,f2(a1))+~P1(f317(f317(f224(a1),x79093),f2(a1)))+~E(x79092,f317(f317(f74(a1),f317(f317(f75(a1),x79091),x79094)),x79093))+~P1(f317(f317(f224(a1),f2(a1)),x79093))+~P1(f317(f317(f225(a1),x79093),x79091))+~P1(f317(f317(f225(a1),x79091),x79093))
% 94.68/94.46 [6950]~P3(x69502)+E(x69501,f2(x69502))+E(x69503,f2(x69502))+~E(f317(f317(f30(x69502),x69504),x69503),f317(f317(f30(x69502),x69505),x69501))+E(f317(f317(f75(x69502),x69504),x69501),f317(f317(f75(x69502),x69503),x69505))+~P1(f317(f317(f277(x69502),x69501),x69505))+~P1(f317(f317(f277(x69502),x69503),x69504))
% 94.68/94.46 [6951]~P3(x69512)+E(x69511,f2(x69512))+E(x69513,f2(x69512))+~E(f317(f317(f75(x69512),x69514),x69513),f317(f317(f75(x69512),x69511),x69515))+E(f317(f317(f30(x69512),x69514),x69511),f317(f317(f30(x69512),x69515),x69513))+~P1(f317(f317(f277(x69512),x69511),x69514))+~P1(f317(f317(f277(x69512),x69513),x69515))
% 94.68/94.46 [7815]~P18(x78152,x78155,x78154)+E(x78151,f178(f904(x78152,a893)))+E(x78153,f178(f904(x78152,a893)))+~P1(f317(f28(x78152),x78151))+~P1(f317(f28(x78152),x78153))+~E(f317(f317(f92(f904(x78152,a893)),x78153),x78151),f178(f904(x78152,a893)))+E(f317(x78154,f317(f317(f91(f904(x78152,a893)),x78153),x78151)),f317(f317(x78155,f317(x78154,x78153)),f317(x78154,x78151)))
% 94.68/94.46 [9516]~P24(x95163,x95161,x95165,x95164)+~P24(x95161,x95163,x95166,x95162)+E(f317(f29(x95161),x95162),f317(f29(x95163),x95164))+~P1(f317(f28(x95163),x95164))+~P1(f317(f28(x95161),x95162))+~P1(f317(f317(f224(f904(x95163,a893)),f317(f300(x95161,x95163,x95166),x95162)),x95164))+~P1(f317(f317(f224(f904(x95161,a893)),f317(f300(x95163,x95161,x95165),x95164)),x95162))
% 94.68/94.46 [9458]~P1(f317(f317(f225(a1),f317(f317(f74(a1),f317(f317(f75(a1),x94585),x94581)),x94586)),f2(a1)))+~E(f317(f317(f74(a1),f317(f317(f75(a1),x94583),x94582)),x94584),f317(f317(f74(a1),f317(f317(f75(a1),x94585),x94581)),x94586))+~P1(f317(f317(f224(a1),f2(a1)),x94586))+~P1(f317(f317(f225(a1),f2(a1)),x94585))+~P1(f317(f317(f224(a1),x94585),x94583))+~P1(f317(f317(f225(a1),x94584),x94583))+P1(f317(f317(f224(a1),x94581),x94582))
% 94.68/94.46 [9216]~E(f317(f317(f74(a1),f317(f317(f75(a1),x92163),x92161)),x92164),f317(f317(f74(a1),f317(f317(f75(a1),x92165),x92162)),x92166))+~P1(f317(f317(f224(a1),f2(a1)),x92164))+~P1(f317(f317(f225(a1),f2(a1)),x92165))+~P1(f317(f317(f224(a1),x92165),x92163))+~P1(f317(f317(f225(a1),x92166),x92165))+P1(f317(f317(f224(a1),x92161),x92162))+~P1(f317(f317(f224(a1),f2(a1)),f317(f317(f74(a1),f317(f317(f75(a1),x92165),x92162)),x92166)))
% 94.68/94.46 [9398]~P130(x93981)+~E(f317(f317(f74(x93981),x93982),x93984),f72(x93981))+~P1(f317(f317(f224(x93981),x93985),x93986))+~P1(f317(f317(f224(x93981),x93983),x93986))+~P1(f317(f317(f224(x93981),f2(x93981)),x93984))+~P1(f317(f317(f224(x93981),f2(x93981)),x93982))+P1(f317(f317(f224(x93981),f317(f317(f74(x93981),f317(f317(f75(x93981),x93982),x93983)),f317(f317(f75(x93981),x93984),x93985))),x93986))
% 94.68/94.46 [9399]~P128(x93991)+~E(f317(f317(f74(x93991),x93992),x93994),f72(x93991))+~P1(f317(f317(f224(x93991),f2(x93991)),x93994))+~P1(f317(f317(f224(x93991),f2(x93991)),x93992))+~P1(f317(f317(f225(x93991),x93995),x93996))+~P1(f317(f317(f225(x93991),x93993),x93996))+P1(f317(f317(f225(x93991),f317(f317(f74(x93991),f317(f317(f75(x93991),x93992),x93993)),f317(f317(f75(x93991),x93994),x93995))),x93996))
% 94.68/94.46 [10233]~P8(x102337,x102336,x102335)+E(x102331,x102332)+~P11(x102337,f904(x102334,a893),x102335,x102333)+E(f317(x102333,f447(x102331,x102332,x102333,x102334,x102335,x102336,x102337)),f317(x102333,f448(x102331,x102332,x102333,x102334,x102335,x102336,x102337)))+~E(f317(f317(f34(x102337,f904(x102334,a893)),x102331),x102333),f317(f317(f34(x102337,f904(x102334,a893)),x102332),x102333))+~P1(f317(f317(f319(f904(x102337,a893)),x102332),f317(f317(f55(x102337),x102336),x102335)))+~P1(f317(f317(f319(f904(x102337,a893)),x102331),f317(f317(f55(x102337),x102336),x102335)))
% 94.68/94.46 [10284]~P8(x102843,x102847,x102846)+E(x102841,x102842)+~P11(x102843,f904(x102845,a893),x102846,x102844)+~E(f317(f317(f34(x102843,f904(x102845,a893)),x102841),x102844),f317(f317(f34(x102843,f904(x102845,a893)),x102842),x102844))+P1(f317(f317(f319(x102843),f448(x102841,x102842,x102844,x102845,x102846,x102847,x102843)),x102847))+~P1(f317(f317(f319(f904(x102843,a893)),x102842),f317(f317(f55(x102843),x102847),x102846)))+~P1(f317(f317(f319(f904(x102843,a893)),x102841),f317(f317(f55(x102843),x102847),x102846)))
% 94.68/94.46 [10285]~P8(x102853,x102857,x102856)+E(x102851,x102852)+~P11(x102853,f904(x102855,a893),x102856,x102854)+~E(f317(f317(f34(x102853,f904(x102855,a893)),x102851),x102854),f317(f317(f34(x102853,f904(x102855,a893)),x102852),x102854))+P1(f317(f317(f319(x102853),f447(x102851,x102852,x102854,x102855,x102856,x102857,x102853)),x102857))+~P1(f317(f317(f319(f904(x102853,a893)),x102852),f317(f317(f55(x102853),x102857),x102856)))+~P1(f317(f317(f319(f904(x102853,a893)),x102851),f317(f317(f55(x102853),x102857),x102856)))
% 94.68/94.46 [10363]E(x103631,x103632)+~P8(x103633,x103636,x103637)+~P11(x103633,f904(x103634,a893),x103637,x103635)+~E(f317(f317(f34(x103633,f904(x103634,a893)),x103631),x103635),f317(f317(f34(x103633,f904(x103634,a893)),x103632),x103635))+~P1(f317(f317(f319(f903(x103633,x103633)),f317(f317(f242(x103633,x103633),f448(x103631,x103632,x103635,x103634,x103637,x103636,x103633)),f447(x103631,x103632,x103635,x103634,x103637,x103636,x103633))),x103637))+~P1(f317(f317(f319(f904(x103633,a893)),x103632),f317(f317(f55(x103633),x103636),x103637)))+~P1(f317(f317(f319(f904(x103633,a893)),x103631),f317(f317(f55(x103633),x103636),x103637)))
% 94.68/94.46 [9215]~P8(x92151,x92157,x92154)+~E(x92155,x92156)+~P1(f317(f317(f319(x92151),x92153),x92156))+~P1(f317(f317(f319(x92151),x92152),x92155))+~P1(f317(f317(f319(f904(x92151,a893)),x92156),f317(f317(f55(x92151),x92157),x92154)))+~P1(f317(f317(f319(f904(x92151,a893)),x92155),f317(f317(f55(x92151),x92157),x92154)))+P1(f317(f317(f319(f903(x92151,x92151)),f317(f317(f242(x92151,x92151),x92152),x92153)),x92154))
% 94.68/94.46 [9354]E(x93541,x93542)+~P8(x93543,x93544,x93545)+~P1(f317(f317(f319(x93543),x93546),x93542))+~P1(f317(f317(f319(x93543),x93547),x93541))+~P1(f317(f317(f319(f904(x93543,a893)),x93542),f317(f317(f55(x93543),x93544),x93545)))+~P1(f317(f317(f319(f904(x93543,a893)),x93541),f317(f317(f55(x93543),x93544),x93545)))+~P1(f317(f317(f319(f903(x93543,x93543)),f317(f317(f242(x93543,x93543),x93547),x93546)),x93545))
% 94.68/94.46 [10390]~P8(x103909,x103908,x103907)+~P8(x103901,x1039011,x1039010)+~P12(x103901,x103909,f904(x103906,a893),x1039010,x103907,x103905)+P1(f317(f317(f319(x103901),f450(x103902,x103903,x103904,x103905,x103906,x103907,x103908,x103909,x1039010,x1039011,x103901)),x1039011))+~P1(f317(f317(f319(f904(x103909,a893)),x103903),f317(f317(f55(x103909),x103908),x103907)))+~P1(f317(f317(f319(f904(x103901,a893)),x103904),f317(f317(f55(x103901),x1039011),x1039010)))+P1(f317(f317(f319(f904(x103906,a893)),f317(f317(f34(x103901,f904(x103906,a893)),x103904),f317(f317(f8(f904(x103909,f904(x103906,a893)),f904(x103906,a893),x103901),f317(f34(x103909,f904(x103906,a893)),x103903)),x103905))),x103902))
% 94.68/94.46 [10391]~P8(x1039111,x1039110,x103919)+~P8(x103911,x103918,x103917)+~P12(x1039111,x103911,f904(x103916,a893),x103919,x103917,x103915)+P1(f317(f317(f319(x103911),f451(x103912,x103913,x103914,x103915,x103916,x103917,x103918,x103911,x103919,x1039110,x1039111)),x103918))+~P1(f317(f317(f319(f904(x1039111,a893)),x103914),f317(f317(f55(x1039111),x1039110),x103919)))+~P1(f317(f317(f319(f904(x103911,a893)),x103913),f317(f317(f55(x103911),x103918),x103917)))+P1(f317(f317(f319(f904(x103916,a893)),f317(f317(f34(x1039111,f904(x103916,a893)),x103914),f317(f317(f8(f904(x103911,f904(x103916,a893)),f904(x103916,a893),x1039111),f317(f34(x103911,f904(x103916,a893)),x103913)),x103915))),x103912))
% 94.68/94.46 [10392]~P8(x103922,x103928,x103929)+~P8(x103924,x1039210,x1039211)+~P12(x103922,x103924,f904(x103921,a893),x103929,x1039211,x103926)+~P1(f317(f317(f319(f904(x103922,a893)),x103923),f317(f317(f55(x103922),x103928),x103929)))+~P1(f317(f317(f319(f904(x103924,a893)),x103925),f317(f317(f55(x103924),x1039210),x1039211)))+~P1(f317(f317(f319(f904(x103921,a893)),f317(f317(x103926,f450(x103927,x103925,x103923,x103926,x103921,x1039211,x1039210,x103924,x103929,x103928,x103922)),f451(x103927,x103925,x103923,x103926,x103921,x1039211,x1039210,x103924,x103929,x103928,x103922))),x103927))+P1(f317(f317(f319(f904(x103921,a893)),f317(f317(f34(x103922,f904(x103921,a893)),x103923),f317(f317(f8(f904(x103924,f904(x103921,a893)),f904(x103921,a893),x103922),f317(f34(x103924,f904(x103921,a893)),x103925)),x103926))),x103927))
% 94.68/94.46 [9251]E(x92511,x92512)+~P66(x92514)+~P24(x92513,x92514,x92515,f317(f317(f91(f904(x92513,a893)),f317(f162(x92513),x92511)),f317(f162(x92513),x92512)))+~E(f317(f162(x92513),x92511),f317(f162(x92513),x92512))+~P13(x92514,f317(f317(f144(x92513,x92514),x92515),x92512))+~P13(x92514,f317(f317(f144(x92513,x92514),x92515),x92511))+~P1(f317(f127(x92514),f317(f317(f144(x92513,x92514),x92515),x92512)))+~P1(f317(f127(x92514),f317(f317(f144(x92513,x92514),x92515),x92511)))
% 94.68/94.46 %EqnAxiom
% 94.68/94.46 [1]E(x11,x11)
% 94.68/94.46 [2]E(x22,x21)+~E(x21,x22)
% 94.68/94.46 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 94.68/94.46 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 94.68/94.46 [5]~E(x51,x52)+E(f90(x51),f90(x52))
% 94.68/94.46 [6]~E(x61,x62)+E(f23(x61),f23(x62))
% 94.68/94.46 [7]~E(x71,x72)+E(f178(x71),f178(x72))
% 94.68/94.46 [8]~E(x81,x82)+E(f317(x81,x83),f317(x82,x83))
% 94.68/94.46 [9]~E(x91,x92)+E(f317(x93,x91),f317(x93,x92))
% 94.68/94.46 [10]~E(x101,x102)+E(f223(x101),f223(x102))
% 94.68/94.46 [11]~E(x111,x112)+E(f91(x111),f91(x112))
% 94.68/94.46 [12]~E(x121,x122)+E(f228(x121),f228(x122))
% 94.68/94.46 [13]~E(x131,x132)+E(f92(x131),f92(x132))
% 94.68/94.46 [14]~E(x141,x142)+E(f93(x141),f93(x142))
% 94.68/94.46 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 94.68/94.46 [16]~E(x161,x162)+E(f78(x161),f78(x162))
% 94.68/94.46 [17]~E(x171,x172)+E(f252(x171),f252(x172))
% 94.68/94.46 [18]~E(x181,x182)+E(f281(x181),f281(x182))
% 94.68/94.46 [19]~E(x191,x192)+E(f898(x191),f898(x192))
% 94.68/94.46 [20]~E(x201,x202)+E(f72(x201),f72(x202))
% 94.68/94.46 [21]~E(x211,x212)+E(f451(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f451(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112))
% 94.68/94.46 [22]~E(x221,x222)+E(f451(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f451(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 94.68/94.46 [23]~E(x231,x232)+E(f451(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f451(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 94.68/94.46 [24]~E(x241,x242)+E(f451(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f451(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412))
% 94.68/94.46 [25]~E(x251,x252)+E(f451(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f451(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512))
% 94.68/94.46 [26]~E(x261,x262)+E(f451(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f451(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612))
% 94.68/94.46 [27]~E(x271,x272)+E(f451(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f451(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712))
% 94.68/94.46 [28]~E(x281,x282)+E(f451(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f451(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812))
% 94.68/94.46 [29]~E(x291,x292)+E(f451(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f451(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912))
% 94.68/94.46 [30]~E(x301,x302)+E(f451(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f451(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012))
% 94.68/94.46 [31]~E(x311,x312)+E(f451(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f451(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312))
% 94.68/94.46 [32]~E(x321,x322)+E(f28(x321),f28(x322))
% 94.68/94.46 [33]~E(x331,x332)+E(f4(x331),f4(x332))
% 94.68/94.46 [34]~E(x341,x342)+E(f450(x341,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412),f450(x342,x343,x344,x345,x346,x347,x348,x349,x3410,x3411,x3412))
% 94.68/94.46 [35]~E(x351,x352)+E(f450(x353,x351,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f450(x353,x352,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 94.68/94.46 [36]~E(x361,x362)+E(f450(x363,x364,x361,x365,x366,x367,x368,x369,x3610,x3611,x3612),f450(x363,x364,x362,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 94.68/94.46 [37]~E(x371,x372)+E(f450(x373,x374,x375,x371,x376,x377,x378,x379,x3710,x3711,x3712),f450(x373,x374,x375,x372,x376,x377,x378,x379,x3710,x3711,x3712))
% 94.68/94.46 [38]~E(x381,x382)+E(f450(x383,x384,x385,x386,x381,x387,x388,x389,x3810,x3811,x3812),f450(x383,x384,x385,x386,x382,x387,x388,x389,x3810,x3811,x3812))
% 94.68/94.46 [39]~E(x391,x392)+E(f450(x393,x394,x395,x396,x397,x391,x398,x399,x3910,x3911,x3912),f450(x393,x394,x395,x396,x397,x392,x398,x399,x3910,x3911,x3912))
% 94.68/94.46 [40]~E(x401,x402)+E(f450(x403,x404,x405,x406,x407,x408,x401,x409,x4010,x4011,x4012),f450(x403,x404,x405,x406,x407,x408,x402,x409,x4010,x4011,x4012))
% 94.68/94.46 [41]~E(x411,x412)+E(f450(x413,x414,x415,x416,x417,x418,x419,x411,x4110,x4111,x4112),f450(x413,x414,x415,x416,x417,x418,x419,x412,x4110,x4111,x4112))
% 94.68/94.46 [42]~E(x421,x422)+E(f450(x423,x424,x425,x426,x427,x428,x429,x4210,x421,x4211,x4212),f450(x423,x424,x425,x426,x427,x428,x429,x4210,x422,x4211,x4212))
% 94.68/94.46 [43]~E(x431,x432)+E(f450(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x431,x4312),f450(x433,x434,x435,x436,x437,x438,x439,x4310,x4311,x432,x4312))
% 94.68/94.46 [44]~E(x441,x442)+E(f450(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x441),f450(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x4412,x442))
% 94.68/94.46 [45]~E(x451,x452)+E(f319(x451),f319(x452))
% 94.68/94.46 [46]~E(x461,x462)+E(f101(x461),f101(x462))
% 94.68/94.46 [47]~E(x471,x472)+E(f904(x471,x473),f904(x472,x473))
% 94.68/94.46 [48]~E(x481,x482)+E(f904(x483,x481),f904(x483,x482))
% 94.68/94.46 [49]~E(x491,x492)+E(f900(x491),f900(x492))
% 94.68/94.46 [50]~E(x501,x502)+E(f224(x501),f224(x502))
% 94.68/94.46 [51]~E(x511,x512)+E(f899(x511),f899(x512))
% 94.68/94.46 [52]~E(x521,x522)+E(f73(x521),f73(x522))
% 94.68/94.46 [53]~E(x531,x532)+E(f225(x531),f225(x532))
% 94.68/94.46 [54]~E(x541,x542)+E(f94(x541),f94(x542))
% 94.68/94.46 [55]~E(x551,x552)+E(f242(x551,x553),f242(x552,x553))
% 94.68/94.46 [56]~E(x561,x562)+E(f242(x563,x561),f242(x563,x562))
% 94.68/94.46 [57]~E(x571,x572)+E(f179(x571),f179(x572))
% 94.68/94.46 [58]~E(x581,x582)+E(f159(x581,x583,x584),f159(x582,x583,x584))
% 94.68/94.46 [59]~E(x591,x592)+E(f159(x593,x591,x594),f159(x593,x592,x594))
% 94.68/94.46 [60]~E(x601,x602)+E(f159(x603,x604,x601),f159(x603,x604,x602))
% 94.68/94.46 [61]~E(x611,x612)+E(f162(x611),f162(x612))
% 94.68/94.46 [62]~E(x621,x622)+E(f8(x621,x623,x624),f8(x622,x623,x624))
% 94.68/94.46 [63]~E(x631,x632)+E(f8(x633,x631,x634),f8(x633,x632,x634))
% 94.68/94.46 [64]~E(x641,x642)+E(f8(x643,x644,x641),f8(x643,x644,x642))
% 94.68/94.46 [65]~E(x651,x652)+E(f141(x651),f141(x652))
% 94.68/94.46 [66]~E(x661,x662)+E(f30(x661),f30(x662))
% 94.68/94.46 [67]~E(x671,x672)+E(f232(x671),f232(x672))
% 94.68/94.46 [68]~E(x681,x682)+E(f129(x681,x683),f129(x682,x683))
% 94.68/94.46 [69]~E(x691,x692)+E(f129(x693,x691),f129(x693,x692))
% 94.68/94.46 [70]~E(x701,x702)+E(f165(x701),f165(x702))
% 94.68/94.46 [71]~E(x711,x712)+E(f745(x711,x713,x714,x715),f745(x712,x713,x714,x715))
% 94.68/94.46 [72]~E(x721,x722)+E(f745(x723,x721,x724,x725),f745(x723,x722,x724,x725))
% 94.68/94.46 [73]~E(x731,x732)+E(f745(x733,x734,x731,x735),f745(x733,x734,x732,x735))
% 94.68/94.46 [74]~E(x741,x742)+E(f745(x743,x744,x745,x741),f745(x743,x744,x745,x742))
% 94.68/94.46 [75]~E(x751,x752)+E(f292(x751,x753),f292(x752,x753))
% 94.68/94.46 [76]~E(x761,x762)+E(f292(x763,x761),f292(x763,x762))
% 94.68/94.46 [77]~E(x771,x772)+E(f7(x771,x773,x774),f7(x772,x773,x774))
% 94.68/94.46 [78]~E(x781,x782)+E(f7(x783,x781,x784),f7(x783,x782,x784))
% 94.68/94.46 [79]~E(x791,x792)+E(f7(x793,x794,x791),f7(x793,x794,x792))
% 94.68/94.46 [80]~E(x801,x802)+E(f637(x801,x803,x804),f637(x802,x803,x804))
% 94.68/94.46 [81]~E(x811,x812)+E(f637(x813,x811,x814),f637(x813,x812,x814))
% 94.68/94.46 [82]~E(x821,x822)+E(f637(x823,x824,x821),f637(x823,x824,x822))
% 94.68/94.46 [83]~E(x831,x832)+E(f299(x831),f299(x832))
% 94.68/94.46 [84]~E(x841,x842)+E(f55(x841),f55(x842))
% 94.68/94.46 [85]~E(x851,x852)+E(f246(x851,x853),f246(x852,x853))
% 94.68/94.46 [86]~E(x861,x862)+E(f246(x863,x861),f246(x863,x862))
% 94.68/94.46 [87]~E(x871,x872)+E(f300(x871,x873,x874),f300(x872,x873,x874))
% 94.68/94.46 [88]~E(x881,x882)+E(f300(x883,x881,x884),f300(x883,x882,x884))
% 94.68/94.46 [89]~E(x891,x892)+E(f300(x893,x894,x891),f300(x893,x894,x892))
% 94.68/94.46 [90]~E(x901,x902)+E(f759(x901,x903,x904,x905),f759(x902,x903,x904,x905))
% 94.68/94.46 [91]~E(x911,x912)+E(f759(x913,x911,x914,x915),f759(x913,x912,x914,x915))
% 94.68/94.46 [92]~E(x921,x922)+E(f759(x923,x924,x921,x925),f759(x923,x924,x922,x925))
% 94.68/94.46 [93]~E(x931,x932)+E(f759(x933,x934,x935,x931),f759(x933,x934,x935,x932))
% 94.68/94.46 [94]~E(x941,x942)+E(f234(x941),f234(x942))
% 94.68/94.46 [95]~E(x951,x952)+E(f135(x951,x953),f135(x952,x953))
% 94.68/94.46 [96]~E(x961,x962)+E(f135(x963,x961),f135(x963,x962))
% 94.68/94.46 [97]~E(x971,x972)+E(f756(x971,x973,x974,x975),f756(x972,x973,x974,x975))
% 94.68/94.46 [98]~E(x981,x982)+E(f756(x983,x981,x984,x985),f756(x983,x982,x984,x985))
% 94.68/94.46 [99]~E(x991,x992)+E(f756(x993,x994,x991,x995),f756(x993,x994,x992,x995))
% 94.68/94.46 [100]~E(x1001,x1002)+E(f756(x1003,x1004,x1005,x1001),f756(x1003,x1004,x1005,x1002))
% 94.68/94.46 [101]~E(x1011,x1012)+E(f332(x1011,x1013),f332(x1012,x1013))
% 94.68/94.46 [102]~E(x1021,x1022)+E(f332(x1023,x1021),f332(x1023,x1022))
% 94.68/94.46 [103]~E(x1031,x1032)+E(f754(x1031,x1033,x1034,x1035),f754(x1032,x1033,x1034,x1035))
% 94.68/94.46 [104]~E(x1041,x1042)+E(f754(x1043,x1041,x1044,x1045),f754(x1043,x1042,x1044,x1045))
% 94.68/94.46 [105]~E(x1051,x1052)+E(f754(x1053,x1054,x1051,x1055),f754(x1053,x1054,x1052,x1055))
% 94.68/94.46 [106]~E(x1061,x1062)+E(f754(x1063,x1064,x1065,x1061),f754(x1063,x1064,x1065,x1062))
% 94.68/94.46 [107]~E(x1071,x1072)+E(f903(x1071,x1073),f903(x1072,x1073))
% 94.68/94.46 [108]~E(x1081,x1082)+E(f903(x1083,x1081),f903(x1083,x1082))
% 94.68/94.46 [109]~E(x1091,x1092)+E(f10(x1091,x1093),f10(x1092,x1093))
% 94.68/94.46 [110]~E(x1101,x1102)+E(f10(x1103,x1101),f10(x1103,x1102))
% 94.68/94.46 [111]~E(x1111,x1112)+E(f9(x1111,x1113),f9(x1112,x1113))
% 94.68/94.46 [112]~E(x1121,x1122)+E(f9(x1123,x1121),f9(x1123,x1122))
% 94.68/94.46 [113]~E(x1131,x1132)+E(f75(x1131),f75(x1132))
% 94.68/94.46 [114]~E(x1141,x1142)+E(f127(x1141),f127(x1142))
% 94.68/94.46 [115]~E(x1151,x1152)+E(f167(x1151,x1153,x1154),f167(x1152,x1153,x1154))
% 94.68/94.46 [116]~E(x1161,x1162)+E(f167(x1163,x1161,x1164),f167(x1163,x1162,x1164))
% 94.68/94.46 [117]~E(x1171,x1172)+E(f167(x1173,x1174,x1171),f167(x1173,x1174,x1172))
% 94.68/94.46 [118]~E(x1181,x1182)+E(f244(x1181,x1183),f244(x1182,x1183))
% 94.68/94.46 [119]~E(x1191,x1192)+E(f244(x1193,x1191),f244(x1193,x1192))
% 94.68/94.46 [120]~E(x1201,x1202)+E(f248(x1201,x1203,x1204,x1205,x1206,x1207),f248(x1202,x1203,x1204,x1205,x1206,x1207))
% 94.68/94.46 [121]~E(x1211,x1212)+E(f248(x1213,x1211,x1214,x1215,x1216,x1217),f248(x1213,x1212,x1214,x1215,x1216,x1217))
% 94.68/94.46 [122]~E(x1221,x1222)+E(f248(x1223,x1224,x1221,x1225,x1226,x1227),f248(x1223,x1224,x1222,x1225,x1226,x1227))
% 94.68/94.46 [123]~E(x1231,x1232)+E(f248(x1233,x1234,x1235,x1231,x1236,x1237),f248(x1233,x1234,x1235,x1232,x1236,x1237))
% 94.68/94.46 [124]~E(x1241,x1242)+E(f248(x1243,x1244,x1245,x1246,x1241,x1247),f248(x1243,x1244,x1245,x1246,x1242,x1247))
% 94.68/94.46 [125]~E(x1251,x1252)+E(f248(x1253,x1254,x1255,x1256,x1257,x1251),f248(x1253,x1254,x1255,x1256,x1257,x1252))
% 94.68/94.46 [126]~E(x1261,x1262)+E(f870(x1261,x1263),f870(x1262,x1263))
% 94.68/94.46 [127]~E(x1271,x1272)+E(f870(x1273,x1271),f870(x1273,x1272))
% 94.68/94.46 [128]~E(x1281,x1282)+E(f104(x1281,x1283),f104(x1282,x1283))
% 94.68/94.46 [129]~E(x1291,x1292)+E(f104(x1293,x1291),f104(x1293,x1292))
% 94.68/94.46 [130]~E(x1301,x1302)+E(f124(x1301),f124(x1302))
% 94.68/94.46 [131]~E(x1311,x1312)+E(f151(x1311,x1313),f151(x1312,x1313))
% 94.68/94.46 [132]~E(x1321,x1322)+E(f151(x1323,x1321),f151(x1323,x1322))
% 94.68/94.46 [133]~E(x1331,x1332)+E(f40(x1331,x1333,x1334),f40(x1332,x1333,x1334))
% 94.68/94.46 [134]~E(x1341,x1342)+E(f40(x1343,x1341,x1344),f40(x1343,x1342,x1344))
% 94.68/94.46 [135]~E(x1351,x1352)+E(f40(x1353,x1354,x1351),f40(x1353,x1354,x1352))
% 94.68/94.46 [136]~E(x1361,x1362)+E(f29(x1361),f29(x1362))
% 94.68/94.46 [137]~E(x1371,x1372)+E(f67(x1371,x1373,x1374,x1375),f67(x1372,x1373,x1374,x1375))
% 94.68/94.46 [138]~E(x1381,x1382)+E(f67(x1383,x1381,x1384,x1385),f67(x1383,x1382,x1384,x1385))
% 94.68/94.46 [139]~E(x1391,x1392)+E(f67(x1393,x1394,x1391,x1395),f67(x1393,x1394,x1392,x1395))
% 94.68/94.46 [140]~E(x1401,x1402)+E(f67(x1403,x1404,x1405,x1401),f67(x1403,x1404,x1405,x1402))
% 94.68/94.46 [141]~E(x1411,x1412)+E(f96(x1411),f96(x1412))
% 94.68/94.46 [142]~E(x1421,x1422)+E(f98(x1421),f98(x1422))
% 94.68/94.46 [143]~E(x1431,x1432)+E(f318(x1431),f318(x1432))
% 94.68/94.46 [144]~E(x1441,x1442)+E(f18(x1441,x1443,x1444),f18(x1442,x1443,x1444))
% 94.68/94.46 [145]~E(x1451,x1452)+E(f18(x1453,x1451,x1454),f18(x1453,x1452,x1454))
% 94.68/94.46 [146]~E(x1461,x1462)+E(f18(x1463,x1464,x1461),f18(x1463,x1464,x1462))
% 94.68/94.46 [147]~E(x1471,x1472)+E(f514(x1471),f514(x1472))
% 94.68/94.46 [148]~E(x1481,x1482)+E(f131(x1481),f131(x1482))
% 94.68/94.46 [149]~E(x1491,x1492)+E(f285(x1491,x1493,x1494),f285(x1492,x1493,x1494))
% 94.68/94.46 [150]~E(x1501,x1502)+E(f285(x1503,x1501,x1504),f285(x1503,x1502,x1504))
% 94.68/94.46 [151]~E(x1511,x1512)+E(f285(x1513,x1514,x1511),f285(x1513,x1514,x1512))
% 94.68/94.46 [152]~E(x1521,x1522)+E(f231(x1521,x1523),f231(x1522,x1523))
% 94.68/94.46 [153]~E(x1531,x1532)+E(f231(x1533,x1531),f231(x1533,x1532))
% 94.68/94.46 [154]~E(x1541,x1542)+E(f74(x1541),f74(x1542))
% 94.68/94.46 [155]~E(x1551,x1552)+E(f298(x1551),f298(x1552))
% 94.68/94.46 [156]~E(x1561,x1562)+E(f80(x1561,x1563),f80(x1562,x1563))
% 94.68/94.46 [157]~E(x1571,x1572)+E(f80(x1573,x1571),f80(x1573,x1572))
% 94.68/94.46 [158]~E(x1581,x1582)+E(f147(x1581,x1583),f147(x1582,x1583))
% 94.68/94.46 [159]~E(x1591,x1592)+E(f147(x1593,x1591),f147(x1593,x1592))
% 94.68/94.46 [160]~E(x1601,x1602)+E(f5(x1601),f5(x1602))
% 94.68/94.46 [161]~E(x1611,x1612)+E(f155(x1611),f155(x1612))
% 94.68/94.46 [162]~E(x1621,x1622)+E(f70(x1621),f70(x1622))
% 94.68/94.46 [163]~E(x1631,x1632)+E(f154(x1631),f154(x1632))
% 94.68/94.46 [164]~E(x1641,x1642)+E(f277(x1641),f277(x1642))
% 94.68/94.46 [165]~E(x1651,x1652)+E(f144(x1651,x1653),f144(x1652,x1653))
% 94.68/94.46 [166]~E(x1661,x1662)+E(f144(x1663,x1661),f144(x1663,x1662))
% 94.68/94.46 [167]~E(x1671,x1672)+E(f103(x1671),f103(x1672))
% 94.68/94.46 [168]~E(x1681,x1682)+E(f6(x1681,x1683),f6(x1682,x1683))
% 94.68/94.46 [169]~E(x1691,x1692)+E(f6(x1693,x1691),f6(x1693,x1692))
% 94.68/94.46 [170]~E(x1701,x1702)+E(f173(x1701,x1703),f173(x1702,x1703))
% 94.68/94.46 [171]~E(x1711,x1712)+E(f173(x1713,x1711),f173(x1713,x1712))
% 94.68/94.46 [172]~E(x1721,x1722)+E(f149(x1721,x1723),f149(x1722,x1723))
% 94.68/94.46 [173]~E(x1731,x1732)+E(f149(x1733,x1731),f149(x1733,x1732))
% 94.68/94.46 [174]~E(x1741,x1742)+E(f520(x1741,x1743,x1744),f520(x1742,x1743,x1744))
% 94.68/94.46 [175]~E(x1751,x1752)+E(f520(x1753,x1751,x1754),f520(x1753,x1752,x1754))
% 94.68/94.46 [176]~E(x1761,x1762)+E(f520(x1763,x1764,x1761),f520(x1763,x1764,x1762))
% 94.68/94.46 [177]~E(x1771,x1772)+E(f45(x1771,x1773),f45(x1772,x1773))
% 94.68/94.46 [178]~E(x1781,x1782)+E(f45(x1783,x1781),f45(x1783,x1782))
% 94.68/94.46 [179]~E(x1791,x1792)+E(f308(x1791,x1793),f308(x1792,x1793))
% 94.68/94.46 [180]~E(x1801,x1802)+E(f308(x1803,x1801),f308(x1803,x1802))
% 94.68/94.46 [181]~E(x1811,x1812)+E(f274(x1811,x1813),f274(x1812,x1813))
% 94.68/94.46 [182]~E(x1821,x1822)+E(f274(x1823,x1821),f274(x1823,x1822))
% 94.68/94.46 [183]~E(x1831,x1832)+E(f522(x1831,x1833,x1834),f522(x1832,x1833,x1834))
% 94.68/94.46 [184]~E(x1841,x1842)+E(f522(x1843,x1841,x1844),f522(x1843,x1842,x1844))
% 94.68/94.46 [185]~E(x1851,x1852)+E(f522(x1853,x1854,x1851),f522(x1853,x1854,x1852))
% 94.68/94.46 [186]~E(x1861,x1862)+E(f441(x1861,x1863,x1864,x1865,x1866),f441(x1862,x1863,x1864,x1865,x1866))
% 94.68/94.46 [187]~E(x1871,x1872)+E(f441(x1873,x1871,x1874,x1875,x1876),f441(x1873,x1872,x1874,x1875,x1876))
% 94.68/94.46 [188]~E(x1881,x1882)+E(f441(x1883,x1884,x1881,x1885,x1886),f441(x1883,x1884,x1882,x1885,x1886))
% 94.68/94.46 [189]~E(x1891,x1892)+E(f441(x1893,x1894,x1895,x1891,x1896),f441(x1893,x1894,x1895,x1892,x1896))
% 94.68/94.46 [190]~E(x1901,x1902)+E(f441(x1903,x1904,x1905,x1906,x1901),f441(x1903,x1904,x1905,x1906,x1902))
% 94.68/94.46 [191]~E(x1911,x1912)+E(f275(x1911,x1913,x1914),f275(x1912,x1913,x1914))
% 94.68/94.46 [192]~E(x1921,x1922)+E(f275(x1923,x1921,x1924),f275(x1923,x1922,x1924))
% 94.68/94.46 [193]~E(x1931,x1932)+E(f275(x1933,x1934,x1931),f275(x1933,x1934,x1932))
% 94.68/94.46 [194]~E(x1941,x1942)+E(f437(x1941,x1943,x1944,x1945),f437(x1942,x1943,x1944,x1945))
% 94.68/94.46 [195]~E(x1951,x1952)+E(f437(x1953,x1951,x1954,x1955),f437(x1953,x1952,x1954,x1955))
% 94.68/94.46 [196]~E(x1961,x1962)+E(f437(x1963,x1964,x1961,x1965),f437(x1963,x1964,x1962,x1965))
% 94.68/94.46 [197]~E(x1971,x1972)+E(f437(x1973,x1974,x1975,x1971),f437(x1973,x1974,x1975,x1972))
% 94.68/94.46 [198]~E(x1981,x1982)+E(f132(x1981,x1983,x1984,x1985),f132(x1982,x1983,x1984,x1985))
% 94.68/94.46 [199]~E(x1991,x1992)+E(f132(x1993,x1991,x1994,x1995),f132(x1993,x1992,x1994,x1995))
% 94.68/94.46 [200]~E(x2001,x2002)+E(f132(x2003,x2004,x2001,x2005),f132(x2003,x2004,x2002,x2005))
% 94.68/94.46 [201]~E(x2011,x2012)+E(f132(x2013,x2014,x2015,x2011),f132(x2013,x2014,x2015,x2012))
% 94.68/94.46 [202]~E(x2021,x2022)+E(f15(x2021,x2023),f15(x2022,x2023))
% 94.68/94.46 [203]~E(x2031,x2032)+E(f15(x2033,x2031),f15(x2033,x2032))
% 94.68/94.46 [204]~E(x2041,x2042)+E(f60(x2041,x2043,x2044,x2045,x2046),f60(x2042,x2043,x2044,x2045,x2046))
% 94.68/94.46 [205]~E(x2051,x2052)+E(f60(x2053,x2051,x2054,x2055,x2056),f60(x2053,x2052,x2054,x2055,x2056))
% 94.68/94.46 [206]~E(x2061,x2062)+E(f60(x2063,x2064,x2061,x2065,x2066),f60(x2063,x2064,x2062,x2065,x2066))
% 94.68/94.46 [207]~E(x2071,x2072)+E(f60(x2073,x2074,x2075,x2071,x2076),f60(x2073,x2074,x2075,x2072,x2076))
% 94.68/94.46 [208]~E(x2081,x2082)+E(f60(x2083,x2084,x2085,x2086,x2081),f60(x2083,x2084,x2085,x2086,x2082))
% 94.68/94.46 [209]~E(x2091,x2092)+E(f202(x2091),f202(x2092))
% 94.68/94.46 [210]~E(x2101,x2102)+E(f748(x2101,x2103,x2104),f748(x2102,x2103,x2104))
% 94.68/94.46 [211]~E(x2111,x2112)+E(f748(x2113,x2111,x2114),f748(x2113,x2112,x2114))
% 94.68/94.46 [212]~E(x2121,x2122)+E(f748(x2123,x2124,x2121),f748(x2123,x2124,x2122))
% 94.68/94.46 [213]~E(x2131,x2132)+E(f128(x2131),f128(x2132))
% 94.68/94.46 [214]~E(x2141,x2142)+E(f14(x2141,x2143),f14(x2142,x2143))
% 94.68/94.46 [215]~E(x2151,x2152)+E(f14(x2153,x2151),f14(x2153,x2152))
% 94.68/94.46 [216]~E(x2161,x2162)+E(f701(x2161,x2163,x2164,x2165),f701(x2162,x2163,x2164,x2165))
% 94.68/94.46 [217]~E(x2171,x2172)+E(f701(x2173,x2171,x2174,x2175),f701(x2173,x2172,x2174,x2175))
% 94.68/94.46 [218]~E(x2181,x2182)+E(f701(x2183,x2184,x2181,x2185),f701(x2183,x2184,x2182,x2185))
% 94.68/94.46 [219]~E(x2191,x2192)+E(f701(x2193,x2194,x2195,x2191),f701(x2193,x2194,x2195,x2192))
% 94.68/94.46 [220]~E(x2201,x2202)+E(f697(x2201,x2203,x2204,x2205,x2206),f697(x2202,x2203,x2204,x2205,x2206))
% 94.68/94.46 [221]~E(x2211,x2212)+E(f697(x2213,x2211,x2214,x2215,x2216),f697(x2213,x2212,x2214,x2215,x2216))
% 94.68/94.46 [222]~E(x2221,x2222)+E(f697(x2223,x2224,x2221,x2225,x2226),f697(x2223,x2224,x2222,x2225,x2226))
% 94.68/94.46 [223]~E(x2231,x2232)+E(f697(x2233,x2234,x2235,x2231,x2236),f697(x2233,x2234,x2235,x2232,x2236))
% 94.68/94.46 [224]~E(x2241,x2242)+E(f697(x2243,x2244,x2245,x2246,x2241),f697(x2243,x2244,x2245,x2246,x2242))
% 94.68/94.46 [225]~E(x2251,x2252)+E(f205(x2251,x2253),f205(x2252,x2253))
% 94.68/94.46 [226]~E(x2261,x2262)+E(f205(x2263,x2261),f205(x2263,x2262))
% 94.68/94.46 [227]~E(x2271,x2272)+E(f438(x2271,x2273,x2274,x2275,x2276),f438(x2272,x2273,x2274,x2275,x2276))
% 94.68/94.46 [228]~E(x2281,x2282)+E(f438(x2283,x2281,x2284,x2285,x2286),f438(x2283,x2282,x2284,x2285,x2286))
% 94.68/94.46 [229]~E(x2291,x2292)+E(f438(x2293,x2294,x2291,x2295,x2296),f438(x2293,x2294,x2292,x2295,x2296))
% 94.68/94.46 [230]~E(x2301,x2302)+E(f438(x2303,x2304,x2305,x2301,x2306),f438(x2303,x2304,x2305,x2302,x2306))
% 94.68/94.46 [231]~E(x2311,x2312)+E(f438(x2313,x2314,x2315,x2316,x2311),f438(x2313,x2314,x2315,x2316,x2312))
% 94.68/94.46 [232]~E(x2321,x2322)+E(f34(x2321,x2323),f34(x2322,x2323))
% 94.68/94.46 [233]~E(x2331,x2332)+E(f34(x2333,x2331),f34(x2333,x2332))
% 94.68/94.46 [234]~E(x2341,x2342)+E(f301(x2341,x2343,x2344),f301(x2342,x2343,x2344))
% 94.68/94.46 [235]~E(x2351,x2352)+E(f301(x2353,x2351,x2354),f301(x2353,x2352,x2354))
% 94.68/94.46 [236]~E(x2361,x2362)+E(f301(x2363,x2364,x2361),f301(x2363,x2364,x2362))
% 94.68/94.46 [237]~E(x2371,x2372)+E(f81(x2371),f81(x2372))
% 94.68/94.46 [238]~E(x2381,x2382)+E(f429(x2381,x2383,x2384),f429(x2382,x2383,x2384))
% 94.68/94.46 [239]~E(x2391,x2392)+E(f429(x2393,x2391,x2394),f429(x2393,x2392,x2394))
% 94.68/94.46 [240]~E(x2401,x2402)+E(f429(x2403,x2404,x2401),f429(x2403,x2404,x2402))
% 94.68/94.46 [241]~E(x2411,x2412)+E(f134(x2411,x2413),f134(x2412,x2413))
% 94.68/94.46 [242]~E(x2421,x2422)+E(f134(x2423,x2421),f134(x2423,x2422))
% 94.68/94.46 [243]~E(x2431,x2432)+E(f763(x2431,x2433,x2434,x2435,x2436,x2437,x2438),f763(x2432,x2433,x2434,x2435,x2436,x2437,x2438))
% 94.68/94.46 [244]~E(x2441,x2442)+E(f763(x2443,x2441,x2444,x2445,x2446,x2447,x2448),f763(x2443,x2442,x2444,x2445,x2446,x2447,x2448))
% 94.68/94.46 [245]~E(x2451,x2452)+E(f763(x2453,x2454,x2451,x2455,x2456,x2457,x2458),f763(x2453,x2454,x2452,x2455,x2456,x2457,x2458))
% 94.68/94.46 [246]~E(x2461,x2462)+E(f763(x2463,x2464,x2465,x2461,x2466,x2467,x2468),f763(x2463,x2464,x2465,x2462,x2466,x2467,x2468))
% 94.68/94.46 [247]~E(x2471,x2472)+E(f763(x2473,x2474,x2475,x2476,x2471,x2477,x2478),f763(x2473,x2474,x2475,x2476,x2472,x2477,x2478))
% 94.68/94.46 [248]~E(x2481,x2482)+E(f763(x2483,x2484,x2485,x2486,x2487,x2481,x2488),f763(x2483,x2484,x2485,x2486,x2487,x2482,x2488))
% 94.68/94.46 [249]~E(x2491,x2492)+E(f763(x2493,x2494,x2495,x2496,x2497,x2498,x2491),f763(x2493,x2494,x2495,x2496,x2497,x2498,x2492))
% 94.68/94.46 [250]~E(x2501,x2502)+E(f809(x2501,x2503,x2504,x2505),f809(x2502,x2503,x2504,x2505))
% 94.68/94.46 [251]~E(x2511,x2512)+E(f809(x2513,x2511,x2514,x2515),f809(x2513,x2512,x2514,x2515))
% 94.68/94.46 [252]~E(x2521,x2522)+E(f809(x2523,x2524,x2521,x2525),f809(x2523,x2524,x2522,x2525))
% 94.68/94.46 [253]~E(x2531,x2532)+E(f809(x2533,x2534,x2535,x2531),f809(x2533,x2534,x2535,x2532))
% 94.68/94.46 [254]~E(x2541,x2542)+E(f157(x2541),f157(x2542))
% 94.68/94.46 [255]~E(x2551,x2552)+E(f612(x2551,x2553),f612(x2552,x2553))
% 94.68/94.46 [256]~E(x2561,x2562)+E(f612(x2563,x2561),f612(x2563,x2562))
% 94.68/94.46 [257]~E(x2571,x2572)+E(f16(x2571,x2573),f16(x2572,x2573))
% 94.68/94.46 [258]~E(x2581,x2582)+E(f16(x2583,x2581),f16(x2583,x2582))
% 94.68/94.46 [259]~E(x2591,x2592)+E(f341(x2591,x2593,x2594),f341(x2592,x2593,x2594))
% 94.68/94.46 [260]~E(x2601,x2602)+E(f341(x2603,x2601,x2604),f341(x2603,x2602,x2604))
% 94.68/94.46 [261]~E(x2611,x2612)+E(f341(x2613,x2614,x2611),f341(x2613,x2614,x2612))
% 94.68/94.46 [262]~E(x2621,x2622)+E(f142(x2621,x2623),f142(x2622,x2623))
% 94.68/94.46 [263]~E(x2631,x2632)+E(f142(x2633,x2631),f142(x2633,x2632))
% 94.68/94.46 [264]~E(x2641,x2642)+E(f247(x2641,x2643,x2644),f247(x2642,x2643,x2644))
% 94.68/94.46 [265]~E(x2651,x2652)+E(f247(x2653,x2651,x2654),f247(x2653,x2652,x2654))
% 94.68/94.46 [266]~E(x2661,x2662)+E(f247(x2663,x2664,x2661),f247(x2663,x2664,x2662))
% 94.68/94.46 [267]~E(x2671,x2672)+E(f181(x2671),f181(x2672))
% 94.68/94.46 [268]~E(x2681,x2682)+E(f32(x2681,x2683),f32(x2682,x2683))
% 94.68/94.46 [269]~E(x2691,x2692)+E(f32(x2693,x2691),f32(x2693,x2692))
% 94.68/94.46 [270]~E(x2701,x2702)+E(f105(x2701),f105(x2702))
% 94.68/94.46 [271]~E(x2711,x2712)+E(f902(x2711,x2713),f902(x2712,x2713))
% 94.68/94.46 [272]~E(x2721,x2722)+E(f902(x2723,x2721),f902(x2723,x2722))
% 94.68/94.46 [273]~E(x2731,x2732)+E(f901(x2731,x2733),f901(x2732,x2733))
% 94.68/94.46 [274]~E(x2741,x2742)+E(f901(x2743,x2741),f901(x2743,x2742))
% 94.68/94.46 [275]~E(x2751,x2752)+E(f474(x2751,x2753,x2754,x2755),f474(x2752,x2753,x2754,x2755))
% 94.68/94.46 [276]~E(x2761,x2762)+E(f474(x2763,x2761,x2764,x2765),f474(x2763,x2762,x2764,x2765))
% 94.68/94.46 [277]~E(x2771,x2772)+E(f474(x2773,x2774,x2771,x2775),f474(x2773,x2774,x2772,x2775))
% 94.68/94.46 [278]~E(x2781,x2782)+E(f474(x2783,x2784,x2785,x2781),f474(x2783,x2784,x2785,x2782))
% 94.68/94.46 [279]~E(x2791,x2792)+E(f86(x2791),f86(x2792))
% 94.68/94.46 [280]~E(x2801,x2802)+E(f283(x2801,x2803),f283(x2802,x2803))
% 94.68/94.46 [281]~E(x2811,x2812)+E(f283(x2813,x2811),f283(x2813,x2812))
% 94.68/94.46 [282]~E(x2821,x2822)+E(f519(x2821,x2823,x2824),f519(x2822,x2823,x2824))
% 94.68/94.46 [283]~E(x2831,x2832)+E(f519(x2833,x2831,x2834),f519(x2833,x2832,x2834))
% 94.68/94.46 [284]~E(x2841,x2842)+E(f519(x2843,x2844,x2841),f519(x2843,x2844,x2842))
% 94.68/94.46 [285]~E(x2851,x2852)+E(f171(x2851,x2853),f171(x2852,x2853))
% 94.68/94.46 [286]~E(x2861,x2862)+E(f171(x2863,x2861),f171(x2863,x2862))
% 94.68/94.46 [287]~E(x2871,x2872)+E(f161(x2871),f161(x2872))
% 94.68/94.46 [288]~E(x2881,x2882)+E(f446(x2881,x2883,x2884,x2885),f446(x2882,x2883,x2884,x2885))
% 94.68/94.46 [289]~E(x2891,x2892)+E(f446(x2893,x2891,x2894,x2895),f446(x2893,x2892,x2894,x2895))
% 94.68/94.46 [290]~E(x2901,x2902)+E(f446(x2903,x2904,x2901,x2905),f446(x2903,x2904,x2902,x2905))
% 94.68/94.46 [291]~E(x2911,x2912)+E(f446(x2913,x2914,x2915,x2911),f446(x2913,x2914,x2915,x2912))
% 94.68/94.46 [292]~E(x2921,x2922)+E(f698(x2921,x2923),f698(x2922,x2923))
% 94.68/94.46 [293]~E(x2931,x2932)+E(f698(x2933,x2931),f698(x2933,x2932))
% 94.68/94.46 [294]~E(x2941,x2942)+E(f51(x2941),f51(x2942))
% 94.68/94.46 [295]~E(x2951,x2952)+E(f158(x2951),f158(x2952))
% 94.68/94.46 [296]~E(x2961,x2962)+E(f280(x2961,x2963,x2964,x2965),f280(x2962,x2963,x2964,x2965))
% 94.68/94.46 [297]~E(x2971,x2972)+E(f280(x2973,x2971,x2974,x2975),f280(x2973,x2972,x2974,x2975))
% 94.68/94.46 [298]~E(x2981,x2982)+E(f280(x2983,x2984,x2981,x2985),f280(x2983,x2984,x2982,x2985))
% 94.68/94.46 [299]~E(x2991,x2992)+E(f280(x2993,x2994,x2995,x2991),f280(x2993,x2994,x2995,x2992))
% 94.68/94.46 [300]~E(x3001,x3002)+E(f184(x3001,x3003),f184(x3002,x3003))
% 94.68/94.46 [301]~E(x3011,x3012)+E(f184(x3013,x3011),f184(x3013,x3012))
% 94.68/94.46 [302]~E(x3021,x3022)+E(f13(x3021,x3023),f13(x3022,x3023))
% 94.68/94.46 [303]~E(x3031,x3032)+E(f13(x3033,x3031),f13(x3033,x3032))
% 94.68/94.46 [304]~E(x3041,x3042)+E(f849(x3041,x3043),f849(x3042,x3043))
% 94.68/94.46 [305]~E(x3051,x3052)+E(f849(x3053,x3051),f849(x3053,x3052))
% 94.68/94.46 [306]~E(x3061,x3062)+E(f306(x3061,x3063),f306(x3062,x3063))
% 94.68/94.46 [307]~E(x3071,x3072)+E(f306(x3073,x3071),f306(x3073,x3072))
% 94.68/94.46 [308]~E(x3081,x3082)+E(f294(x3081),f294(x3082))
% 94.68/94.46 [309]~E(x3091,x3092)+E(f35(x3091,x3093),f35(x3092,x3093))
% 94.68/94.46 [310]~E(x3101,x3102)+E(f35(x3103,x3101),f35(x3103,x3102))
% 94.68/94.46 [311]~E(x3111,x3112)+E(f43(x3111,x3113),f43(x3112,x3113))
% 94.68/94.46 [312]~E(x3121,x3122)+E(f43(x3123,x3121),f43(x3123,x3122))
% 94.68/94.46 [313]~E(x3131,x3132)+E(f444(x3131,x3133,x3134,x3135,x3136),f444(x3132,x3133,x3134,x3135,x3136))
% 94.68/94.46 [314]~E(x3141,x3142)+E(f444(x3143,x3141,x3144,x3145,x3146),f444(x3143,x3142,x3144,x3145,x3146))
% 94.68/94.46 [315]~E(x3151,x3152)+E(f444(x3153,x3154,x3151,x3155,x3156),f444(x3153,x3154,x3152,x3155,x3156))
% 94.68/94.46 [316]~E(x3161,x3162)+E(f444(x3163,x3164,x3165,x3161,x3166),f444(x3163,x3164,x3165,x3162,x3166))
% 94.68/94.46 [317]~E(x3171,x3172)+E(f444(x3173,x3174,x3175,x3176,x3171),f444(x3173,x3174,x3175,x3176,x3172))
% 94.68/94.46 [318]~E(x3181,x3182)+E(f382(x3181,x3183),f382(x3182,x3183))
% 94.68/94.46 [319]~E(x3191,x3192)+E(f382(x3193,x3191),f382(x3193,x3192))
% 94.68/94.46 [320]~E(x3201,x3202)+E(f310(x3201,x3203),f310(x3202,x3203))
% 94.68/94.46 [321]~E(x3211,x3212)+E(f310(x3213,x3211),f310(x3213,x3212))
% 94.68/94.46 [322]~E(x3221,x3222)+E(f432(x3221,x3223,x3224,x3225),f432(x3222,x3223,x3224,x3225))
% 94.68/94.46 [323]~E(x3231,x3232)+E(f432(x3233,x3231,x3234,x3235),f432(x3233,x3232,x3234,x3235))
% 94.68/94.46 [324]~E(x3241,x3242)+E(f432(x3243,x3244,x3241,x3245),f432(x3243,x3244,x3242,x3245))
% 94.68/94.46 [325]~E(x3251,x3252)+E(f432(x3253,x3254,x3255,x3251),f432(x3253,x3254,x3255,x3252))
% 94.68/94.46 [326]~E(x3261,x3262)+E(f841(x3261,x3263,x3264),f841(x3262,x3263,x3264))
% 94.68/94.46 [327]~E(x3271,x3272)+E(f841(x3273,x3271,x3274),f841(x3273,x3272,x3274))
% 94.68/94.46 [328]~E(x3281,x3282)+E(f841(x3283,x3284,x3281),f841(x3283,x3284,x3282))
% 94.68/94.46 [329]~E(x3291,x3292)+E(f729(x3291,x3293,x3294),f729(x3292,x3293,x3294))
% 94.68/94.46 [330]~E(x3301,x3302)+E(f729(x3303,x3301,x3304),f729(x3303,x3302,x3304))
% 94.68/94.46 [331]~E(x3311,x3312)+E(f729(x3313,x3314,x3311),f729(x3313,x3314,x3312))
% 94.68/94.46 [332]~E(x3321,x3322)+E(f126(x3321,x3323),f126(x3322,x3323))
% 94.68/94.46 [333]~E(x3331,x3332)+E(f126(x3333,x3331),f126(x3333,x3332))
% 94.68/94.46 [334]~E(x3341,x3342)+E(f486(x3341,x3343,x3344,x3345,x3346,x3347,x3348),f486(x3342,x3343,x3344,x3345,x3346,x3347,x3348))
% 94.68/94.46 [335]~E(x3351,x3352)+E(f486(x3353,x3351,x3354,x3355,x3356,x3357,x3358),f486(x3353,x3352,x3354,x3355,x3356,x3357,x3358))
% 94.68/94.46 [336]~E(x3361,x3362)+E(f486(x3363,x3364,x3361,x3365,x3366,x3367,x3368),f486(x3363,x3364,x3362,x3365,x3366,x3367,x3368))
% 94.68/94.46 [337]~E(x3371,x3372)+E(f486(x3373,x3374,x3375,x3371,x3376,x3377,x3378),f486(x3373,x3374,x3375,x3372,x3376,x3377,x3378))
% 94.68/94.46 [338]~E(x3381,x3382)+E(f486(x3383,x3384,x3385,x3386,x3381,x3387,x3388),f486(x3383,x3384,x3385,x3386,x3382,x3387,x3388))
% 94.68/94.46 [339]~E(x3391,x3392)+E(f486(x3393,x3394,x3395,x3396,x3397,x3391,x3398),f486(x3393,x3394,x3395,x3396,x3397,x3392,x3398))
% 94.68/94.46 [340]~E(x3401,x3402)+E(f486(x3403,x3404,x3405,x3406,x3407,x3408,x3401),f486(x3403,x3404,x3405,x3406,x3407,x3408,x3402))
% 94.68/94.46 [341]~E(x3411,x3412)+E(f153(x3411,x3413,x3414,x3415),f153(x3412,x3413,x3414,x3415))
% 94.68/94.46 [342]~E(x3421,x3422)+E(f153(x3423,x3421,x3424,x3425),f153(x3423,x3422,x3424,x3425))
% 94.68/94.46 [343]~E(x3431,x3432)+E(f153(x3433,x3434,x3431,x3435),f153(x3433,x3434,x3432,x3435))
% 94.68/94.46 [344]~E(x3441,x3442)+E(f153(x3443,x3444,x3445,x3441),f153(x3443,x3444,x3445,x3442))
% 94.68/94.46 [345]~E(x3451,x3452)+E(f31(x3451,x3453),f31(x3452,x3453))
% 94.68/94.46 [346]~E(x3461,x3462)+E(f31(x3463,x3461),f31(x3463,x3462))
% 94.68/94.46 [347]~E(x3471,x3472)+E(f781(x3471,x3473),f781(x3472,x3473))
% 94.68/94.46 [348]~E(x3481,x3482)+E(f781(x3483,x3481),f781(x3483,x3482))
% 94.68/94.46 [349]~E(x3491,x3492)+E(f279(x3491,x3493,x3494),f279(x3492,x3493,x3494))
% 94.68/94.46 [350]~E(x3501,x3502)+E(f279(x3503,x3501,x3504),f279(x3503,x3502,x3504))
% 94.68/94.46 [351]~E(x3511,x3512)+E(f279(x3513,x3514,x3511),f279(x3513,x3514,x3512))
% 94.68/94.46 [352]~E(x3521,x3522)+E(f624(x3521,x3523,x3524,x3525,x3526,x3527,x3528),f624(x3522,x3523,x3524,x3525,x3526,x3527,x3528))
% 94.68/94.46 [353]~E(x3531,x3532)+E(f624(x3533,x3531,x3534,x3535,x3536,x3537,x3538),f624(x3533,x3532,x3534,x3535,x3536,x3537,x3538))
% 94.68/94.46 [354]~E(x3541,x3542)+E(f624(x3543,x3544,x3541,x3545,x3546,x3547,x3548),f624(x3543,x3544,x3542,x3545,x3546,x3547,x3548))
% 94.68/94.46 [355]~E(x3551,x3552)+E(f624(x3553,x3554,x3555,x3551,x3556,x3557,x3558),f624(x3553,x3554,x3555,x3552,x3556,x3557,x3558))
% 94.68/94.46 [356]~E(x3561,x3562)+E(f624(x3563,x3564,x3565,x3566,x3561,x3567,x3568),f624(x3563,x3564,x3565,x3566,x3562,x3567,x3568))
% 94.68/94.46 [357]~E(x3571,x3572)+E(f624(x3573,x3574,x3575,x3576,x3577,x3571,x3578),f624(x3573,x3574,x3575,x3576,x3577,x3572,x3578))
% 94.68/94.46 [358]~E(x3581,x3582)+E(f624(x3583,x3584,x3585,x3586,x3587,x3588,x3581),f624(x3583,x3584,x3585,x3586,x3587,x3588,x3582))
% 94.68/94.46 [359]~E(x3591,x3592)+E(f387(x3591,x3593,x3594,x3595),f387(x3592,x3593,x3594,x3595))
% 94.68/94.46 [360]~E(x3601,x3602)+E(f387(x3603,x3601,x3604,x3605),f387(x3603,x3602,x3604,x3605))
% 94.68/94.46 [361]~E(x3611,x3612)+E(f387(x3613,x3614,x3611,x3615),f387(x3613,x3614,x3612,x3615))
% 94.68/94.46 [362]~E(x3621,x3622)+E(f387(x3623,x3624,x3625,x3621),f387(x3623,x3624,x3625,x3622))
% 94.68/94.46 [363]~E(x3631,x3632)+E(f276(x3631,x3633),f276(x3632,x3633))
% 94.68/94.46 [364]~E(x3641,x3642)+E(f276(x3643,x3641),f276(x3643,x3642))
% 94.68/94.46 [365]~E(x3651,x3652)+E(f599(x3651,x3653,x3654),f599(x3652,x3653,x3654))
% 94.68/94.46 [366]~E(x3661,x3662)+E(f599(x3663,x3661,x3664),f599(x3663,x3662,x3664))
% 94.68/94.46 [367]~E(x3671,x3672)+E(f599(x3673,x3674,x3671),f599(x3673,x3674,x3672))
% 94.68/94.46 [368]~E(x3681,x3682)+E(f241(x3681,x3683),f241(x3682,x3683))
% 94.68/94.46 [369]~E(x3691,x3692)+E(f241(x3693,x3691),f241(x3693,x3692))
% 94.68/94.46 [370]~E(x3701,x3702)+E(f58(x3701,x3703,x3704),f58(x3702,x3703,x3704))
% 94.68/94.46 [371]~E(x3711,x3712)+E(f58(x3713,x3711,x3714),f58(x3713,x3712,x3714))
% 94.68/94.46 [372]~E(x3721,x3722)+E(f58(x3723,x3724,x3721),f58(x3723,x3724,x3722))
% 94.68/94.46 [373]~E(x3731,x3732)+E(f137(x3731,x3733),f137(x3732,x3733))
% 94.68/94.46 [374]~E(x3741,x3742)+E(f137(x3743,x3741),f137(x3743,x3742))
% 94.68/94.46 [375]~E(x3751,x3752)+E(f109(x3751),f109(x3752))
% 94.68/94.46 [376]~E(x3761,x3762)+E(f110(x3761,x3763),f110(x3762,x3763))
% 94.68/94.46 [377]~E(x3771,x3772)+E(f110(x3773,x3771),f110(x3773,x3772))
% 94.68/94.46 [378]~E(x3781,x3782)+E(f305(x3781,x3783),f305(x3782,x3783))
% 94.68/94.46 [379]~E(x3791,x3792)+E(f305(x3793,x3791),f305(x3793,x3792))
% 94.68/94.46 [380]~E(x3801,x3802)+E(f164(x3801,x3803,x3804),f164(x3802,x3803,x3804))
% 94.68/94.46 [381]~E(x3811,x3812)+E(f164(x3813,x3811,x3814),f164(x3813,x3812,x3814))
% 94.68/94.46 [382]~E(x3821,x3822)+E(f164(x3823,x3824,x3821),f164(x3823,x3824,x3822))
% 94.68/94.46 [383]~E(x3831,x3832)+E(f696(x3831,x3833,x3834),f696(x3832,x3833,x3834))
% 94.68/94.46 [384]~E(x3841,x3842)+E(f696(x3843,x3841,x3844),f696(x3843,x3842,x3844))
% 94.68/94.46 [385]~E(x3851,x3852)+E(f696(x3853,x3854,x3851),f696(x3853,x3854,x3852))
% 94.68/94.46 [386]~E(x3861,x3862)+E(f501(x3861,x3863),f501(x3862,x3863))
% 94.68/94.46 [387]~E(x3871,x3872)+E(f501(x3873,x3871),f501(x3873,x3872))
% 94.68/94.46 [388]~E(x3881,x3882)+E(f79(x3881,x3883),f79(x3882,x3883))
% 94.68/94.46 [389]~E(x3891,x3892)+E(f79(x3893,x3891),f79(x3893,x3892))
% 94.68/94.46 [390]~E(x3901,x3902)+E(f764(x3901,x3903,x3904,x3905,x3906,x3907,x3908),f764(x3902,x3903,x3904,x3905,x3906,x3907,x3908))
% 94.68/94.46 [391]~E(x3911,x3912)+E(f764(x3913,x3911,x3914,x3915,x3916,x3917,x3918),f764(x3913,x3912,x3914,x3915,x3916,x3917,x3918))
% 94.68/94.46 [392]~E(x3921,x3922)+E(f764(x3923,x3924,x3921,x3925,x3926,x3927,x3928),f764(x3923,x3924,x3922,x3925,x3926,x3927,x3928))
% 94.68/94.46 [393]~E(x3931,x3932)+E(f764(x3933,x3934,x3935,x3931,x3936,x3937,x3938),f764(x3933,x3934,x3935,x3932,x3936,x3937,x3938))
% 94.68/94.46 [394]~E(x3941,x3942)+E(f764(x3943,x3944,x3945,x3946,x3941,x3947,x3948),f764(x3943,x3944,x3945,x3946,x3942,x3947,x3948))
% 94.68/94.46 [395]~E(x3951,x3952)+E(f764(x3953,x3954,x3955,x3956,x3957,x3951,x3958),f764(x3953,x3954,x3955,x3956,x3957,x3952,x3958))
% 94.68/94.46 [396]~E(x3961,x3962)+E(f764(x3963,x3964,x3965,x3966,x3967,x3968,x3961),f764(x3963,x3964,x3965,x3966,x3967,x3968,x3962))
% 94.68/94.46 [397]~E(x3971,x3972)+E(f84(x3971,x3973),f84(x3972,x3973))
% 94.68/94.46 [398]~E(x3981,x3982)+E(f84(x3983,x3981),f84(x3983,x3982))
% 94.68/94.46 [399]~E(x3991,x3992)+E(f168(x3991,x3993),f168(x3992,x3993))
% 94.68/94.46 [400]~E(x4001,x4002)+E(f168(x4003,x4001),f168(x4003,x4002))
% 94.68/94.46 [401]~E(x4011,x4012)+E(f143(x4011,x4013),f143(x4012,x4013))
% 94.68/94.46 [402]~E(x4021,x4022)+E(f143(x4023,x4021),f143(x4023,x4022))
% 94.68/94.46 [403]~E(x4031,x4032)+E(f253(x4031,x4033),f253(x4032,x4033))
% 94.68/94.46 [404]~E(x4041,x4042)+E(f253(x4043,x4041),f253(x4043,x4042))
% 94.68/94.46 [405]~E(x4051,x4052)+E(f297(x4051,x4053),f297(x4052,x4053))
% 94.68/94.46 [406]~E(x4061,x4062)+E(f297(x4063,x4061),f297(x4063,x4062))
% 94.68/94.46 [407]~E(x4071,x4072)+E(f148(x4071,x4073),f148(x4072,x4073))
% 94.68/94.46 [408]~E(x4081,x4082)+E(f148(x4083,x4081),f148(x4083,x4082))
% 94.68/94.46 [409]~E(x4091,x4092)+E(f138(x4091,x4093,x4094),f138(x4092,x4093,x4094))
% 94.68/94.46 [410]~E(x4101,x4102)+E(f138(x4103,x4101,x4104),f138(x4103,x4102,x4104))
% 94.68/94.46 [411]~E(x4111,x4112)+E(f138(x4113,x4114,x4111),f138(x4113,x4114,x4112))
% 94.68/94.46 [412]~E(x4121,x4122)+E(f291(x4121),f291(x4122))
% 94.68/94.46 [413]~E(x4131,x4132)+E(f293(x4131,x4133,x4134),f293(x4132,x4133,x4134))
% 94.68/94.46 [414]~E(x4141,x4142)+E(f293(x4143,x4141,x4144),f293(x4143,x4142,x4144))
% 94.68/94.46 [415]~E(x4151,x4152)+E(f293(x4153,x4154,x4151),f293(x4153,x4154,x4152))
% 94.68/94.46 [416]~E(x4161,x4162)+E(f888(x4161,x4163,x4164),f888(x4162,x4163,x4164))
% 94.68/94.46 [417]~E(x4171,x4172)+E(f888(x4173,x4171,x4174),f888(x4173,x4172,x4174))
% 94.68/94.46 [418]~E(x4181,x4182)+E(f888(x4183,x4184,x4181),f888(x4183,x4184,x4182))
% 94.68/94.46 [419]~E(x4191,x4192)+E(f518(x4191),f518(x4192))
% 94.68/94.46 [420]~E(x4201,x4202)+E(f304(x4201),f304(x4202))
% 94.68/94.46 [421]~E(x4211,x4212)+E(f799(x4211,x4213,x4214),f799(x4212,x4213,x4214))
% 94.68/94.46 [422]~E(x4221,x4222)+E(f799(x4223,x4221,x4224),f799(x4223,x4222,x4224))
% 94.68/94.46 [423]~E(x4231,x4232)+E(f799(x4233,x4234,x4231),f799(x4233,x4234,x4232))
% 94.68/94.46 [424]~E(x4241,x4242)+E(f847(x4241,x4243,x4244),f847(x4242,x4243,x4244))
% 94.68/94.46 [425]~E(x4251,x4252)+E(f847(x4253,x4251,x4254),f847(x4253,x4252,x4254))
% 94.68/94.46 [426]~E(x4261,x4262)+E(f847(x4263,x4264,x4261),f847(x4263,x4264,x4262))
% 94.68/94.46 [427]~E(x4271,x4272)+E(f826(x4271,x4273,x4274,x4275,x4276,x4277,x4278,x4279),f826(x4272,x4273,x4274,x4275,x4276,x4277,x4278,x4279))
% 94.68/94.46 [428]~E(x4281,x4282)+E(f826(x4283,x4281,x4284,x4285,x4286,x4287,x4288,x4289),f826(x4283,x4282,x4284,x4285,x4286,x4287,x4288,x4289))
% 94.68/94.46 [429]~E(x4291,x4292)+E(f826(x4293,x4294,x4291,x4295,x4296,x4297,x4298,x4299),f826(x4293,x4294,x4292,x4295,x4296,x4297,x4298,x4299))
% 94.68/94.46 [430]~E(x4301,x4302)+E(f826(x4303,x4304,x4305,x4301,x4306,x4307,x4308,x4309),f826(x4303,x4304,x4305,x4302,x4306,x4307,x4308,x4309))
% 94.68/94.46 [431]~E(x4311,x4312)+E(f826(x4313,x4314,x4315,x4316,x4311,x4317,x4318,x4319),f826(x4313,x4314,x4315,x4316,x4312,x4317,x4318,x4319))
% 94.68/94.46 [432]~E(x4321,x4322)+E(f826(x4323,x4324,x4325,x4326,x4327,x4321,x4328,x4329),f826(x4323,x4324,x4325,x4326,x4327,x4322,x4328,x4329))
% 94.68/94.46 [433]~E(x4331,x4332)+E(f826(x4333,x4334,x4335,x4336,x4337,x4338,x4331,x4339),f826(x4333,x4334,x4335,x4336,x4337,x4338,x4332,x4339))
% 94.68/94.46 [434]~E(x4341,x4342)+E(f826(x4343,x4344,x4345,x4346,x4347,x4348,x4349,x4341),f826(x4343,x4344,x4345,x4346,x4347,x4348,x4349,x4342))
% 94.68/94.46 [435]~E(x4351,x4352)+E(f595(x4351,x4353,x4354),f595(x4352,x4353,x4354))
% 94.68/94.46 [436]~E(x4361,x4362)+E(f595(x4363,x4361,x4364),f595(x4363,x4362,x4364))
% 94.68/94.46 [437]~E(x4371,x4372)+E(f595(x4373,x4374,x4371),f595(x4373,x4374,x4372))
% 94.68/94.46 [438]~E(x4381,x4382)+E(f496(x4381,x4383,x4384,x4385),f496(x4382,x4383,x4384,x4385))
% 94.68/94.46 [439]~E(x4391,x4392)+E(f496(x4393,x4391,x4394,x4395),f496(x4393,x4392,x4394,x4395))
% 94.68/94.46 [440]~E(x4401,x4402)+E(f496(x4403,x4404,x4401,x4405),f496(x4403,x4404,x4402,x4405))
% 94.68/94.46 [441]~E(x4411,x4412)+E(f496(x4413,x4414,x4415,x4411),f496(x4413,x4414,x4415,x4412))
% 94.68/94.46 [442]~E(x4421,x4422)+E(f767(x4421),f767(x4422))
% 94.68/94.46 [443]~E(x4431,x4432)+E(f452(x4431,x4433,x4434,x4435,x4436,x4437,x4438),f452(x4432,x4433,x4434,x4435,x4436,x4437,x4438))
% 94.68/94.46 [444]~E(x4441,x4442)+E(f452(x4443,x4441,x4444,x4445,x4446,x4447,x4448),f452(x4443,x4442,x4444,x4445,x4446,x4447,x4448))
% 94.68/94.46 [445]~E(x4451,x4452)+E(f452(x4453,x4454,x4451,x4455,x4456,x4457,x4458),f452(x4453,x4454,x4452,x4455,x4456,x4457,x4458))
% 94.68/94.46 [446]~E(x4461,x4462)+E(f452(x4463,x4464,x4465,x4461,x4466,x4467,x4468),f452(x4463,x4464,x4465,x4462,x4466,x4467,x4468))
% 94.68/94.46 [447]~E(x4471,x4472)+E(f452(x4473,x4474,x4475,x4476,x4471,x4477,x4478),f452(x4473,x4474,x4475,x4476,x4472,x4477,x4478))
% 94.68/94.46 [448]~E(x4481,x4482)+E(f452(x4483,x4484,x4485,x4486,x4487,x4481,x4488),f452(x4483,x4484,x4485,x4486,x4487,x4482,x4488))
% 94.68/94.46 [449]~E(x4491,x4492)+E(f452(x4493,x4494,x4495,x4496,x4497,x4498,x4491),f452(x4493,x4494,x4495,x4496,x4497,x4498,x4492))
% 94.68/94.46 [450]~E(x4501,x4502)+E(f85(x4501,x4503,x4504,x4505),f85(x4502,x4503,x4504,x4505))
% 94.68/94.46 [451]~E(x4511,x4512)+E(f85(x4513,x4511,x4514,x4515),f85(x4513,x4512,x4514,x4515))
% 94.68/94.46 [452]~E(x4521,x4522)+E(f85(x4523,x4524,x4521,x4525),f85(x4523,x4524,x4522,x4525))
% 94.68/94.46 [453]~E(x4531,x4532)+E(f85(x4533,x4534,x4535,x4531),f85(x4533,x4534,x4535,x4532))
% 94.68/94.46 [454]~E(x4541,x4542)+E(f440(x4541,x4543,x4544,x4545,x4546),f440(x4542,x4543,x4544,x4545,x4546))
% 94.68/94.46 [455]~E(x4551,x4552)+E(f440(x4553,x4551,x4554,x4555,x4556),f440(x4553,x4552,x4554,x4555,x4556))
% 94.68/94.46 [456]~E(x4561,x4562)+E(f440(x4563,x4564,x4561,x4565,x4566),f440(x4563,x4564,x4562,x4565,x4566))
% 94.68/94.46 [457]~E(x4571,x4572)+E(f440(x4573,x4574,x4575,x4571,x4576),f440(x4573,x4574,x4575,x4572,x4576))
% 94.68/94.46 [458]~E(x4581,x4582)+E(f440(x4583,x4584,x4585,x4586,x4581),f440(x4583,x4584,x4585,x4586,x4582))
% 94.68/94.46 [459]~E(x4591,x4592)+E(f273(x4591),f273(x4592))
% 94.68/94.46 [460]~E(x4601,x4602)+E(f367(x4601,x4603,x4604,x4605),f367(x4602,x4603,x4604,x4605))
% 94.68/94.46 [461]~E(x4611,x4612)+E(f367(x4613,x4611,x4614,x4615),f367(x4613,x4612,x4614,x4615))
% 94.68/94.46 [462]~E(x4621,x4622)+E(f367(x4623,x4624,x4621,x4625),f367(x4623,x4624,x4622,x4625))
% 94.68/94.46 [463]~E(x4631,x4632)+E(f367(x4633,x4634,x4635,x4631),f367(x4633,x4634,x4635,x4632))
% 94.68/94.46 [464]~E(x4641,x4642)+E(f343(x4641,x4643,x4644),f343(x4642,x4643,x4644))
% 94.68/94.46 [465]~E(x4651,x4652)+E(f343(x4653,x4651,x4654),f343(x4653,x4652,x4654))
% 94.68/94.46 [466]~E(x4661,x4662)+E(f343(x4663,x4664,x4661),f343(x4663,x4664,x4662))
% 94.68/94.46 [467]~E(x4671,x4672)+E(f605(x4671,x4673,x4674,x4675),f605(x4672,x4673,x4674,x4675))
% 94.68/94.46 [468]~E(x4681,x4682)+E(f605(x4683,x4681,x4684,x4685),f605(x4683,x4682,x4684,x4685))
% 94.68/94.46 [469]~E(x4691,x4692)+E(f605(x4693,x4694,x4691,x4695),f605(x4693,x4694,x4692,x4695))
% 94.68/94.46 [470]~E(x4701,x4702)+E(f605(x4703,x4704,x4705,x4701),f605(x4703,x4704,x4705,x4702))
% 94.68/94.46 [471]~E(x4711,x4712)+E(f695(x4711,x4713,x4714),f695(x4712,x4713,x4714))
% 94.68/94.46 [472]~E(x4721,x4722)+E(f695(x4723,x4721,x4724),f695(x4723,x4722,x4724))
% 94.68/94.46 [473]~E(x4731,x4732)+E(f695(x4733,x4734,x4731),f695(x4733,x4734,x4732))
% 94.68/94.46 [474]~E(x4741,x4742)+E(f510(x4741,x4743,x4744),f510(x4742,x4743,x4744))
% 94.68/94.46 [475]~E(x4751,x4752)+E(f510(x4753,x4751,x4754),f510(x4753,x4752,x4754))
% 94.68/94.46 [476]~E(x4761,x4762)+E(f510(x4763,x4764,x4761),f510(x4763,x4764,x4762))
% 94.68/94.46 [477]~E(x4771,x4772)+E(f140(x4771,x4773,x4774,x4775),f140(x4772,x4773,x4774,x4775))
% 94.68/94.46 [478]~E(x4781,x4782)+E(f140(x4783,x4781,x4784,x4785),f140(x4783,x4782,x4784,x4785))
% 94.68/94.46 [479]~E(x4791,x4792)+E(f140(x4793,x4794,x4791,x4795),f140(x4793,x4794,x4792,x4795))
% 94.68/94.46 [480]~E(x4801,x4802)+E(f140(x4803,x4804,x4805,x4801),f140(x4803,x4804,x4805,x4802))
% 94.68/94.46 [481]~E(x4811,x4812)+E(f169(x4811,x4813),f169(x4812,x4813))
% 94.68/94.46 [482]~E(x4821,x4822)+E(f169(x4823,x4821),f169(x4823,x4822))
% 94.68/94.46 [483]~E(x4831,x4832)+E(f383(x4831,x4833),f383(x4832,x4833))
% 94.68/94.46 [484]~E(x4841,x4842)+E(f383(x4843,x4841),f383(x4843,x4842))
% 94.68/94.46 [485]~E(x4851,x4852)+E(f38(x4851),f38(x4852))
% 94.68/94.46 [486]~E(x4861,x4862)+E(f761(x4861,x4863,x4864),f761(x4862,x4863,x4864))
% 94.68/94.46 [487]~E(x4871,x4872)+E(f761(x4873,x4871,x4874),f761(x4873,x4872,x4874))
% 94.68/94.46 [488]~E(x4881,x4882)+E(f761(x4883,x4884,x4881),f761(x4883,x4884,x4882))
% 94.68/94.46 [489]~E(x4891,x4892)+E(f44(x4891,x4893),f44(x4892,x4893))
% 94.68/94.46 [490]~E(x4901,x4902)+E(f44(x4903,x4901),f44(x4903,x4902))
% 94.68/94.46 [491]~E(x4911,x4912)+E(f662(x4911,x4913,x4914,x4915),f662(x4912,x4913,x4914,x4915))
% 94.68/94.46 [492]~E(x4921,x4922)+E(f662(x4923,x4921,x4924,x4925),f662(x4923,x4922,x4924,x4925))
% 94.68/94.46 [493]~E(x4931,x4932)+E(f662(x4933,x4934,x4931,x4935),f662(x4933,x4934,x4932,x4935))
% 94.68/94.46 [494]~E(x4941,x4942)+E(f662(x4943,x4944,x4945,x4941),f662(x4943,x4944,x4945,x4942))
% 94.68/94.46 [495]~E(x4951,x4952)+E(f419(x4951,x4953,x4954,x4955,x4956),f419(x4952,x4953,x4954,x4955,x4956))
% 94.68/94.46 [496]~E(x4961,x4962)+E(f419(x4963,x4961,x4964,x4965,x4966),f419(x4963,x4962,x4964,x4965,x4966))
% 94.68/94.46 [497]~E(x4971,x4972)+E(f419(x4973,x4974,x4971,x4975,x4976),f419(x4973,x4974,x4972,x4975,x4976))
% 94.68/94.46 [498]~E(x4981,x4982)+E(f419(x4983,x4984,x4985,x4981,x4986),f419(x4983,x4984,x4985,x4982,x4986))
% 94.68/94.46 [499]~E(x4991,x4992)+E(f419(x4993,x4994,x4995,x4996,x4991),f419(x4993,x4994,x4995,x4996,x4992))
% 94.68/94.46 [500]~E(x5001,x5002)+E(f249(x5001,x5003,x5004,x5005),f249(x5002,x5003,x5004,x5005))
% 94.68/94.46 [501]~E(x5011,x5012)+E(f249(x5013,x5011,x5014,x5015),f249(x5013,x5012,x5014,x5015))
% 94.68/94.46 [502]~E(x5021,x5022)+E(f249(x5023,x5024,x5021,x5025),f249(x5023,x5024,x5022,x5025))
% 94.68/94.46 [503]~E(x5031,x5032)+E(f249(x5033,x5034,x5035,x5031),f249(x5033,x5034,x5035,x5032))
% 94.68/94.46 [504]~E(x5041,x5042)+E(f834(x5041,x5043,x5044),f834(x5042,x5043,x5044))
% 94.68/94.46 [505]~E(x5051,x5052)+E(f834(x5053,x5051,x5054),f834(x5053,x5052,x5054))
% 94.68/94.46 [506]~E(x5061,x5062)+E(f834(x5063,x5064,x5061),f834(x5063,x5064,x5062))
% 94.68/94.46 [507]~E(x5071,x5072)+E(f303(x5071,x5073,x5074,x5075),f303(x5072,x5073,x5074,x5075))
% 94.68/94.46 [508]~E(x5081,x5082)+E(f303(x5083,x5081,x5084,x5085),f303(x5083,x5082,x5084,x5085))
% 94.68/94.46 [509]~E(x5091,x5092)+E(f303(x5093,x5094,x5091,x5095),f303(x5093,x5094,x5092,x5095))
% 94.68/94.46 [510]~E(x5101,x5102)+E(f303(x5103,x5104,x5105,x5101),f303(x5103,x5104,x5105,x5102))
% 94.68/94.46 [511]~E(x5111,x5112)+E(f369(x5111,x5113,x5114,x5115),f369(x5112,x5113,x5114,x5115))
% 94.68/94.46 [512]~E(x5121,x5122)+E(f369(x5123,x5121,x5124,x5125),f369(x5123,x5122,x5124,x5125))
% 94.68/94.46 [513]~E(x5131,x5132)+E(f369(x5133,x5134,x5131,x5135),f369(x5133,x5134,x5132,x5135))
% 94.68/94.46 [514]~E(x5141,x5142)+E(f369(x5143,x5144,x5145,x5141),f369(x5143,x5144,x5145,x5142))
% 94.68/94.46 [515]~E(x5151,x5152)+E(f755(x5151,x5153,x5154,x5155),f755(x5152,x5153,x5154,x5155))
% 94.68/94.46 [516]~E(x5161,x5162)+E(f755(x5163,x5161,x5164,x5165),f755(x5163,x5162,x5164,x5165))
% 94.68/94.46 [517]~E(x5171,x5172)+E(f755(x5173,x5174,x5171,x5175),f755(x5173,x5174,x5172,x5175))
% 94.68/94.46 [518]~E(x5181,x5182)+E(f755(x5183,x5184,x5185,x5181),f755(x5183,x5184,x5185,x5182))
% 94.68/94.46 [519]~E(x5191,x5192)+E(f11(x5191,x5193,x5194),f11(x5192,x5193,x5194))
% 94.68/94.46 [520]~E(x5201,x5202)+E(f11(x5203,x5201,x5204),f11(x5203,x5202,x5204))
% 94.68/94.46 [521]~E(x5211,x5212)+E(f11(x5213,x5214,x5211),f11(x5213,x5214,x5212))
% 94.68/94.46 [522]~E(x5221,x5222)+E(f272(x5221),f272(x5222))
% 94.68/94.46 [523]~E(x5231,x5232)+E(f290(x5231,x5233,x5234,x5235,x5236),f290(x5232,x5233,x5234,x5235,x5236))
% 94.68/94.46 [524]~E(x5241,x5242)+E(f290(x5243,x5241,x5244,x5245,x5246),f290(x5243,x5242,x5244,x5245,x5246))
% 94.68/94.46 [525]~E(x5251,x5252)+E(f290(x5253,x5254,x5251,x5255,x5256),f290(x5253,x5254,x5252,x5255,x5256))
% 94.68/94.46 [526]~E(x5261,x5262)+E(f290(x5263,x5264,x5265,x5261,x5266),f290(x5263,x5264,x5265,x5262,x5266))
% 94.68/94.46 [527]~E(x5271,x5272)+E(f290(x5273,x5274,x5275,x5276,x5271),f290(x5273,x5274,x5275,x5276,x5272))
% 94.68/94.46 [528]~E(x5281,x5282)+E(f588(x5281,x5283,x5284,x5285,x5286,x5287,x5288),f588(x5282,x5283,x5284,x5285,x5286,x5287,x5288))
% 94.68/94.46 [529]~E(x5291,x5292)+E(f588(x5293,x5291,x5294,x5295,x5296,x5297,x5298),f588(x5293,x5292,x5294,x5295,x5296,x5297,x5298))
% 94.68/94.46 [530]~E(x5301,x5302)+E(f588(x5303,x5304,x5301,x5305,x5306,x5307,x5308),f588(x5303,x5304,x5302,x5305,x5306,x5307,x5308))
% 94.68/94.46 [531]~E(x5311,x5312)+E(f588(x5313,x5314,x5315,x5311,x5316,x5317,x5318),f588(x5313,x5314,x5315,x5312,x5316,x5317,x5318))
% 94.68/94.46 [532]~E(x5321,x5322)+E(f588(x5323,x5324,x5325,x5326,x5321,x5327,x5328),f588(x5323,x5324,x5325,x5326,x5322,x5327,x5328))
% 94.68/94.46 [533]~E(x5331,x5332)+E(f588(x5333,x5334,x5335,x5336,x5337,x5331,x5338),f588(x5333,x5334,x5335,x5336,x5337,x5332,x5338))
% 94.68/94.46 [534]~E(x5341,x5342)+E(f588(x5343,x5344,x5345,x5346,x5347,x5348,x5341),f588(x5343,x5344,x5345,x5346,x5347,x5348,x5342))
% 94.68/94.46 [535]~E(x5351,x5352)+E(f175(x5351,x5353,x5354,x5355),f175(x5352,x5353,x5354,x5355))
% 94.68/94.46 [536]~E(x5361,x5362)+E(f175(x5363,x5361,x5364,x5365),f175(x5363,x5362,x5364,x5365))
% 94.68/94.46 [537]~E(x5371,x5372)+E(f175(x5373,x5374,x5371,x5375),f175(x5373,x5374,x5372,x5375))
% 94.68/94.46 [538]~E(x5381,x5382)+E(f175(x5383,x5384,x5385,x5381),f175(x5383,x5384,x5385,x5382))
% 94.68/94.46 [539]~E(x5391,x5392)+E(f869(x5391,x5393,x5394,x5395),f869(x5392,x5393,x5394,x5395))
% 94.68/94.46 [540]~E(x5401,x5402)+E(f869(x5403,x5401,x5404,x5405),f869(x5403,x5402,x5404,x5405))
% 94.68/94.46 [541]~E(x5411,x5412)+E(f869(x5413,x5414,x5411,x5415),f869(x5413,x5414,x5412,x5415))
% 94.68/94.46 [542]~E(x5421,x5422)+E(f869(x5423,x5424,x5425,x5421),f869(x5423,x5424,x5425,x5422))
% 94.68/94.46 [543]~E(x5431,x5432)+E(f833(x5431,x5433,x5434),f833(x5432,x5433,x5434))
% 94.68/94.46 [544]~E(x5441,x5442)+E(f833(x5443,x5441,x5444),f833(x5443,x5442,x5444))
% 94.68/94.46 [545]~E(x5451,x5452)+E(f833(x5453,x5454,x5451),f833(x5453,x5454,x5452))
% 94.68/94.46 [546]~E(x5461,x5462)+E(f873(x5461,x5463,x5464),f873(x5462,x5463,x5464))
% 94.68/94.46 [547]~E(x5471,x5472)+E(f873(x5473,x5471,x5474),f873(x5473,x5472,x5474))
% 94.68/94.46 [548]~E(x5481,x5482)+E(f873(x5483,x5484,x5481),f873(x5483,x5484,x5482))
% 94.68/94.46 [549]~E(x5491,x5492)+E(f653(x5491,x5493,x5494),f653(x5492,x5493,x5494))
% 94.68/94.46 [550]~E(x5501,x5502)+E(f653(x5503,x5501,x5504),f653(x5503,x5502,x5504))
% 94.68/94.46 [551]~E(x5511,x5512)+E(f653(x5513,x5514,x5511),f653(x5513,x5514,x5512))
% 94.68/94.46 [552]~E(x5521,x5522)+E(f239(x5521,x5523,x5524),f239(x5522,x5523,x5524))
% 94.68/94.46 [553]~E(x5531,x5532)+E(f239(x5533,x5531,x5534),f239(x5533,x5532,x5534))
% 94.68/94.46 [554]~E(x5541,x5542)+E(f239(x5543,x5544,x5541),f239(x5543,x5544,x5542))
% 94.68/94.46 [555]~E(x5551,x5552)+E(f645(x5551,x5553,x5554,x5555),f645(x5552,x5553,x5554,x5555))
% 94.68/94.46 [556]~E(x5561,x5562)+E(f645(x5563,x5561,x5564,x5565),f645(x5563,x5562,x5564,x5565))
% 94.68/94.46 [557]~E(x5571,x5572)+E(f645(x5573,x5574,x5571,x5575),f645(x5573,x5574,x5572,x5575))
% 94.68/94.46 [558]~E(x5581,x5582)+E(f645(x5583,x5584,x5585,x5581),f645(x5583,x5584,x5585,x5582))
% 94.68/94.46 [559]~E(x5591,x5592)+E(f296(x5591,x5593,x5594),f296(x5592,x5593,x5594))
% 94.68/94.46 [560]~E(x5601,x5602)+E(f296(x5603,x5601,x5604),f296(x5603,x5602,x5604))
% 94.68/94.46 [561]~E(x5611,x5612)+E(f296(x5613,x5614,x5611),f296(x5613,x5614,x5612))
% 94.68/94.46 [562]~E(x5621,x5622)+E(f156(x5621,x5623,x5624),f156(x5622,x5623,x5624))
% 94.68/94.46 [563]~E(x5631,x5632)+E(f156(x5633,x5631,x5634),f156(x5633,x5632,x5634))
% 94.68/94.46 [564]~E(x5641,x5642)+E(f156(x5643,x5644,x5641),f156(x5643,x5644,x5642))
% 94.68/94.46 [565]~E(x5651,x5652)+E(f758(x5651,x5653,x5654,x5655),f758(x5652,x5653,x5654,x5655))
% 94.68/94.46 [566]~E(x5661,x5662)+E(f758(x5663,x5661,x5664,x5665),f758(x5663,x5662,x5664,x5665))
% 94.68/94.46 [567]~E(x5671,x5672)+E(f758(x5673,x5674,x5671,x5675),f758(x5673,x5674,x5672,x5675))
% 94.68/94.46 [568]~E(x5681,x5682)+E(f758(x5683,x5684,x5685,x5681),f758(x5683,x5684,x5685,x5682))
% 94.68/94.46 [569]~E(x5691,x5692)+E(f348(x5691,x5693,x5694,x5695,x5696),f348(x5692,x5693,x5694,x5695,x5696))
% 94.68/94.46 [570]~E(x5701,x5702)+E(f348(x5703,x5701,x5704,x5705,x5706),f348(x5703,x5702,x5704,x5705,x5706))
% 94.68/94.46 [571]~E(x5711,x5712)+E(f348(x5713,x5714,x5711,x5715,x5716),f348(x5713,x5714,x5712,x5715,x5716))
% 94.68/94.46 [572]~E(x5721,x5722)+E(f348(x5723,x5724,x5725,x5721,x5726),f348(x5723,x5724,x5725,x5722,x5726))
% 94.68/94.46 [573]~E(x5731,x5732)+E(f348(x5733,x5734,x5735,x5736,x5731),f348(x5733,x5734,x5735,x5736,x5732))
% 94.68/94.46 [574]~E(x5741,x5742)+E(f12(x5741,x5743,x5744),f12(x5742,x5743,x5744))
% 94.68/94.46 [575]~E(x5751,x5752)+E(f12(x5753,x5751,x5754),f12(x5753,x5752,x5754))
% 94.68/94.46 [576]~E(x5761,x5762)+E(f12(x5763,x5764,x5761),f12(x5763,x5764,x5762))
% 94.68/94.46 [577]~E(x5771,x5772)+E(f581(x5771,x5773,x5774,x5775),f581(x5772,x5773,x5774,x5775))
% 94.68/94.46 [578]~E(x5781,x5782)+E(f581(x5783,x5781,x5784,x5785),f581(x5783,x5782,x5784,x5785))
% 94.68/94.46 [579]~E(x5791,x5792)+E(f581(x5793,x5794,x5791,x5795),f581(x5793,x5794,x5792,x5795))
% 94.68/94.46 [580]~E(x5801,x5802)+E(f581(x5803,x5804,x5805,x5801),f581(x5803,x5804,x5805,x5802))
% 94.68/94.46 [581]~E(x5811,x5812)+E(f591(x5811,x5813,x5814),f591(x5812,x5813,x5814))
% 94.68/94.46 [582]~E(x5821,x5822)+E(f591(x5823,x5821,x5824),f591(x5823,x5822,x5824))
% 94.68/94.46 [583]~E(x5831,x5832)+E(f591(x5833,x5834,x5831),f591(x5833,x5834,x5832))
% 94.68/94.46 [584]~E(x5841,x5842)+E(f749(x5841,x5843,x5844,x5845),f749(x5842,x5843,x5844,x5845))
% 94.68/94.46 [585]~E(x5851,x5852)+E(f749(x5853,x5851,x5854,x5855),f749(x5853,x5852,x5854,x5855))
% 94.68/94.46 [586]~E(x5861,x5862)+E(f749(x5863,x5864,x5861,x5865),f749(x5863,x5864,x5862,x5865))
% 94.68/94.46 [587]~E(x5871,x5872)+E(f749(x5873,x5874,x5875,x5871),f749(x5873,x5874,x5875,x5872))
% 94.68/94.46 [588]~E(x5881,x5882)+E(f59(x5881,x5883,x5884),f59(x5882,x5883,x5884))
% 94.68/94.46 [589]~E(x5891,x5892)+E(f59(x5893,x5891,x5894),f59(x5893,x5892,x5894))
% 94.68/94.46 [590]~E(x5901,x5902)+E(f59(x5903,x5904,x5901),f59(x5903,x5904,x5902))
% 94.68/94.46 [591]~E(x5911,x5912)+E(f115(x5911,x5913),f115(x5912,x5913))
% 94.68/94.46 [592]~E(x5921,x5922)+E(f115(x5923,x5921),f115(x5923,x5922))
% 94.68/94.46 [593]~E(x5931,x5932)+E(f536(x5931,x5933,x5934),f536(x5932,x5933,x5934))
% 94.68/94.46 [594]~E(x5941,x5942)+E(f536(x5943,x5941,x5944),f536(x5943,x5942,x5944))
% 94.68/94.46 [595]~E(x5951,x5952)+E(f536(x5953,x5954,x5951),f536(x5953,x5954,x5952))
% 94.68/94.46 [596]~E(x5961,x5962)+E(f233(x5961,x5963,x5964),f233(x5962,x5963,x5964))
% 94.68/94.46 [597]~E(x5971,x5972)+E(f233(x5973,x5971,x5974),f233(x5973,x5972,x5974))
% 94.68/94.46 [598]~E(x5981,x5982)+E(f233(x5983,x5984,x5981),f233(x5983,x5984,x5982))
% 94.68/94.46 [599]~E(x5991,x5992)+E(f664(x5991,x5993,x5994,x5995),f664(x5992,x5993,x5994,x5995))
% 94.68/94.46 [600]~E(x6001,x6002)+E(f664(x6003,x6001,x6004,x6005),f664(x6003,x6002,x6004,x6005))
% 94.68/94.46 [601]~E(x6011,x6012)+E(f664(x6013,x6014,x6011,x6015),f664(x6013,x6014,x6012,x6015))
% 94.68/94.46 [602]~E(x6021,x6022)+E(f664(x6023,x6024,x6025,x6021),f664(x6023,x6024,x6025,x6022))
% 94.68/94.46 [603]~E(x6031,x6032)+E(f457(x6031,x6033,x6034,x6035),f457(x6032,x6033,x6034,x6035))
% 94.68/94.46 [604]~E(x6041,x6042)+E(f457(x6043,x6041,x6044,x6045),f457(x6043,x6042,x6044,x6045))
% 94.68/94.46 [605]~E(x6051,x6052)+E(f457(x6053,x6054,x6051,x6055),f457(x6053,x6054,x6052,x6055))
% 94.68/94.46 [606]~E(x6061,x6062)+E(f457(x6063,x6064,x6065,x6061),f457(x6063,x6064,x6065,x6062))
% 94.68/94.46 [607]~E(x6071,x6072)+E(f449(x6071,x6073,x6074,x6075,x6076,x6077,x6078),f449(x6072,x6073,x6074,x6075,x6076,x6077,x6078))
% 94.68/94.46 [608]~E(x6081,x6082)+E(f449(x6083,x6081,x6084,x6085,x6086,x6087,x6088),f449(x6083,x6082,x6084,x6085,x6086,x6087,x6088))
% 94.68/94.46 [609]~E(x6091,x6092)+E(f449(x6093,x6094,x6091,x6095,x6096,x6097,x6098),f449(x6093,x6094,x6092,x6095,x6096,x6097,x6098))
% 94.68/94.46 [610]~E(x6101,x6102)+E(f449(x6103,x6104,x6105,x6101,x6106,x6107,x6108),f449(x6103,x6104,x6105,x6102,x6106,x6107,x6108))
% 94.68/94.46 [611]~E(x6111,x6112)+E(f449(x6113,x6114,x6115,x6116,x6111,x6117,x6118),f449(x6113,x6114,x6115,x6116,x6112,x6117,x6118))
% 94.68/94.46 [612]~E(x6121,x6122)+E(f449(x6123,x6124,x6125,x6126,x6127,x6121,x6128),f449(x6123,x6124,x6125,x6126,x6127,x6122,x6128))
% 94.68/94.46 [613]~E(x6131,x6132)+E(f449(x6133,x6134,x6135,x6136,x6137,x6138,x6131),f449(x6133,x6134,x6135,x6136,x6137,x6138,x6132))
% 94.68/94.46 [614]~E(x6141,x6142)+E(f160(x6141,x6143,x6144),f160(x6142,x6143,x6144))
% 94.68/94.46 [615]~E(x6151,x6152)+E(f160(x6153,x6151,x6154),f160(x6153,x6152,x6154))
% 94.68/94.46 [616]~E(x6161,x6162)+E(f160(x6163,x6164,x6161),f160(x6163,x6164,x6162))
% 94.68/94.46 [617]~E(x6171,x6172)+E(f254(x6171,x6173),f254(x6172,x6173))
% 94.68/94.46 [618]~E(x6181,x6182)+E(f254(x6183,x6181),f254(x6183,x6182))
% 94.68/94.46 [619]~E(x6191,x6192)+E(f791(x6191,x6193,x6194,x6195,x6196),f791(x6192,x6193,x6194,x6195,x6196))
% 94.68/94.46 [620]~E(x6201,x6202)+E(f791(x6203,x6201,x6204,x6205,x6206),f791(x6203,x6202,x6204,x6205,x6206))
% 94.68/94.46 [621]~E(x6211,x6212)+E(f791(x6213,x6214,x6211,x6215,x6216),f791(x6213,x6214,x6212,x6215,x6216))
% 94.68/94.46 [622]~E(x6221,x6222)+E(f791(x6223,x6224,x6225,x6221,x6226),f791(x6223,x6224,x6225,x6222,x6226))
% 94.68/94.46 [623]~E(x6231,x6232)+E(f791(x6233,x6234,x6235,x6236,x6231),f791(x6233,x6234,x6235,x6236,x6232))
% 94.68/94.46 [624]~E(x6241,x6242)+E(f508(x6241,x6243),f508(x6242,x6243))
% 94.68/94.46 [625]~E(x6251,x6252)+E(f508(x6253,x6251),f508(x6253,x6252))
% 94.68/94.46 [626]~E(x6261,x6262)+E(f278(x6261,x6263),f278(x6262,x6263))
% 94.68/94.46 [627]~E(x6271,x6272)+E(f278(x6273,x6271),f278(x6273,x6272))
% 94.68/94.46 [628]~E(x6281,x6282)+E(f846(x6281,x6283,x6284),f846(x6282,x6283,x6284))
% 94.68/94.46 [629]~E(x6291,x6292)+E(f846(x6293,x6291,x6294),f846(x6293,x6292,x6294))
% 94.68/94.46 [630]~E(x6301,x6302)+E(f846(x6303,x6304,x6301),f846(x6303,x6304,x6302))
% 94.68/94.46 [631]~E(x6311,x6312)+E(f886(x6311,x6313,x6314),f886(x6312,x6313,x6314))
% 94.68/94.46 [632]~E(x6321,x6322)+E(f886(x6323,x6321,x6324),f886(x6323,x6322,x6324))
% 94.68/94.46 [633]~E(x6331,x6332)+E(f886(x6333,x6334,x6331),f886(x6333,x6334,x6332))
% 94.68/94.46 [634]~E(x6341,x6342)+E(f150(x6341,x6343),f150(x6342,x6343))
% 94.68/94.46 [635]~E(x6351,x6352)+E(f150(x6353,x6351),f150(x6353,x6352))
% 94.68/94.46 [636]~E(x6361,x6362)+E(f82(x6361),f82(x6362))
% 94.68/94.46 [637]~E(x6371,x6372)+E(f649(x6371,x6373,x6374),f649(x6372,x6373,x6374))
% 94.68/94.46 [638]~E(x6381,x6382)+E(f649(x6383,x6381,x6384),f649(x6383,x6382,x6384))
% 94.68/94.46 [639]~E(x6391,x6392)+E(f649(x6393,x6394,x6391),f649(x6393,x6394,x6392))
% 94.68/94.46 [640]~E(x6401,x6402)+E(f719(x6401,x6403,x6404,x6405),f719(x6402,x6403,x6404,x6405))
% 94.68/94.46 [641]~E(x6411,x6412)+E(f719(x6413,x6411,x6414,x6415),f719(x6413,x6412,x6414,x6415))
% 94.68/94.46 [642]~E(x6421,x6422)+E(f719(x6423,x6424,x6421,x6425),f719(x6423,x6424,x6422,x6425))
% 94.68/94.46 [643]~E(x6431,x6432)+E(f719(x6433,x6434,x6435,x6431),f719(x6433,x6434,x6435,x6432))
% 94.68/94.46 [644]~E(x6441,x6442)+E(f54(x6441,x6443,x6444,x6445),f54(x6442,x6443,x6444,x6445))
% 94.68/94.46 [645]~E(x6451,x6452)+E(f54(x6453,x6451,x6454,x6455),f54(x6453,x6452,x6454,x6455))
% 94.68/94.46 [646]~E(x6461,x6462)+E(f54(x6463,x6464,x6461,x6465),f54(x6463,x6464,x6462,x6465))
% 94.68/94.46 [647]~E(x6471,x6472)+E(f54(x6473,x6474,x6475,x6471),f54(x6473,x6474,x6475,x6472))
% 94.68/94.46 [648]~E(x6481,x6482)+E(f584(x6481,x6483,x6484,x6485,x6486),f584(x6482,x6483,x6484,x6485,x6486))
% 94.68/94.46 [649]~E(x6491,x6492)+E(f584(x6493,x6491,x6494,x6495,x6496),f584(x6493,x6492,x6494,x6495,x6496))
% 94.68/94.46 [650]~E(x6501,x6502)+E(f584(x6503,x6504,x6501,x6505,x6506),f584(x6503,x6504,x6502,x6505,x6506))
% 94.68/94.46 [651]~E(x6511,x6512)+E(f584(x6513,x6514,x6515,x6511,x6516),f584(x6513,x6514,x6515,x6512,x6516))
% 94.68/94.46 [652]~E(x6521,x6522)+E(f584(x6523,x6524,x6525,x6526,x6521),f584(x6523,x6524,x6525,x6526,x6522))
% 94.68/94.46 [653]~E(x6531,x6532)+E(f350(x6531,x6533),f350(x6532,x6533))
% 94.68/94.46 [654]~E(x6541,x6542)+E(f350(x6543,x6541),f350(x6543,x6542))
% 94.68/94.46 [655]~E(x6551,x6552)+E(f690(x6551,x6553,x6554),f690(x6552,x6553,x6554))
% 94.68/94.46 [656]~E(x6561,x6562)+E(f690(x6563,x6561,x6564),f690(x6563,x6562,x6564))
% 94.68/94.46 [657]~E(x6571,x6572)+E(f690(x6573,x6574,x6571),f690(x6573,x6574,x6572))
% 94.68/94.46 [658]~E(x6581,x6582)+E(f240(x6581,x6583,x6584),f240(x6582,x6583,x6584))
% 94.68/94.46 [659]~E(x6591,x6592)+E(f240(x6593,x6591,x6594),f240(x6593,x6592,x6594))
% 94.68/94.46 [660]~E(x6601,x6602)+E(f240(x6603,x6604,x6601),f240(x6603,x6604,x6602))
% 94.68/94.46 [661]~E(x6611,x6612)+E(f810(x6611,x6613,x6614,x6615),f810(x6612,x6613,x6614,x6615))
% 94.68/94.46 [662]~E(x6621,x6622)+E(f810(x6623,x6621,x6624,x6625),f810(x6623,x6622,x6624,x6625))
% 94.68/94.46 [663]~E(x6631,x6632)+E(f810(x6633,x6634,x6631,x6635),f810(x6633,x6634,x6632,x6635))
% 94.68/94.46 [664]~E(x6641,x6642)+E(f810(x6643,x6644,x6645,x6641),f810(x6643,x6644,x6645,x6642))
% 94.68/94.46 [665]~E(x6651,x6652)+E(f866(x6651,x6653,x6654),f866(x6652,x6653,x6654))
% 94.68/94.46 [666]~E(x6661,x6662)+E(f866(x6663,x6661,x6664),f866(x6663,x6662,x6664))
% 94.68/94.46 [667]~E(x6671,x6672)+E(f866(x6673,x6674,x6671),f866(x6673,x6674,x6672))
% 94.68/94.46 [668]~E(x6681,x6682)+E(f766(x6681,x6683,x6684,x6685,x6686,x6687,x6688),f766(x6682,x6683,x6684,x6685,x6686,x6687,x6688))
% 94.68/94.46 [669]~E(x6691,x6692)+E(f766(x6693,x6691,x6694,x6695,x6696,x6697,x6698),f766(x6693,x6692,x6694,x6695,x6696,x6697,x6698))
% 94.68/94.46 [670]~E(x6701,x6702)+E(f766(x6703,x6704,x6701,x6705,x6706,x6707,x6708),f766(x6703,x6704,x6702,x6705,x6706,x6707,x6708))
% 94.68/94.46 [671]~E(x6711,x6712)+E(f766(x6713,x6714,x6715,x6711,x6716,x6717,x6718),f766(x6713,x6714,x6715,x6712,x6716,x6717,x6718))
% 94.68/94.46 [672]~E(x6721,x6722)+E(f766(x6723,x6724,x6725,x6726,x6721,x6727,x6728),f766(x6723,x6724,x6725,x6726,x6722,x6727,x6728))
% 94.68/94.46 [673]~E(x6731,x6732)+E(f766(x6733,x6734,x6735,x6736,x6737,x6731,x6738),f766(x6733,x6734,x6735,x6736,x6737,x6732,x6738))
% 94.68/94.46 [674]~E(x6741,x6742)+E(f766(x6743,x6744,x6745,x6746,x6747,x6748,x6741),f766(x6743,x6744,x6745,x6746,x6747,x6748,x6742))
% 94.68/94.46 [675]~E(x6751,x6752)+E(f707(x6751,x6753),f707(x6752,x6753))
% 94.68/94.46 [676]~E(x6761,x6762)+E(f707(x6763,x6761),f707(x6763,x6762))
% 94.68/94.46 [677]~E(x6771,x6772)+E(f845(x6771,x6773,x6774),f845(x6772,x6773,x6774))
% 94.68/94.46 [678]~E(x6781,x6782)+E(f845(x6783,x6781,x6784),f845(x6783,x6782,x6784))
% 94.68/94.46 [679]~E(x6791,x6792)+E(f845(x6793,x6794,x6791),f845(x6793,x6794,x6792))
% 94.68/94.46 [680]~E(x6801,x6802)+E(f551(x6801,x6803,x6804,x6805,x6806,x6807,x6808,x6809),f551(x6802,x6803,x6804,x6805,x6806,x6807,x6808,x6809))
% 94.68/94.46 [681]~E(x6811,x6812)+E(f551(x6813,x6811,x6814,x6815,x6816,x6817,x6818,x6819),f551(x6813,x6812,x6814,x6815,x6816,x6817,x6818,x6819))
% 94.68/94.46 [682]~E(x6821,x6822)+E(f551(x6823,x6824,x6821,x6825,x6826,x6827,x6828,x6829),f551(x6823,x6824,x6822,x6825,x6826,x6827,x6828,x6829))
% 94.68/94.46 [683]~E(x6831,x6832)+E(f551(x6833,x6834,x6835,x6831,x6836,x6837,x6838,x6839),f551(x6833,x6834,x6835,x6832,x6836,x6837,x6838,x6839))
% 94.68/94.46 [684]~E(x6841,x6842)+E(f551(x6843,x6844,x6845,x6846,x6841,x6847,x6848,x6849),f551(x6843,x6844,x6845,x6846,x6842,x6847,x6848,x6849))
% 94.68/94.46 [685]~E(x6851,x6852)+E(f551(x6853,x6854,x6855,x6856,x6857,x6851,x6858,x6859),f551(x6853,x6854,x6855,x6856,x6857,x6852,x6858,x6859))
% 94.68/94.46 [686]~E(x6861,x6862)+E(f551(x6863,x6864,x6865,x6866,x6867,x6868,x6861,x6869),f551(x6863,x6864,x6865,x6866,x6867,x6868,x6862,x6869))
% 94.68/94.46 [687]~E(x6871,x6872)+E(f551(x6873,x6874,x6875,x6876,x6877,x6878,x6879,x6871),f551(x6873,x6874,x6875,x6876,x6877,x6878,x6879,x6872))
% 94.68/94.46 [688]~E(x6881,x6882)+E(f57(x6881,x6883),f57(x6882,x6883))
% 94.68/94.46 [689]~E(x6891,x6892)+E(f57(x6893,x6891),f57(x6893,x6892))
% 94.68/94.46 [690]~E(x6901,x6902)+E(f650(x6901,x6903,x6904),f650(x6902,x6903,x6904))
% 94.68/94.46 [691]~E(x6911,x6912)+E(f650(x6913,x6911,x6914),f650(x6913,x6912,x6914))
% 94.68/94.46 [692]~E(x6921,x6922)+E(f650(x6923,x6924,x6921),f650(x6923,x6924,x6922))
% 94.68/94.46 [693]~E(x6931,x6932)+E(f256(x6931,x6933),f256(x6932,x6933))
% 94.68/94.46 [694]~E(x6941,x6942)+E(f256(x6943,x6941),f256(x6943,x6942))
% 94.68/94.46 [695]~E(x6951,x6952)+E(f271(x6951),f271(x6952))
% 94.68/94.46 [696]~E(x6961,x6962)+E(f447(x6961,x6963,x6964,x6965,x6966,x6967,x6968),f447(x6962,x6963,x6964,x6965,x6966,x6967,x6968))
% 94.68/94.46 [697]~E(x6971,x6972)+E(f447(x6973,x6971,x6974,x6975,x6976,x6977,x6978),f447(x6973,x6972,x6974,x6975,x6976,x6977,x6978))
% 94.68/94.46 [698]~E(x6981,x6982)+E(f447(x6983,x6984,x6981,x6985,x6986,x6987,x6988),f447(x6983,x6984,x6982,x6985,x6986,x6987,x6988))
% 94.68/94.46 [699]~E(x6991,x6992)+E(f447(x6993,x6994,x6995,x6991,x6996,x6997,x6998),f447(x6993,x6994,x6995,x6992,x6996,x6997,x6998))
% 94.68/94.46 [700]~E(x7001,x7002)+E(f447(x7003,x7004,x7005,x7006,x7001,x7007,x7008),f447(x7003,x7004,x7005,x7006,x7002,x7007,x7008))
% 94.68/94.46 [701]~E(x7011,x7012)+E(f447(x7013,x7014,x7015,x7016,x7017,x7011,x7018),f447(x7013,x7014,x7015,x7016,x7017,x7012,x7018))
% 94.68/94.46 [702]~E(x7021,x7022)+E(f447(x7023,x7024,x7025,x7026,x7027,x7028,x7021),f447(x7023,x7024,x7025,x7026,x7027,x7028,x7022))
% 94.68/94.46 [703]~E(x7031,x7032)+E(f166(x7031,x7033,x7034),f166(x7032,x7033,x7034))
% 94.68/94.46 [704]~E(x7041,x7042)+E(f166(x7043,x7041,x7044),f166(x7043,x7042,x7044))
% 94.68/94.46 [705]~E(x7051,x7052)+E(f166(x7053,x7054,x7051),f166(x7053,x7054,x7052))
% 94.68/94.46 [706]~E(x7061,x7062)+E(f116(x7061,x7063,x7064),f116(x7062,x7063,x7064))
% 94.68/94.46 [707]~E(x7071,x7072)+E(f116(x7073,x7071,x7074),f116(x7073,x7072,x7074))
% 94.68/94.46 [708]~E(x7081,x7082)+E(f116(x7083,x7084,x7081),f116(x7083,x7084,x7082))
% 94.68/94.46 [709]~E(x7091,x7092)+E(f598(x7091,x7093,x7094),f598(x7092,x7093,x7094))
% 94.68/94.46 [710]~E(x7101,x7102)+E(f598(x7103,x7101,x7104),f598(x7103,x7102,x7104))
% 94.68/94.46 [711]~E(x7111,x7112)+E(f598(x7113,x7114,x7111),f598(x7113,x7114,x7112))
% 94.68/94.46 [712]~E(x7121,x7122)+E(f487(x7121,x7123),f487(x7122,x7123))
% 94.68/94.46 [713]~E(x7131,x7132)+E(f487(x7133,x7131),f487(x7133,x7132))
% 94.68/94.46 [714]~E(x7141,x7142)+E(f553(x7141,x7143),f553(x7142,x7143))
% 94.68/94.46 [715]~E(x7151,x7152)+E(f553(x7153,x7151),f553(x7153,x7152))
% 94.68/94.46 [716]~E(x7161,x7162)+E(f611(x7161,x7163),f611(x7162,x7163))
% 94.68/94.46 [717]~E(x7171,x7172)+E(f611(x7173,x7171),f611(x7173,x7172))
% 94.68/94.46 [718]~E(x7181,x7182)+E(f174(x7181,x7183,x7184),f174(x7182,x7183,x7184))
% 94.68/94.46 [719]~E(x7191,x7192)+E(f174(x7193,x7191,x7194),f174(x7193,x7192,x7194))
% 94.68/94.46 [720]~E(x7201,x7202)+E(f174(x7203,x7204,x7201),f174(x7203,x7204,x7202))
% 94.68/94.46 [721]~E(x7211,x7212)+E(f548(x7211,x7213,x7214,x7215),f548(x7212,x7213,x7214,x7215))
% 94.68/94.46 [722]~E(x7221,x7222)+E(f548(x7223,x7221,x7224,x7225),f548(x7223,x7222,x7224,x7225))
% 94.68/94.46 [723]~E(x7231,x7232)+E(f548(x7233,x7234,x7231,x7235),f548(x7233,x7234,x7232,x7235))
% 94.68/94.46 [724]~E(x7241,x7242)+E(f548(x7243,x7244,x7245,x7241),f548(x7243,x7244,x7245,x7242))
% 94.68/94.46 [725]~E(x7251,x7252)+E(f56(x7251,x7253,x7254),f56(x7252,x7253,x7254))
% 94.68/94.46 [726]~E(x7261,x7262)+E(f56(x7263,x7261,x7264),f56(x7263,x7262,x7264))
% 94.68/94.46 [727]~E(x7271,x7272)+E(f56(x7273,x7274,x7271),f56(x7273,x7274,x7272))
% 94.68/94.46 [728]~E(x7281,x7282)+E(f428(x7281,x7283,x7284,x7285,x7286),f428(x7282,x7283,x7284,x7285,x7286))
% 94.68/94.46 [729]~E(x7291,x7292)+E(f428(x7293,x7291,x7294,x7295,x7296),f428(x7293,x7292,x7294,x7295,x7296))
% 94.68/94.46 [730]~E(x7301,x7302)+E(f428(x7303,x7304,x7301,x7305,x7306),f428(x7303,x7304,x7302,x7305,x7306))
% 94.68/94.46 [731]~E(x7311,x7312)+E(f428(x7313,x7314,x7315,x7311,x7316),f428(x7313,x7314,x7315,x7312,x7316))
% 94.68/94.46 [732]~E(x7321,x7322)+E(f428(x7323,x7324,x7325,x7326,x7321),f428(x7323,x7324,x7325,x7326,x7322))
% 94.68/94.46 [733]~E(x7331,x7332)+E(f793(x7331,x7333,x7334,x7335,x7336,x7337),f793(x7332,x7333,x7334,x7335,x7336,x7337))
% 94.68/94.46 [734]~E(x7341,x7342)+E(f793(x7343,x7341,x7344,x7345,x7346,x7347),f793(x7343,x7342,x7344,x7345,x7346,x7347))
% 94.68/94.46 [735]~E(x7351,x7352)+E(f793(x7353,x7354,x7351,x7355,x7356,x7357),f793(x7353,x7354,x7352,x7355,x7356,x7357))
% 94.68/94.46 [736]~E(x7361,x7362)+E(f793(x7363,x7364,x7365,x7361,x7366,x7367),f793(x7363,x7364,x7365,x7362,x7366,x7367))
% 94.68/94.46 [737]~E(x7371,x7372)+E(f793(x7373,x7374,x7375,x7376,x7371,x7377),f793(x7373,x7374,x7375,x7376,x7372,x7377))
% 94.68/94.46 [738]~E(x7381,x7382)+E(f793(x7383,x7384,x7385,x7386,x7387,x7381),f793(x7383,x7384,x7385,x7386,x7387,x7382))
% 94.68/94.46 [739]~E(x7391,x7392)+E(f715(x7391,x7393),f715(x7392,x7393))
% 94.68/94.46 [740]~E(x7401,x7402)+E(f715(x7403,x7401),f715(x7403,x7402))
% 94.68/94.46 [741]~E(x7411,x7412)+E(f633(x7411,x7413,x7414,x7415,x7416),f633(x7412,x7413,x7414,x7415,x7416))
% 94.68/94.46 [742]~E(x7421,x7422)+E(f633(x7423,x7421,x7424,x7425,x7426),f633(x7423,x7422,x7424,x7425,x7426))
% 94.68/94.46 [743]~E(x7431,x7432)+E(f633(x7433,x7434,x7431,x7435,x7436),f633(x7433,x7434,x7432,x7435,x7436))
% 94.68/94.46 [744]~E(x7441,x7442)+E(f633(x7443,x7444,x7445,x7441,x7446),f633(x7443,x7444,x7445,x7442,x7446))
% 94.68/94.46 [745]~E(x7451,x7452)+E(f633(x7453,x7454,x7455,x7456,x7451),f633(x7453,x7454,x7455,x7456,x7452))
% 94.68/94.46 [746]~E(x7461,x7462)+E(f42(x7461,x7463),f42(x7462,x7463))
% 94.68/94.46 [747]~E(x7471,x7472)+E(f42(x7473,x7471),f42(x7473,x7472))
% 94.68/94.46 [748]~E(x7481,x7482)+E(f427(x7481,x7483,x7484),f427(x7482,x7483,x7484))
% 94.68/94.46 [749]~E(x7491,x7492)+E(f427(x7493,x7491,x7494),f427(x7493,x7492,x7494))
% 94.68/94.46 [750]~E(x7501,x7502)+E(f427(x7503,x7504,x7501),f427(x7503,x7504,x7502))
% 94.68/94.46 [751]~E(x7511,x7512)+E(f403(x7511,x7513,x7514,x7515,x7516),f403(x7512,x7513,x7514,x7515,x7516))
% 94.68/94.46 [752]~E(x7521,x7522)+E(f403(x7523,x7521,x7524,x7525,x7526),f403(x7523,x7522,x7524,x7525,x7526))
% 94.68/94.46 [753]~E(x7531,x7532)+E(f403(x7533,x7534,x7531,x7535,x7536),f403(x7533,x7534,x7532,x7535,x7536))
% 94.68/94.46 [754]~E(x7541,x7542)+E(f403(x7543,x7544,x7545,x7541,x7546),f403(x7543,x7544,x7545,x7542,x7546))
% 94.68/94.46 [755]~E(x7551,x7552)+E(f403(x7553,x7554,x7555,x7556,x7551),f403(x7553,x7554,x7555,x7556,x7552))
% 94.68/94.46 [756]~E(x7561,x7562)+E(f867(x7561,x7563,x7564),f867(x7562,x7563,x7564))
% 94.68/94.46 [757]~E(x7571,x7572)+E(f867(x7573,x7571,x7574),f867(x7573,x7572,x7574))
% 94.68/94.46 [758]~E(x7581,x7582)+E(f867(x7583,x7584,x7581),f867(x7583,x7584,x7582))
% 94.68/94.46 [759]~E(x7591,x7592)+E(f726(x7591,x7593,x7594,x7595,x7596,x7597,x7598),f726(x7592,x7593,x7594,x7595,x7596,x7597,x7598))
% 94.68/94.46 [760]~E(x7601,x7602)+E(f726(x7603,x7601,x7604,x7605,x7606,x7607,x7608),f726(x7603,x7602,x7604,x7605,x7606,x7607,x7608))
% 94.68/94.46 [761]~E(x7611,x7612)+E(f726(x7613,x7614,x7611,x7615,x7616,x7617,x7618),f726(x7613,x7614,x7612,x7615,x7616,x7617,x7618))
% 94.68/94.46 [762]~E(x7621,x7622)+E(f726(x7623,x7624,x7625,x7621,x7626,x7627,x7628),f726(x7623,x7624,x7625,x7622,x7626,x7627,x7628))
% 94.68/94.46 [763]~E(x7631,x7632)+E(f726(x7633,x7634,x7635,x7636,x7631,x7637,x7638),f726(x7633,x7634,x7635,x7636,x7632,x7637,x7638))
% 94.68/94.46 [764]~E(x7641,x7642)+E(f726(x7643,x7644,x7645,x7646,x7647,x7641,x7648),f726(x7643,x7644,x7645,x7646,x7647,x7642,x7648))
% 94.68/94.46 [765]~E(x7651,x7652)+E(f726(x7653,x7654,x7655,x7656,x7657,x7658,x7651),f726(x7653,x7654,x7655,x7656,x7657,x7658,x7652))
% 94.68/94.46 [766]~E(x7661,x7662)+E(f909(x7661),f909(x7662))
% 94.68/94.46 [767]~E(x7671,x7672)+E(f515(x7671),f515(x7672))
% 94.68/94.46 [768]~E(x7681,x7682)+E(f212(x7681,x7683,x7684),f212(x7682,x7683,x7684))
% 94.68/94.46 [769]~E(x7691,x7692)+E(f212(x7693,x7691,x7694),f212(x7693,x7692,x7694))
% 94.68/94.46 [770]~E(x7701,x7702)+E(f212(x7703,x7704,x7701),f212(x7703,x7704,x7702))
% 94.68/94.46 [771]~E(x7711,x7712)+E(f448(x7711,x7713,x7714,x7715,x7716,x7717,x7718),f448(x7712,x7713,x7714,x7715,x7716,x7717,x7718))
% 94.68/94.46 [772]~E(x7721,x7722)+E(f448(x7723,x7721,x7724,x7725,x7726,x7727,x7728),f448(x7723,x7722,x7724,x7725,x7726,x7727,x7728))
% 94.68/94.46 [773]~E(x7731,x7732)+E(f448(x7733,x7734,x7731,x7735,x7736,x7737,x7738),f448(x7733,x7734,x7732,x7735,x7736,x7737,x7738))
% 94.68/94.46 [774]~E(x7741,x7742)+E(f448(x7743,x7744,x7745,x7741,x7746,x7747,x7748),f448(x7743,x7744,x7745,x7742,x7746,x7747,x7748))
% 94.68/94.46 [775]~E(x7751,x7752)+E(f448(x7753,x7754,x7755,x7756,x7751,x7757,x7758),f448(x7753,x7754,x7755,x7756,x7752,x7757,x7758))
% 94.68/94.46 [776]~E(x7761,x7762)+E(f448(x7763,x7764,x7765,x7766,x7767,x7761,x7768),f448(x7763,x7764,x7765,x7766,x7767,x7762,x7768))
% 94.68/94.46 [777]~E(x7771,x7772)+E(f448(x7773,x7774,x7775,x7776,x7777,x7778,x7771),f448(x7773,x7774,x7775,x7776,x7777,x7778,x7772))
% 94.68/94.46 [778]~E(x7781,x7782)+E(f513(x7781,x7783,x7784,x7785),f513(x7782,x7783,x7784,x7785))
% 94.68/94.46 [779]~E(x7791,x7792)+E(f513(x7793,x7791,x7794,x7795),f513(x7793,x7792,x7794,x7795))
% 94.68/94.46 [780]~E(x7801,x7802)+E(f513(x7803,x7804,x7801,x7805),f513(x7803,x7804,x7802,x7805))
% 94.68/94.46 [781]~E(x7811,x7812)+E(f513(x7813,x7814,x7815,x7811),f513(x7813,x7814,x7815,x7812))
% 94.68/94.46 [782]~E(x7821,x7822)+E(f546(x7821,x7823,x7824,x7825,x7826,x7827),f546(x7822,x7823,x7824,x7825,x7826,x7827))
% 94.68/94.46 [783]~E(x7831,x7832)+E(f546(x7833,x7831,x7834,x7835,x7836,x7837),f546(x7833,x7832,x7834,x7835,x7836,x7837))
% 94.68/94.46 [784]~E(x7841,x7842)+E(f546(x7843,x7844,x7841,x7845,x7846,x7847),f546(x7843,x7844,x7842,x7845,x7846,x7847))
% 94.68/94.46 [785]~E(x7851,x7852)+E(f546(x7853,x7854,x7855,x7851,x7856,x7857),f546(x7853,x7854,x7855,x7852,x7856,x7857))
% 94.68/94.46 [786]~E(x7861,x7862)+E(f546(x7863,x7864,x7865,x7866,x7861,x7867),f546(x7863,x7864,x7865,x7866,x7862,x7867))
% 94.68/94.46 [787]~E(x7871,x7872)+E(f546(x7873,x7874,x7875,x7876,x7877,x7871),f546(x7873,x7874,x7875,x7876,x7877,x7872))
% 94.68/94.46 [788]~E(x7881,x7882)+E(f693(x7881,x7883,x7884,x7885,x7886),f693(x7882,x7883,x7884,x7885,x7886))
% 94.68/94.46 [789]~E(x7891,x7892)+E(f693(x7893,x7891,x7894,x7895,x7896),f693(x7893,x7892,x7894,x7895,x7896))
% 94.68/94.46 [790]~E(x7901,x7902)+E(f693(x7903,x7904,x7901,x7905,x7906),f693(x7903,x7904,x7902,x7905,x7906))
% 94.68/94.46 [791]~E(x7911,x7912)+E(f693(x7913,x7914,x7915,x7911,x7916),f693(x7913,x7914,x7915,x7912,x7916))
% 94.68/94.46 [792]~E(x7921,x7922)+E(f693(x7923,x7924,x7925,x7926,x7921),f693(x7923,x7924,x7925,x7926,x7922))
% 94.68/94.46 [793]~E(x7931,x7932)+E(f459(x7931),f459(x7932))
% 94.68/94.46 [794]~E(x7941,x7942)+E(f836(x7941,x7943,x7944,x7945,x7946,x7947,x7948),f836(x7942,x7943,x7944,x7945,x7946,x7947,x7948))
% 94.68/94.46 [795]~E(x7951,x7952)+E(f836(x7953,x7951,x7954,x7955,x7956,x7957,x7958),f836(x7953,x7952,x7954,x7955,x7956,x7957,x7958))
% 94.68/94.46 [796]~E(x7961,x7962)+E(f836(x7963,x7964,x7961,x7965,x7966,x7967,x7968),f836(x7963,x7964,x7962,x7965,x7966,x7967,x7968))
% 94.68/94.46 [797]~E(x7971,x7972)+E(f836(x7973,x7974,x7975,x7971,x7976,x7977,x7978),f836(x7973,x7974,x7975,x7972,x7976,x7977,x7978))
% 94.68/94.46 [798]~E(x7981,x7982)+E(f836(x7983,x7984,x7985,x7986,x7981,x7987,x7988),f836(x7983,x7984,x7985,x7986,x7982,x7987,x7988))
% 94.68/94.46 [799]~E(x7991,x7992)+E(f836(x7993,x7994,x7995,x7996,x7997,x7991,x7998),f836(x7993,x7994,x7995,x7996,x7997,x7992,x7998))
% 94.68/94.46 [800]~E(x8001,x8002)+E(f836(x8003,x8004,x8005,x8006,x8007,x8008,x8001),f836(x8003,x8004,x8005,x8006,x8007,x8008,x8002))
% 94.68/94.46 [801]~E(x8011,x8012)+E(f710(x8011,x8013,x8014,x8015,x8016,x8017,x8018,x8019),f710(x8012,x8013,x8014,x8015,x8016,x8017,x8018,x8019))
% 94.68/94.46 [802]~E(x8021,x8022)+E(f710(x8023,x8021,x8024,x8025,x8026,x8027,x8028,x8029),f710(x8023,x8022,x8024,x8025,x8026,x8027,x8028,x8029))
% 94.68/94.46 [803]~E(x8031,x8032)+E(f710(x8033,x8034,x8031,x8035,x8036,x8037,x8038,x8039),f710(x8033,x8034,x8032,x8035,x8036,x8037,x8038,x8039))
% 94.68/94.46 [804]~E(x8041,x8042)+E(f710(x8043,x8044,x8045,x8041,x8046,x8047,x8048,x8049),f710(x8043,x8044,x8045,x8042,x8046,x8047,x8048,x8049))
% 94.68/94.46 [805]~E(x8051,x8052)+E(f710(x8053,x8054,x8055,x8056,x8051,x8057,x8058,x8059),f710(x8053,x8054,x8055,x8056,x8052,x8057,x8058,x8059))
% 94.68/94.46 [806]~E(x8061,x8062)+E(f710(x8063,x8064,x8065,x8066,x8067,x8061,x8068,x8069),f710(x8063,x8064,x8065,x8066,x8067,x8062,x8068,x8069))
% 94.68/94.46 [807]~E(x8071,x8072)+E(f710(x8073,x8074,x8075,x8076,x8077,x8078,x8071,x8079),f710(x8073,x8074,x8075,x8076,x8077,x8078,x8072,x8079))
% 94.68/94.46 [808]~E(x8081,x8082)+E(f710(x8083,x8084,x8085,x8086,x8087,x8088,x8089,x8081),f710(x8083,x8084,x8085,x8086,x8087,x8088,x8089,x8082))
% 94.68/94.46 [809]~E(x8091,x8092)+E(f475(x8091,x8093,x8094,x8095,x8096,x8097),f475(x8092,x8093,x8094,x8095,x8096,x8097))
% 94.68/94.46 [810]~E(x8101,x8102)+E(f475(x8103,x8101,x8104,x8105,x8106,x8107),f475(x8103,x8102,x8104,x8105,x8106,x8107))
% 94.68/94.46 [811]~E(x8111,x8112)+E(f475(x8113,x8114,x8111,x8115,x8116,x8117),f475(x8113,x8114,x8112,x8115,x8116,x8117))
% 94.68/94.46 [812]~E(x8121,x8122)+E(f475(x8123,x8124,x8125,x8121,x8126,x8127),f475(x8123,x8124,x8125,x8122,x8126,x8127))
% 94.68/94.46 [813]~E(x8131,x8132)+E(f475(x8133,x8134,x8135,x8136,x8131,x8137),f475(x8133,x8134,x8135,x8136,x8132,x8137))
% 94.68/94.46 [814]~E(x8141,x8142)+E(f475(x8143,x8144,x8145,x8146,x8147,x8141),f475(x8143,x8144,x8145,x8146,x8147,x8142))
% 94.68/94.46 [815]~E(x8151,x8152)+E(f370(x8151,x8153,x8154,x8155),f370(x8152,x8153,x8154,x8155))
% 94.68/94.46 [816]~E(x8161,x8162)+E(f370(x8163,x8161,x8164,x8165),f370(x8163,x8162,x8164,x8165))
% 94.68/94.46 [817]~E(x8171,x8172)+E(f370(x8173,x8174,x8171,x8175),f370(x8173,x8174,x8172,x8175))
% 94.68/94.46 [818]~E(x8181,x8182)+E(f370(x8183,x8184,x8185,x8181),f370(x8183,x8184,x8185,x8182))
% 94.68/94.46 [819]~E(x8191,x8192)+E(f114(x8191),f114(x8192))
% 94.68/94.46 [820]~E(x8201,x8202)+E(f287(x8201,x8203,x8204,x8205,x8206),f287(x8202,x8203,x8204,x8205,x8206))
% 94.68/94.46 [821]~E(x8211,x8212)+E(f287(x8213,x8211,x8214,x8215,x8216),f287(x8213,x8212,x8214,x8215,x8216))
% 94.68/94.46 [822]~E(x8221,x8222)+E(f287(x8223,x8224,x8221,x8225,x8226),f287(x8223,x8224,x8222,x8225,x8226))
% 94.68/94.46 [823]~E(x8231,x8232)+E(f287(x8233,x8234,x8235,x8231,x8236),f287(x8233,x8234,x8235,x8232,x8236))
% 94.68/94.46 [824]~E(x8241,x8242)+E(f287(x8243,x8244,x8245,x8246,x8241),f287(x8243,x8244,x8245,x8246,x8242))
% 94.68/94.46 [825]~E(x8251,x8252)+E(f720(x8251,x8253,x8254,x8255,x8256),f720(x8252,x8253,x8254,x8255,x8256))
% 94.68/94.46 [826]~E(x8261,x8262)+E(f720(x8263,x8261,x8264,x8265,x8266),f720(x8263,x8262,x8264,x8265,x8266))
% 94.68/94.46 [827]~E(x8271,x8272)+E(f720(x8273,x8274,x8271,x8275,x8276),f720(x8273,x8274,x8272,x8275,x8276))
% 94.68/94.46 [828]~E(x8281,x8282)+E(f720(x8283,x8284,x8285,x8281,x8286),f720(x8283,x8284,x8285,x8282,x8286))
% 94.68/94.46 [829]~E(x8291,x8292)+E(f720(x8293,x8294,x8295,x8296,x8291),f720(x8293,x8294,x8295,x8296,x8292))
% 94.68/94.46 [830]~E(x8301,x8302)+E(f324(x8301),f324(x8302))
% 94.68/94.46 [831]~E(x8311,x8312)+E(f245(x8311,x8313,x8314,x8315),f245(x8312,x8313,x8314,x8315))
% 94.68/94.46 [832]~E(x8321,x8322)+E(f245(x8323,x8321,x8324,x8325),f245(x8323,x8322,x8324,x8325))
% 94.68/94.46 [833]~E(x8331,x8332)+E(f245(x8333,x8334,x8331,x8335),f245(x8333,x8334,x8332,x8335))
% 94.68/94.46 [834]~E(x8341,x8342)+E(f245(x8343,x8344,x8345,x8341),f245(x8343,x8344,x8345,x8342))
% 94.68/94.46 [835]~E(x8351,x8352)+E(f333(x8351,x8353),f333(x8352,x8353))
% 94.68/94.46 [836]~E(x8361,x8362)+E(f333(x8363,x8361),f333(x8363,x8362))
% 94.68/94.46 [837]~E(x8371,x8372)+E(f724(x8371,x8373,x8374,x8375,x8376,x8377,x8378),f724(x8372,x8373,x8374,x8375,x8376,x8377,x8378))
% 94.68/94.46 [838]~E(x8381,x8382)+E(f724(x8383,x8381,x8384,x8385,x8386,x8387,x8388),f724(x8383,x8382,x8384,x8385,x8386,x8387,x8388))
% 94.68/94.46 [839]~E(x8391,x8392)+E(f724(x8393,x8394,x8391,x8395,x8396,x8397,x8398),f724(x8393,x8394,x8392,x8395,x8396,x8397,x8398))
% 94.68/94.46 [840]~E(x8401,x8402)+E(f724(x8403,x8404,x8405,x8401,x8406,x8407,x8408),f724(x8403,x8404,x8405,x8402,x8406,x8407,x8408))
% 94.68/94.46 [841]~E(x8411,x8412)+E(f724(x8413,x8414,x8415,x8416,x8411,x8417,x8418),f724(x8413,x8414,x8415,x8416,x8412,x8417,x8418))
% 94.68/94.46 [842]~E(x8421,x8422)+E(f724(x8423,x8424,x8425,x8426,x8427,x8421,x8428),f724(x8423,x8424,x8425,x8426,x8427,x8422,x8428))
% 94.68/94.46 [843]~E(x8431,x8432)+E(f724(x8433,x8434,x8435,x8436,x8437,x8438,x8431),f724(x8433,x8434,x8435,x8436,x8437,x8438,x8432))
% 94.68/94.46 [844]~E(x8441,x8442)+E(f843(x8441),f843(x8442))
% 94.68/94.46 [845]~E(x8451,x8452)+E(f76(x8451,x8453),f76(x8452,x8453))
% 94.68/94.46 [846]~E(x8461,x8462)+E(f76(x8463,x8461),f76(x8463,x8462))
% 94.68/94.46 [847]~E(x8471,x8472)+E(f689(x8471,x8473,x8474),f689(x8472,x8473,x8474))
% 94.68/94.46 [848]~E(x8481,x8482)+E(f689(x8483,x8481,x8484),f689(x8483,x8482,x8484))
% 94.68/94.46 [849]~E(x8491,x8492)+E(f689(x8493,x8494,x8491),f689(x8493,x8494,x8492))
% 94.68/94.46 [850]~E(x8501,x8502)+E(f480(x8501,x8503,x8504),f480(x8502,x8503,x8504))
% 94.68/94.46 [851]~E(x8511,x8512)+E(f480(x8513,x8511,x8514),f480(x8513,x8512,x8514))
% 94.68/94.46 [852]~E(x8521,x8522)+E(f480(x8523,x8524,x8521),f480(x8523,x8524,x8522))
% 94.68/94.46 [853]~E(x8531,x8532)+E(f330(x8531,x8533,x8534,x8535),f330(x8532,x8533,x8534,x8535))
% 94.68/94.46 [854]~E(x8541,x8542)+E(f330(x8543,x8541,x8544,x8545),f330(x8543,x8542,x8544,x8545))
% 94.68/94.46 [855]~E(x8551,x8552)+E(f330(x8553,x8554,x8551,x8555),f330(x8553,x8554,x8552,x8555))
% 94.68/94.46 [856]~E(x8561,x8562)+E(f330(x8563,x8564,x8565,x8561),f330(x8563,x8564,x8565,x8562))
% 94.68/94.46 [857]~E(x8571,x8572)+E(f339(x8571,x8573,x8574),f339(x8572,x8573,x8574))
% 94.68/94.46 [858]~E(x8581,x8582)+E(f339(x8583,x8581,x8584),f339(x8583,x8582,x8584))
% 94.68/94.46 [859]~E(x8591,x8592)+E(f339(x8593,x8594,x8591),f339(x8593,x8594,x8592))
% 94.68/94.46 [860]~E(x8601,x8602)+E(f564(x8601,x8603,x8604,x8605,x8606),f564(x8602,x8603,x8604,x8605,x8606))
% 94.68/94.46 [861]~E(x8611,x8612)+E(f564(x8613,x8611,x8614,x8615,x8616),f564(x8613,x8612,x8614,x8615,x8616))
% 94.68/94.46 [862]~E(x8621,x8622)+E(f564(x8623,x8624,x8621,x8625,x8626),f564(x8623,x8624,x8622,x8625,x8626))
% 94.68/94.46 [863]~E(x8631,x8632)+E(f564(x8633,x8634,x8635,x8631,x8636),f564(x8633,x8634,x8635,x8632,x8636))
% 94.68/94.46 [864]~E(x8641,x8642)+E(f564(x8643,x8644,x8645,x8646,x8641),f564(x8643,x8644,x8645,x8646,x8642))
% 94.68/94.46 [865]~E(x8651,x8652)+E(f824(x8651,x8653,x8654,x8655,x8656,x8657),f824(x8652,x8653,x8654,x8655,x8656,x8657))
% 94.68/94.46 [866]~E(x8661,x8662)+E(f824(x8663,x8661,x8664,x8665,x8666,x8667),f824(x8663,x8662,x8664,x8665,x8666,x8667))
% 94.68/94.46 [867]~E(x8671,x8672)+E(f824(x8673,x8674,x8671,x8675,x8676,x8677),f824(x8673,x8674,x8672,x8675,x8676,x8677))
% 94.68/94.46 [868]~E(x8681,x8682)+E(f824(x8683,x8684,x8685,x8681,x8686,x8687),f824(x8683,x8684,x8685,x8682,x8686,x8687))
% 94.68/94.46 [869]~E(x8691,x8692)+E(f824(x8693,x8694,x8695,x8696,x8691,x8697),f824(x8693,x8694,x8695,x8696,x8692,x8697))
% 94.68/94.46 [870]~E(x8701,x8702)+E(f824(x8703,x8704,x8705,x8706,x8707,x8701),f824(x8703,x8704,x8705,x8706,x8707,x8702))
% 94.68/94.46 [871]~E(x8711,x8712)+E(f694(x8711,x8713),f694(x8712,x8713))
% 94.68/94.46 [872]~E(x8721,x8722)+E(f694(x8723,x8721),f694(x8723,x8722))
% 94.68/94.46 [873]~E(x8731,x8732)+E(f528(x8731,x8733),f528(x8732,x8733))
% 94.68/94.46 [874]~E(x8741,x8742)+E(f528(x8743,x8741),f528(x8743,x8742))
% 94.68/94.46 [875]~E(x8751,x8752)+E(f368(x8751,x8753,x8754,x8755),f368(x8752,x8753,x8754,x8755))
% 94.68/94.46 [876]~E(x8761,x8762)+E(f368(x8763,x8761,x8764,x8765),f368(x8763,x8762,x8764,x8765))
% 94.68/94.46 [877]~E(x8771,x8772)+E(f368(x8773,x8774,x8771,x8775),f368(x8773,x8774,x8772,x8775))
% 94.68/94.46 [878]~E(x8781,x8782)+E(f368(x8783,x8784,x8785,x8781),f368(x8783,x8784,x8785,x8782))
% 94.68/94.46 [879]~E(x8791,x8792)+E(f376(x8791,x8793,x8794,x8795),f376(x8792,x8793,x8794,x8795))
% 94.68/94.46 [880]~E(x8801,x8802)+E(f376(x8803,x8801,x8804,x8805),f376(x8803,x8802,x8804,x8805))
% 94.68/94.46 [881]~E(x8811,x8812)+E(f376(x8813,x8814,x8811,x8815),f376(x8813,x8814,x8812,x8815))
% 94.68/94.46 [882]~E(x8821,x8822)+E(f376(x8823,x8824,x8825,x8821),f376(x8823,x8824,x8825,x8822))
% 94.68/94.46 [883]~E(x8831,x8832)+E(f688(x8831,x8833,x8834),f688(x8832,x8833,x8834))
% 94.68/94.46 [884]~E(x8841,x8842)+E(f688(x8843,x8841,x8844),f688(x8843,x8842,x8844))
% 94.68/94.46 [885]~E(x8851,x8852)+E(f688(x8853,x8854,x8851),f688(x8853,x8854,x8852))
% 94.68/94.46 [886]~E(x8861,x8862)+E(f661(x8861,x8863,x8864,x8865,x8866),f661(x8862,x8863,x8864,x8865,x8866))
% 94.68/94.46 [887]~E(x8871,x8872)+E(f661(x8873,x8871,x8874,x8875,x8876),f661(x8873,x8872,x8874,x8875,x8876))
% 94.68/94.46 [888]~E(x8881,x8882)+E(f661(x8883,x8884,x8881,x8885,x8886),f661(x8883,x8884,x8882,x8885,x8886))
% 94.68/94.46 [889]~E(x8891,x8892)+E(f661(x8893,x8894,x8895,x8891,x8896),f661(x8893,x8894,x8895,x8892,x8896))
% 94.68/94.46 [890]~E(x8901,x8902)+E(f661(x8903,x8904,x8905,x8906,x8901),f661(x8903,x8904,x8905,x8906,x8902))
% 94.68/94.46 [891]~E(x8911,x8912)+E(f868(x8911,x8913,x8914),f868(x8912,x8913,x8914))
% 94.68/94.46 [892]~E(x8921,x8922)+E(f868(x8923,x8921,x8924),f868(x8923,x8922,x8924))
% 94.68/94.46 [893]~E(x8931,x8932)+E(f868(x8933,x8934,x8931),f868(x8933,x8934,x8932))
% 94.68/94.46 [894]~E(x8941,x8942)+E(f832(x8941,x8943,x8944),f832(x8942,x8943,x8944))
% 94.68/94.46 [895]~E(x8951,x8952)+E(f832(x8953,x8951,x8954),f832(x8953,x8952,x8954))
% 94.68/94.46 [896]~E(x8961,x8962)+E(f832(x8963,x8964,x8961),f832(x8963,x8964,x8962))
% 94.68/94.46 [897]~E(x8971,x8972)+E(f357(x8971,x8973,x8974),f357(x8972,x8973,x8974))
% 94.68/94.46 [898]~E(x8981,x8982)+E(f357(x8983,x8981,x8984),f357(x8983,x8982,x8984))
% 94.68/94.46 [899]~E(x8991,x8992)+E(f357(x8993,x8994,x8991),f357(x8993,x8994,x8992))
% 94.68/94.46 [900]~E(x9001,x9002)+E(f422(x9001,x9003,x9004),f422(x9002,x9003,x9004))
% 94.68/94.46 [901]~E(x9011,x9012)+E(f422(x9013,x9011,x9014),f422(x9013,x9012,x9014))
% 94.68/94.46 [902]~E(x9021,x9022)+E(f422(x9023,x9024,x9021),f422(x9023,x9024,x9022))
% 94.68/94.46 [903]~E(x9031,x9032)+E(f678(x9031,x9033,x9034,x9035,x9036),f678(x9032,x9033,x9034,x9035,x9036))
% 94.68/94.46 [904]~E(x9041,x9042)+E(f678(x9043,x9041,x9044,x9045,x9046),f678(x9043,x9042,x9044,x9045,x9046))
% 94.68/94.46 [905]~E(x9051,x9052)+E(f678(x9053,x9054,x9051,x9055,x9056),f678(x9053,x9054,x9052,x9055,x9056))
% 94.68/94.46 [906]~E(x9061,x9062)+E(f678(x9063,x9064,x9065,x9061,x9066),f678(x9063,x9064,x9065,x9062,x9066))
% 94.68/94.46 [907]~E(x9071,x9072)+E(f678(x9073,x9074,x9075,x9076,x9071),f678(x9073,x9074,x9075,x9076,x9072))
% 94.68/94.46 [908]~E(x9081,x9082)+E(f498(x9081,x9083,x9084,x9085),f498(x9082,x9083,x9084,x9085))
% 94.68/94.46 [909]~E(x9091,x9092)+E(f498(x9093,x9091,x9094,x9095),f498(x9093,x9092,x9094,x9095))
% 94.68/94.46 [910]~E(x9101,x9102)+E(f498(x9103,x9104,x9101,x9105),f498(x9103,x9104,x9102,x9105))
% 94.68/94.46 [911]~E(x9111,x9112)+E(f498(x9113,x9114,x9115,x9111),f498(x9113,x9114,x9115,x9112))
% 94.68/94.46 [912]~E(x9121,x9122)+E(f400(x9121,x9123,x9124),f400(x9122,x9123,x9124))
% 94.68/94.46 [913]~E(x9131,x9132)+E(f400(x9133,x9131,x9134),f400(x9133,x9132,x9134))
% 94.68/94.46 [914]~E(x9141,x9142)+E(f400(x9143,x9144,x9141),f400(x9143,x9144,x9142))
% 94.68/94.46 [915]~E(x9151,x9152)+E(f853(x9151,x9153,x9154),f853(x9152,x9153,x9154))
% 94.68/94.46 [916]~E(x9161,x9162)+E(f853(x9163,x9161,x9164),f853(x9163,x9162,x9164))
% 94.68/94.46 [917]~E(x9171,x9172)+E(f853(x9173,x9174,x9171),f853(x9173,x9174,x9172))
% 94.68/94.46 [918]~E(x9181,x9182)+E(f699(x9181,x9183),f699(x9182,x9183))
% 94.68/94.46 [919]~E(x9191,x9192)+E(f699(x9193,x9191),f699(x9193,x9192))
% 94.68/94.46 [920]~E(x9201,x9202)+E(f393(x9201,x9203),f393(x9202,x9203))
% 94.68/94.46 [921]~E(x9211,x9212)+E(f393(x9213,x9211),f393(x9213,x9212))
% 94.68/94.46 [922]~E(x9221,x9222)+E(f206(x9221,x9223),f206(x9222,x9223))
% 94.68/94.46 [923]~E(x9231,x9232)+E(f206(x9233,x9231),f206(x9233,x9232))
% 94.68/94.46 [924]~E(x9241,x9242)+E(f614(x9241,x9243,x9244),f614(x9242,x9243,x9244))
% 94.68/94.46 [925]~E(x9251,x9252)+E(f614(x9253,x9251,x9254),f614(x9253,x9252,x9254))
% 94.68/94.46 [926]~E(x9261,x9262)+E(f614(x9263,x9264,x9261),f614(x9263,x9264,x9262))
% 94.68/94.46 [927]~E(x9271,x9272)+E(f188(x9271,x9273,x9274,x9275),f188(x9272,x9273,x9274,x9275))
% 94.68/94.46 [928]~E(x9281,x9282)+E(f188(x9283,x9281,x9284,x9285),f188(x9283,x9282,x9284,x9285))
% 94.68/94.46 [929]~E(x9291,x9292)+E(f188(x9293,x9294,x9291,x9295),f188(x9293,x9294,x9292,x9295))
% 94.68/94.46 [930]~E(x9301,x9302)+E(f188(x9303,x9304,x9305,x9301),f188(x9303,x9304,x9305,x9302))
% 94.68/94.46 [931]~E(x9311,x9312)+E(f651(x9311,x9313,x9314),f651(x9312,x9313,x9314))
% 94.68/94.46 [932]~E(x9321,x9322)+E(f651(x9323,x9321,x9324),f651(x9323,x9322,x9324))
% 94.68/94.46 [933]~E(x9331,x9332)+E(f651(x9333,x9334,x9331),f651(x9333,x9334,x9332))
% 94.68/94.46 [934]~E(x9341,x9342)+E(f182(x9341,x9343),f182(x9342,x9343))
% 94.68/94.46 [935]~E(x9351,x9352)+E(f182(x9353,x9351),f182(x9353,x9352))
% 94.68/94.46 [936]~E(x9361,x9362)+E(f585(x9361,x9363,x9364,x9365,x9366),f585(x9362,x9363,x9364,x9365,x9366))
% 94.68/94.46 [937]~E(x9371,x9372)+E(f585(x9373,x9371,x9374,x9375,x9376),f585(x9373,x9372,x9374,x9375,x9376))
% 94.68/94.46 [938]~E(x9381,x9382)+E(f585(x9383,x9384,x9381,x9385,x9386),f585(x9383,x9384,x9382,x9385,x9386))
% 94.68/94.46 [939]~E(x9391,x9392)+E(f585(x9393,x9394,x9395,x9391,x9396),f585(x9393,x9394,x9395,x9392,x9396))
% 94.68/94.46 [940]~E(x9401,x9402)+E(f585(x9403,x9404,x9405,x9406,x9401),f585(x9403,x9404,x9405,x9406,x9402))
% 94.68/94.46 [941]~E(x9411,x9412)+E(f111(x9411,x9413),f111(x9412,x9413))
% 94.68/94.46 [942]~E(x9421,x9422)+E(f111(x9423,x9421),f111(x9423,x9422))
% 94.68/94.46 [943]~E(x9431,x9432)+E(f840(x9431,x9433,x9434),f840(x9432,x9433,x9434))
% 94.68/94.46 [944]~E(x9441,x9442)+E(f840(x9443,x9441,x9444),f840(x9443,x9442,x9444))
% 94.68/94.46 [945]~E(x9451,x9452)+E(f840(x9453,x9454,x9451),f840(x9453,x9454,x9452))
% 94.68/94.46 [946]~E(x9461,x9462)+E(f210(x9461,x9463,x9464,x9465),f210(x9462,x9463,x9464,x9465))
% 94.68/94.46 [947]~E(x9471,x9472)+E(f210(x9473,x9471,x9474,x9475),f210(x9473,x9472,x9474,x9475))
% 94.68/94.46 [948]~E(x9481,x9482)+E(f210(x9483,x9484,x9481,x9485),f210(x9483,x9484,x9482,x9485))
% 94.68/94.46 [949]~E(x9491,x9492)+E(f210(x9493,x9494,x9495,x9491),f210(x9493,x9494,x9495,x9492))
% 94.68/94.46 [950]~E(x9501,x9502)+E(f52(x9501),f52(x9502))
% 94.68/94.46 [951]~E(x9511,x9512)+E(f549(x9511,x9513,x9514,x9515),f549(x9512,x9513,x9514,x9515))
% 94.68/94.46 [952]~E(x9521,x9522)+E(f549(x9523,x9521,x9524,x9525),f549(x9523,x9522,x9524,x9525))
% 94.68/94.46 [953]~E(x9531,x9532)+E(f549(x9533,x9534,x9531,x9535),f549(x9533,x9534,x9532,x9535))
% 94.68/94.46 [954]~E(x9541,x9542)+E(f549(x9543,x9544,x9545,x9541),f549(x9543,x9544,x9545,x9542))
% 94.68/94.46 [955]~E(x9551,x9552)+E(f163(x9551,x9553,x9554),f163(x9552,x9553,x9554))
% 94.68/94.46 [956]~E(x9561,x9562)+E(f163(x9563,x9561,x9564),f163(x9563,x9562,x9564))
% 94.68/94.46 [957]~E(x9571,x9572)+E(f163(x9573,x9574,x9571),f163(x9573,x9574,x9572))
% 94.68/94.46 [958]~E(x9581,x9582)+E(f190(x9581),f190(x9582))
% 94.68/94.46 [959]~E(x9591,x9592)+E(f728(x9591),f728(x9592))
% 94.68/94.46 [960]~E(x9601,x9602)+E(f579(x9601,x9603,x9604),f579(x9602,x9603,x9604))
% 94.68/94.46 [961]~E(x9611,x9612)+E(f579(x9613,x9611,x9614),f579(x9613,x9612,x9614))
% 94.68/94.46 [962]~E(x9621,x9622)+E(f579(x9623,x9624,x9621),f579(x9623,x9624,x9622))
% 94.68/94.46 [963]~E(x9631,x9632)+E(f309(x9631,x9633,x9634,x9635),f309(x9632,x9633,x9634,x9635))
% 94.68/94.46 [964]~E(x9641,x9642)+E(f309(x9643,x9641,x9644,x9645),f309(x9643,x9642,x9644,x9645))
% 94.68/94.46 [965]~E(x9651,x9652)+E(f309(x9653,x9654,x9651,x9655),f309(x9653,x9654,x9652,x9655))
% 94.68/94.46 [966]~E(x9661,x9662)+E(f309(x9663,x9664,x9665,x9661),f309(x9663,x9664,x9665,x9662))
% 94.68/94.46 [967]~E(x9671,x9672)+E(f860(x9671,x9673,x9674),f860(x9672,x9673,x9674))
% 94.68/94.46 [968]~E(x9681,x9682)+E(f860(x9683,x9681,x9684),f860(x9683,x9682,x9684))
% 94.68/94.46 [969]~E(x9691,x9692)+E(f860(x9693,x9694,x9691),f860(x9693,x9694,x9692))
% 94.68/94.46 [970]~E(x9701,x9702)+E(f358(x9701,x9703,x9704,x9705),f358(x9702,x9703,x9704,x9705))
% 94.68/94.46 [971]~E(x9711,x9712)+E(f358(x9713,x9711,x9714,x9715),f358(x9713,x9712,x9714,x9715))
% 94.68/94.46 [972]~E(x9721,x9722)+E(f358(x9723,x9724,x9721,x9725),f358(x9723,x9724,x9722,x9725))
% 94.68/94.46 [973]~E(x9731,x9732)+E(f358(x9733,x9734,x9735,x9731),f358(x9733,x9734,x9735,x9732))
% 94.68/94.46 [974]~E(x9741,x9742)+E(f711(x9741,x9743),f711(x9742,x9743))
% 94.68/94.46 [975]~E(x9751,x9752)+E(f711(x9753,x9751),f711(x9753,x9752))
% 94.68/94.46 [976]~E(x9761,x9762)+E(f139(x9761,x9763,x9764,x9765,x9766),f139(x9762,x9763,x9764,x9765,x9766))
% 94.68/94.46 [977]~E(x9771,x9772)+E(f139(x9773,x9771,x9774,x9775,x9776),f139(x9773,x9772,x9774,x9775,x9776))
% 94.68/94.46 [978]~E(x9781,x9782)+E(f139(x9783,x9784,x9781,x9785,x9786),f139(x9783,x9784,x9782,x9785,x9786))
% 94.68/94.46 [979]~E(x9791,x9792)+E(f139(x9793,x9794,x9795,x9791,x9796),f139(x9793,x9794,x9795,x9792,x9796))
% 94.68/94.46 [980]~E(x9801,x9802)+E(f139(x9803,x9804,x9805,x9806,x9801),f139(x9803,x9804,x9805,x9806,x9802))
% 94.68/94.46 [981]~E(x9811,x9812)+E(f638(x9811,x9813,x9814),f638(x9812,x9813,x9814))
% 94.68/94.46 [982]~E(x9821,x9822)+E(f638(x9823,x9821,x9824),f638(x9823,x9822,x9824))
% 94.68/94.46 [983]~E(x9831,x9832)+E(f638(x9833,x9834,x9831),f638(x9833,x9834,x9832))
% 94.68/94.46 [984]~E(x9841,x9842)+E(f811(x9841,x9843,x9844,x9845),f811(x9842,x9843,x9844,x9845))
% 94.68/94.46 [985]~E(x9851,x9852)+E(f811(x9853,x9851,x9854,x9855),f811(x9853,x9852,x9854,x9855))
% 94.68/94.46 [986]~E(x9861,x9862)+E(f811(x9863,x9864,x9861,x9865),f811(x9863,x9864,x9862,x9865))
% 94.68/94.46 [987]~E(x9871,x9872)+E(f811(x9873,x9874,x9875,x9871),f811(x9873,x9874,x9875,x9872))
% 94.68/94.46 [988]~E(x9881,x9882)+E(f462(x9881,x9883,x9884),f462(x9882,x9883,x9884))
% 94.68/94.46 [989]~E(x9891,x9892)+E(f462(x9893,x9891,x9894),f462(x9893,x9892,x9894))
% 94.68/94.46 [990]~E(x9901,x9902)+E(f462(x9903,x9904,x9901),f462(x9903,x9904,x9902))
% 94.68/94.46 [991]~E(x9911,x9912)+E(f62(x9911,x9913,x9914),f62(x9912,x9913,x9914))
% 94.68/94.46 [992]~E(x9921,x9922)+E(f62(x9923,x9921,x9924),f62(x9923,x9922,x9924))
% 94.68/94.46 [993]~E(x9931,x9932)+E(f62(x9933,x9934,x9931),f62(x9933,x9934,x9932))
% 94.68/94.46 [994]~E(x9941,x9942)+E(f201(x9941,x9943,x9944,x9945,x9946,x9947,x9948),f201(x9942,x9943,x9944,x9945,x9946,x9947,x9948))
% 94.68/94.46 [995]~E(x9951,x9952)+E(f201(x9953,x9951,x9954,x9955,x9956,x9957,x9958),f201(x9953,x9952,x9954,x9955,x9956,x9957,x9958))
% 94.68/94.46 [996]~E(x9961,x9962)+E(f201(x9963,x9964,x9961,x9965,x9966,x9967,x9968),f201(x9963,x9964,x9962,x9965,x9966,x9967,x9968))
% 94.68/94.46 [997]~E(x9971,x9972)+E(f201(x9973,x9974,x9975,x9971,x9976,x9977,x9978),f201(x9973,x9974,x9975,x9972,x9976,x9977,x9978))
% 94.68/94.46 [998]~E(x9981,x9982)+E(f201(x9983,x9984,x9985,x9986,x9981,x9987,x9988),f201(x9983,x9984,x9985,x9986,x9982,x9987,x9988))
% 94.68/94.46 [999]~E(x9991,x9992)+E(f201(x9993,x9994,x9995,x9996,x9997,x9991,x9998),f201(x9993,x9994,x9995,x9996,x9997,x9992,x9998))
% 94.68/94.46 [1000]~E(x10001,x10002)+E(f201(x10003,x10004,x10005,x10006,x10007,x10008,x10001),f201(x10003,x10004,x10005,x10006,x10007,x10008,x10002))
% 94.68/94.46 [1001]~E(x10011,x10012)+E(f623(x10011,x10013,x10014,x10015,x10016,x10017),f623(x10012,x10013,x10014,x10015,x10016,x10017))
% 94.68/94.46 [1002]~E(x10021,x10022)+E(f623(x10023,x10021,x10024,x10025,x10026,x10027),f623(x10023,x10022,x10024,x10025,x10026,x10027))
% 94.68/94.46 [1003]~E(x10031,x10032)+E(f623(x10033,x10034,x10031,x10035,x10036,x10037),f623(x10033,x10034,x10032,x10035,x10036,x10037))
% 94.68/94.46 [1004]~E(x10041,x10042)+E(f623(x10043,x10044,x10045,x10041,x10046,x10047),f623(x10043,x10044,x10045,x10042,x10046,x10047))
% 94.68/94.46 [1005]~E(x10051,x10052)+E(f623(x10053,x10054,x10055,x10056,x10051,x10057),f623(x10053,x10054,x10055,x10056,x10052,x10057))
% 94.68/94.46 [1006]~E(x10061,x10062)+E(f623(x10063,x10064,x10065,x10066,x10067,x10061),f623(x10063,x10064,x10065,x10066,x10067,x10062))
% 94.68/94.46 [1007]~E(x10071,x10072)+E(f835(x10071,x10073,x10074),f835(x10072,x10073,x10074))
% 94.68/94.46 [1008]~E(x10081,x10082)+E(f835(x10083,x10081,x10084),f835(x10083,x10082,x10084))
% 94.68/94.46 [1009]~E(x10091,x10092)+E(f835(x10093,x10094,x10091),f835(x10093,x10094,x10092))
% 94.68/94.46 [1010]~E(x10101,x10102)+E(f727(x10101,x10103),f727(x10102,x10103))
% 94.68/94.46 [1011]~E(x10111,x10112)+E(f727(x10113,x10111),f727(x10113,x10112))
% 94.68/94.46 [1012]~E(x10121,x10122)+E(f665(x10121,x10123,x10124,x10125),f665(x10122,x10123,x10124,x10125))
% 94.68/94.46 [1013]~E(x10131,x10132)+E(f665(x10133,x10131,x10134,x10135),f665(x10133,x10132,x10134,x10135))
% 94.68/94.46 [1014]~E(x10141,x10142)+E(f665(x10143,x10144,x10141,x10145),f665(x10143,x10144,x10142,x10145))
% 94.68/94.46 [1015]~E(x10151,x10152)+E(f665(x10153,x10154,x10155,x10151),f665(x10153,x10154,x10155,x10152))
% 94.68/94.46 [1016]~E(x10161,x10162)+E(f837(x10161,x10163,x10164),f837(x10162,x10163,x10164))
% 94.68/94.46 [1017]~E(x10171,x10172)+E(f837(x10173,x10171,x10174),f837(x10173,x10172,x10174))
% 94.68/94.46 [1018]~E(x10181,x10182)+E(f837(x10183,x10184,x10181),f837(x10183,x10184,x10182))
% 94.68/94.46 [1019]~E(x10191,x10192)+E(f136(x10191,x10193),f136(x10192,x10193))
% 94.68/94.46 [1020]~E(x10201,x10202)+E(f136(x10203,x10201),f136(x10203,x10202))
% 94.68/94.46 [1021]~E(x10211,x10212)+E(f541(x10211,x10213,x10214),f541(x10212,x10213,x10214))
% 94.68/94.46 [1022]~E(x10221,x10222)+E(f541(x10223,x10221,x10224),f541(x10223,x10222,x10224))
% 94.68/94.46 [1023]~E(x10231,x10232)+E(f541(x10233,x10234,x10231),f541(x10233,x10234,x10232))
% 94.68/94.46 [1024]~E(x10241,x10242)+E(f657(x10241,x10243,x10244,x10245,x10246),f657(x10242,x10243,x10244,x10245,x10246))
% 94.68/94.46 [1025]~E(x10251,x10252)+E(f657(x10253,x10251,x10254,x10255,x10256),f657(x10253,x10252,x10254,x10255,x10256))
% 94.68/94.46 [1026]~E(x10261,x10262)+E(f657(x10263,x10264,x10261,x10265,x10266),f657(x10263,x10264,x10262,x10265,x10266))
% 94.68/94.46 [1027]~E(x10271,x10272)+E(f657(x10273,x10274,x10275,x10271,x10276),f657(x10273,x10274,x10275,x10272,x10276))
% 94.68/94.46 [1028]~E(x10281,x10282)+E(f657(x10283,x10284,x10285,x10286,x10281),f657(x10283,x10284,x10285,x10286,x10282))
% 94.68/94.46 [1029]~E(x10291,x10292)+E(f386(x10291,x10293,x10294,x10295),f386(x10292,x10293,x10294,x10295))
% 94.68/94.46 [1030]~E(x10301,x10302)+E(f386(x10303,x10301,x10304,x10305),f386(x10303,x10302,x10304,x10305))
% 94.68/94.46 [1031]~E(x10311,x10312)+E(f386(x10313,x10314,x10311,x10315),f386(x10313,x10314,x10312,x10315))
% 94.68/94.46 [1032]~E(x10321,x10322)+E(f386(x10323,x10324,x10325,x10321),f386(x10323,x10324,x10325,x10322))
% 94.68/94.46 [1033]~E(x10331,x10332)+E(f263(x10331,x10333,x10334,x10335),f263(x10332,x10333,x10334,x10335))
% 94.68/94.46 [1034]~E(x10341,x10342)+E(f263(x10343,x10341,x10344,x10345),f263(x10343,x10342,x10344,x10345))
% 94.68/94.46 [1035]~E(x10351,x10352)+E(f263(x10353,x10354,x10351,x10355),f263(x10353,x10354,x10352,x10355))
% 94.68/94.46 [1036]~E(x10361,x10362)+E(f263(x10363,x10364,x10365,x10361),f263(x10363,x10364,x10365,x10362))
% 94.68/94.46 [1037]~E(x10371,x10372)+E(f130(x10371,x10373,x10374),f130(x10372,x10373,x10374))
% 94.68/94.46 [1038]~E(x10381,x10382)+E(f130(x10383,x10381,x10384),f130(x10383,x10382,x10384))
% 94.68/94.46 [1039]~E(x10391,x10392)+E(f130(x10393,x10394,x10391),f130(x10393,x10394,x10392))
% 94.68/94.46 [1040]~E(x10401,x10402)+E(f532(x10401,x10403,x10404,x10405,x10406,x10407,x10408,x10409),f532(x10402,x10403,x10404,x10405,x10406,x10407,x10408,x10409))
% 94.68/94.46 [1041]~E(x10411,x10412)+E(f532(x10413,x10411,x10414,x10415,x10416,x10417,x10418,x10419),f532(x10413,x10412,x10414,x10415,x10416,x10417,x10418,x10419))
% 94.68/94.46 [1042]~E(x10421,x10422)+E(f532(x10423,x10424,x10421,x10425,x10426,x10427,x10428,x10429),f532(x10423,x10424,x10422,x10425,x10426,x10427,x10428,x10429))
% 94.68/94.46 [1043]~E(x10431,x10432)+E(f532(x10433,x10434,x10435,x10431,x10436,x10437,x10438,x10439),f532(x10433,x10434,x10435,x10432,x10436,x10437,x10438,x10439))
% 94.68/94.46 [1044]~E(x10441,x10442)+E(f532(x10443,x10444,x10445,x10446,x10441,x10447,x10448,x10449),f532(x10443,x10444,x10445,x10446,x10442,x10447,x10448,x10449))
% 94.68/94.46 [1045]~E(x10451,x10452)+E(f532(x10453,x10454,x10455,x10456,x10457,x10451,x10458,x10459),f532(x10453,x10454,x10455,x10456,x10457,x10452,x10458,x10459))
% 94.68/94.46 [1046]~E(x10461,x10462)+E(f532(x10463,x10464,x10465,x10466,x10467,x10468,x10461,x10469),f532(x10463,x10464,x10465,x10466,x10467,x10468,x10462,x10469))
% 94.68/94.46 [1047]~E(x10471,x10472)+E(f532(x10473,x10474,x10475,x10476,x10477,x10478,x10479,x10471),f532(x10473,x10474,x10475,x10476,x10477,x10478,x10479,x10472))
% 94.68/94.46 [1048]~E(x10481,x10482)+E(f535(x10481,x10483,x10484),f535(x10482,x10483,x10484))
% 94.68/94.46 [1049]~E(x10491,x10492)+E(f535(x10493,x10491,x10494),f535(x10493,x10492,x10494))
% 94.68/94.46 [1050]~E(x10501,x10502)+E(f535(x10503,x10504,x10501),f535(x10503,x10504,x10502))
% 94.68/94.46 [1051]~E(x10511,x10512)+E(f885(x10511,x10513,x10514),f885(x10512,x10513,x10514))
% 94.68/94.46 [1052]~E(x10521,x10522)+E(f885(x10523,x10521,x10524),f885(x10523,x10522,x10524))
% 94.68/94.46 [1053]~E(x10531,x10532)+E(f885(x10533,x10534,x10531),f885(x10533,x10534,x10532))
% 94.68/94.46 [1054]~E(x10541,x10542)+E(f50(x10541,x10543,x10544),f50(x10542,x10543,x10544))
% 94.68/94.46 [1055]~E(x10551,x10552)+E(f50(x10553,x10551,x10554),f50(x10553,x10552,x10554))
% 94.68/94.46 [1056]~E(x10561,x10562)+E(f50(x10563,x10564,x10561),f50(x10563,x10564,x10562))
% 94.68/94.46 [1057]~E(x10571,x10572)+E(f796(x10571),f796(x10572))
% 94.68/94.46 [1058]~E(x10581,x10582)+E(f112(x10581,x10583,x10584,x10585),f112(x10582,x10583,x10584,x10585))
% 94.68/94.46 [1059]~E(x10591,x10592)+E(f112(x10593,x10591,x10594,x10595),f112(x10593,x10592,x10594,x10595))
% 94.68/94.46 [1060]~E(x10601,x10602)+E(f112(x10603,x10604,x10601,x10605),f112(x10603,x10604,x10602,x10605))
% 94.68/94.46 [1061]~E(x10611,x10612)+E(f112(x10613,x10614,x10615,x10611),f112(x10613,x10614,x10615,x10612))
% 94.68/94.46 [1062]~E(x10621,x10622)+E(f61(x10621,x10623,x10624),f61(x10622,x10623,x10624))
% 94.68/94.46 [1063]~E(x10631,x10632)+E(f61(x10633,x10631,x10634),f61(x10633,x10632,x10634))
% 94.68/94.46 [1064]~E(x10641,x10642)+E(f61(x10643,x10644,x10641),f61(x10643,x10644,x10642))
% 94.68/94.46 [1065]~E(x10651,x10652)+E(f145(x10651,x10653,x10654),f145(x10652,x10653,x10654))
% 94.68/94.46 [1066]~E(x10661,x10662)+E(f145(x10663,x10661,x10664),f145(x10663,x10662,x10664))
% 94.68/94.46 [1067]~E(x10671,x10672)+E(f145(x10673,x10674,x10671),f145(x10673,x10674,x10672))
% 94.68/94.46 [1068]~E(x10681,x10682)+E(f765(x10681,x10683,x10684,x10685,x10686,x10687,x10688),f765(x10682,x10683,x10684,x10685,x10686,x10687,x10688))
% 94.68/94.46 [1069]~E(x10691,x10692)+E(f765(x10693,x10691,x10694,x10695,x10696,x10697,x10698),f765(x10693,x10692,x10694,x10695,x10696,x10697,x10698))
% 94.68/94.46 [1070]~E(x10701,x10702)+E(f765(x10703,x10704,x10701,x10705,x10706,x10707,x10708),f765(x10703,x10704,x10702,x10705,x10706,x10707,x10708))
% 94.68/94.46 [1071]~E(x10711,x10712)+E(f765(x10713,x10714,x10715,x10711,x10716,x10717,x10718),f765(x10713,x10714,x10715,x10712,x10716,x10717,x10718))
% 94.68/94.46 [1072]~E(x10721,x10722)+E(f765(x10723,x10724,x10725,x10726,x10721,x10727,x10728),f765(x10723,x10724,x10725,x10726,x10722,x10727,x10728))
% 94.68/94.46 [1073]~E(x10731,x10732)+E(f765(x10733,x10734,x10735,x10736,x10737,x10731,x10738),f765(x10733,x10734,x10735,x10736,x10737,x10732,x10738))
% 94.68/94.46 [1074]~E(x10741,x10742)+E(f765(x10743,x10744,x10745,x10746,x10747,x10748,x10741),f765(x10743,x10744,x10745,x10746,x10747,x10748,x10742))
% 94.68/94.46 [1075]~E(x10751,x10752)+E(f433(x10751),f433(x10752))
% 94.68/94.46 [1076]~E(x10761,x10762)+E(f572(x10761,x10763,x10764,x10765,x10766),f572(x10762,x10763,x10764,x10765,x10766))
% 94.68/94.46 [1077]~E(x10771,x10772)+E(f572(x10773,x10771,x10774,x10775,x10776),f572(x10773,x10772,x10774,x10775,x10776))
% 94.68/94.46 [1078]~E(x10781,x10782)+E(f572(x10783,x10784,x10781,x10785,x10786),f572(x10783,x10784,x10782,x10785,x10786))
% 94.68/94.46 [1079]~E(x10791,x10792)+E(f572(x10793,x10794,x10795,x10791,x10796),f572(x10793,x10794,x10795,x10792,x10796))
% 94.68/94.46 [1080]~E(x10801,x10802)+E(f572(x10803,x10804,x10805,x10806,x10801),f572(x10803,x10804,x10805,x10806,x10802))
% 94.68/94.46 [1081]~E(x10811,x10812)+E(f852(x10811,x10813,x10814),f852(x10812,x10813,x10814))
% 94.68/94.46 [1082]~E(x10821,x10822)+E(f852(x10823,x10821,x10824),f852(x10823,x10822,x10824))
% 94.68/94.46 [1083]~E(x10831,x10832)+E(f852(x10833,x10834,x10831),f852(x10833,x10834,x10832))
% 94.68/94.46 [1084]~E(x10841,x10842)+E(f326(x10841,x10843,x10844,x10845),f326(x10842,x10843,x10844,x10845))
% 94.68/94.46 [1085]~E(x10851,x10852)+E(f326(x10853,x10851,x10854,x10855),f326(x10853,x10852,x10854,x10855))
% 94.68/94.46 [1086]~E(x10861,x10862)+E(f326(x10863,x10864,x10861,x10865),f326(x10863,x10864,x10862,x10865))
% 94.68/94.46 [1087]~E(x10871,x10872)+E(f326(x10873,x10874,x10875,x10871),f326(x10873,x10874,x10875,x10872))
% 94.68/94.46 [1088]~E(x10881,x10882)+E(f822(x10881,x10883,x10884,x10885,x10886,x10887,x10888),f822(x10882,x10883,x10884,x10885,x10886,x10887,x10888))
% 94.68/94.46 [1089]~E(x10891,x10892)+E(f822(x10893,x10891,x10894,x10895,x10896,x10897,x10898),f822(x10893,x10892,x10894,x10895,x10896,x10897,x10898))
% 94.68/94.46 [1090]~E(x10901,x10902)+E(f822(x10903,x10904,x10901,x10905,x10906,x10907,x10908),f822(x10903,x10904,x10902,x10905,x10906,x10907,x10908))
% 94.68/94.46 [1091]~E(x10911,x10912)+E(f822(x10913,x10914,x10915,x10911,x10916,x10917,x10918),f822(x10913,x10914,x10915,x10912,x10916,x10917,x10918))
% 94.68/94.46 [1092]~E(x10921,x10922)+E(f822(x10923,x10924,x10925,x10926,x10921,x10927,x10928),f822(x10923,x10924,x10925,x10926,x10922,x10927,x10928))
% 94.68/94.46 [1093]~E(x10931,x10932)+E(f822(x10933,x10934,x10935,x10936,x10937,x10931,x10938),f822(x10933,x10934,x10935,x10936,x10937,x10932,x10938))
% 94.68/94.46 [1094]~E(x10941,x10942)+E(f822(x10943,x10944,x10945,x10946,x10947,x10948,x10941),f822(x10943,x10944,x10945,x10946,x10947,x10948,x10942))
% 94.68/94.46 [1095]~E(x10951,x10952)+E(f497(x10951,x10953,x10954,x10955),f497(x10952,x10953,x10954,x10955))
% 94.68/94.46 [1096]~E(x10961,x10962)+E(f497(x10963,x10961,x10964,x10965),f497(x10963,x10962,x10964,x10965))
% 94.68/94.46 [1097]~E(x10971,x10972)+E(f497(x10973,x10974,x10971,x10975),f497(x10973,x10974,x10972,x10975))
% 94.68/94.46 [1098]~E(x10981,x10982)+E(f497(x10983,x10984,x10985,x10981),f497(x10983,x10984,x10985,x10982))
% 94.68/94.46 [1099]~E(x10991,x10992)+E(f533(x10991,x10993,x10994),f533(x10992,x10993,x10994))
% 94.68/94.46 [1100]~E(x11001,x11002)+E(f533(x11003,x11001,x11004),f533(x11003,x11002,x11004))
% 94.68/94.46 [1101]~E(x11011,x11012)+E(f533(x11013,x11014,x11011),f533(x11013,x11014,x11012))
% 94.68/94.46 [1102]~E(x11021,x11022)+E(f560(x11021,x11023),f560(x11022,x11023))
% 94.68/94.46 [1103]~E(x11031,x11032)+E(f560(x11033,x11031),f560(x11033,x11032))
% 94.68/94.46 [1104]~E(x11041,x11042)+E(f329(x11041,x11043,x11044,x11045),f329(x11042,x11043,x11044,x11045))
% 94.68/94.46 [1105]~E(x11051,x11052)+E(f329(x11053,x11051,x11054,x11055),f329(x11053,x11052,x11054,x11055))
% 94.68/94.46 [1106]~E(x11061,x11062)+E(f329(x11063,x11064,x11061,x11065),f329(x11063,x11064,x11062,x11065))
% 94.68/94.46 [1107]~E(x11071,x11072)+E(f329(x11073,x11074,x11075,x11071),f329(x11073,x11074,x11075,x11072))
% 94.68/94.46 [1108]~E(x11081,x11082)+E(f217(x11081,x11083),f217(x11082,x11083))
% 94.68/94.46 [1109]~E(x11091,x11092)+E(f217(x11093,x11091),f217(x11093,x11092))
% 94.68/94.46 [1110]~E(x11101,x11102)+E(f264(x11101,x11103,x11104),f264(x11102,x11103,x11104))
% 94.68/94.46 [1111]~E(x11111,x11112)+E(f264(x11113,x11111,x11114),f264(x11113,x11112,x11114))
% 94.68/94.46 [1112]~E(x11121,x11122)+E(f264(x11123,x11124,x11121),f264(x11123,x11124,x11122))
% 94.68/94.46 [1113]~E(x11131,x11132)+E(f797(x11131),f797(x11132))
% 94.68/94.46 [1114]~E(x11141,x11142)+E(f100(x11141),f100(x11142))
% 94.68/94.46 [1115]~E(x11151,x11152)+E(f709(x11151,x11153),f709(x11152,x11153))
% 94.68/94.46 [1116]~E(x11161,x11162)+E(f709(x11163,x11161),f709(x11163,x11162))
% 94.68/94.46 [1117]~E(x11171,x11172)+E(f617(x11171,x11173),f617(x11172,x11173))
% 94.68/94.46 [1118]~E(x11181,x11182)+E(f617(x11183,x11181),f617(x11183,x11182))
% 94.68/94.46 [1119]~E(x11191,x11192)+E(f41(x11191,x11193),f41(x11192,x11193))
% 94.68/94.46 [1120]~E(x11201,x11202)+E(f41(x11203,x11201),f41(x11203,x11202))
% 94.68/94.46 [1121]~E(x11211,x11212)+E(f220(x11211,x11213,x11214),f220(x11212,x11213,x11214))
% 94.68/94.46 [1122]~E(x11221,x11222)+E(f220(x11223,x11221,x11224),f220(x11223,x11222,x11224))
% 94.68/94.46 [1123]~E(x11231,x11232)+E(f220(x11233,x11234,x11231),f220(x11233,x11234,x11232))
% 94.68/94.46 [1124]~E(x11241,x11242)+E(f586(x11241,x11243,x11244,x11245,x11246),f586(x11242,x11243,x11244,x11245,x11246))
% 94.68/94.46 [1125]~E(x11251,x11252)+E(f586(x11253,x11251,x11254,x11255,x11256),f586(x11253,x11252,x11254,x11255,x11256))
% 94.68/94.46 [1126]~E(x11261,x11262)+E(f586(x11263,x11264,x11261,x11265,x11266),f586(x11263,x11264,x11262,x11265,x11266))
% 94.68/94.46 [1127]~E(x11271,x11272)+E(f586(x11273,x11274,x11275,x11271,x11276),f586(x11273,x11274,x11275,x11272,x11276))
% 94.68/94.46 [1128]~E(x11281,x11282)+E(f586(x11283,x11284,x11285,x11286,x11281),f586(x11283,x11284,x11285,x11286,x11282))
% 94.68/94.46 [1129]~E(x11291,x11292)+E(f133(x11291,x11293),f133(x11292,x11293))
% 94.68/94.46 [1130]~E(x11301,x11302)+E(f133(x11303,x11301),f133(x11303,x11302))
% 94.68/94.46 [1131]~E(x11311,x11312)+E(f477(x11311,x11313,x11314,x11315,x11316),f477(x11312,x11313,x11314,x11315,x11316))
% 94.68/94.46 [1132]~E(x11321,x11322)+E(f477(x11323,x11321,x11324,x11325,x11326),f477(x11323,x11322,x11324,x11325,x11326))
% 94.68/94.46 [1133]~E(x11331,x11332)+E(f477(x11333,x11334,x11331,x11335,x11336),f477(x11333,x11334,x11332,x11335,x11336))
% 94.68/94.46 [1134]~E(x11341,x11342)+E(f477(x11343,x11344,x11345,x11341,x11346),f477(x11343,x11344,x11345,x11342,x11346))
% 94.68/94.46 [1135]~E(x11351,x11352)+E(f477(x11353,x11354,x11355,x11356,x11351),f477(x11353,x11354,x11355,x11356,x11352))
% 94.68/94.46 [1136]~E(x11361,x11362)+E(f757(x11361,x11363,x11364,x11365),f757(x11362,x11363,x11364,x11365))
% 94.68/94.46 [1137]~E(x11371,x11372)+E(f757(x11373,x11371,x11374,x11375),f757(x11373,x11372,x11374,x11375))
% 94.68/94.46 [1138]~E(x11381,x11382)+E(f757(x11383,x11384,x11381,x11385),f757(x11383,x11384,x11382,x11385))
% 94.68/94.46 [1139]~E(x11391,x11392)+E(f757(x11393,x11394,x11395,x11391),f757(x11393,x11394,x11395,x11392))
% 94.68/94.46 [1140]~E(x11401,x11402)+E(f890(x11401,x11403),f890(x11402,x11403))
% 94.68/94.46 [1141]~E(x11411,x11412)+E(f890(x11413,x11411),f890(x11413,x11412))
% 94.68/94.46 [1142]~E(x11421,x11422)+E(f806(x11421,x11423,x11424,x11425,x11426),f806(x11422,x11423,x11424,x11425,x11426))
% 94.68/94.46 [1143]~E(x11431,x11432)+E(f806(x11433,x11431,x11434,x11435,x11436),f806(x11433,x11432,x11434,x11435,x11436))
% 94.68/94.46 [1144]~E(x11441,x11442)+E(f806(x11443,x11444,x11441,x11445,x11446),f806(x11443,x11444,x11442,x11445,x11446))
% 94.68/94.46 [1145]~E(x11451,x11452)+E(f806(x11453,x11454,x11455,x11451,x11456),f806(x11453,x11454,x11455,x11452,x11456))
% 94.68/94.46 [1146]~E(x11461,x11462)+E(f806(x11463,x11464,x11465,x11466,x11461),f806(x11463,x11464,x11465,x11466,x11462))
% 94.68/94.46 [1147]~E(x11471,x11472)+E(f325(x11471,x11473,x11474,x11475),f325(x11472,x11473,x11474,x11475))
% 94.68/94.46 [1148]~E(x11481,x11482)+E(f325(x11483,x11481,x11484,x11485),f325(x11483,x11482,x11484,x11485))
% 94.68/94.46 [1149]~E(x11491,x11492)+E(f325(x11493,x11494,x11491,x11495),f325(x11493,x11494,x11492,x11495))
% 94.68/94.46 [1150]~E(x11501,x11502)+E(f325(x11503,x11504,x11505,x11501),f325(x11503,x11504,x11505,x11502))
% 94.68/94.46 [1151]~E(x11511,x11512)+E(f730(x11511,x11513,x11514),f730(x11512,x11513,x11514))
% 94.68/94.46 [1152]~E(x11521,x11522)+E(f730(x11523,x11521,x11524),f730(x11523,x11522,x11524))
% 94.68/94.46 [1153]~E(x11531,x11532)+E(f730(x11533,x11534,x11531),f730(x11533,x11534,x11532))
% 94.68/94.46 [1154]~E(x11541,x11542)+E(f118(x11541,x11543),f118(x11542,x11543))
% 94.68/94.46 [1155]~E(x11551,x11552)+E(f118(x11553,x11551),f118(x11553,x11552))
% 94.68/94.46 [1156]~E(x11561,x11562)+E(f122(x11561,x11563),f122(x11562,x11563))
% 94.68/94.46 [1157]~E(x11571,x11572)+E(f122(x11573,x11571),f122(x11573,x11572))
% 94.68/94.46 [1158]~E(x11581,x11582)+E(f402(x11581,x11583,x11584,x11585,x11586),f402(x11582,x11583,x11584,x11585,x11586))
% 94.68/94.46 [1159]~E(x11591,x11592)+E(f402(x11593,x11591,x11594,x11595,x11596),f402(x11593,x11592,x11594,x11595,x11596))
% 94.68/94.46 [1160]~E(x11601,x11602)+E(f402(x11603,x11604,x11601,x11605,x11606),f402(x11603,x11604,x11602,x11605,x11606))
% 94.68/94.46 [1161]~E(x11611,x11612)+E(f402(x11613,x11614,x11615,x11611,x11616),f402(x11613,x11614,x11615,x11612,x11616))
% 94.68/94.46 [1162]~E(x11621,x11622)+E(f402(x11623,x11624,x11625,x11626,x11621),f402(x11623,x11624,x11625,x11626,x11622))
% 94.68/94.46 [1163]~E(x11631,x11632)+E(f875(x11631,x11633),f875(x11632,x11633))
% 94.68/94.46 [1164]~E(x11641,x11642)+E(f875(x11643,x11641),f875(x11643,x11642))
% 94.68/94.46 [1165]~E(x11651,x11652)+E(f379(x11651,x11653),f379(x11652,x11653))
% 94.68/94.46 [1166]~E(x11661,x11662)+E(f379(x11663,x11661),f379(x11663,x11662))
% 94.68/94.46 [1167]~E(x11671,x11672)+E(f260(x11671,x11673),f260(x11672,x11673))
% 94.68/94.46 [1168]~E(x11681,x11682)+E(f260(x11683,x11681),f260(x11683,x11682))
% 94.68/94.46 [1169]~E(x11691,x11692)+E(f751(x11691,x11693,x11694),f751(x11692,x11693,x11694))
% 94.68/94.46 [1170]~E(x11701,x11702)+E(f751(x11703,x11701,x11704),f751(x11703,x11702,x11704))
% 94.68/94.46 [1171]~E(x11711,x11712)+E(f751(x11713,x11714,x11711),f751(x11713,x11714,x11712))
% 94.68/94.46 [1172]~E(x11721,x11722)+E(f891(x11721,x11723),f891(x11722,x11723))
% 94.68/94.46 [1173]~E(x11731,x11732)+E(f891(x11733,x11731),f891(x11733,x11732))
% 94.68/94.46 [1174]~E(x11741,x11742)+E(f659(x11741,x11743,x11744,x11745,x11746),f659(x11742,x11743,x11744,x11745,x11746))
% 94.68/94.46 [1175]~E(x11751,x11752)+E(f659(x11753,x11751,x11754,x11755,x11756),f659(x11753,x11752,x11754,x11755,x11756))
% 94.68/94.46 [1176]~E(x11761,x11762)+E(f659(x11763,x11764,x11761,x11765,x11766),f659(x11763,x11764,x11762,x11765,x11766))
% 94.68/94.46 [1177]~E(x11771,x11772)+E(f659(x11773,x11774,x11775,x11771,x11776),f659(x11773,x11774,x11775,x11772,x11776))
% 94.68/94.46 [1178]~E(x11781,x11782)+E(f659(x11783,x11784,x11785,x11786,x11781),f659(x11783,x11784,x11785,x11786,x11782))
% 94.68/94.46 [1179]~E(x11791,x11792)+E(f858(x11791,x11793,x11794,x11795),f858(x11792,x11793,x11794,x11795))
% 94.68/94.46 [1180]~E(x11801,x11802)+E(f858(x11803,x11801,x11804,x11805),f858(x11803,x11802,x11804,x11805))
% 94.68/94.46 [1181]~E(x11811,x11812)+E(f858(x11813,x11814,x11811,x11815),f858(x11813,x11814,x11812,x11815))
% 94.68/94.46 [1182]~E(x11821,x11822)+E(f858(x11823,x11824,x11825,x11821),f858(x11823,x11824,x11825,x11822))
% 94.68/94.46 [1183]~E(x11831,x11832)+E(f627(x11831,x11833,x11834,x11835),f627(x11832,x11833,x11834,x11835))
% 94.68/94.46 [1184]~E(x11841,x11842)+E(f627(x11843,x11841,x11844,x11845),f627(x11843,x11842,x11844,x11845))
% 94.68/94.46 [1185]~E(x11851,x11852)+E(f627(x11853,x11854,x11851,x11855),f627(x11853,x11854,x11852,x11855))
% 94.68/94.46 [1186]~E(x11861,x11862)+E(f627(x11863,x11864,x11865,x11861),f627(x11863,x11864,x11865,x11862))
% 94.68/94.46 [1187]~E(x11871,x11872)+E(f243(x11871,x11873,x11874,x11875,x11876),f243(x11872,x11873,x11874,x11875,x11876))
% 94.68/94.46 [1188]~E(x11881,x11882)+E(f243(x11883,x11881,x11884,x11885,x11886),f243(x11883,x11882,x11884,x11885,x11886))
% 94.68/94.46 [1189]~E(x11891,x11892)+E(f243(x11893,x11894,x11891,x11895,x11896),f243(x11893,x11894,x11892,x11895,x11896))
% 94.68/94.46 [1190]~E(x11901,x11902)+E(f243(x11903,x11904,x11905,x11901,x11906),f243(x11903,x11904,x11905,x11902,x11906))
% 94.68/94.46 [1191]~E(x11911,x11912)+E(f243(x11913,x11914,x11915,x11916,x11911),f243(x11913,x11914,x11915,x11916,x11912))
% 94.68/94.46 [1192]~E(x11921,x11922)+E(f359(x11921,x11923,x11924,x11925),f359(x11922,x11923,x11924,x11925))
% 94.68/94.46 [1193]~E(x11931,x11932)+E(f359(x11933,x11931,x11934,x11935),f359(x11933,x11932,x11934,x11935))
% 94.68/94.46 [1194]~E(x11941,x11942)+E(f359(x11943,x11944,x11941,x11945),f359(x11943,x11944,x11942,x11945))
% 94.68/94.46 [1195]~E(x11951,x11952)+E(f359(x11953,x11954,x11955,x11951),f359(x11953,x11954,x11955,x11952))
% 94.68/94.46 [1196]~E(x11961,x11962)+E(f523(x11961,x11963,x11964,x11965),f523(x11962,x11963,x11964,x11965))
% 94.68/94.46 [1197]~E(x11971,x11972)+E(f523(x11973,x11971,x11974,x11975),f523(x11973,x11972,x11974,x11975))
% 94.68/94.46 [1198]~E(x11981,x11982)+E(f523(x11983,x11984,x11981,x11985),f523(x11983,x11984,x11982,x11985))
% 94.68/94.46 [1199]~E(x11991,x11992)+E(f523(x11993,x11994,x11995,x11991),f523(x11993,x11994,x11995,x11992))
% 94.68/94.46 [1200]~E(x12001,x12002)+E(f189(x12001,x12003),f189(x12002,x12003))
% 94.68/94.46 [1201]~E(x12011,x12012)+E(f189(x12013,x12011),f189(x12013,x12012))
% 94.68/94.46 [1202]~E(x12021,x12022)+E(f356(x12021,x12023,x12024),f356(x12022,x12023,x12024))
% 94.68/94.46 [1203]~E(x12031,x12032)+E(f356(x12033,x12031,x12034),f356(x12033,x12032,x12034))
% 94.68/94.46 [1204]~E(x12041,x12042)+E(f356(x12043,x12044,x12041),f356(x12043,x12044,x12042))
% 94.68/94.46 [1205]~E(x12051,x12052)+E(f119(x12051),f119(x12052))
% 94.68/94.46 [1206]~E(x12061,x12062)+E(f652(x12061,x12063),f652(x12062,x12063))
% 94.68/94.46 [1207]~E(x12071,x12072)+E(f652(x12073,x12071),f652(x12073,x12072))
% 94.68/94.46 [1208]~E(x12081,x12082)+E(f490(x12081,x12083),f490(x12082,x12083))
% 94.68/94.46 [1209]~E(x12091,x12092)+E(f490(x12093,x12091),f490(x12093,x12092))
% 94.68/94.46 [1210]~E(x12101,x12102)+E(f49(x12101,x12103),f49(x12102,x12103))
% 94.68/94.46 [1211]~E(x12111,x12112)+E(f49(x12113,x12111),f49(x12113,x12112))
% 94.68/94.46 [1212]~E(x12121,x12122)+E(f784(x12121),f784(x12122))
% 94.68/94.46 [1213]~E(x12131,x12132)+E(f861(x12131,x12133,x12134),f861(x12132,x12133,x12134))
% 94.68/94.46 [1214]~E(x12141,x12142)+E(f861(x12143,x12141,x12144),f861(x12143,x12142,x12144))
% 94.68/94.46 [1215]~E(x12151,x12152)+E(f861(x12153,x12154,x12151),f861(x12153,x12154,x12152))
% 94.68/94.46 [1216]~E(x12161,x12162)+E(f516(x12161,x12163),f516(x12162,x12163))
% 94.68/94.46 [1217]~E(x12171,x12172)+E(f516(x12173,x12171),f516(x12173,x12172))
% 94.68/94.46 [1218]~E(x12181,x12182)+E(f887(x12181,x12183,x12184),f887(x12182,x12183,x12184))
% 94.68/94.46 [1219]~E(x12191,x12192)+E(f887(x12193,x12191,x12194),f887(x12193,x12192,x12194))
% 94.68/94.46 [1220]~E(x12201,x12202)+E(f887(x12203,x12204,x12201),f887(x12203,x12204,x12202))
% 94.68/94.46 [1221]~E(x12211,x12212)+E(f582(x12211,x12213,x12214,x12215),f582(x12212,x12213,x12214,x12215))
% 94.68/94.46 [1222]~E(x12221,x12222)+E(f582(x12223,x12221,x12224,x12225),f582(x12223,x12222,x12224,x12225))
% 94.68/94.46 [1223]~E(x12231,x12232)+E(f582(x12233,x12234,x12231,x12235),f582(x12233,x12234,x12232,x12235))
% 94.68/94.46 [1224]~E(x12241,x12242)+E(f582(x12243,x12244,x12245,x12241),f582(x12243,x12244,x12245,x12242))
% 94.68/94.46 [1225]~E(x12251,x12252)+E(f752(x12251,x12253,x12254),f752(x12252,x12253,x12254))
% 94.68/94.46 [1226]~E(x12261,x12262)+E(f752(x12263,x12261,x12264),f752(x12263,x12262,x12264))
% 94.68/94.46 [1227]~E(x12271,x12272)+E(f752(x12273,x12274,x12271),f752(x12273,x12274,x12272))
% 94.68/94.46 [1228]~E(x12281,x12282)+E(f655(x12281,x12283,x12284),f655(x12282,x12283,x12284))
% 94.68/94.46 [1229]~E(x12291,x12292)+E(f655(x12293,x12291,x12294),f655(x12293,x12292,x12294))
% 94.68/94.46 [1230]~E(x12301,x12302)+E(f655(x12303,x12304,x12301),f655(x12303,x12304,x12302))
% 94.68/94.46 [1231]~E(x12311,x12312)+E(f589(x12311,x12313,x12314),f589(x12312,x12313,x12314))
% 94.68/94.46 [1232]~E(x12321,x12322)+E(f589(x12323,x12321,x12324),f589(x12323,x12322,x12324))
% 94.68/94.46 [1233]~E(x12331,x12332)+E(f589(x12333,x12334,x12331),f589(x12333,x12334,x12332))
% 94.68/94.46 [1234]~E(x12341,x12342)+E(f426(x12341,x12343,x12344,x12345,x12346),f426(x12342,x12343,x12344,x12345,x12346))
% 94.68/94.46 [1235]~E(x12351,x12352)+E(f426(x12353,x12351,x12354,x12355,x12356),f426(x12353,x12352,x12354,x12355,x12356))
% 94.68/94.46 [1236]~E(x12361,x12362)+E(f426(x12363,x12364,x12361,x12365,x12366),f426(x12363,x12364,x12362,x12365,x12366))
% 94.68/94.46 [1237]~E(x12371,x12372)+E(f426(x12373,x12374,x12375,x12371,x12376),f426(x12373,x12374,x12375,x12372,x12376))
% 94.68/94.46 [1238]~E(x12381,x12382)+E(f426(x12383,x12384,x12385,x12386,x12381),f426(x12383,x12384,x12385,x12386,x12382))
% 94.68/94.46 [1239]~E(x12391,x12392)+E(f259(x12391,x12393),f259(x12392,x12393))
% 94.68/94.46 [1240]~E(x12401,x12402)+E(f259(x12403,x12401),f259(x12403,x12402))
% 94.68/94.46 [1241]~E(x12411,x12412)+E(f483(x12411,x12413,x12414,x12415,x12416,x12417,x12418,x12419),f483(x12412,x12413,x12414,x12415,x12416,x12417,x12418,x12419))
% 94.68/94.46 [1242]~E(x12421,x12422)+E(f483(x12423,x12421,x12424,x12425,x12426,x12427,x12428,x12429),f483(x12423,x12422,x12424,x12425,x12426,x12427,x12428,x12429))
% 94.68/94.46 [1243]~E(x12431,x12432)+E(f483(x12433,x12434,x12431,x12435,x12436,x12437,x12438,x12439),f483(x12433,x12434,x12432,x12435,x12436,x12437,x12438,x12439))
% 94.68/94.46 [1244]~E(x12441,x12442)+E(f483(x12443,x12444,x12445,x12441,x12446,x12447,x12448,x12449),f483(x12443,x12444,x12445,x12442,x12446,x12447,x12448,x12449))
% 94.68/94.46 [1245]~E(x12451,x12452)+E(f483(x12453,x12454,x12455,x12456,x12451,x12457,x12458,x12459),f483(x12453,x12454,x12455,x12456,x12452,x12457,x12458,x12459))
% 94.68/94.46 [1246]~E(x12461,x12462)+E(f483(x12463,x12464,x12465,x12466,x12467,x12461,x12468,x12469),f483(x12463,x12464,x12465,x12466,x12467,x12462,x12468,x12469))
% 94.68/94.46 [1247]~E(x12471,x12472)+E(f483(x12473,x12474,x12475,x12476,x12477,x12478,x12471,x12479),f483(x12473,x12474,x12475,x12476,x12477,x12478,x12472,x12479))
% 94.68/94.46 [1248]~E(x12481,x12482)+E(f483(x12483,x12484,x12485,x12486,x12487,x12488,x12489,x12481),f483(x12483,x12484,x12485,x12486,x12487,x12488,x12489,x12482))
% 94.68/94.46 [1249]~E(x12491,x12492)+E(f703(x12491,x12493),f703(x12492,x12493))
% 94.68/94.46 [1250]~E(x12501,x12502)+E(f703(x12503,x12501),f703(x12503,x12502))
% 94.68/94.46 [1251]~E(x12511,x12512)+E(f216(x12511,x12513,x12514,x12515,x12516),f216(x12512,x12513,x12514,x12515,x12516))
% 94.68/94.46 [1252]~E(x12521,x12522)+E(f216(x12523,x12521,x12524,x12525,x12526),f216(x12523,x12522,x12524,x12525,x12526))
% 94.68/94.46 [1253]~E(x12531,x12532)+E(f216(x12533,x12534,x12531,x12535,x12536),f216(x12533,x12534,x12532,x12535,x12536))
% 94.68/94.46 [1254]~E(x12541,x12542)+E(f216(x12543,x12544,x12545,x12541,x12546),f216(x12543,x12544,x12545,x12542,x12546))
% 94.68/94.46 [1255]~E(x12551,x12552)+E(f216(x12553,x12554,x12555,x12556,x12551),f216(x12553,x12554,x12555,x12556,x12552))
% 94.68/94.46 [1256]~E(x12561,x12562)+E(f397(x12561),f397(x12562))
% 94.68/94.46 [1257]~E(x12571,x12572)+E(f106(x12571,x12573,x12574),f106(x12572,x12573,x12574))
% 94.68/94.46 [1258]~E(x12581,x12582)+E(f106(x12583,x12581,x12584),f106(x12583,x12582,x12584))
% 94.68/94.46 [1259]~E(x12591,x12592)+E(f106(x12593,x12594,x12591),f106(x12593,x12594,x12592))
% 94.68/94.46 [1260]~E(x12601,x12602)+E(f198(x12601),f198(x12602))
% 94.68/94.46 [1261]~E(x12611,x12612)+E(f409(x12611,x12613,x12614),f409(x12612,x12613,x12614))
% 94.68/94.46 [1262]~E(x12621,x12622)+E(f409(x12623,x12621,x12624),f409(x12623,x12622,x12624))
% 94.68/94.46 [1263]~E(x12631,x12632)+E(f409(x12633,x12634,x12631),f409(x12633,x12634,x12632))
% 94.68/94.46 [1264]~E(x12641,x12642)+E(f734(x12641,x12643,x12644),f734(x12642,x12643,x12644))
% 94.68/94.46 [1265]~E(x12651,x12652)+E(f734(x12653,x12651,x12654),f734(x12653,x12652,x12654))
% 94.68/94.46 [1266]~E(x12661,x12662)+E(f734(x12663,x12664,x12661),f734(x12663,x12664,x12662))
% 94.68/94.46 [1267]~E(x12671,x12672)+E(f146(x12671,x12673,x12674,x12675),f146(x12672,x12673,x12674,x12675))
% 94.68/94.46 [1268]~E(x12681,x12682)+E(f146(x12683,x12681,x12684,x12685),f146(x12683,x12682,x12684,x12685))
% 94.68/94.46 [1269]~E(x12691,x12692)+E(f146(x12693,x12694,x12691,x12695),f146(x12693,x12694,x12692,x12695))
% 94.68/94.46 [1270]~E(x12701,x12702)+E(f146(x12703,x12704,x12705,x12701),f146(x12703,x12704,x12705,x12702))
% 94.68/94.46 [1271]~E(x12711,x12712)+E(f311(x12711,x12713,x12714),f311(x12712,x12713,x12714))
% 94.68/94.46 [1272]~E(x12721,x12722)+E(f311(x12723,x12721,x12724),f311(x12723,x12722,x12724))
% 94.68/94.46 [1273]~E(x12731,x12732)+E(f311(x12733,x12734,x12731),f311(x12733,x12734,x12732))
% 94.68/94.46 [1274]~E(x12741,x12742)+E(f381(x12741,x12743),f381(x12742,x12743))
% 94.68/94.46 [1275]~E(x12751,x12752)+E(f381(x12753,x12751),f381(x12753,x12752))
% 94.68/94.46 [1276]~E(x12761,x12762)+E(f421(x12761,x12763),f421(x12762,x12763))
% 94.68/94.46 [1277]~E(x12771,x12772)+E(f421(x12773,x12771),f421(x12773,x12772))
% 94.68/94.46 [1278]~E(x12781,x12782)+E(f373(x12781,x12783,x12784,x12785),f373(x12782,x12783,x12784,x12785))
% 94.68/94.46 [1279]~E(x12791,x12792)+E(f373(x12793,x12791,x12794,x12795),f373(x12793,x12792,x12794,x12795))
% 94.68/94.46 [1280]~E(x12801,x12802)+E(f373(x12803,x12804,x12801,x12805),f373(x12803,x12804,x12802,x12805))
% 94.68/94.46 [1281]~E(x12811,x12812)+E(f373(x12813,x12814,x12815,x12811),f373(x12813,x12814,x12815,x12812))
% 94.68/94.46 [1282]~E(x12821,x12822)+E(f631(x12821,x12823,x12824,x12825,x12826),f631(x12822,x12823,x12824,x12825,x12826))
% 94.68/94.46 [1283]~E(x12831,x12832)+E(f631(x12833,x12831,x12834,x12835,x12836),f631(x12833,x12832,x12834,x12835,x12836))
% 94.68/94.46 [1284]~E(x12841,x12842)+E(f631(x12843,x12844,x12841,x12845,x12846),f631(x12843,x12844,x12842,x12845,x12846))
% 94.68/94.46 [1285]~E(x12851,x12852)+E(f631(x12853,x12854,x12855,x12851,x12856),f631(x12853,x12854,x12855,x12852,x12856))
% 94.68/94.46 [1286]~E(x12861,x12862)+E(f631(x12863,x12864,x12865,x12866,x12861),f631(x12863,x12864,x12865,x12866,x12862))
% 94.68/94.46 [1287]~E(x12871,x12872)+E(f208(x12871,x12873),f208(x12872,x12873))
% 94.68/94.46 [1288]~E(x12881,x12882)+E(f208(x12883,x12881),f208(x12883,x12882))
% 94.68/94.46 [1289]~E(x12891,x12892)+E(f691(x12891,x12893,x12894),f691(x12892,x12893,x12894))
% 94.68/94.46 [1290]~E(x12901,x12902)+E(f691(x12903,x12901,x12904),f691(x12903,x12902,x12904))
% 94.68/94.46 [1291]~E(x12911,x12912)+E(f691(x12913,x12914,x12911),f691(x12913,x12914,x12912))
% 94.68/94.46 [1292]~E(x12921,x12922)+E(f289(x12921,x12923,x12924,x12925),f289(x12922,x12923,x12924,x12925))
% 94.68/94.46 [1293]~E(x12931,x12932)+E(f289(x12933,x12931,x12934,x12935),f289(x12933,x12932,x12934,x12935))
% 94.68/94.46 [1294]~E(x12941,x12942)+E(f289(x12943,x12944,x12941,x12945),f289(x12943,x12944,x12942,x12945))
% 94.68/94.46 [1295]~E(x12951,x12952)+E(f289(x12953,x12954,x12955,x12951),f289(x12953,x12954,x12955,x12952))
% 94.68/94.46 [1296]~E(x12961,x12962)+E(f460(x12961,x12963,x12964),f460(x12962,x12963,x12964))
% 94.68/94.46 [1297]~E(x12971,x12972)+E(f460(x12973,x12971,x12974),f460(x12973,x12972,x12974))
% 94.68/94.46 [1298]~E(x12981,x12982)+E(f460(x12983,x12984,x12981),f460(x12983,x12984,x12982))
% 94.68/94.46 [1299]~E(x12991,x12992)+E(f630(x12991,x12993,x12994,x12995),f630(x12992,x12993,x12994,x12995))
% 94.68/94.46 [1300]~E(x13001,x13002)+E(f630(x13003,x13001,x13004,x13005),f630(x13003,x13002,x13004,x13005))
% 94.68/94.46 [1301]~E(x13011,x13012)+E(f630(x13013,x13014,x13011,x13015),f630(x13013,x13014,x13012,x13015))
% 94.68/94.46 [1302]~E(x13021,x13022)+E(f630(x13023,x13024,x13025,x13021),f630(x13023,x13024,x13025,x13022))
% 94.68/94.46 [1303]~E(x13031,x13032)+E(f186(x13031,x13033,x13034,x13035),f186(x13032,x13033,x13034,x13035))
% 94.68/94.46 [1304]~E(x13041,x13042)+E(f186(x13043,x13041,x13044,x13045),f186(x13043,x13042,x13044,x13045))
% 94.68/94.46 [1305]~E(x13051,x13052)+E(f186(x13053,x13054,x13051,x13055),f186(x13053,x13054,x13052,x13055))
% 94.68/94.46 [1306]~E(x13061,x13062)+E(f186(x13063,x13064,x13065,x13061),f186(x13063,x13064,x13065,x13062))
% 94.68/94.46 [1307]~E(x13071,x13072)+E(f482(x13071,x13073,x13074,x13075,x13076,x13077,x13078,x13079),f482(x13072,x13073,x13074,x13075,x13076,x13077,x13078,x13079))
% 94.68/94.46 [1308]~E(x13081,x13082)+E(f482(x13083,x13081,x13084,x13085,x13086,x13087,x13088,x13089),f482(x13083,x13082,x13084,x13085,x13086,x13087,x13088,x13089))
% 94.68/94.46 [1309]~E(x13091,x13092)+E(f482(x13093,x13094,x13091,x13095,x13096,x13097,x13098,x13099),f482(x13093,x13094,x13092,x13095,x13096,x13097,x13098,x13099))
% 94.68/94.46 [1310]~E(x13101,x13102)+E(f482(x13103,x13104,x13105,x13101,x13106,x13107,x13108,x13109),f482(x13103,x13104,x13105,x13102,x13106,x13107,x13108,x13109))
% 94.68/94.46 [1311]~E(x13111,x13112)+E(f482(x13113,x13114,x13115,x13116,x13111,x13117,x13118,x13119),f482(x13113,x13114,x13115,x13116,x13112,x13117,x13118,x13119))
% 94.68/94.46 [1312]~E(x13121,x13122)+E(f482(x13123,x13124,x13125,x13126,x13127,x13121,x13128,x13129),f482(x13123,x13124,x13125,x13126,x13127,x13122,x13128,x13129))
% 94.68/94.46 [1313]~E(x13131,x13132)+E(f482(x13133,x13134,x13135,x13136,x13137,x13138,x13131,x13139),f482(x13133,x13134,x13135,x13136,x13137,x13138,x13132,x13139))
% 94.68/94.46 [1314]~E(x13141,x13142)+E(f482(x13143,x13144,x13145,x13146,x13147,x13148,x13149,x13141),f482(x13143,x13144,x13145,x13146,x13147,x13148,x13149,x13142))
% 94.68/94.46 [1315]~E(x13151,x13152)+E(f608(x13151,x13153,x13154,x13155),f608(x13152,x13153,x13154,x13155))
% 94.68/94.46 [1316]~E(x13161,x13162)+E(f608(x13163,x13161,x13164,x13165),f608(x13163,x13162,x13164,x13165))
% 94.68/94.46 [1317]~E(x13171,x13172)+E(f608(x13173,x13174,x13171,x13175),f608(x13173,x13174,x13172,x13175))
% 94.68/94.46 [1318]~E(x13181,x13182)+E(f608(x13183,x13184,x13185,x13181),f608(x13183,x13184,x13185,x13182))
% 94.68/94.46 [1319]~E(x13191,x13192)+E(f561(x13191,x13193,x13194),f561(x13192,x13193,x13194))
% 94.68/94.46 [1320]~E(x13201,x13202)+E(f561(x13203,x13201,x13204),f561(x13203,x13202,x13204))
% 94.68/94.46 [1321]~E(x13211,x13212)+E(f561(x13213,x13214,x13211),f561(x13213,x13214,x13212))
% 94.68/94.46 [1322]~E(x13221,x13222)+E(f199(x13221,x13223,x13224,x13225),f199(x13222,x13223,x13224,x13225))
% 94.68/94.46 [1323]~E(x13231,x13232)+E(f199(x13233,x13231,x13234,x13235),f199(x13233,x13232,x13234,x13235))
% 94.68/94.46 [1324]~E(x13241,x13242)+E(f199(x13243,x13244,x13241,x13245),f199(x13243,x13244,x13242,x13245))
% 94.68/94.46 [1325]~E(x13251,x13252)+E(f199(x13253,x13254,x13255,x13251),f199(x13253,x13254,x13255,x13252))
% 94.68/94.46 [1326]~E(x13261,x13262)+E(f675(x13261,x13263),f675(x13262,x13263))
% 94.68/94.46 [1327]~E(x13271,x13272)+E(f675(x13273,x13271),f675(x13273,x13272))
% 94.68/94.46 [1328]~E(x13281,x13282)+E(f576(x13281,x13283,x13284,x13285),f576(x13282,x13283,x13284,x13285))
% 94.68/94.46 [1329]~E(x13291,x13292)+E(f576(x13293,x13291,x13294,x13295),f576(x13293,x13292,x13294,x13295))
% 94.68/94.46 [1330]~E(x13301,x13302)+E(f576(x13303,x13304,x13301,x13305),f576(x13303,x13304,x13302,x13305))
% 94.68/94.46 [1331]~E(x13311,x13312)+E(f576(x13313,x13314,x13315,x13311),f576(x13313,x13314,x13315,x13312))
% 94.68/94.46 [1332]~E(x13321,x13322)+E(f865(x13321,x13323,x13324),f865(x13322,x13323,x13324))
% 94.68/94.46 [1333]~E(x13331,x13332)+E(f865(x13333,x13331,x13334),f865(x13333,x13332,x13334))
% 94.68/94.46 [1334]~E(x13341,x13342)+E(f865(x13343,x13344,x13341),f865(x13343,x13344,x13342))
% 94.68/94.46 [1335]~E(x13351,x13352)+E(f813(x13351,x13353,x13354),f813(x13352,x13353,x13354))
% 94.68/94.46 [1336]~E(x13361,x13362)+E(f813(x13363,x13361,x13364),f813(x13363,x13362,x13364))
% 94.68/94.46 [1337]~E(x13371,x13372)+E(f813(x13373,x13374,x13371),f813(x13373,x13374,x13372))
% 94.68/94.46 [1338]~E(x13381,x13382)+E(f21(x13381,x13383),f21(x13382,x13383))
% 94.68/94.46 [1339]~E(x13391,x13392)+E(f21(x13393,x13391),f21(x13393,x13392))
% 94.68/94.46 [1340]~E(x13401,x13402)+E(f380(x13401,x13403),f380(x13402,x13403))
% 94.68/94.46 [1341]~E(x13411,x13412)+E(f380(x13413,x13411),f380(x13413,x13412))
% 94.68/94.46 [1342]~E(x13421,x13422)+E(f269(x13421,x13423,x13424,x13425),f269(x13422,x13423,x13424,x13425))
% 94.68/94.46 [1343]~E(x13431,x13432)+E(f269(x13433,x13431,x13434,x13435),f269(x13433,x13432,x13434,x13435))
% 94.68/94.46 [1344]~E(x13441,x13442)+E(f269(x13443,x13444,x13441,x13445),f269(x13443,x13444,x13442,x13445))
% 94.68/94.46 [1345]~E(x13451,x13452)+E(f269(x13453,x13454,x13455,x13451),f269(x13453,x13454,x13455,x13452))
% 94.68/94.46 [1346]~E(x13461,x13462)+E(f411(x13461,x13463,x13464,x13465),f411(x13462,x13463,x13464,x13465))
% 94.68/94.46 [1347]~E(x13471,x13472)+E(f411(x13473,x13471,x13474,x13475),f411(x13473,x13472,x13474,x13475))
% 94.68/94.46 [1348]~E(x13481,x13482)+E(f411(x13483,x13484,x13481,x13485),f411(x13483,x13484,x13482,x13485))
% 94.68/94.46 [1349]~E(x13491,x13492)+E(f411(x13493,x13494,x13495,x13491),f411(x13493,x13494,x13495,x13492))
% 94.68/94.46 [1350]~E(x13501,x13502)+E(f473(x13501,x13503,x13504,x13505,x13506,x13507),f473(x13502,x13503,x13504,x13505,x13506,x13507))
% 94.68/94.46 [1351]~E(x13511,x13512)+E(f473(x13513,x13511,x13514,x13515,x13516,x13517),f473(x13513,x13512,x13514,x13515,x13516,x13517))
% 94.68/94.46 [1352]~E(x13521,x13522)+E(f473(x13523,x13524,x13521,x13525,x13526,x13527),f473(x13523,x13524,x13522,x13525,x13526,x13527))
% 94.68/94.46 [1353]~E(x13531,x13532)+E(f473(x13533,x13534,x13535,x13531,x13536,x13537),f473(x13533,x13534,x13535,x13532,x13536,x13537))
% 94.68/94.46 [1354]~E(x13541,x13542)+E(f473(x13543,x13544,x13545,x13546,x13541,x13547),f473(x13543,x13544,x13545,x13546,x13542,x13547))
% 94.68/94.46 [1355]~E(x13551,x13552)+E(f473(x13553,x13554,x13555,x13556,x13557,x13551),f473(x13553,x13554,x13555,x13556,x13557,x13552))
% 94.68/94.46 [1356]~E(x13561,x13562)+E(f415(x13561,x13563,x13564,x13565,x13566),f415(x13562,x13563,x13564,x13565,x13566))
% 94.68/94.46 [1357]~E(x13571,x13572)+E(f415(x13573,x13571,x13574,x13575,x13576),f415(x13573,x13572,x13574,x13575,x13576))
% 94.68/94.46 [1358]~E(x13581,x13582)+E(f415(x13583,x13584,x13581,x13585,x13586),f415(x13583,x13584,x13582,x13585,x13586))
% 94.68/94.46 [1359]~E(x13591,x13592)+E(f415(x13593,x13594,x13595,x13591,x13596),f415(x13593,x13594,x13595,x13592,x13596))
% 94.68/94.46 [1360]~E(x13601,x13602)+E(f415(x13603,x13604,x13605,x13606,x13601),f415(x13603,x13604,x13605,x13606,x13602))
% 94.68/94.46 [1361]~E(x13611,x13612)+E(f668(x13611,x13613,x13614),f668(x13612,x13613,x13614))
% 94.68/94.46 [1362]~E(x13621,x13622)+E(f668(x13623,x13621,x13624),f668(x13623,x13622,x13624))
% 94.68/94.46 [1363]~E(x13631,x13632)+E(f668(x13633,x13634,x13631),f668(x13633,x13634,x13632))
% 94.68/94.46 [1364]~E(x13641,x13642)+E(f753(x13641,x13643,x13644,x13645,x13646),f753(x13642,x13643,x13644,x13645,x13646))
% 94.68/94.46 [1365]~E(x13651,x13652)+E(f753(x13653,x13651,x13654,x13655,x13656),f753(x13653,x13652,x13654,x13655,x13656))
% 94.68/94.46 [1366]~E(x13661,x13662)+E(f753(x13663,x13664,x13661,x13665,x13666),f753(x13663,x13664,x13662,x13665,x13666))
% 94.68/94.46 [1367]~E(x13671,x13672)+E(f753(x13673,x13674,x13675,x13671,x13676),f753(x13673,x13674,x13675,x13672,x13676))
% 94.68/94.46 [1368]~E(x13681,x13682)+E(f753(x13683,x13684,x13685,x13686,x13681),f753(x13683,x13684,x13685,x13686,x13682))
% 94.68/94.46 [1369]~E(x13691,x13692)+E(f625(x13691,x13693,x13694,x13695,x13696,x13697),f625(x13692,x13693,x13694,x13695,x13696,x13697))
% 94.68/94.46 [1370]~E(x13701,x13702)+E(f625(x13703,x13701,x13704,x13705,x13706,x13707),f625(x13703,x13702,x13704,x13705,x13706,x13707))
% 94.68/94.46 [1371]~E(x13711,x13712)+E(f625(x13713,x13714,x13711,x13715,x13716,x13717),f625(x13713,x13714,x13712,x13715,x13716,x13717))
% 94.68/94.46 [1372]~E(x13721,x13722)+E(f625(x13723,x13724,x13725,x13721,x13726,x13727),f625(x13723,x13724,x13725,x13722,x13726,x13727))
% 94.68/94.46 [1373]~E(x13731,x13732)+E(f625(x13733,x13734,x13735,x13736,x13731,x13737),f625(x13733,x13734,x13735,x13736,x13732,x13737))
% 94.68/94.46 [1374]~E(x13741,x13742)+E(f625(x13743,x13744,x13745,x13746,x13747,x13741),f625(x13743,x13744,x13745,x13746,x13747,x13742))
% 94.68/94.46 [1375]~E(x13751,x13752)+E(f713(x13751,x13753,x13754,x13755),f713(x13752,x13753,x13754,x13755))
% 94.68/94.46 [1376]~E(x13761,x13762)+E(f713(x13763,x13761,x13764,x13765),f713(x13763,x13762,x13764,x13765))
% 94.68/94.46 [1377]~E(x13771,x13772)+E(f713(x13773,x13774,x13771,x13775),f713(x13773,x13774,x13772,x13775))
% 94.68/94.46 [1378]~E(x13781,x13782)+E(f713(x13783,x13784,x13785,x13781),f713(x13783,x13784,x13785,x13782))
% 94.68/94.46 [1379]~E(x13791,x13792)+E(f600(x13791,x13793,x13794),f600(x13792,x13793,x13794))
% 94.68/94.46 [1380]~E(x13801,x13802)+E(f600(x13803,x13801,x13804),f600(x13803,x13802,x13804))
% 94.68/94.46 [1381]~E(x13811,x13812)+E(f600(x13813,x13814,x13811),f600(x13813,x13814,x13812))
% 94.68/94.46 [1382]~E(x13821,x13822)+E(f481(x13821,x13823,x13824,x13825,x13826),f481(x13822,x13823,x13824,x13825,x13826))
% 94.68/94.46 [1383]~E(x13831,x13832)+E(f481(x13833,x13831,x13834,x13835,x13836),f481(x13833,x13832,x13834,x13835,x13836))
% 94.68/94.46 [1384]~E(x13841,x13842)+E(f481(x13843,x13844,x13841,x13845,x13846),f481(x13843,x13844,x13842,x13845,x13846))
% 94.68/94.46 [1385]~E(x13851,x13852)+E(f481(x13853,x13854,x13855,x13851,x13856),f481(x13853,x13854,x13855,x13852,x13856))
% 94.68/94.46 [1386]~E(x13861,x13862)+E(f481(x13863,x13864,x13865,x13866,x13861),f481(x13863,x13864,x13865,x13866,x13862))
% 94.68/94.46 [1387]~E(x13871,x13872)+E(f839(x13871,x13873,x13874,x13875),f839(x13872,x13873,x13874,x13875))
% 94.68/94.46 [1388]~E(x13881,x13882)+E(f839(x13883,x13881,x13884,x13885),f839(x13883,x13882,x13884,x13885))
% 94.68/94.46 [1389]~E(x13891,x13892)+E(f839(x13893,x13894,x13891,x13895),f839(x13893,x13894,x13892,x13895))
% 94.68/94.46 [1390]~E(x13901,x13902)+E(f839(x13903,x13904,x13905,x13901),f839(x13903,x13904,x13905,x13902))
% 94.68/94.46 [1391]~E(x13911,x13912)+E(f121(x13911,x13913,x13914,x13915),f121(x13912,x13913,x13914,x13915))
% 94.68/94.46 [1392]~E(x13921,x13922)+E(f121(x13923,x13921,x13924,x13925),f121(x13923,x13922,x13924,x13925))
% 94.68/94.46 [1393]~E(x13931,x13932)+E(f121(x13933,x13934,x13931,x13935),f121(x13933,x13934,x13932,x13935))
% 94.68/94.46 [1394]~E(x13941,x13942)+E(f121(x13943,x13944,x13945,x13941),f121(x13943,x13944,x13945,x13942))
% 94.68/94.46 [1395]~E(x13951,x13952)+E(f794(x13951,x13953,x13954,x13955,x13956,x13957),f794(x13952,x13953,x13954,x13955,x13956,x13957))
% 94.68/94.46 [1396]~E(x13961,x13962)+E(f794(x13963,x13961,x13964,x13965,x13966,x13967),f794(x13963,x13962,x13964,x13965,x13966,x13967))
% 94.68/94.46 [1397]~E(x13971,x13972)+E(f794(x13973,x13974,x13971,x13975,x13976,x13977),f794(x13973,x13974,x13972,x13975,x13976,x13977))
% 94.68/94.46 [1398]~E(x13981,x13982)+E(f794(x13983,x13984,x13985,x13981,x13986,x13987),f794(x13983,x13984,x13985,x13982,x13986,x13987))
% 94.68/94.46 [1399]~E(x13991,x13992)+E(f794(x13993,x13994,x13995,x13996,x13991,x13997),f794(x13993,x13994,x13995,x13996,x13992,x13997))
% 94.68/94.46 [1400]~E(x14001,x14002)+E(f794(x14003,x14004,x14005,x14006,x14007,x14001),f794(x14003,x14004,x14005,x14006,x14007,x14002))
% 94.68/94.46 [1401]~E(x14011,x14012)+E(f747(x14011,x14013,x14014),f747(x14012,x14013,x14014))
% 94.68/94.46 [1402]~E(x14021,x14022)+E(f747(x14023,x14021,x14024),f747(x14023,x14022,x14024))
% 94.68/94.46 [1403]~E(x14031,x14032)+E(f747(x14033,x14034,x14031),f747(x14033,x14034,x14032))
% 94.68/94.46 [1404]~E(x14041,x14042)+E(f238(x14041,x14043),f238(x14042,x14043))
% 94.68/94.46 [1405]~E(x14051,x14052)+E(f238(x14053,x14051),f238(x14053,x14052))
% 94.68/94.46 [1406]~E(x14061,x14062)+E(f663(x14061,x14063,x14064,x14065),f663(x14062,x14063,x14064,x14065))
% 94.68/94.46 [1407]~E(x14071,x14072)+E(f663(x14073,x14071,x14074,x14075),f663(x14073,x14072,x14074,x14075))
% 94.68/94.46 [1408]~E(x14081,x14082)+E(f663(x14083,x14084,x14081,x14085),f663(x14083,x14084,x14082,x14085))
% 94.68/94.46 [1409]~E(x14091,x14092)+E(f663(x14093,x14094,x14095,x14091),f663(x14093,x14094,x14095,x14092))
% 94.68/94.46 [1410]~E(x14101,x14102)+E(f470(x14101),f470(x14102))
% 94.68/94.46 [1411]~E(x14111,x14112)+E(f468(x14111,x14113,x14114),f468(x14112,x14113,x14114))
% 94.68/94.46 [1412]~E(x14121,x14122)+E(f468(x14123,x14121,x14124),f468(x14123,x14122,x14124))
% 94.68/94.46 [1413]~E(x14131,x14132)+E(f468(x14133,x14134,x14131),f468(x14133,x14134,x14132))
% 94.68/94.46 [1414]~E(x14141,x14142)+E(f435(x14141,x14143,x14144),f435(x14142,x14143,x14144))
% 94.68/94.46 [1415]~E(x14151,x14152)+E(f435(x14153,x14151,x14154),f435(x14153,x14152,x14154))
% 94.68/94.46 [1416]~E(x14161,x14162)+E(f435(x14163,x14164,x14161),f435(x14163,x14164,x14162))
% 94.68/94.46 [1417]~E(x14171,x14172)+E(f185(x14171,x14173,x14174,x14175),f185(x14172,x14173,x14174,x14175))
% 94.68/94.46 [1418]~E(x14181,x14182)+E(f185(x14183,x14181,x14184,x14185),f185(x14183,x14182,x14184,x14185))
% 94.68/94.46 [1419]~E(x14191,x14192)+E(f185(x14193,x14194,x14191,x14195),f185(x14193,x14194,x14192,x14195))
% 94.68/94.46 [1420]~E(x14201,x14202)+E(f185(x14203,x14204,x14205,x14201),f185(x14203,x14204,x14205,x14202))
% 94.68/94.46 [1421]~E(x14211,x14212)+E(f125(x14211),f125(x14212))
% 94.68/94.46 [1422]~E(x14221,x14222)+E(f430(x14221,x14223,x14224,x14225),f430(x14222,x14223,x14224,x14225))
% 94.68/94.46 [1423]~E(x14231,x14232)+E(f430(x14233,x14231,x14234,x14235),f430(x14233,x14232,x14234,x14235))
% 94.68/94.46 [1424]~E(x14241,x14242)+E(f430(x14243,x14244,x14241,x14245),f430(x14243,x14244,x14242,x14245))
% 94.68/94.46 [1425]~E(x14251,x14252)+E(f430(x14253,x14254,x14255,x14251),f430(x14253,x14254,x14255,x14252))
% 94.68/94.46 [1426]~E(x14261,x14262)+E(f593(x14261,x14263,x14264),f593(x14262,x14263,x14264))
% 94.68/94.46 [1427]~E(x14271,x14272)+E(f593(x14273,x14271,x14274),f593(x14273,x14272,x14274))
% 94.68/94.46 [1428]~E(x14281,x14282)+E(f593(x14283,x14284,x14281),f593(x14283,x14284,x14282))
% 94.68/94.46 [1429]~E(x14291,x14292)+E(f808(x14291,x14293,x14294),f808(x14292,x14293,x14294))
% 94.68/94.46 [1430]~E(x14301,x14302)+E(f808(x14303,x14301,x14304),f808(x14303,x14302,x14304))
% 94.68/94.46 [1431]~E(x14311,x14312)+E(f808(x14313,x14314,x14311),f808(x14313,x14314,x14312))
% 94.68/94.46 [1432]~E(x14321,x14322)+E(f347(x14321,x14323,x14324),f347(x14322,x14323,x14324))
% 94.68/94.46 [1433]~E(x14331,x14332)+E(f347(x14333,x14331,x14334),f347(x14333,x14332,x14334))
% 94.68/94.46 [1434]~E(x14341,x14342)+E(f347(x14343,x14344,x14341),f347(x14343,x14344,x14342))
% 94.68/94.46 [1435]~E(x14351,x14352)+E(f881(x14351,x14353,x14354),f881(x14352,x14353,x14354))
% 94.68/94.46 [1436]~E(x14361,x14362)+E(f881(x14363,x14361,x14364),f881(x14363,x14362,x14364))
% 94.68/94.46 [1437]~E(x14371,x14372)+E(f881(x14373,x14374,x14371),f881(x14373,x14374,x14372))
% 94.68/94.46 [1438]~E(x14381,x14382)+E(f476(x14381,x14383,x14384,x14385,x14386,x14387),f476(x14382,x14383,x14384,x14385,x14386,x14387))
% 94.68/94.46 [1439]~E(x14391,x14392)+E(f476(x14393,x14391,x14394,x14395,x14396,x14397),f476(x14393,x14392,x14394,x14395,x14396,x14397))
% 94.68/94.46 [1440]~E(x14401,x14402)+E(f476(x14403,x14404,x14401,x14405,x14406,x14407),f476(x14403,x14404,x14402,x14405,x14406,x14407))
% 94.68/94.46 [1441]~E(x14411,x14412)+E(f476(x14413,x14414,x14415,x14411,x14416,x14417),f476(x14413,x14414,x14415,x14412,x14416,x14417))
% 94.68/94.46 [1442]~E(x14421,x14422)+E(f476(x14423,x14424,x14425,x14426,x14421,x14427),f476(x14423,x14424,x14425,x14426,x14422,x14427))
% 94.68/94.46 [1443]~E(x14431,x14432)+E(f476(x14433,x14434,x14435,x14436,x14437,x14431),f476(x14433,x14434,x14435,x14436,x14437,x14432))
% 94.68/94.46 [1444]~E(x14441,x14442)+E(f509(x14441,x14443,x14444),f509(x14442,x14443,x14444))
% 94.68/94.46 [1445]~E(x14451,x14452)+E(f509(x14453,x14451,x14454),f509(x14453,x14452,x14454))
% 94.68/94.46 [1446]~E(x14461,x14462)+E(f509(x14463,x14464,x14461),f509(x14463,x14464,x14462))
% 94.68/94.46 [1447]~E(x14471,x14472)+E(f267(x14471,x14473,x14474,x14475),f267(x14472,x14473,x14474,x14475))
% 94.68/94.46 [1448]~E(x14481,x14482)+E(f267(x14483,x14481,x14484,x14485),f267(x14483,x14482,x14484,x14485))
% 94.68/94.46 [1449]~E(x14491,x14492)+E(f267(x14493,x14494,x14491,x14495),f267(x14493,x14494,x14492,x14495))
% 94.68/94.46 [1450]~E(x14501,x14502)+E(f267(x14503,x14504,x14505,x14501),f267(x14503,x14504,x14505,x14502))
% 94.68/94.46 [1451]~E(x14511,x14512)+E(f674(x14511,x14513),f674(x14512,x14513))
% 94.68/94.46 [1452]~E(x14521,x14522)+E(f674(x14523,x14521),f674(x14523,x14522))
% 94.68/94.46 [1453]~E(x14531,x14532)+E(f388(x14531,x14533,x14534,x14535),f388(x14532,x14533,x14534,x14535))
% 94.68/94.46 [1454]~E(x14541,x14542)+E(f388(x14543,x14541,x14544,x14545),f388(x14543,x14542,x14544,x14545))
% 94.68/94.46 [1455]~E(x14551,x14552)+E(f388(x14553,x14554,x14551,x14555),f388(x14553,x14554,x14552,x14555))
% 94.68/94.46 [1456]~E(x14561,x14562)+E(f388(x14563,x14564,x14565,x14561),f388(x14563,x14564,x14565,x14562))
% 94.68/94.46 [1457]~E(x14571,x14572)+E(f261(x14571,x14573,x14574,x14575),f261(x14572,x14573,x14574,x14575))
% 94.68/94.46 [1458]~E(x14581,x14582)+E(f261(x14583,x14581,x14584,x14585),f261(x14583,x14582,x14584,x14585))
% 94.68/94.46 [1459]~E(x14591,x14592)+E(f261(x14593,x14594,x14591,x14595),f261(x14593,x14594,x14592,x14595))
% 94.68/94.46 [1460]~E(x14601,x14602)+E(f261(x14603,x14604,x14605,x14601),f261(x14603,x14604,x14605,x14602))
% 94.68/94.46 [1461]~E(x14611,x14612)+E(f69(x14611,x14613,x14614,x14615,x14616),f69(x14612,x14613,x14614,x14615,x14616))
% 94.68/94.46 [1462]~E(x14621,x14622)+E(f69(x14623,x14621,x14624,x14625,x14626),f69(x14623,x14622,x14624,x14625,x14626))
% 94.68/94.46 [1463]~E(x14631,x14632)+E(f69(x14633,x14634,x14631,x14635,x14636),f69(x14633,x14634,x14632,x14635,x14636))
% 94.68/94.46 [1464]~E(x14641,x14642)+E(f69(x14643,x14644,x14645,x14641,x14646),f69(x14643,x14644,x14645,x14642,x14646))
% 94.68/94.46 [1465]~E(x14651,x14652)+E(f69(x14653,x14654,x14655,x14656,x14651),f69(x14653,x14654,x14655,x14656,x14652))
% 94.68/94.46 [1466]~E(x14661,x14662)+E(f71(x14661,x14663,x14664,x14665),f71(x14662,x14663,x14664,x14665))
% 94.68/94.46 [1467]~E(x14671,x14672)+E(f71(x14673,x14671,x14674,x14675),f71(x14673,x14672,x14674,x14675))
% 94.68/94.46 [1468]~E(x14681,x14682)+E(f71(x14683,x14684,x14681,x14685),f71(x14683,x14684,x14682,x14685))
% 94.68/94.46 [1469]~E(x14691,x14692)+E(f71(x14693,x14694,x14695,x14691),f71(x14693,x14694,x14695,x14692))
% 94.68/94.46 [1470]~E(x14701,x14702)+E(f768(x14701,x14703),f768(x14702,x14703))
% 94.68/94.46 [1471]~E(x14711,x14712)+E(f768(x14713,x14711),f768(x14713,x14712))
% 94.68/94.46 [1472]~E(x14721,x14722)+E(f410(x14721,x14723,x14724,x14725),f410(x14722,x14723,x14724,x14725))
% 94.68/94.46 [1473]~E(x14731,x14732)+E(f410(x14733,x14731,x14734,x14735),f410(x14733,x14732,x14734,x14735))
% 94.68/94.46 [1474]~E(x14741,x14742)+E(f410(x14743,x14744,x14741,x14745),f410(x14743,x14744,x14742,x14745))
% 94.68/94.46 [1475]~E(x14751,x14752)+E(f410(x14753,x14754,x14755,x14751),f410(x14753,x14754,x14755,x14752))
% 94.68/94.46 [1476]~E(x14761,x14762)+E(f681(x14761,x14763,x14764),f681(x14762,x14763,x14764))
% 94.68/94.46 [1477]~E(x14771,x14772)+E(f681(x14773,x14771,x14774),f681(x14773,x14772,x14774))
% 94.68/94.46 [1478]~E(x14781,x14782)+E(f681(x14783,x14784,x14781),f681(x14783,x14784,x14782))
% 94.68/94.46 [1479]~E(x14791,x14792)+E(f644(x14791,x14793),f644(x14792,x14793))
% 94.68/94.46 [1480]~E(x14801,x14802)+E(f644(x14803,x14801),f644(x14803,x14802))
% 94.68/94.46 [1481]~E(x14811,x14812)+E(f366(x14811,x14813,x14814,x14815),f366(x14812,x14813,x14814,x14815))
% 94.68/94.46 [1482]~E(x14821,x14822)+E(f366(x14823,x14821,x14824,x14825),f366(x14823,x14822,x14824,x14825))
% 94.68/94.46 [1483]~E(x14831,x14832)+E(f366(x14833,x14834,x14831,x14835),f366(x14833,x14834,x14832,x14835))
% 94.68/94.46 [1484]~E(x14841,x14842)+E(f366(x14843,x14844,x14845,x14841),f366(x14843,x14844,x14845,x14842))
% 94.68/94.46 [1485]~E(x14851,x14852)+E(f467(x14851,x14853,x14854),f467(x14852,x14853,x14854))
% 94.68/94.46 [1486]~E(x14861,x14862)+E(f467(x14863,x14861,x14864),f467(x14863,x14862,x14864))
% 94.68/94.46 [1487]~E(x14871,x14872)+E(f467(x14873,x14874,x14871),f467(x14873,x14874,x14872))
% 94.68/94.46 [1488]~E(x14881,x14882)+E(f725(x14881,x14883,x14884,x14885,x14886),f725(x14882,x14883,x14884,x14885,x14886))
% 94.68/94.46 [1489]~E(x14891,x14892)+E(f725(x14893,x14891,x14894,x14895,x14896),f725(x14893,x14892,x14894,x14895,x14896))
% 94.68/94.46 [1490]~E(x14901,x14902)+E(f725(x14903,x14904,x14901,x14905,x14906),f725(x14903,x14904,x14902,x14905,x14906))
% 94.68/94.46 [1491]~E(x14911,x14912)+E(f725(x14913,x14914,x14915,x14911,x14916),f725(x14913,x14914,x14915,x14912,x14916))
% 94.68/94.46 [1492]~E(x14921,x14922)+E(f725(x14923,x14924,x14925,x14926,x14921),f725(x14923,x14924,x14925,x14926,x14922))
% 94.68/94.46 [1493]~E(x14931,x14932)+E(f556(x14931,x14933,x14934),f556(x14932,x14933,x14934))
% 94.68/94.46 [1494]~E(x14941,x14942)+E(f556(x14943,x14941,x14944),f556(x14943,x14942,x14944))
% 94.68/94.46 [1495]~E(x14951,x14952)+E(f556(x14953,x14954,x14951),f556(x14953,x14954,x14952))
% 94.68/94.46 [1496]~E(x14961,x14962)+E(f708(x14961,x14963),f708(x14962,x14963))
% 94.68/94.46 [1497]~E(x14971,x14972)+E(f708(x14973,x14971),f708(x14973,x14972))
% 94.68/94.46 [1498]~E(x14981,x14982)+E(f295(x14981,x14983,x14984),f295(x14982,x14983,x14984))
% 94.68/94.46 [1499]~E(x14991,x14992)+E(f295(x14993,x14991,x14994),f295(x14993,x14992,x14994))
% 94.68/94.46 [1500]~E(x15001,x15002)+E(f295(x15003,x15004,x15001),f295(x15003,x15004,x15002))
% 94.68/94.46 [1501]~E(x15011,x15012)+E(f705(x15011,x15013),f705(x15012,x15013))
% 94.68/94.46 [1502]~E(x15021,x15022)+E(f705(x15023,x15021),f705(x15023,x15022))
% 94.68/94.46 [1503]~E(x15031,x15032)+E(f180(x15031,x15033,x15034,x15035),f180(x15032,x15033,x15034,x15035))
% 94.68/94.46 [1504]~E(x15041,x15042)+E(f180(x15043,x15041,x15044,x15045),f180(x15043,x15042,x15044,x15045))
% 94.68/94.46 [1505]~E(x15051,x15052)+E(f180(x15053,x15054,x15051,x15055),f180(x15053,x15054,x15052,x15055))
% 94.68/94.46 [1506]~E(x15061,x15062)+E(f180(x15063,x15064,x15065,x15061),f180(x15063,x15064,x15065,x15062))
% 94.68/94.46 [1507]~E(x15071,x15072)+E(f392(x15071,x15073,x15074),f392(x15072,x15073,x15074))
% 94.68/94.46 [1508]~E(x15081,x15082)+E(f392(x15083,x15081,x15084),f392(x15083,x15082,x15084))
% 94.68/94.46 [1509]~E(x15091,x15092)+E(f392(x15093,x15094,x15091),f392(x15093,x15094,x15092))
% 94.68/94.46 [1510]~E(x15101,x15102)+E(f683(x15101,x15103),f683(x15102,x15103))
% 94.68/94.46 [1511]~E(x15111,x15112)+E(f683(x15113,x15111),f683(x15113,x15112))
% 94.68/94.46 [1512]~E(x15121,x15122)+E(f194(x15121),f194(x15122))
% 94.68/94.46 [1513]~E(x15131,x15132)+E(f876(x15131,x15133),f876(x15132,x15133))
% 94.68/94.46 [1514]~E(x15141,x15142)+E(f876(x15143,x15141),f876(x15143,x15142))
% 94.68/94.46 [1515]~E(x15151,x15152)+E(f856(x15151,x15153,x15154),f856(x15152,x15153,x15154))
% 94.68/94.46 [1516]~E(x15161,x15162)+E(f856(x15163,x15161,x15164),f856(x15163,x15162,x15164))
% 94.68/94.46 [1517]~E(x15171,x15172)+E(f856(x15173,x15174,x15171),f856(x15173,x15174,x15172))
% 94.68/94.46 [1518]~E(x15181,x15182)+E(f640(x15181,x15183,x15184),f640(x15182,x15183,x15184))
% 94.68/94.46 [1519]~E(x15191,x15192)+E(f640(x15193,x15191,x15194),f640(x15193,x15192,x15194))
% 94.68/94.46 [1520]~E(x15201,x15202)+E(f640(x15203,x15204,x15201),f640(x15203,x15204,x15202))
% 94.68/94.46 [1521]~E(x15211,x15212)+E(f607(x15211,x15213,x15214,x15215,x15216,x15217,x15218),f607(x15212,x15213,x15214,x15215,x15216,x15217,x15218))
% 94.68/94.46 [1522]~E(x15221,x15222)+E(f607(x15223,x15221,x15224,x15225,x15226,x15227,x15228),f607(x15223,x15222,x15224,x15225,x15226,x15227,x15228))
% 94.68/94.46 [1523]~E(x15231,x15232)+E(f607(x15233,x15234,x15231,x15235,x15236,x15237,x15238),f607(x15233,x15234,x15232,x15235,x15236,x15237,x15238))
% 94.68/94.46 [1524]~E(x15241,x15242)+E(f607(x15243,x15244,x15245,x15241,x15246,x15247,x15248),f607(x15243,x15244,x15245,x15242,x15246,x15247,x15248))
% 94.68/94.46 [1525]~E(x15251,x15252)+E(f607(x15253,x15254,x15255,x15256,x15251,x15257,x15258),f607(x15253,x15254,x15255,x15256,x15252,x15257,x15258))
% 94.68/94.46 [1526]~E(x15261,x15262)+E(f607(x15263,x15264,x15265,x15266,x15267,x15261,x15268),f607(x15263,x15264,x15265,x15266,x15267,x15262,x15268))
% 94.68/94.46 [1527]~E(x15271,x15272)+E(f607(x15273,x15274,x15275,x15276,x15277,x15278,x15271),f607(x15273,x15274,x15275,x15276,x15277,x15278,x15272))
% 94.68/94.46 [1528]~E(x15281,x15282)+E(f503(x15281,x15283,x15284),f503(x15282,x15283,x15284))
% 94.68/94.46 [1529]~E(x15291,x15292)+E(f503(x15293,x15291,x15294),f503(x15293,x15292,x15294))
% 94.68/94.46 [1530]~E(x15301,x15302)+E(f503(x15303,x15304,x15301),f503(x15303,x15304,x15302))
% 94.68/94.46 [1531]~E(x15311,x15312)+E(f484(x15311,x15313,x15314),f484(x15312,x15313,x15314))
% 94.68/94.46 [1532]~E(x15321,x15322)+E(f484(x15323,x15321,x15324),f484(x15323,x15322,x15324))
% 94.68/94.46 [1533]~E(x15331,x15332)+E(f484(x15333,x15334,x15331),f484(x15333,x15334,x15332))
% 94.68/94.46 [1534]~E(x15341,x15342)+E(f286(x15341,x15343,x15344),f286(x15342,x15343,x15344))
% 94.68/94.46 [1535]~E(x15351,x15352)+E(f286(x15353,x15351,x15354),f286(x15353,x15352,x15354))
% 94.68/94.46 [1536]~E(x15361,x15362)+E(f286(x15363,x15364,x15361),f286(x15363,x15364,x15362))
% 94.68/94.46 [1537]~E(x15371,x15372)+E(f602(x15371,x15373,x15374),f602(x15372,x15373,x15374))
% 94.68/94.46 [1538]~E(x15381,x15382)+E(f602(x15383,x15381,x15384),f602(x15383,x15382,x15384))
% 94.68/94.46 [1539]~E(x15391,x15392)+E(f602(x15393,x15394,x15391),f602(x15393,x15394,x15392))
% 94.68/94.46 [1540]~E(x15401,x15402)+E(f580(x15401,x15403,x15404),f580(x15402,x15403,x15404))
% 94.68/94.46 [1541]~E(x15411,x15412)+E(f580(x15413,x15411,x15414),f580(x15413,x15412,x15414))
% 94.68/94.46 [1542]~E(x15421,x15422)+E(f580(x15423,x15424,x15421),f580(x15423,x15424,x15422))
% 94.68/94.46 [1543]~E(x15431,x15432)+E(f443(x15431,x15433,x15434,x15435,x15436),f443(x15432,x15433,x15434,x15435,x15436))
% 94.68/94.46 [1544]~E(x15441,x15442)+E(f443(x15443,x15441,x15444,x15445,x15446),f443(x15443,x15442,x15444,x15445,x15446))
% 94.68/94.46 [1545]~E(x15451,x15452)+E(f443(x15453,x15454,x15451,x15455,x15456),f443(x15453,x15454,x15452,x15455,x15456))
% 94.68/94.46 [1546]~E(x15461,x15462)+E(f443(x15463,x15464,x15465,x15461,x15466),f443(x15463,x15464,x15465,x15462,x15466))
% 94.68/94.46 [1547]~E(x15471,x15472)+E(f443(x15473,x15474,x15475,x15476,x15471),f443(x15473,x15474,x15475,x15476,x15472))
% 94.68/94.46 [1548]~E(x15481,x15482)+E(f594(x15481,x15483,x15484),f594(x15482,x15483,x15484))
% 94.68/94.46 [1549]~E(x15491,x15492)+E(f594(x15493,x15491,x15494),f594(x15493,x15492,x15494))
% 94.68/94.46 [1550]~E(x15501,x15502)+E(f594(x15503,x15504,x15501),f594(x15503,x15504,x15502))
% 94.68/94.46 [1551]~E(x15511,x15512)+E(f568(x15511,x15513),f568(x15512,x15513))
% 94.68/94.46 [1552]~E(x15521,x15522)+E(f568(x15523,x15521),f568(x15523,x15522))
% 94.68/94.46 [1553]~E(x15531,x15532)+E(f288(x15531,x15533,x15534),f288(x15532,x15533,x15534))
% 94.68/94.46 [1554]~E(x15541,x15542)+E(f288(x15543,x15541,x15544),f288(x15543,x15542,x15544))
% 94.68/94.46 [1555]~E(x15551,x15552)+E(f288(x15553,x15554,x15551),f288(x15553,x15554,x15552))
% 94.68/94.46 [1556]~E(x15561,x15562)+E(f646(x15561,x15563,x15564,x15565),f646(x15562,x15563,x15564,x15565))
% 94.68/94.46 [1557]~E(x15571,x15572)+E(f646(x15573,x15571,x15574,x15575),f646(x15573,x15572,x15574,x15575))
% 94.68/94.46 [1558]~E(x15581,x15582)+E(f646(x15583,x15584,x15581,x15585),f646(x15583,x15584,x15582,x15585))
% 94.68/94.46 [1559]~E(x15591,x15592)+E(f646(x15593,x15594,x15595,x15591),f646(x15593,x15594,x15595,x15592))
% 94.68/94.46 [1560]~E(x15601,x15602)+E(f656(x15601,x15603,x15604,x15605,x15606),f656(x15602,x15603,x15604,x15605,x15606))
% 94.68/94.46 [1561]~E(x15611,x15612)+E(f656(x15613,x15611,x15614,x15615,x15616),f656(x15613,x15612,x15614,x15615,x15616))
% 94.68/94.46 [1562]~E(x15621,x15622)+E(f656(x15623,x15624,x15621,x15625,x15626),f656(x15623,x15624,x15622,x15625,x15626))
% 94.68/94.46 [1563]~E(x15631,x15632)+E(f656(x15633,x15634,x15635,x15631,x15636),f656(x15633,x15634,x15635,x15632,x15636))
% 94.68/94.46 [1564]~E(x15641,x15642)+E(f656(x15643,x15644,x15645,x15646,x15641),f656(x15643,x15644,x15645,x15646,x15642))
% 94.68/94.46 [1565]~E(x15651,x15652)+E(f351(x15651,x15653,x15654,x15655,x15656),f351(x15652,x15653,x15654,x15655,x15656))
% 94.68/94.46 [1566]~E(x15661,x15662)+E(f351(x15663,x15661,x15664,x15665,x15666),f351(x15663,x15662,x15664,x15665,x15666))
% 94.68/94.46 [1567]~E(x15671,x15672)+E(f351(x15673,x15674,x15671,x15675,x15676),f351(x15673,x15674,x15672,x15675,x15676))
% 94.68/94.46 [1568]~E(x15681,x15682)+E(f351(x15683,x15684,x15685,x15681,x15686),f351(x15683,x15684,x15685,x15682,x15686))
% 94.68/94.46 [1569]~E(x15691,x15692)+E(f351(x15693,x15694,x15695,x15696,x15691),f351(x15693,x15694,x15695,x15696,x15692))
% 94.68/94.46 [1570]~E(x15701,x15702)+E(f817(x15701,x15703,x15704,x15705,x15706,x15707),f817(x15702,x15703,x15704,x15705,x15706,x15707))
% 94.68/94.46 [1571]~E(x15711,x15712)+E(f817(x15713,x15711,x15714,x15715,x15716,x15717),f817(x15713,x15712,x15714,x15715,x15716,x15717))
% 94.68/94.46 [1572]~E(x15721,x15722)+E(f817(x15723,x15724,x15721,x15725,x15726,x15727),f817(x15723,x15724,x15722,x15725,x15726,x15727))
% 94.68/94.46 [1573]~E(x15731,x15732)+E(f817(x15733,x15734,x15735,x15731,x15736,x15737),f817(x15733,x15734,x15735,x15732,x15736,x15737))
% 94.68/94.46 [1574]~E(x15741,x15742)+E(f817(x15743,x15744,x15745,x15746,x15741,x15747),f817(x15743,x15744,x15745,x15746,x15742,x15747))
% 94.68/94.46 [1575]~E(x15751,x15752)+E(f817(x15753,x15754,x15755,x15756,x15757,x15751),f817(x15753,x15754,x15755,x15756,x15757,x15752))
% 94.68/94.46 [1576]~E(x15761,x15762)+E(f820(x15761,x15763,x15764,x15765,x15766,x15767,x15768,x15769),f820(x15762,x15763,x15764,x15765,x15766,x15767,x15768,x15769))
% 94.68/94.46 [1577]~E(x15771,x15772)+E(f820(x15773,x15771,x15774,x15775,x15776,x15777,x15778,x15779),f820(x15773,x15772,x15774,x15775,x15776,x15777,x15778,x15779))
% 94.68/94.46 [1578]~E(x15781,x15782)+E(f820(x15783,x15784,x15781,x15785,x15786,x15787,x15788,x15789),f820(x15783,x15784,x15782,x15785,x15786,x15787,x15788,x15789))
% 94.68/94.46 [1579]~E(x15791,x15792)+E(f820(x15793,x15794,x15795,x15791,x15796,x15797,x15798,x15799),f820(x15793,x15794,x15795,x15792,x15796,x15797,x15798,x15799))
% 94.68/94.46 [1580]~E(x15801,x15802)+E(f820(x15803,x15804,x15805,x15806,x15801,x15807,x15808,x15809),f820(x15803,x15804,x15805,x15806,x15802,x15807,x15808,x15809))
% 94.68/94.46 [1581]~E(x15811,x15812)+E(f820(x15813,x15814,x15815,x15816,x15817,x15811,x15818,x15819),f820(x15813,x15814,x15815,x15816,x15817,x15812,x15818,x15819))
% 94.68/94.46 [1582]~E(x15821,x15822)+E(f820(x15823,x15824,x15825,x15826,x15827,x15828,x15821,x15829),f820(x15823,x15824,x15825,x15826,x15827,x15828,x15822,x15829))
% 94.68/94.46 [1583]~E(x15831,x15832)+E(f820(x15833,x15834,x15835,x15836,x15837,x15838,x15839,x15831),f820(x15833,x15834,x15835,x15836,x15837,x15838,x15839,x15832))
% 94.68/94.46 [1584]~E(x15841,x15842)+E(f648(x15841,x15843),f648(x15842,x15843))
% 94.68/94.46 [1585]~E(x15851,x15852)+E(f648(x15853,x15851),f648(x15853,x15852))
% 94.68/94.46 [1586]~E(x15861,x15862)+E(f700(x15861,x15863,x15864),f700(x15862,x15863,x15864))
% 94.68/94.46 [1587]~E(x15871,x15872)+E(f700(x15873,x15871,x15874),f700(x15873,x15872,x15874))
% 94.68/94.46 [1588]~E(x15881,x15882)+E(f700(x15883,x15884,x15881),f700(x15883,x15884,x15882))
% 94.68/94.46 [1589]~E(x15891,x15892)+E(f721(x15891,x15893,x15894,x15895,x15896),f721(x15892,x15893,x15894,x15895,x15896))
% 94.68/94.46 [1590]~E(x15901,x15902)+E(f721(x15903,x15901,x15904,x15905,x15906),f721(x15903,x15902,x15904,x15905,x15906))
% 94.68/94.46 [1591]~E(x15911,x15912)+E(f721(x15913,x15914,x15911,x15915,x15916),f721(x15913,x15914,x15912,x15915,x15916))
% 94.68/94.46 [1592]~E(x15921,x15922)+E(f721(x15923,x15924,x15925,x15921,x15926),f721(x15923,x15924,x15925,x15922,x15926))
% 94.68/94.46 [1593]~E(x15931,x15932)+E(f721(x15933,x15934,x15935,x15936,x15931),f721(x15933,x15934,x15935,x15936,x15932))
% 94.68/94.46 [1594]~E(x15941,x15942)+E(f466(x15941,x15943,x15944),f466(x15942,x15943,x15944))
% 94.68/94.46 [1595]~E(x15951,x15952)+E(f466(x15953,x15951,x15954),f466(x15953,x15952,x15954))
% 94.68/94.46 [1596]~E(x15961,x15962)+E(f466(x15963,x15964,x15961),f466(x15963,x15964,x15962))
% 94.68/94.46 [1597]~E(x15971,x15972)+E(f270(x15971,x15973,x15974,x15975),f270(x15972,x15973,x15974,x15975))
% 94.68/94.46 [1598]~E(x15981,x15982)+E(f270(x15983,x15981,x15984,x15985),f270(x15983,x15982,x15984,x15985))
% 94.68/94.46 [1599]~E(x15991,x15992)+E(f270(x15993,x15994,x15991,x15995),f270(x15993,x15994,x15992,x15995))
% 94.68/94.46 [1600]~E(x16001,x16002)+E(f270(x16003,x16004,x16005,x16001),f270(x16003,x16004,x16005,x16002))
% 94.68/94.46 [1601]~E(x16011,x16012)+E(f882(x16011,x16013,x16014),f882(x16012,x16013,x16014))
% 94.68/94.46 [1602]~E(x16021,x16022)+E(f882(x16023,x16021,x16024),f882(x16023,x16022,x16024))
% 94.68/94.46 [1603]~E(x16031,x16032)+E(f882(x16033,x16034,x16031),f882(x16033,x16034,x16032))
% 94.68/94.46 [1604]~E(x16041,x16042)+E(f48(x16041,x16043),f48(x16042,x16043))
% 94.68/94.46 [1605]~E(x16051,x16052)+E(f48(x16053,x16051),f48(x16053,x16052))
% 94.68/94.46 [1606]~E(x16061,x16062)+E(f385(x16061,x16063),f385(x16062,x16063))
% 94.68/94.46 [1607]~E(x16071,x16072)+E(f385(x16073,x16071),f385(x16073,x16072))
% 94.68/94.46 [1608]~E(x16081,x16082)+E(f798(x16081,x16083,x16084),f798(x16082,x16083,x16084))
% 94.68/94.46 [1609]~E(x16091,x16092)+E(f798(x16093,x16091,x16094),f798(x16093,x16092,x16094))
% 94.68/94.46 [1610]~E(x16101,x16102)+E(f798(x16103,x16104,x16101),f798(x16103,x16104,x16102))
% 94.68/94.46 [1611]~E(x16111,x16112)+E(f801(x16111,x16113),f801(x16112,x16113))
% 94.68/94.46 [1612]~E(x16121,x16122)+E(f801(x16123,x16121),f801(x16123,x16122))
% 94.68/94.46 [1613]~E(x16131,x16132)+E(f741(x16131,x16133,x16134),f741(x16132,x16133,x16134))
% 94.68/94.46 [1614]~E(x16141,x16142)+E(f741(x16143,x16141,x16144),f741(x16143,x16142,x16144))
% 94.68/94.46 [1615]~E(x16151,x16152)+E(f741(x16153,x16154,x16151),f741(x16153,x16154,x16152))
% 94.68/94.46 [1616]~E(x16161,x16162)+E(f407(x16161,x16163,x16164,x16165,x16166),f407(x16162,x16163,x16164,x16165,x16166))
% 94.68/94.46 [1617]~E(x16171,x16172)+E(f407(x16173,x16171,x16174,x16175,x16176),f407(x16173,x16172,x16174,x16175,x16176))
% 94.68/94.46 [1618]~E(x16181,x16182)+E(f407(x16183,x16184,x16181,x16185,x16186),f407(x16183,x16184,x16182,x16185,x16186))
% 94.68/94.46 [1619]~E(x16191,x16192)+E(f407(x16193,x16194,x16195,x16191,x16196),f407(x16193,x16194,x16195,x16192,x16196))
% 94.68/94.46 [1620]~E(x16201,x16202)+E(f407(x16203,x16204,x16205,x16206,x16201),f407(x16203,x16204,x16205,x16206,x16202))
% 94.68/94.46 [1621]~E(x16211,x16212)+E(f371(x16211,x16213,x16214,x16215),f371(x16212,x16213,x16214,x16215))
% 94.68/94.46 [1622]~E(x16221,x16222)+E(f371(x16223,x16221,x16224,x16225),f371(x16223,x16222,x16224,x16225))
% 94.68/94.46 [1623]~E(x16231,x16232)+E(f371(x16233,x16234,x16231,x16235),f371(x16233,x16234,x16232,x16235))
% 94.68/94.46 [1624]~E(x16241,x16242)+E(f371(x16243,x16244,x16245,x16241),f371(x16243,x16244,x16245,x16242))
% 94.68/94.46 [1625]~E(x16251,x16252)+E(f783(x16251,x16253),f783(x16252,x16253))
% 94.68/94.46 [1626]~E(x16261,x16262)+E(f783(x16263,x16261),f783(x16263,x16262))
% 94.68/94.46 [1627]~E(x16271,x16272)+E(f788(x16271,x16273,x16274),f788(x16272,x16273,x16274))
% 94.68/94.46 [1628]~E(x16281,x16282)+E(f788(x16283,x16281,x16284),f788(x16283,x16282,x16284))
% 94.68/94.46 [1629]~E(x16291,x16292)+E(f788(x16293,x16294,x16291),f788(x16293,x16294,x16292))
% 94.68/94.46 [1630]~E(x16301,x16302)+E(f284(x16301,x16303,x16304),f284(x16302,x16303,x16304))
% 94.68/94.46 [1631]~E(x16311,x16312)+E(f284(x16313,x16311,x16314),f284(x16313,x16312,x16314))
% 94.68/94.46 [1632]~E(x16321,x16322)+E(f284(x16323,x16324,x16321),f284(x16323,x16324,x16322))
% 94.68/94.46 [1633]~E(x16331,x16332)+E(f563(x16331,x16333,x16334,x16335,x16336),f563(x16332,x16333,x16334,x16335,x16336))
% 94.68/94.46 [1634]~E(x16341,x16342)+E(f563(x16343,x16341,x16344,x16345,x16346),f563(x16343,x16342,x16344,x16345,x16346))
% 94.68/94.46 [1635]~E(x16351,x16352)+E(f563(x16353,x16354,x16351,x16355,x16356),f563(x16353,x16354,x16352,x16355,x16356))
% 94.68/94.46 [1636]~E(x16361,x16362)+E(f563(x16363,x16364,x16365,x16361,x16366),f563(x16363,x16364,x16365,x16362,x16366))
% 94.68/94.46 [1637]~E(x16371,x16372)+E(f563(x16373,x16374,x16375,x16376,x16371),f563(x16373,x16374,x16375,x16376,x16372))
% 94.68/94.46 [1638]~E(x16381,x16382)+E(f416(x16381,x16383,x16384,x16385,x16386),f416(x16382,x16383,x16384,x16385,x16386))
% 94.68/94.46 [1639]~E(x16391,x16392)+E(f416(x16393,x16391,x16394,x16395,x16396),f416(x16393,x16392,x16394,x16395,x16396))
% 94.68/94.46 [1640]~E(x16401,x16402)+E(f416(x16403,x16404,x16401,x16405,x16406),f416(x16403,x16404,x16402,x16405,x16406))
% 94.68/94.46 [1641]~E(x16411,x16412)+E(f416(x16413,x16414,x16415,x16411,x16416),f416(x16413,x16414,x16415,x16412,x16416))
% 94.68/94.46 [1642]~E(x16421,x16422)+E(f416(x16423,x16424,x16425,x16426,x16421),f416(x16423,x16424,x16425,x16426,x16422))
% 94.68/94.46 [1643]~E(x16431,x16432)+E(f639(x16431,x16433,x16434,x16435),f639(x16432,x16433,x16434,x16435))
% 94.68/94.46 [1644]~E(x16441,x16442)+E(f639(x16443,x16441,x16444,x16445),f639(x16443,x16442,x16444,x16445))
% 94.68/94.46 [1645]~E(x16451,x16452)+E(f639(x16453,x16454,x16451,x16455),f639(x16453,x16454,x16452,x16455))
% 94.68/94.46 [1646]~E(x16461,x16462)+E(f639(x16463,x16464,x16465,x16461),f639(x16463,x16464,x16465,x16462))
% 94.68/94.46 [1647]~E(x16471,x16472)+E(f774(x16471,x16473,x16474),f774(x16472,x16473,x16474))
% 94.68/94.46 [1648]~E(x16481,x16482)+E(f774(x16483,x16481,x16484),f774(x16483,x16482,x16484))
% 94.68/94.46 [1649]~E(x16491,x16492)+E(f774(x16493,x16494,x16491),f774(x16493,x16494,x16492))
% 94.68/94.46 [1650]~E(x16501,x16502)+E(f108(x16501,x16503,x16504),f108(x16502,x16503,x16504))
% 94.68/94.46 [1651]~E(x16511,x16512)+E(f108(x16513,x16511,x16514),f108(x16513,x16512,x16514))
% 94.68/94.46 [1652]~E(x16521,x16522)+E(f108(x16523,x16524,x16521),f108(x16523,x16524,x16522))
% 94.68/94.46 [1653]~E(x16531,x16532)+E(f692(x16531,x16533,x16534),f692(x16532,x16533,x16534))
% 94.68/94.46 [1654]~E(x16541,x16542)+E(f692(x16543,x16541,x16544),f692(x16543,x16542,x16544))
% 94.68/94.46 [1655]~E(x16551,x16552)+E(f692(x16553,x16554,x16551),f692(x16553,x16554,x16552))
% 94.68/94.46 [1656]~E(x16561,x16562)+E(f818(x16561,x16563,x16564,x16565,x16566,x16567,x16568,x16569),f818(x16562,x16563,x16564,x16565,x16566,x16567,x16568,x16569))
% 94.68/94.46 [1657]~E(x16571,x16572)+E(f818(x16573,x16571,x16574,x16575,x16576,x16577,x16578,x16579),f818(x16573,x16572,x16574,x16575,x16576,x16577,x16578,x16579))
% 94.68/94.46 [1658]~E(x16581,x16582)+E(f818(x16583,x16584,x16581,x16585,x16586,x16587,x16588,x16589),f818(x16583,x16584,x16582,x16585,x16586,x16587,x16588,x16589))
% 94.68/94.46 [1659]~E(x16591,x16592)+E(f818(x16593,x16594,x16595,x16591,x16596,x16597,x16598,x16599),f818(x16593,x16594,x16595,x16592,x16596,x16597,x16598,x16599))
% 94.68/94.46 [1660]~E(x16601,x16602)+E(f818(x16603,x16604,x16605,x16606,x16601,x16607,x16608,x16609),f818(x16603,x16604,x16605,x16606,x16602,x16607,x16608,x16609))
% 94.68/94.46 [1661]~E(x16611,x16612)+E(f818(x16613,x16614,x16615,x16616,x16617,x16611,x16618,x16619),f818(x16613,x16614,x16615,x16616,x16617,x16612,x16618,x16619))
% 94.68/94.46 [1662]~E(x16621,x16622)+E(f818(x16623,x16624,x16625,x16626,x16627,x16628,x16621,x16629),f818(x16623,x16624,x16625,x16626,x16627,x16628,x16622,x16629))
% 94.68/94.46 [1663]~E(x16631,x16632)+E(f818(x16633,x16634,x16635,x16636,x16637,x16638,x16639,x16631),f818(x16633,x16634,x16635,x16636,x16637,x16638,x16639,x16632))
% 94.68/94.46 [1664]~E(x16641,x16642)+E(f505(x16641,x16643,x16644,x16645),f505(x16642,x16643,x16644,x16645))
% 94.68/94.46 [1665]~E(x16651,x16652)+E(f505(x16653,x16651,x16654,x16655),f505(x16653,x16652,x16654,x16655))
% 94.68/94.46 [1666]~E(x16661,x16662)+E(f505(x16663,x16664,x16661,x16665),f505(x16663,x16664,x16662,x16665))
% 94.68/94.46 [1667]~E(x16671,x16672)+E(f505(x16673,x16674,x16675,x16671),f505(x16673,x16674,x16675,x16672))
% 94.68/94.46 [1668]~E(x16681,x16682)+E(f405(x16681,x16683,x16684,x16685,x16686),f405(x16682,x16683,x16684,x16685,x16686))
% 94.68/94.46 [1669]~E(x16691,x16692)+E(f405(x16693,x16691,x16694,x16695,x16696),f405(x16693,x16692,x16694,x16695,x16696))
% 94.68/94.46 [1670]~E(x16701,x16702)+E(f405(x16703,x16704,x16701,x16705,x16706),f405(x16703,x16704,x16702,x16705,x16706))
% 94.68/94.46 [1671]~E(x16711,x16712)+E(f405(x16713,x16714,x16715,x16711,x16716),f405(x16713,x16714,x16715,x16712,x16716))
% 94.68/94.46 [1672]~E(x16721,x16722)+E(f405(x16723,x16724,x16725,x16726,x16721),f405(x16723,x16724,x16725,x16726,x16722))
% 94.68/94.46 [1673]~E(x16731,x16732)+E(f152(x16731,x16733),f152(x16732,x16733))
% 94.68/94.46 [1674]~E(x16741,x16742)+E(f152(x16743,x16741),f152(x16743,x16742))
% 94.68/94.46 [1675]~E(x16751,x16752)+E(f687(x16751,x16753),f687(x16752,x16753))
% 94.68/94.46 [1676]~E(x16761,x16762)+E(f687(x16763,x16761),f687(x16763,x16762))
% 94.68/94.46 [1677]~E(x16771,x16772)+E(f643(x16771,x16773),f643(x16772,x16773))
% 94.68/94.46 [1678]~E(x16781,x16782)+E(f643(x16783,x16781),f643(x16783,x16782))
% 94.68/94.46 [1679]~E(x16791,x16792)+E(f540(x16791,x16793,x16794,x16795,x16796,x16797),f540(x16792,x16793,x16794,x16795,x16796,x16797))
% 94.68/94.46 [1680]~E(x16801,x16802)+E(f540(x16803,x16801,x16804,x16805,x16806,x16807),f540(x16803,x16802,x16804,x16805,x16806,x16807))
% 94.68/94.46 [1681]~E(x16811,x16812)+E(f540(x16813,x16814,x16811,x16815,x16816,x16817),f540(x16813,x16814,x16812,x16815,x16816,x16817))
% 94.68/94.46 [1682]~E(x16821,x16822)+E(f540(x16823,x16824,x16825,x16821,x16826,x16827),f540(x16823,x16824,x16825,x16822,x16826,x16827))
% 94.68/94.46 [1683]~E(x16831,x16832)+E(f540(x16833,x16834,x16835,x16836,x16831,x16837),f540(x16833,x16834,x16835,x16836,x16832,x16837))
% 94.68/94.46 [1684]~E(x16841,x16842)+E(f540(x16843,x16844,x16845,x16846,x16847,x16841),f540(x16843,x16844,x16845,x16846,x16847,x16842))
% 94.68/94.46 [1685]~E(x16851,x16852)+E(f610(x16851,x16853),f610(x16852,x16853))
% 94.68/94.46 [1686]~E(x16861,x16862)+E(f610(x16863,x16861),f610(x16863,x16862))
% 94.68/94.46 [1687]~E(x16871,x16872)+E(f760(x16871,x16873),f760(x16872,x16873))
% 94.68/94.46 [1688]~E(x16881,x16882)+E(f760(x16883,x16881),f760(x16883,x16882))
% 94.68/94.46 [1689]~E(x16891,x16892)+E(f377(x16891,x16893,x16894,x16895),f377(x16892,x16893,x16894,x16895))
% 94.68/94.46 [1690]~E(x16901,x16902)+E(f377(x16903,x16901,x16904,x16905),f377(x16903,x16902,x16904,x16905))
% 94.68/94.46 [1691]~E(x16911,x16912)+E(f377(x16913,x16914,x16911,x16915),f377(x16913,x16914,x16912,x16915))
% 94.68/94.46 [1692]~E(x16921,x16922)+E(f377(x16923,x16924,x16925,x16921),f377(x16923,x16924,x16925,x16922))
% 94.68/94.46 [1693]~E(x16931,x16932)+E(f176(x16931),f176(x16932))
% 94.68/94.46 [1694]~E(x16941,x16942)+E(f218(x16941,x16943,x16944),f218(x16942,x16943,x16944))
% 94.68/94.46 [1695]~E(x16951,x16952)+E(f218(x16953,x16951,x16954),f218(x16953,x16952,x16954))
% 94.68/94.46 [1696]~E(x16961,x16962)+E(f218(x16963,x16964,x16961),f218(x16963,x16964,x16962))
% 94.68/94.46 [1697]~E(x16971,x16972)+E(f442(x16971,x16973,x16974,x16975,x16976),f442(x16972,x16973,x16974,x16975,x16976))
% 94.68/94.46 [1698]~E(x16981,x16982)+E(f442(x16983,x16981,x16984,x16985,x16986),f442(x16983,x16982,x16984,x16985,x16986))
% 94.68/94.46 [1699]~E(x16991,x16992)+E(f442(x16993,x16994,x16991,x16995,x16996),f442(x16993,x16994,x16992,x16995,x16996))
% 94.68/94.46 [1700]~E(x17001,x17002)+E(f442(x17003,x17004,x17005,x17001,x17006),f442(x17003,x17004,x17005,x17002,x17006))
% 94.68/94.46 [1701]~E(x17011,x17012)+E(f442(x17013,x17014,x17015,x17016,x17011),f442(x17013,x17014,x17015,x17016,x17012))
% 94.68/94.46 [1702]~E(x17021,x17022)+E(f575(x17021,x17023,x17024,x17025,x17026),f575(x17022,x17023,x17024,x17025,x17026))
% 94.68/94.46 [1703]~E(x17031,x17032)+E(f575(x17033,x17031,x17034,x17035,x17036),f575(x17033,x17032,x17034,x17035,x17036))
% 94.68/94.46 [1704]~E(x17041,x17042)+E(f575(x17043,x17044,x17041,x17045,x17046),f575(x17043,x17044,x17042,x17045,x17046))
% 94.68/94.46 [1705]~E(x17051,x17052)+E(f575(x17053,x17054,x17055,x17051,x17056),f575(x17053,x17054,x17055,x17052,x17056))
% 94.68/94.46 [1706]~E(x17061,x17062)+E(f575(x17063,x17064,x17065,x17066,x17061),f575(x17063,x17064,x17065,x17066,x17062))
% 94.68/94.46 [1707]~E(x17071,x17072)+E(f491(x17071,x17073),f491(x17072,x17073))
% 94.68/94.46 [1708]~E(x17081,x17082)+E(f491(x17083,x17081),f491(x17083,x17082))
% 94.68/94.46 [1709]~E(x17091,x17092)+E(f197(x17091,x17093,x17094,x17095,x17096,x17097,x17098),f197(x17092,x17093,x17094,x17095,x17096,x17097,x17098))
% 94.68/94.46 [1710]~E(x17101,x17102)+E(f197(x17103,x17101,x17104,x17105,x17106,x17107,x17108),f197(x17103,x17102,x17104,x17105,x17106,x17107,x17108))
% 94.68/94.46 [1711]~E(x17111,x17112)+E(f197(x17113,x17114,x17111,x17115,x17116,x17117,x17118),f197(x17113,x17114,x17112,x17115,x17116,x17117,x17118))
% 94.68/94.46 [1712]~E(x17121,x17122)+E(f197(x17123,x17124,x17125,x17121,x17126,x17127,x17128),f197(x17123,x17124,x17125,x17122,x17126,x17127,x17128))
% 94.68/94.46 [1713]~E(x17131,x17132)+E(f197(x17133,x17134,x17135,x17136,x17131,x17137,x17138),f197(x17133,x17134,x17135,x17136,x17132,x17137,x17138))
% 94.68/94.46 [1714]~E(x17141,x17142)+E(f197(x17143,x17144,x17145,x17146,x17147,x17141,x17148),f197(x17143,x17144,x17145,x17146,x17147,x17142,x17148))
% 94.68/94.46 [1715]~E(x17151,x17152)+E(f197(x17153,x17154,x17155,x17156,x17157,x17158,x17151),f197(x17153,x17154,x17155,x17156,x17157,x17158,x17152))
% 94.68/94.46 [1716]~E(x17161,x17162)+E(f258(x17161,x17163),f258(x17162,x17163))
% 94.68/94.46 [1717]~E(x17171,x17172)+E(f258(x17173,x17171),f258(x17173,x17172))
% 94.68/94.46 [1718]~E(x17181,x17182)+E(f680(x17181,x17183,x17184,x17185,x17186),f680(x17182,x17183,x17184,x17185,x17186))
% 94.68/94.46 [1719]~E(x17191,x17192)+E(f680(x17193,x17191,x17194,x17195,x17196),f680(x17193,x17192,x17194,x17195,x17196))
% 94.68/94.46 [1720]~E(x17201,x17202)+E(f680(x17203,x17204,x17201,x17205,x17206),f680(x17203,x17204,x17202,x17205,x17206))
% 94.68/94.46 [1721]~E(x17211,x17212)+E(f680(x17213,x17214,x17215,x17211,x17216),f680(x17213,x17214,x17215,x17212,x17216))
% 94.68/94.46 [1722]~E(x17221,x17222)+E(f680(x17223,x17224,x17225,x17226,x17221),f680(x17223,x17224,x17225,x17226,x17222))
% 94.68/94.46 [1723]~E(x17231,x17232)+E(f545(x17231,x17233,x17234),f545(x17232,x17233,x17234))
% 94.68/94.46 [1724]~E(x17241,x17242)+E(f545(x17243,x17241,x17244),f545(x17243,x17242,x17244))
% 94.68/94.46 [1725]~E(x17251,x17252)+E(f545(x17253,x17254,x17251),f545(x17253,x17254,x17252))
% 94.68/94.46 [1726]~E(x17261,x17262)+E(f375(x17261,x17263,x17264,x17265),f375(x17262,x17263,x17264,x17265))
% 94.68/94.46 [1727]~E(x17271,x17272)+E(f375(x17273,x17271,x17274,x17275),f375(x17273,x17272,x17274,x17275))
% 94.68/94.46 [1728]~E(x17281,x17282)+E(f375(x17283,x17284,x17281,x17285),f375(x17283,x17284,x17282,x17285))
% 94.68/94.46 [1729]~E(x17291,x17292)+E(f375(x17293,x17294,x17295,x17291),f375(x17293,x17294,x17295,x17292))
% 94.68/94.46 [1730]~E(x17301,x17302)+E(f577(x17301,x17303,x17304,x17305,x17306),f577(x17302,x17303,x17304,x17305,x17306))
% 94.68/94.46 [1731]~E(x17311,x17312)+E(f577(x17313,x17311,x17314,x17315,x17316),f577(x17313,x17312,x17314,x17315,x17316))
% 94.68/94.46 [1732]~E(x17321,x17322)+E(f577(x17323,x17324,x17321,x17325,x17326),f577(x17323,x17324,x17322,x17325,x17326))
% 94.68/94.46 [1733]~E(x17331,x17332)+E(f577(x17333,x17334,x17335,x17331,x17336),f577(x17333,x17334,x17335,x17332,x17336))
% 94.68/94.46 [1734]~E(x17341,x17342)+E(f577(x17343,x17344,x17345,x17346,x17341),f577(x17343,x17344,x17345,x17346,x17342))
% 94.68/94.46 [1735]~E(x17351,x17352)+E(f227(x17351,x17353),f227(x17352,x17353))
% 94.68/94.46 [1736]~E(x17361,x17362)+E(f227(x17363,x17361),f227(x17363,x17362))
% 94.68/94.46 [1737]~E(x17371,x17372)+E(f739(x17371,x17373,x17374),f739(x17372,x17373,x17374))
% 94.68/94.46 [1738]~E(x17381,x17382)+E(f739(x17383,x17381,x17384),f739(x17383,x17382,x17384))
% 94.68/94.46 [1739]~E(x17391,x17392)+E(f739(x17393,x17394,x17391),f739(x17393,x17394,x17392))
% 94.68/94.46 [1740]~E(x17401,x17402)+E(f590(x17401,x17403),f590(x17402,x17403))
% 94.68/94.46 [1741]~E(x17411,x17412)+E(f590(x17413,x17411),f590(x17413,x17412))
% 94.68/94.46 [1742]~E(x17421,x17422)+E(f257(x17421),f257(x17422))
% 94.68/94.46 [1743]~E(x17431,x17432)+E(f596(x17431,x17433,x17434),f596(x17432,x17433,x17434))
% 94.68/94.46 [1744]~E(x17441,x17442)+E(f596(x17443,x17441,x17444),f596(x17443,x17442,x17444))
% 94.68/94.46 [1745]~E(x17451,x17452)+E(f596(x17453,x17454,x17451),f596(x17453,x17454,x17452))
% 94.68/94.46 [1746]~E(x17461,x17462)+E(f554(x17461,x17463,x17464,x17465,x17466),f554(x17462,x17463,x17464,x17465,x17466))
% 94.68/94.46 [1747]~E(x17471,x17472)+E(f554(x17473,x17471,x17474,x17475,x17476),f554(x17473,x17472,x17474,x17475,x17476))
% 94.68/94.46 [1748]~E(x17481,x17482)+E(f554(x17483,x17484,x17481,x17485,x17486),f554(x17483,x17484,x17482,x17485,x17486))
% 94.68/94.46 [1749]~E(x17491,x17492)+E(f554(x17493,x17494,x17495,x17491,x17496),f554(x17493,x17494,x17495,x17492,x17496))
% 94.68/94.46 [1750]~E(x17501,x17502)+E(f554(x17503,x17504,x17505,x17506,x17501),f554(x17503,x17504,x17505,x17506,x17502))
% 94.68/94.46 [1751]~E(x17511,x17512)+E(f733(x17511,x17513,x17514),f733(x17512,x17513,x17514))
% 94.68/94.46 [1752]~E(x17521,x17522)+E(f733(x17523,x17521,x17524),f733(x17523,x17522,x17524))
% 94.68/94.46 [1753]~E(x17531,x17532)+E(f733(x17533,x17534,x17531),f733(x17533,x17534,x17532))
% 94.68/94.46 [1754]~E(x17541,x17542)+E(f527(x17541,x17543,x17544,x17545,x17546,x17547),f527(x17542,x17543,x17544,x17545,x17546,x17547))
% 94.68/94.46 [1755]~E(x17551,x17552)+E(f527(x17553,x17551,x17554,x17555,x17556,x17557),f527(x17553,x17552,x17554,x17555,x17556,x17557))
% 94.68/94.46 [1756]~E(x17561,x17562)+E(f527(x17563,x17564,x17561,x17565,x17566,x17567),f527(x17563,x17564,x17562,x17565,x17566,x17567))
% 94.68/94.46 [1757]~E(x17571,x17572)+E(f527(x17573,x17574,x17575,x17571,x17576,x17577),f527(x17573,x17574,x17575,x17572,x17576,x17577))
% 94.68/94.46 [1758]~E(x17581,x17582)+E(f527(x17583,x17584,x17585,x17586,x17581,x17587),f527(x17583,x17584,x17585,x17586,x17582,x17587))
% 94.68/94.46 [1759]~E(x17591,x17592)+E(f527(x17593,x17594,x17595,x17596,x17597,x17591),f527(x17593,x17594,x17595,x17596,x17597,x17592))
% 94.68/94.46 [1760]~E(x17601,x17602)+E(f36(x17601),f36(x17602))
% 94.68/94.46 [1761]~E(x17611,x17612)+E(f120(x17611,x17613,x17614,x17615),f120(x17612,x17613,x17614,x17615))
% 94.68/94.46 [1762]~E(x17621,x17622)+E(f120(x17623,x17621,x17624,x17625),f120(x17623,x17622,x17624,x17625))
% 94.68/94.46 [1763]~E(x17631,x17632)+E(f120(x17633,x17634,x17631,x17635),f120(x17633,x17634,x17632,x17635))
% 94.68/94.46 [1764]~E(x17641,x17642)+E(f120(x17643,x17644,x17645,x17641),f120(x17643,x17644,x17645,x17642))
% 94.68/94.46 [1765]~E(x17651,x17652)+E(f524(x17651,x17653,x17654,x17655,x17656,x17657),f524(x17652,x17653,x17654,x17655,x17656,x17657))
% 94.68/94.46 [1766]~E(x17661,x17662)+E(f524(x17663,x17661,x17664,x17665,x17666,x17667),f524(x17663,x17662,x17664,x17665,x17666,x17667))
% 94.68/94.46 [1767]~E(x17671,x17672)+E(f524(x17673,x17674,x17671,x17675,x17676,x17677),f524(x17673,x17674,x17672,x17675,x17676,x17677))
% 94.68/94.46 [1768]~E(x17681,x17682)+E(f524(x17683,x17684,x17685,x17681,x17686,x17687),f524(x17683,x17684,x17685,x17682,x17686,x17687))
% 94.68/94.46 [1769]~E(x17691,x17692)+E(f524(x17693,x17694,x17695,x17696,x17691,x17697),f524(x17693,x17694,x17695,x17696,x17692,x17697))
% 94.68/94.46 [1770]~E(x17701,x17702)+E(f524(x17703,x17704,x17705,x17706,x17707,x17701),f524(x17703,x17704,x17705,x17706,x17707,x17702))
% 94.68/94.46 [1771]~E(x17711,x17712)+E(f506(x17711,x17713,x17714,x17715),f506(x17712,x17713,x17714,x17715))
% 94.68/94.46 [1772]~E(x17721,x17722)+E(f506(x17723,x17721,x17724,x17725),f506(x17723,x17722,x17724,x17725))
% 94.68/94.46 [1773]~E(x17731,x17732)+E(f506(x17733,x17734,x17731,x17735),f506(x17733,x17734,x17732,x17735))
% 94.68/94.46 [1774]~E(x17741,x17742)+E(f506(x17743,x17744,x17745,x17741),f506(x17743,x17744,x17745,x17742))
% 94.68/94.46 [1775]~E(x17751,x17752)+E(f613(x17751,x17753,x17754),f613(x17752,x17753,x17754))
% 94.68/94.46 [1776]~E(x17761,x17762)+E(f613(x17763,x17761,x17764),f613(x17763,x17762,x17764))
% 94.68/94.46 [1777]~E(x17771,x17772)+E(f613(x17773,x17774,x17771),f613(x17773,x17774,x17772))
% 94.68/94.46 [1778]~E(x17781,x17782)+E(f850(x17781,x17783),f850(x17782,x17783))
% 94.68/94.46 [1779]~E(x17791,x17792)+E(f850(x17793,x17791),f850(x17793,x17792))
% 94.68/94.46 [1780]~E(x17801,x17802)+E(f404(x17801,x17803,x17804,x17805,x17806),f404(x17802,x17803,x17804,x17805,x17806))
% 94.68/94.46 [1781]~E(x17811,x17812)+E(f404(x17813,x17811,x17814,x17815,x17816),f404(x17813,x17812,x17814,x17815,x17816))
% 94.68/94.46 [1782]~E(x17821,x17822)+E(f404(x17823,x17824,x17821,x17825,x17826),f404(x17823,x17824,x17822,x17825,x17826))
% 94.68/94.46 [1783]~E(x17831,x17832)+E(f404(x17833,x17834,x17835,x17831,x17836),f404(x17833,x17834,x17835,x17832,x17836))
% 94.68/94.46 [1784]~E(x17841,x17842)+E(f404(x17843,x17844,x17845,x17846,x17841),f404(x17843,x17844,x17845,x17846,x17842))
% 94.68/94.46 [1785]~E(x17851,x17852)+E(f547(x17851,x17853,x17854,x17855),f547(x17852,x17853,x17854,x17855))
% 94.68/94.46 [1786]~E(x17861,x17862)+E(f547(x17863,x17861,x17864,x17865),f547(x17863,x17862,x17864,x17865))
% 94.68/94.46 [1787]~E(x17871,x17872)+E(f547(x17873,x17874,x17871,x17875),f547(x17873,x17874,x17872,x17875))
% 94.68/94.46 [1788]~E(x17881,x17882)+E(f547(x17883,x17884,x17885,x17881),f547(x17883,x17884,x17885,x17882))
% 94.68/94.46 [1789]~E(x17891,x17892)+E(f569(x17891,x17893,x17894,x17895),f569(x17892,x17893,x17894,x17895))
% 94.68/94.46 [1790]~E(x17901,x17902)+E(f569(x17903,x17901,x17904,x17905),f569(x17903,x17902,x17904,x17905))
% 94.68/94.46 [1791]~E(x17911,x17912)+E(f569(x17913,x17914,x17911,x17915),f569(x17913,x17914,x17912,x17915))
% 94.68/94.46 [1792]~E(x17921,x17922)+E(f569(x17923,x17924,x17925,x17921),f569(x17923,x17924,x17925,x17922))
% 94.68/94.46 [1793]~E(x17931,x17932)+E(f323(x17931),f323(x17932))
% 94.68/94.46 [1794]~E(x17941,x17942)+E(f825(x17941,x17943,x17944,x17945,x17946,x17947),f825(x17942,x17943,x17944,x17945,x17946,x17947))
% 94.68/94.46 [1795]~E(x17951,x17952)+E(f825(x17953,x17951,x17954,x17955,x17956,x17957),f825(x17953,x17952,x17954,x17955,x17956,x17957))
% 94.68/94.46 [1796]~E(x17961,x17962)+E(f825(x17963,x17964,x17961,x17965,x17966,x17967),f825(x17963,x17964,x17962,x17965,x17966,x17967))
% 94.68/94.46 [1797]~E(x17971,x17972)+E(f825(x17973,x17974,x17975,x17971,x17976,x17977),f825(x17973,x17974,x17975,x17972,x17976,x17977))
% 94.68/94.46 [1798]~E(x17981,x17982)+E(f825(x17983,x17984,x17985,x17986,x17981,x17987),f825(x17983,x17984,x17985,x17986,x17982,x17987))
% 94.68/94.46 [1799]~E(x17991,x17992)+E(f825(x17993,x17994,x17995,x17996,x17997,x17991),f825(x17993,x17994,x17995,x17996,x17997,x17992))
% 94.68/94.46 [1800]~E(x18001,x18002)+E(f399(x18001,x18003,x18004),f399(x18002,x18003,x18004))
% 94.68/94.46 [1801]~E(x18011,x18012)+E(f399(x18013,x18011,x18014),f399(x18013,x18012,x18014))
% 94.68/94.46 [1802]~E(x18021,x18022)+E(f399(x18023,x18024,x18021),f399(x18023,x18024,x18022))
% 94.68/94.46 [1803]~E(x18031,x18032)+E(f445(x18031,x18033,x18034,x18035,x18036),f445(x18032,x18033,x18034,x18035,x18036))
% 94.68/94.46 [1804]~E(x18041,x18042)+E(f445(x18043,x18041,x18044,x18045,x18046),f445(x18043,x18042,x18044,x18045,x18046))
% 94.68/94.46 [1805]~E(x18051,x18052)+E(f445(x18053,x18054,x18051,x18055,x18056),f445(x18053,x18054,x18052,x18055,x18056))
% 94.68/94.46 [1806]~E(x18061,x18062)+E(f445(x18063,x18064,x18065,x18061,x18066),f445(x18063,x18064,x18065,x18062,x18066))
% 94.68/94.46 [1807]~E(x18071,x18072)+E(f445(x18073,x18074,x18075,x18076,x18071),f445(x18073,x18074,x18075,x18076,x18072))
% 94.68/94.46 [1808]~E(x18081,x18082)+E(f782(x18081,x18083),f782(x18082,x18083))
% 94.68/94.46 [1809]~E(x18091,x18092)+E(f782(x18093,x18091),f782(x18093,x18092))
% 94.68/94.46 [1810]~E(x18101,x18102)+E(f170(x18101),f170(x18102))
% 94.68/94.46 [1811]~E(x18111,x18112)+E(f226(x18111,x18113),f226(x18112,x18113))
% 94.68/94.46 [1812]~E(x18121,x18122)+E(f226(x18123,x18121),f226(x18123,x18122))
% 94.68/94.46 [1813]~E(x18131,x18132)+E(f622(x18131,x18133,x18134,x18135,x18136,x18137),f622(x18132,x18133,x18134,x18135,x18136,x18137))
% 94.68/94.46 [1814]~E(x18141,x18142)+E(f622(x18143,x18141,x18144,x18145,x18146,x18147),f622(x18143,x18142,x18144,x18145,x18146,x18147))
% 94.68/94.46 [1815]~E(x18151,x18152)+E(f622(x18153,x18154,x18151,x18155,x18156,x18157),f622(x18153,x18154,x18152,x18155,x18156,x18157))
% 94.68/94.46 [1816]~E(x18161,x18162)+E(f622(x18163,x18164,x18165,x18161,x18166,x18167),f622(x18163,x18164,x18165,x18162,x18166,x18167))
% 94.68/94.46 [1817]~E(x18171,x18172)+E(f622(x18173,x18174,x18175,x18176,x18171,x18177),f622(x18173,x18174,x18175,x18176,x18172,x18177))
% 94.68/94.46 [1818]~E(x18181,x18182)+E(f622(x18183,x18184,x18185,x18186,x18187,x18181),f622(x18183,x18184,x18185,x18186,x18187,x18182))
% 94.68/94.46 [1819]~E(x18191,x18192)+E(f425(x18191,x18193,x18194,x18195,x18196),f425(x18192,x18193,x18194,x18195,x18196))
% 94.68/94.46 [1820]~E(x18201,x18202)+E(f425(x18203,x18201,x18204,x18205,x18206),f425(x18203,x18202,x18204,x18205,x18206))
% 94.68/94.46 [1821]~E(x18211,x18212)+E(f425(x18213,x18214,x18211,x18215,x18216),f425(x18213,x18214,x18212,x18215,x18216))
% 94.68/94.46 [1822]~E(x18221,x18222)+E(f425(x18223,x18224,x18225,x18221,x18226),f425(x18223,x18224,x18225,x18222,x18226))
% 94.68/94.46 [1823]~E(x18231,x18232)+E(f425(x18233,x18234,x18235,x18236,x18231),f425(x18233,x18234,x18235,x18236,x18232))
% 94.68/94.46 [1824]~E(x18241,x18242)+E(f472(x18241,x18243,x18244,x18245),f472(x18242,x18243,x18244,x18245))
% 94.68/94.46 [1825]~E(x18251,x18252)+E(f472(x18253,x18251,x18254,x18255),f472(x18253,x18252,x18254,x18255))
% 94.68/94.46 [1826]~E(x18261,x18262)+E(f472(x18263,x18264,x18261,x18265),f472(x18263,x18264,x18262,x18265))
% 94.68/94.46 [1827]~E(x18271,x18272)+E(f472(x18273,x18274,x18275,x18271),f472(x18273,x18274,x18275,x18272))
% 94.68/94.46 [1828]~E(x18281,x18282)+E(f723(x18281,x18283,x18284,x18285,x18286),f723(x18282,x18283,x18284,x18285,x18286))
% 94.68/94.46 [1829]~E(x18291,x18292)+E(f723(x18293,x18291,x18294,x18295,x18296),f723(x18293,x18292,x18294,x18295,x18296))
% 94.68/94.46 [1830]~E(x18301,x18302)+E(f723(x18303,x18304,x18301,x18305,x18306),f723(x18303,x18304,x18302,x18305,x18306))
% 94.68/94.46 [1831]~E(x18311,x18312)+E(f723(x18313,x18314,x18315,x18311,x18316),f723(x18313,x18314,x18315,x18312,x18316))
% 94.68/94.46 [1832]~E(x18321,x18322)+E(f723(x18323,x18324,x18325,x18326,x18321),f723(x18323,x18324,x18325,x18326,x18322))
% 94.68/94.46 [1833]~E(x18331,x18332)+E(f439(x18331,x18333,x18334,x18335,x18336),f439(x18332,x18333,x18334,x18335,x18336))
% 94.68/94.46 [1834]~E(x18341,x18342)+E(f439(x18343,x18341,x18344,x18345,x18346),f439(x18343,x18342,x18344,x18345,x18346))
% 94.68/94.46 [1835]~E(x18351,x18352)+E(f439(x18353,x18354,x18351,x18355,x18356),f439(x18353,x18354,x18352,x18355,x18356))
% 94.68/94.46 [1836]~E(x18361,x18362)+E(f439(x18363,x18364,x18365,x18361,x18366),f439(x18363,x18364,x18365,x18362,x18366))
% 94.68/94.46 [1837]~E(x18371,x18372)+E(f439(x18373,x18374,x18375,x18376,x18371),f439(x18373,x18374,x18375,x18376,x18372))
% 94.68/94.46 [1838]~E(x18381,x18382)+E(f722(x18381,x18383,x18384,x18385,x18386),f722(x18382,x18383,x18384,x18385,x18386))
% 94.68/94.46 [1839]~E(x18391,x18392)+E(f722(x18393,x18391,x18394,x18395,x18396),f722(x18393,x18392,x18394,x18395,x18396))
% 94.68/94.46 [1840]~E(x18401,x18402)+E(f722(x18403,x18404,x18401,x18405,x18406),f722(x18403,x18404,x18402,x18405,x18406))
% 94.68/94.46 [1841]~E(x18411,x18412)+E(f722(x18413,x18414,x18415,x18411,x18416),f722(x18413,x18414,x18415,x18412,x18416))
% 94.68/94.46 [1842]~E(x18421,x18422)+E(f722(x18423,x18424,x18425,x18426,x18421),f722(x18423,x18424,x18425,x18426,x18422))
% 94.68/94.46 [1843]~E(x18431,x18432)+E(f636(x18431,x18433,x18434),f636(x18432,x18433,x18434))
% 94.68/94.46 [1844]~E(x18441,x18442)+E(f636(x18443,x18441,x18444),f636(x18443,x18442,x18444))
% 94.68/94.46 [1845]~E(x18451,x18452)+E(f636(x18453,x18454,x18451),f636(x18453,x18454,x18452))
% 94.68/94.46 [1846]~E(x18461,x18462)+E(f676(x18461,x18463,x18464,x18465),f676(x18462,x18463,x18464,x18465))
% 94.68/94.46 [1847]~E(x18471,x18472)+E(f676(x18473,x18471,x18474,x18475),f676(x18473,x18472,x18474,x18475))
% 94.68/94.46 [1848]~E(x18481,x18482)+E(f676(x18483,x18484,x18481,x18485),f676(x18483,x18484,x18482,x18485))
% 94.68/94.46 [1849]~E(x18491,x18492)+E(f676(x18493,x18494,x18495,x18491),f676(x18493,x18494,x18495,x18492))
% 94.68/94.46 [1850]~E(x18501,x18502)+E(f384(x18501,x18503),f384(x18502,x18503))
% 94.68/94.46 [1851]~E(x18511,x18512)+E(f384(x18513,x18511),f384(x18513,x18512))
% 94.68/94.46 [1852]~E(x18521,x18522)+E(f775(x18521,x18523,x18524,x18525),f775(x18522,x18523,x18524,x18525))
% 94.68/94.46 [1853]~E(x18531,x18532)+E(f775(x18533,x18531,x18534,x18535),f775(x18533,x18532,x18534,x18535))
% 94.68/94.46 [1854]~E(x18541,x18542)+E(f775(x18543,x18544,x18541,x18545),f775(x18543,x18544,x18542,x18545))
% 94.68/94.46 [1855]~E(x18551,x18552)+E(f775(x18553,x18554,x18555,x18551),f775(x18553,x18554,x18555,x18552))
% 94.68/94.46 [1856]~E(x18561,x18562)+E(f566(x18561,x18563,x18564,x18565,x18566),f566(x18562,x18563,x18564,x18565,x18566))
% 94.68/94.46 [1857]~E(x18571,x18572)+E(f566(x18573,x18571,x18574,x18575,x18576),f566(x18573,x18572,x18574,x18575,x18576))
% 94.68/94.46 [1858]~E(x18581,x18582)+E(f566(x18583,x18584,x18581,x18585,x18586),f566(x18583,x18584,x18582,x18585,x18586))
% 94.68/94.46 [1859]~E(x18591,x18592)+E(f566(x18593,x18594,x18595,x18591,x18596),f566(x18593,x18594,x18595,x18592,x18596))
% 94.68/94.46 [1860]~E(x18601,x18602)+E(f566(x18603,x18604,x18605,x18606,x18601),f566(x18603,x18604,x18605,x18606,x18602))
% 94.68/94.46 [1861]~E(x18611,x18612)+E(f738(x18611,x18613,x18614),f738(x18612,x18613,x18614))
% 94.68/94.46 [1862]~E(x18621,x18622)+E(f738(x18623,x18621,x18624),f738(x18623,x18622,x18624))
% 94.68/94.46 [1863]~E(x18631,x18632)+E(f738(x18633,x18634,x18631),f738(x18633,x18634,x18632))
% 94.68/94.46 [1864]~E(x18641,x18642)+E(f268(x18641),f268(x18642))
% 94.68/94.46 [1865]~E(x18651,x18652)+E(f792(x18651,x18653,x18654,x18655,x18656,x18657),f792(x18652,x18653,x18654,x18655,x18656,x18657))
% 94.68/94.46 [1866]~E(x18661,x18662)+E(f792(x18663,x18661,x18664,x18665,x18666,x18667),f792(x18663,x18662,x18664,x18665,x18666,x18667))
% 94.68/94.46 [1867]~E(x18671,x18672)+E(f792(x18673,x18674,x18671,x18675,x18676,x18677),f792(x18673,x18674,x18672,x18675,x18676,x18677))
% 94.68/94.46 [1868]~E(x18681,x18682)+E(f792(x18683,x18684,x18685,x18681,x18686,x18687),f792(x18683,x18684,x18685,x18682,x18686,x18687))
% 94.68/94.46 [1869]~E(x18691,x18692)+E(f792(x18693,x18694,x18695,x18696,x18691,x18697),f792(x18693,x18694,x18695,x18696,x18692,x18697))
% 94.68/94.46 [1870]~E(x18701,x18702)+E(f792(x18703,x18704,x18705,x18706,x18707,x18701),f792(x18703,x18704,x18705,x18706,x18707,x18702))
% 94.68/94.46 [1871]~E(x18711,x18712)+E(f213(x18711,x18713,x18714,x18715,x18716),f213(x18712,x18713,x18714,x18715,x18716))
% 94.68/94.46 [1872]~E(x18721,x18722)+E(f213(x18723,x18721,x18724,x18725,x18726),f213(x18723,x18722,x18724,x18725,x18726))
% 94.68/94.46 [1873]~E(x18731,x18732)+E(f213(x18733,x18734,x18731,x18735,x18736),f213(x18733,x18734,x18732,x18735,x18736))
% 94.68/94.46 [1874]~E(x18741,x18742)+E(f213(x18743,x18744,x18745,x18741,x18746),f213(x18743,x18744,x18745,x18742,x18746))
% 94.68/94.46 [1875]~E(x18751,x18752)+E(f213(x18753,x18754,x18755,x18756,x18751),f213(x18753,x18754,x18755,x18756,x18752))
% 94.68/94.46 [1876]~E(x18761,x18762)+E(f469(x18761),f469(x18762))
% 94.68/94.46 [1877]~E(x18771,x18772)+E(f394(x18771,x18773),f394(x18772,x18773))
% 94.68/94.46 [1878]~E(x18781,x18782)+E(f394(x18783,x18781),f394(x18783,x18782))
% 94.68/94.46 [1879]~E(x18791,x18792)+E(f807(x18791,x18793,x18794),f807(x18792,x18793,x18794))
% 94.68/94.46 [1880]~E(x18801,x18802)+E(f807(x18803,x18801,x18804),f807(x18803,x18802,x18804))
% 94.68/94.46 [1881]~E(x18811,x18812)+E(f807(x18813,x18814,x18811),f807(x18813,x18814,x18812))
% 94.68/94.46 [1882]~E(x18821,x18822)+E(f237(x18821,x18823,x18824),f237(x18822,x18823,x18824))
% 94.68/94.46 [1883]~E(x18831,x18832)+E(f237(x18833,x18831,x18834),f237(x18833,x18832,x18834))
% 94.68/94.46 [1884]~E(x18841,x18842)+E(f237(x18843,x18844,x18841),f237(x18843,x18844,x18842))
% 94.68/94.46 [1885]~E(x18851,x18852)+E(f565(x18851,x18853,x18854,x18855,x18856),f565(x18852,x18853,x18854,x18855,x18856))
% 94.68/94.46 [1886]~E(x18861,x18862)+E(f565(x18863,x18861,x18864,x18865,x18866),f565(x18863,x18862,x18864,x18865,x18866))
% 94.68/94.46 [1887]~E(x18871,x18872)+E(f565(x18873,x18874,x18871,x18875,x18876),f565(x18873,x18874,x18872,x18875,x18876))
% 94.68/94.46 [1888]~E(x18881,x18882)+E(f565(x18883,x18884,x18885,x18881,x18886),f565(x18883,x18884,x18885,x18882,x18886))
% 94.68/94.46 [1889]~E(x18891,x18892)+E(f565(x18893,x18894,x18895,x18896,x18891),f565(x18893,x18894,x18895,x18896,x18892))
% 94.68/94.46 [1890]~E(x18901,x18902)+E(f401(x18901,x18903,x18904),f401(x18902,x18903,x18904))
% 94.68/94.46 [1891]~E(x18911,x18912)+E(f401(x18913,x18911,x18914),f401(x18913,x18912,x18914))
% 94.68/94.46 [1892]~E(x18921,x18922)+E(f401(x18923,x18924,x18921),f401(x18923,x18924,x18922))
% 94.68/94.46 [1893]~E(x18931,x18932)+E(f342(x18931,x18933,x18934),f342(x18932,x18933,x18934))
% 94.68/94.46 [1894]~E(x18941,x18942)+E(f342(x18943,x18941,x18944),f342(x18943,x18942,x18944))
% 94.68/94.46 [1895]~E(x18951,x18952)+E(f342(x18953,x18954,x18951),f342(x18953,x18954,x18952))
% 94.68/94.46 [1896]~E(x18961,x18962)+E(f828(x18961,x18963,x18964,x18965,x18966,x18967,x18968,x18969),f828(x18962,x18963,x18964,x18965,x18966,x18967,x18968,x18969))
% 94.68/94.46 [1897]~E(x18971,x18972)+E(f828(x18973,x18971,x18974,x18975,x18976,x18977,x18978,x18979),f828(x18973,x18972,x18974,x18975,x18976,x18977,x18978,x18979))
% 94.68/94.46 [1898]~E(x18981,x18982)+E(f828(x18983,x18984,x18981,x18985,x18986,x18987,x18988,x18989),f828(x18983,x18984,x18982,x18985,x18986,x18987,x18988,x18989))
% 94.68/94.46 [1899]~E(x18991,x18992)+E(f828(x18993,x18994,x18995,x18991,x18996,x18997,x18998,x18999),f828(x18993,x18994,x18995,x18992,x18996,x18997,x18998,x18999))
% 94.68/94.46 [1900]~E(x19001,x19002)+E(f828(x19003,x19004,x19005,x19006,x19001,x19007,x19008,x19009),f828(x19003,x19004,x19005,x19006,x19002,x19007,x19008,x19009))
% 94.68/94.46 [1901]~E(x19011,x19012)+E(f828(x19013,x19014,x19015,x19016,x19017,x19011,x19018,x19019),f828(x19013,x19014,x19015,x19016,x19017,x19012,x19018,x19019))
% 94.68/94.46 [1902]~E(x19021,x19022)+E(f828(x19023,x19024,x19025,x19026,x19027,x19028,x19021,x19029),f828(x19023,x19024,x19025,x19026,x19027,x19028,x19022,x19029))
% 94.68/94.46 [1903]~E(x19031,x19032)+E(f828(x19033,x19034,x19035,x19036,x19037,x19038,x19039,x19031),f828(x19033,x19034,x19035,x19036,x19037,x19038,x19039,x19032))
% 94.68/94.46 [1904]~E(x19041,x19042)+E(f635(x19041,x19043,x19044,x19045,x19046,x19047,x19048),f635(x19042,x19043,x19044,x19045,x19046,x19047,x19048))
% 94.68/94.46 [1905]~E(x19051,x19052)+E(f635(x19053,x19051,x19054,x19055,x19056,x19057,x19058),f635(x19053,x19052,x19054,x19055,x19056,x19057,x19058))
% 94.68/94.46 [1906]~E(x19061,x19062)+E(f635(x19063,x19064,x19061,x19065,x19066,x19067,x19068),f635(x19063,x19064,x19062,x19065,x19066,x19067,x19068))
% 94.68/94.46 [1907]~E(x19071,x19072)+E(f635(x19073,x19074,x19075,x19071,x19076,x19077,x19078),f635(x19073,x19074,x19075,x19072,x19076,x19077,x19078))
% 94.68/94.46 [1908]~E(x19081,x19082)+E(f635(x19083,x19084,x19085,x19086,x19081,x19087,x19088),f635(x19083,x19084,x19085,x19086,x19082,x19087,x19088))
% 94.68/94.46 [1909]~E(x19091,x19092)+E(f635(x19093,x19094,x19095,x19096,x19097,x19091,x19098),f635(x19093,x19094,x19095,x19096,x19097,x19092,x19098))
% 94.68/94.46 [1910]~E(x19101,x19102)+E(f635(x19103,x19104,x19105,x19106,x19107,x19108,x19101),f635(x19103,x19104,x19105,x19106,x19107,x19108,x19102))
% 94.68/94.46 [1911]~E(x19111,x19112)+E(f191(x19111),f191(x19112))
% 94.68/94.46 [1912]~E(x19121,x19122)+E(f68(x19121,x19123),f68(x19122,x19123))
% 94.68/94.46 [1913]~E(x19131,x19132)+E(f68(x19133,x19131),f68(x19133,x19132))
% 94.68/94.46 [1914]~E(x19141,x19142)+E(f735(x19141,x19143,x19144),f735(x19142,x19143,x19144))
% 94.68/94.46 [1915]~E(x19151,x19152)+E(f735(x19153,x19151,x19154),f735(x19153,x19152,x19154))
% 94.68/94.46 [1916]~E(x19161,x19162)+E(f735(x19163,x19164,x19161),f735(x19163,x19164,x19162))
% 94.68/94.46 [1917]~E(x19171,x19172)+E(f780(x19171,x19173),f780(x19172,x19173))
% 94.68/94.46 [1918]~E(x19181,x19182)+E(f780(x19183,x19181),f780(x19183,x19182))
% 94.68/94.46 [1919]~E(x19191,x19192)+E(f597(x19191,x19193,x19194,x19195,x19196,x19197,x19198,x19199),f597(x19192,x19193,x19194,x19195,x19196,x19197,x19198,x19199))
% 94.68/94.46 [1920]~E(x19201,x19202)+E(f597(x19203,x19201,x19204,x19205,x19206,x19207,x19208,x19209),f597(x19203,x19202,x19204,x19205,x19206,x19207,x19208,x19209))
% 94.68/94.46 [1921]~E(x19211,x19212)+E(f597(x19213,x19214,x19211,x19215,x19216,x19217,x19218,x19219),f597(x19213,x19214,x19212,x19215,x19216,x19217,x19218,x19219))
% 94.68/94.46 [1922]~E(x19221,x19222)+E(f597(x19223,x19224,x19225,x19221,x19226,x19227,x19228,x19229),f597(x19223,x19224,x19225,x19222,x19226,x19227,x19228,x19229))
% 94.68/94.46 [1923]~E(x19231,x19232)+E(f597(x19233,x19234,x19235,x19236,x19231,x19237,x19238,x19239),f597(x19233,x19234,x19235,x19236,x19232,x19237,x19238,x19239))
% 94.68/94.46 [1924]~E(x19241,x19242)+E(f597(x19243,x19244,x19245,x19246,x19247,x19241,x19248,x19249),f597(x19243,x19244,x19245,x19246,x19247,x19242,x19248,x19249))
% 94.68/94.46 [1925]~E(x19251,x19252)+E(f597(x19253,x19254,x19255,x19256,x19257,x19258,x19251,x19259),f597(x19253,x19254,x19255,x19256,x19257,x19258,x19252,x19259))
% 94.68/94.46 [1926]~E(x19261,x19262)+E(f597(x19263,x19264,x19265,x19266,x19267,x19268,x19269,x19261),f597(x19263,x19264,x19265,x19266,x19267,x19268,x19269,x19262))
% 94.68/94.46 [1927]~E(x19271,x19272)+E(f770(x19271,x19273),f770(x19272,x19273))
% 94.68/94.46 [1928]~E(x19281,x19282)+E(f770(x19283,x19281),f770(x19283,x19282))
% 94.68/94.46 [1929]~E(x19291,x19292)+E(f192(x19291,x19293),f192(x19292,x19293))
% 94.68/94.46 [1930]~E(x19301,x19302)+E(f192(x19303,x19301),f192(x19303,x19302))
% 94.68/94.46 [1931]~E(x19311,x19312)+E(f772(x19311,x19313,x19314),f772(x19312,x19313,x19314))
% 94.68/94.46 [1932]~E(x19321,x19322)+E(f772(x19323,x19321,x19324),f772(x19323,x19322,x19324))
% 94.68/94.46 [1933]~E(x19331,x19332)+E(f772(x19333,x19334,x19331),f772(x19333,x19334,x19332))
% 94.68/94.46 [1934]~E(x19341,x19342)+E(f785(x19341),f785(x19342))
% 94.68/94.46 [1935]~E(x19351,x19352)+E(f436(x19351,x19353,x19354,x19355),f436(x19352,x19353,x19354,x19355))
% 94.68/94.46 [1936]~E(x19361,x19362)+E(f436(x19363,x19361,x19364,x19365),f436(x19363,x19362,x19364,x19365))
% 94.68/94.46 [1937]~E(x19371,x19372)+E(f436(x19373,x19374,x19371,x19375),f436(x19373,x19374,x19372,x19375))
% 94.68/94.46 [1938]~E(x19381,x19382)+E(f436(x19383,x19384,x19385,x19381),f436(x19383,x19384,x19385,x19382))
% 94.68/94.46 [1939]~E(x19391,x19392)+E(f414(x19391,x19393),f414(x19392,x19393))
% 94.68/94.46 [1940]~E(x19401,x19402)+E(f414(x19403,x19401),f414(x19403,x19402))
% 94.68/94.46 [1941]~E(x19411,x19412)+E(f829(x19411,x19413,x19414,x19415,x19416,x19417,x19418,x19419),f829(x19412,x19413,x19414,x19415,x19416,x19417,x19418,x19419))
% 94.68/94.46 [1942]~E(x19421,x19422)+E(f829(x19423,x19421,x19424,x19425,x19426,x19427,x19428,x19429),f829(x19423,x19422,x19424,x19425,x19426,x19427,x19428,x19429))
% 94.68/94.46 [1943]~E(x19431,x19432)+E(f829(x19433,x19434,x19431,x19435,x19436,x19437,x19438,x19439),f829(x19433,x19434,x19432,x19435,x19436,x19437,x19438,x19439))
% 94.68/94.46 [1944]~E(x19441,x19442)+E(f829(x19443,x19444,x19445,x19441,x19446,x19447,x19448,x19449),f829(x19443,x19444,x19445,x19442,x19446,x19447,x19448,x19449))
% 94.68/94.46 [1945]~E(x19451,x19452)+E(f829(x19453,x19454,x19455,x19456,x19451,x19457,x19458,x19459),f829(x19453,x19454,x19455,x19456,x19452,x19457,x19458,x19459))
% 94.68/94.46 [1946]~E(x19461,x19462)+E(f829(x19463,x19464,x19465,x19466,x19467,x19461,x19468,x19469),f829(x19463,x19464,x19465,x19466,x19467,x19462,x19468,x19469))
% 94.68/94.46 [1947]~E(x19471,x19472)+E(f829(x19473,x19474,x19475,x19476,x19477,x19478,x19471,x19479),f829(x19473,x19474,x19475,x19476,x19477,x19478,x19472,x19479))
% 94.68/94.46 [1948]~E(x19481,x19482)+E(f829(x19483,x19484,x19485,x19486,x19487,x19488,x19489,x19481),f829(x19483,x19484,x19485,x19486,x19487,x19488,x19489,x19482))
% 94.68/94.46 [1949]~E(x19491,x19492)+E(f344(x19491,x19493,x19494),f344(x19492,x19493,x19494))
% 94.68/94.46 [1950]~E(x19501,x19502)+E(f344(x19503,x19501,x19504),f344(x19503,x19502,x19504))
% 94.68/94.46 [1951]~E(x19511,x19512)+E(f344(x19513,x19514,x19511),f344(x19513,x19514,x19512))
% 94.68/94.46 [1952]~E(x19521,x19522)+E(f626(x19521,x19523,x19524,x19525),f626(x19522,x19523,x19524,x19525))
% 94.68/94.46 [1953]~E(x19531,x19532)+E(f626(x19533,x19531,x19534,x19535),f626(x19533,x19532,x19534,x19535))
% 94.68/94.46 [1954]~E(x19541,x19542)+E(f626(x19543,x19544,x19541,x19545),f626(x19543,x19544,x19542,x19545))
% 94.68/94.46 [1955]~E(x19551,x19552)+E(f626(x19553,x19554,x19555,x19551),f626(x19553,x19554,x19555,x19552))
% 94.68/94.46 [1956]~E(x19561,x19562)+E(f871(x19561,x19563),f871(x19562,x19563))
% 94.68/94.46 [1957]~E(x19571,x19572)+E(f871(x19573,x19571),f871(x19573,x19572))
% 94.68/94.46 [1958]~E(x19581,x19582)+E(f673(x19581,x19583,x19584,x19585,x19586),f673(x19582,x19583,x19584,x19585,x19586))
% 94.68/94.46 [1959]~E(x19591,x19592)+E(f673(x19593,x19591,x19594,x19595,x19596),f673(x19593,x19592,x19594,x19595,x19596))
% 94.68/94.46 [1960]~E(x19601,x19602)+E(f673(x19603,x19604,x19601,x19605,x19606),f673(x19603,x19604,x19602,x19605,x19606))
% 94.68/94.46 [1961]~E(x19611,x19612)+E(f673(x19613,x19614,x19615,x19611,x19616),f673(x19613,x19614,x19615,x19612,x19616))
% 94.68/94.46 [1962]~E(x19621,x19622)+E(f673(x19623,x19624,x19625,x19626,x19621),f673(x19623,x19624,x19625,x19626,x19622))
% 94.68/94.46 [1963]~E(x19631,x19632)+E(f187(x19631,x19633,x19634,x19635),f187(x19632,x19633,x19634,x19635))
% 94.68/94.46 [1964]~E(x19641,x19642)+E(f187(x19643,x19641,x19644,x19645),f187(x19643,x19642,x19644,x19645))
% 94.68/94.46 [1965]~E(x19651,x19652)+E(f187(x19653,x19654,x19651,x19655),f187(x19653,x19654,x19652,x19655))
% 94.68/94.46 [1966]~E(x19661,x19662)+E(f187(x19663,x19664,x19665,x19661),f187(x19663,x19664,x19665,x19662))
% 94.68/94.46 [1967]~E(x19671,x19672)+E(f557(x19671,x19673,x19674),f557(x19672,x19673,x19674))
% 94.68/94.46 [1968]~E(x19681,x19682)+E(f557(x19683,x19681,x19684),f557(x19683,x19682,x19684))
% 94.68/94.46 [1969]~E(x19691,x19692)+E(f557(x19693,x19694,x19691),f557(x19693,x19694,x19692))
% 94.68/94.46 [1970]~E(x19701,x19702)+E(f33(x19701),f33(x19702))
% 94.68/94.46 [1971]~E(x19711,x19712)+E(f417(x19711,x19713,x19714),f417(x19712,x19713,x19714))
% 94.68/94.46 [1972]~E(x19721,x19722)+E(f417(x19723,x19721,x19724),f417(x19723,x19722,x19724))
% 94.68/94.46 [1973]~E(x19731,x19732)+E(f417(x19733,x19734,x19731),f417(x19733,x19734,x19732))
% 94.68/94.46 [1974]~E(x19741,x19742)+E(f732(x19741,x19743,x19744),f732(x19742,x19743,x19744))
% 94.68/94.46 [1975]~E(x19751,x19752)+E(f732(x19753,x19751,x19754),f732(x19753,x19752,x19754))
% 94.68/94.46 [1976]~E(x19761,x19762)+E(f732(x19763,x19764,x19761),f732(x19763,x19764,x19762))
% 94.68/94.46 [1977]~E(x19771,x19772)+E(f578(x19771,x19773,x19774),f578(x19772,x19773,x19774))
% 94.68/94.46 [1978]~E(x19781,x19782)+E(f578(x19783,x19781,x19784),f578(x19783,x19782,x19784))
% 94.68/94.46 [1979]~E(x19791,x19792)+E(f578(x19793,x19794,x19791),f578(x19793,x19794,x19792))
% 94.68/94.46 [1980]~E(x19801,x19802)+E(f567(x19801,x19803,x19804),f567(x19802,x19803,x19804))
% 94.68/94.46 [1981]~E(x19811,x19812)+E(f567(x19813,x19811,x19814),f567(x19813,x19812,x19814))
% 94.68/94.46 [1982]~E(x19821,x19822)+E(f567(x19823,x19824,x19821),f567(x19823,x19824,x19822))
% 94.68/94.46 [1983]~E(x19831,x19832)+E(f805(x19831,x19833,x19834,x19835,x19836,x19837),f805(x19832,x19833,x19834,x19835,x19836,x19837))
% 94.68/94.46 [1984]~E(x19841,x19842)+E(f805(x19843,x19841,x19844,x19845,x19846,x19847),f805(x19843,x19842,x19844,x19845,x19846,x19847))
% 94.68/94.46 [1985]~E(x19851,x19852)+E(f805(x19853,x19854,x19851,x19855,x19856,x19857),f805(x19853,x19854,x19852,x19855,x19856,x19857))
% 94.68/94.46 [1986]~E(x19861,x19862)+E(f805(x19863,x19864,x19865,x19861,x19866,x19867),f805(x19863,x19864,x19865,x19862,x19866,x19867))
% 94.68/94.46 [1987]~E(x19871,x19872)+E(f805(x19873,x19874,x19875,x19876,x19871,x19877),f805(x19873,x19874,x19875,x19876,x19872,x19877))
% 94.68/94.46 [1988]~E(x19881,x19882)+E(f805(x19883,x19884,x19885,x19886,x19887,x19881),f805(x19883,x19884,x19885,x19886,x19887,x19882))
% 94.68/94.46 [1989]~E(x19891,x19892)+E(f618(x19891,x19893,x19894,x19895,x19896),f618(x19892,x19893,x19894,x19895,x19896))
% 94.68/94.46 [1990]~E(x19901,x19902)+E(f618(x19903,x19901,x19904,x19905,x19906),f618(x19903,x19902,x19904,x19905,x19906))
% 94.68/94.46 [1991]~E(x19911,x19912)+E(f618(x19913,x19914,x19911,x19915,x19916),f618(x19913,x19914,x19912,x19915,x19916))
% 94.68/94.46 [1992]~E(x19921,x19922)+E(f618(x19923,x19924,x19925,x19921,x19926),f618(x19923,x19924,x19925,x19922,x19926))
% 94.68/94.46 [1993]~E(x19931,x19932)+E(f618(x19933,x19934,x19935,x19936,x19931),f618(x19933,x19934,x19935,x19936,x19932))
% 94.68/94.46 [1994]~E(x19941,x19942)+E(f471(x19941,x19943,x19944),f471(x19942,x19943,x19944))
% 94.68/94.46 [1995]~E(x19951,x19952)+E(f471(x19953,x19951,x19954),f471(x19953,x19952,x19954))
% 94.68/94.46 [1996]~E(x19961,x19962)+E(f471(x19963,x19964,x19961),f471(x19963,x19964,x19962))
% 94.68/94.46 [1997]~E(x19971,x19972)+E(f647(x19971,x19973,x19974,x19975),f647(x19972,x19973,x19974,x19975))
% 94.68/94.46 [1998]~E(x19981,x19982)+E(f647(x19983,x19981,x19984,x19985),f647(x19983,x19982,x19984,x19985))
% 94.68/94.46 [1999]~E(x19991,x19992)+E(f647(x19993,x19994,x19991,x19995),f647(x19993,x19994,x19992,x19995))
% 94.68/94.46 [2000]~E(x20001,x20002)+E(f647(x20003,x20004,x20005,x20001),f647(x20003,x20004,x20005,x20002))
% 94.68/94.46 [2001]~E(x20011,x20012)+E(f337(x20011,x20013,x20014),f337(x20012,x20013,x20014))
% 94.68/94.46 [2002]~E(x20021,x20022)+E(f337(x20023,x20021,x20024),f337(x20023,x20022,x20024))
% 94.68/94.46 [2003]~E(x20031,x20032)+E(f337(x20033,x20034,x20031),f337(x20033,x20034,x20032))
% 94.68/94.46 [2004]~E(x20041,x20042)+E(f619(x20041,x20043,x20044,x20045),f619(x20042,x20043,x20044,x20045))
% 94.68/94.46 [2005]~E(x20051,x20052)+E(f619(x20053,x20051,x20054,x20055),f619(x20053,x20052,x20054,x20055))
% 94.68/94.46 [2006]~E(x20061,x20062)+E(f619(x20063,x20064,x20061,x20065),f619(x20063,x20064,x20062,x20065))
% 94.68/94.46 [2007]~E(x20071,x20072)+E(f619(x20073,x20074,x20075,x20071),f619(x20073,x20074,x20075,x20072))
% 94.68/94.46 [2008]~E(x20081,x20082)+E(f716(x20081,x20083,x20084),f716(x20082,x20083,x20084))
% 94.68/94.46 [2009]~E(x20091,x20092)+E(f716(x20093,x20091,x20094),f716(x20093,x20092,x20094))
% 94.68/94.46 [2010]~E(x20101,x20102)+E(f716(x20103,x20104,x20101),f716(x20103,x20104,x20102))
% 94.68/94.46 [2011]~E(x20111,x20112)+E(f493(x20111,x20113,x20114,x20115),f493(x20112,x20113,x20114,x20115))
% 94.68/94.46 [2012]~E(x20121,x20122)+E(f493(x20123,x20121,x20124,x20125),f493(x20123,x20122,x20124,x20125))
% 94.68/94.46 [2013]~E(x20131,x20132)+E(f493(x20133,x20134,x20131,x20135),f493(x20133,x20134,x20132,x20135))
% 94.68/94.46 [2014]~E(x20141,x20142)+E(f493(x20143,x20144,x20145,x20141),f493(x20143,x20144,x20145,x20142))
% 94.68/94.46 [2015]~E(x20151,x20152)+E(f454(x20151,x20153,x20154,x20155,x20156),f454(x20152,x20153,x20154,x20155,x20156))
% 94.68/94.46 [2016]~E(x20161,x20162)+E(f454(x20163,x20161,x20164,x20165,x20166),f454(x20163,x20162,x20164,x20165,x20166))
% 94.68/94.46 [2017]~E(x20171,x20172)+E(f454(x20173,x20174,x20171,x20175,x20176),f454(x20173,x20174,x20172,x20175,x20176))
% 94.68/94.46 [2018]~E(x20181,x20182)+E(f454(x20183,x20184,x20185,x20181,x20186),f454(x20183,x20184,x20185,x20182,x20186))
% 94.68/94.46 [2019]~E(x20191,x20192)+E(f454(x20193,x20194,x20195,x20196,x20191),f454(x20193,x20194,x20195,x20196,x20192))
% 94.68/94.46 [2020]~E(x20201,x20202)+E(f195(x20201,x20203,x20204,x20205),f195(x20202,x20203,x20204,x20205))
% 94.68/94.46 [2021]~E(x20211,x20212)+E(f195(x20213,x20211,x20214,x20215),f195(x20213,x20212,x20214,x20215))
% 94.68/94.46 [2022]~E(x20221,x20222)+E(f195(x20223,x20224,x20221,x20225),f195(x20223,x20224,x20222,x20225))
% 94.68/94.46 [2023]~E(x20231,x20232)+E(f195(x20233,x20234,x20235,x20231),f195(x20233,x20234,x20235,x20232))
% 94.68/94.46 [2024]~E(x20241,x20242)+E(f571(x20241,x20243,x20244,x20245,x20246),f571(x20242,x20243,x20244,x20245,x20246))
% 94.68/94.46 [2025]~E(x20251,x20252)+E(f571(x20253,x20251,x20254,x20255,x20256),f571(x20253,x20252,x20254,x20255,x20256))
% 94.68/94.46 [2026]~E(x20261,x20262)+E(f571(x20263,x20264,x20261,x20265,x20266),f571(x20263,x20264,x20262,x20265,x20266))
% 94.68/94.46 [2027]~E(x20271,x20272)+E(f571(x20273,x20274,x20275,x20271,x20276),f571(x20273,x20274,x20275,x20272,x20276))
% 94.68/94.46 [2028]~E(x20281,x20282)+E(f571(x20283,x20284,x20285,x20286,x20281),f571(x20283,x20284,x20285,x20286,x20282))
% 94.68/94.46 [2029]~E(x20291,x20292)+E(f364(x20291,x20293,x20294,x20295),f364(x20292,x20293,x20294,x20295))
% 94.68/94.46 [2030]~E(x20301,x20302)+E(f364(x20303,x20301,x20304,x20305),f364(x20303,x20302,x20304,x20305))
% 94.68/94.46 [2031]~E(x20311,x20312)+E(f364(x20313,x20314,x20311,x20315),f364(x20313,x20314,x20312,x20315))
% 94.68/94.46 [2032]~E(x20321,x20322)+E(f364(x20323,x20324,x20325,x20321),f364(x20323,x20324,x20325,x20322))
% 94.68/94.46 [2033]~E(x20331,x20332)+E(f461(x20331,x20333,x20334),f461(x20332,x20333,x20334))
% 94.68/94.46 [2034]~E(x20341,x20342)+E(f461(x20343,x20341,x20344),f461(x20343,x20342,x20344))
% 94.68/94.46 [2035]~E(x20351,x20352)+E(f461(x20353,x20354,x20351),f461(x20353,x20354,x20352))
% 94.68/94.46 [2036]~E(x20361,x20362)+E(f883(x20361,x20363,x20364),f883(x20362,x20363,x20364))
% 94.68/94.46 [2037]~E(x20371,x20372)+E(f883(x20373,x20371,x20374),f883(x20373,x20372,x20374))
% 94.68/94.46 [2038]~E(x20381,x20382)+E(f883(x20383,x20384,x20381),f883(x20383,x20384,x20382))
% 94.68/94.46 [2039]~E(x20391,x20392)+E(f538(x20391,x20393,x20394),f538(x20392,x20393,x20394))
% 94.68/94.46 [2040]~E(x20401,x20402)+E(f538(x20403,x20401,x20404),f538(x20403,x20402,x20404))
% 94.68/94.46 [2041]~E(x20411,x20412)+E(f538(x20413,x20414,x20411),f538(x20413,x20414,x20412))
% 94.68/94.46 [2042]~E(x20421,x20422)+E(f355(x20421,x20423,x20424,x20425),f355(x20422,x20423,x20424,x20425))
% 94.68/94.46 [2043]~E(x20431,x20432)+E(f355(x20433,x20431,x20434,x20435),f355(x20433,x20432,x20434,x20435))
% 94.68/94.46 [2044]~E(x20441,x20442)+E(f355(x20443,x20444,x20441,x20445),f355(x20443,x20444,x20442,x20445))
% 94.68/94.46 [2045]~E(x20451,x20452)+E(f355(x20453,x20454,x20455,x20451),f355(x20453,x20454,x20455,x20452))
% 94.68/94.46 [2046]~E(x20461,x20462)+E(f543(x20461,x20463,x20464,x20465,x20466),f543(x20462,x20463,x20464,x20465,x20466))
% 94.68/94.46 [2047]~E(x20471,x20472)+E(f543(x20473,x20471,x20474,x20475,x20476),f543(x20473,x20472,x20474,x20475,x20476))
% 94.68/94.46 [2048]~E(x20481,x20482)+E(f543(x20483,x20484,x20481,x20485,x20486),f543(x20483,x20484,x20482,x20485,x20486))
% 94.68/94.46 [2049]~E(x20491,x20492)+E(f543(x20493,x20494,x20495,x20491,x20496),f543(x20493,x20494,x20495,x20492,x20496))
% 94.68/94.46 [2050]~E(x20501,x20502)+E(f543(x20503,x20504,x20505,x20506,x20501),f543(x20503,x20504,x20505,x20506,x20502))
% 94.68/94.46 [2051]~E(x20511,x20512)+E(f302(x20511,x20513),f302(x20512,x20513))
% 94.68/94.46 [2052]~E(x20521,x20522)+E(f302(x20523,x20521),f302(x20523,x20522))
% 94.68/94.46 [2053]~E(x20531,x20532)+E(f804(x20531,x20533),f804(x20532,x20533))
% 94.68/94.46 [2054]~E(x20541,x20542)+E(f804(x20543,x20541),f804(x20543,x20542))
% 94.68/94.46 [2055]~E(x20551,x20552)+E(f222(x20551,x20553),f222(x20552,x20553))
% 94.68/94.46 [2056]~E(x20561,x20562)+E(f222(x20563,x20561),f222(x20563,x20562))
% 94.68/94.46 [2057]~E(x20571,x20572)+E(f365(x20571,x20573,x20574,x20575),f365(x20572,x20573,x20574,x20575))
% 94.68/94.46 [2058]~E(x20581,x20582)+E(f365(x20583,x20581,x20584,x20585),f365(x20583,x20582,x20584,x20585))
% 94.68/94.46 [2059]~E(x20591,x20592)+E(f365(x20593,x20594,x20591,x20595),f365(x20593,x20594,x20592,x20595))
% 94.68/94.46 [2060]~E(x20601,x20602)+E(f365(x20603,x20604,x20605,x20601),f365(x20603,x20604,x20605,x20602))
% 94.68/94.46 [2061]~E(x20611,x20612)+E(f107(x20611,x20613,x20614),f107(x20612,x20613,x20614))
% 94.68/94.46 [2062]~E(x20621,x20622)+E(f107(x20623,x20621,x20624),f107(x20623,x20622,x20624))
% 94.68/94.46 [2063]~E(x20631,x20632)+E(f107(x20633,x20634,x20631),f107(x20633,x20634,x20632))
% 94.68/94.46 [2064]~E(x20641,x20642)+E(f604(x20641,x20643,x20644,x20645),f604(x20642,x20643,x20644,x20645))
% 94.68/94.46 [2065]~E(x20651,x20652)+E(f604(x20653,x20651,x20654,x20655),f604(x20653,x20652,x20654,x20655))
% 94.68/94.46 [2066]~E(x20661,x20662)+E(f604(x20663,x20664,x20661,x20665),f604(x20663,x20664,x20662,x20665))
% 94.68/94.46 [2067]~E(x20671,x20672)+E(f604(x20673,x20674,x20675,x20671),f604(x20673,x20674,x20675,x20672))
% 94.68/94.46 [2068]~E(x20681,x20682)+E(f406(x20681,x20683,x20684,x20685,x20686),f406(x20682,x20683,x20684,x20685,x20686))
% 94.68/94.46 [2069]~E(x20691,x20692)+E(f406(x20693,x20691,x20694,x20695,x20696),f406(x20693,x20692,x20694,x20695,x20696))
% 94.68/94.46 [2070]~E(x20701,x20702)+E(f406(x20703,x20704,x20701,x20705,x20706),f406(x20703,x20704,x20702,x20705,x20706))
% 94.68/94.46 [2071]~E(x20711,x20712)+E(f406(x20713,x20714,x20715,x20711,x20716),f406(x20713,x20714,x20715,x20712,x20716))
% 94.68/94.46 [2072]~E(x20721,x20722)+E(f406(x20723,x20724,x20725,x20726,x20721),f406(x20723,x20724,x20725,x20726,x20722))
% 94.68/94.46 [2073]~E(x20731,x20732)+E(f398(x20731,x20733,x20734),f398(x20732,x20733,x20734))
% 94.68/94.46 [2074]~E(x20741,x20742)+E(f398(x20743,x20741,x20744),f398(x20743,x20742,x20744))
% 94.68/94.46 [2075]~E(x20751,x20752)+E(f398(x20753,x20754,x20751),f398(x20753,x20754,x20752))
% 94.68/94.46 [2076]~E(x20761,x20762)+E(f660(x20761,x20763,x20764,x20765,x20766),f660(x20762,x20763,x20764,x20765,x20766))
% 94.68/94.46 [2077]~E(x20771,x20772)+E(f660(x20773,x20771,x20774,x20775,x20776),f660(x20773,x20772,x20774,x20775,x20776))
% 94.68/94.46 [2078]~E(x20781,x20782)+E(f660(x20783,x20784,x20781,x20785,x20786),f660(x20783,x20784,x20782,x20785,x20786))
% 94.68/94.46 [2079]~E(x20791,x20792)+E(f660(x20793,x20794,x20795,x20791,x20796),f660(x20793,x20794,x20795,x20792,x20796))
% 94.68/94.46 [2080]~E(x20801,x20802)+E(f660(x20803,x20804,x20805,x20806,x20801),f660(x20803,x20804,x20805,x20806,x20802))
% 94.68/94.46 [2081]~E(x20811,x20812)+E(f353(x20811,x20813),f353(x20812,x20813))
% 94.68/94.46 [2082]~E(x20821,x20822)+E(f353(x20823,x20821),f353(x20823,x20822))
% 94.68/94.46 [2083]~E(x20831,x20832)+E(f677(x20831,x20833,x20834,x20835,x20836),f677(x20832,x20833,x20834,x20835,x20836))
% 94.68/94.46 [2084]~E(x20841,x20842)+E(f677(x20843,x20841,x20844,x20845,x20846),f677(x20843,x20842,x20844,x20845,x20846))
% 94.68/94.46 [2085]~E(x20851,x20852)+E(f677(x20853,x20854,x20851,x20855,x20856),f677(x20853,x20854,x20852,x20855,x20856))
% 94.68/94.46 [2086]~E(x20861,x20862)+E(f677(x20863,x20864,x20865,x20861,x20866),f677(x20863,x20864,x20865,x20862,x20866))
% 94.68/94.46 [2087]~E(x20871,x20872)+E(f677(x20873,x20874,x20875,x20876,x20871),f677(x20873,x20874,x20875,x20876,x20872))
% 94.68/94.46 [2088]~E(x20881,x20882)+E(f606(x20881,x20883,x20884,x20885,x20886,x20887),f606(x20882,x20883,x20884,x20885,x20886,x20887))
% 94.68/94.46 [2089]~E(x20891,x20892)+E(f606(x20893,x20891,x20894,x20895,x20896,x20897),f606(x20893,x20892,x20894,x20895,x20896,x20897))
% 94.68/94.46 [2090]~E(x20901,x20902)+E(f606(x20903,x20904,x20901,x20905,x20906,x20907),f606(x20903,x20904,x20902,x20905,x20906,x20907))
% 94.68/94.46 [2091]~E(x20911,x20912)+E(f606(x20913,x20914,x20915,x20911,x20916,x20917),f606(x20913,x20914,x20915,x20912,x20916,x20917))
% 94.68/94.46 [2092]~E(x20921,x20922)+E(f606(x20923,x20924,x20925,x20926,x20921,x20927),f606(x20923,x20924,x20925,x20926,x20922,x20927))
% 94.68/94.46 [2093]~E(x20931,x20932)+E(f606(x20933,x20934,x20935,x20936,x20937,x20931),f606(x20933,x20934,x20935,x20936,x20937,x20932))
% 94.68/94.46 [2094]~E(x20941,x20942)+E(f389(x20941,x20943,x20944,x20945),f389(x20942,x20943,x20944,x20945))
% 94.68/94.46 [2095]~E(x20951,x20952)+E(f389(x20953,x20951,x20954,x20955),f389(x20953,x20952,x20954,x20955))
% 94.68/94.46 [2096]~E(x20961,x20962)+E(f389(x20963,x20964,x20961,x20965),f389(x20963,x20964,x20962,x20965))
% 94.68/94.46 [2097]~E(x20971,x20972)+E(f389(x20973,x20974,x20975,x20971),f389(x20973,x20974,x20975,x20972))
% 94.68/94.46 [2098]~E(x20981,x20982)+E(f667(x20981,x20983,x20984),f667(x20982,x20983,x20984))
% 94.68/94.46 [2099]~E(x20991,x20992)+E(f667(x20993,x20991,x20994),f667(x20993,x20992,x20994))
% 94.68/94.46 [2100]~E(x21001,x21002)+E(f667(x21003,x21004,x21001),f667(x21003,x21004,x21002))
% 94.68/94.46 [2101]~E(x21011,x21012)+E(f19(x21011,x21013,x21014,x21015),f19(x21012,x21013,x21014,x21015))
% 94.68/94.46 [2102]~E(x21021,x21022)+E(f19(x21023,x21021,x21024,x21025),f19(x21023,x21022,x21024,x21025))
% 94.68/94.46 [2103]~E(x21031,x21032)+E(f19(x21033,x21034,x21031,x21035),f19(x21033,x21034,x21032,x21035))
% 94.68/94.46 [2104]~E(x21041,x21042)+E(f19(x21043,x21044,x21045,x21041),f19(x21043,x21044,x21045,x21042))
% 94.68/94.46 [2105]~E(x21051,x21052)+E(f672(x21051,x21053,x21054,x21055,x21056),f672(x21052,x21053,x21054,x21055,x21056))
% 94.68/94.47 [2106]~E(x21061,x21062)+E(f672(x21063,x21061,x21064,x21065,x21066),f672(x21063,x21062,x21064,x21065,x21066))
% 94.68/94.47 [2107]~E(x21071,x21072)+E(f672(x21073,x21074,x21071,x21075,x21076),f672(x21073,x21074,x21072,x21075,x21076))
% 94.68/94.47 [2108]~E(x21081,x21082)+E(f672(x21083,x21084,x21085,x21081,x21086),f672(x21083,x21084,x21085,x21082,x21086))
% 94.68/94.47 [2109]~E(x21091,x21092)+E(f672(x21093,x21094,x21095,x21096,x21091),f672(x21093,x21094,x21095,x21096,x21092))
% 94.68/94.47 [2110]~E(x21101,x21102)+E(f682(x21101,x21103,x21104),f682(x21102,x21103,x21104))
% 94.68/94.47 [2111]~E(x21111,x21112)+E(f682(x21113,x21111,x21114),f682(x21113,x21112,x21114))
% 94.68/94.47 [2112]~E(x21121,x21122)+E(f682(x21123,x21124,x21121),f682(x21123,x21124,x21122))
% 94.68/94.47 [2113]~E(x21131,x21132)+E(f499(x21131,x21133,x21134),f499(x21132,x21133,x21134))
% 94.68/94.47 [2114]~E(x21141,x21142)+E(f499(x21143,x21141,x21144),f499(x21143,x21142,x21144))
% 94.68/94.47 [2115]~E(x21151,x21152)+E(f499(x21153,x21154,x21151),f499(x21153,x21154,x21152))
% 94.68/94.47 [2116]~E(x21161,x21162)+E(f877(x21161,x21163,x21164),f877(x21162,x21163,x21164))
% 94.68/94.47 [2117]~E(x21171,x21172)+E(f877(x21173,x21171,x21174),f877(x21173,x21172,x21174))
% 94.68/94.47 [2118]~E(x21181,x21182)+E(f877(x21183,x21184,x21181),f877(x21183,x21184,x21182))
% 94.68/94.47 [2119]~E(x21191,x21192)+E(f542(x21191,x21193,x21194,x21195),f542(x21192,x21193,x21194,x21195))
% 94.68/94.47 [2120]~E(x21201,x21202)+E(f542(x21203,x21201,x21204,x21205),f542(x21203,x21202,x21204,x21205))
% 94.68/94.47 [2121]~E(x21211,x21212)+E(f542(x21213,x21214,x21211,x21215),f542(x21213,x21214,x21212,x21215))
% 94.68/94.47 [2122]~E(x21221,x21222)+E(f542(x21223,x21224,x21225,x21221),f542(x21223,x21224,x21225,x21222))
% 94.68/94.47 [2123]~E(x21231,x21232)+E(f334(x21231,x21233),f334(x21232,x21233))
% 94.68/94.47 [2124]~E(x21241,x21242)+E(f334(x21243,x21241),f334(x21243,x21242))
% 94.68/94.47 [2125]~E(x21251,x21252)+E(f340(x21251,x21253,x21254),f340(x21252,x21253,x21254))
% 94.68/94.47 [2126]~E(x21261,x21262)+E(f340(x21263,x21261,x21264),f340(x21263,x21262,x21264))
% 94.68/94.47 [2127]~E(x21271,x21272)+E(f340(x21273,x21274,x21271),f340(x21273,x21274,x21272))
% 94.68/94.47 [2128]~E(x21281,x21282)+E(f570(x21281,x21283,x21284,x21285,x21286),f570(x21282,x21283,x21284,x21285,x21286))
% 94.68/94.47 [2129]~E(x21291,x21292)+E(f570(x21293,x21291,x21294,x21295,x21296),f570(x21293,x21292,x21294,x21295,x21296))
% 94.68/94.47 [2130]~E(x21301,x21302)+E(f570(x21303,x21304,x21301,x21305,x21306),f570(x21303,x21304,x21302,x21305,x21306))
% 94.68/94.47 [2131]~E(x21311,x21312)+E(f570(x21313,x21314,x21315,x21311,x21316),f570(x21313,x21314,x21315,x21312,x21316))
% 94.68/94.47 [2132]~E(x21321,x21322)+E(f570(x21323,x21324,x21325,x21326,x21321),f570(x21323,x21324,x21325,x21326,x21322))
% 94.68/94.47 [2133]~E(x21331,x21332)+E(f455(x21331,x21333,x21334,x21335,x21336),f455(x21332,x21333,x21334,x21335,x21336))
% 94.68/94.47 [2134]~E(x21341,x21342)+E(f455(x21343,x21341,x21344,x21345,x21346),f455(x21343,x21342,x21344,x21345,x21346))
% 94.68/94.47 [2135]~E(x21351,x21352)+E(f455(x21353,x21354,x21351,x21355,x21356),f455(x21353,x21354,x21352,x21355,x21356))
% 94.68/94.47 [2136]~E(x21361,x21362)+E(f455(x21363,x21364,x21365,x21361,x21366),f455(x21363,x21364,x21365,x21362,x21366))
% 94.68/94.47 [2137]~E(x21371,x21372)+E(f455(x21373,x21374,x21375,x21376,x21371),f455(x21373,x21374,x21375,x21376,x21372))
% 94.68/94.47 [2138]~E(x21381,x21382)+E(f795(x21381,x21383),f795(x21382,x21383))
% 94.68/94.47 [2139]~E(x21391,x21392)+E(f795(x21393,x21391),f795(x21393,x21392))
% 94.68/94.47 [2140]~E(x21401,x21402)+E(f706(x21401,x21403,x21404,x21405),f706(x21402,x21403,x21404,x21405))
% 94.68/94.47 [2141]~E(x21411,x21412)+E(f706(x21413,x21411,x21414,x21415),f706(x21413,x21412,x21414,x21415))
% 94.68/94.47 [2142]~E(x21421,x21422)+E(f706(x21423,x21424,x21421,x21425),f706(x21423,x21424,x21422,x21425))
% 94.68/94.47 [2143]~E(x21431,x21432)+E(f706(x21433,x21434,x21435,x21431),f706(x21433,x21434,x21435,x21432))
% 94.68/94.47 [2144]~E(x21441,x21442)+E(f204(x21441,x21443),f204(x21442,x21443))
% 94.68/94.47 [2145]~E(x21451,x21452)+E(f204(x21453,x21451),f204(x21453,x21452))
% 94.68/94.47 [2146]~E(x21461,x21462)+E(f544(x21461,x21463,x21464),f544(x21462,x21463,x21464))
% 94.68/94.47 [2147]~E(x21471,x21472)+E(f544(x21473,x21471,x21474),f544(x21473,x21472,x21474))
% 94.68/94.47 [2148]~E(x21481,x21482)+E(f544(x21483,x21484,x21481),f544(x21483,x21484,x21482))
% 94.68/94.47 [2149]~E(x21491,x21492)+E(f737(x21491,x21493,x21494),f737(x21492,x21493,x21494))
% 94.68/94.47 [2150]~E(x21501,x21502)+E(f737(x21503,x21501,x21504),f737(x21503,x21502,x21504))
% 94.68/94.47 [2151]~E(x21511,x21512)+E(f737(x21513,x21514,x21511),f737(x21513,x21514,x21512))
% 94.68/94.47 [2152]~E(x21521,x21522)+E(f265(x21521,x21523),f265(x21522,x21523))
% 94.68/94.47 [2153]~E(x21531,x21532)+E(f265(x21533,x21531),f265(x21533,x21532))
% 94.68/94.47 [2154]~E(x21541,x21542)+E(f479(x21541,x21543,x21544),f479(x21542,x21543,x21544))
% 94.68/94.47 [2155]~E(x21551,x21552)+E(f479(x21553,x21551,x21554),f479(x21553,x21552,x21554))
% 94.68/94.47 [2156]~E(x21561,x21562)+E(f479(x21563,x21564,x21561),f479(x21563,x21564,x21562))
% 94.68/94.47 [2157]~E(x21571,x21572)+E(f616(x21571,x21573,x21574),f616(x21572,x21573,x21574))
% 94.68/94.47 [2158]~E(x21581,x21582)+E(f616(x21583,x21581,x21584),f616(x21583,x21582,x21584))
% 94.68/94.47 [2159]~E(x21591,x21592)+E(f616(x21593,x21594,x21591),f616(x21593,x21594,x21592))
% 94.68/94.47 [2160]~E(x21601,x21602)+E(f378(x21601),f378(x21602))
% 94.68/94.47 [2161]~E(x21611,x21612)+E(f779(x21611),f779(x21612))
% 94.68/94.47 [2162]~E(x21621,x21622)+E(f878(x21621,x21623,x21624),f878(x21622,x21623,x21624))
% 94.68/94.47 [2163]~E(x21631,x21632)+E(f878(x21633,x21631,x21634),f878(x21633,x21632,x21634))
% 94.68/94.47 [2164]~E(x21641,x21642)+E(f878(x21643,x21644,x21641),f878(x21643,x21644,x21642))
% 94.68/94.47 [2165]~E(x21651,x21652)+E(f773(x21651,x21653,x21654,x21655),f773(x21652,x21653,x21654,x21655))
% 94.68/94.47 [2166]~E(x21661,x21662)+E(f773(x21663,x21661,x21664,x21665),f773(x21663,x21662,x21664,x21665))
% 94.68/94.47 [2167]~E(x21671,x21672)+E(f773(x21673,x21674,x21671,x21675),f773(x21673,x21674,x21672,x21675))
% 94.68/94.47 [2168]~E(x21681,x21682)+E(f773(x21683,x21684,x21685,x21681),f773(x21683,x21684,x21685,x21682))
% 94.68/94.47 [2169]~E(x21691,x21692)+E(f634(x21691,x21693,x21694,x21695,x21696),f634(x21692,x21693,x21694,x21695,x21696))
% 94.68/94.47 [2170]~E(x21701,x21702)+E(f634(x21703,x21701,x21704,x21705,x21706),f634(x21703,x21702,x21704,x21705,x21706))
% 94.68/94.47 [2171]~E(x21711,x21712)+E(f634(x21713,x21714,x21711,x21715,x21716),f634(x21713,x21714,x21712,x21715,x21716))
% 94.68/94.47 [2172]~E(x21721,x21722)+E(f634(x21723,x21724,x21725,x21721,x21726),f634(x21723,x21724,x21725,x21722,x21726))
% 94.68/94.47 [2173]~E(x21731,x21732)+E(f634(x21733,x21734,x21735,x21736,x21731),f634(x21733,x21734,x21735,x21736,x21732))
% 94.68/94.47 [2174]~E(x21741,x21742)+E(f507(x21741,x21743,x21744,x21745),f507(x21742,x21743,x21744,x21745))
% 94.68/94.47 [2175]~E(x21751,x21752)+E(f507(x21753,x21751,x21754,x21755),f507(x21753,x21752,x21754,x21755))
% 94.68/94.47 [2176]~E(x21761,x21762)+E(f507(x21763,x21764,x21761,x21765),f507(x21763,x21764,x21762,x21765))
% 94.68/94.47 [2177]~E(x21771,x21772)+E(f507(x21773,x21774,x21775,x21771),f507(x21773,x21774,x21775,x21772))
% 94.68/94.47 [2178]~E(x21781,x21782)+E(f193(x21781,x21783,x21784),f193(x21782,x21783,x21784))
% 94.68/94.47 [2179]~E(x21791,x21792)+E(f193(x21793,x21791,x21794),f193(x21793,x21792,x21794))
% 94.68/94.47 [2180]~E(x21801,x21802)+E(f193(x21803,x21804,x21801),f193(x21803,x21804,x21802))
% 94.68/94.47 [2181]~E(x21811,x21812)+E(f463(x21811,x21813,x21814,x21815),f463(x21812,x21813,x21814,x21815))
% 94.68/94.47 [2182]~E(x21821,x21822)+E(f463(x21823,x21821,x21824,x21825),f463(x21823,x21822,x21824,x21825))
% 94.68/94.47 [2183]~E(x21831,x21832)+E(f463(x21833,x21834,x21831,x21835),f463(x21833,x21834,x21832,x21835))
% 94.68/94.47 [2184]~E(x21841,x21842)+E(f463(x21843,x21844,x21845,x21841),f463(x21843,x21844,x21845,x21842))
% 94.68/94.47 [2185]~E(x21851,x21852)+E(f555(x21851,x21853),f555(x21852,x21853))
% 94.68/94.47 [2186]~E(x21861,x21862)+E(f555(x21863,x21861),f555(x21863,x21862))
% 94.68/94.47 [2187]~E(x21871,x21872)+E(f838(x21871,x21873,x21874),f838(x21872,x21873,x21874))
% 94.68/94.47 [2188]~E(x21881,x21882)+E(f838(x21883,x21881,x21884),f838(x21883,x21882,x21884))
% 94.68/94.47 [2189]~E(x21891,x21892)+E(f838(x21893,x21894,x21891),f838(x21893,x21894,x21892))
% 94.68/94.47 [2190]~E(x21901,x21902)+E(f819(x21901,x21903,x21904,x21905,x21906,x21907,x21908,x21909),f819(x21902,x21903,x21904,x21905,x21906,x21907,x21908,x21909))
% 94.68/94.47 [2191]~E(x21911,x21912)+E(f819(x21913,x21911,x21914,x21915,x21916,x21917,x21918,x21919),f819(x21913,x21912,x21914,x21915,x21916,x21917,x21918,x21919))
% 94.68/94.47 [2192]~E(x21921,x21922)+E(f819(x21923,x21924,x21921,x21925,x21926,x21927,x21928,x21929),f819(x21923,x21924,x21922,x21925,x21926,x21927,x21928,x21929))
% 94.68/94.47 [2193]~E(x21931,x21932)+E(f819(x21933,x21934,x21935,x21931,x21936,x21937,x21938,x21939),f819(x21933,x21934,x21935,x21932,x21936,x21937,x21938,x21939))
% 94.68/94.47 [2194]~E(x21941,x21942)+E(f819(x21943,x21944,x21945,x21946,x21941,x21947,x21948,x21949),f819(x21943,x21944,x21945,x21946,x21942,x21947,x21948,x21949))
% 94.68/94.47 [2195]~E(x21951,x21952)+E(f819(x21953,x21954,x21955,x21956,x21957,x21951,x21958,x21959),f819(x21953,x21954,x21955,x21956,x21957,x21952,x21958,x21959))
% 94.68/94.47 [2196]~E(x21961,x21962)+E(f819(x21963,x21964,x21965,x21966,x21967,x21968,x21961,x21969),f819(x21963,x21964,x21965,x21966,x21967,x21968,x21962,x21969))
% 94.68/94.47 [2197]~E(x21971,x21972)+E(f819(x21973,x21974,x21975,x21976,x21977,x21978,x21979,x21971),f819(x21973,x21974,x21975,x21976,x21977,x21978,x21979,x21972))
% 94.68/94.47 [2198]~E(x21981,x21982)+E(f821(x21981,x21983,x21984,x21985,x21986,x21987,x21988,x21989),f821(x21982,x21983,x21984,x21985,x21986,x21987,x21988,x21989))
% 94.68/94.47 [2199]~E(x21991,x21992)+E(f821(x21993,x21991,x21994,x21995,x21996,x21997,x21998,x21999),f821(x21993,x21992,x21994,x21995,x21996,x21997,x21998,x21999))
% 94.68/94.47 [2200]~E(x22001,x22002)+E(f821(x22003,x22004,x22001,x22005,x22006,x22007,x22008,x22009),f821(x22003,x22004,x22002,x22005,x22006,x22007,x22008,x22009))
% 94.68/94.47 [2201]~E(x22011,x22012)+E(f821(x22013,x22014,x22015,x22011,x22016,x22017,x22018,x22019),f821(x22013,x22014,x22015,x22012,x22016,x22017,x22018,x22019))
% 94.68/94.47 [2202]~E(x22021,x22022)+E(f821(x22023,x22024,x22025,x22026,x22021,x22027,x22028,x22029),f821(x22023,x22024,x22025,x22026,x22022,x22027,x22028,x22029))
% 94.68/94.47 [2203]~E(x22031,x22032)+E(f821(x22033,x22034,x22035,x22036,x22037,x22031,x22038,x22039),f821(x22033,x22034,x22035,x22036,x22037,x22032,x22038,x22039))
% 94.68/94.47 [2204]~E(x22041,x22042)+E(f821(x22043,x22044,x22045,x22046,x22047,x22048,x22041,x22049),f821(x22043,x22044,x22045,x22046,x22047,x22048,x22042,x22049))
% 94.68/94.47 [2205]~E(x22051,x22052)+E(f821(x22053,x22054,x22055,x22056,x22057,x22058,x22059,x22051),f821(x22053,x22054,x22055,x22056,x22057,x22058,x22059,x22052))
% 94.68/94.47 [2206]~E(x22061,x22062)+E(f666(x22061,x22063,x22064,x22065,x22066),f666(x22062,x22063,x22064,x22065,x22066))
% 94.68/94.47 [2207]~E(x22071,x22072)+E(f666(x22073,x22071,x22074,x22075,x22076),f666(x22073,x22072,x22074,x22075,x22076))
% 94.68/94.47 [2208]~E(x22081,x22082)+E(f666(x22083,x22084,x22081,x22085,x22086),f666(x22083,x22084,x22082,x22085,x22086))
% 94.68/94.47 [2209]~E(x22091,x22092)+E(f666(x22093,x22094,x22095,x22091,x22096),f666(x22093,x22094,x22095,x22092,x22096))
% 94.68/94.47 [2210]~E(x22101,x22102)+E(f666(x22103,x22104,x22105,x22106,x22101),f666(x22103,x22104,x22105,x22106,x22102))
% 94.68/94.47 [2211]~E(x22111,x22112)+E(f521(x22111,x22113,x22114,x22115),f521(x22112,x22113,x22114,x22115))
% 94.68/94.47 [2212]~E(x22121,x22122)+E(f521(x22123,x22121,x22124,x22125),f521(x22123,x22122,x22124,x22125))
% 94.68/94.47 [2213]~E(x22131,x22132)+E(f521(x22133,x22134,x22131,x22135),f521(x22133,x22134,x22132,x22135))
% 94.68/94.47 [2214]~E(x22141,x22142)+E(f521(x22143,x22144,x22145,x22141),f521(x22143,x22144,x22145,x22142))
% 94.68/94.47 [2215]~E(x22151,x22152)+E(f431(x22151,x22153,x22154,x22155),f431(x22152,x22153,x22154,x22155))
% 94.68/94.47 [2216]~E(x22161,x22162)+E(f431(x22163,x22161,x22164,x22165),f431(x22163,x22162,x22164,x22165))
% 94.68/94.47 [2217]~E(x22171,x22172)+E(f431(x22173,x22174,x22171,x22175),f431(x22173,x22174,x22172,x22175))
% 94.68/94.47 [2218]~E(x22181,x22182)+E(f431(x22183,x22184,x22185,x22181),f431(x22183,x22184,x22185,x22182))
% 94.68/94.47 [2219]~E(x22191,x22192)+E(f889(x22191,x22193,x22194,x22195),f889(x22192,x22193,x22194,x22195))
% 94.68/94.47 [2220]~E(x22201,x22202)+E(f889(x22203,x22201,x22204,x22205),f889(x22203,x22202,x22204,x22205))
% 94.68/94.47 [2221]~E(x22211,x22212)+E(f889(x22213,x22214,x22211,x22215),f889(x22213,x22214,x22212,x22215))
% 94.68/94.47 [2222]~E(x22221,x22222)+E(f889(x22223,x22224,x22225,x22221),f889(x22223,x22224,x22225,x22222))
% 94.68/94.47 [2223]~E(x22231,x22232)+E(f327(x22231,x22233,x22234,x22235),f327(x22232,x22233,x22234,x22235))
% 94.68/94.47 [2224]~E(x22241,x22242)+E(f327(x22243,x22241,x22244,x22245),f327(x22243,x22242,x22244,x22245))
% 94.68/94.47 [2225]~E(x22251,x22252)+E(f327(x22253,x22254,x22251,x22255),f327(x22253,x22254,x22252,x22255))
% 94.68/94.47 [2226]~E(x22261,x22262)+E(f327(x22263,x22264,x22265,x22261),f327(x22263,x22264,x22265,x22262))
% 94.68/94.47 [2227]~E(x22271,x22272)+E(f338(x22271,x22273,x22274),f338(x22272,x22273,x22274))
% 94.68/94.47 [2228]~E(x22281,x22282)+E(f338(x22283,x22281,x22284),f338(x22283,x22282,x22284))
% 94.68/94.47 [2229]~E(x22291,x22292)+E(f338(x22293,x22294,x22291),f338(x22293,x22294,x22292))
% 94.68/94.47 [2230]~E(x22301,x22302)+E(f857(x22301,x22303,x22304),f857(x22302,x22303,x22304))
% 94.68/94.47 [2231]~E(x22311,x22312)+E(f857(x22313,x22311,x22314),f857(x22313,x22312,x22314))
% 94.68/94.47 [2232]~E(x22321,x22322)+E(f857(x22323,x22324,x22321),f857(x22323,x22324,x22322))
% 94.68/94.47 [2233]~E(x22331,x22332)+E(f235(x22331,x22333,x22334),f235(x22332,x22333,x22334))
% 94.68/94.47 [2234]~E(x22341,x22342)+E(f235(x22343,x22341,x22344),f235(x22343,x22342,x22344))
% 94.68/94.47 [2235]~E(x22351,x22352)+E(f235(x22353,x22354,x22351),f235(x22353,x22354,x22352))
% 94.68/94.47 [2236]~E(x22361,x22362)+E(f504(x22361,x22363,x22364,x22365),f504(x22362,x22363,x22364,x22365))
% 94.68/94.47 [2237]~E(x22371,x22372)+E(f504(x22373,x22371,x22374,x22375),f504(x22373,x22372,x22374,x22375))
% 94.68/94.47 [2238]~E(x22381,x22382)+E(f504(x22383,x22384,x22381,x22385),f504(x22383,x22384,x22382,x22385))
% 94.68/94.47 [2239]~E(x22391,x22392)+E(f504(x22393,x22394,x22395,x22391),f504(x22393,x22394,x22395,x22392))
% 94.68/94.47 [2240]~E(x22401,x22402)+E(f495(x22401,x22403,x22404,x22405,x22406,x22407),f495(x22402,x22403,x22404,x22405,x22406,x22407))
% 94.68/94.47 [2241]~E(x22411,x22412)+E(f495(x22413,x22411,x22414,x22415,x22416,x22417),f495(x22413,x22412,x22414,x22415,x22416,x22417))
% 94.68/94.47 [2242]~E(x22421,x22422)+E(f495(x22423,x22424,x22421,x22425,x22426,x22427),f495(x22423,x22424,x22422,x22425,x22426,x22427))
% 94.68/94.47 [2243]~E(x22431,x22432)+E(f495(x22433,x22434,x22435,x22431,x22436,x22437),f495(x22433,x22434,x22435,x22432,x22436,x22437))
% 94.68/94.47 [2244]~E(x22441,x22442)+E(f495(x22443,x22444,x22445,x22446,x22441,x22447),f495(x22443,x22444,x22445,x22446,x22442,x22447))
% 94.68/94.47 [2245]~E(x22451,x22452)+E(f495(x22453,x22454,x22455,x22456,x22457,x22451),f495(x22453,x22454,x22455,x22456,x22457,x22452))
% 94.68/94.47 [2246]~E(x22461,x22462)+E(f331(x22461,x22463,x22464,x22465),f331(x22462,x22463,x22464,x22465))
% 94.68/94.47 [2247]~E(x22471,x22472)+E(f331(x22473,x22471,x22474,x22475),f331(x22473,x22472,x22474,x22475))
% 94.68/94.47 [2248]~E(x22481,x22482)+E(f331(x22483,x22484,x22481,x22485),f331(x22483,x22484,x22482,x22485))
% 94.68/94.47 [2249]~E(x22491,x22492)+E(f331(x22493,x22494,x22495,x22491),f331(x22493,x22494,x22495,x22492))
% 94.68/94.47 [2250]~E(x22501,x22502)+E(f363(x22501,x22503,x22504),f363(x22502,x22503,x22504))
% 94.68/94.47 [2251]~E(x22511,x22512)+E(f363(x22513,x22511,x22514),f363(x22513,x22512,x22514))
% 94.68/94.47 [2252]~E(x22521,x22522)+E(f363(x22523,x22524,x22521),f363(x22523,x22524,x22522))
% 94.68/94.47 [2253]~E(x22531,x22532)+E(f262(x22531,x22533),f262(x22532,x22533))
% 94.68/94.47 [2254]~E(x22541,x22542)+E(f262(x22543,x22541),f262(x22543,x22542))
% 94.68/94.47 [2255]~E(x22551,x22552)+E(f787(x22551,x22553),f787(x22552,x22553))
% 94.68/94.47 [2256]~E(x22561,x22562)+E(f787(x22563,x22561),f787(x22563,x22562))
% 94.68/94.47 [2257]~E(x22571,x22572)+E(f391(x22571,x22573,x22574,x22575,x22576),f391(x22572,x22573,x22574,x22575,x22576))
% 94.68/94.47 [2258]~E(x22581,x22582)+E(f391(x22583,x22581,x22584,x22585,x22586),f391(x22583,x22582,x22584,x22585,x22586))
% 94.68/94.47 [2259]~E(x22591,x22592)+E(f391(x22593,x22594,x22591,x22595,x22596),f391(x22593,x22594,x22592,x22595,x22596))
% 94.68/94.47 [2260]~E(x22601,x22602)+E(f391(x22603,x22604,x22605,x22601,x22606),f391(x22603,x22604,x22605,x22602,x22606))
% 94.68/94.47 [2261]~E(x22611,x22612)+E(f391(x22613,x22614,x22615,x22616,x22611),f391(x22613,x22614,x22615,x22616,x22612))
% 94.68/94.47 [2262]~E(x22621,x22622)+E(f742(x22621,x22623,x22624),f742(x22622,x22623,x22624))
% 94.68/94.47 [2263]~E(x22631,x22632)+E(f742(x22633,x22631,x22634),f742(x22633,x22632,x22634))
% 94.68/94.47 [2264]~E(x22641,x22642)+E(f742(x22643,x22644,x22641),f742(x22643,x22644,x22642))
% 94.68/94.47 [2265]~E(x22651,x22652)+E(f615(x22651,x22653,x22654),f615(x22652,x22653,x22654))
% 94.68/94.47 [2266]~E(x22661,x22662)+E(f615(x22663,x22661,x22664),f615(x22663,x22662,x22664))
% 94.68/94.47 [2267]~E(x22671,x22672)+E(f615(x22673,x22674,x22671),f615(x22673,x22674,x22672))
% 94.68/94.47 [2268]~E(x22681,x22682)+E(f354(x22681,x22683),f354(x22682,x22683))
% 94.68/94.47 [2269]~E(x22691,x22692)+E(f354(x22693,x22691),f354(x22693,x22692))
% 94.68/94.47 [2270]~E(x22701,x22702)+E(f531(x22701,x22703,x22704,x22705,x22706,x22707),f531(x22702,x22703,x22704,x22705,x22706,x22707))
% 94.68/94.47 [2271]~E(x22711,x22712)+E(f531(x22713,x22711,x22714,x22715,x22716,x22717),f531(x22713,x22712,x22714,x22715,x22716,x22717))
% 94.68/94.47 [2272]~E(x22721,x22722)+E(f531(x22723,x22724,x22721,x22725,x22726,x22727),f531(x22723,x22724,x22722,x22725,x22726,x22727))
% 94.68/94.47 [2273]~E(x22731,x22732)+E(f531(x22733,x22734,x22735,x22731,x22736,x22737),f531(x22733,x22734,x22735,x22732,x22736,x22737))
% 94.68/94.47 [2274]~E(x22741,x22742)+E(f531(x22743,x22744,x22745,x22746,x22741,x22747),f531(x22743,x22744,x22745,x22746,x22742,x22747))
% 94.68/94.47 [2275]~E(x22751,x22752)+E(f531(x22753,x22754,x22755,x22756,x22757,x22751),f531(x22753,x22754,x22755,x22756,x22757,x22752))
% 94.68/94.47 [2276]~E(x22761,x22762)+E(f196(x22761,x22763,x22764,x22765),f196(x22762,x22763,x22764,x22765))
% 94.68/94.47 [2277]~E(x22771,x22772)+E(f196(x22773,x22771,x22774,x22775),f196(x22773,x22772,x22774,x22775))
% 94.68/94.47 [2278]~E(x22781,x22782)+E(f196(x22783,x22784,x22781,x22785),f196(x22783,x22784,x22782,x22785))
% 94.68/94.47 [2279]~E(x22791,x22792)+E(f196(x22793,x22794,x22795,x22791),f196(x22793,x22794,x22795,x22792))
% 94.68/94.47 [2280]~E(x22801,x22802)+E(f420(x22801,x22803,x22804,x22805,x22806,x22807),f420(x22802,x22803,x22804,x22805,x22806,x22807))
% 94.68/94.47 [2281]~E(x22811,x22812)+E(f420(x22813,x22811,x22814,x22815,x22816,x22817),f420(x22813,x22812,x22814,x22815,x22816,x22817))
% 94.68/94.47 [2282]~E(x22821,x22822)+E(f420(x22823,x22824,x22821,x22825,x22826,x22827),f420(x22823,x22824,x22822,x22825,x22826,x22827))
% 94.68/94.47 [2283]~E(x22831,x22832)+E(f420(x22833,x22834,x22835,x22831,x22836,x22837),f420(x22833,x22834,x22835,x22832,x22836,x22837))
% 94.68/94.47 [2284]~E(x22841,x22842)+E(f420(x22843,x22844,x22845,x22846,x22841,x22847),f420(x22843,x22844,x22845,x22846,x22842,x22847))
% 94.68/94.47 [2285]~E(x22851,x22852)+E(f420(x22853,x22854,x22855,x22856,x22857,x22851),f420(x22853,x22854,x22855,x22856,x22857,x22852))
% 94.68/94.47 [2286]~E(x22861,x22862)+E(f502(x22861,x22863),f502(x22862,x22863))
% 94.68/94.47 [2287]~E(x22871,x22872)+E(f502(x22873,x22871),f502(x22873,x22872))
% 94.68/94.47 [2288]~E(x22881,x22882)+E(f458(x22881,x22883,x22884,x22885),f458(x22882,x22883,x22884,x22885))
% 94.68/94.47 [2289]~E(x22891,x22892)+E(f458(x22893,x22891,x22894,x22895),f458(x22893,x22892,x22894,x22895))
% 94.68/94.47 [2290]~E(x22901,x22902)+E(f458(x22903,x22904,x22901,x22905),f458(x22903,x22904,x22902,x22905))
% 94.68/94.47 [2291]~E(x22911,x22912)+E(f458(x22913,x22914,x22915,x22911),f458(x22913,x22914,x22915,x22912))
% 94.68/94.47 [2292]~E(x22921,x22922)+E(f418(x22921,x22923,x22924,x22925,x22926),f418(x22922,x22923,x22924,x22925,x22926))
% 94.68/94.47 [2293]~E(x22931,x22932)+E(f418(x22933,x22931,x22934,x22935,x22936),f418(x22933,x22932,x22934,x22935,x22936))
% 94.68/94.47 [2294]~E(x22941,x22942)+E(f418(x22943,x22944,x22941,x22945,x22946),f418(x22943,x22944,x22942,x22945,x22946))
% 94.68/94.47 [2295]~E(x22951,x22952)+E(f418(x22953,x22954,x22955,x22951,x22956),f418(x22953,x22954,x22955,x22952,x22956))
% 94.68/94.47 [2296]~E(x22961,x22962)+E(f418(x22963,x22964,x22965,x22966,x22961),f418(x22963,x22964,x22965,x22966,x22962))
% 94.68/94.47 [2297]~E(x22971,x22972)+E(f511(x22971,x22973,x22974),f511(x22972,x22973,x22974))
% 94.68/94.47 [2298]~E(x22981,x22982)+E(f511(x22983,x22981,x22984),f511(x22983,x22982,x22984))
% 94.68/94.47 [2299]~E(x22991,x22992)+E(f511(x22993,x22994,x22991),f511(x22993,x22994,x22992))
% 94.68/94.47 [2300]~E(x23001,x23002)+E(f740(x23001,x23003,x23004),f740(x23002,x23003,x23004))
% 94.68/94.47 [2301]~E(x23011,x23012)+E(f740(x23013,x23011,x23014),f740(x23013,x23012,x23014))
% 94.68/94.47 [2302]~E(x23021,x23022)+E(f740(x23023,x23024,x23021),f740(x23023,x23024,x23022))
% 94.68/94.47 [2303]~E(x23031,x23032)+E(f872(x23031,x23033,x23034,x23035),f872(x23032,x23033,x23034,x23035))
% 94.68/94.47 [2304]~E(x23041,x23042)+E(f872(x23043,x23041,x23044,x23045),f872(x23043,x23042,x23044,x23045))
% 94.68/94.47 [2305]~E(x23051,x23052)+E(f872(x23053,x23054,x23051,x23055),f872(x23053,x23054,x23052,x23055))
% 94.68/94.47 [2306]~E(x23061,x23062)+E(f872(x23063,x23064,x23065,x23061),f872(x23063,x23064,x23065,x23062))
% 94.68/94.47 [2307]~E(x23071,x23072)+E(f762(x23071,x23073),f762(x23072,x23073))
% 94.68/94.47 [2308]~E(x23081,x23082)+E(f762(x23083,x23081),f762(x23083,x23082))
% 94.68/94.47 [2309]~E(x23091,x23092)+E(f702(x23091,x23093,x23094,x23095),f702(x23092,x23093,x23094,x23095))
% 94.68/94.47 [2310]~E(x23101,x23102)+E(f702(x23103,x23101,x23104,x23105),f702(x23103,x23102,x23104,x23105))
% 94.68/94.47 [2311]~E(x23111,x23112)+E(f702(x23113,x23114,x23111,x23115),f702(x23113,x23114,x23112,x23115))
% 94.68/94.47 [2312]~E(x23121,x23122)+E(f702(x23123,x23124,x23125,x23121),f702(x23123,x23124,x23125,x23122))
% 94.68/94.47 [2313]~E(x23131,x23132)+E(f823(x23131,x23133,x23134,x23135,x23136,x23137,x23138),f823(x23132,x23133,x23134,x23135,x23136,x23137,x23138))
% 94.68/94.47 [2314]~E(x23141,x23142)+E(f823(x23143,x23141,x23144,x23145,x23146,x23147,x23148),f823(x23143,x23142,x23144,x23145,x23146,x23147,x23148))
% 94.68/94.47 [2315]~E(x23151,x23152)+E(f823(x23153,x23154,x23151,x23155,x23156,x23157,x23158),f823(x23153,x23154,x23152,x23155,x23156,x23157,x23158))
% 94.68/94.47 [2316]~E(x23161,x23162)+E(f823(x23163,x23164,x23165,x23161,x23166,x23167,x23168),f823(x23163,x23164,x23165,x23162,x23166,x23167,x23168))
% 94.68/94.47 [2317]~E(x23171,x23172)+E(f823(x23173,x23174,x23175,x23176,x23171,x23177,x23178),f823(x23173,x23174,x23175,x23176,x23172,x23177,x23178))
% 94.68/94.47 [2318]~E(x23181,x23182)+E(f823(x23183,x23184,x23185,x23186,x23187,x23181,x23188),f823(x23183,x23184,x23185,x23186,x23187,x23182,x23188))
% 94.68/94.47 [2319]~E(x23191,x23192)+E(f823(x23193,x23194,x23195,x23196,x23197,x23198,x23191),f823(x23193,x23194,x23195,x23196,x23197,x23198,x23192))
% 94.68/94.47 [2320]~E(x23201,x23202)+E(f345(x23201,x23203,x23204),f345(x23202,x23203,x23204))
% 94.68/94.47 [2321]~E(x23211,x23212)+E(f345(x23213,x23211,x23214),f345(x23213,x23212,x23214))
% 94.68/94.47 [2322]~E(x23221,x23222)+E(f345(x23223,x23224,x23221),f345(x23223,x23224,x23222))
% 94.68/94.47 [2323]~E(x23231,x23232)+E(f550(x23231,x23233,x23234),f550(x23232,x23233,x23234))
% 94.68/94.47 [2324]~E(x23241,x23242)+E(f550(x23243,x23241,x23244),f550(x23243,x23242,x23244))
% 94.68/94.47 [2325]~E(x23251,x23252)+E(f550(x23253,x23254,x23251),f550(x23253,x23254,x23252))
% 94.68/94.47 [2326]~E(x23261,x23262)+E(f583(x23261,x23263,x23264,x23265,x23266),f583(x23262,x23263,x23264,x23265,x23266))
% 94.68/94.47 [2327]~E(x23271,x23272)+E(f583(x23273,x23271,x23274,x23275,x23276),f583(x23273,x23272,x23274,x23275,x23276))
% 94.68/94.47 [2328]~E(x23281,x23282)+E(f583(x23283,x23284,x23281,x23285,x23286),f583(x23283,x23284,x23282,x23285,x23286))
% 94.68/94.47 [2329]~E(x23291,x23292)+E(f583(x23293,x23294,x23295,x23291,x23296),f583(x23293,x23294,x23295,x23292,x23296))
% 94.68/94.47 [2330]~E(x23301,x23302)+E(f583(x23303,x23304,x23305,x23306,x23301),f583(x23303,x23304,x23305,x23306,x23302))
% 94.68/94.47 [2331]~E(x23311,x23312)+E(f552(x23311,x23313,x23314,x23315,x23316,x23317,x23318,x23319),f552(x23312,x23313,x23314,x23315,x23316,x23317,x23318,x23319))
% 94.68/94.47 [2332]~E(x23321,x23322)+E(f552(x23323,x23321,x23324,x23325,x23326,x23327,x23328,x23329),f552(x23323,x23322,x23324,x23325,x23326,x23327,x23328,x23329))
% 94.68/94.47 [2333]~E(x23331,x23332)+E(f552(x23333,x23334,x23331,x23335,x23336,x23337,x23338,x23339),f552(x23333,x23334,x23332,x23335,x23336,x23337,x23338,x23339))
% 94.68/94.47 [2334]~E(x23341,x23342)+E(f552(x23343,x23344,x23345,x23341,x23346,x23347,x23348,x23349),f552(x23343,x23344,x23345,x23342,x23346,x23347,x23348,x23349))
% 94.68/94.47 [2335]~E(x23351,x23352)+E(f552(x23353,x23354,x23355,x23356,x23351,x23357,x23358,x23359),f552(x23353,x23354,x23355,x23356,x23352,x23357,x23358,x23359))
% 94.68/94.47 [2336]~E(x23361,x23362)+E(f552(x23363,x23364,x23365,x23366,x23367,x23361,x23368,x23369),f552(x23363,x23364,x23365,x23366,x23367,x23362,x23368,x23369))
% 94.68/94.47 [2337]~E(x23371,x23372)+E(f552(x23373,x23374,x23375,x23376,x23377,x23378,x23371,x23379),f552(x23373,x23374,x23375,x23376,x23377,x23378,x23372,x23379))
% 94.68/94.47 [2338]~E(x23381,x23382)+E(f552(x23383,x23384,x23385,x23386,x23387,x23388,x23389,x23381),f552(x23383,x23384,x23385,x23386,x23387,x23388,x23389,x23382))
% 94.68/94.47 [2339]~E(x23391,x23392)+E(f685(x23391,x23393),f685(x23392,x23393))
% 94.68/94.47 [2340]~E(x23401,x23402)+E(f685(x23403,x23401),f685(x23403,x23402))
% 94.68/94.47 [2341]~E(x23411,x23412)+E(f654(x23411,x23413,x23414,x23415),f654(x23412,x23413,x23414,x23415))
% 94.68/94.47 [2342]~E(x23421,x23422)+E(f654(x23423,x23421,x23424,x23425),f654(x23423,x23422,x23424,x23425))
% 94.68/94.47 [2343]~E(x23431,x23432)+E(f654(x23433,x23434,x23431,x23435),f654(x23433,x23434,x23432,x23435))
% 94.68/94.47 [2344]~E(x23441,x23442)+E(f654(x23443,x23444,x23445,x23441),f654(x23443,x23444,x23445,x23442))
% 94.68/94.47 [2345]~E(x23451,x23452)+E(f539(x23451,x23453,x23454),f539(x23452,x23453,x23454))
% 94.68/94.47 [2346]~E(x23461,x23462)+E(f539(x23463,x23461,x23464),f539(x23463,x23462,x23464))
% 94.68/94.47 [2347]~E(x23471,x23472)+E(f539(x23473,x23474,x23471),f539(x23473,x23474,x23472))
% 94.68/94.47 [2348]~E(x23481,x23482)+E(f573(x23481,x23483,x23484,x23485,x23486),f573(x23482,x23483,x23484,x23485,x23486))
% 94.68/94.47 [2349]~E(x23491,x23492)+E(f573(x23493,x23491,x23494,x23495,x23496),f573(x23493,x23492,x23494,x23495,x23496))
% 94.68/94.47 [2350]~E(x23501,x23502)+E(f573(x23503,x23504,x23501,x23505,x23506),f573(x23503,x23504,x23502,x23505,x23506))
% 94.68/94.47 [2351]~E(x23511,x23512)+E(f573(x23513,x23514,x23515,x23511,x23516),f573(x23513,x23514,x23515,x23512,x23516))
% 94.68/94.47 [2352]~E(x23521,x23522)+E(f573(x23523,x23524,x23525,x23526,x23521),f573(x23523,x23524,x23525,x23526,x23522))
% 94.68/94.47 [2353]~E(x23531,x23532)+E(f743(x23531,x23533,x23534),f743(x23532,x23533,x23534))
% 94.68/94.47 [2354]~E(x23541,x23542)+E(f743(x23543,x23541,x23544),f743(x23543,x23542,x23544))
% 94.68/94.47 [2355]~E(x23551,x23552)+E(f743(x23553,x23554,x23551),f743(x23553,x23554,x23552))
% 94.68/94.47 [2356]~E(x23561,x23562)+E(f525(x23561,x23563,x23564,x23565,x23566,x23567),f525(x23562,x23563,x23564,x23565,x23566,x23567))
% 94.68/94.47 [2357]~E(x23571,x23572)+E(f525(x23573,x23571,x23574,x23575,x23576,x23577),f525(x23573,x23572,x23574,x23575,x23576,x23577))
% 94.68/94.47 [2358]~E(x23581,x23582)+E(f525(x23583,x23584,x23581,x23585,x23586,x23587),f525(x23583,x23584,x23582,x23585,x23586,x23587))
% 94.68/94.47 [2359]~E(x23591,x23592)+E(f525(x23593,x23594,x23595,x23591,x23596,x23597),f525(x23593,x23594,x23595,x23592,x23596,x23597))
% 94.68/94.47 [2360]~E(x23601,x23602)+E(f525(x23603,x23604,x23605,x23606,x23601,x23607),f525(x23603,x23604,x23605,x23606,x23602,x23607))
% 94.68/94.47 [2361]~E(x23611,x23612)+E(f525(x23613,x23614,x23615,x23616,x23617,x23611),f525(x23613,x23614,x23615,x23616,x23617,x23612))
% 94.68/94.47 [2362]~E(x23621,x23622)+E(f814(x23621,x23623,x23624,x23625,x23626),f814(x23622,x23623,x23624,x23625,x23626))
% 94.68/94.47 [2363]~E(x23631,x23632)+E(f814(x23633,x23631,x23634,x23635,x23636),f814(x23633,x23632,x23634,x23635,x23636))
% 94.68/94.47 [2364]~E(x23641,x23642)+E(f814(x23643,x23644,x23641,x23645,x23646),f814(x23643,x23644,x23642,x23645,x23646))
% 94.68/94.47 [2365]~E(x23651,x23652)+E(f814(x23653,x23654,x23655,x23651,x23656),f814(x23653,x23654,x23655,x23652,x23656))
% 94.68/94.47 [2366]~E(x23661,x23662)+E(f814(x23663,x23664,x23665,x23666,x23661),f814(x23663,x23664,x23665,x23666,x23662))
% 94.68/94.47 [2367]~E(x23671,x23672)+E(f529(x23671,x23673,x23674),f529(x23672,x23673,x23674))
% 94.68/94.47 [2368]~E(x23681,x23682)+E(f529(x23683,x23681,x23684),f529(x23683,x23682,x23684))
% 94.68/94.47 [2369]~E(x23691,x23692)+E(f529(x23693,x23694,x23691),f529(x23693,x23694,x23692))
% 94.68/94.47 [2370]~E(x23701,x23702)+E(f117(x23701,x23703,x23704,x23705,x23706),f117(x23702,x23703,x23704,x23705,x23706))
% 94.68/94.47 [2371]~E(x23711,x23712)+E(f117(x23713,x23711,x23714,x23715,x23716),f117(x23713,x23712,x23714,x23715,x23716))
% 94.68/94.47 [2372]~E(x23721,x23722)+E(f117(x23723,x23724,x23721,x23725,x23726),f117(x23723,x23724,x23722,x23725,x23726))
% 94.68/94.47 [2373]~E(x23731,x23732)+E(f117(x23733,x23734,x23735,x23731,x23736),f117(x23733,x23734,x23735,x23732,x23736))
% 94.68/94.47 [2374]~E(x23741,x23742)+E(f117(x23743,x23744,x23745,x23746,x23741),f117(x23743,x23744,x23745,x23746,x23742))
% 94.68/94.47 [2375]~E(x23751,x23752)+E(f603(x23751,x23753,x23754,x23755),f603(x23752,x23753,x23754,x23755))
% 94.68/94.47 [2376]~E(x23761,x23762)+E(f603(x23763,x23761,x23764,x23765),f603(x23763,x23762,x23764,x23765))
% 94.68/94.47 [2377]~E(x23771,x23772)+E(f603(x23773,x23774,x23771,x23775),f603(x23773,x23774,x23772,x23775))
% 94.68/94.47 [2378]~E(x23781,x23782)+E(f603(x23783,x23784,x23785,x23781),f603(x23783,x23784,x23785,x23782))
% 94.68/94.47 [2379]~E(x23791,x23792)+E(f412(x23791,x23793,x23794),f412(x23792,x23793,x23794))
% 94.68/94.47 [2380]~E(x23801,x23802)+E(f412(x23803,x23801,x23804),f412(x23803,x23802,x23804))
% 94.68/94.47 [2381]~E(x23811,x23812)+E(f412(x23813,x23814,x23811),f412(x23813,x23814,x23812))
% 94.68/94.47 [2382]~E(x23821,x23822)+E(f790(x23821,x23823),f790(x23822,x23823))
% 94.68/94.47 [2383]~E(x23831,x23832)+E(f790(x23833,x23831),f790(x23833,x23832))
% 94.68/94.47 [2384]~E(x23841,x23842)+E(f658(x23841,x23843,x23844,x23845,x23846),f658(x23842,x23843,x23844,x23845,x23846))
% 94.68/94.47 [2385]~E(x23851,x23852)+E(f658(x23853,x23851,x23854,x23855,x23856),f658(x23853,x23852,x23854,x23855,x23856))
% 94.68/94.47 [2386]~E(x23861,x23862)+E(f658(x23863,x23864,x23861,x23865,x23866),f658(x23863,x23864,x23862,x23865,x23866))
% 94.68/94.47 [2387]~E(x23871,x23872)+E(f658(x23873,x23874,x23875,x23871,x23876),f658(x23873,x23874,x23875,x23872,x23876))
% 94.68/94.47 [2388]~E(x23881,x23882)+E(f658(x23883,x23884,x23885,x23886,x23881),f658(x23883,x23884,x23885,x23886,x23882))
% 94.68/94.47 [2389]~E(x23891,x23892)+E(f512(x23891,x23893,x23894),f512(x23892,x23893,x23894))
% 94.68/94.47 [2390]~E(x23901,x23902)+E(f512(x23903,x23901,x23904),f512(x23903,x23902,x23904))
% 94.68/94.47 [2391]~E(x23911,x23912)+E(f512(x23913,x23914,x23911),f512(x23913,x23914,x23912))
% 94.68/94.47 [2392]~E(x23921,x23922)+E(f282(x23921,x23923),f282(x23922,x23923))
% 94.68/94.47 [2393]~E(x23931,x23932)+E(f282(x23933,x23931),f282(x23933,x23932))
% 94.68/94.47 [2394]~E(x23941,x23942)+E(f854(x23941,x23943,x23944),f854(x23942,x23943,x23944))
% 94.68/94.47 [2395]~E(x23951,x23952)+E(f854(x23953,x23951,x23954),f854(x23953,x23952,x23954))
% 94.68/94.47 [2396]~E(x23961,x23962)+E(f854(x23963,x23964,x23961),f854(x23963,x23964,x23962))
% 94.68/94.47 [2397]~E(x23971,x23972)+E(f746(x23971,x23973),f746(x23972,x23973))
% 94.68/94.47 [2398]~E(x23981,x23982)+E(f746(x23983,x23981),f746(x23983,x23982))
% 94.68/94.47 [2399]~E(x23991,x23992)+E(f328(x23991,x23993),f328(x23992,x23993))
% 94.68/94.47 [2400]~E(x24001,x24002)+E(f328(x24003,x24001),f328(x24003,x24002))
% 94.68/94.47 [2401]~E(x24011,x24012)+E(f771(x24011,x24013),f771(x24012,x24013))
% 94.68/94.47 [2402]~E(x24021,x24022)+E(f771(x24023,x24021),f771(x24023,x24022))
% 94.68/94.47 [2403]~E(x24031,x24032)+E(f349(x24031,x24033,x24034,x24035,x24036),f349(x24032,x24033,x24034,x24035,x24036))
% 94.68/94.47 [2404]~E(x24041,x24042)+E(f349(x24043,x24041,x24044,x24045,x24046),f349(x24043,x24042,x24044,x24045,x24046))
% 94.68/94.47 [2405]~E(x24051,x24052)+E(f349(x24053,x24054,x24051,x24055,x24056),f349(x24053,x24054,x24052,x24055,x24056))
% 94.68/94.47 [2406]~E(x24061,x24062)+E(f349(x24063,x24064,x24065,x24061,x24066),f349(x24063,x24064,x24065,x24062,x24066))
% 94.68/94.47 [2407]~E(x24071,x24072)+E(f349(x24073,x24074,x24075,x24076,x24071),f349(x24073,x24074,x24075,x24076,x24072))
% 94.68/94.47 [2408]~E(x24081,x24082)+E(f424(x24081,x24083,x24084,x24085,x24086),f424(x24082,x24083,x24084,x24085,x24086))
% 94.68/94.47 [2409]~E(x24091,x24092)+E(f424(x24093,x24091,x24094,x24095,x24096),f424(x24093,x24092,x24094,x24095,x24096))
% 94.68/94.47 [2410]~E(x24101,x24102)+E(f424(x24103,x24104,x24101,x24105,x24106),f424(x24103,x24104,x24102,x24105,x24106))
% 94.68/94.47 [2411]~E(x24111,x24112)+E(f424(x24113,x24114,x24115,x24111,x24116),f424(x24113,x24114,x24115,x24112,x24116))
% 94.68/94.47 [2412]~E(x24121,x24122)+E(f424(x24123,x24124,x24125,x24126,x24121),f424(x24123,x24124,x24125,x24126,x24122))
% 94.68/94.47 [2413]~E(x24131,x24132)+E(f800(x24131,x24133),f800(x24132,x24133))
% 94.68/94.47 [2414]~E(x24141,x24142)+E(f800(x24143,x24141),f800(x24143,x24142))
% 94.68/94.47 [2415]~E(x24151,x24152)+E(f777(x24151,x24153,x24154,x24155,x24156),f777(x24152,x24153,x24154,x24155,x24156))
% 94.68/94.47 [2416]~E(x24161,x24162)+E(f777(x24163,x24161,x24164,x24165,x24166),f777(x24163,x24162,x24164,x24165,x24166))
% 94.68/94.47 [2417]~E(x24171,x24172)+E(f777(x24173,x24174,x24171,x24175,x24176),f777(x24173,x24174,x24172,x24175,x24176))
% 94.68/94.47 [2418]~E(x24181,x24182)+E(f777(x24183,x24184,x24185,x24181,x24186),f777(x24183,x24184,x24185,x24182,x24186))
% 94.68/94.47 [2419]~E(x24191,x24192)+E(f777(x24193,x24194,x24195,x24196,x24191),f777(x24193,x24194,x24195,x24196,x24192))
% 94.68/94.47 [2420]~E(x24201,x24202)+E(f500(x24201,x24203,x24204,x24205),f500(x24202,x24203,x24204,x24205))
% 94.68/94.47 [2421]~E(x24211,x24212)+E(f500(x24213,x24211,x24214,x24215),f500(x24213,x24212,x24214,x24215))
% 94.68/94.47 [2422]~E(x24221,x24222)+E(f500(x24223,x24224,x24221,x24225),f500(x24223,x24224,x24222,x24225))
% 94.68/94.47 [2423]~E(x24231,x24232)+E(f500(x24233,x24234,x24235,x24231),f500(x24233,x24234,x24235,x24232))
% 94.68/94.47 [2424]~E(x24241,x24242)+E(f621(x24241,x24243,x24244,x24245),f621(x24242,x24243,x24244,x24245))
% 94.68/94.47 [2425]~E(x24251,x24252)+E(f621(x24253,x24251,x24254,x24255),f621(x24253,x24252,x24254,x24255))
% 94.68/94.47 [2426]~E(x24261,x24262)+E(f621(x24263,x24264,x24261,x24265),f621(x24263,x24264,x24262,x24265))
% 94.68/94.47 [2427]~E(x24271,x24272)+E(f621(x24273,x24274,x24275,x24271),f621(x24273,x24274,x24275,x24272))
% 94.68/94.47 [2428]~E(x24281,x24282)+E(f255(x24281,x24283,x24284),f255(x24282,x24283,x24284))
% 94.68/94.47 [2429]~E(x24291,x24292)+E(f255(x24293,x24291,x24294),f255(x24293,x24292,x24294))
% 94.68/94.47 [2430]~E(x24301,x24302)+E(f255(x24303,x24304,x24301),f255(x24303,x24304,x24302))
% 94.68/94.47 [2431]~E(x24311,x24312)+E(f670(x24311,x24313,x24314,x24315,x24316),f670(x24312,x24313,x24314,x24315,x24316))
% 94.68/94.47 [2432]~E(x24321,x24322)+E(f670(x24323,x24321,x24324,x24325,x24326),f670(x24323,x24322,x24324,x24325,x24326))
% 94.68/94.47 [2433]~E(x24331,x24332)+E(f670(x24333,x24334,x24331,x24335,x24336),f670(x24333,x24334,x24332,x24335,x24336))
% 94.68/94.47 [2434]~E(x24341,x24342)+E(f670(x24343,x24344,x24345,x24341,x24346),f670(x24343,x24344,x24345,x24342,x24346))
% 94.68/94.47 [2435]~E(x24351,x24352)+E(f670(x24353,x24354,x24355,x24356,x24351),f670(x24353,x24354,x24355,x24356,x24352))
% 94.68/94.47 [2436]~E(x24361,x24362)+E(f221(x24361,x24363,x24364,x24365),f221(x24362,x24363,x24364,x24365))
% 94.68/94.47 [2437]~E(x24371,x24372)+E(f221(x24373,x24371,x24374,x24375),f221(x24373,x24372,x24374,x24375))
% 94.68/94.47 [2438]~E(x24381,x24382)+E(f221(x24383,x24384,x24381,x24385),f221(x24383,x24384,x24382,x24385))
% 94.68/94.47 [2439]~E(x24391,x24392)+E(f221(x24393,x24394,x24395,x24391),f221(x24393,x24394,x24395,x24392))
% 94.68/94.47 [2440]~E(x24401,x24402)+E(f744(x24401,x24403,x24404),f744(x24402,x24403,x24404))
% 94.68/94.47 [2441]~E(x24411,x24412)+E(f744(x24413,x24411,x24414),f744(x24413,x24412,x24414))
% 94.68/94.47 [2442]~E(x24421,x24422)+E(f744(x24423,x24424,x24421),f744(x24423,x24424,x24422))
% 94.68/94.47 [2443]~E(x24431,x24432)+E(f830(x24431,x24433,x24434,x24435,x24436,x24437),f830(x24432,x24433,x24434,x24435,x24436,x24437))
% 94.68/94.47 [2444]~E(x24441,x24442)+E(f830(x24443,x24441,x24444,x24445,x24446,x24447),f830(x24443,x24442,x24444,x24445,x24446,x24447))
% 94.68/94.47 [2445]~E(x24451,x24452)+E(f830(x24453,x24454,x24451,x24455,x24456,x24457),f830(x24453,x24454,x24452,x24455,x24456,x24457))
% 94.68/94.47 [2446]~E(x24461,x24462)+E(f830(x24463,x24464,x24465,x24461,x24466,x24467),f830(x24463,x24464,x24465,x24462,x24466,x24467))
% 94.68/94.47 [2447]~E(x24471,x24472)+E(f830(x24473,x24474,x24475,x24476,x24471,x24477),f830(x24473,x24474,x24475,x24476,x24472,x24477))
% 94.68/94.47 [2448]~E(x24481,x24482)+E(f830(x24483,x24484,x24485,x24486,x24487,x24481),f830(x24483,x24484,x24485,x24486,x24487,x24482))
% 94.68/94.47 [2449]~E(x24491,x24492)+E(f862(x24491,x24493,x24494),f862(x24492,x24493,x24494))
% 94.68/94.47 [2450]~E(x24501,x24502)+E(f862(x24503,x24501,x24504),f862(x24503,x24502,x24504))
% 94.68/94.47 [2451]~E(x24511,x24512)+E(f862(x24513,x24514,x24511),f862(x24513,x24514,x24512))
% 94.68/94.47 [2452]~E(x24521,x24522)+E(f803(x24521,x24523,x24524,x24525),f803(x24522,x24523,x24524,x24525))
% 94.68/94.47 [2453]~E(x24531,x24532)+E(f803(x24533,x24531,x24534,x24535),f803(x24533,x24532,x24534,x24535))
% 94.68/94.47 [2454]~E(x24541,x24542)+E(f803(x24543,x24544,x24541,x24545),f803(x24543,x24544,x24542,x24545))
% 94.68/94.47 [2455]~E(x24551,x24552)+E(f803(x24553,x24554,x24555,x24551),f803(x24553,x24554,x24555,x24552))
% 94.68/94.47 [2456]~E(x24561,x24562)+E(f592(x24561,x24563,x24564),f592(x24562,x24563,x24564))
% 94.68/94.47 [2457]~E(x24571,x24572)+E(f592(x24573,x24571,x24574),f592(x24573,x24572,x24574))
% 94.68/94.47 [2458]~E(x24581,x24582)+E(f592(x24583,x24584,x24581),f592(x24583,x24584,x24582))
% 94.68/94.47 [2459]~E(x24591,x24592)+E(f786(x24591),f786(x24592))
% 94.68/94.47 [2460]~E(x24601,x24602)+E(f413(x24601,x24603,x24604),f413(x24602,x24603,x24604))
% 94.68/94.47 [2461]~E(x24611,x24612)+E(f413(x24613,x24611,x24614),f413(x24613,x24612,x24614))
% 94.68/94.47 [2462]~E(x24621,x24622)+E(f413(x24623,x24624,x24621),f413(x24623,x24624,x24622))
% 94.68/94.47 [2463]~E(x24631,x24632)+E(f362(x24631,x24633,x24634),f362(x24632,x24633,x24634))
% 94.68/94.47 [2464]~E(x24641,x24642)+E(f362(x24643,x24641,x24644),f362(x24643,x24642,x24644))
% 94.68/94.47 [2465]~E(x24651,x24652)+E(f362(x24653,x24654,x24651),f362(x24653,x24654,x24652))
% 94.68/94.47 [2466]~E(x24661,x24662)+E(f574(x24661,x24663,x24664,x24665,x24666),f574(x24662,x24663,x24664,x24665,x24666))
% 94.68/94.47 [2467]~E(x24671,x24672)+E(f574(x24673,x24671,x24674,x24675,x24676),f574(x24673,x24672,x24674,x24675,x24676))
% 94.68/94.47 [2468]~E(x24681,x24682)+E(f574(x24683,x24684,x24681,x24685,x24686),f574(x24683,x24684,x24682,x24685,x24686))
% 94.68/94.47 [2469]~E(x24691,x24692)+E(f574(x24693,x24694,x24695,x24691,x24696),f574(x24693,x24694,x24695,x24692,x24696))
% 94.68/94.47 [2470]~E(x24701,x24702)+E(f574(x24703,x24704,x24705,x24706,x24701),f574(x24703,x24704,x24705,x24706,x24702))
% 94.68/94.47 [2471]~E(x24711,x24712)+E(f374(x24711,x24713,x24714,x24715),f374(x24712,x24713,x24714,x24715))
% 94.68/94.47 [2472]~E(x24721,x24722)+E(f374(x24723,x24721,x24724,x24725),f374(x24723,x24722,x24724,x24725))
% 94.68/94.47 [2473]~E(x24731,x24732)+E(f374(x24733,x24734,x24731,x24735),f374(x24733,x24734,x24732,x24735))
% 94.68/94.47 [2474]~E(x24741,x24742)+E(f374(x24743,x24744,x24745,x24741),f374(x24743,x24744,x24745,x24742))
% 94.68/94.47 [2475]~E(x24751,x24752)+E(f534(x24751),f534(x24752))
% 94.68/94.47 [2476]~E(x24761,x24762)+E(f629(x24761,x24763),f629(x24762,x24763))
% 94.68/94.47 [2477]~E(x24771,x24772)+E(f629(x24773,x24771),f629(x24773,x24772))
% 94.68/94.47 [2478]~E(x24781,x24782)+E(f632(x24781,x24783,x24784,x24785,x24786),f632(x24782,x24783,x24784,x24785,x24786))
% 94.68/94.47 [2479]~E(x24791,x24792)+E(f632(x24793,x24791,x24794,x24795,x24796),f632(x24793,x24792,x24794,x24795,x24796))
% 94.68/94.47 [2480]~E(x24801,x24802)+E(f632(x24803,x24804,x24801,x24805,x24806),f632(x24803,x24804,x24802,x24805,x24806))
% 94.68/94.47 [2481]~E(x24811,x24812)+E(f632(x24813,x24814,x24815,x24811,x24816),f632(x24813,x24814,x24815,x24812,x24816))
% 94.68/94.47 [2482]~E(x24821,x24822)+E(f632(x24823,x24824,x24825,x24826,x24821),f632(x24823,x24824,x24825,x24826,x24822))
% 94.68/94.47 [2483]~E(x24831,x24832)+E(f478(x24831),f478(x24832))
% 94.68/94.47 [2484]~E(x24841,x24842)+E(f352(x24841,x24843),f352(x24842,x24843))
% 94.68/94.47 [2485]~E(x24851,x24852)+E(f352(x24853,x24851),f352(x24853,x24852))
% 94.68/94.47 [2486]~E(x24861,x24862)+E(f684(x24861,x24863),f684(x24862,x24863))
% 94.68/94.47 [2487]~E(x24871,x24872)+E(f684(x24873,x24871),f684(x24873,x24872))
% 94.68/94.47 [2488]~E(x24881,x24882)+E(f346(x24881,x24883,x24884,x24885),f346(x24882,x24883,x24884,x24885))
% 94.68/94.47 [2489]~E(x24891,x24892)+E(f346(x24893,x24891,x24894,x24895),f346(x24893,x24892,x24894,x24895))
% 94.68/94.47 [2490]~E(x24901,x24902)+E(f346(x24903,x24904,x24901,x24905),f346(x24903,x24904,x24902,x24905))
% 94.68/94.47 [2491]~E(x24911,x24912)+E(f346(x24913,x24914,x24915,x24911),f346(x24913,x24914,x24915,x24912))
% 94.68/94.47 [2492]~E(x24921,x24922)+E(f642(x24921,x24923,x24924,x24925),f642(x24922,x24923,x24924,x24925))
% 94.68/94.47 [2493]~E(x24931,x24932)+E(f642(x24933,x24931,x24934,x24935),f642(x24933,x24932,x24934,x24935))
% 94.68/94.47 [2494]~E(x24941,x24942)+E(f642(x24943,x24944,x24941,x24945),f642(x24943,x24944,x24942,x24945))
% 94.68/94.47 [2495]~E(x24951,x24952)+E(f642(x24953,x24954,x24955,x24951),f642(x24953,x24954,x24955,x24952))
% 94.68/94.47 [2496]~E(x24961,x24962)+E(f562(x24961,x24963,x24964,x24965,x24966),f562(x24962,x24963,x24964,x24965,x24966))
% 94.68/94.47 [2497]~E(x24971,x24972)+E(f562(x24973,x24971,x24974,x24975,x24976),f562(x24973,x24972,x24974,x24975,x24976))
% 94.68/94.47 [2498]~E(x24981,x24982)+E(f562(x24983,x24984,x24981,x24985,x24986),f562(x24983,x24984,x24982,x24985,x24986))
% 94.68/94.47 [2499]~E(x24991,x24992)+E(f562(x24993,x24994,x24995,x24991,x24996),f562(x24993,x24994,x24995,x24992,x24996))
% 94.68/94.47 [2500]~E(x25001,x25002)+E(f562(x25003,x25004,x25005,x25006,x25001),f562(x25003,x25004,x25005,x25006,x25002))
% 94.68/94.47 [2501]~E(x25011,x25012)+E(f851(x25011,x25013),f851(x25012,x25013))
% 94.68/94.47 [2502]~E(x25021,x25022)+E(f851(x25023,x25021),f851(x25023,x25022))
% 94.68/94.47 [2503]~E(x25031,x25032)+E(f880(x25031,x25033,x25034),f880(x25032,x25033,x25034))
% 94.68/94.47 [2504]~E(x25041,x25042)+E(f880(x25043,x25041,x25044),f880(x25043,x25042,x25044))
% 94.68/94.47 [2505]~E(x25051,x25052)+E(f880(x25053,x25054,x25051),f880(x25053,x25054,x25052))
% 94.68/94.47 [2506]~E(x25061,x25062)+E(f558(x25061,x25063,x25064),f558(x25062,x25063,x25064))
% 94.68/94.47 [2507]~E(x25071,x25072)+E(f558(x25073,x25071,x25074),f558(x25073,x25072,x25074))
% 94.68/94.47 [2508]~E(x25081,x25082)+E(f558(x25083,x25084,x25081),f558(x25083,x25084,x25082))
% 94.68/94.47 [2509]~E(x25091,x25092)+E(f827(x25091,x25093,x25094,x25095,x25096,x25097,x25098,x25099),f827(x25092,x25093,x25094,x25095,x25096,x25097,x25098,x25099))
% 94.68/94.47 [2510]~E(x25101,x25102)+E(f827(x25103,x25101,x25104,x25105,x25106,x25107,x25108,x25109),f827(x25103,x25102,x25104,x25105,x25106,x25107,x25108,x25109))
% 94.68/94.47 [2511]~E(x25111,x25112)+E(f827(x25113,x25114,x25111,x25115,x25116,x25117,x25118,x25119),f827(x25113,x25114,x25112,x25115,x25116,x25117,x25118,x25119))
% 94.68/94.47 [2512]~E(x25121,x25122)+E(f827(x25123,x25124,x25125,x25121,x25126,x25127,x25128,x25129),f827(x25123,x25124,x25125,x25122,x25126,x25127,x25128,x25129))
% 94.68/94.47 [2513]~E(x25131,x25132)+E(f827(x25133,x25134,x25135,x25136,x25131,x25137,x25138,x25139),f827(x25133,x25134,x25135,x25136,x25132,x25137,x25138,x25139))
% 94.68/94.47 [2514]~E(x25141,x25142)+E(f827(x25143,x25144,x25145,x25146,x25147,x25141,x25148,x25149),f827(x25143,x25144,x25145,x25146,x25147,x25142,x25148,x25149))
% 94.68/94.47 [2515]~E(x25151,x25152)+E(f827(x25153,x25154,x25155,x25156,x25157,x25158,x25151,x25159),f827(x25153,x25154,x25155,x25156,x25157,x25158,x25152,x25159))
% 94.68/94.47 [2516]~E(x25161,x25162)+E(f827(x25163,x25164,x25165,x25166,x25167,x25168,x25169,x25161),f827(x25163,x25164,x25165,x25166,x25167,x25168,x25169,x25162))
% 94.68/94.47 [2517]~E(x25171,x25172)+E(f884(x25171,x25173,x25174),f884(x25172,x25173,x25174))
% 94.68/94.47 [2518]~E(x25181,x25182)+E(f884(x25183,x25181,x25184),f884(x25183,x25182,x25184))
% 94.68/94.47 [2519]~E(x25191,x25192)+E(f884(x25193,x25194,x25191),f884(x25193,x25194,x25192))
% 94.68/94.47 [2520]~E(x25201,x25202)+E(f587(x25201,x25203,x25204,x25205,x25206,x25207,x25208),f587(x25202,x25203,x25204,x25205,x25206,x25207,x25208))
% 94.68/94.47 [2521]~E(x25211,x25212)+E(f587(x25213,x25211,x25214,x25215,x25216,x25217,x25218),f587(x25213,x25212,x25214,x25215,x25216,x25217,x25218))
% 94.68/94.47 [2522]~E(x25221,x25222)+E(f587(x25223,x25224,x25221,x25225,x25226,x25227,x25228),f587(x25223,x25224,x25222,x25225,x25226,x25227,x25228))
% 94.68/94.47 [2523]~E(x25231,x25232)+E(f587(x25233,x25234,x25235,x25231,x25236,x25237,x25238),f587(x25233,x25234,x25235,x25232,x25236,x25237,x25238))
% 94.68/94.47 [2524]~E(x25241,x25242)+E(f587(x25243,x25244,x25245,x25246,x25241,x25247,x25248),f587(x25243,x25244,x25245,x25246,x25242,x25247,x25248))
% 94.68/94.47 [2525]~E(x25251,x25252)+E(f587(x25253,x25254,x25255,x25256,x25257,x25251,x25258),f587(x25253,x25254,x25255,x25256,x25257,x25252,x25258))
% 94.68/94.47 [2526]~E(x25261,x25262)+E(f587(x25263,x25264,x25265,x25266,x25267,x25268,x25261),f587(x25263,x25264,x25265,x25266,x25267,x25268,x25262))
% 94.68/94.47 [2527]~E(x25271,x25272)+E(f219(x25271,x25273,x25274,x25275),f219(x25272,x25273,x25274,x25275))
% 94.68/94.47 [2528]~E(x25281,x25282)+E(f219(x25283,x25281,x25284,x25285),f219(x25283,x25282,x25284,x25285))
% 94.68/94.47 [2529]~E(x25291,x25292)+E(f219(x25293,x25294,x25291,x25295),f219(x25293,x25294,x25292,x25295))
% 94.68/94.47 [2530]~E(x25301,x25302)+E(f219(x25303,x25304,x25305,x25301),f219(x25303,x25304,x25305,x25302))
% 94.68/94.47 [2531]~E(x25311,x25312)+E(f609(x25311,x25313,x25314,x25315),f609(x25312,x25313,x25314,x25315))
% 94.68/94.47 [2532]~E(x25321,x25322)+E(f609(x25323,x25321,x25324,x25325),f609(x25323,x25322,x25324,x25325))
% 94.68/94.47 [2533]~E(x25331,x25332)+E(f609(x25333,x25334,x25331,x25335),f609(x25333,x25334,x25332,x25335))
% 94.68/94.47 [2534]~E(x25341,x25342)+E(f609(x25343,x25344,x25345,x25341),f609(x25343,x25344,x25345,x25342))
% 94.68/94.47 [2535]~E(x25351,x25352)+E(f559(x25351,x25353,x25354),f559(x25352,x25353,x25354))
% 94.68/94.47 [2536]~E(x25361,x25362)+E(f559(x25363,x25361,x25364),f559(x25363,x25362,x25364))
% 94.68/94.47 [2537]~E(x25371,x25372)+E(f559(x25373,x25374,x25371),f559(x25373,x25374,x25372))
% 94.68/94.47 [2538]~E(x25381,x25382)+E(f423(x25381,x25383,x25384),f423(x25382,x25383,x25384))
% 94.68/94.47 [2539]~E(x25391,x25392)+E(f423(x25393,x25391,x25394),f423(x25393,x25392,x25394))
% 94.68/94.47 [2540]~E(x25401,x25402)+E(f423(x25403,x25404,x25401),f423(x25403,x25404,x25402))
% 94.68/94.47 [2541]~E(x25411,x25412)+E(f434(x25411,x25413),f434(x25412,x25413))
% 94.68/94.47 [2542]~E(x25421,x25422)+E(f434(x25423,x25421),f434(x25423,x25422))
% 94.68/94.47 [2543]~E(x25431,x25432)+E(f679(x25431,x25433,x25434,x25435,x25436),f679(x25432,x25433,x25434,x25435,x25436))
% 94.68/94.47 [2544]~E(x25441,x25442)+E(f679(x25443,x25441,x25444,x25445,x25446),f679(x25443,x25442,x25444,x25445,x25446))
% 94.68/94.47 [2545]~E(x25451,x25452)+E(f679(x25453,x25454,x25451,x25455,x25456),f679(x25453,x25454,x25452,x25455,x25456))
% 94.68/94.47 [2546]~E(x25461,x25462)+E(f679(x25463,x25464,x25465,x25461,x25466),f679(x25463,x25464,x25465,x25462,x25466))
% 94.68/94.47 [2547]~E(x25471,x25472)+E(f679(x25473,x25474,x25475,x25476,x25471),f679(x25473,x25474,x25475,x25476,x25472))
% 94.68/94.47 [2548]~E(x25481,x25482)+E(f396(x25481,x25483,x25484),f396(x25482,x25483,x25484))
% 94.68/94.47 [2549]~E(x25491,x25492)+E(f396(x25493,x25491,x25494),f396(x25493,x25492,x25494))
% 94.68/94.47 [2550]~E(x25501,x25502)+E(f396(x25503,x25504,x25501),f396(x25503,x25504,x25502))
% 94.68/94.47 [2551]~E(x25511,x25512)+E(f812(x25511,x25513,x25514,x25515),f812(x25512,x25513,x25514,x25515))
% 94.68/94.47 [2552]~E(x25521,x25522)+E(f812(x25523,x25521,x25524,x25525),f812(x25523,x25522,x25524,x25525))
% 94.68/94.47 [2553]~E(x25531,x25532)+E(f812(x25533,x25534,x25531,x25535),f812(x25533,x25534,x25532,x25535))
% 94.68/94.47 [2554]~E(x25541,x25542)+E(f812(x25543,x25544,x25545,x25541),f812(x25543,x25544,x25545,x25542))
% 94.68/94.47 [2555]~E(x25551,x25552)+E(f408(x25551,x25553,x25554,x25555,x25556),f408(x25552,x25553,x25554,x25555,x25556))
% 94.68/94.47 [2556]~E(x25561,x25562)+E(f408(x25563,x25561,x25564,x25565,x25566),f408(x25563,x25562,x25564,x25565,x25566))
% 94.68/94.47 [2557]~E(x25571,x25572)+E(f408(x25573,x25574,x25571,x25575,x25576),f408(x25573,x25574,x25572,x25575,x25576))
% 94.68/94.47 [2558]~E(x25581,x25582)+E(f408(x25583,x25584,x25585,x25581,x25586),f408(x25583,x25584,x25585,x25582,x25586))
% 94.68/94.47 [2559]~E(x25591,x25592)+E(f408(x25593,x25594,x25595,x25596,x25591),f408(x25593,x25594,x25595,x25596,x25592))
% 94.68/94.47 [2560]~E(x25601,x25602)+E(f776(x25601,x25603,x25604,x25605),f776(x25602,x25603,x25604,x25605))
% 94.68/94.47 [2561]~E(x25611,x25612)+E(f776(x25613,x25611,x25614,x25615),f776(x25613,x25612,x25614,x25615))
% 94.68/94.47 [2562]~E(x25621,x25622)+E(f776(x25623,x25624,x25621,x25625),f776(x25623,x25624,x25622,x25625))
% 94.68/94.47 [2563]~E(x25631,x25632)+E(f776(x25633,x25634,x25635,x25631),f776(x25633,x25634,x25635,x25632))
% 94.68/94.47 [2564]~E(x25641,x25642)+E(f39(x25641),f39(x25642))
% 94.68/94.47 [2565]~E(x25651,x25652)+E(f390(x25651,x25653,x25654,x25655,x25656),f390(x25652,x25653,x25654,x25655,x25656))
% 94.68/94.47 [2566]~E(x25661,x25662)+E(f390(x25663,x25661,x25664,x25665,x25666),f390(x25663,x25662,x25664,x25665,x25666))
% 94.68/94.47 [2567]~E(x25671,x25672)+E(f390(x25673,x25674,x25671,x25675,x25676),f390(x25673,x25674,x25672,x25675,x25676))
% 94.68/94.47 [2568]~E(x25681,x25682)+E(f390(x25683,x25684,x25685,x25681,x25686),f390(x25683,x25684,x25685,x25682,x25686))
% 94.68/94.47 [2569]~E(x25691,x25692)+E(f390(x25693,x25694,x25695,x25696,x25691),f390(x25693,x25694,x25695,x25696,x25692))
% 94.68/94.47 [2570]~E(x25701,x25702)+E(f335(x25701,x25703),f335(x25702,x25703))
% 94.68/94.47 [2571]~E(x25711,x25712)+E(f335(x25713,x25711),f335(x25713,x25712))
% 94.68/94.47 [2572]~E(x25721,x25722)+E(f530(x25721,x25723,x25724,x25725,x25726,x25727),f530(x25722,x25723,x25724,x25725,x25726,x25727))
% 94.68/94.47 [2573]~E(x25731,x25732)+E(f530(x25733,x25731,x25734,x25735,x25736,x25737),f530(x25733,x25732,x25734,x25735,x25736,x25737))
% 94.68/94.47 [2574]~E(x25741,x25742)+E(f530(x25743,x25744,x25741,x25745,x25746,x25747),f530(x25743,x25744,x25742,x25745,x25746,x25747))
% 94.68/94.47 [2575]~E(x25751,x25752)+E(f530(x25753,x25754,x25755,x25751,x25756,x25757),f530(x25753,x25754,x25755,x25752,x25756,x25757))
% 94.68/94.47 [2576]~E(x25761,x25762)+E(f530(x25763,x25764,x25765,x25766,x25761,x25767),f530(x25763,x25764,x25765,x25766,x25762,x25767))
% 94.68/94.47 [2577]~E(x25771,x25772)+E(f530(x25773,x25774,x25775,x25776,x25777,x25771),f530(x25773,x25774,x25775,x25776,x25777,x25772))
% 94.68/94.47 [2578]~E(x25781,x25782)+E(f266(x25781,x25783,x25784,x25785),f266(x25782,x25783,x25784,x25785))
% 94.68/94.47 [2579]~E(x25791,x25792)+E(f266(x25793,x25791,x25794,x25795),f266(x25793,x25792,x25794,x25795))
% 94.68/94.47 [2580]~E(x25801,x25802)+E(f266(x25803,x25804,x25801,x25805),f266(x25803,x25804,x25802,x25805))
% 94.68/94.47 [2581]~E(x25811,x25812)+E(f266(x25813,x25814,x25815,x25811),f266(x25813,x25814,x25815,x25812))
% 94.68/94.47 [2582]~E(x25821,x25822)+E(f37(x25821),f37(x25822))
% 94.68/94.47 [2583]~E(x25831,x25832)+E(f712(x25831),f712(x25832))
% 94.68/94.47 [2584]~E(x25841,x25842)+E(f200(x25841,x25843,x25844,x25845),f200(x25842,x25843,x25844,x25845))
% 94.68/94.47 [2585]~E(x25851,x25852)+E(f200(x25853,x25851,x25854,x25855),f200(x25853,x25852,x25854,x25855))
% 94.68/94.47 [2586]~E(x25861,x25862)+E(f200(x25863,x25864,x25861,x25865),f200(x25863,x25864,x25862,x25865))
% 94.68/94.47 [2587]~E(x25871,x25872)+E(f200(x25873,x25874,x25875,x25871),f200(x25873,x25874,x25875,x25872))
% 94.68/94.47 [2588]~E(x25881,x25882)+E(f718(x25881),f718(x25882))
% 94.68/94.47 [2589]~E(x25891,x25892)+E(f250(x25891,x25893,x25894,x25895,x25896),f250(x25892,x25893,x25894,x25895,x25896))
% 94.68/94.47 [2590]~E(x25901,x25902)+E(f250(x25903,x25901,x25904,x25905,x25906),f250(x25903,x25902,x25904,x25905,x25906))
% 94.68/94.47 [2591]~E(x25911,x25912)+E(f250(x25913,x25914,x25911,x25915,x25916),f250(x25913,x25914,x25912,x25915,x25916))
% 94.68/94.47 [2592]~E(x25921,x25922)+E(f250(x25923,x25924,x25925,x25921,x25926),f250(x25923,x25924,x25925,x25922,x25926))
% 94.68/94.47 [2593]~E(x25931,x25932)+E(f250(x25933,x25934,x25935,x25936,x25931),f250(x25933,x25934,x25935,x25936,x25932))
% 94.68/94.47 [2594]~E(x25941,x25942)+E(f816(x25941,x25943,x25944),f816(x25942,x25943,x25944))
% 94.68/94.47 [2595]~E(x25951,x25952)+E(f816(x25953,x25951,x25954),f816(x25953,x25952,x25954))
% 94.68/94.47 [2596]~E(x25961,x25962)+E(f816(x25963,x25964,x25961),f816(x25963,x25964,x25962))
% 94.68/94.47 [2597]~E(x25971,x25972)+E(f714(x25971,x25973,x25974,x25975,x25976),f714(x25972,x25973,x25974,x25975,x25976))
% 94.68/94.47 [2598]~E(x25981,x25982)+E(f714(x25983,x25981,x25984,x25985,x25986),f714(x25983,x25982,x25984,x25985,x25986))
% 94.68/94.47 [2599]~E(x25991,x25992)+E(f714(x25993,x25994,x25991,x25995,x25996),f714(x25993,x25994,x25992,x25995,x25996))
% 94.68/94.47 [2600]~E(x26001,x26002)+E(f714(x26003,x26004,x26005,x26001,x26006),f714(x26003,x26004,x26005,x26002,x26006))
% 94.68/94.47 [2601]~E(x26011,x26012)+E(f714(x26013,x26014,x26015,x26016,x26011),f714(x26013,x26014,x26015,x26016,x26012))
% 94.68/94.47 [2602]~E(x26021,x26022)+E(f465(x26021,x26023,x26024,x26025),f465(x26022,x26023,x26024,x26025))
% 94.68/94.47 [2603]~E(x26031,x26032)+E(f465(x26033,x26031,x26034,x26035),f465(x26033,x26032,x26034,x26035))
% 94.68/94.47 [2604]~E(x26041,x26042)+E(f465(x26043,x26044,x26041,x26045),f465(x26043,x26044,x26042,x26045))
% 94.68/94.47 [2605]~E(x26051,x26052)+E(f465(x26053,x26054,x26055,x26051),f465(x26053,x26054,x26055,x26052))
% 94.68/94.47 [2606]~E(x26061,x26062)+E(f731(x26061,x26063,x26064,x26065),f731(x26062,x26063,x26064,x26065))
% 94.68/94.47 [2607]~E(x26071,x26072)+E(f731(x26073,x26071,x26074,x26075),f731(x26073,x26072,x26074,x26075))
% 94.68/94.47 [2608]~E(x26081,x26082)+E(f731(x26083,x26084,x26081,x26085),f731(x26083,x26084,x26082,x26085))
% 94.68/94.47 [2609]~E(x26091,x26092)+E(f731(x26093,x26094,x26095,x26091),f731(x26093,x26094,x26095,x26092))
% 94.68/94.47 [2610]~E(x26101,x26102)+E(f395(x26101,x26103),f395(x26102,x26103))
% 94.68/94.47 [2611]~E(x26111,x26112)+E(f395(x26113,x26111),f395(x26113,x26112))
% 94.68/94.47 [2612]~E(x26121,x26122)+E(f526(x26121,x26123,x26124,x26125,x26126,x26127),f526(x26122,x26123,x26124,x26125,x26126,x26127))
% 94.68/94.47 [2613]~E(x26131,x26132)+E(f526(x26133,x26131,x26134,x26135,x26136,x26137),f526(x26133,x26132,x26134,x26135,x26136,x26137))
% 94.68/94.47 [2614]~E(x26141,x26142)+E(f526(x26143,x26144,x26141,x26145,x26146,x26147),f526(x26143,x26144,x26142,x26145,x26146,x26147))
% 94.68/94.47 [2615]~E(x26151,x26152)+E(f526(x26153,x26154,x26155,x26151,x26156,x26157),f526(x26153,x26154,x26155,x26152,x26156,x26157))
% 94.68/94.47 [2616]~E(x26161,x26162)+E(f526(x26163,x26164,x26165,x26166,x26161,x26167),f526(x26163,x26164,x26165,x26166,x26162,x26167))
% 94.68/94.47 [2617]~E(x26171,x26172)+E(f526(x26173,x26174,x26175,x26176,x26177,x26171),f526(x26173,x26174,x26175,x26176,x26177,x26172))
% 94.68/94.47 [2618]~E(x26181,x26182)+E(f336(x26181,x26183,x26184),f336(x26182,x26183,x26184))
% 94.68/94.47 [2619]~E(x26191,x26192)+E(f336(x26193,x26191,x26194),f336(x26193,x26192,x26194))
% 94.68/94.47 [2620]~E(x26201,x26202)+E(f336(x26203,x26204,x26201),f336(x26203,x26204,x26202))
% 94.68/94.47 [2621]~E(x26211,x26212)+E(f778(x26211,x26213,x26214,x26215),f778(x26212,x26213,x26214,x26215))
% 94.68/94.47 [2622]~E(x26221,x26222)+E(f778(x26223,x26221,x26224,x26225),f778(x26223,x26222,x26224,x26225))
% 94.68/94.47 [2623]~E(x26231,x26232)+E(f778(x26233,x26234,x26231,x26235),f778(x26233,x26234,x26232,x26235))
% 94.68/94.47 [2624]~E(x26241,x26242)+E(f778(x26243,x26244,x26245,x26241),f778(x26243,x26244,x26245,x26242))
% 94.68/94.47 [2625]~E(x26251,x26252)+E(f214(x26251,x26253,x26254,x26255,x26256),f214(x26252,x26253,x26254,x26255,x26256))
% 94.68/94.47 [2626]~E(x26261,x26262)+E(f214(x26263,x26261,x26264,x26265,x26266),f214(x26263,x26262,x26264,x26265,x26266))
% 94.68/94.47 [2627]~E(x26271,x26272)+E(f214(x26273,x26274,x26271,x26275,x26276),f214(x26273,x26274,x26272,x26275,x26276))
% 94.68/94.47 [2628]~E(x26281,x26282)+E(f214(x26283,x26284,x26285,x26281,x26286),f214(x26283,x26284,x26285,x26282,x26286))
% 94.68/94.47 [2629]~E(x26291,x26292)+E(f214(x26293,x26294,x26295,x26296,x26291),f214(x26293,x26294,x26295,x26296,x26292))
% 94.68/94.47 [2630]~E(x26301,x26302)+E(f842(x26301),f842(x26302))
% 94.68/94.47 [2631]~E(x26311,x26312)+E(f815(x26311,x26313,x26314),f815(x26312,x26313,x26314))
% 94.68/94.47 [2632]~E(x26321,x26322)+E(f815(x26323,x26321,x26324),f815(x26323,x26322,x26324))
% 94.68/94.47 [2633]~E(x26331,x26332)+E(f815(x26333,x26334,x26331),f815(x26333,x26334,x26332))
% 94.68/94.47 [2634]~E(x26341,x26342)+E(f844(x26341),f844(x26342))
% 94.68/94.47 [2635]~E(x26351,x26352)+E(f601(x26351,x26353,x26354),f601(x26352,x26353,x26354))
% 94.68/94.47 [2636]~E(x26361,x26362)+E(f601(x26363,x26361,x26364),f601(x26363,x26362,x26364))
% 94.68/94.47 [2637]~E(x26371,x26372)+E(f601(x26373,x26374,x26371),f601(x26373,x26374,x26372))
% 94.68/94.47 [2638]~E(x26381,x26382)+E(f113(x26381),f113(x26382))
% 94.68/94.47 [2639]~E(x26391,x26392)+E(f372(x26391,x26393,x26394,x26395),f372(x26392,x26393,x26394,x26395))
% 94.68/94.47 [2640]~E(x26401,x26402)+E(f372(x26403,x26401,x26404,x26405),f372(x26403,x26402,x26404,x26405))
% 94.68/94.47 [2641]~E(x26411,x26412)+E(f372(x26413,x26414,x26411,x26415),f372(x26413,x26414,x26412,x26415))
% 94.68/94.47 [2642]~E(x26421,x26422)+E(f372(x26423,x26424,x26425,x26421),f372(x26423,x26424,x26425,x26422))
% 94.68/94.47 [2643]~E(x26431,x26432)+E(f517(x26431,x26433),f517(x26432,x26433))
% 94.68/94.47 [2644]~E(x26441,x26442)+E(f517(x26443,x26441),f517(x26443,x26442))
% 94.68/94.47 [2645]~E(x26451,x26452)+E(f464(x26451,x26453,x26454,x26455,x26456),f464(x26452,x26453,x26454,x26455,x26456))
% 94.68/94.47 [2646]~E(x26461,x26462)+E(f464(x26463,x26461,x26464,x26465,x26466),f464(x26463,x26462,x26464,x26465,x26466))
% 94.68/94.47 [2647]~E(x26471,x26472)+E(f464(x26473,x26474,x26471,x26475,x26476),f464(x26473,x26474,x26472,x26475,x26476))
% 94.68/94.47 [2648]~E(x26481,x26482)+E(f464(x26483,x26484,x26485,x26481,x26486),f464(x26483,x26484,x26485,x26482,x26486))
% 94.68/94.47 [2649]~E(x26491,x26492)+E(f464(x26493,x26494,x26495,x26496,x26491),f464(x26493,x26494,x26495,x26496,x26492))
% 94.68/94.47 [2650]~E(x26501,x26502)+E(f802(x26501,x26503),f802(x26502,x26503))
% 94.68/94.47 [2651]~E(x26511,x26512)+E(f802(x26513,x26511),f802(x26513,x26512))
% 94.68/94.47 [2652]~E(x26521,x26522)+E(f620(x26521,x26523,x26524,x26525),f620(x26522,x26523,x26524,x26525))
% 94.68/94.47 [2653]~E(x26531,x26532)+E(f620(x26533,x26531,x26534,x26535),f620(x26533,x26532,x26534,x26535))
% 94.68/94.47 [2654]~E(x26541,x26542)+E(f620(x26543,x26544,x26541,x26545),f620(x26543,x26544,x26542,x26545))
% 94.68/94.47 [2655]~E(x26551,x26552)+E(f620(x26553,x26554,x26555,x26551),f620(x26553,x26554,x26555,x26552))
% 94.68/94.47 [2656]~E(x26561,x26562)+E(f628(x26561,x26563,x26564,x26565),f628(x26562,x26563,x26564,x26565))
% 94.68/94.47 [2657]~E(x26571,x26572)+E(f628(x26573,x26571,x26574,x26575),f628(x26573,x26572,x26574,x26575))
% 94.68/94.47 [2658]~E(x26581,x26582)+E(f628(x26583,x26584,x26581,x26585),f628(x26583,x26584,x26582,x26585))
% 94.68/94.47 [2659]~E(x26591,x26592)+E(f628(x26593,x26594,x26595,x26591),f628(x26593,x26594,x26595,x26592))
% 94.68/94.47 [2660]~E(x26601,x26602)+E(f489(x26601,x26603),f489(x26602,x26603))
% 94.68/94.47 [2661]~E(x26611,x26612)+E(f489(x26613,x26611),f489(x26613,x26612))
% 94.68/94.47 [2662]~E(x26621,x26622)+E(f641(x26621,x26623,x26624),f641(x26622,x26623,x26624))
% 94.68/94.47 [2663]~E(x26631,x26632)+E(f641(x26633,x26631,x26634),f641(x26633,x26632,x26634))
% 94.68/94.47 [2664]~E(x26641,x26642)+E(f641(x26643,x26644,x26641),f641(x26643,x26644,x26642))
% 94.68/94.47 [2665]~E(x26651,x26652)+E(f855(x26651,x26653,x26654),f855(x26652,x26653,x26654))
% 94.68/94.47 [2666]~E(x26661,x26662)+E(f855(x26663,x26661,x26664),f855(x26663,x26662,x26664))
% 94.68/94.47 [2667]~E(x26671,x26672)+E(f855(x26673,x26674,x26671),f855(x26673,x26674,x26672))
% 94.68/94.47 [2668]~E(x26681,x26682)+E(f322(x26681),f322(x26682))
% 94.68/94.47 [2669]~E(x26691,x26692)+E(f456(x26691,x26693,x26694),f456(x26692,x26693,x26694))
% 94.68/94.47 [2670]~E(x26701,x26702)+E(f456(x26703,x26701,x26704),f456(x26703,x26702,x26704))
% 94.68/94.47 [2671]~E(x26711,x26712)+E(f456(x26713,x26714,x26711),f456(x26713,x26714,x26712))
% 94.68/94.47 [2672]~E(x26721,x26722)+E(f360(x26721,x26723,x26724,x26725),f360(x26722,x26723,x26724,x26725))
% 94.68/94.47 [2673]~E(x26731,x26732)+E(f360(x26733,x26731,x26734,x26735),f360(x26733,x26732,x26734,x26735))
% 94.68/94.47 [2674]~E(x26741,x26742)+E(f360(x26743,x26744,x26741,x26745),f360(x26743,x26744,x26742,x26745))
% 94.68/94.47 [2675]~E(x26751,x26752)+E(f360(x26753,x26754,x26755,x26751),f360(x26753,x26754,x26755,x26752))
% 94.68/94.47 [2676]~E(x26761,x26762)+E(f671(x26761,x26763,x26764),f671(x26762,x26763,x26764))
% 94.68/94.47 [2677]~E(x26771,x26772)+E(f671(x26773,x26771,x26774),f671(x26773,x26772,x26774))
% 94.68/94.47 [2678]~E(x26781,x26782)+E(f671(x26783,x26784,x26781),f671(x26783,x26784,x26782))
% 94.68/94.47 [2679]~E(x26791,x26792)+E(f17(x26791,x26793,x26794,x26795),f17(x26792,x26793,x26794,x26795))
% 94.68/94.47 [2680]~E(x26801,x26802)+E(f17(x26803,x26801,x26804,x26805),f17(x26803,x26802,x26804,x26805))
% 94.68/94.47 [2681]~E(x26811,x26812)+E(f17(x26813,x26814,x26811,x26815),f17(x26813,x26814,x26812,x26815))
% 94.68/94.47 [2682]~E(x26821,x26822)+E(f17(x26823,x26824,x26825,x26821),f17(x26823,x26824,x26825,x26822))
% 94.68/94.47 [2683]~E(x26831,x26832)+E(f686(x26831,x26833),f686(x26832,x26833))
% 94.68/94.47 [2684]~E(x26841,x26842)+E(f686(x26843,x26841),f686(x26843,x26842))
% 94.68/94.47 [2685]~E(x26851,x26852)+E(f361(x26851,x26853,x26854,x26855),f361(x26852,x26853,x26854,x26855))
% 94.68/94.47 [2686]~E(x26861,x26862)+E(f361(x26863,x26861,x26864,x26865),f361(x26863,x26862,x26864,x26865))
% 94.68/94.47 [2687]~E(x26871,x26872)+E(f361(x26873,x26874,x26871,x26875),f361(x26873,x26874,x26872,x26875))
% 94.68/94.47 [2688]~E(x26881,x26882)+E(f361(x26883,x26884,x26885,x26881),f361(x26883,x26884,x26885,x26882))
% 94.68/94.47 [2689]~E(x26891,x26892)+E(f769(x26891,x26893,x26894,x26895),f769(x26892,x26893,x26894,x26895))
% 94.68/94.47 [2690]~E(x26901,x26902)+E(f769(x26903,x26901,x26904,x26905),f769(x26903,x26902,x26904,x26905))
% 94.68/94.47 [2691]~E(x26911,x26912)+E(f769(x26913,x26914,x26911,x26915),f769(x26913,x26914,x26912,x26915))
% 94.68/94.47 [2692]~E(x26921,x26922)+E(f769(x26923,x26924,x26925,x26921),f769(x26923,x26924,x26925,x26922))
% 94.68/94.47 [2693]~E(x26931,x26932)+E(f864(x26931,x26933),f864(x26932,x26933))
% 94.68/94.47 [2694]~E(x26941,x26942)+E(f864(x26943,x26941),f864(x26943,x26942))
% 94.68/94.47 [2695]~E(x26951,x26952)+E(f717(x26951,x26953),f717(x26952,x26953))
% 94.68/94.47 [2696]~E(x26961,x26962)+E(f717(x26963,x26961),f717(x26963,x26962))
% 94.68/94.47 [2697]~E(x26971,x26972)+E(f453(x26971,x26973,x26974,x26975),f453(x26972,x26973,x26974,x26975))
% 94.68/94.47 [2698]~E(x26981,x26982)+E(f453(x26983,x26981,x26984,x26985),f453(x26983,x26982,x26984,x26985))
% 94.68/94.47 [2699]~E(x26991,x26992)+E(f453(x26993,x26994,x26991,x26995),f453(x26993,x26994,x26992,x26995))
% 94.68/94.47 [2700]~E(x27001,x27002)+E(f453(x27003,x27004,x27005,x27001),f453(x27003,x27004,x27005,x27002))
% 94.68/94.47 [2701]~E(x27011,x27012)+E(f321(x27011,x27013,x27014,x27015),f321(x27012,x27013,x27014,x27015))
% 94.68/94.47 [2702]~E(x27021,x27022)+E(f321(x27023,x27021,x27024,x27025),f321(x27023,x27022,x27024,x27025))
% 94.68/94.47 [2703]~E(x27031,x27032)+E(f321(x27033,x27034,x27031,x27035),f321(x27033,x27034,x27032,x27035))
% 94.68/94.47 [2704]~E(x27041,x27042)+E(f321(x27043,x27044,x27045,x27041),f321(x27043,x27044,x27045,x27042))
% 94.68/94.47 [2705]~E(x27051,x27052)+E(f750(x27051,x27053,x27054,x27055),f750(x27052,x27053,x27054,x27055))
% 94.68/94.47 [2706]~E(x27061,x27062)+E(f750(x27063,x27061,x27064,x27065),f750(x27063,x27062,x27064,x27065))
% 94.68/94.47 [2707]~E(x27071,x27072)+E(f750(x27073,x27074,x27071,x27075),f750(x27073,x27074,x27072,x27075))
% 94.68/94.47 [2708]~E(x27081,x27082)+E(f750(x27083,x27084,x27085,x27081),f750(x27083,x27084,x27085,x27082))
% 94.68/94.47 [2709]~E(x27091,x27092)+E(f488(x27091,x27093),f488(x27092,x27093))
% 94.68/94.47 [2710]~E(x27101,x27102)+E(f488(x27103,x27101),f488(x27103,x27102))
% 94.68/94.47 [2711]~E(x27111,x27112)+E(f863(x27111,x27113),f863(x27112,x27113))
% 94.68/94.47 [2712]~E(x27121,x27122)+E(f863(x27123,x27121),f863(x27123,x27122))
% 94.68/94.47 [2713]~E(x27131,x27132)+E(f831(x27131,x27133,x27134,x27135,x27136,x27137),f831(x27132,x27133,x27134,x27135,x27136,x27137))
% 94.68/94.47 [2714]~E(x27141,x27142)+E(f831(x27143,x27141,x27144,x27145,x27146,x27147),f831(x27143,x27142,x27144,x27145,x27146,x27147))
% 94.68/94.47 [2715]~E(x27151,x27152)+E(f831(x27153,x27154,x27151,x27155,x27156,x27157),f831(x27153,x27154,x27152,x27155,x27156,x27157))
% 94.68/94.47 [2716]~E(x27161,x27162)+E(f831(x27163,x27164,x27165,x27161,x27166,x27167),f831(x27163,x27164,x27165,x27162,x27166,x27167))
% 94.68/94.47 [2717]~E(x27171,x27172)+E(f831(x27173,x27174,x27175,x27176,x27171,x27177),f831(x27173,x27174,x27175,x27176,x27172,x27177))
% 94.68/94.47 [2718]~E(x27181,x27182)+E(f831(x27183,x27184,x27185,x27186,x27187,x27181),f831(x27183,x27184,x27185,x27186,x27187,x27182))
% 94.68/94.47 [2719]~E(x27191,x27192)+E(f789(x27191,x27193),f789(x27192,x27193))
% 94.68/94.47 [2720]~E(x27201,x27202)+E(f789(x27203,x27201),f789(x27203,x27202))
% 94.68/94.47 [2721]~E(x27211,x27212)+E(f494(x27211,x27213,x27214,x27215,x27216,x27217),f494(x27212,x27213,x27214,x27215,x27216,x27217))
% 94.68/94.47 [2722]~E(x27221,x27222)+E(f494(x27223,x27221,x27224,x27225,x27226,x27227),f494(x27223,x27222,x27224,x27225,x27226,x27227))
% 94.68/94.47 [2723]~E(x27231,x27232)+E(f494(x27233,x27234,x27231,x27235,x27236,x27237),f494(x27233,x27234,x27232,x27235,x27236,x27237))
% 94.68/94.47 [2724]~E(x27241,x27242)+E(f494(x27243,x27244,x27245,x27241,x27246,x27247),f494(x27243,x27244,x27245,x27242,x27246,x27247))
% 94.68/94.47 [2725]~E(x27251,x27252)+E(f494(x27253,x27254,x27255,x27256,x27251,x27257),f494(x27253,x27254,x27255,x27256,x27252,x27257))
% 94.68/94.47 [2726]~E(x27261,x27262)+E(f494(x27263,x27264,x27265,x27266,x27267,x27261),f494(x27263,x27264,x27265,x27266,x27267,x27262))
% 94.68/94.47 [2727]~E(x27271,x27272)+E(f874(x27271,x27273,x27274),f874(x27272,x27273,x27274))
% 94.68/94.47 [2728]~E(x27281,x27282)+E(f874(x27283,x27281,x27284),f874(x27283,x27282,x27284))
% 94.68/94.47 [2729]~E(x27291,x27292)+E(f874(x27293,x27294,x27291),f874(x27293,x27294,x27292))
% 94.68/94.47 [2730]~E(x27301,x27302)+E(f215(x27301,x27303,x27304,x27305,x27306),f215(x27302,x27303,x27304,x27305,x27306))
% 94.68/94.47 [2731]~E(x27311,x27312)+E(f215(x27313,x27311,x27314,x27315,x27316),f215(x27313,x27312,x27314,x27315,x27316))
% 94.68/94.47 [2732]~E(x27321,x27322)+E(f215(x27323,x27324,x27321,x27325,x27326),f215(x27323,x27324,x27322,x27325,x27326))
% 94.68/94.47 [2733]~E(x27331,x27332)+E(f215(x27333,x27334,x27335,x27331,x27336),f215(x27333,x27334,x27335,x27332,x27336))
% 94.68/94.47 [2734]~E(x27341,x27342)+E(f215(x27343,x27344,x27345,x27346,x27341),f215(x27343,x27344,x27345,x27346,x27342))
% 94.68/94.47 [2735]~E(x27351,x27352)+E(f669(x27351,x27353,x27354),f669(x27352,x27353,x27354))
% 94.68/94.47 [2736]~E(x27361,x27362)+E(f669(x27363,x27361,x27364),f669(x27363,x27362,x27364))
% 94.68/94.47 [2737]~E(x27371,x27372)+E(f669(x27373,x27374,x27371),f669(x27373,x27374,x27372))
% 94.68/94.47 [2738]~E(x27381,x27382)+E(f848(x27381,x27383),f848(x27382,x27383))
% 94.68/94.47 [2739]~E(x27391,x27392)+E(f848(x27393,x27391),f848(x27393,x27392))
% 94.68/94.47 [2740]~E(x27401,x27402)+E(f251(x27401,x27403,x27404,x27405,x27406),f251(x27402,x27403,x27404,x27405,x27406))
% 94.68/94.47 [2741]~E(x27411,x27412)+E(f251(x27413,x27411,x27414,x27415,x27416),f251(x27413,x27412,x27414,x27415,x27416))
% 94.68/94.47 [2742]~E(x27421,x27422)+E(f251(x27423,x27424,x27421,x27425,x27426),f251(x27423,x27424,x27422,x27425,x27426))
% 94.68/94.47 [2743]~E(x27431,x27432)+E(f251(x27433,x27434,x27435,x27431,x27436),f251(x27433,x27434,x27435,x27432,x27436))
% 94.68/94.47 [2744]~E(x27441,x27442)+E(f251(x27443,x27444,x27445,x27446,x27441),f251(x27443,x27444,x27445,x27446,x27442))
% 94.68/94.47 [2745]~E(x27451,x27452)+E(f859(x27451,x27453,x27454),f859(x27452,x27453,x27454))
% 94.68/94.47 [2746]~E(x27461,x27462)+E(f859(x27463,x27461,x27464),f859(x27463,x27462,x27464))
% 94.68/94.47 [2747]~E(x27471,x27472)+E(f859(x27473,x27474,x27471),f859(x27473,x27474,x27472))
% 94.68/94.47 [2748]~E(x27481,x27482)+E(f879(x27481,x27483),f879(x27482,x27483))
% 94.68/94.47 [2749]~E(x27491,x27492)+E(f879(x27493,x27491),f879(x27493,x27492))
% 94.68/94.47 [2750]~E(x27501,x27502)+E(f736(x27501),f736(x27502))
% 94.68/94.47 [2751]~E(x27511,x27512)+E(f704(x27511,x27513),f704(x27512,x27513))
% 94.68/94.47 [2752]~E(x27521,x27522)+E(f704(x27523,x27521),f704(x27523,x27522))
% 94.68/94.47 [2753]~E(x27531,x27532)+E(f492(x27531,x27533),f492(x27532,x27533))
% 94.68/94.47 [2754]~E(x27541,x27542)+E(f492(x27543,x27541),f492(x27543,x27542))
% 94.68/94.47 [2755]~E(x27551,x27552)+E(f537(x27551,x27553),f537(x27552,x27553))
% 94.68/94.47 [2756]~E(x27561,x27562)+E(f537(x27563,x27561),f537(x27563,x27562))
% 94.68/94.47 [2757]~E(x27571,x27572)+E(f485(x27571,x27573),f485(x27572,x27573))
% 94.68/94.47 [2758]~E(x27581,x27582)+E(f485(x27583,x27581),f485(x27583,x27582))
% 94.68/94.47 [2759]~E(x27591,x27592)+E(f236(x27591,x27593,x27594,x27595,x27596,x27597),f236(x27592,x27593,x27594,x27595,x27596,x27597))
% 94.68/94.47 [2760]~E(x27601,x27602)+E(f236(x27603,x27601,x27604,x27605,x27606,x27607),f236(x27603,x27602,x27604,x27605,x27606,x27607))
% 94.68/94.47 [2761]~E(x27611,x27612)+E(f236(x27613,x27614,x27611,x27615,x27616,x27617),f236(x27613,x27614,x27612,x27615,x27616,x27617))
% 94.68/94.47 [2762]~E(x27621,x27622)+E(f236(x27623,x27624,x27625,x27621,x27626,x27627),f236(x27623,x27624,x27625,x27622,x27626,x27627))
% 94.68/94.47 [2763]~E(x27631,x27632)+E(f236(x27633,x27634,x27635,x27636,x27631,x27637),f236(x27633,x27634,x27635,x27636,x27632,x27637))
% 94.68/94.47 [2764]~E(x27641,x27642)+E(f236(x27643,x27644,x27645,x27646,x27647,x27641),f236(x27643,x27644,x27645,x27646,x27647,x27642))
% 94.68/94.47 [2765]~P1(x27651)+P1(x27652)+~E(x27651,x27652)
% 94.68/94.47 [2766]~P2(x27661)+P2(x27662)+~E(x27661,x27662)
% 94.68/94.47 [2767]P13(x27672,x27673)+~E(x27671,x27672)+~P13(x27671,x27673)
% 94.68/94.47 [2768]P13(x27683,x27682)+~E(x27681,x27682)+~P13(x27683,x27681)
% 94.68/94.47 [2769]~P65(x27691)+P65(x27692)+~E(x27691,x27692)
% 94.68/94.47 [2770]~P66(x27701)+P66(x27702)+~E(x27701,x27702)
% 94.68/94.47 [2771]~P3(x27711)+P3(x27712)+~E(x27711,x27712)
% 94.68/94.47 [2772]~P108(x27721)+P108(x27722)+~E(x27721,x27722)
% 94.68/94.47 [2773]~P4(x27731)+P4(x27732)+~E(x27731,x27732)
% 94.68/94.47 [2774]P148(x27742,x27743,x27744)+~E(x27741,x27742)+~P148(x27741,x27743,x27744)
% 94.68/94.47 [2775]P148(x27753,x27752,x27754)+~E(x27751,x27752)+~P148(x27753,x27751,x27754)
% 94.68/94.47 [2776]P148(x27763,x27764,x27762)+~E(x27761,x27762)+~P148(x27763,x27764,x27761)
% 94.68/94.47 [2777]~P99(x27771)+P99(x27772)+~E(x27771,x27772)
% 94.68/94.47 [2778]~P5(x27781)+P5(x27782)+~E(x27781,x27782)
% 94.68/94.47 [2779]~P112(x27791)+P112(x27792)+~E(x27791,x27792)
% 94.68/94.47 [2780]~P109(x27801)+P109(x27802)+~E(x27801,x27802)
% 94.68/94.47 [2781]P147(x27812,x27813,x27814)+~E(x27811,x27812)+~P147(x27811,x27813,x27814)
% 94.68/94.47 [2782]P147(x27823,x27822,x27824)+~E(x27821,x27822)+~P147(x27823,x27821,x27824)
% 94.68/94.47 [2783]P147(x27833,x27834,x27832)+~E(x27831,x27832)+~P147(x27833,x27834,x27831)
% 94.68/94.47 [2784]~P111(x27841)+P111(x27842)+~E(x27841,x27842)
% 94.68/94.47 [2785]~P125(x27851)+P125(x27852)+~E(x27851,x27852)
% 94.68/94.47 [2786]~P64(x27861)+P64(x27862)+~E(x27861,x27862)
% 94.68/94.47 [2787]~P110(x27871)+P110(x27872)+~E(x27871,x27872)
% 94.68/94.47 [2788]~P67(x27881)+P67(x27882)+~E(x27881,x27882)
% 94.68/94.47 [2789]~P68(x27891)+P68(x27892)+~E(x27891,x27892)
% 94.68/94.47 [2790]~P94(x27901)+P94(x27902)+~E(x27901,x27902)
% 94.68/94.47 [2791]P24(x27912,x27913,x27914,x27915)+~E(x27911,x27912)+~P24(x27911,x27913,x27914,x27915)
% 94.68/94.47 [2792]P24(x27923,x27922,x27924,x27925)+~E(x27921,x27922)+~P24(x27923,x27921,x27924,x27925)
% 94.68/94.47 [2793]P24(x27933,x27934,x27932,x27935)+~E(x27931,x27932)+~P24(x27933,x27934,x27931,x27935)
% 94.68/94.47 [2794]P24(x27943,x27944,x27945,x27942)+~E(x27941,x27942)+~P24(x27943,x27944,x27945,x27941)
% 94.68/94.47 [2795]~P77(x27951)+P77(x27952)+~E(x27951,x27952)
% 94.68/94.47 [2796]~P83(x27961)+P83(x27962)+~E(x27961,x27962)
% 94.68/94.47 [2797]~P95(x27971)+P95(x27972)+~E(x27971,x27972)
% 94.68/94.47 [2798]~P69(x27981)+P69(x27982)+~E(x27981,x27982)
% 94.68/94.47 [2799]~P80(x27991)+P80(x27992)+~E(x27991,x27992)
% 94.68/94.47 [2800]~P63(x28001)+P63(x28002)+~E(x28001,x28002)
% 94.68/94.47 [2801]~P62(x28011)+P62(x28012)+~E(x28011,x28012)
% 94.68/94.47 [2802]~P70(x28021)+P70(x28022)+~E(x28021,x28022)
% 94.68/94.47 [2803]P32(x28032,x28033,x28034)+~E(x28031,x28032)+~P32(x28031,x28033,x28034)
% 94.68/94.47 [2804]P32(x28043,x28042,x28044)+~E(x28041,x28042)+~P32(x28043,x28041,x28044)
% 94.68/94.47 [2805]P32(x28053,x28054,x28052)+~E(x28051,x28052)+~P32(x28053,x28054,x28051)
% 94.68/94.47 [2806]P20(x28062,x28063,x28064,x28065)+~E(x28061,x28062)+~P20(x28061,x28063,x28064,x28065)
% 94.68/94.47 [2807]P20(x28073,x28072,x28074,x28075)+~E(x28071,x28072)+~P20(x28073,x28071,x28074,x28075)
% 94.68/94.47 [2808]P20(x28083,x28084,x28082,x28085)+~E(x28081,x28082)+~P20(x28083,x28084,x28081,x28085)
% 94.68/94.47 [2809]P20(x28093,x28094,x28095,x28092)+~E(x28091,x28092)+~P20(x28093,x28094,x28095,x28091)
% 94.68/94.47 [2810]~P71(x28101)+P71(x28102)+~E(x28101,x28102)
% 94.68/94.47 [2811]~P100(x28111)+P100(x28112)+~E(x28111,x28112)
% 94.68/94.47 [2812]~P140(x28121)+P140(x28122)+~E(x28121,x28122)
% 94.68/94.47 [2813]~P72(x28131)+P72(x28132)+~E(x28131,x28132)
% 94.68/94.47 [2814]P7(x28142,x28143)+~E(x28141,x28142)+~P7(x28141,x28143)
% 94.68/94.47 [2815]P7(x28153,x28152)+~E(x28151,x28152)+~P7(x28153,x28151)
% 94.68/94.47 [2816]P37(x28162,x28163)+~E(x28161,x28162)+~P37(x28161,x28163)
% 94.68/94.47 [2817]P37(x28173,x28172)+~E(x28171,x28172)+~P37(x28173,x28171)
% 94.68/94.47 [2818]~P84(x28181)+P84(x28182)+~E(x28181,x28182)
% 94.68/94.47 [2819]P57(x28192,x28193)+~E(x28191,x28192)+~P57(x28191,x28193)
% 94.68/94.47 [2820]P57(x28203,x28202)+~E(x28201,x28202)+~P57(x28203,x28201)
% 94.68/94.47 [2821]P43(x28212,x28213)+~E(x28211,x28212)+~P43(x28211,x28213)
% 94.68/94.47 [2822]P43(x28223,x28222)+~E(x28221,x28222)+~P43(x28223,x28221)
% 94.68/94.47 [2823]~P85(x28231)+P85(x28232)+~E(x28231,x28232)
% 94.68/94.47 [2824]~P141(x28241)+P141(x28242)+~E(x28241,x28242)
% 94.68/94.47 [2825]~P61(x28251)+P61(x28252)+~E(x28251,x28252)
% 94.68/94.47 [2826]~P75(x28261)+P75(x28262)+~E(x28261,x28262)
% 94.68/94.47 [2827]~P87(x28271)+P87(x28272)+~E(x28271,x28272)
% 94.68/94.47 [2828]P30(x28282,x28283,x28284)+~E(x28281,x28282)+~P30(x28281,x28283,x28284)
% 94.68/94.47 [2829]P30(x28293,x28292,x28294)+~E(x28291,x28292)+~P30(x28293,x28291,x28294)
% 94.68/94.47 [2830]P30(x28303,x28304,x28302)+~E(x28301,x28302)+~P30(x28303,x28304,x28301)
% 94.68/94.47 [2831]~P86(x28311)+P86(x28312)+~E(x28311,x28312)
% 94.68/94.47 [2832]~P136(x28321)+P136(x28322)+~E(x28321,x28322)
% 94.68/94.47 [2833]P36(x28332,x28333)+~E(x28331,x28332)+~P36(x28331,x28333)
% 94.68/94.47 [2834]P36(x28343,x28342)+~E(x28341,x28342)+~P36(x28343,x28341)
% 94.68/94.47 [2835]~P89(x28351)+P89(x28352)+~E(x28351,x28352)
% 94.68/94.47 [2836]~P88(x28361)+P88(x28362)+~E(x28361,x28362)
% 94.68/94.47 [2837]~P76(x28371)+P76(x28372)+~E(x28371,x28372)
% 94.68/94.47 [2838]~P143(x28381)+P143(x28382)+~E(x28381,x28382)
% 94.68/94.47 [2839]~P127(x28391)+P127(x28392)+~E(x28391,x28392)
% 94.68/94.47 [2840]P16(x28402,x28403,x28404)+~E(x28401,x28402)+~P16(x28401,x28403,x28404)
% 94.68/94.47 [2841]P16(x28413,x28412,x28414)+~E(x28411,x28412)+~P16(x28413,x28411,x28414)
% 94.68/94.47 [2842]P16(x28423,x28424,x28422)+~E(x28421,x28422)+~P16(x28423,x28424,x28421)
% 94.68/94.47 [2843]P25(x28432,x28433,x28434,x28435,x28436)+~E(x28431,x28432)+~P25(x28431,x28433,x28434,x28435,x28436)
% 94.68/94.47 [2844]P25(x28443,x28442,x28444,x28445,x28446)+~E(x28441,x28442)+~P25(x28443,x28441,x28444,x28445,x28446)
% 94.68/94.47 [2845]P25(x28453,x28454,x28452,x28455,x28456)+~E(x28451,x28452)+~P25(x28453,x28454,x28451,x28455,x28456)
% 94.68/94.47 [2846]P25(x28463,x28464,x28465,x28462,x28466)+~E(x28461,x28462)+~P25(x28463,x28464,x28465,x28461,x28466)
% 94.68/94.47 [2847]P25(x28473,x28474,x28475,x28476,x28472)+~E(x28471,x28472)+~P25(x28473,x28474,x28475,x28476,x28471)
% 94.68/94.47 [2848]~P93(x28481)+P93(x28482)+~E(x28481,x28482)
% 94.68/94.47 [2849]~P82(x28491)+P82(x28492)+~E(x28491,x28492)
% 94.68/94.47 [2850]~P6(x28501)+P6(x28502)+~E(x28501,x28502)
% 94.68/94.47 [2851]~P81(x28511)+P81(x28512)+~E(x28511,x28512)
% 94.68/94.47 [2852]P26(x28522,x28523)+~E(x28521,x28522)+~P26(x28521,x28523)
% 94.68/94.47 [2853]P26(x28533,x28532)+~E(x28531,x28532)+~P26(x28533,x28531)
% 94.68/94.47 [2854]P33(x28542,x28543,x28544,x28545,x28546)+~E(x28541,x28542)+~P33(x28541,x28543,x28544,x28545,x28546)
% 94.68/94.47 [2855]P33(x28553,x28552,x28554,x28555,x28556)+~E(x28551,x28552)+~P33(x28553,x28551,x28554,x28555,x28556)
% 94.68/94.47 [2856]P33(x28563,x28564,x28562,x28565,x28566)+~E(x28561,x28562)+~P33(x28563,x28564,x28561,x28565,x28566)
% 94.68/94.47 [2857]P33(x28573,x28574,x28575,x28572,x28576)+~E(x28571,x28572)+~P33(x28573,x28574,x28575,x28571,x28576)
% 94.68/94.47 [2858]P33(x28583,x28584,x28585,x28586,x28582)+~E(x28581,x28582)+~P33(x28583,x28584,x28585,x28586,x28581)
% 94.68/94.47 [2859]~P78(x28591)+P78(x28592)+~E(x28591,x28592)
% 94.68/94.47 [2860]~P103(x28601)+P103(x28602)+~E(x28601,x28602)
% 94.68/94.47 [2861]~P73(x28611)+P73(x28612)+~E(x28611,x28612)
% 94.68/94.47 [2862]P28(x28622,x28623,x28624)+~E(x28621,x28622)+~P28(x28621,x28623,x28624)
% 94.68/94.47 [2863]P28(x28633,x28632,x28634)+~E(x28631,x28632)+~P28(x28633,x28631,x28634)
% 94.68/94.47 [2864]P28(x28643,x28644,x28642)+~E(x28641,x28642)+~P28(x28643,x28644,x28641)
% 94.68/94.47 [2865]P52(x28652,x28653,x28654)+~E(x28651,x28652)+~P52(x28651,x28653,x28654)
% 94.68/94.47 [2866]P52(x28663,x28662,x28664)+~E(x28661,x28662)+~P52(x28663,x28661,x28664)
% 94.68/94.47 [2867]P52(x28673,x28674,x28672)+~E(x28671,x28672)+~P52(x28673,x28674,x28671)
% 94.68/94.47 [2868]P21(x28682,x28683,x28684,x28685,x28686)+~E(x28681,x28682)+~P21(x28681,x28683,x28684,x28685,x28686)
% 94.68/94.47 [2869]P21(x28693,x28692,x28694,x28695,x28696)+~E(x28691,x28692)+~P21(x28693,x28691,x28694,x28695,x28696)
% 94.68/94.47 [2870]P21(x28703,x28704,x28702,x28705,x28706)+~E(x28701,x28702)+~P21(x28703,x28704,x28701,x28705,x28706)
% 94.68/94.47 [2871]P21(x28713,x28714,x28715,x28712,x28716)+~E(x28711,x28712)+~P21(x28713,x28714,x28715,x28711,x28716)
% 94.68/94.47 [2872]P21(x28723,x28724,x28725,x28726,x28722)+~E(x28721,x28722)+~P21(x28723,x28724,x28725,x28726,x28721)
% 94.68/94.47 [2873]~P133(x28731)+P133(x28732)+~E(x28731,x28732)
% 94.68/94.47 [2874]P14(x28742,x28743,x28744)+~E(x28741,x28742)+~P14(x28741,x28743,x28744)
% 94.68/94.47 [2875]P14(x28753,x28752,x28754)+~E(x28751,x28752)+~P14(x28753,x28751,x28754)
% 94.68/94.47 [2876]P14(x28763,x28764,x28762)+~E(x28761,x28762)+~P14(x28763,x28764,x28761)
% 94.68/94.47 [2877]~P146(x28771)+P146(x28772)+~E(x28771,x28772)
% 94.68/94.47 [2878]P54(x28782,x28783,x28784)+~E(x28781,x28782)+~P54(x28781,x28783,x28784)
% 94.68/94.47 [2879]P54(x28793,x28792,x28794)+~E(x28791,x28792)+~P54(x28793,x28791,x28794)
% 94.68/94.47 [2880]P54(x28803,x28804,x28802)+~E(x28801,x28802)+~P54(x28803,x28804,x28801)
% 94.68/94.47 [2881]~P44(x28811)+P44(x28812)+~E(x28811,x28812)
% 94.68/94.47 [2882]~P97(x28821)+P97(x28822)+~E(x28821,x28822)
% 94.68/94.47 [2883]P38(x28832,x28833)+~E(x28831,x28832)+~P38(x28831,x28833)
% 94.68/94.47 [2884]P38(x28843,x28842)+~E(x28841,x28842)+~P38(x28843,x28841)
% 94.68/94.47 [2885]P55(x28852,x28853,x28854)+~E(x28851,x28852)+~P55(x28851,x28853,x28854)
% 94.68/94.47 [2886]P55(x28863,x28862,x28864)+~E(x28861,x28862)+~P55(x28863,x28861,x28864)
% 94.68/94.47 [2887]P55(x28873,x28874,x28872)+~E(x28871,x28872)+~P55(x28873,x28874,x28871)
% 94.68/94.47 [2888]~P128(x28881)+P128(x28882)+~E(x28881,x28882)
% 94.68/94.47 [2889]P8(x28892,x28893,x28894)+~E(x28891,x28892)+~P8(x28891,x28893,x28894)
% 94.68/94.47 [2890]P8(x28903,x28902,x28904)+~E(x28901,x28902)+~P8(x28903,x28901,x28904)
% 94.68/94.47 [2891]P8(x28913,x28914,x28912)+~E(x28911,x28912)+~P8(x28913,x28914,x28911)
% 94.68/94.47 [2892]P58(x28922,x28923,x28924,x28925)+~E(x28921,x28922)+~P58(x28921,x28923,x28924,x28925)
% 94.68/94.47 [2893]P58(x28933,x28932,x28934,x28935)+~E(x28931,x28932)+~P58(x28933,x28931,x28934,x28935)
% 94.68/94.47 [2894]P58(x28943,x28944,x28942,x28945)+~E(x28941,x28942)+~P58(x28943,x28944,x28941,x28945)
% 94.68/94.47 [2895]P58(x28953,x28954,x28955,x28952)+~E(x28951,x28952)+~P58(x28953,x28954,x28955,x28951)
% 94.68/94.47 [2896]P56(x28962,x28963,x28964,x28965,x28966)+~E(x28961,x28962)+~P56(x28961,x28963,x28964,x28965,x28966)
% 94.68/94.47 [2897]P56(x28973,x28972,x28974,x28975,x28976)+~E(x28971,x28972)+~P56(x28973,x28971,x28974,x28975,x28976)
% 94.68/94.47 [2898]P56(x28983,x28984,x28982,x28985,x28986)+~E(x28981,x28982)+~P56(x28983,x28984,x28981,x28985,x28986)
% 94.68/94.47 [2899]P56(x28993,x28994,x28995,x28992,x28996)+~E(x28991,x28992)+~P56(x28993,x28994,x28995,x28991,x28996)
% 94.68/94.47 [2900]P56(x29003,x29004,x29005,x29006,x29002)+~E(x29001,x29002)+~P56(x29003,x29004,x29005,x29006,x29001)
% 94.68/94.47 [2901]~P120(x29011)+P120(x29012)+~E(x29011,x29012)
% 94.68/94.47 [2902]~P131(x29021)+P131(x29022)+~E(x29021,x29022)
% 94.68/94.47 [2903]~P144(x29031)+P144(x29032)+~E(x29031,x29032)
% 94.68/94.47 [2904]P27(x29042,x29043)+~E(x29041,x29042)+~P27(x29041,x29043)
% 94.68/94.47 [2905]P27(x29053,x29052)+~E(x29051,x29052)+~P27(x29053,x29051)
% 94.68/94.47 [2906]~P96(x29061)+P96(x29062)+~E(x29061,x29062)
% 94.68/94.47 [2907]~P122(x29071)+P122(x29072)+~E(x29071,x29072)
% 94.68/94.47 [2908]~P132(x29081)+P132(x29082)+~E(x29081,x29082)
% 94.68/94.47 [2909]P31(x29092,x29093,x29094,x29095)+~E(x29091,x29092)+~P31(x29091,x29093,x29094,x29095)
% 94.68/94.47 [2910]P31(x29103,x29102,x29104,x29105)+~E(x29101,x29102)+~P31(x29103,x29101,x29104,x29105)
% 94.68/94.47 [2911]P31(x29113,x29114,x29112,x29115)+~E(x29111,x29112)+~P31(x29113,x29114,x29111,x29115)
% 94.68/94.47 [2912]P31(x29123,x29124,x29125,x29122)+~E(x29121,x29122)+~P31(x29123,x29124,x29125,x29121)
% 94.68/94.47 [2913]P29(x29132,x29133,x29134)+~E(x29131,x29132)+~P29(x29131,x29133,x29134)
% 94.68/94.47 [2914]P29(x29143,x29142,x29144)+~E(x29141,x29142)+~P29(x29143,x29141,x29144)
% 94.68/94.47 [2915]P29(x29153,x29154,x29152)+~E(x29151,x29152)+~P29(x29153,x29154,x29151)
% 94.68/94.47 [2916]~P142(x29161)+P142(x29162)+~E(x29161,x29162)
% 94.68/94.47 [2917]~P134(x29171)+P134(x29172)+~E(x29171,x29172)
% 94.68/94.47 [2918]~P104(x29181)+P104(x29182)+~E(x29181,x29182)
% 94.68/94.47 [2919]~P101(x29191)+P101(x29192)+~E(x29191,x29192)
% 94.68/94.47 [2920]~P113(x29201)+P113(x29202)+~E(x29201,x29202)
% 94.68/94.47 [2921]~P126(x29211)+P126(x29212)+~E(x29211,x29212)
% 94.68/94.47 [2922]~P115(x29221)+P115(x29222)+~E(x29221,x29222)
% 94.68/94.47 [2923]P9(x29232,x29233,x29234)+~E(x29231,x29232)+~P9(x29231,x29233,x29234)
% 94.68/94.47 [2924]P9(x29243,x29242,x29244)+~E(x29241,x29242)+~P9(x29243,x29241,x29244)
% 94.68/94.47 [2925]P9(x29253,x29254,x29252)+~E(x29251,x29252)+~P9(x29253,x29254,x29251)
% 94.68/94.47 [2926]P59(x29262,x29263)+~E(x29261,x29262)+~P59(x29261,x29263)
% 94.68/94.47 [2927]P59(x29273,x29272)+~E(x29271,x29272)+~P59(x29273,x29271)
% 94.68/94.47 [2928]~P92(x29281)+P92(x29282)+~E(x29281,x29282)
% 94.68/94.47 [2929]P22(x29292,x29293,x29294,x29295,x29296,x29297)+~E(x29291,x29292)+~P22(x29291,x29293,x29294,x29295,x29296,x29297)
% 94.68/94.47 [2930]P22(x29303,x29302,x29304,x29305,x29306,x29307)+~E(x29301,x29302)+~P22(x29303,x29301,x29304,x29305,x29306,x29307)
% 94.68/94.47 [2931]P22(x29313,x29314,x29312,x29315,x29316,x29317)+~E(x29311,x29312)+~P22(x29313,x29314,x29311,x29315,x29316,x29317)
% 94.68/94.47 [2932]P22(x29323,x29324,x29325,x29322,x29326,x29327)+~E(x29321,x29322)+~P22(x29323,x29324,x29325,x29321,x29326,x29327)
% 94.68/94.47 [2933]P22(x29333,x29334,x29335,x29336,x29332,x29337)+~E(x29331,x29332)+~P22(x29333,x29334,x29335,x29336,x29331,x29337)
% 94.68/94.47 [2934]P22(x29343,x29344,x29345,x29346,x29347,x29342)+~E(x29341,x29342)+~P22(x29343,x29344,x29345,x29346,x29347,x29341)
% 94.68/94.47 [2935]~P39(x29351)+P39(x29352)+~E(x29351,x29352)
% 94.68/94.47 [2936]P23(x29362,x29363,x29364,x29365,x29366,x29367)+~E(x29361,x29362)+~P23(x29361,x29363,x29364,x29365,x29366,x29367)
% 94.68/94.47 [2937]P23(x29373,x29372,x29374,x29375,x29376,x29377)+~E(x29371,x29372)+~P23(x29373,x29371,x29374,x29375,x29376,x29377)
% 94.68/94.47 [2938]P23(x29383,x29384,x29382,x29385,x29386,x29387)+~E(x29381,x29382)+~P23(x29383,x29384,x29381,x29385,x29386,x29387)
% 94.68/94.47 [2939]P23(x29393,x29394,x29395,x29392,x29396,x29397)+~E(x29391,x29392)+~P23(x29393,x29394,x29395,x29391,x29396,x29397)
% 94.68/94.47 [2940]P23(x29403,x29404,x29405,x29406,x29402,x29407)+~E(x29401,x29402)+~P23(x29403,x29404,x29405,x29406,x29401,x29407)
% 94.68/94.47 [2941]P23(x29413,x29414,x29415,x29416,x29417,x29412)+~E(x29411,x29412)+~P23(x29413,x29414,x29415,x29416,x29417,x29411)
% 94.68/94.47 [2942]~P135(x29421)+P135(x29422)+~E(x29421,x29422)
% 94.68/94.47 [2943]P49(x29432,x29433)+~E(x29431,x29432)+~P49(x29431,x29433)
% 94.68/94.47 [2944]P49(x29443,x29442)+~E(x29441,x29442)+~P49(x29443,x29441)
% 94.68/94.47 [2945]~P105(x29451)+P105(x29452)+~E(x29451,x29452)
% 94.68/94.47 [2946]~P98(x29461)+P98(x29462)+~E(x29461,x29462)
% 94.68/94.47 [2947]~P138(x29471)+P138(x29472)+~E(x29471,x29472)
% 94.68/94.47 [2948]P51(x29482,x29483)+~E(x29481,x29482)+~P51(x29481,x29483)
% 94.68/94.47 [2949]P51(x29493,x29492)+~E(x29491,x29492)+~P51(x29493,x29491)
% 94.68/94.47 [2950]P17(x29502,x29503,x29504)+~E(x29501,x29502)+~P17(x29501,x29503,x29504)
% 94.68/94.47 [2951]P17(x29513,x29512,x29514)+~E(x29511,x29512)+~P17(x29513,x29511,x29514)
% 94.68/94.47 [2952]P17(x29523,x29524,x29522)+~E(x29521,x29522)+~P17(x29523,x29524,x29521)
% 94.68/94.47 [2953]~P137(x29531)+P137(x29532)+~E(x29531,x29532)
% 94.68/94.47 [2954]P11(x29542,x29543,x29544,x29545)+~E(x29541,x29542)+~P11(x29541,x29543,x29544,x29545)
% 94.68/94.47 [2955]P11(x29553,x29552,x29554,x29555)+~E(x29551,x29552)+~P11(x29553,x29551,x29554,x29555)
% 94.68/94.47 [2956]P11(x29563,x29564,x29562,x29565)+~E(x29561,x29562)+~P11(x29563,x29564,x29561,x29565)
% 94.68/94.47 [2957]P11(x29573,x29574,x29575,x29572)+~E(x29571,x29572)+~P11(x29573,x29574,x29575,x29571)
% 94.68/94.47 [2958]~P118(x29581)+P118(x29582)+~E(x29581,x29582)
% 94.68/94.47 [2959]~P106(x29591)+P106(x29592)+~E(x29591,x29592)
% 94.68/94.47 [2960]~P60(x29601)+P60(x29602)+~E(x29601,x29602)
% 94.68/94.47 [2961]~P119(x29611)+P119(x29612)+~E(x29611,x29612)
% 94.68/94.47 [2962]P34(x29622,x29623,x29624)+~E(x29621,x29622)+~P34(x29621,x29623,x29624)
% 94.68/94.47 [2963]P34(x29633,x29632,x29634)+~E(x29631,x29632)+~P34(x29633,x29631,x29634)
% 94.68/94.47 [2964]P34(x29643,x29644,x29642)+~E(x29641,x29642)+~P34(x29643,x29644,x29641)
% 94.68/94.47 [2965]P53(x29652,x29653)+~E(x29651,x29652)+~P53(x29651,x29653)
% 94.68/94.47 [2966]P53(x29663,x29662)+~E(x29661,x29662)+~P53(x29663,x29661)
% 94.68/94.47 [2967]P18(x29672,x29673,x29674)+~E(x29671,x29672)+~P18(x29671,x29673,x29674)
% 94.68/94.47 [2968]P18(x29683,x29682,x29684)+~E(x29681,x29682)+~P18(x29683,x29681,x29684)
% 94.68/94.47 [2969]P18(x29693,x29694,x29692)+~E(x29691,x29692)+~P18(x29693,x29694,x29691)
% 94.68/94.47 [2970]P46(x29702,x29703,x29704)+~E(x29701,x29702)+~P46(x29701,x29703,x29704)
% 94.68/94.47 [2971]P46(x29713,x29712,x29714)+~E(x29711,x29712)+~P46(x29713,x29711,x29714)
% 94.68/94.47 [2972]P46(x29723,x29724,x29722)+~E(x29721,x29722)+~P46(x29723,x29724,x29721)
% 94.68/94.47 [2973]~P90(x29731)+P90(x29732)+~E(x29731,x29732)
% 94.68/94.47 [2974]~P129(x29741)+P129(x29742)+~E(x29741,x29742)
% 94.68/94.47 [2975]~P102(x29751)+P102(x29752)+~E(x29751,x29752)
% 94.68/94.47 [2976]P41(x29762,x29763,x29764,x29765,x29766,x29767)+~E(x29761,x29762)+~P41(x29761,x29763,x29764,x29765,x29766,x29767)
% 94.68/94.47 [2977]P41(x29773,x29772,x29774,x29775,x29776,x29777)+~E(x29771,x29772)+~P41(x29773,x29771,x29774,x29775,x29776,x29777)
% 94.68/94.47 [2978]P41(x29783,x29784,x29782,x29785,x29786,x29787)+~E(x29781,x29782)+~P41(x29783,x29784,x29781,x29785,x29786,x29787)
% 94.68/94.47 [2979]P41(x29793,x29794,x29795,x29792,x29796,x29797)+~E(x29791,x29792)+~P41(x29793,x29794,x29795,x29791,x29796,x29797)
% 94.68/94.47 [2980]P41(x29803,x29804,x29805,x29806,x29802,x29807)+~E(x29801,x29802)+~P41(x29803,x29804,x29805,x29806,x29801,x29807)
% 94.68/94.47 [2981]P41(x29813,x29814,x29815,x29816,x29817,x29812)+~E(x29811,x29812)+~P41(x29813,x29814,x29815,x29816,x29817,x29811)
% 94.68/94.47 [2982]~P130(x29821)+P130(x29822)+~E(x29821,x29822)
% 94.68/94.47 [2983]P42(x29832,x29833)+~E(x29831,x29832)+~P42(x29831,x29833)
% 94.68/94.47 [2984]P42(x29843,x29842)+~E(x29841,x29842)+~P42(x29843,x29841)
% 94.68/94.47 [2985]P19(x29852,x29853,x29854,x29855)+~E(x29851,x29852)+~P19(x29851,x29853,x29854,x29855)
% 94.68/94.47 [2986]P19(x29863,x29862,x29864,x29865)+~E(x29861,x29862)+~P19(x29863,x29861,x29864,x29865)
% 94.68/94.47 [2987]P19(x29873,x29874,x29872,x29875)+~E(x29871,x29872)+~P19(x29873,x29874,x29871,x29875)
% 94.68/94.47 [2988]P19(x29883,x29884,x29885,x29882)+~E(x29881,x29882)+~P19(x29883,x29884,x29885,x29881)
% 94.68/94.47 [2989]~P139(x29891)+P139(x29892)+~E(x29891,x29892)
% 94.68/94.47 [2990]P15(x29902,x29903)+~E(x29901,x29902)+~P15(x29901,x29903)
% 94.68/94.47 [2991]P15(x29913,x29912)+~E(x29911,x29912)+~P15(x29913,x29911)
% 94.68/94.47 [2992]P150(x29922,x29923)+~E(x29921,x29922)+~P150(x29921,x29923)
% 94.68/94.47 [2993]P150(x29933,x29932)+~E(x29931,x29932)+~P150(x29933,x29931)
% 94.68/94.47 [2994]P45(x29942,x29943)+~E(x29941,x29942)+~P45(x29941,x29943)
% 94.68/94.47 [2995]P45(x29953,x29952)+~E(x29951,x29952)+~P45(x29953,x29951)
% 94.68/94.47 [2996]~P116(x29961)+P116(x29962)+~E(x29961,x29962)
% 94.68/94.47 [2997]~P121(x29971)+P121(x29972)+~E(x29971,x29972)
% 94.68/94.47 [2998]P47(x29982,x29983,x29984)+~E(x29981,x29982)+~P47(x29981,x29983,x29984)
% 94.68/94.47 [2999]P47(x29993,x29992,x29994)+~E(x29991,x29992)+~P47(x29993,x29991,x29994)
% 94.68/94.47 [3000]P47(x30003,x30004,x30002)+~E(x30001,x30002)+~P47(x30003,x30004,x30001)
% 94.68/94.47 [3001]P50(x30012,x30013)+~E(x30011,x30012)+~P50(x30011,x30013)
% 94.68/94.47 [3002]P50(x30023,x30022)+~E(x30021,x30022)+~P50(x30023,x30021)
% 94.68/94.47 [3003]~P114(x30031)+P114(x30032)+~E(x30031,x30032)
% 94.68/94.47 [3004]~P145(x30041)+P145(x30042)+~E(x30041,x30042)
% 94.68/94.47 [3005]~P74(x30051)+P74(x30052)+~E(x30051,x30052)
% 94.68/94.47 [3006]~P35(x30061)+P35(x30062)+~E(x30061,x30062)
% 94.68/94.47 [3007]P12(x30072,x30073,x30074,x30075,x30076,x30077)+~E(x30071,x30072)+~P12(x30071,x30073,x30074,x30075,x30076,x30077)
% 94.68/94.47 [3008]P12(x30083,x30082,x30084,x30085,x30086,x30087)+~E(x30081,x30082)+~P12(x30083,x30081,x30084,x30085,x30086,x30087)
% 94.68/94.47 [3009]P12(x30093,x30094,x30092,x30095,x30096,x30097)+~E(x30091,x30092)+~P12(x30093,x30094,x30091,x30095,x30096,x30097)
% 94.68/94.47 [3010]P12(x30103,x30104,x30105,x30102,x30106,x30107)+~E(x30101,x30102)+~P12(x30103,x30104,x30105,x30101,x30106,x30107)
% 94.68/94.47 [3011]P12(x30113,x30114,x30115,x30116,x30112,x30117)+~E(x30111,x30112)+~P12(x30113,x30114,x30115,x30116,x30111,x30117)
% 94.68/94.47 [3012]P12(x30123,x30124,x30125,x30126,x30127,x30122)+~E(x30121,x30122)+~P12(x30123,x30124,x30125,x30126,x30127,x30121)
% 94.68/94.47 [3013]~P107(x30131)+P107(x30132)+~E(x30131,x30132)
% 94.68/94.47 [3014]~P149(x30141)+P149(x30142)+~E(x30141,x30142)
% 94.68/94.47 [3015]~P117(x30151)+P117(x30152)+~E(x30151,x30152)
% 94.68/94.47 [3016]P40(x30162,x30163,x30164,x30165)+~E(x30161,x30162)+~P40(x30161,x30163,x30164,x30165)
% 94.68/94.47 [3017]P40(x30173,x30172,x30174,x30175)+~E(x30171,x30172)+~P40(x30173,x30171,x30174,x30175)
% 94.68/94.47 [3018]P40(x30183,x30184,x30182,x30185)+~E(x30181,x30182)+~P40(x30183,x30184,x30181,x30185)
% 94.68/94.47 [3019]P40(x30193,x30194,x30195,x30192)+~E(x30191,x30192)+~P40(x30193,x30194,x30195,x30191)
% 94.68/94.47 [3020]~P91(x30201)+P91(x30202)+~E(x30201,x30202)
% 94.68/94.47 [3021]~P123(x30211)+P123(x30212)+~E(x30211,x30212)
% 94.68/94.47 [3022]~P124(x30221)+P124(x30222)+~E(x30221,x30222)
% 94.68/94.47 [3023]~P79(x30231)+P79(x30232)+~E(x30231,x30232)
% 94.68/94.47 [3024]P48(x30242,x30243,x30244,x30245)+~E(x30241,x30242)+~P48(x30241,x30243,x30244,x30245)
% 94.68/94.47 [3025]P48(x30253,x30252,x30254,x30255)+~E(x30251,x30252)+~P48(x30253,x30251,x30254,x30255)
% 94.68/94.47 [3026]P48(x30263,x30264,x30262,x30265)+~E(x30261,x30262)+~P48(x30263,x30264,x30261,x30265)
% 94.68/94.47 [3027]P48(x30273,x30274,x30275,x30272)+~E(x30271,x30272)+~P48(x30273,x30274,x30275,x30271)
% 94.68/94.47 [3028]P10(x30282,x30283,x30284,x30285,x30286)+~E(x30281,x30282)+~P10(x30281,x30283,x30284,x30285,x30286)
% 94.68/94.47 [3029]P10(x30293,x30292,x30294,x30295,x30296)+~E(x30291,x30292)+~P10(x30293,x30291,x30294,x30295,x30296)
% 94.68/94.47 [3030]P10(x30303,x30304,x30302,x30305,x30306)+~E(x30301,x30302)+~P10(x30303,x30304,x30301,x30305,x30306)
% 94.68/94.47 [3031]P10(x30313,x30314,x30315,x30312,x30316)+~E(x30311,x30312)+~P10(x30313,x30314,x30315,x30311,x30316)
% 94.68/94.47 [3032]P10(x30323,x30324,x30325,x30326,x30322)+~E(x30321,x30322)+~P10(x30323,x30324,x30325,x30326,x30321)
% 94.68/94.47
% 94.68/94.47 %-------------------------------------------
% 94.68/94.49 cnf(10396,plain,
% 94.68/94.49 (~E(f317(a102,x103961),x103961)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10406,plain,
% 94.68/94.49 (~E(f317(a102,x104061),x104061)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10419,plain,
% 94.68/94.49 (~E(f317(a102,x104191),x104191)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10424,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x104241),f103(x104241)),x104242))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10427,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x104271),f103(x104271)),x104272))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10430,plain,
% 94.68/94.49 (~E(f317(a102,x104301),x104301)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10433,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x104331),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10436,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x104361),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10453,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x104531)),x104531))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(10456,plain,
% 94.68/94.49 (~E(f317(f317(f141(x104561),x104562),x104563),x104563)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(10462,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x104621),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10465,plain,
% 94.68/94.49 (E(f317(f274(x104651,x104651),f253(x104651,x104652)),x104652)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(10468,plain,
% 94.68/94.49 (E(f317(f274(x104681,x104681),f253(x104681,x104682)),x104682)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(10473,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x104731),x104731))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(10478,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x104781),x104782)),x104782))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(10481,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x104811),x104812)),x104812))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(10502,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x105021),x105021))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(10505,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f40(a897,x105051,x105052)),x105051))),
% 94.68/94.49 inference(rename_variables,[],[3876])).
% 94.68/94.49 cnf(10526,plain,
% 94.68/94.49 (E(f317(f29(a897),f317(f272(a897),x105261)),x105261)),
% 94.68/94.49 inference(rename_variables,[],[3323])).
% 94.68/94.49 cnf(10534,plain,
% 94.68/94.49 (~E(f317(a102,x105341),x105341)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10539,plain,
% 94.68/94.49 (~E(f317(a102,x105391),x105391)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10542,plain,
% 94.68/94.49 (~E(f317(a102,x105421),x105421)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10547,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x105471),f317(a102,x105471)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10556,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x105561),x105561))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(10563,plain,
% 94.68/94.49 (E(f317(f274(x105631,x105631),f253(x105631,x105632)),x105632)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(10566,plain,
% 94.68/94.49 (E(f317(f274(x105661,x105661),f253(x105661,x105662)),x105662)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(10583,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x105831),x105831))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(10588,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x105881),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10591,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x105911,a893)),x105912),f232(f904(x105911,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(10596,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x105961),f103(x105961)),x105962))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10625,plain,
% 94.68/94.49 (~E(f317(f317(f141(x106251),x106252),x106253),x106253)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(10628,plain,
% 94.68/94.49 (~E(f317(a102,x106281),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(10639,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x106391),x106391))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(10644,plain,
% 94.68/94.49 (~E(f317(a102,x106441),x106441)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10647,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x106471,f904(x106472,a893))),x106473),x106474))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(10654,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x106541),x106541))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(10667,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x106671),f317(a102,x106671)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10688,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x106881,a893)),x106882),f232(f904(x106881,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(10691,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x106911),f103(x106911)),x106912))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10714,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107141),f103(x107141)),x107142))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10721,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107211),f103(x107211)),x107212))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10732,plain,
% 94.68/94.49 (~E(f317(a102,x107321),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(10737,plain,
% 94.68/94.49 (P1(f317(f317(f319(x107371),x107372),f232(f904(x107371,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(10744,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107441),f103(x107441)),x107442))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10749,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x107491),f317(a102,x107491)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10752,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107521),f103(x107521)),x107522))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10755,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107551),f103(x107551)),x107552))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10758,plain,
% 94.68/94.49 (~P1(f317(f56(x107581,x107582,f178(f904(x107581,a893))),x107583))),
% 94.68/94.49 inference(rename_variables,[],[4626])).
% 94.68/94.49 cnf(10761,plain,
% 94.68/94.49 (~P1(f317(f56(x107611,x107612,f178(f904(x107611,a893))),x107613))),
% 94.68/94.49 inference(rename_variables,[],[4626])).
% 94.68/94.49 cnf(10764,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x107641,f904(x107642,a893))),x107643),x107644))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(10767,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x107671),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10772,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x107721),f103(x107721)),x107722))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10783,plain,
% 94.68/94.49 (~E(f317(a102,x107831),x107831)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(10808,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x108081),x108081))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(10811,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x108111),f317(f317(f75(a897),x108111),x108111)))),
% 94.68/94.49 inference(rename_variables,[],[3686])).
% 94.68/94.49 cnf(10814,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x108141),f317(f317(f75(a897),x108141),x108141)))),
% 94.68/94.49 inference(rename_variables,[],[3686])).
% 94.68/94.49 cnf(10817,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x108171),f317(a102,f317(f317(f74(a897),x108172),x108171))))),
% 94.68/94.49 inference(rename_variables,[],[3869])).
% 94.68/94.49 cnf(10822,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x108221),f317(a102,x108221)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10825,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x108251),f317(a102,x108251)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10828,plain,
% 94.68/94.49 (P1(f317(f317(f319(x108281),x108282),f232(f904(x108281,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(10847,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x108471)),x108471))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(10850,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x108501)),x108501))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(10853,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x108531),x108532)),x108532))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(10856,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x108561),x108562)),x108562))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(10859,plain,
% 94.68/94.49 (P1(f317(f232(f904(x108591,a893)),x108592))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(10862,plain,
% 94.68/94.49 (E(f317(f29(a897),f317(f272(a897),x108621)),x108621)),
% 94.68/94.49 inference(rename_variables,[],[3323])).
% 94.68/94.49 cnf(10865,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x108651),f317(a102,x108651)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10872,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x108721),x108721))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(10877,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x108771),x108771))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(10880,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x108801,a893)),f317(f162(x108801),f317(f126(x108801,x108802),x108803))),f317(f162(x108801),x108803)))),
% 94.68/94.49 inference(rename_variables,[],[4065])).
% 94.68/94.49 cnf(10889,plain,
% 94.68/94.49 (E(f317(f274(x108891,x108891),f253(x108891,x108892)),x108892)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(10892,plain,
% 94.68/94.49 (P1(f317(f232(f904(x108921,a893)),x108922))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(10895,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x108951))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(10898,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x108981,a893)),f178(f904(x108981,a893))),x108982))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(10901,plain,
% 94.68/94.49 (P1(f317(f232(f904(x109011,a893)),x109012))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(10904,plain,
% 94.68/94.49 (P1(f317(f232(f904(x109041,a893)),x109042))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(10907,plain,
% 94.68/94.49 (P1(f317(f232(f904(x109071,a893)),x109072))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(10910,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x109101),f317(f317(f75(a897),x109101),x109101)))),
% 94.68/94.49 inference(rename_variables,[],[3686])).
% 94.68/94.49 cnf(10950,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x109501),x109501))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(10963,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x109631),f103(x109631)),x109632))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(10970,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x109701),f317(a102,x109701)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(10973,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x109731),x109731))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(10978,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x109781),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10993,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x109931),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(10996,plain,
% 94.68/94.49 (~P1(f317(f317(f225(f904(x109961,a893)),x109962),f178(f904(x109961,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4624])).
% 94.68/94.49 cnf(10999,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x109991),x109991))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11002,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x110021),x110021))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11017,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x110171),x110171))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(11026,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x110261),x110262),f178(f904(x110261,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11033,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x110331),x110331))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11036,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x110361,a893)),f317(f300(x110362,x110361,x110363),f317(f301(x110362,x110361,x110363),x110364))),x110364))),
% 94.68/94.49 inference(rename_variables,[],[4292])).
% 94.68/94.49 cnf(11045,plain,
% 94.68/94.49 (E(f317(f300(x110451,x110451,f5(x110451)),x110452),x110452)),
% 94.68/94.49 inference(rename_variables,[],[3483])).
% 94.68/94.49 cnf(11050,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x110501))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(11053,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x110531),x110531))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11056,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x110561),x110561))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(11065,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x110651),x110651))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(11076,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x110761),f317(f317(f75(a897),x110761),x110761)))),
% 94.68/94.49 inference(rename_variables,[],[3686])).
% 94.68/94.49 cnf(11082,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x110821),f317(a102,f317(f317(f74(a897),x110822),x110821))))),
% 94.68/94.49 inference(rename_variables,[],[3869])).
% 94.68/94.49 cnf(11089,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x110891),x110891))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11092,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x110921),x110921))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(11095,plain,
% 94.68/94.49 (~E(f317(a102,x110951),x110951)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11100,plain,
% 94.68/94.49 (P1(f317(f317(f319(x111001),x111002),f232(f904(x111001,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11107,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x111071),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(11122,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x111221))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(11129,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x111291),x111291))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11138,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x111381),x111382),f178(f904(x111381,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11146,plain,
% 94.68/94.49 (P1(f317(f317(f319(x111461),x111462),f232(f904(x111461,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11149,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x111491),f898(x111491))),f317(f317(f242(f898(x111491),f898(x111491)),x111492),f103(x111491))),f135(x111491,x111493)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11159,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x111591),x111592),f178(f904(x111591,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11162,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x111621),x111622),f178(f904(x111621,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11165,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x111651,a893)),x111652),f317(f317(f299(x111651),x111653),x111652)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(11168,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x111681),x111681))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11171,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x111711,a893)),x111712),f317(f317(f299(x111711),x111713),x111712)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(11174,plain,
% 94.68/94.49 (E(f317(f300(x111741,x111741,f5(x111741)),x111742),x111742)),
% 94.68/94.49 inference(rename_variables,[],[3483])).
% 94.68/94.49 cnf(11189,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x111891,a893)),x111892),f317(f317(f299(x111891),x111893),x111892)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(11200,plain,
% 94.68/94.49 (~E(f317(a102,x112001),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(11203,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x112031),f103(x112031)),x112032))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(11216,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x112161),f317(a102,x112161)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(11226,plain,
% 94.68/94.49 (~E(f317(f300(x112261,f904(x112261,a893),x112262),x112263),f317(f298(x112261),x112263))),
% 94.68/94.49 inference(rename_variables,[],[4614])).
% 94.68/94.49 cnf(11229,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x112291),x112292),f178(f904(x112291,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11232,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x112321),x112322),f178(f904(x112321,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11235,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x112351,x112351)),f317(f317(f242(x112351,x112351),x112352),x112353)),f143(x112351,f103(f904(x112351,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11238,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x112381,x112381)),f317(f317(f242(x112381,x112381),x112382),x112383)),f143(x112381,f103(f904(x112381,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11243,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x112431),x112432),f178(f904(x112431,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11246,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x112461,x112461)),f317(f317(f242(x112461,x112461),x112462),x112462)),f297(x112461,x112463)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(11249,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x112491,a893)),f317(f162(x112491),f166(x112491,x112492,x112493))),f317(f162(x112491),x112492)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(11252,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x112521,a893)),x112522),f232(f904(x112521,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(11268,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x112681,a893)),f178(f904(x112681,a893))),x112682))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(11279,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x112791),f898(x112791))),f317(f317(f242(f898(x112791),f898(x112791)),x112792),f103(x112791))),f137(x112791,x112793)))),
% 94.68/94.49 inference(rename_variables,[],[4634])).
% 94.68/94.49 cnf(11290,plain,
% 94.68/94.49 (~E(f317(a102,x112901),x112901)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11293,plain,
% 94.68/94.49 (~E(f317(a102,x112931),x112931)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11300,plain,
% 94.68/94.49 (~E(f317(a102,x113001),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(11311,plain,
% 94.68/94.49 (~E(f317(a102,x113111),x113111)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11314,plain,
% 94.68/94.49 (~E(f317(a102,x113141),x113141)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11319,plain,
% 94.68/94.49 (P24(x113191,x113191,f5(x113191),x113192)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(11324,plain,
% 94.68/94.49 (~E(f317(f300(x113241,f904(x113241,a893),x113242),x113243),f317(f298(x113241),x113243))),
% 94.68/94.49 inference(rename_variables,[],[4614])).
% 94.68/94.49 cnf(11331,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x113311,a893)),x113312),f232(f904(x113311,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(11347,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x113471),x113472),f178(f904(x113471,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11350,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x113501)),x113501))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11355,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x113551),x113552),f178(f904(x113551,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11366,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x113661)),x113661))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11369,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x113691),x113692),f178(f904(x113691,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11378,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x113781,x113781)),f317(f317(f242(x113781,x113781),x113782),x113782)),f297(x113781,x113783)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(11381,plain,
% 94.68/94.49 (P1(f317(f317(f319(x113811),x113812),f232(f904(x113811,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11384,plain,
% 94.68/94.49 (P1(f317(f317(f319(x113841),x113842),f232(f904(x113841,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11391,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x113911),f898(x113911))),f317(f317(f242(f898(x113911),f898(x113911)),x113912),f103(x113911))),f135(x113911,x113913)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11394,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x113941),f898(x113941))),f317(f317(f242(f898(x113941),f898(x113941)),x113942),f103(x113941))),f137(x113941,x113943)))),
% 94.68/94.49 inference(rename_variables,[],[4634])).
% 94.68/94.49 cnf(11397,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x113971),f898(x113971))),f317(f317(f242(f898(x113971),f898(x113971)),x113972),f103(x113971))),f147(x113971,x113973)))),
% 94.68/94.49 inference(rename_variables,[],[4635])).
% 94.68/94.49 cnf(11402,plain,
% 94.68/94.49 (~P1(f317(f317(f225(f904(x114021,a893)),x114022),f178(f904(x114021,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4624])).
% 94.68/94.49 cnf(11405,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x114051),x114052),f178(f904(x114051,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11410,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x114101,a893)),x114102),f232(f904(x114101,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(11417,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x114171),f103(x114171)),x114172))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(11422,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x114221),x114222),f178(f904(x114221,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11425,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x114251,x114251)),f317(f317(f242(x114251,x114251),x114252),x114253)),f143(x114251,f103(f904(x114251,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11430,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x114301),x114302),f178(f904(x114301,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11433,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x114331,a893)),f178(f904(x114331,a893))),x114332))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(11436,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x114361,x114361)),f317(f317(f242(x114361,x114361),x114362),x114362)),f297(x114361,x114363)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(11447,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x114471),f898(x114471))),f317(f317(f242(f898(x114471),f898(x114471)),x114472),f103(x114471))),f147(x114471,x114473)))),
% 94.68/94.49 inference(rename_variables,[],[4635])).
% 94.68/94.49 cnf(11454,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x114541),f898(x114541))),f317(f317(f242(f898(x114541),f898(x114541)),f103(x114541)),x114542)),f135(x114541,x114543)))),
% 94.68/94.49 inference(rename_variables,[],[4636])).
% 94.68/94.49 cnf(11462,plain,
% 94.68/94.49 (P1(f317(f317(f319(x114621),x114622),f232(f904(x114621,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11467,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x114671,a893)),f178(f904(x114671,a893))),x114672))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(11470,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x114701),x114702),f178(f904(x114701,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11473,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x114731,a893)),x114732),f232(f904(x114731,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(11478,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x114781,a893)),f178(f904(x114781,a893))),x114782))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(11491,plain,
% 94.68/94.49 (P1(f317(f232(f904(x114911,a893)),x114912))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(11499,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x114991),f898(x114991))),f317(f317(f242(f898(x114991),f898(x114991)),x114992),f103(x114991))),f135(x114991,x114993)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11502,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x115021),f898(x115021))),f317(f317(f242(f898(x115021),f898(x115021)),x115022),f103(x115021))),f137(x115021,x115023)))),
% 94.68/94.49 inference(rename_variables,[],[4634])).
% 94.68/94.49 cnf(11505,plain,
% 94.68/94.49 (~E(f317(f317(f141(x115051),x115052),x115053),x115053)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(11508,plain,
% 94.68/94.49 (~E(f317(a102,x115081),x115081)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11511,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115111),x115112),f178(f904(x115111,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11516,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115161),x115162),f178(f904(x115161,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11519,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115191),x115192),f178(f904(x115191,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11522,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(f898(x115221),f898(x115221))),f317(f317(f242(f898(x115221),f898(x115221)),x115222),x115222)),f148(x115221,f297(x115221,x115223))))),
% 94.68/94.49 inference(rename_variables,[],[4189])).
% 94.68/94.49 cnf(11525,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x115251),f898(x115251))),f317(f317(f242(f898(x115251),f898(x115251)),x115252),f103(x115251))),f135(x115251,x115253)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11535,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x115351,x115351)),f317(f317(f242(x115351,x115351),x115352),x115353)),f143(x115351,f103(f904(x115351,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11538,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115381),x115382),f178(f904(x115381,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11541,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115411),x115412),f178(f904(x115411,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11544,plain,
% 94.68/94.49 (P1(f317(f317(f319(x115441),x115442),f232(f904(x115441,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11547,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x115471),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(11552,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x115521,x115521)),f317(f317(f242(x115521,x115521),x115522),x115523)),f143(x115521,f103(f904(x115521,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11561,plain,
% 94.68/94.49 (~E(f317(f300(x115611,f904(x115611,a893),x115612),x115613),f317(f298(x115611),x115613))),
% 94.68/94.49 inference(rename_variables,[],[4614])).
% 94.68/94.49 cnf(11564,plain,
% 94.68/94.49 (~E(f317(f300(x115641,f904(x115641,a893),x115642),x115643),f317(f298(x115641),x115643))),
% 94.68/94.49 inference(rename_variables,[],[4614])).
% 94.68/94.49 cnf(11569,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x115691),f898(x115691))),f317(f317(f242(f898(x115691),f898(x115691)),x115692),f103(x115691))),f135(x115691,x115693)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11575,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x115751),f898(x115751))),f317(f317(f242(f898(x115751),f898(x115751)),x115752),f103(x115751))),f135(x115751,x115753)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(11578,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115781),x115782),f178(f904(x115781,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11583,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115831),x115832),f178(f904(x115831,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11586,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115861),x115862),f178(f904(x115861,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11589,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115891),x115892),f178(f904(x115891,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11592,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x115921),x115922),f178(f904(x115921,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11595,plain,
% 94.68/94.49 (P1(f317(f317(f319(x115951),f317(x115952,x115953)),f317(f300(x115954,x115951,x115952),f232(f904(x115954,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(11598,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(x115981,x115981)),f317(f317(f242(x115981,x115981),x115982),x115983)),f143(x115981,f103(f904(x115981,a897)))))),
% 94.68/94.49 inference(rename_variables,[],[4631])).
% 94.68/94.49 cnf(11606,plain,
% 94.68/94.49 (E(f104(x116061,f103(x116061)),f103(x116061))),
% 94.68/94.49 inference(rename_variables,[],[3274])).
% 94.68/94.49 cnf(11609,plain,
% 94.68/94.49 (~E(f317(a102,x116091),x116091)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11616,plain,
% 94.68/94.49 (~E(f317(a102,x116161),x116161)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11621,plain,
% 94.68/94.49 (E(f317(f274(x116211,x116211),f253(x116211,x116212)),x116212)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11624,plain,
% 94.68/94.49 (E(f317(f274(x116241,x116241),f253(x116241,x116242)),x116242)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11630,plain,
% 94.68/94.49 (~E(f317(a102,x116301),x116301)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11635,plain,
% 94.68/94.49 (~E(f317(f317(f74(a1),x116351),x116351),a87)),
% 94.68/94.49 inference(rename_variables,[],[4582])).
% 94.68/94.49 cnf(11642,plain,
% 94.68/94.49 (E(f317(f317(f23(a897),f2(a897)),x116421),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[3345])).
% 94.68/94.49 cnf(11645,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x116451,a893)),x116452),f232(f904(x116451,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(11652,plain,
% 94.68/94.49 (E(f317(f317(f74(a1),f317(f317(f75(a1),x116521),f317(f317(f30(a1),x116522),x116521))),f40(a1,x116522,x116521)),x116522)),
% 94.68/94.49 inference(rename_variables,[],[3969])).
% 94.68/94.49 cnf(11676,plain,
% 94.68/94.49 (~E(f317(a102,x116761),x116761)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11679,plain,
% 94.68/94.49 (~E(f317(a102,x116791),x116791)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11705,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x117051),f103(x117051)),x117052))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(11711,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),f2(a897)),f317(a102,x117111)))),
% 94.68/94.49 inference(rename_variables,[],[3506])).
% 94.68/94.49 cnf(11712,plain,
% 94.68/94.49 (~E(f317(a102,x117121),x117121)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11715,plain,
% 94.68/94.49 (P1(f317(f317(f319(x117151),x117152),f232(f904(x117151,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11727,plain,
% 94.68/94.49 (~E(f317(a102,x117271),x117271)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11730,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x117301),x117301))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(11737,plain,
% 94.68/94.49 (P1(f317(f60(x117371,x117372,x117373,x117374,f178(f904(x117371,a893))),x117374))),
% 94.68/94.49 inference(rename_variables,[],[4331])).
% 94.68/94.49 cnf(11738,plain,
% 94.68/94.49 (E(f317(f274(x117381,x117381),f253(x117381,x117382)),x117382)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11751,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x117511),x117512)),x117512))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(11754,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x117541)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(11777,plain,
% 94.68/94.49 (E(f317(f274(x117771,x117771),f253(x117771,x117772)),x117772)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11782,plain,
% 94.68/94.49 (E(f317(f274(x117821,x117821),f253(x117821,x117822)),x117822)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11785,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x117851)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(11790,plain,
% 94.68/94.49 (~E(f317(a102,x117901),x117901)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11799,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x117991),f103(x117991)),x117992))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(11822,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x118221)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(11825,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x118251),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(11826,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x118261),f317(a102,x118261)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(11829,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x118291)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(11832,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x118321),x118322),f178(f904(x118321,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11833,plain,
% 94.68/94.49 (P1(f317(f317(f319(f904(x118331,a893)),x118332),f317(f298(x118331),x118332)))),
% 94.68/94.49 inference(rename_variables,[],[3785])).
% 94.68/94.49 cnf(11848,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x118481)),x118481))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11849,plain,
% 94.68/94.49 (~E(f317(a102,x118491),x118491)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11859,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x118591),x118592)),x118591))),
% 94.68/94.49 inference(rename_variables,[],[4628])).
% 94.68/94.49 cnf(11862,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x118621)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(11865,plain,
% 94.68/94.49 (~E(f317(a102,x118651),x118651)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(11878,plain,
% 94.68/94.49 (P1(f317(f317(f319(x118781),x118782),f317(f317(f299(x118781),x118782),x118783)))),
% 94.68/94.49 inference(rename_variables,[],[3733])).
% 94.68/94.49 cnf(11879,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a1),f2(a1)),f317(f73(a1),f317(f90(a1),f317(a102,x118791)))))),
% 94.68/94.49 inference(rename_variables,[],[4629])).
% 94.68/94.49 cnf(11882,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),f317(f317(f23(a897),x118821),x118822)),f317(a102,x118821)))),
% 94.68/94.49 inference(rename_variables,[],[3871])).
% 94.68/94.49 cnf(11885,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f40(a897,x118851,x118852)),x118851))),
% 94.68/94.49 inference(rename_variables,[],[3876])).
% 94.68/94.49 cnf(11891,plain,
% 94.68/94.49 (E(f317(f274(x118911,x118911),f253(x118911,x118912)),x118912)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(11896,plain,
% 94.68/94.49 (E(f317(f317(f124(x118961),f159(x118961,x118962,x118963)),f159(x118961,x118964,x118963)),f317(f317(f124(x118961),f159(x118961,x118964,x118963)),f159(x118961,x118962,x118963)))),
% 94.68/94.49 inference(rename_variables,[],[3984])).
% 94.68/94.49 cnf(11901,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x119011)),x119011))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11910,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x119101),x119101))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(11913,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f40(a897,x119131,x119132)),x119131))),
% 94.68/94.49 inference(rename_variables,[],[3876])).
% 94.68/94.49 cnf(11914,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x119141))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(11931,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x119311),x119311))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(11934,plain,
% 94.68/94.49 (P1(f317(f317(f319(x119341),f317(x119342,x119343)),f317(f300(x119344,x119341,x119342),f232(f904(x119344,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(11935,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x119351)),x119351))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11938,plain,
% 94.68/94.49 (P1(f317(f317(f319(x119381),f317(x119382,x119383)),f317(f300(x119384,x119381,x119382),f232(f904(x119384,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(11939,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x119391),x119392)),x119392))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(11944,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x119441),x119442)),x119441))),
% 94.68/94.49 inference(rename_variables,[],[4628])).
% 94.68/94.49 cnf(11947,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x119471),f103(x119471)),x119472))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(11950,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x119501),x119501))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(11958,plain,
% 94.68/94.49 (~P34(x119581,x119582,f103(x119581))),
% 94.68/94.49 inference(rename_variables,[],[4591])).
% 94.68/94.49 cnf(11961,plain,
% 94.68/94.49 (P1(f317(f317(f319(x119611),x119612),f232(f904(x119611,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(11962,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x119621)),x119621))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(11975,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x119751),x119752),f178(f904(x119751,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(11978,plain,
% 94.68/94.49 (E(f317(f317(f16(x119781,x119782),x119783),x119784),x119783)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(11981,plain,
% 94.68/94.49 (E(f317(f317(f16(x119811,x119812),x119813),x119814),x119813)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(11993,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),f2(a897)),f317(a102,x119931)))),
% 94.68/94.49 inference(rename_variables,[],[3506])).
% 94.68/94.49 cnf(11996,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x119961),x119961))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12001,plain,
% 94.68/94.49 (P1(f317(f28(x120011),f317(f162(x120011),x120012)))),
% 94.68/94.49 inference(rename_variables,[],[3468])).
% 94.68/94.49 cnf(12004,plain,
% 94.68/94.49 (P1(f317(f28(x120041),f317(f162(x120041),x120042)))),
% 94.68/94.49 inference(rename_variables,[],[3468])).
% 94.68/94.49 cnf(12007,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x120071))),f317(f90(a1),x120072)))),
% 94.68/94.49 inference(rename_variables,[],[3900])).
% 94.68/94.49 cnf(12010,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x120101),x120102),f178(f904(x120101,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12031,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x120311),x120311))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12034,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x120341),f317(a102,x120341)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12037,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x120371),x120371))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12048,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x120481),x120481))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12051,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x120511),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12056,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x120561),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12065,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x120651))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(12066,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x120661)),x120661))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12069,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x120691),f103(x120691)),x120692))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(12072,plain,
% 94.68/94.49 (~P1(f317(f317(f162(x120721),f103(x120721)),x120722))),
% 94.68/94.49 inference(rename_variables,[],[4611])).
% 94.68/94.49 cnf(12080,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x120801),f317(a102,x120801)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12095,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x120951)),x120951))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12098,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x120981)),x120981))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12101,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x121011)),x121011))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12104,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x121041)),x121041))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12107,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x121071),x121071))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12110,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x121101),x121101))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12113,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x121131),x121131))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12116,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x121161),x121161))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12133,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x121331),x121331))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12136,plain,
% 94.68/94.49 (P24(a897,a897,a102,x121361)),
% 94.68/94.49 inference(rename_variables,[],[3629])).
% 94.68/94.49 cnf(12139,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x121391),x121391))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12150,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x121501),x121501))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12153,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(f903(f898(x121531),f898(x121531)),a893)),f148(x121531,x121532)),f297(f898(x121531),f147(x121531,x121532))))),
% 94.68/94.49 inference(rename_variables,[],[4117])).
% 94.68/94.49 cnf(12160,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x121601),f317(a102,x121601)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12163,plain,
% 94.68/94.49 (P1(f317(f317(f319(f904(x121631,a893)),x121632),f317(f298(x121631),x121632)))),
% 94.68/94.49 inference(rename_variables,[],[3785])).
% 94.68/94.49 cnf(12164,plain,
% 94.68/94.49 (~E(f317(a102,x121641),x121641)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12169,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x121691),x121691))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12174,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x121741),x121741))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12185,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x121851,a893)),x121852),f317(f317(f299(x121851),x121853),x121852)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(12188,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x121881),x121881))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12189,plain,
% 94.68/94.49 (~E(f317(a102,x121891),x121891)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12202,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122021),x122021))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12203,plain,
% 94.68/94.49 (~E(f317(a102,x122031),x122031)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12206,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x122061),x122061))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12209,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x122091),x122091))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12212,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x122121),x122121))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12215,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x122151),x122151))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12218,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x122181),x122181))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12221,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122211),x122211))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12224,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122241),x122241))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12225,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x122251),f317(a102,x122251)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12232,plain,
% 94.68/94.49 (~E(f317(a102,x122321),x122321)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12237,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122371),x122371))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12238,plain,
% 94.68/94.49 (~E(f317(a102,x122381),x122381)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12241,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x122411),x122411))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12258,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x122581),x122581))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(12263,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x122631))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(12279,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122791),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12282,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122821),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12285,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x122851),x122852),f178(f904(x122851,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12288,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x122881),x122882),f178(f904(x122881,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12291,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122911),x122911))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12294,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122941),x122941))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12297,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x122971),x122971))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12300,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x123001),x123001))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12303,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x123031),f317(a102,x123031)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12310,plain,
% 94.68/94.49 (P1(f317(f317(f319(f904(x123101,a893)),x123102),f317(f298(x123101),x123102)))),
% 94.68/94.49 inference(rename_variables,[],[3785])).
% 94.68/94.49 cnf(12315,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x123151,a893)),x123152),f317(f317(f299(x123151),x123153),x123152)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(12322,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x123221),x123222),f178(f904(x123221,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12331,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x123311,a893)),x123312),f232(f904(x123311,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12332,plain,
% 94.68/94.49 (~E(f317(a102,x123321),x123321)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12338,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x123381),f317(a102,x123381)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12347,plain,
% 94.68/94.49 (E(f317(f274(x123471,x123471),f253(x123471,x123472)),x123472)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12358,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x123581)),x123581))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(12359,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x123591),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12364,plain,
% 94.68/94.49 (P1(f317(f28(x123641),f178(f904(x123641,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(12365,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x123651),x123652),f178(f904(x123651,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12374,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x123741,a893)),f317(f162(x123741),f166(x123741,x123742,x123743))),f317(f162(x123741),x123742)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(12377,plain,
% 94.68/94.49 (P24(x123771,x123771,f5(x123771),x123772)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12382,plain,
% 94.68/94.49 (P1(f317(f317(f319(f904(x123821,a893)),x123822),f317(f298(x123821),x123822)))),
% 94.68/94.49 inference(rename_variables,[],[3785])).
% 94.68/94.49 cnf(12389,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x123891),x123891))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12392,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x123921),x123922),f178(f904(x123921,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12395,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x123951,a893)),x123952),f317(f317(f299(x123951),x123953),x123952)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(12396,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x123961,a893)),x123962),f232(f904(x123961,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12403,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x124031),x124031))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12406,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x124061),x124061))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12409,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x124091),x124091))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12412,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x124121),x124121))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12415,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x124151),f317(a102,x124151)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12418,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x124181),f317(a102,x124181)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12421,plain,
% 94.68/94.49 (P1(f317(f317(f277(a897),x124211),x124211))),
% 94.68/94.49 inference(rename_variables,[],[3431])).
% 94.68/94.49 cnf(12424,plain,
% 94.68/94.49 (P1(f317(f317(f277(a897),x124241),x124241))),
% 94.68/94.49 inference(rename_variables,[],[3431])).
% 94.68/94.49 cnf(12427,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x124271,a893)),x124272),x124272))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12434,plain,
% 94.68/94.49 (P1(f317(f317(f319(f904(x124341,a893)),x124342),f317(f298(x124341),x124342)))),
% 94.68/94.49 inference(rename_variables,[],[3785])).
% 94.68/94.49 cnf(12443,plain,
% 94.68/94.49 (~E(f317(a102,x124431),x124431)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12444,plain,
% 94.68/94.49 (E(f317(f300(x124441,x124441,f5(x124441)),x124442),x124442)),
% 94.68/94.49 inference(rename_variables,[],[3483])).
% 94.68/94.49 cnf(12447,plain,
% 94.68/94.49 (P31(x124471,x124472,f103(x124471),f103(x124471))),
% 94.68/94.49 inference(rename_variables,[],[3670])).
% 94.68/94.49 cnf(12450,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x124501,a893)),f317(f162(x124501),f166(x124501,x124502,x124503))),f317(f162(x124501),x124502)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(12451,plain,
% 94.68/94.49 (P1(f317(f28(x124511),f317(f162(x124511),x124512)))),
% 94.68/94.49 inference(rename_variables,[],[3468])).
% 94.68/94.49 cnf(12462,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x124621),x124621))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12465,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x124651),x124651))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12470,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x124701))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(12479,plain,
% 94.68/94.49 (P13(a897,f317(f158(a897),f317(f317(f144(f898(x124791),a897),f179(f898(x124791))),f169(x124791,x124792))))),
% 94.68/94.49 inference(rename_variables,[],[3980])).
% 94.68/94.49 cnf(12482,plain,
% 94.68/94.49 (P24(x124821,x124821,f5(x124821),x124822)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12485,plain,
% 94.68/94.49 (P24(x124851,x124851,f5(x124851),x124852)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12488,plain,
% 94.68/94.49 (P1(f317(f317(f319(f898(x124881)),f103(x124881)),f151(x124881,x124882)))),
% 94.68/94.49 inference(rename_variables,[],[3621])).
% 94.68/94.49 cnf(12491,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x124911,f904(x124912,a893))),x124913),x124914))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(12496,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x124961),x124961))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12497,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x124971))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(12500,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x125001,f904(x125002,a893))),x125003),x125004))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(12503,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(f903(f898(x125031),f898(x125031)),a893)),f148(x125031,x125032)),f297(f898(x125031),f147(x125031,x125032))))),
% 94.68/94.49 inference(rename_variables,[],[4117])).
% 94.68/94.49 cnf(12509,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125091,a893)),f317(f300(x125092,x125091,x125093),f317(f301(x125092,x125091,x125093),x125094))),x125094))),
% 94.68/94.49 inference(rename_variables,[],[4292])).
% 94.68/94.49 cnf(12512,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125121,a893)),f317(f162(x125121),f166(x125121,x125122,x125123))),f317(f162(x125121),x125122)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(12513,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125131,a893)),f317(f162(x125131),f317(f126(x125131,x125132),x125133))),f317(f162(x125131),x125133)))),
% 94.68/94.49 inference(rename_variables,[],[4065])).
% 94.68/94.49 cnf(12516,plain,
% 94.68/94.49 (~P1(f317(f317(f225(f904(x125161,a893)),x125162),f178(f904(x125161,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4624])).
% 94.68/94.49 cnf(12524,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125241,a893)),f317(f300(x125242,x125241,x125243),f317(f301(x125242,x125241,x125243),x125244))),x125244))),
% 94.68/94.49 inference(rename_variables,[],[4292])).
% 94.68/94.49 cnf(12529,plain,
% 94.68/94.49 (P1(f317(f317(f319(f898(x125291)),f103(x125291)),f151(x125291,x125292)))),
% 94.68/94.49 inference(rename_variables,[],[3621])).
% 94.68/94.49 cnf(12532,plain,
% 94.68/94.49 (~P1(f317(f317(f319(f903(f898(x125321),f898(x125321))),f317(f317(f242(f898(x125321),f898(x125321)),x125322),f103(x125321))),f135(x125321,x125323)))),
% 94.68/94.49 inference(rename_variables,[],[4633])).
% 94.68/94.49 cnf(12535,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x125351),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12542,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x125421),x125422),f178(f904(x125421,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12545,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x125451,f904(x125452,a893))),x125453),x125454))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(12548,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125481,a893)),x125482),x125482))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12553,plain,
% 94.68/94.49 (E(f317(f274(x125531,x125531),f253(x125531,x125532)),x125532)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12556,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x125561,a893)),f317(f162(x125561),f166(x125561,x125562,x125563))),f317(f162(x125561),x125562)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(12557,plain,
% 94.68/94.49 (P1(f317(f28(x125571),f317(f162(x125571),x125572)))),
% 94.68/94.49 inference(rename_variables,[],[3468])).
% 94.68/94.49 cnf(12560,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x125601),x125601))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12563,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x125631),x125631))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12566,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x125661),x125661))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12577,plain,
% 94.68/94.49 (P24(x125771,x125771,f5(x125771),x125772)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12585,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x125851),x125852),f178(f904(x125851,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12588,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x125881,x125881)),f317(f317(f242(x125881,x125881),x125882),x125882)),f297(x125881,x125883)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(12591,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x125911),x125912),f178(f904(x125911,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12594,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x125941,x125941)),f317(f317(f242(x125941,x125941),x125942),x125942)),f297(x125941,x125943)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(12604,plain,
% 94.68/94.49 (~E(f317(f317(f141(x126041),x126042),x126043),x126043)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(12611,plain,
% 94.68/94.49 (P1(f317(f317(f319(x126111),x126112),f232(f904(x126111,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(12612,plain,
% 94.68/94.49 (~E(f317(a102,x126121),x126121)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12615,plain,
% 94.68/94.49 (P1(f317(f317(f319(f898(x126151)),f103(x126151)),f151(x126151,x126152)))),
% 94.68/94.49 inference(rename_variables,[],[3621])).
% 94.68/94.49 cnf(12616,plain,
% 94.68/94.49 (~E(f317(f317(f141(x126161),x126162),x126163),f103(x126161))),
% 94.68/94.49 inference(rename_variables,[],[4587])).
% 94.68/94.49 cnf(12619,plain,
% 94.68/94.49 (P24(x126191,x126191,f5(x126191),x126192)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12622,plain,
% 94.68/94.49 (P1(f317(f317(f319(x126221),f317(x126222,x126223)),f317(f300(x126224,x126221,x126222),f232(f904(x126224,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(12623,plain,
% 94.68/94.49 (P24(x126231,x126231,f5(x126231),x126232)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12626,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126261,a893)),f178(f904(x126261,a893))),x126262))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(12627,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126271,a893)),x126272),x126272))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12630,plain,
% 94.68/94.49 (P1(f317(f317(f319(x126301),f317(x126302,x126303)),f317(f300(x126304,x126301,x126302),f232(f904(x126304,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(12631,plain,
% 94.68/94.49 (P24(x126311,x126311,f5(x126311),x126312)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12634,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(f898(x126341),f898(x126341))),f317(f317(f242(f898(x126341),f898(x126341)),f103(x126341)),f103(x126341))),f148(x126341,x126342)))),
% 94.68/94.49 inference(rename_variables,[],[4196])).
% 94.68/94.49 cnf(12638,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x126381),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12644,plain,
% 94.68/94.49 (E(f317(f317(f124(x126441),x126442),f103(x126441)),x126442)),
% 94.68/94.49 inference(rename_variables,[],[3360])).
% 94.68/94.49 cnf(12645,plain,
% 94.68/94.49 (~E(f317(f317(f141(x126451),x126452),x126453),x126453)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(12648,plain,
% 94.68/94.49 (E(f317(f317(f124(x126481),x126482),f103(x126481)),x126482)),
% 94.68/94.49 inference(rename_variables,[],[3360])).
% 94.68/94.49 cnf(12649,plain,
% 94.68/94.49 (~E(f317(f317(f141(x126491),x126492),x126493),x126493)),
% 94.68/94.49 inference(rename_variables,[],[4584])).
% 94.68/94.49 cnf(12652,plain,
% 94.68/94.49 (E(f317(f317(f124(x126521),x126522),f103(x126521)),x126522)),
% 94.68/94.49 inference(rename_variables,[],[3360])).
% 94.68/94.49 cnf(12659,plain,
% 94.68/94.49 (P51(x126591,f253(x126591,x126592))),
% 94.68/94.49 inference(rename_variables,[],[3302])).
% 94.68/94.49 cnf(12662,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126621,a893)),f317(f162(x126621),f317(f126(x126621,x126622),x126623))),f317(f162(x126621),x126623)))),
% 94.68/94.49 inference(rename_variables,[],[4065])).
% 94.68/94.49 cnf(12663,plain,
% 94.68/94.49 (E(f317(f300(x126631,x126631,f5(x126631)),x126632),x126632)),
% 94.68/94.49 inference(rename_variables,[],[3483])).
% 94.68/94.49 cnf(12668,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126681,a893)),x126682),f232(f904(x126681,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12672,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x126721),x126721))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12673,plain,
% 94.68/94.49 (~E(f317(a102,x126731),x126731)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12676,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126761,a893)),f178(f904(x126761,a893))),x126762))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(12679,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x126791),x126791))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12682,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126821,a893)),x126822),x126822))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12687,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126871,a893)),x126872),f317(f317(f299(x126871),x126873),x126872)))),
% 94.68/94.49 inference(rename_variables,[],[3866])).
% 94.68/94.49 cnf(12690,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x126901,a893)),x126902),x126902))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12691,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x126911),x126912),f178(f904(x126911,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12694,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x126941),x126942),f178(f904(x126941,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12703,plain,
% 94.68/94.49 (P24(x127031,x127031,f5(x127031),x127032)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12706,plain,
% 94.68/94.49 (E(f317(f179(f898(x127061)),f159(x127061,x127062,x127063)),x127062)),
% 94.68/94.49 inference(rename_variables,[],[3493])).
% 94.68/94.49 cnf(12709,plain,
% 94.68/94.49 (P25(x127091,x127091,f25(x127091),x127092,x127092)),
% 94.68/94.49 inference(rename_variables,[],[4080])).
% 94.68/94.49 cnf(12712,plain,
% 94.68/94.49 (P24(x127121,x127121,f5(x127121),x127122)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12715,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x127151),x127151))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12716,plain,
% 94.68/94.49 (P1(f317(f232(f904(x127161,a893)),x127162))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(12719,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x127191),x127192),f178(f904(x127191,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12722,plain,
% 94.68/94.49 (P1(f317(f317(f319(x127221),f317(x127222,x127223)),f317(f300(x127224,x127221,x127222),f232(f904(x127224,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(12723,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x127231,x127231)),f317(f317(f242(x127231,x127231),x127232),x127232)),f297(x127231,x127233)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(12726,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x127261,x127261)),f317(f317(f242(x127261,x127261),x127262),x127262)),f297(x127261,x127263)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(12729,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x127291),x127291))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(12730,plain,
% 94.68/94.49 (P1(f317(f232(f904(x127301,a893)),x127302))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(12733,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x127331,a893)),x127332),f232(f904(x127331,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12734,plain,
% 94.68/94.49 (P25(x127341,x127341,f25(x127341),x127342,x127342)),
% 94.68/94.49 inference(rename_variables,[],[4080])).
% 94.68/94.49 cnf(12737,plain,
% 94.68/94.49 (P1(f317(f28(x127371),f317(f162(x127371),x127372)))),
% 94.68/94.49 inference(rename_variables,[],[3468])).
% 94.68/94.49 cnf(12747,plain,
% 94.68/94.49 (~P1(f317(f317(f178(f904(x127471,f904(x127472,a893))),x127473),x127474))),
% 94.68/94.49 inference(rename_variables,[],[4630])).
% 94.68/94.49 cnf(12753,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x127531,a893)),x127532),f232(f904(x127531,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12756,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(x127561,x127561)),f317(f317(f242(x127561,x127561),x127562),x127562)),f297(x127561,x127563)))),
% 94.68/94.49 inference(rename_variables,[],[4055])).
% 94.68/94.49 cnf(12759,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),f317(f317(f74(a897),x127591),x127592)),x127592))),
% 94.68/94.49 inference(rename_variables,[],[4627])).
% 94.68/94.49 cnf(12760,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x127601),f317(a102,x127601)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(12763,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x127631,a893)),x127632),f232(f904(x127631,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(12766,plain,
% 94.68/94.49 (E(f317(f274(x127661,x127661),f253(x127661,x127662)),x127662)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12777,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x127771),x127772),f178(f904(x127771,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12778,plain,
% 94.68/94.49 (P1(f317(f317(f319(f903(f898(x127781),f898(x127781))),f317(f317(f242(f898(x127781),f898(x127781)),f103(x127781)),f103(x127781))),f148(x127781,x127782)))),
% 94.68/94.49 inference(rename_variables,[],[4196])).
% 94.68/94.49 cnf(12783,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x127831),x127832),f178(f904(x127831,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12788,plain,
% 94.68/94.49 (P30(x127881,x127882,f103(x127881))),
% 94.68/94.49 inference(rename_variables,[],[3365])).
% 94.68/94.49 cnf(12791,plain,
% 94.68/94.49 (E(f317(f179(f898(x127911)),f159(x127911,x127912,x127913)),x127912)),
% 94.68/94.49 inference(rename_variables,[],[3493])).
% 94.68/94.49 cnf(12794,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x127941),x127942),f178(f904(x127941,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12799,plain,
% 94.68/94.49 (P1(f317(f317(f319(x127991),x127992),f232(f904(x127991,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(12803,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x128031),x128031))),
% 94.68/94.49 inference(rename_variables,[],[4604])).
% 94.68/94.49 cnf(12806,plain,
% 94.68/94.49 (P1(f317(f317(f319(x128061),x128062),f232(f904(x128061,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(12810,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x128101,a893)),x128102),x128102))),
% 94.68/94.49 inference(rename_variables,[],[3717])).
% 94.68/94.49 cnf(12813,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x128131),x128132),f178(f904(x128131,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(12816,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),f2(a1)),f317(f317(f234(a1),f317(f70(a1),x128161)),x128162)))),
% 94.68/94.49 inference(rename_variables,[],[3899])).
% 94.68/94.49 cnf(12819,plain,
% 94.68/94.49 (~E(f317(a102,x128191),x128191)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(12821,plain,
% 94.68/94.49 (E(f317(f274(x128211,x128211),f253(x128211,x128212)),x128212)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12823,plain,
% 94.68/94.49 (E(f317(f274(x128231,x128231),f253(x128231,x128232)),x128232)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12830,plain,
% 94.68/94.49 (E(f317(f274(x128301,x128301),f253(x128301,x128302)),x128302)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12835,plain,
% 94.68/94.49 (E(f317(f274(x128351,x128351),f253(x128351,x128352)),x128352)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12837,plain,
% 94.68/94.49 (E(f317(f274(x128371,x128371),f253(x128371,x128372)),x128372)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12839,plain,
% 94.68/94.49 (P24(x128391,x128391,f5(x128391),x128392)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12841,plain,
% 94.68/94.49 (P24(x128411,x128411,f5(x128411),x128412)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(12848,plain,
% 94.68/94.49 (E(f317(f274(x128481,x128481),f253(x128481,x128482)),x128482)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12852,plain,
% 94.68/94.49 (P37(x128521,f253(x128521,x128522))),
% 94.68/94.49 inference(rename_variables,[],[3299])).
% 94.68/94.49 cnf(12856,plain,
% 94.68/94.49 (E(f317(f274(x128561,x128561),f253(x128561,x128562)),x128562)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12862,plain,
% 94.68/94.49 (P36(x128621,f143(x128621,x128622))),
% 94.68/94.49 inference(rename_variables,[],[3298])).
% 94.68/94.49 cnf(12866,plain,
% 94.68/94.49 (P25(x128661,x128661,f25(x128661),x128662,x128662)),
% 94.68/94.49 inference(rename_variables,[],[4080])).
% 94.68/94.49 cnf(12868,plain,
% 94.68/94.49 (P25(x128681,x128681,f25(x128681),x128682,x128682)),
% 94.68/94.49 inference(rename_variables,[],[4080])).
% 94.68/94.49 cnf(12870,plain,
% 94.68/94.49 (P25(x128701,x128701,f25(x128701),x128702,x128702)),
% 94.68/94.49 inference(rename_variables,[],[4080])).
% 94.68/94.49 cnf(12875,plain,
% 94.68/94.49 (E(f317(f274(x128751,x128751),f253(x128751,x128752)),x128752)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12881,plain,
% 94.68/94.49 (P52(x128811,x128812,f253(x128811,x128812))),
% 94.68/94.49 inference(rename_variables,[],[3398])).
% 94.68/94.49 cnf(12883,plain,
% 94.68/94.49 (P52(x128831,x128832,f253(x128831,x128832))),
% 94.68/94.49 inference(rename_variables,[],[3398])).
% 94.68/94.49 cnf(12885,plain,
% 94.68/94.49 (P52(x128851,x128852,f253(x128851,x128852))),
% 94.68/94.49 inference(rename_variables,[],[3398])).
% 94.68/94.49 cnf(12887,plain,
% 94.68/94.49 (P14(x128871,f904(x128871,a893),f299(x128871))),
% 94.68/94.49 inference(rename_variables,[],[3402])).
% 94.68/94.49 cnf(12891,plain,
% 94.68/94.49 (P54(x128911,x128911,f253(x128911,x128912))),
% 94.68/94.49 inference(rename_variables,[],[3399])).
% 94.68/94.49 cnf(12901,plain,
% 94.68/94.49 (P55(x129011,f178(f904(x129011,a893)),x129012)),
% 94.68/94.49 inference(rename_variables,[],[3448])).
% 94.68/94.49 cnf(12907,plain,
% 94.68/94.49 (E(f178(f904(f903(x129071,x129071),a893)),f253(x129071,f178(f904(x129071,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3497])).
% 94.68/94.49 cnf(12912,plain,
% 94.68/94.49 (P31(x129121,x129122,f103(x129121),f103(x129121))),
% 94.68/94.49 inference(rename_variables,[],[3670])).
% 94.68/94.49 cnf(12914,plain,
% 94.68/94.49 (P31(x129141,x129142,f103(x129141),f103(x129141))),
% 94.68/94.49 inference(rename_variables,[],[3670])).
% 94.68/94.49 cnf(12920,plain,
% 94.68/94.49 (E(f317(f274(x129201,x129201),f253(x129201,x129202)),x129202)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12922,plain,
% 94.68/94.49 (P51(x129221,f253(x129221,x129222))),
% 94.68/94.49 inference(rename_variables,[],[3302])).
% 94.68/94.49 cnf(12936,plain,
% 94.68/94.49 (P41(x129361,x129362,x129363,x129364,f178(f904(x129361,a893)),x129364)),
% 94.68/94.49 inference(rename_variables,[],[4353])).
% 94.68/94.49 cnf(12948,plain,
% 94.68/94.49 (E(f317(f274(x129481,x129481),f253(x129481,x129482)),x129482)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(12952,plain,
% 94.68/94.49 (E(f178(f904(f903(x129521,x129521),a893)),f253(x129521,f178(f904(x129521,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3497])).
% 94.68/94.49 cnf(12965,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x129651),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12974,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x129741)),f317(f73(a1),f317(f90(a1),x129742))))),
% 94.68/94.49 inference(rename_variables,[],[4625])).
% 94.68/94.49 cnf(12984,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x129841),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12987,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x129871),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(12990,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x129901,x129902)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(12993,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x129931,x129932)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(12996,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x129961,x129962)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(12999,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x129991,x129992)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13006,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),f317(f73(a1),f317(f90(a1),x130061))),f317(f90(a1),x130062)))),
% 94.68/94.49 inference(rename_variables,[],[3900])).
% 94.68/94.49 cnf(13011,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x130111),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13012,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x130121),x130121))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13019,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x130191),f317(a102,x130191)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13024,plain,
% 94.68/94.49 (~E(f317(a102,x130241),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(13029,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x130291),x130291))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13032,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x130321,x130322)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13035,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x130351,x130352)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13038,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x130381),x130381))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13055,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f40(a897,x130551,x130552)),x130551))),
% 94.68/94.49 inference(rename_variables,[],[3876])).
% 94.68/94.49 cnf(13060,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x130601),f317(a102,x130601)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13063,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x130631),f317(a102,x130631)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13064,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x130641),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13073,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x130731)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(13074,plain,
% 94.68/94.49 (P1(f317(f232(f904(x130741,a893)),x130742))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(13077,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a1),f317(f90(a1),x130771)),f2(a1)))),
% 94.68/94.49 inference(rename_variables,[],[4620])).
% 94.68/94.49 cnf(13078,plain,
% 94.68/94.49 (P1(f317(f232(f904(x130781,a893)),x130782))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(13081,plain,
% 94.68/94.49 (P1(f317(f232(f904(x130811,a893)),x130812))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(13084,plain,
% 94.68/94.49 (P1(f317(f232(f904(x130841,a893)),x130842))),
% 94.68/94.49 inference(rename_variables,[],[3487])).
% 94.68/94.49 cnf(13092,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x130921),x130922),f178(f904(x130921,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13093,plain,
% 94.68/94.49 (P1(f317(f28(x130931),f178(f904(x130931,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13096,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x130961),x130961))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13105,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x131051))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(13108,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x131081),x131082),f178(f904(x131081,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13111,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x131111),x131112),f178(f904(x131111,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13116,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131161),x131161))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13124,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x131241),f317(a102,x131241)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13127,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131271),x131271))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13132,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131321),x131321))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13135,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131351),x131351))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13138,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131381),x131381))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13141,plain,
% 94.68/94.49 (E(f317(f317(f23(f904(x131411,a893)),f178(f904(x131411,a893))),x131412),f178(f904(x131411,a893)))),
% 94.68/94.49 inference(rename_variables,[],[3688])).
% 94.68/94.49 cnf(13142,plain,
% 94.68/94.49 (P1(f317(f28(x131421),f178(f904(x131421,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13145,plain,
% 94.68/94.49 (E(f317(f317(f23(f904(x131451,a893)),f178(f904(x131451,a893))),x131452),f178(f904(x131451,a893)))),
% 94.68/94.49 inference(rename_variables,[],[3688])).
% 94.68/94.49 cnf(13146,plain,
% 94.68/94.49 (P1(f317(f28(x131461),f178(f904(x131461,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13149,plain,
% 94.68/94.49 (E(f317(f317(f23(f904(x131491,a893)),f178(f904(x131491,a893))),x131492),f178(f904(x131491,a893)))),
% 94.68/94.49 inference(rename_variables,[],[3688])).
% 94.68/94.49 cnf(13150,plain,
% 94.68/94.49 (P1(f317(f28(x131501),f178(f904(x131501,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13153,plain,
% 94.68/94.49 (E(f317(f317(f23(f904(x131531,a893)),f178(f904(x131531,a893))),x131532),f178(f904(x131531,a893)))),
% 94.68/94.49 inference(rename_variables,[],[3688])).
% 94.68/94.49 cnf(13154,plain,
% 94.68/94.49 (P1(f317(f28(x131541),f178(f904(x131541,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13158,plain,
% 94.68/94.49 (E(f317(f274(x131581,x131581),f253(x131581,x131582)),x131582)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(13163,plain,
% 94.68/94.49 (E(f317(f317(f23(f904(x131631,a893)),f178(f904(x131631,a893))),x131632),f178(f904(x131631,a893)))),
% 94.68/94.49 inference(rename_variables,[],[3688])).
% 94.68/94.49 cnf(13164,plain,
% 94.68/94.49 (P1(f317(f28(x131641),f178(f904(x131641,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13168,plain,
% 94.68/94.49 (P1(f317(f28(x131681),f178(f904(x131681,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3502])).
% 94.68/94.49 cnf(13171,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131711),x131711))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13175,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x131751),x131751))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13182,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x131821),x131821))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13195,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x131951),x131951))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13208,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x132081),x132082),f178(f904(x132081,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13219,plain,
% 94.68/94.49 (P1(f317(f317(f319(x132191),x132192),f232(f904(x132191,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3577])).
% 94.68/94.49 cnf(13220,plain,
% 94.68/94.49 (E(f317(f182(x132201,x132202),x132203),f111(x132201,x132202))),
% 94.68/94.49 inference(rename_variables,[],[3343])).
% 94.68/94.49 cnf(13223,plain,
% 94.68/94.49 (P1(f317(f317(f319(x132231),f317(x132232,x132233)),f317(f300(x132234,x132231,x132232),f232(f904(x132234,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(13227,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x132271,a893)),x132272),f232(f904(x132271,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(13235,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x132351),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13236,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x132361),x132361))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13240,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x132401),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13241,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x132411),x132411))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13246,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x132461),x132461))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13253,plain,
% 94.68/94.49 (E(f317(f317(f16(x132531,x132532),x132533),x132534),x132533)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13258,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x132581,a893)),f317(f162(x132581),f166(x132581,x132582,x132583))),f317(f162(x132581),x132582)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(13265,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x132651),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13266,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x132661),x132661))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13270,plain,
% 94.68/94.49 (~P1(f317(f317(f225(a897),x132701),f2(a897)))),
% 94.68/94.49 inference(rename_variables,[],[4608])).
% 94.68/94.49 cnf(13271,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),x132711),x132711))),
% 94.68/94.49 inference(rename_variables,[],[3430])).
% 94.68/94.49 cnf(13276,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x132761),x132761))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13279,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),x132791),x132791))),
% 94.68/94.49 inference(rename_variables,[],[3429])).
% 94.68/94.49 cnf(13282,plain,
% 94.68/94.49 (~P1(f317(f317(f224(a897),f317(a102,x132821)),x132821))),
% 94.68/94.49 inference(rename_variables,[],[4613])).
% 94.68/94.49 cnf(13288,plain,
% 94.68/94.49 (P1(f317(f317(f319(x132881),f317(x132882,x132883)),f317(f300(x132884,x132881,x132882),f232(f904(x132884,a893)))))),
% 94.68/94.49 inference(rename_variables,[],[4020])).
% 94.68/94.49 cnf(13289,plain,
% 94.68/94.49 (P24(x132891,x132891,f5(x132891),x132892)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13294,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x132941,a893)),x132942),f232(f904(x132941,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(13295,plain,
% 94.68/94.49 (P24(x132951,x132951,f5(x132951),x132952)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13299,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x132991,a893)),x132992),f232(f904(x132991,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(13300,plain,
% 94.68/94.49 (P24(x133001,x133001,f5(x133001),x133002)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13304,plain,
% 94.68/94.49 (P24(x133041,x133041,f5(x133041),x133042)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13307,plain,
% 94.68/94.49 (~P1(f317(f317(f225(f904(x133071,a893)),x133072),f178(f904(x133071,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4624])).
% 94.68/94.49 cnf(13310,plain,
% 94.68/94.49 (P24(x133101,x133101,f5(x133101),x133102)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13313,plain,
% 94.68/94.49 (P24(x133131,x133131,f5(x133131),x133132)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13319,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x133191,a893)),x133192),f232(f904(x133191,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(13324,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x133241,a893)),f178(f904(x133241,a893))),x133242))),
% 94.68/94.49 inference(rename_variables,[],[3868])).
% 94.68/94.49 cnf(13328,plain,
% 94.68/94.49 (E(f317(f274(x133281,x133281),f253(x133281,x133282)),x133282)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(13332,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x133321),x133322),f178(f904(x133321,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13337,plain,
% 94.68/94.49 (P24(x133371,x133371,f5(x133371),x133372)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13340,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x133401,a893)),x133402),f232(f904(x133401,a893))))),
% 94.68/94.49 inference(rename_variables,[],[3802])).
% 94.68/94.49 cnf(13348,plain,
% 94.68/94.49 (E(f317(f317(f16(x133481,x133482),x133483),x133484),x133483)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13351,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x133511),x133512),f178(f904(x133511,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13354,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x133541),x133542),f178(f904(x133541,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13359,plain,
% 94.68/94.49 (~E(f317(a102,x133591),x133591)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(13365,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x133651),f317(a102,x133651)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13366,plain,
% 94.68/94.49 (~E(f317(a102,x133661),x133661)),
% 94.68/94.49 inference(rename_variables,[],[4571])).
% 94.68/94.49 cnf(13369,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x133691),f317(a102,f317(f317(f74(a897),x133692),x133691))))),
% 94.68/94.49 inference(rename_variables,[],[3869])).
% 94.68/94.49 cnf(13370,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),x133701),f317(a102,x133701)))),
% 94.68/94.49 inference(rename_variables,[],[3494])).
% 94.68/94.49 cnf(13379,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x133791)))),
% 94.68/94.49 inference(rename_variables,[],[3526])).
% 94.68/94.49 cnf(13382,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x133821))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(13386,plain,
% 94.68/94.49 (~E(f317(a102,x133861),f2(a897))),
% 94.68/94.49 inference(rename_variables,[],[4577])).
% 94.68/94.49 cnf(13389,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x133891,a893)),f317(f162(x133891),f166(x133891,x133892,x133893))),f317(f162(x133891),x133892)))),
% 94.68/94.49 inference(rename_variables,[],[4112])).
% 94.68/94.49 cnf(13394,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x133941),x133942),f178(f904(x133941,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13397,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x133971,x133972)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13398,plain,
% 94.68/94.49 (E(f317(f317(f228(a897),f317(a102,x133981)),f317(a102,x133982)),f317(a102,f317(f317(f228(a897),x133981),x133982)))),
% 94.68/94.49 inference(rename_variables,[],[3595])).
% 94.68/94.49 cnf(13401,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x134011,x134012)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13402,plain,
% 94.68/94.49 (E(f317(f317(f223(a897),f317(a102,x134021)),f317(a102,x134022)),f317(a102,f317(f317(f223(a897),x134021),x134022)))),
% 94.68/94.49 inference(rename_variables,[],[3596])).
% 94.68/94.49 cnf(13405,plain,
% 94.68/94.49 (P1(f317(f28(a897),f295(a897,x134051,x134052)))),
% 94.68/94.49 inference(rename_variables,[],[3631])).
% 94.68/94.49 cnf(13414,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x134141),x134142),f178(f904(x134141,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13415,plain,
% 94.68/94.49 (E(f317(f317(f16(x134151,x134152),x134153),x134154),x134153)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13418,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x134181,a893)),f317(f162(x134181),f317(f126(x134181,x134182),x134183))),f317(f162(x134181),x134183)))),
% 94.68/94.49 inference(rename_variables,[],[4065])).
% 94.68/94.49 cnf(13419,plain,
% 94.68/94.49 (E(f317(f317(f16(x134191,x134192),x134193),x134194),x134193)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13422,plain,
% 94.68/94.49 (P1(f317(f317(f224(f904(x134221,a893)),f317(f162(x134221),f317(f317(f165(x134221),x134222),x134223))),f317(f162(x134221),x134223)))),
% 94.68/94.49 inference(rename_variables,[],[4107])).
% 94.68/94.49 cnf(13423,plain,
% 94.68/94.49 (E(f317(f317(f16(x134231,x134232),x134233),x134234),x134233)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13427,plain,
% 94.68/94.49 (E(f317(f317(f16(x134271,x134272),x134273),x134274),x134273)),
% 94.68/94.49 inference(rename_variables,[],[3420])).
% 94.68/94.49 cnf(13440,plain,
% 94.68/94.49 (P1(f317(f317(f224(a1),f2(a1)),f317(f90(a1),x134401)))),
% 94.68/94.49 inference(rename_variables,[],[3526])).
% 94.68/94.49 cnf(13445,plain,
% 94.68/94.49 (P24(x134451,x134451,f5(x134451),x134452)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13448,plain,
% 94.68/94.49 (~P1(f317(f317(f319(x134481),x134482),f178(f904(x134481,a893))))),
% 94.68/94.49 inference(rename_variables,[],[4616])).
% 94.68/94.49 cnf(13449,plain,
% 94.68/94.49 (E(f317(f274(x134491,x134491),f253(x134491,x134492)),x134492)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(13450,plain,
% 94.68/94.49 (P24(x134501,x134501,f5(x134501),x134502)),
% 94.68/94.49 inference(rename_variables,[],[3661])).
% 94.68/94.49 cnf(13454,plain,
% 94.68/94.49 (E(f317(f274(x134541,x134541),f253(x134541,x134542)),x134542)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(13468,plain,
% 94.68/94.49 (P1(f317(f317(f224(a897),f2(a897)),x134681))),
% 94.68/94.49 inference(rename_variables,[],[3450])).
% 94.68/94.49 cnf(13469,plain,
% 94.68/94.49 (P1(f317(f317(f225(a897),f2(a897)),f317(a102,x134691)))),
% 94.68/94.49 inference(rename_variables,[],[3506])).
% 94.68/94.49 cnf(13470,plain,
% 94.68/94.49 (E(f317(f274(x134701,x134701),f253(x134701,x134702)),x134702)),
% 94.68/94.49 inference(rename_variables,[],[3389])).
% 94.68/94.49 cnf(13587,plain,
% 94.68/94.49 ($false),
% 94.68/94.49 inference(scs_inference,[],[4632,4080,12709,12734,12866,12868,12870,3661,11319,12377,12482,12485,12577,12619,12623,12631,12703,12712,12839,12841,13289,13295,13300,13304,13310,13313,13337,13445,13450,3670,12447,12912,12914,3677,3398,12881,12883,12885,3399,12891,3365,12788,4590,4591,11958,4353,12936,3402,12887,3241,3298,12862,3299,12852,3300,3301,3302,12659,12922,4589,3719,4571,10396,10406,10419,10430,10534,10539,10542,10644,10783,11095,11290,11293,11311,11314,11508,11609,11616,11630,11676,11679,11712,11727,11790,11849,11865,12164,12189,12203,12232,12238,12332,12443,12612,12673,12819,13359,13366,3482,3448,12901,3629,12136,3349,4577,10628,10732,11200,11300,13024,13386,3040,3041,3043,3044,3046,3047,3048,3050,3051,3054,3061,3065,3074,3078,3080,3081,3084,3093,3094,3099,3100,3101,3103,3104,3107,3108,3110,3114,3115,3118,3122,3127,3133,3140,3149,3155,3164,3165,3176,3179,3184,3185,3186,3187,3191,3192,3196,3197,3198,3199,3200,3210,3220,3225,3297,4569,3758,3984,11896,3274,11606,3411,3386,3389,10465,10468,10563,10566,10889,11621,11624,11738,11777,11782,11891,12347,12553,12766,12821,12823,12830,12835,12837,12848,12856,12875,12920,12948,13158,13328,13449,13454,13470,3360,12644,12648,12652,3366,3375,3878,4182,3343,13220,3493,12706,12791,3263,3264,4258,3623,3969,11652,3328,3260,3288,3738,3283,3481,4089,3978,3800,3271,3272,3251,3890,3308,3483,11045,11174,12444,12663,3359,4053,4584,10456,10625,11505,12604,12645,12649,4587,12616,3420,11978,11981,13253,13348,13415,13419,13423,13427,4010,4614,11226,11324,11561,11564,3394,3819,3415,3530,3744,3522,4593,3497,12907,12952,3323,10526,10862,3324,4602,3582,3316,3242,3345,11642,4196,12634,12778,4055,11246,11378,11436,12588,12594,12723,12726,12756,4633,11149,11391,11499,11525,11569,11575,12532,4634,11279,11394,11502,4635,11397,11447,4636,11454,4637,3344,3621,12488,12529,12615,3784,3570,4467,4468,3605,3642,4582,11635,3762,3721,3764,3933,3688,13141,13145,13149,13153,13163,3980,12479,3607,3861,3494,10547,10667,10749,10822,10825,10865,10970,11216,11826,12034,12080,12160,12225,12303,12338,12415,12418,12760,13019,13060,13063,13124,13365,13370,3871,11882,3413,3506,11711,11993,13469,3683,4608,10433,10436,10462,10588,10767,10978,10993,11107,11547,11825,12051,12056,12279,12282,12359,12535,12638,12965,12984,12987,13011,13064,13235,13240,13265,13270,4620,11754,11785,11822,11829,11862,13073,13077,3858,3630,3631,12990,12993,12996,12999,13032,13035,13397,13401,13405,4002,3595,13398,3596,13402,3456,3458,3432,4605,3322,3287,4579,3810,4118,3614,4621,4189,11522,3743,3468,12001,12004,12451,12557,12737,4611,10424,10427,10596,10691,10714,10721,10744,10752,10755,10772,10963,11203,11417,11705,11799,11947,12069,12072,4158,4117,12153,12503,4065,10880,12513,12662,13418,4107,13422,4112,11249,12374,12450,12512,12556,13258,13389,4113,3785,11833,12163,12310,12382,12434,4146,3802,10591,10688,11252,11331,11410,11473,11645,12331,12396,12668,12733,12753,12763,13227,13294,13299,13319,13340,4624,10996,11402,12516,13307,3429,10556,10654,10808,10872,10950,10999,11002,11033,11053,11089,11129,11168,11950,11996,12133,12188,12206,12209,12212,12215,12389,12403,12406,12409,12412,12496,12560,12679,12729,13012,13038,13096,13116,13127,13132,13135,13138,13171,13182,13246,13276,13279,3430,10583,10639,10877,10973,11092,11730,12031,12037,12048,12139,12150,12169,12174,12218,12241,12258,13029,13175,13195,13236,13241,13266,13271,3431,12421,12424,3502,12364,13093,13142,13146,13150,13154,13164,13168,4604,10473,10502,11017,11056,11065,11910,11931,12107,12110,12113,12116,12202,12221,12224,12237,12291,12294,12297,12300,12462,12465,12563,12566,12672,12715,12803,3577,10737,10828,11100,11146,11381,11384,11462,11544,11715,11961,12611,12799,12806,13219,4616,11026,11138,11159,11162,11229,11232,11243,11347,11355,11369,11405,11422,11430,11470,11511,11516,11519,11538,11541,11578,11583,11586,11589,11592,11832,11975,12010,12285,12288,12322,12365,12392,12542,12585,12591,12691,12694,12719,12777,12783,12794,12813,13092,13108,13111,13208,13332,13351,13354,13394,13414,13448,3487,10859,10892,10901,10904,10907,11491,12716,12730,13074,13078,13081,13084,3526,13379,13440,3519,3937,3876,10505,11885,11913,13055,4613,10453,10847,10850,11350,11366,11848,11901,11935,11962,12066,12095,12098,12101,12104,12358,13282,3450,10895,11050,11122,11914,12065,12263,12470,12497,13105,13382,13468,3900,12007,13006,4237,3636,3971,4609,3911,3945,4596,4599,4600,3405,3410,4598,4612,3409,4597,4360,4404,3733,11878,4331,11737,4626,10758,10761,4631,11235,11238,11425,11535,11552,11598,4020,11595,11934,11938,12622,12630,12722,13223,13288,3866,11165,11171,11189,12185,12315,12395,12687,3717,12427,12548,12627,12682,12690,12810,4194,3868,10898,11268,11433,11467,11478,12626,12676,13324,3578,3686,10811,10814,10910,11076,3685,4629,11879,4625,12974,4630,10647,10764,12491,12500,12545,12747,4292,11036,12509,12524,4200,3899,12816,3844,3845,4627,10478,10481,10853,10856,11751,11939,12759,4628,11859,11944,3869,10817,11082,13369,3870,4132,4644,4670,4725,4729,4753,4768,4775,4777,4813,4818,4847,4853,4939,4965,4966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% 94.68/94.49 ['proof']).
% 94.68/94.49 % SZS output end Proof
% 94.68/94.49 % Total time :80.130000s
%------------------------------------------------------------------------------