TSTP Solution File: SCT159+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n032.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 : Thu Aug 31 14:10:18 EDT 2023
% Result : Theorem 4.70s 4.83s
% Output : CNFRefutation 4.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Thu Aug 24 14:58:42 EDT 2023
% 0.11/0.29 % CPUTime :
% 0.14/0.46 start to proof:theBenchmark
% 4.70/4.80 %-------------------------------------------
% 4.70/4.80 % File :CSE---1.6
% 4.70/4.80 % Problem :theBenchmark
% 4.70/4.80 % Transform :cnf
% 4.70/4.80 % Format :tptp:raw
% 4.70/4.80 % Command :java -jar mcs_scs.jar %d %s
% 4.70/4.80
% 4.70/4.80 % Result :Theorem 4.080000s
% 4.70/4.80 % Output :CNFRefutation 4.080000s
% 4.70/4.80 %-------------------------------------------
% 4.70/4.80 %------------------------------------------------------------------------------
% 4.70/4.80 % File : SCT159+1 : TPTP v8.1.2. Released v5.2.0.
% 4.70/4.80 % Domain : Social Choice Theory
% 4.70/4.80 % Problem : Arrow's Impossibility Theorem 433377, 500 axioms selected
% 4.70/4.80 % Version : Especial.
% 4.70/4.80 % English :
% 4.70/4.80
% 4.70/4.80 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 4.70/4.80 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 4.70/4.80 % Source : [Bla11]
% 4.70/4.80 % Names : arrow_433377.500.p [Bla11]
% 4.70/4.80
% 4.70/4.80 % Status : ContradictoryAxioms
% 4.70/4.80 % Rating : 0.47 v8.1.0, 0.53 v7.5.0, 0.56 v7.4.0, 0.50 v7.3.0, 0.52 v7.2.0, 0.48 v7.1.0, 0.35 v7.0.0, 0.37 v6.4.0, 0.38 v6.2.0, 0.48 v6.1.0, 0.60 v6.0.0, 0.57 v5.5.0, 0.63 v5.4.0, 0.68 v5.3.0, 0.78 v5.2.0
% 4.70/4.80 % Syntax : Number of formulae : 533 ( 113 unt; 0 def)
% 4.70/4.80 % Number of atoms : 1401 ( 356 equ)
% 4.70/4.80 % Maximal formula atoms : 8 ( 2 avg)
% 4.70/4.80 % Number of connectives : 1002 ( 134 ~; 30 |; 63 &)
% 4.70/4.80 % ( 130 <=>; 645 =>; 0 <=; 0 <~>)
% 4.70/4.80 % Maximal formula depth : 16 ( 6 avg)
% 4.70/4.80 % Maximal term depth : 7 ( 1 avg)
% 4.70/4.80 % Number of predicates : 39 ( 38 usr; 1 prp; 0-6 aty)
% 4.70/4.80 % Number of functors : 42 ( 42 usr; 8 con; 0-5 aty)
% 4.70/4.80 % Number of variables : 1533 (1509 !; 24 ?)
% 4.70/4.80 % SPC : FOF_CAX_RFO_SEQ
% 4.70/4.80
% 4.70/4.80 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.70/4.80 % 2011-03-01 11:24:27
% 4.70/4.80 % : Renamed from SWW161+1
% 4.70/4.80 %------------------------------------------------------------------------------
% 4.70/4.80 %----Relevant facts (491)
% 4.70/4.80 fof(fact_ext,axiom,
% 4.70/4.80 ! [V_g_2,V_f_2] :
% 4.70/4.80 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 4.70/4.80 => V_f_2 = V_g_2 ) ).
% 4.70/4.80
% 4.70/4.80 fof(fact_card__image,axiom,
% 4.70/4.80 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.80 => c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ).
% 4.70/4.80
% 4.70/4.80 fof(fact_inj__image__eq__iff,axiom,
% 4.70/4.80 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.80 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.80 => ( c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) = c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)
% 4.70/4.80 <=> V_A_2 = V_B_2 ) ) ).
% 4.70/4.80
% 4.70/4.80 fof(fact_top1I,axiom,
% 4.70/4.80 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__eq,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_injD,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 4.70/4.81 => V_x_2 = V_y_2 ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_top__apply,axiom,
% 4.70/4.81 ! [V_x_2,T_b,T_a] :
% 4.70/4.81 ( class_Orderings_Otop(T_a)
% 4.70/4.81 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__on__def,axiom,
% 4.70/4.81 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.81 <=> ! [B_x] :
% 4.70/4.81 ( c_member(T_a,B_x,V_A_2)
% 4.70/4.81 => ! [B_xa] :
% 4.70/4.81 ( c_member(T_a,B_xa,V_A_2)
% 4.70/4.81 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 4.70/4.81 => B_x = B_xa ) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_zero__reorient,axiom,
% 4.70/4.81 ! [V_x_2,T_a] :
% 4.70/4.81 ( class_Groups_Ozero(T_a)
% 4.70/4.81 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 4.70/4.81 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_assms_I3_J,axiom,
% 4.70/4.81 c_Arrow__Order__Mirabelle_OIIA(v_F) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_u,axiom,
% 4.70/4.81 c_Arrow__Order__Mirabelle_Ounanimity(v_F) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__indi,axiom,
% 4.70/4.81 c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__imageI,axiom,
% 4.70/4.81 ! [V_h_2,T_b,V_Fa_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,V_Fa_2)
% 4.70/4.81 => c_Finite__Set_Ofinite(T_b,c_Set_Oimage(T_a,T_b,V_h_2,V_Fa_2)) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite,axiom,
% 4.70/4.81 ! [V_A_2,T_a] :
% 4.70/4.81 ( class_Finite__Set_Ofinite(T_a)
% 4.70/4.81 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__option__UNIV,axiom,
% 4.70/4.81 ! [T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(tc_Option_Ooption(T_a),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_a),tc_HOL_Obool)))
% 4.70/4.81 <=> c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__Plus__UNIV__iff,axiom,
% 4.70/4.81 ! [T_b,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)))
% 4.70/4.81 <=> ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 & c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__code,axiom,
% 4.70/4.81 ! [V_A_2,T_a] :
% 4.70/4.81 ( class_Finite__Set_Ofinite(T_a)
% 4.70/4.81 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__fun__UNIVD2,axiom,
% 4.70/4.81 ! [T_b,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))
% 4.70/4.81 => c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__Prod__UNIV,axiom,
% 4.70/4.81 ! [T_b,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_Finite__Set_Ofinite(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 4.70/4.81 => c_Finite__Set_Ofinite(tc_prod(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool))) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__UNIV,axiom,
% 4.70/4.81 ! [T_a] :
% 4.70/4.81 ( class_Finite__Set_Ofinite(T_a)
% 4.70/4.81 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_card__infinite,axiom,
% 4.70/4.81 ! [V_A_2,T_a] :
% 4.70/4.81 ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.81 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__imageD,axiom,
% 4.70/4.81 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
% 4.70/4.81 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2)
% 4.70/4.81 => c_Finite__Set_Ofinite(T_b,V_A_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 4.70/4.81 ! [V_A_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__UNIV__surj__inj,axiom,
% 4.70/4.81 ! [V_f_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.81 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__UNIV__inj__surj,axiom,
% 4.70/4.81 ! [V_f_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => c_Set_Oimage(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_eq__card__imp__inj__on,axiom,
% 4.70/4.81 ! [V_f_2,T_b,V_A_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.81 => ( c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2)
% 4.70/4.81 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__on__iff__eq__card,axiom,
% 4.70/4.81 ! [V_f_2,T_b,V_A_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.81 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.81 <=> c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_card__bij__eq,axiom,
% 4.70/4.81 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)
% 4.70/4.81 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_b,T_a,V_g_2,V_B_2),V_A_2)
% 4.70/4.81 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.81 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 4.70/4.81 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Finite__Set_Ocard(T_b,V_B_2) ) ) ) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite__UNIV__card__ge__0,axiom,
% 4.70/4.81 ! [T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_the__inv__into__onto,axiom,
% 4.70/4.81 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.81 => c_Set_Oimage(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = V_A_2 ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__on__the__inv__into,axiom,
% 4.70/4.81 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.81 => c_Fun_Oinj__on(T_b,T_a,c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_the__inv__f__f,axiom,
% 4.70/4.81 ! [V_x_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_card__eq__0__iff,axiom,
% 4.70/4.81 ! [V_A_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.81 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.81 | ~ c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_pigeonhole,axiom,
% 4.70/4.81 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_b,V_A_2))
% 4.70/4.81 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__image__subset__iff,axiom,
% 4.70/4.81 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2))
% 4.70/4.81 <=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__image__mem__iff,axiom,
% 4.70/4.81 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_member(T_b,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))
% 4.70/4.81 <=> c_member(T_a,V_a_2,V_A_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_range__ex1__eq,axiom,
% 4.70/4.81 ! [V_b_2,V_f_2,T_b,T_a] :
% 4.70/4.81 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.81 => ( c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))))
% 4.70/4.81 <=> ? [B_x] :
% 4.70/4.81 ( V_b_2 = hAPP(V_f_2,B_x)
% 4.70/4.81 & ! [B_y] :
% 4.70/4.81 ( V_b_2 = hAPP(V_f_2,B_y)
% 4.70/4.81 => B_y = B_x ) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_card__image__le,axiom,
% 4.70/4.81 ! [V_f_2,T_b,V_A_2,T_a] :
% 4.70/4.81 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_b,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)),c_Finite__Set_Ocard(T_a,V_A_2)) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__refl,axiom,
% 4.70/4.81 ! [V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_finite_OemptyI,axiom,
% 4.70/4.81 ! [T_a] : c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_inj__on__empty,axiom,
% 4.70/4.81 ! [V_f_2,T_b,T_a] : c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__irrefl,axiom,
% 4.70/4.81 ! [V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_bot__least,axiom,
% 4.70/4.81 ! [V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Obot(T_a)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_a,c_Orderings_Obot__class_Obot(T_a),V_x) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_bot__apply,axiom,
% 4.70/4.81 ! [V_x_2,T_b,T_a] :
% 4.70/4.81 ( class_Orderings_Obot(T_a)
% 4.70/4.81 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__not__less,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__not__le,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__neq__iff,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( V_x_2 != V_y_2
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_not__less__iff__gr__or__eq,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 4.70/4.81 | V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_le__fun__def,axiom,
% 4.70/4.81 ! [V_g_2,V_f_2,T_a,T_b] :
% 4.70/4.81 ( class_Orderings_Oord(T_b)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.70/4.81 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__le__less__linear,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.81 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__linear,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.81 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__le,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 & V_x_2 != V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_less__le__not__le,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__eq__iff,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( V_x_2 = V_y_2
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__le__less,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 | V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__less__linear,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 | V_x = V_y
% 4.70/4.81 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_eq__mem,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( c_member(T_a,V_x_2,c_fequal(V_y_2))
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_leI,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_not__leE,axiom,
% 4.70/4.81 ! [V_x,V_y,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.81 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__antisym__conv3,axiom,
% 4.70/4.81 ! [V_x_2,V_y_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__antisym__conv1,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__neq__le__trans,axiom,
% 4.70/4.81 ! [V_b,V_a,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( V_a != V_b
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.81 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_xt1_I12_J,axiom,
% 4.70/4.81 ! [V_b,V_a,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( V_a != V_b
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.70/4.81 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__neqE,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( V_x != V_y
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_rev__predicate1D,axiom,
% 4.70/4.81 ! [V_Q_2,T_a,V_x_2,V_P_2] :
% 4.70/4.81 ( hBOOL(hAPP(V_P_2,V_x_2))
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)
% 4.70/4.81 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_less__imp__neq,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => V_x != V_y ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__not__sym,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_leD,axiom,
% 4.70/4.81 ! [V_x,V_y,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.81 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__eq__refl,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ( V_x = V_y
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__imp__le,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__imp__not__less,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Opreorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_linorder__antisym__conv2,axiom,
% 4.70/4.81 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.81 ( class_Orderings_Olinorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_le__funD,axiom,
% 4.70/4.81 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 4.70/4.81 ( class_Orderings_Oord(T_b)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.70/4.81 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__imp__not__eq,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => V_x != V_y ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__less__imp__not__eq2,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 => V_y != V_x ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__le__imp__less__or__eq,axiom,
% 4.70/4.81 ! [V_y,V_x,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.81 | V_x = V_y ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__antisym__conv,axiom,
% 4.70/4.81 ! [V_x_2,V_y_2,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.70/4.81 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_order__le__neq__trans,axiom,
% 4.70/4.81 ! [V_b,V_a,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.81 => ( V_a != V_b
% 4.70/4.81 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.70/4.81
% 4.70/4.81 fof(fact_xt1_I11_J,axiom,
% 4.70/4.81 ! [V_a,V_b,T_a] :
% 4.70/4.81 ( class_Orderings_Oorder(T_a)
% 4.70/4.81 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.70/4.82 => ( V_a != V_b
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_predicate1D,axiom,
% 4.70/4.82 ! [V_x_2,V_Q_2,V_P_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_P_2,V_Q_2)
% 4.70/4.82 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 4.70/4.82 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__less__asym_H,axiom,
% 4.70/4.82 ! [V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.82 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I9_J,axiom,
% 4.70/4.82 ! [V_a,V_b,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.70/4.82 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord__eq__less__trans,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oord(T_a)
% 4.70/4.82 => ( V_a = V_b
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I1_J,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( V_a = V_b
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord__eq__le__trans,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oord(T_a)
% 4.70/4.82 => ( V_a = V_b
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I3_J,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( V_a = V_b
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord__less__eq__trans,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oord(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.82 => ( V_b = V_c
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I2_J,axiom,
% 4.70/4.82 ! [V_c,V_a,V_b,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.70/4.82 => ( V_b = V_c
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__less__trans,axiom,
% 4.70/4.82 ! [V_z,V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__less__le__trans,axiom,
% 4.70/4.82 ! [V_z,V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I10_J,axiom,
% 4.70/4.82 ! [V_z,V_x,V_y,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I7_J,axiom,
% 4.70/4.82 ! [V_z,V_x,V_y,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord__le__eq__trans,axiom,
% 4.70/4.82 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.82 ( class_Orderings_Oord(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.82 => ( V_b = V_c
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I4_J,axiom,
% 4.70/4.82 ! [V_c,V_a,V_b,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.70/4.82 => ( V_b = V_c
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__le__less__trans,axiom,
% 4.70/4.82 ! [V_z,V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__antisym,axiom,
% 4.70/4.82 ! [V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.82 => V_x = V_y ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__trans,axiom,
% 4.70/4.82 ! [V_z,V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I8_J,axiom,
% 4.70/4.82 ! [V_z,V_x,V_y,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I5_J,axiom,
% 4.70/4.82 ! [V_x,V_y,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.82 => V_x = V_y ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_xt1_I6_J,axiom,
% 4.70/4.82 ! [V_z,V_x,V_y,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_order__less__asym,axiom,
% 4.70/4.82 ! [V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Opreorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.82 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__funE,axiom,
% 4.70/4.82 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 4.70/4.82 ( class_Orderings_Oord(T_b)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_linorder__le__cases,axiom,
% 4.70/4.82 ! [V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_linorder__cases,axiom,
% 4.70/4.82 ! [V_y,V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.82 => ( V_x != V_y
% 4.70/4.82 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_the__inv__into__f__eq,axiom,
% 4.70/4.82 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_the__inv__into__f__f,axiom,
% 4.70/4.82 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_the__inv__into__into,axiom,
% 4.70/4.82 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( c_member(T_b,V_x_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_member(T_a,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_x_2),V_B_2) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__seteq,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_B_2),c_Finite__Set_Ocard(T_a,V_A_2))
% 4.70/4.82 => V_A_2 = V_B_2 ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__mono,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__subset,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_rev__finite__subset,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_top__greatest,axiom,
% 4.70/4.82 ! [V_x,T_a] :
% 4.70/4.82 ( class_Orderings_Otop(T_a)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,c_Orderings_Otop__class_Otop(T_a)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite_Oequations_I1_J,axiom,
% 4.70/4.82 ! [T_a] : c_Finite__Set_Ofinite(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__on__contraD,axiom,
% 4.70/4.82 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( V_x_2 != V_y_2
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => ( c_member(T_a,V_y_2,V_A_2)
% 4.70/4.82 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__on__iff,axiom,
% 4.70/4.82 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => ( c_member(T_a,V_y_2,V_A_2)
% 4.70/4.82 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 4.70/4.82 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__onD,axiom,
% 4.70/4.82 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => ( c_member(T_a,V_y_2,V_A_2)
% 4.70/4.82 => V_x_2 = V_y_2 ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__inj__on,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_f__the__inv__into__f,axiom,
% 4.70/4.82 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( c_member(T_b,V_y_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))
% 4.70/4.82 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__gt__0__iff,axiom,
% 4.70/4.82 ! [V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))
% 4.70/4.82 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.82 & c_Finite__Set_Ofinite(T_a,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__inj__on__le,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),V_B_2)
% 4.70/4.82 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__surj,axiom,
% 4.70/4.82 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2))
% 4.70/4.82 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card_Oempty,axiom,
% 4.70/4.82 ! [T_a] : c_Finite__Set_Ocard(T_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__ge__0__finite,axiom,
% 4.70/4.82 ! [V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2))
% 4.70/4.82 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__surj__inj,axiom,
% 4.70/4.82 ! [V_f_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oimage(T_a,T_a,V_f_2,V_A_2))
% 4.70/4.82 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_endo__inj__surj,axiom,
% 4.70/4.82 ! [V_f_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oimage(T_a,T_a,V_f_2,V_A_2),V_A_2)
% 4.70/4.82 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2)
% 4.70/4.82 => c_Set_Oimage(T_a,T_a,V_f_2,V_A_2) = V_A_2 ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__on__iff__card__le,axiom,
% 4.70/4.82 ! [V_B_2,T_b,V_A_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.82 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 4.70/4.82 => ( ? [B_f] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 4.70/4.82 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_B_2) )
% 4.70/4.82 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le0,axiom,
% 4.70/4.82 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__zeroE,axiom,
% 4.70/4.82 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_empty__subsetI,axiom,
% 4.70/4.82 ! [V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_A_2) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_image__eqI,axiom,
% 4.70/4.82 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] :
% 4.70/4.82 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 4.70/4.82 => ( c_member(T_b,V_x_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_UNIV__I,axiom,
% 4.70/4.82 ! [V_x_2,T_a] : c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subsetD,axiom,
% 4.70/4.82 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_member(T_a,V_c_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_c_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_emptyE,axiom,
% 4.70/4.82 ! [V_a_2,T_a] : ~ c_member(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__on__iff__surj,axiom,
% 4.70/4.82 ! [V_A_H_2,T_b,T_a,V_A_2] :
% 4.70/4.82 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.82 => ( ? [B_f] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2)
% 4.70/4.82 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,B_f,V_A_2),V_A_H_2) )
% 4.70/4.82 <=> ? [B_g] : c_Set_Oimage(T_b,T_a,B_g,V_A_H_2) = V_A_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ex__nat__less__eq,axiom,
% 4.70/4.82 ! [V_P_2,V_n_2] :
% 4.70/4.82 ( ? [B_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)
% 4.70/4.82 & hBOOL(hAPP(V_P_2,B_m)) )
% 4.70/4.82 <=> ? [B_x] :
% 4.70/4.82 ( c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
% 4.70/4.82 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equalityCE,axiom,
% 4.70/4.82 ! [V_c_2,T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 => ( ( c_member(T_a,V_c_2,V_A_2)
% 4.70/4.82 => ~ c_member(T_a,V_c_2,V_B_2) )
% 4.70/4.82 => ~ ( ~ c_member(T_a,V_c_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_c_2,V_B_2) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equalityI,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
% 4.70/4.82 => V_A_2 = V_B_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__atLeastLessThan,axiom,
% 4.70/4.82 ! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2,V_u_2)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubsetD,axiom,
% 4.70/4.82 ! [V_c_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_member(T_a,V_c_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_c_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_not__psubset__empty,axiom,
% 4.70/4.82 ! [V_A_2,T_a] : ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubset__eq,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 & V_A_2 != V_B_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__iff__psubset__eq,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 | V_A_2 = V_B_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubset__imp__subset,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubset__subset__trans,axiom,
% 4.70/4.82 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__psubset__trans,axiom,
% 4.70/4.82 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_bot__nat__def,axiom,
% 4.70/4.82 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__fun__def,axiom,
% 4.70/4.82 ! [V_g_2,V_f_2,T_a,T_b] :
% 4.70/4.82 ( class_Orderings_Oord(T_b)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.70/4.82 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_inj__on__strict__subset,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubset__card__mono,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_mem__def,axiom,
% 4.70/4.82 ! [V_A_2,V_x_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_eqset__imp__iff,axiom,
% 4.70/4.82 ! [V_x_2,T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 <=> c_member(T_a,V_x_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_eqelem__imp__iff,axiom,
% 4.70/4.82 ! [V_A_2,T_a,V_y_2,V_x_2] :
% 4.70/4.82 ( V_x_2 = V_y_2
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 <=> c_member(T_a,V_y_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_eq__mem__trans,axiom,
% 4.70/4.82 ! [V_A_2,T_a,V_b_2,V_a_2] :
% 4.70/4.82 ( V_a_2 = V_b_2
% 4.70/4.82 => ( c_member(T_a,V_b_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_a_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__not__refl,axiom,
% 4.70/4.82 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_nat__neq__iff,axiom,
% 4.70/4.82 ! [V_n_2,V_m_2] :
% 4.70/4.82 ( V_m_2 != V_n_2
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_linorder__neqE__nat,axiom,
% 4.70/4.82 ! [V_y,V_x] :
% 4.70/4.82 ( V_x != V_y
% 4.70/4.82 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__irrefl__nat,axiom,
% 4.70/4.82 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__not__refl2,axiom,
% 4.70/4.82 ! [V_m,V_n] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 4.70/4.82 => V_m != V_n ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__not__refl3,axiom,
% 4.70/4.82 ! [V_t,V_s] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 4.70/4.82 => V_s != V_t ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_nat__less__cases,axiom,
% 4.70/4.82 ! [V_P_2,V_n_2,V_m_2] :
% 4.70/4.82 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 4.70/4.82 => ( ( V_m_2 = V_n_2
% 4.70/4.82 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 4.70/4.82 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 4.70/4.82 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 4.70/4.82 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__nat__set__iff__bounded,axiom,
% 4.70/4.82 ! [V_N_2] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 4.70/4.82 <=> ? [B_m] :
% 4.70/4.82 ! [B_x] :
% 4.70/4.82 ( c_member(tc_Nat_Onat,B_x,V_N_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_x,B_m) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__refl,axiom,
% 4.70/4.82 ! [V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_A_2) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_set__eq__subset,axiom,
% 4.70/4.82 ! [T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equalityD1,axiom,
% 4.70/4.82 ! [T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equalityD2,axiom,
% 4.70/4.82 ! [T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__trans,axiom,
% 4.70/4.82 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equalityE,axiom,
% 4.70/4.82 ! [T_a,V_B_2,V_A_2] :
% 4.70/4.82 ( V_A_2 = V_B_2
% 4.70/4.82 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__refl,axiom,
% 4.70/4.82 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_nat__le__linear,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_eq__imp__le,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( V_m = V_n
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__trans,axiom,
% 4.70/4.82 ! [V_k,V_j,V_i] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__antisym,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.70/4.82 => V_m = V_n ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 4.70/4.82 ! [V_N_2] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(tc_Nat_Onat,V_N_2)
% 4.70/4.82 <=> ? [B_m] :
% 4.70/4.82 ! [B_x] :
% 4.70/4.82 ( c_member(tc_Nat_Onat,B_x,V_N_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_x,B_m) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_card__psubset,axiom,
% 4.70/4.82 ! [V_A_2,V_B_2,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(T_a,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,V_B_2))
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_all__not__in__conv,axiom,
% 4.70/4.82 ! [V_A_2,T_a] :
% 4.70/4.82 ( ! [B_x] : ~ c_member(T_a,B_x,V_A_2)
% 4.70/4.82 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ex__in__conv,axiom,
% 4.70/4.82 ! [V_A_2,T_a] :
% 4.70/4.82 ( ? [B_x] : c_member(T_a,B_x,V_A_2)
% 4.70/4.82 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_empty__iff,axiom,
% 4.70/4.82 ! [V_c_2,T_a] : ~ c_member(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_equals0D,axiom,
% 4.70/4.82 ! [V_a_2,T_a,V_A_2] :
% 4.70/4.82 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.82 => ~ c_member(T_a,V_a_2,V_A_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_in__mono,axiom,
% 4.70/4.82 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_x_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_set__rev__mp,axiom,
% 4.70/4.82 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_member(T_a,V_x_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_set__mp,axiom,
% 4.70/4.82 ! [V_x_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => c_member(T_a,V_x_2,V_B_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_rev__image__eqI,axiom,
% 4.70/4.82 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 4.70/4.82 => c_member(T_b,V_b_2,c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_imageI,axiom,
% 4.70/4.82 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.82 => c_member(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_image__iff,axiom,
% 4.70/4.82 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_z_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
% 4.70/4.82 <=> ? [B_x] :
% 4.70/4.82 ( c_member(T_b,B_x,V_A_2)
% 4.70/4.82 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__empty,axiom,
% 4.70/4.82 ! [V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.82 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_UNIV__not__empty,axiom,
% 4.70/4.82 ! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_image__is__empty,axiom,
% 4.70/4.82 ! [V_A_2,V_f_2,T_a,T_b] :
% 4.70/4.82 ( c_Set_Oimage(T_b,T_a,V_f_2,V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.82 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_image__empty,axiom,
% 4.70/4.82 ! [V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_empty__is__image,axiom,
% 4.70/4.82 ! [V_A_2,V_f_2,T_b,T_a] :
% 4.70/4.82 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_Set_Oimage(T_b,T_a,V_f_2,V_A_2)
% 4.70/4.82 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_gr0I,axiom,
% 4.70/4.82 ! [V_n] :
% 4.70/4.82 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_gr__implies__not0,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__nat__zero__code,axiom,
% 4.70/4.82 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_neq0__conv,axiom,
% 4.70/4.82 ! [V_n_2] :
% 4.70/4.82 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.82 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_not__less0,axiom,
% 4.70/4.82 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__UNIV,axiom,
% 4.70/4.82 ! [V_A_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_image__mono,axiom,
% 4.70/4.82 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2),c_Set_Oimage(T_a,T_b,V_f_2,V_B_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_subset__image__iff,axiom,
% 4.70/4.82 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oimage(T_b,T_a,V_f_2,V_A_2))
% 4.70/4.82 <=> ? [B_AA] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),B_AA,V_A_2)
% 4.70/4.82 & V_B_2 = c_Set_Oimage(T_b,T_a,V_f_2,B_AA) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__0__eq,axiom,
% 4.70/4.82 ! [V_n_2] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.82 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 4.70/4.82 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_nat__less__le,axiom,
% 4.70/4.82 ! [V_n_2,V_m_2] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 & V_m_2 != V_n_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__eq__less__or__eq,axiom,
% 4.70/4.82 ! [V_n_2,V_m_2] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.82 | V_m_2 = V_n_2 ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__imp__le__nat,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_le__neq__implies__less,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 => ( V_m != V_n
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_less__or__eq__imp__le,axiom,
% 4.70/4.82 ! [V_n,V_m] :
% 4.70/4.82 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.82 | V_m = V_n )
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 4.70/4.82 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)
% 4.70/4.82 => V_b_2 = V_d_2 ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 4.70/4.82 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)
% 4.70/4.82 => V_a_2 = V_c_2 ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__eq__iff,axiom,
% 4.70/4.82 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)
% 4.70/4.82 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)
% 4.70/4.82 <=> ( V_a_2 = V_c_2
% 4.70/4.82 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan0,axiom,
% 4.70/4.82 ! [V_m_2] : 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)) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_range__eqI,axiom,
% 4.70/4.82 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] :
% 4.70/4.82 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 4.70/4.82 => c_member(T_a,V_b_2,c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_rangeI,axiom,
% 4.70/4.82 ! [T_b,V_x_2,V_f_2,T_a] : c_member(T_a,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__empty,axiom,
% 4.70/4.82 ! [V_a_2,V_b_2,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2)
% 4.70/4.82 => c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 4.70/4.82 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)
% 4.70/4.82 <=> ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__empty__iff,axiom,
% 4.70/4.82 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Oorder(T_a)
% 4.70/4.82 => ( c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.82 <=> ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_atLeastLessThan__subset__iff,axiom,
% 4.70/4.82 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.82 ( class_Orderings_Olinorder(T_a)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2))
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2)
% 4.70/4.82 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2)
% 4.70/4.82 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2) ) ) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_all__nat__less__eq,axiom,
% 4.70/4.82 ! [V_P_2,V_n_2] :
% 4.70/4.82 ( ! [B_m] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_m,V_n_2)
% 4.70/4.82 => hBOOL(hAPP(V_P_2,B_m)) )
% 4.70/4.82 <=> ! [B_x] :
% 4.70/4.82 ( c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
% 4.70/4.82 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OatMost__iff,axiom,
% 4.70/4.82 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))
% 4.70/4.82 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OatLeast__iff,axiom,
% 4.70/4.82 ! [V_k_2,V_less__eq_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))
% 4.70/4.82 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OlessThan__iff,axiom,
% 4.70/4.82 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))
% 4.70/4.82 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OgreaterThan__iff,axiom,
% 4.70/4.82 ! [V_k_2,V_less_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))
% 4.70/4.82 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 4.70/4.82 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastAtMost(T_a,V_less__eq_2,V_l_2,V_u_2))
% 4.70/4.82 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 4.70/4.82 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 4.70/4.82 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanLessThan(T_a,V_less_2,V_l_2,V_u_2))
% 4.70/4.82 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 4.70/4.82 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_psubset__trans,axiom,
% 4.70/4.82 ! [V_C_2,V_B_2,V_A_2,T_a] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.82 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_C_2)
% 4.70/4.82 => c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_C_2) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_infinite__UNIV__nat,axiom,
% 4.70/4.82 ~ c_Finite__Set_Ofinite(tc_Nat_Onat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 4.70/4.82 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OgreaterThanAtMost(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))
% 4.70/4.82 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 4.70/4.82 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 4.70/4.82 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] :
% 4.70/4.82 ( c_member(T_a,V_i_2,c_SetInterval_Oord_OatLeastLessThan(T_a,V_less__eq_2,V_less_2,V_l_2,V_u_2))
% 4.70/4.82 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 4.70/4.82 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_termination__basic__simps_I5_J,axiom,
% 4.70/4.82 ! [V_y,V_x] :
% 4.70/4.82 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.70/4.82 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_iso__tuple__UNIV__I,axiom,
% 4.70/4.82 ! [V_x_2,T_a] : c_member(T_a,V_x_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ).
% 4.70/4.82
% 4.70/4.82 fof(fact_finite__fun__UNIVD1,axiom,
% 4.70/4.82 ! [T_b,T_a] :
% 4.70/4.82 ( c_Finite__Set_Ofinite(tc_fun(T_a,T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_a,T_b),tc_HOL_Obool)))
% 4.70/4.83 => ( c_Finite__Set_Ocard(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 => c_Finite__Set_Ofinite(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,V_A_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool),V_B_2,V_A_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,hAPP(V_Fa_2,V_B_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 4.70/4.83 => ( c_member(T_b,V_x_2,V_A_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__mono,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_lessI,axiom,
% 4.70/4.83 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__less__Suc,axiom,
% 4.70/4.83 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_n__not__Suc__n,axiom,
% 4.70/4.83 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__n__not__n,axiom,
% 4.70/4.83 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Oinject,axiom,
% 4.70/4.83 ! [V_nat_H_2,V_nat_2] :
% 4.70/4.83 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 4.70/4.83 <=> V_nat_2 = V_nat_H_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__inject,axiom,
% 4.70/4.83 ! [V_y,V_x] :
% 4.70/4.83 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 4.70/4.83 => V_x = V_y ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_inj__Suc,axiom,
% 4.70/4.83 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one__idem_Oidem,axiom,
% 4.70/4.83 ! [V_x_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 4.70/4.83 ! [V_x_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_image__Suc__atLeastLessThan,axiom,
% 4.70/4.83 ! [V_j_2,V_i_2] : c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2),hAPP(c_Nat_OSuc,V_j_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__n__not__le__n,axiom,
% 4.70/4.83 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n),V_n) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__less__eq__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__Suc__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__le__mono,axiom,
% 4.70/4.83 ! [V_m_2,V_n_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__SucI,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__SucE,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))
% 4.70/4.83 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__leD,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__less__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__Suc__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 | V_m_2 = V_n_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__less__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__less__less__Suc__eq,axiom,
% 4.70/4.83 ! [V_m_2,V_n_2] :
% 4.70/4.83 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))
% 4.70/4.83 <=> V_n_2 = V_m_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__antisym,axiom,
% 4.70/4.83 ! [V_m,V_n] :
% 4.70/4.83 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(c_Nat_OSuc,V_m))
% 4.70/4.83 => V_m = V_n ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__SucI,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__lessI,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__trans__Suc,axiom,
% 4.70/4.83 ! [V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i),V_k) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__SucE,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n))
% 4.70/4.83 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => V_m = V_n ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__lessD,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__less__SucD,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),hAPP(c_Nat_OSuc,V_n))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__neq__Zero,axiom,
% 4.70/4.83 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Zero__neq__Suc,axiom,
% 4.70/4.83 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osimps_I3_J,axiom,
% 4.70/4.83 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__not__Zero,axiom,
% 4.70/4.83 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osimps_I2_J,axiom,
% 4.70/4.83 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Zero__not__Suc,axiom,
% 4.70/4.83 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_gr0__conv__Suc,axiom,
% 4.70/4.83 ! [V_n_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 4.70/4.83 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__Suc0,axiom,
% 4.70/4.83 ! [V_n_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 4.70/4.83 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__Suc__eq__0__disj,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 | ? [B_j] :
% 4.70/4.83 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 4.70/4.83 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__le__lessD,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__less__Suc__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,hAPP(c_Nat_OSuc,V_m_2))
% 4.70/4.83 <=> V_n_2 = V_m_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__leI,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__imp__less__Suc,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__le__eq,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2)
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__Suc__eq__le,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__eq__Suc__le,axiom,
% 4.70/4.83 ! [V_m_2,V_n_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one__idem_Oin__idem,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) = hAPP(V_Fa_2,V_A_2) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 4.70/4.83 ! [V_N_2,V_h_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => ( ! [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))
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_N_2)
% 4.70/4.83 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 => hAPP(V_h_2,hAPP(V_Fa_2,V_N_2)) = hAPP(V_Fa_2,c_Set_Oimage(T_a,T_a,V_h_2,V_N_2)) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_greaterThan__0,axiom,
% 4.70/4.83 c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = 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))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__PlusD_I2_J,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 4.70/4.83 => c_Finite__Set_Ofinite(T_b,V_B_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_greaterThan__eq__iff,axiom,
% 4.70/4.83 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.83 ( class_Orderings_Olinorder(T_a)
% 4.70/4.83 => ( c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2) = c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2)
% 4.70/4.83 <=> V_x_2 = V_y_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_greaterThan__iff,axiom,
% 4.70/4.83 ! [V_k_2,V_i_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oord(T_a)
% 4.70/4.83 => ( c_member(T_a,V_i_2,c_SetInterval_Oord__class_OgreaterThan(T_a,V_k_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_k_2,V_i_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_greaterThan__subset__iff,axiom,
% 4.70/4.83 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.83 ( class_Orderings_Olinorder(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OgreaterThan(T_a,V_x_2),c_SetInterval_Oord__class_OgreaterThan(T_a,V_y_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__Plus__iff,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 4.70/4.83 <=> ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 & c_Finite__Set_Ofinite(T_b,V_B_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__Plus,axiom,
% 4.70/4.83 ! [V_B_2,T_b,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 4.70/4.83 => c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__PlusD_I1_J,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2))
% 4.70/4.83 => c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_UNIV__Plus__UNIV,axiom,
% 4.70/4.83 ! [T_b,T_a] : c_Sum__Type_OPlus(T_a,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Plus__eq__empty__conv,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,T_b,T_a] :
% 4.70/4.83 ( c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_a,T_b),tc_HOL_Obool))
% 4.70/4.83 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__Plus__conv__if,axiom,
% 4.70/4.83 ! [V_B_2,T_b,V_A_2,T_a] :
% 4.70/4.83 ( ( ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 4.70/4.83 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)) )
% 4.70/4.83 & ( ~ ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 & c_Finite__Set_Ofinite(T_b,V_B_2) )
% 4.70/4.83 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_termination__basic__simps_I1_J,axiom,
% 4.70/4.83 ! [V_z,V_y,V_x] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_termination__basic__simps_I2_J,axiom,
% 4.70/4.83 ! [V_y,V_z,V_x] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_termination__basic__simps_I4_J,axiom,
% 4.70/4.83 ! [V_y,V_z,V_x] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_termination__basic__simps_I3_J,axiom,
% 4.70/4.83 ! [V_z,V_y,V_x] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__commute,axiom,
% 4.70/4.83 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__left__commute,axiom,
% 4.70/4.83 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__assoc,axiom,
% 4.70/4.83 ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__left__cancel,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2,V_k_2] :
% 4.70/4.83 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 4.70/4.83 <=> V_m_2 = V_n_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__right__cancel,axiom,
% 4.70/4.83 ! [V_n_2,V_k_2,V_m_2] :
% 4.70/4.83 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 4.70/4.83 <=> V_m_2 = V_n_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oab__semigroup__add(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__left__cancel,axiom,
% 4.70/4.83 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2)
% 4.70/4.83 <=> V_b_2 = V_c_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__right__cancel,axiom,
% 4.70/4.83 ! [V_c_2,V_a_2,V_b_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2)
% 4.70/4.83 <=> V_b_2 = V_c_2 ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__left__imp__eq,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 4.70/4.83 => V_b = V_c ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__imp__eq,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 4.70/4.83 => V_b = V_c ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__right__imp__eq,axiom,
% 4.70/4.83 ! [V_c,V_a,V_b,T_a] :
% 4.70/4.83 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 4.70/4.83 => V_b = V_c ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_subset__card__intvl__is__intvl,axiom,
% 4.70/4.83 ! [V_k_2,V_A_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool),V_A_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))))
% 4.70/4.83 => V_A_2 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,c_Finite__Set_Ocard(tc_Nat_Onat,V_A_2))) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__add2,axiom,
% 4.70/4.83 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__add1,axiom,
% 4.70/4.83 ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_le__iff__add,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__left__cancel__le,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2,V_k_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_trans__le__add1,axiom,
% 4.70/4.83 ! [V_m,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_trans__le__add2,axiom,
% 4.70/4.83 ! [V_m,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__mono1,axiom,
% 4.70/4.83 ! [V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__mono,axiom,
% 4.70/4.83 ! [V_l,V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__leD2,axiom,
% 4.70/4.83 ! [V_n,V_k,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__leD1,axiom,
% 4.70/4.83 ! [V_n,V_k,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__leE,axiom,
% 4.70/4.83 ! [V_n,V_k,V_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.70/4.83 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.70/4.83 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__add__less1,axiom,
% 4.70/4.83 ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__add__less2,axiom,
% 4.70/4.83 ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__add__left__cancel__less,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2,V_k_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_trans__less__add1,axiom,
% 4.70/4.83 ! [V_m,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_trans__less__add2,axiom,
% 4.70/4.83 ! [V_m,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__mono1,axiom,
% 4.70/4.83 ! [V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__mono,axiom,
% 4.70/4.83 ! [V_l,V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__add__eq__less,axiom,
% 4.70/4.83 ! [V_n,V_m,V_l,V_k] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__lessD1,axiom,
% 4.70/4.83 ! [V_k,V_j,V_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__eq__self__zero,axiom,
% 4.70/4.83 ! [V_n,V_m] :
% 4.70/4.83 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 4.70/4.83 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__is__0,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Nat_Oadd__0__right,axiom,
% 4.70/4.83 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 4.70/4.83
% 4.70/4.83 fof(fact_plus__nat_Oadd__0,axiom,
% 4.70/4.83 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__imp__less__left,axiom,
% 4.70/4.83 ! [V_b,V_a,V_c,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__imp__less__right,axiom,
% 4.70/4.83 ! [V_b,V_c,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__strict__mono,axiom,
% 4.70/4.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__strict__left__mono,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__strict__right__mono,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__cancel__left,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__cancel__right,axiom,
% 4.70/4.83 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add_Ocomm__neutral,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__0__right,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Groups_Omonoid__add(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_double__zero__sym,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 4.70/4.83 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__0,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__0__left,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Groups_Omonoid__add(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__imp__le__left,axiom,
% 4.70/4.83 ! [V_b,V_a,V_c,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__imp__le__right,axiom,
% 4.70/4.83 ! [V_b,V_c,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__mono,axiom,
% 4.70/4.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__left__mono,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__right__mono,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__cancel__left,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,V_c_2,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__cancel__right,axiom,
% 4.70/4.83 ! [V_b_2,V_c_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__Suc__shift,axiom,
% 4.70/4.83 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__Suc,axiom,
% 4.70/4.83 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__Suc__right,axiom,
% 4.70/4.83 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__nonpos__nonpos,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__increasing2,axiom,
% 4.70/4.83 ! [V_a,V_b,V_c,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__increasing,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__nonneg__eq__0__iff,axiom,
% 4.70/4.83 ! [V_y_2,V_x_2,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.70/4.83 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.70/4.83 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__nonneg__nonneg,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__less__le__mono,axiom,
% 4.70/4.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__le__less__mono,axiom,
% 4.70/4.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__neg__neg,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__pos__pos,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__is__1,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 4.70/4.83 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_one__is__add,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 4.70/4.83 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__gr__0,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
% 4.70/4.83 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
% 4.70/4.83 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__add__Suc1,axiom,
% 4.70/4.83 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__add__Suc2,axiom,
% 4.70/4.83 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__iff__Suc__add,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__pos__nonneg,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__nonneg__pos,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__strict__increasing,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__strict__increasing2,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__neg__nonpos,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__nonpos__neg,axiom,
% 4.70/4.83 ! [V_b,V_a,T_a] :
% 4.70/4.83 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__Plus,axiom,
% 4.70/4.83 ! [V_B_2,T_b,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_b,V_B_2)
% 4.70/4.83 => c_Finite__Set_Ocard(tc_sum(T_a,T_b),c_Sum__Type_OPlus(T_a,T_b,V_A_2,V_B_2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_b,V_B_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_pos__add__strict,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_even__less__0__iff,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__idom(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_double__eq__0__iff,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.70/4.83 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_linorder__neqE__linordered__idom,axiom,
% 4.70/4.83 ! [V_y,V_x,T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__idom(T_a)
% 4.70/4.83 => ( V_x != V_y
% 4.70/4.83 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 4.70/4.83 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 4.70/4.83 ! [V_c,V_b,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 4.70/4.83 ! [V_d,V_c,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 4.70/4.83 ! [V_d,V_c,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 4.70/4.83 ! [V_c,V_a,T_a] :
% 4.70/4.83 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_add__0__iff,axiom,
% 4.70/4.83 ! [V_a_2,V_b_2,T_a] :
% 4.70/4.83 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 4.70/4.83 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 4.70/4.83 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osize_I2_J,axiom,
% 4.70/4.83 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = 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))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__op__ivl__Suc,axiom,
% 4.70/4.83 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) )
% 4.70/4.83 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,V_n_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osize_I1_J,axiom,
% 4.70/4.83 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__add__nat__ivl,axiom,
% 4.70/4.83 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_p_2)
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2,V_p_2))) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_p_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 4.70/4.83 ! [V_k_2,V_f_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__head__upt__Suc,axiom,
% 4.70/4.83 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum_Oinfinite,axiom,
% 4.70/4.83 ! [V_g_2,V_A_2,T_a,T_b] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 => ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__infinite,axiom,
% 4.70/4.83 ! [V_f_2,V_A_2,T_a,T_b] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 => ( ~ c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__eq__0__iff,axiom,
% 4.70/4.83 ! [V_f_2,V_Fa_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_Fa_2)
% 4.70/4.83 => ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_Fa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 <=> ! [B_x] :
% 4.70/4.83 ( c_member(T_a,B_x,V_Fa_2)
% 4.70/4.83 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__eq__Suc0__iff,axiom,
% 4.70/4.83 ! [V_f_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 <=> ? [B_x] :
% 4.70/4.83 ( c_member(T_a,B_x,V_A_2)
% 4.70/4.83 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.70/4.83 & ! [B_xa] :
% 4.70/4.83 ( c_member(T_a,B_xa,V_A_2)
% 4.70/4.83 => ( B_x != B_xa
% 4.70/4.83 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__empty,axiom,
% 4.70/4.83 ! [V_f_2,T_b,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum_Oempty,axiom,
% 4.70/4.83 ! [V_g_2,T_b,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_a,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osize_I4_J,axiom,
% 4.70/4.83 ! [V_nat] : c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_nat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__strict__mono,axiom,
% 4.70/4.83 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] :
% 4.70/4.83 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) )
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 => ( ! [B_x] :
% 4.70/4.83 ( c_member(T_a,B_x,V_A_2)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_b,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_A_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat__size,axiom,
% 4.70/4.83 ! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n ).
% 4.70/4.83
% 4.70/4.83 fof(fact_nat_Osize_I3_J,axiom,
% 4.70/4.83 c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__SucD,axiom,
% 4.70/4.83 ! [V_n_2,V_A_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 4.70/4.83 => ? [B_x] :
% 4.70/4.83 ( c_member(T_a,B_x,V_A_2)
% 4.70/4.83 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(V_f_2,B_x)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__reindex__cong,axiom,
% 4.70/4.83 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_c)
% 4.70/4.83 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.83 => ( V_B_2 = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)
% 4.70/4.83 => ( ! [B_a] :
% 4.70/4.83 ( c_member(T_a,B_a,V_A_2)
% 4.70/4.83 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c,V_h_2,V_B_2) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_c,V_g_2,V_A_2) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__ivl__cong,axiom,
% 4.70/4.83 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] :
% 4.70/4.83 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 & class_Orderings_Oord(T_a) )
% 4.70/4.83 => ( V_a_2 = V_c_2
% 4.70/4.83 => ( V_b_2 = V_d_2
% 4.70/4.83 => ( ! [B_x] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,B_x)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,B_x,V_d_2)
% 4.70/4.83 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2,V_b_2)) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2,V_d_2)) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__cl__ivl__Suc,axiom,
% 4.70/4.83 ! [V_f_2,V_m_2,V_n_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Ozero__class_Ozero(T_a) )
% 4.70/4.83 & ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),V_m_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))) = c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__atLeastAtMost,axiom,
% 4.70/4.83 ! [V_u_2,V_l_2] : c_Finite__Set_Ofinite(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastatMost__subset__iff,axiom,
% 4.70/4.83 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))
% 4.70/4.83 <=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 4.70/4.83 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2)
% 4.70/4.83 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastatMost__empty,axiom,
% 4.70/4.83 ! [V_a_2,V_b_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastatMost__empty__iff,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 <=> ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastatMost__empty__iff2,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)
% 4.70/4.83 <=> ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 4.70/4.83 ! [V_u_2,V_l_2] : 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) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_ex__nat__less,axiom,
% 4.70/4.83 ! [V_P_2,V_n_2] :
% 4.70/4.83 ( ? [B_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,V_n_2)
% 4.70/4.83 & hBOOL(hAPP(V_P_2,B_m)) )
% 4.70/4.83 <=> ? [B_x] :
% 4.70/4.83 ( c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
% 4.70/4.83 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_all__nat__less,axiom,
% 4.70/4.83 ! [V_P_2,V_n_2] :
% 4.70/4.83 ( ! [B_m] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,V_n_2)
% 4.70/4.83 => hBOOL(hAPP(V_P_2,B_m)) )
% 4.70/4.83 <=> ! [B_x] :
% 4.70/4.83 ( c_member(tc_Nat_Onat,B_x,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2))
% 4.70/4.83 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_image__Suc__atLeastAtMost,axiom,
% 4.70/4.83 ! [V_j_2,V_i_2] : 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)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 4.70/4.83 ! [V_k_2,V_f_2] :
% 4.70/4.83 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 => 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)) = 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)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastatMost__psubset__iff,axiom,
% 4.70/4.83 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))
% 4.70/4.83 <=> ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 4.70/4.83 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_a_2)
% 4.70/4.83 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_d_2)
% 4.70/4.83 & ( c_Orderings_Oord__class_Oless(T_a,V_c_2,V_a_2)
% 4.70/4.83 | c_Orderings_Oord__class_Oless(T_a,V_b_2,V_d_2) ) ) )
% 4.70/4.83 & c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,V_d_2) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__head__Suc,axiom,
% 4.70/4.83 ! [V_f_2,V_n_2,V_m_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(V_f_2,V_m_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__ub__add__nat,axiom,
% 4.70/4.83 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2))) = c_Groups_Oplus__class_Oplus(T_a,c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_a,V_f_2,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_p_2)))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_bool_Osize_I1_J,axiom,
% 4.70/4.83 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__UNIV__unit,axiom,
% 4.70/4.83 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) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_less__add__one,axiom,
% 4.70/4.83 ! [V_a,T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__one__le__zero,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__le__one,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_not__one__less__zero,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__less__one,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_one__neq__zero,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Ozero__neq__one(T_a)
% 4.70/4.83 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__neq__one,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Ozero__neq__one(T_a)
% 4.70/4.83 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_One__nat__def,axiom,
% 4.70/4.83 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__eq__plus1__left,axiom,
% 4.70/4.83 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Suc__eq__plus1,axiom,
% 4.70/4.83 ! [V_n] : hAPP(c_Nat_OSuc,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_one__reorient,axiom,
% 4.70/4.83 ! [V_x_2,T_a] :
% 4.70/4.83 ( class_Groups_Oone(T_a)
% 4.70/4.83 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 4.70/4.83 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_zero__less__two,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__semidom(T_a)
% 4.70/4.83 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__eq__1__iff,axiom,
% 4.70/4.83 ! [V_f_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat,V_f_2,V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.70/4.83 <=> ? [B_x] :
% 4.70/4.83 ( c_member(T_a,B_x,V_A_2)
% 4.70/4.83 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.70/4.83 & ! [B_xa] :
% 4.70/4.83 ( c_member(T_a,B_xa,V_A_2)
% 4.70/4.83 => ( B_x != B_xa
% 4.70/4.83 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_bool_Osize_I2_J,axiom,
% 4.70/4.83 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__odd__less__0,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Rings_Olinordered__idom(T_a)
% 4.70/4.83 => ( c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_ex__least__nat__less,axiom,
% 4.70/4.83 ! [V_n_2,V_P_2] :
% 4.70/4.83 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 4.70/4.83 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 4.70/4.83 => ? [B_k] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)
% 4.70/4.83 & ! [B_i] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 4.70/4.83 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 4.70/4.83 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__0,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Oring__1(T_a)
% 4.70/4.83 => c_member(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Oring__1__class_OInts(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__add,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Rings_Oring__1(T_a)
% 4.70/4.83 => ( c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))
% 4.70/4.83 => ( c_member(T_a,V_b_2,c_Int_Oring__1__class_OInts(T_a))
% 4.70/4.83 => c_member(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2),c_Int_Oring__1__class_OInts(T_a)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__1,axiom,
% 4.70/4.83 ! [T_a] :
% 4.70/4.83 ( class_Rings_Oring__1(T_a)
% 4.70/4.83 => c_member(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Oring__1__class_OInts(T_a)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__double__eq__0__iff,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Int_Oring__char__0(T_a)
% 4.70/4.83 => ( c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))
% 4.70/4.83 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.70/4.83 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_Ints__odd__nonzero,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Int_Oring__char__0(T_a)
% 4.70/4.83 => ( c_member(T_a,V_a_2,c_Int_Oring__1__class_OInts(T_a))
% 4.70/4.83 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card_Oneutral,axiom,
% 4.70/4.83 ! [V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ( ? [B_x] : c_member(T_a,B_x,V_A_2)
% 4.70/4.83 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card_Oinsert,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insertE,axiom,
% 4.70/4.83 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))
% 4.70/4.83 => ( V_a_2 != V_b_2
% 4.70/4.83 => c_member(T_a,V_a_2,V_A_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insertCI,axiom,
% 4.70/4.83 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 4.70/4.83 ( ( ~ c_member(T_a,V_a_2,V_B_2)
% 4.70/4.83 => V_a_2 = V_b_2 )
% 4.70/4.83 => c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite_OinsertI,axiom,
% 4.70/4.83 ! [V_a_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_Fa_2,V_g_2,V_z_2,V_f_2,T_b,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_b,V_A_2)
% 4.70/4.83 => hAPP(V_Fa_2,c_Set_Oinsert(T_b,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_Fa_2,V_A_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__mono,axiom,
% 4.70/4.83 ! [V_a_2,V_D_2,V_C_2,T_a] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_C_2,V_D_2)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_a_2,V_C_2),c_Set_Oinsert(T_a,V_a_2,V_D_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_subset__insertI2,axiom,
% 4.70/4.83 ! [V_b_2,V_B_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_subset__insertI,axiom,
% 4.70/4.83 ! [V_a_2,V_B_2,T_a] : c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_B_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_singleton__iff,axiom,
% 4.70/4.83 ! [V_a_2,V_b_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 4.70/4.83 <=> V_b_2 = V_a_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_singletonE,axiom,
% 4.70/4.83 ! [V_a_2,V_b_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_b_2,c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 4.70/4.83 => V_b_2 = V_a_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__subset,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a,V_x_2,V_A_2),V_B_2)
% 4.70/4.83 <=> ( c_member(T_a,V_x_2,V_B_2)
% 4.70/4.83 & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_subset__insert,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 4.70/4.83 ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,V_B_2))
% 4.70/4.83 <=> c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,V_B_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__image,axiom,
% 4.70/4.83 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Set_Oinsert(T_b,hAPP(V_f_2,V_x_2),c_Set_Oimage(T_a,T_b,V_f_2,V_A_2)) = c_Set_Oimage(T_a,T_b,V_f_2,V_A_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_subset__singletonD,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 4.70/4.83 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 | V_A_2 = c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_image__insert,axiom,
% 4.70/4.83 ! [V_B_2,V_a_2,V_f_2,T_a,T_b] : c_Set_Oimage(T_b,T_a,V_f_2,c_Set_Oinsert(T_b,V_a_2,V_B_2)) = c_Set_Oinsert(T_a,hAPP(V_f_2,V_a_2),c_Set_Oimage(T_b,T_a,V_f_2,V_B_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__absorb2,axiom,
% 4.70/4.83 ! [V_A_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Set_Oinsert(T_a,V_x_2,V_A_2) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__commute,axiom,
% 4.70/4.83 ! [V_A_2,V_y_2,V_x_2,T_a] : c_Set_Oinsert(T_a,V_x_2,c_Set_Oinsert(T_a,V_y_2,V_A_2)) = c_Set_Oinsert(T_a,V_y_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__code,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_y_2,T_a] :
% 4.70/4.83 ( hBOOL(hAPP(c_Set_Oinsert(T_a,V_y_2,V_A_2),V_x_2))
% 4.70/4.83 <=> ( V_y_2 = V_x_2
% 4.70/4.83 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_finite__insert,axiom,
% 4.70/4.83 ! [V_A_2,V_a_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,c_Set_Oinsert(T_a,V_a_2,V_A_2))
% 4.70/4.83 <=> c_Finite__Set_Ofinite(T_a,V_A_2) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insertI1,axiom,
% 4.70/4.83 ! [V_B_2,V_a_2,T_a] : c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_a_2,V_B_2)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__iff,axiom,
% 4.70/4.83 ! [V_A_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_A_2))
% 4.70/4.83 <=> ( V_a_2 = V_b_2
% 4.70/4.83 | c_member(T_a,V_a_2,V_A_2) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__ident,axiom,
% 4.70/4.83 ! [V_B_2,V_A_2,V_x_2,T_a] :
% 4.70/4.83 ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_x_2,V_B_2)
% 4.70/4.83 => ( c_Set_Oinsert(T_a,V_x_2,V_A_2) = c_Set_Oinsert(T_a,V_x_2,V_B_2)
% 4.70/4.83 <=> V_A_2 = V_B_2 ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insertI2,axiom,
% 4.70/4.83 ! [V_b_2,V_B_2,V_a_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_a_2,V_B_2)
% 4.70/4.83 => c_member(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,V_B_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__absorb,axiom,
% 4.70/4.83 ! [V_A_2,V_a_2,T_a] :
% 4.70/4.83 ( c_member(T_a,V_a_2,V_A_2)
% 4.70/4.83 => c_Set_Oinsert(T_a,V_a_2,V_A_2) = V_A_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_singleton__inject,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.83 => V_a_2 = V_b_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_doubleton__eq__iff,axiom,
% 4.70/4.83 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( c_Set_Oinsert(T_a,V_a_2,c_Set_Oinsert(T_a,V_b_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Set_Oinsert(T_a,V_c_2,c_Set_Oinsert(T_a,V_d_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))
% 4.70/4.83 <=> ( ( V_a_2 = V_c_2
% 4.70/4.83 & V_b_2 = V_d_2 )
% 4.70/4.83 | ( V_a_2 = V_d_2
% 4.70/4.83 & V_b_2 = V_c_2 ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_insert__not__empty,axiom,
% 4.70/4.83 ! [V_A_2,V_a_2,T_a] : c_Set_Oinsert(T_a,V_a_2,V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_empty__not__insert,axiom,
% 4.70/4.83 ! [V_A_2,V_a_2,T_a] : c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) != c_Set_Oinsert(T_a,V_a_2,V_A_2) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastAtMost__singleton_H,axiom,
% 4.70/4.83 ! [V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( V_a_2 = V_b_2
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 4.70/4.83 ! [V_c_2,V_b_2,V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = c_Set_Oinsert(T_a,V_c_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))
% 4.70/4.83 <=> ( V_a_2 = V_b_2
% 4.70/4.83 & V_b_2 = V_c_2 ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastAtMost__singleton,axiom,
% 4.70/4.83 ! [V_a_2,T_a] :
% 4.70/4.83 ( class_Orderings_Oorder(T_a)
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_a_2) = c_Set_Oinsert(T_a,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__insert__le,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Finite__Set_Ocard(T_a,V_A_2),c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2))) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastAtMostSuc__conv,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2))
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = c_Set_Oinsert(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_n_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastLessThan__singleton,axiom,
% 4.70/4.83 ! [V_m_2] : c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_m_2)) = c_Set_Oinsert(tc_Nat_Onat,V_m_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 => hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum_Oinsert,axiom,
% 4.70/4.83 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(V_g_2,V_x_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_g_2,V_A_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_setsum__insert,axiom,
% 4.70/4.83 ! [V_f_2,V_a_2,V_Fa_2,T_a,T_b] :
% 4.70/4.83 ( class_Groups_Ocomm__monoid__add(T_b)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_Fa_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_a_2,V_Fa_2)
% 4.70/4.83 => c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,c_Set_Oinsert(T_a,V_a_2,V_Fa_2)) = c_Groups_Oplus__class_Oplus(T_b,hAPP(V_f_2,V_a_2),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b,V_f_2,V_Fa_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__insert__disjoint,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__insert__if,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = c_Finite__Set_Ocard(T_a,V_A_2) )
% 4.70/4.83 & ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(c_Nat_OSuc,c_Finite__Set_Ocard(T_a,V_A_2)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_atLeastLessThanSuc,axiom,
% 4.70/4.83 ! [V_n_2,V_m_2] :
% 4.70/4.83 ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = c_Set_Oinsert(tc_Nat_Onat,V_n_2,c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,V_n_2)) )
% 4.70/4.83 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
% 4.70/4.83 => c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_n_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_the__elem__eq,axiom,
% 4.70/4.83 ! [V_x_2,T_a] : c_Set_Othe__elem(T_a,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_x_2 ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card__Suc__eq,axiom,
% 4.70/4.83 ! [V_k_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ocard(T_a,V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 4.70/4.83 <=> ? [B_b,B_B] :
% 4.70/4.83 ( V_A_2 = c_Set_Oinsert(T_a,B_b,B_B)
% 4.70/4.83 & ~ c_member(T_a,B_b,B_B)
% 4.70/4.83 & c_Finite__Set_Ocard(T_a,B_B) = V_k_2
% 4.70/4.83 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.70/4.83 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_folding__one_Oinsert,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,V_Fa_2,V_f_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_Fa_2)
% 4.70/4.83 => ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( ~ c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))
% 4.70/4.83 => hAPP(V_Fa_2,c_Set_Oinsert(T_a,V_x_2,V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_Fa_2,V_A_2)) ) ) ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(fact_card_Oremove,axiom,
% 4.70/4.83 ! [V_x_2,V_A_2,T_a] :
% 4.70/4.83 ( c_Finite__Set_Ofinite(T_a,V_A_2)
% 4.70/4.83 => ( c_member(T_a,V_x_2,V_A_2)
% 4.70/4.83 => c_Finite__Set_Ocard(T_a,V_A_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Finite__Set_Ocard(T_a,c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool),V_A_2,c_Set_Oinsert(T_a,V_x_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))))) ) ) ).
% 4.70/4.83
% 4.70/4.83 %----Arity declarations (36)
% 4.70/4.83 fof(arity_fun__Orderings_Opreorder,axiom,
% 4.70/4.83 ! [T_2,T_1] :
% 4.70/4.83 ( class_Orderings_Opreorder(T_1)
% 4.70/4.83 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 4.70/4.83 ! [T_1,T_2] :
% 4.70/4.83 ( ( class_Finite__Set_Ofinite(T_2)
% 4.70/4.83 & class_Finite__Set_Ofinite(T_1) )
% 4.70/4.83 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_fun__Orderings_Oorder,axiom,
% 4.70/4.83 ! [T_2,T_1] :
% 4.70/4.83 ( class_Orderings_Oorder(T_1)
% 4.70/4.83 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_fun__Orderings_Otop,axiom,
% 4.70/4.83 ! [T_2,T_1] :
% 4.70/4.83 ( class_Orderings_Otop(T_1)
% 4.70/4.83 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_fun__Orderings_Oord,axiom,
% 4.70/4.83 ! [T_2,T_1] :
% 4.70/4.83 ( class_Orderings_Oord(T_1)
% 4.70/4.83 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_fun__Orderings_Obot,axiom,
% 4.70/4.83 ! [T_2,T_1] :
% 4.70/4.83 ( class_Orderings_Obot(T_1)
% 4.70/4.83 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.70/4.83 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 4.70/4.83 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 4.70/4.83 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 4.70/4.83 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 4.70/4.83 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.70/4.83 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 4.70/4.83 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 4.70/4.83 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 4.70/4.83 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 4.70/4.83 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 4.70/4.83 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 4.70/4.83 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 4.70/4.83 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 4.70/4.83 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 4.70/4.83 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 4.70/4.83 class_Orderings_Oorder(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 4.70/4.83 class_Orderings_Oord(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 4.70/4.83 class_Orderings_Obot(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 4.70/4.83 class_Groups_Ozero(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 4.70/4.83 class_Groups_Oone(tc_Nat_Onat) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 4.70/4.83 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 4.70/4.83 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 4.70/4.83 class_Orderings_Oorder(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 4.70/4.83 class_Orderings_Otop(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 4.70/4.83 class_Orderings_Oord(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 4.70/4.83 class_Orderings_Obot(tc_HOL_Obool) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 4.70/4.83 ! [T_1,T_2] :
% 4.70/4.83 ( ( class_Finite__Set_Ofinite(T_2)
% 4.70/4.83 & class_Finite__Set_Ofinite(T_1) )
% 4.70/4.83 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 4.70/4.83 ! [T_1] :
% 4.70/4.83 ( class_Finite__Set_Ofinite(T_1)
% 4.70/4.83 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 4.70/4.83 ! [T_1,T_2] :
% 4.70/4.83 ( ( class_Finite__Set_Ofinite(T_2)
% 4.70/4.83 & class_Finite__Set_Ofinite(T_1) )
% 4.70/4.83 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 4.70/4.83 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 4.70/4.83
% 4.70/4.83 %----Helper facts (4)
% 4.70/4.83 fof(help_c__fequal__1,axiom,
% 4.70/4.83 ! [V_y_2,V_x_2] :
% 4.70/4.83 ( ~ hBOOL(hAPP(c_fequal(V_x_2),V_y_2))
% 4.70/4.83 | V_x_2 = V_y_2 ) ).
% 4.70/4.83
% 4.70/4.83 fof(help_c__fequal__2,axiom,
% 4.70/4.83 ! [V_y_2,V_x_2] :
% 4.70/4.83 ( V_x_2 != V_y_2
% 4.70/4.83 | hBOOL(hAPP(c_fequal(V_x_2),V_y_2)) ) ).
% 4.70/4.83
% 4.70/4.83 fof(help_c__fFalse__1,axiom,
% 4.70/4.83 ~ hBOOL(c_fFalse) ).
% 4.70/4.83
% 4.70/4.83 fof(help_c__fTrue__1,axiom,
% 4.70/4.83 hBOOL(c_fTrue) ).
% 4.70/4.83
% 4.70/4.83 %----Conjectures (2)
% 4.70/4.83 fof(conj_0,hypothesis,
% 4.70/4.83 ! [B_h] :
% 4.70/4.83 ( c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool)))
% 4.70/4.83 => ( c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi,tc_Nat_Onat,B_h,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_HOL_Obool))))
% 4.70/4.83 => v_thesis____ ) ) ).
% 4.70/4.83
% 4.70/4.83 fof(conj_1,conjecture,
% 4.70/4.83 v_thesis____ ).
% 4.70/4.83
% 4.70/4.83 %------------------------------------------------------------------------------
% 4.70/4.83 %-------------------------------------------
% 4.70/4.83 % Proof found
% 4.70/4.83 % SZS status Theorem for theBenchmark
% 4.70/4.83 % SZS output start Proof
% 4.70/4.84 %ClaNum:1020(EqnAxiom:285)
% 4.70/4.84 %VarNum:4513(SingletonVarNum:1693)
% 4.70/4.84 %MaxLitNum:7
% 4.70/4.84 %MaxfuncDepth:6
% 4.70/4.84 %SharedTerms:73
% 4.70/4.84 %goalClause: 374
% 4.70/4.84 %singleGoalClaCount:1
% 4.70/4.84 [286]P1(a1)
% 4.70/4.84 [287]P2(a32)
% 4.70/4.84 [288]P3(a80)
% 4.70/4.84 [289]P4(a81)
% 4.70/4.84 [290]P5(a81)
% 4.70/4.84 [291]P6(a32)
% 4.70/4.84 [292]P6(a82)
% 4.70/4.84 [293]P26(a32)
% 4.70/4.84 [294]P26(a80)
% 4.70/4.84 [295]P27(a32)
% 4.70/4.84 [296]P27(a80)
% 4.70/4.84 [297]P29(a80)
% 4.70/4.84 [298]P30(a32)
% 4.70/4.84 [299]P30(a80)
% 4.70/4.84 [300]P31(a32)
% 4.70/4.84 [301]P31(a80)
% 4.70/4.84 [302]P15(a80)
% 4.70/4.84 [303]P16(a80)
% 4.70/4.84 [304]P17(a80)
% 4.70/4.84 [305]P18(a80)
% 4.70/4.84 [306]P24(a80)
% 4.70/4.84 [307]P19(a80)
% 4.70/4.84 [308]P20(a80)
% 4.70/4.84 [309]P22(a80)
% 4.70/4.84 [310]P25(a80)
% 4.70/4.84 [311]P32(a80)
% 4.70/4.84 [312]P33(a80)
% 4.70/4.84 [313]P35(a80)
% 4.70/4.84 [314]P36(a80)
% 4.70/4.84 [315]P23(a80)
% 4.70/4.84 [374]~P38(a500)
% 4.70/4.84 [375]~P1(a15)
% 4.70/4.84 [316]E(f2(a80),f9(a80))
% 4.70/4.84 [317]E(f10(a1),f2(a80))
% 4.70/4.84 [318]E(f10(a15),f2(a80))
% 4.70/4.84 [319]E(f11(f2(a80)),f2(a80))
% 4.70/4.84 [321]E(f33(a12,f2(a80)),f3(a80))
% 4.70/4.84 [328]P8(a79,f16(f84(a79,a32)))
% 4.70/4.84 [390]~P8(a80,f16(f84(a80,a32)))
% 4.70/4.84 [329]E(f4(a82,f16(f84(a82,a32))),f3(a80))
% 4.70/4.84 [364]E(f28(a80,a80,a12,f16(f84(a80,a32))),f29(a80,f2(a80)))
% 4.70/4.84 [323]P7(a80,x3231,x3231)
% 4.70/4.84 [360]P10(a80,a80,a12,x3601)
% 4.70/4.84 [385]~P9(a80,x3851,x3851)
% 4.70/4.84 [320]E(f14(a80,x3201),x3201)
% 4.70/4.84 [325]P7(a80,f2(a80),x3251)
% 4.70/4.84 [335]P9(a80,x3351,f33(a12,x3351))
% 4.70/4.84 [337]P9(a80,f2(a80),f33(a12,x3371))
% 4.70/4.84 [377]~E(f33(a12,x3771),x3771)
% 4.70/4.84 [383]~E(f33(a12,x3831),f2(a80))
% 4.70/4.84 [389]~P9(a80,x3891,f2(a80))
% 4.70/4.84 [391]~P7(a80,f33(a12,x3911),x3911)
% 4.70/4.84 [326]E(f8(a80,x3261,f2(a80)),x3261)
% 4.70/4.84 [327]E(f8(a80,f2(a80),x3271),x3271)
% 4.70/4.84 [331]P8(x3311,f9(f84(x3311,a32)))
% 4.70/4.84 [332]E(f8(a80,x3321,f3(a80)),f33(a12,x3321))
% 4.70/4.84 [333]E(f8(a80,f3(a80),x3331),f33(a12,x3331))
% 4.70/4.84 [338]E(f17(a80,x3381,f2(a80)),f9(f84(a80,a32)))
% 4.70/4.84 [386]~E(f16(f84(x3861,a32)),f9(f84(x3861,a32)))
% 4.70/4.84 [334]E(f4(x3341,f9(f84(x3341,a32))),f2(a80))
% 4.70/4.84 [342]E(f8(a80,f11(x3421),f33(a12,f2(a80))),f11(f33(a12,x3421)))
% 4.70/4.84 [349]E(f8(a80,f14(a80,x3491),f33(a12,f2(a80))),f14(a80,f33(a12,x3491)))
% 4.70/4.84 [354]E(f17(a80,x3541,f33(a12,x3541)),f27(a80,x3541,f9(f84(a80,a32))))
% 4.70/4.84 [336]P7(f84(x3361,a32),x3362,x3362)
% 4.70/4.84 [339]E(f8(a80,x3391,x3392),f8(a80,x3392,x3391))
% 4.70/4.84 [343]P8(a80,f17(a80,x3431,x3432))
% 4.70/4.84 [344]P8(a80,f18(a80,x3441,x3442))
% 4.70/4.84 [351]P7(a80,x3511,f8(a80,x3512,x3511))
% 4.70/4.84 [352]P7(a80,x3521,f8(a80,x3521,x3522))
% 4.70/4.84 [397]~P9(a80,f8(a80,x3971,x3972),x3972)
% 4.70/4.84 [398]~P9(a80,f8(a80,x3981,x3982),x3981)
% 4.70/4.84 [341]P14(x3411,x3412,f16(f84(x3411,a32)))
% 4.70/4.84 [345]E(f17(a80,x3451,f33(a12,x3452)),f18(a80,x3451,x3452))
% 4.70/4.84 [346]P7(f84(x3461,a32),x3462,f16(f84(x3461,a32)))
% 4.70/4.84 [347]P7(f84(x3471,a32),f9(f84(x3471,a32)),x3472)
% 4.70/4.84 [350]E(f8(a80,f33(a12,x3501),x3502),f8(a80,x3501,f33(a12,x3502)))
% 4.70/4.84 [356]E(f8(a80,x3561,f33(a12,x3562)),f33(a12,f8(a80,x3561,x3562)))
% 4.70/4.84 [357]E(f8(a80,f33(a12,x3571),x3572),f33(a12,f8(a80,x3571,x3572)))
% 4.70/4.84 [361]P9(a80,x3611,f33(a12,f8(a80,x3612,x3611)))
% 4.70/4.84 [362]P9(a80,x3621,f33(a12,f8(a80,x3621,x3622)))
% 4.70/4.84 [370]E(f28(a80,a80,a12,f17(a80,x3701,x3702)),f17(a80,f33(a12,x3701),f33(a12,x3702)))
% 4.70/4.84 [371]E(f28(a80,a80,a12,f18(a80,x3711,x3712)),f18(a80,f33(a12,x3711),f33(a12,x3712)))
% 4.70/4.84 [395]~P14(x3951,x3952,f9(f84(x3951,a32)))
% 4.70/4.84 [396]~P9(f84(x3961,a32),x3962,f9(f84(x3961,a32)))
% 4.70/4.84 [348]P1(f33(f16(f84(x3481,a32)),x3482))
% 4.70/4.84 [369]E(f31(x3691,x3692,f16(f84(x3691,a32)),f16(f84(x3692,a32))),f16(f84(f85(x3691,x3692),a32)))
% 4.70/4.84 [359]E(f30(x3591,f27(x3591,x3592,f9(f84(x3591,a32)))),x3592)
% 4.70/4.84 [353]P14(x3531,x3532,f27(x3531,x3532,x3533))
% 4.70/4.84 [355]P7(f84(x3551,a32),x3552,f27(x3551,x3553,x3552))
% 4.70/4.84 [358]E(f27(x3581,x3582,f27(x3581,x3582,x3583)),f27(x3581,x3582,x3583))
% 4.70/4.84 [363]P10(x3631,x3632,x3633,f9(f84(x3631,a32)))
% 4.70/4.84 [365]E(f8(a80,x3651,f8(a80,x3652,x3653)),f8(a80,x3652,f8(a80,x3651,x3653)))
% 4.70/4.84 [366]E(f8(a80,f8(a80,x3661,x3662),x3663),f8(a80,x3661,f8(a80,x3662,x3663)))
% 4.70/4.84 [392]~E(f27(x3921,x3922,x3923),f9(f84(x3921,a32)))
% 4.70/4.84 [393]~E(f9(f84(x3931,a32)),f27(x3931,x3932,x3933))
% 4.70/4.84 [368]E(f28(x3681,x3682,x3683,f9(f84(x3681,a32))),f9(f84(x3682,a32)))
% 4.70/4.84 [367]E(f27(x3671,x3672,f27(x3671,x3673,x3674)),f27(x3671,x3673,f27(x3671,x3672,x3674)))
% 4.70/4.84 [372]P14(x3721,f33(x3722,x3723),f28(x3724,x3721,x3722,f16(f84(x3724,a32))))
% 4.70/4.84 [373]E(f28(x3731,x3732,x3733,f27(x3731,x3734,x3735)),f27(x3732,f33(x3733,x3734),f28(x3731,x3732,x3733,x3735)))
% 4.70/4.84 [399]~P6(x3991)+P6(f83(x3991))
% 4.70/4.84 [401]~P36(x4011)+~E(f3(x4011),f2(x4011))
% 4.70/4.84 [423]E(x4231,f2(a80))+P9(a80,f2(a80),x4231)
% 4.70/4.84 [444]~P37(x4441)+P14(x4441,f2(x4441),f13(x4441))
% 4.70/4.84 [445]~P37(x4451)+P14(x4451,f3(x4451),f13(x4451))
% 4.70/4.84 [446]~P32(x4461)+P7(x4461,f2(x4461),f3(x4461))
% 4.70/4.84 [447]~P32(x4471)+P9(x4471,f2(x4471),f3(x4471))
% 4.70/4.84 [475]E(x4751,f2(a80))+~P7(a80,x4751,f2(a80))
% 4.70/4.84 [501]~P32(x5011)+~P7(x5011,f3(x5011),f2(x5011))
% 4.70/4.84 [502]~P32(x5021)+~P9(x5021,f3(x5021),f2(x5021))
% 4.70/4.84 [496]~P9(a80,f2(a80),x4961)+E(f33(a12,f41(x4961)),x4961)
% 4.70/4.84 [536]E(x5361,f2(a80))+~P9(a80,x5361,f33(a12,f2(a80)))
% 4.70/4.84 [648]~P32(x6481)+P9(x6481,f2(x6481),f8(x6481,f3(x6481),f3(x6481)))
% 4.70/4.84 [655]~P8(x6551,f16(f84(x6551,a32)))+P8(f83(x6551),f16(f84(f83(x6551),a32)))
% 4.70/4.84 [670]P8(x6701,f16(f84(x6701,a32)))+~P8(f83(x6701),f16(f84(f83(x6701),a32)))
% 4.70/4.84 [739]~P8(x7391,f16(f84(x7391,a32)))+P9(a80,f2(a80),f4(x7391,f16(f84(x7391,a32))))
% 4.70/4.84 [403]~P6(x4031)+P8(x4031,x4032)
% 4.70/4.84 [421]~E(x4211,x4212)+P7(a80,x4211,x4212)
% 4.70/4.84 [425]~P26(x4251)+P7(x4251,x4252,x4252)
% 4.70/4.84 [467]~E(x4671,x4672)+~P9(a80,x4671,x4672)
% 4.70/4.84 [476]~P9(x4761,x4762,x4762)+~P26(x4761)
% 4.70/4.84 [495]P7(a80,x4952,x4951)+P7(a80,x4951,x4952)
% 4.70/4.84 [543]~P9(a80,x5431,x5432)+P7(a80,x5431,x5432)
% 4.70/4.84 [405]P8(x4051,x4052)+E(f4(x4051,x4052),f2(a80))
% 4.70/4.84 [406]~P2(x4062)+P2(f84(x4061,x4062))
% 4.70/4.84 [407]~P26(x4072)+P26(f84(x4071,x4072))
% 4.70/4.84 [408]~P27(x4082)+P27(f84(x4081,x4082))
% 4.70/4.84 [409]~P30(x4092)+P30(f84(x4091,x4092))
% 4.70/4.84 [410]~P31(x4102)+P31(f84(x4101,x4102))
% 4.70/4.84 [412]E(x4121,x4122)+~E(f33(a12,x4121),f33(a12,x4122))
% 4.70/4.84 [433]~P2(x4331)+P7(x4331,x4332,f16(x4331))
% 4.70/4.84 [434]~P27(x4341)+P7(x4341,f9(x4341),x4342)
% 4.70/4.84 [451]~E(x4511,f33(a12,x4512))+P9(a80,f2(a80),x4511)
% 4.70/4.84 [452]~E(x4521,x4522)+P9(a80,x4521,f33(a12,x4522))
% 4.70/4.84 [460]~E(x4601,f2(a80))+P9(a80,x4601,f33(a12,x4602))
% 4.70/4.84 [469]~E(f8(a80,x4692,x4691),x4692)+E(x4691,f2(a80))
% 4.70/4.84 [470]~P9(a80,x4702,x4701)+~E(x4701,f2(a80))
% 4.70/4.84 [471]E(x4711,f2(a80))+~E(f8(a80,x4712,x4711),f2(a80))
% 4.70/4.84 [472]E(x4721,f2(a80))+~E(f8(a80,x4721,x4722),f2(a80))
% 4.70/4.84 [473]P8(a80,x4731)+P14(a80,f35(x4731,x4732),x4731)
% 4.70/4.84 [474]P8(a80,x4741)+P14(a80,f39(x4741,x4742),x4741)
% 4.70/4.84 [531]P9(a80,x5311,x5312)+P9(a80,x5312,f33(a12,x5311))
% 4.70/4.84 [532]P7(a80,x5321,x5322)+P7(a80,f33(a12,x5322),x5321)
% 4.70/4.84 [544]P8(a80,x5441)+~P7(a80,f39(x5441,x5442),x5442)
% 4.70/4.84 [545]P8(a80,x5451)+~P9(a80,f35(x5451,x5452),x5452)
% 4.70/4.84 [558]P8(x5581,x5582)+~P9(a80,f2(a80),f4(x5581,x5582))
% 4.70/4.84 [578]~P7(a80,x5781,x5782)+P7(a80,x5781,f33(a12,x5782))
% 4.70/4.84 [580]~P7(a80,x5801,x5802)+P9(a80,x5801,f33(a12,x5802))
% 4.70/4.84 [582]~P9(a80,x5821,x5822)+P9(a80,x5821,f33(a12,x5822))
% 4.70/4.84 [585]~P9(a80,x5851,x5852)+P7(a80,f33(a12,x5851),x5852)
% 4.70/4.84 [601]P7(a80,x6011,x6012)+~P9(a80,x6011,f33(a12,x6012))
% 4.70/4.84 [602]P7(a80,x6021,x6022)+~P7(a80,f33(a12,x6021),x6022)
% 4.70/4.84 [605]P9(a80,x6051,x6052)+~P7(a80,f33(a12,x6051),x6052)
% 4.70/4.84 [606]P9(a80,x6061,x6062)+~P9(a80,f33(a12,x6061),x6062)
% 4.70/4.84 [639]~P7(a80,x6391,x6392)+P7(a80,f33(a12,x6391),f33(a12,x6392))
% 4.70/4.84 [641]~P9(a80,x6411,x6412)+P9(a80,f33(a12,x6411),f33(a12,x6412))
% 4.70/4.84 [660]~P9(a80,x6601,x6602)+~P9(a80,x6602,f33(a12,x6601))
% 4.70/4.84 [661]~P7(a80,x6611,x6612)+~P7(a80,f33(a12,x6612),x6611)
% 4.70/4.84 [664]P7(a80,x6641,x6642)+~P7(a80,f33(a12,x6641),f33(a12,x6642))
% 4.70/4.84 [666]P9(a80,x6661,x6662)+~P9(a80,f33(a12,x6661),f33(a12,x6662))
% 4.70/4.84 [416]~E(x4161,x4162)+P1(f33(f34(x4161),x4162))
% 4.70/4.84 [424]E(f4(x4241,x4242),f2(a80))+~E(x4242,f9(f84(x4241,a32)))
% 4.70/4.84 [435]~P19(x4351)+E(f8(x4351,x4352,f2(x4351)),x4352)
% 4.70/4.84 [436]~P20(x4361)+E(f8(x4361,x4362,f2(x4361)),x4362)
% 4.70/4.84 [437]~P33(x4371)+E(f8(x4371,x4372,f2(x4371)),x4372)
% 4.70/4.84 [438]~P19(x4381)+E(f8(x4381,f2(x4381),x4382),x4382)
% 4.70/4.84 [439]~P20(x4391)+E(f8(x4391,f2(x4391),x4392),x4392)
% 4.70/4.84 [440]~P33(x4401)+E(f8(x4401,f2(x4401),x4402),x4402)
% 4.70/4.84 [441]E(x4411,x4412)+~P1(f33(f34(x4411),x4412))
% 4.70/4.84 [497]P14(x4972,f42(x4971,x4972),x4971)+E(x4971,f9(f84(x4972,a32)))
% 4.70/4.84 [498]P14(x4982,f43(x4981,x4982),x4981)+E(x4981,f9(f84(x4982,a32)))
% 4.70/4.84 [525]E(x5251,x5252)+~E(f33(x5251,f44(x5252,x5251)),f33(x5252,f44(x5252,x5251)))
% 4.70/4.84 [574]P7(a80,x5741,x5742)+E(f17(a80,x5741,f33(a12,x5742)),f9(f84(a80,a32)))
% 4.70/4.84 [592]~P7(a80,x5921,x5922)+E(f8(a80,x5921,f52(x5922,x5921)),x5922)
% 4.70/4.84 [607]~P9(a80,f2(a80),f4(x6072,x6071))+~E(x6071,f9(f84(x6072,a32)))
% 4.70/4.84 [633]~P32(x6331)+P9(x6331,x6332,f8(x6331,x6332,f3(x6331)))
% 4.70/4.84 [677]~P7(f84(x6772,a32),x6771,f9(f84(x6772,a32)))+E(x6771,f9(f84(x6772,a32)))
% 4.70/4.84 [763]~P7(a80,x7632,x7631)+E(f27(a80,x7631,f17(a80,x7632,x7631)),f17(a80,x7632,f33(a12,x7631)))
% 4.70/4.84 [829]~P7(a80,x8292,f33(a12,x8291))+E(f27(a80,f33(a12,x8291),f18(a80,x8292,x8291)),f18(a80,x8292,f33(a12,x8291)))
% 4.70/4.84 [595]~P31(x5951)+E(f18(x5951,x5952,x5952),f27(x5951,x5952,f9(f84(x5951,a32))))
% 4.70/4.84 [715]~P9(a80,x7151,x7152)+E(f33(a12,f8(a80,x7151,f56(x7152,x7151))),x7152)
% 4.70/4.84 [826]P8(x8261,f16(f84(x8261,a32)))+~P8(f84(x8262,x8261),f16(f84(f84(x8262,x8261),a32)))
% 4.70/4.84 [827]P8(x8271,f16(f84(x8271,a32)))+~P8(f85(x8272,x8271),f16(f84(f85(x8272,x8271),a32)))
% 4.70/4.84 [828]P8(x8281,f16(f84(x8281,a32)))+~P8(f85(x8281,x8282),f16(f84(f85(x8281,x8282),a32)))
% 4.70/4.84 [948]~P7(f84(a80,a32),x9482,f17(a80,x9481,f8(a80,x9481,f4(a80,x9482))))+E(f17(a80,x9481,f8(a80,x9481,f4(a80,x9482))),x9482)
% 4.70/4.84 [919]~E(f33(x9191,f2(a80)),f2(a80))+E(f5(a80,a80,x9191,f18(a80,f33(a12,f2(a80)),x9192)),f5(a80,a80,x9191,f18(a80,f2(a80),x9192)))
% 4.70/4.84 [427]~E(x4272,x4273)+P14(x4271,x4272,f34(x4273))
% 4.70/4.84 [453]~E(x4533,x4532)+P7(f84(x4531,a32),x4532,x4533)
% 4.70/4.84 [459]~E(x4592,x4593)+P7(f84(x4591,a32),x4592,x4593)
% 4.70/4.84 [486]E(x4861,x4862)+~P14(x4863,x4861,f34(x4862))
% 4.70/4.84 [492]P14(x4921,x4922,x4923)+~P1(f33(x4923,x4922))
% 4.70/4.84 [505]~P33(x5051)+E(f8(x5051,x5052,x5053),f8(x5051,x5053,x5052))
% 4.70/4.84 [506]~P14(x5063,x5062,x5061)+P1(f33(x5061,x5062))
% 4.70/4.84 [523]~E(x5231,x5232)+~P9(f84(x5233,a32),x5231,x5232)
% 4.70/4.84 [546]P7(a80,x5461,x5462)+~E(x5462,f8(a80,x5461,x5463))
% 4.70/4.84 [552]~P14(x5521,x5522,x5523)+E(f27(x5521,x5522,x5523),x5523)
% 4.70/4.84 [560]~P8(x5601,x5603)+P8(x5601,f27(x5601,x5602,x5603))
% 4.70/4.84 [596]E(x5961,x5962)+~E(f8(a80,x5963,x5961),f8(a80,x5963,x5962))
% 4.70/4.84 [597]E(x5971,x5972)+~E(f8(a80,x5971,x5973),f8(a80,x5972,x5973))
% 4.70/4.84 [651]~P9(f84(x6511,a32),x6512,x6513)+P7(f84(x6511,a32),x6512,x6513)
% 4.70/4.84 [662]P8(x6621,x6622)+~P8(x6621,f27(x6621,x6623,x6622))
% 4.70/4.84 [691]~P7(a80,x6911,x6913)+P7(a80,x6911,f8(a80,x6912,x6913))
% 4.70/4.84 [693]~P7(a80,x6931,x6932)+P7(a80,x6931,f8(a80,x6932,x6933))
% 4.70/4.84 [695]~P9(a80,x6951,x6953)+P9(a80,x6951,f8(a80,x6952,x6953))
% 4.70/4.84 [697]~P9(a80,x6971,x6972)+P9(a80,x6971,f8(a80,x6972,x6973))
% 4.70/4.84 [750]P7(a80,x7501,x7502)+~P7(a80,f8(a80,x7503,x7501),x7502)
% 4.70/4.84 [751]P7(a80,x7511,x7512)+~P7(a80,f8(a80,x7511,x7513),x7512)
% 4.70/4.84 [752]P9(a80,x7521,x7522)+~P9(a80,f8(a80,x7521,x7523),x7522)
% 4.70/4.84 [789]~P7(a80,x7892,x7893)+P7(a80,f8(a80,x7891,x7892),f8(a80,x7891,x7893))
% 4.70/4.84 [790]~P7(a80,x7901,x7903)+P7(a80,f8(a80,x7901,x7902),f8(a80,x7903,x7902))
% 4.70/4.84 [791]~P9(a80,x7912,x7913)+P9(a80,f8(a80,x7911,x7912),f8(a80,x7911,x7913))
% 4.70/4.84 [792]~P9(a80,x7921,x7923)+P9(a80,f8(a80,x7921,x7922),f8(a80,x7923,x7922))
% 4.70/4.84 [861]P7(a80,x8611,x8612)+~P7(a80,f8(a80,x8613,x8611),f8(a80,x8613,x8612))
% 4.70/4.84 [862]P9(a80,x8621,x8622)+~P9(a80,f8(a80,x8623,x8621),f8(a80,x8623,x8622))
% 4.70/4.84 [863]~P14(x8631,f72(x8633,x8632,x8631),f71(x8633,x8632,x8631))+~E(f4(x8631,x8632),f33(a12,x8633))
% 4.70/4.84 [535]~P14(x5352,x5353,x5351)+~E(x5351,f9(f84(x5352,a32)))
% 4.70/4.84 [591]~E(f4(x5911,x5913),f33(a12,x5912))+E(f4(x5911,f71(x5912,x5913,x5911)),x5912)
% 4.70/4.84 [689]P9(a80,x6891,x6892)+~E(x6892,f33(a12,f8(a80,x6891,x6893)))
% 4.70/4.84 [759]~E(f4(x7591,x7593),f33(a12,x7592))+E(f27(x7591,f72(x7592,x7593,x7591),f71(x7592,x7593,x7591)),x7593)
% 4.70/4.84 [788]~P8(x7881,x7882)+P7(a80,f4(x7881,x7882),f4(x7881,f27(x7881,x7883,x7882)))
% 4.70/4.84 [461]~P2(x4612)+E(f33(f16(f84(x4611,x4612)),x4613),f16(x4612))
% 4.70/4.84 [462]~P27(x4622)+E(f33(f9(f84(x4621,x4622)),x4623),f9(x4622))
% 4.70/4.84 [758]~P19(x7582)+E(f5(x7581,x7582,x7583,f9(f84(x7581,a32))),f2(x7582))
% 4.70/4.84 [787]E(x7871,x7872)+~E(f27(x7873,x7871,f9(f84(x7873,a32))),f27(x7873,x7872,f9(f84(x7873,a32))))
% 4.70/4.84 [847]E(x8471,x8472)+~P14(x8473,x8471,f27(x8473,x8472,f9(f84(x8473,a32))))
% 4.70/4.84 [594]~E(x5942,x5943)+P14(x5941,x5942,f27(x5941,x5943,x5944))
% 4.70/4.84 [710]~P14(x7101,x7102,x7104)+P14(x7101,x7102,f27(x7101,x7103,x7104))
% 4.70/4.84 [756]~P7(f84(x7561,a32),x7562,x7564)+P7(f84(x7561,a32),x7562,f27(x7561,x7563,x7564))
% 4.70/4.84 [793]P14(x7931,x7932,x7933)+~P7(f84(x7931,a32),f27(x7931,x7932,x7934),x7933)
% 4.70/4.84 [825]~P7(f84(x8251,a32),f27(x8251,x8254,x8252),x8253)+P7(f84(x8251,a32),x8252,x8253)
% 4.70/4.84 [841]~P7(f84(x8411,a32),x8413,x8414)+P7(f84(x8411,a32),f27(x8411,x8412,x8413),f27(x8411,x8412,x8414))
% 4.70/4.84 [880]~P8(x8802,x8804)+P8(x8801,f28(x8802,x8801,x8803,x8804))
% 4.70/4.84 [920]P10(x9201,x9202,x9203,x9204)+P14(x9201,f59(x9204,x9203,x9202,x9201),x9204)
% 4.70/4.84 [921]P10(x9211,x9212,x9213,x9214)+P14(x9211,f70(x9214,x9213,x9212,x9211),x9214)
% 4.70/4.84 [933]P8(x9331,x9332)+~P8(f85(x9333,x9331),f31(x9333,x9331,x9334,x9332))
% 4.70/4.84 [934]P8(x9341,x9342)+~P8(f85(x9341,x9343),f31(x9341,x9343,x9342,x9344))
% 4.70/4.84 [947]P14(x9471,f61(x9472,x9473,x9474,x9471),x9473)+~E(f5(x9471,a80,x9474,x9473),f33(a12,x9472))
% 4.70/4.84 [954]P10(x9541,x9542,x9543,x9544)+~E(f70(x9544,x9543,x9542,x9541),f59(x9544,x9543,x9542,x9541))
% 4.70/4.84 [983]~P10(x9832,x9831,x9834,x9833)+P10(x9831,x9832,f6(x9832,x9831,x9833,x9834),f28(x9832,x9831,x9834,x9833))
% 4.70/4.84 [524]~P11(x5243,x5241,x5244)+E(f33(f33(x5241,x5242),x5242),x5242)
% 4.70/4.84 [707]~E(x7072,x7074)+P1(f33(f27(x7071,x7072,x7073),x7074))
% 4.70/4.84 [740]P14(x7401,x7402,f19(x7401,x7403,x7404))+~P1(f33(f33(x7403,x7404),x7402))
% 4.70/4.84 [741]P14(x7411,x7412,f20(x7411,x7413,x7414))+~P1(f33(f33(x7413,x7414),x7412))
% 4.70/4.84 [742]P14(x7421,x7422,f21(x7421,x7423,x7424))+~P1(f33(f33(x7423,x7422),x7424))
% 4.70/4.84 [743]P14(x7431,x7432,f24(x7431,x7433,x7434))+~P1(f33(f33(x7433,x7432),x7434))
% 4.70/4.84 [744]~P1(f33(x7443,x7444))+P1(f33(f27(x7441,x7442,x7443),x7444))
% 4.70/4.84 [765]~E(x7654,f9(f84(x7651,a32)))+E(f28(x7651,x7652,x7653,x7654),f9(f84(x7652,a32)))
% 4.70/4.84 [773]~P33(x7731)+E(f8(x7731,x7732,f8(x7731,x7733,x7734)),f8(x7731,x7733,f8(x7731,x7732,x7734)))
% 4.70/4.84 [775]~P15(x7751)+E(f8(x7751,f8(x7751,x7752,x7753),x7754),f8(x7751,x7752,f8(x7751,x7753,x7754)))
% 4.70/4.84 [776]~P33(x7761)+E(f8(x7761,f8(x7761,x7762,x7763),x7764),f8(x7761,x7762,f8(x7761,x7763,x7764)))
% 4.70/4.84 [777]~P33(x7771)+E(f8(x7771,f8(x7771,x7772,x7773),x7774),f8(x7771,f8(x7771,x7772,x7774),x7773))
% 4.70/4.84 [783]~P14(x7834,x7833,f19(x7834,x7831,x7832))+P1(f33(f33(x7831,x7832),x7833))
% 4.70/4.84 [784]~P14(x7844,x7843,f20(x7844,x7841,x7842))+P1(f33(f33(x7841,x7842),x7843))
% 4.70/4.84 [785]~P14(x7854,x7852,f21(x7854,x7851,x7853))+P1(f33(f33(x7851,x7852),x7853))
% 4.70/4.84 [786]~P14(x7864,x7862,f24(x7864,x7861,x7863))+P1(f33(f33(x7861,x7862),x7863))
% 4.70/4.84 [860]~E(f28(x8602,x8603,x8604,x8601),f9(f84(x8603,a32)))+E(x8601,f9(f84(x8602,a32)))
% 4.70/4.84 [886]P8(x8862,x8864)+E(f4(f85(x8861,x8862),f31(x8861,x8862,x8863,x8864)),f2(a80))
% 4.70/4.84 [887]P8(x8871,x8873)+E(f4(f85(x8871,x8872),f31(x8871,x8872,x8873,x8874)),f2(a80))
% 4.70/4.84 [937]~P10(x9372,x9371,x9373,x9374)+E(f4(x9371,f28(x9372,x9371,x9373,x9374)),f4(x9372,x9374))
% 4.70/4.84 [958]~P10(x9581,x9582,x9583,f16(f84(x9581,a32)))+E(f33(f6(x9581,x9582,f16(f84(x9581,a32)),x9583),f33(x9583,x9584)),x9584)
% 4.70/4.84 [959]~P8(x9592,x9594)+P7(a80,f4(x9591,f28(x9592,x9591,x9593,x9594)),f4(x9592,x9594))
% 4.70/4.84 [970]P10(x9704,x9703,x9701,x9702)+E(f33(x9701,f70(x9702,x9701,x9703,x9704)),f33(x9701,f59(x9702,x9701,x9703,x9704)))
% 4.70/4.84 [980]~E(f5(x9804,a80,x9801,x9803),f33(a12,x9802))+P9(a80,f2(a80),f33(x9801,f61(x9802,x9803,x9801,x9804)))
% 4.70/4.84 [984]~P10(x9842,x9841,x9844,x9843)+E(f28(x9841,x9842,f6(x9842,x9841,x9843,x9844),f28(x9842,x9841,x9844,x9843)),x9843)
% 4.70/4.84 [992]~P10(x9921,x9922,x9923,x9924)+~P9(a80,f4(x9922,f28(x9921,x9922,x9923,x9924)),f4(x9921,x9924))
% 4.70/4.84 [883]E(x8831,f9(f84(x8832,a32)))+~E(f31(x8833,x8832,x8834,x8831),f9(f84(f85(x8833,x8832),a32)))
% 4.70/4.84 [884]E(x8841,f9(f84(x8842,a32)))+~E(f31(x8842,x8843,x8841,x8844),f9(f84(f85(x8842,x8843),a32)))
% 4.70/4.84 [912]~P14(x9124,x9123,x9125)+P14(x9121,f33(x9122,x9123),f28(x9124,x9121,x9122,x9125))
% 4.70/4.84 [965]~P7(f84(x9652,a32),x9654,x9655)+P7(f84(x9651,a32),f28(x9652,x9651,x9653,x9654),f28(x9652,x9651,x9653,x9655))
% 4.70/4.84 [976]P14(x9761,f45(x9762,x9763,x9761,x9764),x9762)+~P14(x9765,x9764,f28(x9761,x9765,x9763,x9762))
% 4.70/4.84 [1002]~P7(f84(x10025,a32),x10024,f28(x10021,x10025,x10023,x10022))+P7(f84(x10021,a32),f46(x10022,x10023,x10021,x10024,x10025),x10022)
% 4.70/4.84 [885]~P33(x8851)+E(f8(x8851,f8(x8851,x8852,x8853),f8(x8851,x8854,x8855)),f8(x8851,f8(x8851,x8852,x8854),f8(x8851,x8853,x8855)))
% 4.70/4.84 [936]~P14(x9364,x9363,x9365)+E(f27(x9361,f33(x9362,x9363),f28(x9364,x9361,x9362,x9365)),f28(x9364,x9361,x9362,x9365))
% 4.70/4.84 [942]~P14(x9424,x9423,f22(x9424,x9421,x9422,x9425))+P1(f33(f33(x9421,x9422),x9423))
% 4.70/4.84 [943]~P14(x9434,x9433,f25(x9434,x9431,x9432,x9435))+P1(f33(f33(x9431,x9432),x9433))
% 4.70/4.84 [944]~P14(x9444,x9442,f22(x9444,x9441,x9445,x9443))+P1(f33(f33(x9441,x9442),x9443))
% 4.70/4.84 [945]~P14(x9454,x9452,f25(x9454,x9451,x9455,x9453))+P1(f33(f33(x9451,x9452),x9453))
% 4.70/4.84 [975]~P14(x9755,x9754,f28(x9753,x9755,x9751,x9752))+E(f33(x9751,f45(x9752,x9751,x9753,x9754)),x9754)
% 4.70/4.84 [1003]~P7(f84(x10032,a32),x10035,f28(x10031,x10032,x10033,x10034))+E(f28(x10031,x10032,x10033,f46(x10034,x10033,x10031,x10035,x10032)),x10035)
% 4.70/4.84 [914]~E(x9142,f33(x9144,x9145))+P14(x9141,x9142,f28(x9143,x9141,x9144,f16(f84(x9143,a32))))
% 4.70/4.84 [1006]~P14(x10064,x10063,f26(x10064,x10065,x10061,x10062,x10066))+P1(f33(f33(x10061,x10062),x10063))
% 4.70/4.84 [1007]~P14(x10074,x10073,f23(x10074,x10071,x10075,x10072,x10076))+P1(f33(f33(x10071,x10072),x10073))
% 4.70/4.84 [1008]~P14(x10084,x10082,f26(x10084,x10081,x10085,x10086,x10083))+P1(f33(f33(x10081,x10082),x10083))
% 4.70/4.84 [1009]~P14(x10094,x10092,f23(x10094,x10095,x10091,x10096,x10093))+P1(f33(f33(x10091,x10092),x10093))
% 4.70/4.84 [1010]~P13(x10103,x10104,x10101,x10105,x10106,x10107)+E(f33(f33(x10101,x10102),x10102),x10102)
% 4.70/4.84 [963]P38(a500)+~P10(a79,a80,x9631,f16(f84(a79,a32)))+~E(f28(a79,a80,x9631,f16(f84(a79,a32))),f17(a80,f2(a80),f4(a79,f16(f84(a79,a32)))))
% 4.70/4.84 [500]E(x5001,x5002)+P9(a80,x5002,x5001)+P9(a80,x5001,x5002)
% 4.70/4.84 [549]E(x5491,x5492)+P9(a80,x5491,x5492)+~P7(a80,x5491,x5492)
% 4.70/4.84 [598]E(x5981,x5982)+~P7(a80,x5982,x5981)+~P7(a80,x5981,x5982)
% 4.70/4.84 [413]~P6(x4132)+~P6(x4131)+P6(f84(x4131,x4132))
% 4.70/4.84 [414]~P6(x4142)+~P6(x4141)+P6(f85(x4141,x4142))
% 4.70/4.84 [415]~P6(x4152)+~P6(x4151)+P6(f86(x4151,x4152))
% 4.70/4.84 [417]~P8(x4171,x4172)+E(f4(x4171,x4172),f2(a80))+~E(f3(a80),f2(a80))
% 4.70/4.84 [432]~E(x4322,f2(a80))+~E(x4321,f2(a80))+E(f8(a80,x4321,x4322),f2(a80))
% 4.70/4.84 [449]~P21(x4491)+~E(x4492,f2(x4491))+E(f8(x4491,x4492,x4492),f2(x4491))
% 4.70/4.84 [494]~P21(x4942)+~E(f8(x4942,x4941,x4941),f2(x4942))+E(x4941,f2(x4942))
% 4.70/4.84 [521]~P8(x5211,x5212)+P14(x5211,f49(x5212,x5211),x5212)+E(f4(x5211,x5212),f2(a80))
% 4.70/4.84 [588]~P14(a80,x5881,x5882)+~P8(a80,x5882)+P7(a80,x5881,f40(x5882))
% 4.70/4.84 [589]~P14(a80,x5891,x5892)+~P8(a80,x5892)+P9(a80,x5891,f36(x5892))
% 4.70/4.84 [608]~P9(a80,x6081,x6082)+E(f33(a12,x6081),x6082)+P9(a80,f33(a12,x6081),x6082)
% 4.70/4.84 [617]E(x6171,x6172)+P9(a80,x6171,x6172)+~P9(a80,x6171,f33(a12,x6172))
% 4.70/4.84 [644]P7(a80,x6441,x6442)+E(x6441,f33(a12,x6442))+~P7(a80,x6441,f33(a12,x6442))
% 4.70/4.84 [658]P9(a80,f50(x6582,x6581),x6582)+~P9(a80,x6581,f33(a12,x6582))+E(x6581,f2(a80))
% 4.70/4.84 [663]E(x6631,x6632)+~P7(a80,x6632,x6631)+~P9(a80,x6631,f33(a12,x6632))
% 4.70/4.84 [728]~P21(x7281)+~P7(x7281,f2(x7281),x7282)+P7(x7281,f2(x7281),f8(x7281,x7282,x7282))
% 4.70/4.84 [729]~P21(x7291)+~P9(x7291,f2(x7291),x7292)+P9(x7291,f2(x7291),f8(x7291,x7292,x7292))
% 4.70/4.84 [730]~P21(x7301)+~P7(x7301,x7302,f2(x7301))+P7(x7301,f8(x7301,x7302,x7302),f2(x7301))
% 4.70/4.84 [731]~P21(x7311)+~P9(x7311,x7312,f2(x7311))+P9(x7311,f8(x7311,x7312,x7312),f2(x7311))
% 4.70/4.84 [732]~P34(x7321)+~P9(x7321,x7322,f2(x7321))+P9(x7321,f8(x7321,x7322,x7322),f2(x7321))
% 4.70/4.84 [778]~P21(x7781)+~P7(x7781,f8(x7781,x7782,x7782),f2(x7781))+P7(x7781,x7782,f2(x7781))
% 4.70/4.84 [779]~P21(x7791)+~P9(x7791,f8(x7791,x7792,x7792),f2(x7791))+P9(x7791,x7792,f2(x7791))
% 4.70/4.84 [780]~P34(x7801)+~P9(x7801,f8(x7801,x7802,x7802),f2(x7801))+P9(x7801,x7802,f2(x7801))
% 4.70/4.84 [781]~P21(x7811)+~P7(x7811,f2(x7811),f8(x7811,x7812,x7812))+P7(x7811,f2(x7811),x7812)
% 4.70/4.84 [782]~P21(x7821)+~P9(x7821,f2(x7821),f8(x7821,x7822,x7822))+P9(x7821,f2(x7821),x7822)
% 4.70/4.84 [813]P9(a80,f2(a80),x8131)+P9(a80,f2(a80),x8132)+~P9(a80,f2(a80),f8(a80,x8132,x8131))
% 4.70/4.84 [450]~P8(x4502,x4501)+~E(f4(x4502,x4501),f2(a80))+E(x4501,f9(f84(x4502,a32)))
% 4.70/4.84 [490]~E(x4902,f2(a80))+~E(x4901,f33(a12,f2(a80)))+E(f8(a80,x4901,x4902),f33(a12,f2(a80)))
% 4.70/4.84 [491]~E(x4911,f2(a80))+~E(x4912,f33(a12,f2(a80)))+E(f8(a80,x4911,x4912),f33(a12,f2(a80)))
% 4.70/4.84 [504]E(x5041,f2(a80))+E(x5042,f2(a80))+~E(f8(a80,x5042,x5041),f33(a12,f2(a80)))
% 4.70/4.84 [528]E(x5281,f2(a80))+E(x5281,f33(a12,f2(a80)))+~E(f8(a80,x5282,x5281),f33(a12,f2(a80)))
% 4.70/4.84 [529]E(x5291,f2(a80))+E(x5291,f33(a12,f2(a80)))+~E(f8(a80,x5291,x5292),f33(a12,f2(a80)))
% 4.70/4.84 [538]~P8(x5382,x5381)+P9(a80,f2(a80),f4(x5382,x5381))+E(x5381,f9(f84(x5382,a32)))
% 4.70/4.84 [551]E(x5511,f33(a12,f2(a80)))+E(x5512,f33(a12,f2(a80)))+~E(f8(a80,x5511,x5512),f33(a12,f2(a80)))
% 4.70/4.84 [586]~P9(a80,x5861,f33(a12,x5862))+E(x5861,f2(a80))+E(f33(a12,f50(x5862,x5861)),x5861)
% 4.70/4.84 [590]P9(a80,f51(x5902,x5901),x5902)+~P1(f33(x5901,x5902))+P1(f33(x5901,f2(a80)))
% 4.70/4.84 [717]E(x7171,f16(f84(x7172,a32)))+~P8(x7172,f16(f84(x7172,a32)))+~E(f4(x7172,x7171),f4(x7172,f16(f84(x7172,a32))))
% 4.70/4.84 [831]~P28(x8311)+~P14(x8311,x8312,f13(x8311))+~E(f8(x8311,f8(x8311,f3(x8311),x8312),x8312),f2(x8311))
% 4.70/4.84 [839]~P8(x8392,f16(f84(x8392,a32)))+~P8(x8391,f16(f84(x8391,a32)))+P8(f85(x8391,x8392),f16(f84(f85(x8391,x8392),a32)))
% 4.70/4.84 [840]~P8(x8402,f16(f84(x8402,a32)))+~P8(x8401,f16(f84(x8401,a32)))+P8(f86(x8401,x8402),f16(f84(f86(x8401,x8402),a32)))
% 4.70/4.84 [852]~P1(f33(x8521,x8522))+P1(f33(x8521,f2(a80)))+P1(f33(x8521,f8(a80,f51(x8522,x8521),f3(a80))))
% 4.70/4.84 [858]P8(x8582,f16(f84(x8582,a32)))+E(f4(x8581,f16(f84(x8581,a32))),f33(a12,f2(a80)))+~P8(f84(x8582,x8581),f16(f84(f84(x8582,x8581),a32)))
% 4.70/4.84 [935]~P10(x9351,x9351,x9352,f16(f84(x9351,a32)))+~P8(x9351,f16(f84(x9351,a32)))+E(f28(x9351,x9351,x9352,f16(f84(x9351,a32))),f16(f84(x9351,a32)))
% 4.70/4.84 [938]P10(x9381,x9381,x9382,f16(f84(x9381,a32)))+~P8(x9381,f16(f84(x9381,a32)))+~E(f28(x9381,x9381,x9382,f16(f84(x9381,a32))),f16(f84(x9381,a32)))
% 4.70/4.84 [429]~E(x4292,x4293)+~P26(x4291)+P7(x4291,x4292,x4293)
% 4.70/4.84 [431]~E(x4312,x4313)+~P31(x4311)+P7(x4311,x4312,x4313)
% 4.70/4.84 [483]~P9(x4833,x4831,x4832)+~E(x4831,x4832)+~P29(x4833)
% 4.70/4.84 [484]~P9(x4843,x4841,x4842)+~E(x4841,x4842)+~P31(x4843)
% 4.70/4.84 [508]P7(x5081,x5083,x5082)+~P29(x5081)+P7(x5081,x5082,x5083)
% 4.70/4.84 [513]P9(x5131,x5133,x5132)+~P29(x5131)+P7(x5131,x5132,x5133)
% 4.70/4.84 [562]~P26(x5621)+~P9(x5621,x5622,x5623)+P7(x5621,x5622,x5623)
% 4.70/4.84 [564]~P31(x5641)+~P9(x5641,x5642,x5643)+P7(x5641,x5642,x5643)
% 4.70/4.84 [618]~P9(x6181,x6183,x6182)+~P26(x6181)+~P7(x6181,x6182,x6183)
% 4.70/4.84 [622]~P9(x6221,x6223,x6222)+~P26(x6221)+~P9(x6221,x6222,x6223)
% 4.70/4.84 [625]~P9(x6251,x6253,x6252)+~P29(x6251)+~P7(x6251,x6252,x6253)
% 4.70/4.84 [626]~P9(x6261,x6263,x6262)+~P29(x6261)+~P9(x6261,x6262,x6263)
% 4.70/4.84 [627]~P9(x6271,x6273,x6272)+~P31(x6271)+~P9(x6271,x6272,x6273)
% 4.70/4.84 [671]~P7(a80,x6711,x6713)+P7(a80,x6711,x6712)+~P7(a80,x6713,x6712)
% 4.70/4.84 [418]~P29(x4183)+E(x4181,x4182)+~E(f29(x4183,x4181),f29(x4183,x4182))
% 4.70/4.84 [442]~P35(x4421)+~E(x4423,f2(x4421))+E(f8(x4421,x4422,x4423),x4422)
% 4.70/4.84 [487]~P35(x4872)+~E(f8(x4872,x4873,x4871),x4873)+E(x4871,f2(x4872))
% 4.70/4.84 [576]P8(x5761,x5762)+~P8(x5761,x5763)+~P7(f84(x5761,a32),x5762,x5763)
% 4.70/4.84 [610]~P30(x6101)+~P9(x6101,x6103,x6102)+P14(x6101,x6102,f29(x6101,x6103))
% 4.70/4.84 [634]~P9(a80,x6343,x6342)+~E(x6341,f33(a12,x6343))+P9(a80,x6341,f33(a12,x6342))
% 4.70/4.84 [645]~P30(x6451)+P9(x6451,x6452,x6453)+~P14(x6451,x6453,f29(x6451,x6452))
% 4.70/4.84 [657]E(x6571,x6572)+~P7(f84(x6573,a32),x6571,x6572)+P9(f84(x6573,a32),x6571,x6572)
% 4.70/4.84 [676]~P29(x6761)+~P7(x6761,x6763,x6762)+P7(f84(x6761,a32),f29(x6761,x6762),f29(x6761,x6763))
% 4.70/4.84 [704]~P9(a80,x7041,x7043)+~P9(a80,x7043,x7042)+P9(a80,f33(a12,x7041),x7042)
% 4.70/4.84 [706]E(x7061,x7062)+~P7(f84(x7063,a32),x7061,x7062)+~P7(f84(x7063,a32),x7062,x7061)
% 4.70/4.84 [713]~P8(x7131,x7133)+~P7(f84(x7131,a32),x7132,x7133)+P7(a80,f4(x7131,x7132),f4(x7131,x7133))
% 4.70/4.84 [714]~P8(x7141,x7143)+~P9(f84(x7141,a32),x7142,x7143)+P9(a80,f4(x7141,x7142),f4(x7141,x7143))
% 4.70/4.84 [726]~P29(x7261)+P7(x7261,x7262,x7263)+~P7(f84(x7261,a32),f29(x7261,x7263),f29(x7261,x7262))
% 4.70/4.84 [851]~P8(x8511,x8513)+P14(x8511,f57(x8512,x8513,x8511),x8513)+E(f5(x8511,a80,x8512,x8513),f2(a80))
% 4.70/4.84 [892]~P8(x8921,x8923)+P14(x8921,f68(x8922,x8923,x8921),x8923)+~E(f5(x8921,a80,x8922,x8923),f3(a80))
% 4.70/4.84 [962]~P8(x9621,x9623)+P10(x9621,x9621,x9622,x9623)+~P7(f84(x9621,a32),x9623,f28(x9621,x9621,x9622,x9623))
% 4.70/4.84 [530]~E(f4(x5303,x5302),f33(a12,x5301))+~E(x5301,f2(a80))+E(f71(x5301,x5302,x5303),f9(f84(x5303,a32)))
% 4.70/4.84 [553]P9(x5531,x5532,x5533)+~P31(x5531)+E(f17(x5531,x5532,x5533),f9(f84(x5531,a32)))
% 4.70/4.84 [554]P7(x5541,x5542,x5543)+~P31(x5541)+E(f18(x5541,x5542,x5543),f9(f84(x5541,a32)))
% 4.70/4.84 [555]P9(x5551,x5552,x5553)+~P31(x5551)+E(f9(f84(x5551,a32)),f17(x5551,x5552,x5553))
% 4.70/4.84 [556]P7(x5561,x5562,x5563)+~P31(x5561)+E(f9(f84(x5561,a32)),f18(x5561,x5562,x5563))
% 4.70/4.84 [611]~P31(x6111)+~P7(x6111,x6113,x6112)+E(f17(x6111,x6112,x6113),f9(f84(x6111,a32)))
% 4.70/4.84 [612]~P31(x6121)+~P9(x6121,x6123,x6122)+E(f18(x6121,x6122,x6123),f9(f84(x6121,a32)))
% 4.70/4.84 [667]~P9(a80,x6673,x6672)+~P1(f33(x6671,x6673))+P1(f33(x6671,f37(x6671,x6672)))
% 4.70/4.84 [668]~P7(a80,x6683,x6682)+~P1(f33(x6681,x6683))+P1(f33(x6681,f55(x6681,x6682)))
% 4.70/4.84 [672]~P31(x6721)+~P9(x6721,x6722,x6723)+~E(f17(x6721,x6722,x6723),f9(f84(x6721,a32)))
% 4.70/4.84 [673]~P31(x6731)+~P7(x6731,x6732,x6733)+~E(f18(x6731,x6732,x6733),f9(f84(x6731,a32)))
% 4.70/4.84 [674]~P31(x6741)+~P9(x6741,x6742,x6743)+~E(f9(f84(x6741,a32)),f17(x6741,x6742,x6743))
% 4.70/4.84 [675]~P31(x6751)+~P7(x6751,x6752,x6753)+~E(f9(f84(x6751,a32)),f18(x6751,x6752,x6753))
% 4.70/4.84 [687]P14(x6871,x6872,x6873)+~P8(x6871,x6873)+E(f4(x6871,f27(x6871,x6872,x6873)),f33(a12,f4(x6871,x6873)))
% 4.70/4.84 [701]~P7(a80,x7012,x7013)+P1(f33(x7011,x7012))+~P1(f33(x7011,f65(x7011,x7013)))
% 4.70/4.84 [702]~P9(a80,x7022,x7023)+P1(f33(x7021,x7022))+~P1(f33(x7021,f47(x7021,x7023)))
% 4.70/4.84 [703]~P8(x7031,x7033)+~P14(x7031,x7032,x7033)+E(f4(x7031,f27(x7031,x7032,x7033)),f4(x7031,x7033))
% 4.70/4.84 [737]P14(x7371,x7372,x7373)+~P8(x7371,x7373)+E(f4(x7371,f27(x7371,x7372,x7373)),f8(a80,f3(a80),f4(x7371,x7373)))
% 4.70/4.84 [753]~P9(a80,x7532,x7533)+P1(f33(x7531,x7532))+P14(a80,f47(x7531,x7533),f17(a80,f2(a80),x7533))
% 4.70/4.84 [754]~P7(a80,x7542,x7543)+P1(f33(x7541,x7542))+P14(a80,f65(x7541,x7543),f18(a80,f2(a80),x7543))
% 4.70/4.84 [766]~P9(a80,x7663,x7662)+~P1(f33(x7661,x7663))+P14(a80,f37(x7661,x7662),f17(a80,f2(a80),x7662))
% 4.70/4.84 [767]~P7(a80,x7673,x7672)+~P1(f33(x7671,x7673))+P14(a80,f55(x7671,x7672),f18(a80,f2(a80),x7672))
% 4.70/4.84 [814]P7(a80,f66(x8141,x8143),x8143)+P1(f33(x8141,x8142))+~P14(a80,x8142,f18(a80,f2(a80),x8143))
% 4.70/4.84 [815]P9(a80,f48(x8151,x8153),x8153)+P1(f33(x8151,x8152))+~P14(a80,x8152,f17(a80,f2(a80),x8153))
% 4.70/4.84 [832]P7(a80,f67(x8321,x8322),x8322)+~P1(f33(x8321,x8323))+~P14(a80,x8323,f18(a80,f2(a80),x8322))
% 4.70/4.84 [833]P9(a80,f38(x8331,x8332),x8332)+~P1(f33(x8331,x8333))+~P14(a80,x8333,f17(a80,f2(a80),x8332))
% 4.70/4.84 [834]~P1(f33(x8341,x8343))+~P14(a80,x8343,f17(a80,f2(a80),x8342))+P1(f33(x8341,f38(x8341,x8342)))
% 4.70/4.84 [835]~P1(f33(x8351,x8353))+~P14(a80,x8353,f18(a80,f2(a80),x8352))+P1(f33(x8351,f67(x8351,x8352)))
% 4.70/4.84 [844]P1(f33(x8441,x8442))+~P14(a80,x8442,f17(a80,f2(a80),x8443))+~P1(f33(x8441,f48(x8441,x8443)))
% 4.70/4.84 [845]P1(f33(x8451,x8452))+~P14(a80,x8452,f18(a80,f2(a80),x8453))+~P1(f33(x8451,f66(x8451,x8453)))
% 4.70/4.84 [864]~P8(x8641,x8643)+E(f5(x8641,a80,x8642,x8643),f2(a80))+~E(f33(x8642,f57(x8642,x8643,x8641)),f2(a80))
% 4.70/4.84 [881]~P8(x8813,x8812)+~E(f5(x8813,a80,x8811,x8812),f3(a80))+E(f33(x8811,f68(x8811,x8812,x8813)),f3(a80))
% 4.70/4.84 [888]~P8(x8883,x8882)+E(f33(x8881,f58(x8881,x8882,x8883)),f33(a12,f2(a80)))+~E(f5(x8883,a80,x8881,x8882),f33(a12,f2(a80)))
% 4.70/4.84 [897]~P8(x8971,x8973)+P14(x8971,f58(x8972,x8973,x8971),x8973)+~E(f5(x8971,a80,x8972,x8973),f33(a12,f2(a80)))
% 4.70/4.84 [600]~E(x6002,x6003)+~P31(x6001)+E(f18(x6001,x6002,x6003),f27(x6001,x6002,f9(f84(x6001,a32))))
% 4.70/4.84 [895]~P7(f84(x8952,a32),x8951,f27(x8952,x8953,f9(f84(x8952,a32))))+E(x8951,f9(f84(x8952,a32)))+E(x8951,f27(x8952,x8953,f9(f84(x8952,a32))))
% 4.70/4.84 [923]~P19(x9231)+~E(f33(x9232,f2(a80)),f2(x9231))+E(f5(a80,x9231,x9232,f17(a80,f33(a12,f2(a80)),x9233)),f5(a80,x9231,x9232,f17(a80,f2(a80),x9233)))
% 4.70/4.84 [974]~P8(x9741,x9742)+~P14(x9741,x9743,x9742)+E(f8(a80,f3(a80),f4(x9741,f7(f84(x9741,a32),x9742,f27(x9741,x9743,f9(f84(x9741,a32)))))),f4(x9741,x9742))
% 4.70/4.84 [629]~P16(x6293)+E(x6291,x6292)+~E(f8(x6293,x6294,x6291),f8(x6293,x6294,x6292))
% 4.70/4.84 [630]~P17(x6303)+E(x6301,x6302)+~E(f8(x6303,x6304,x6301),f8(x6303,x6304,x6302))
% 4.70/4.84 [632]~P16(x6323)+E(x6321,x6322)+~E(f8(x6323,x6321,x6324),f8(x6323,x6322,x6324))
% 4.70/4.84 [653]~P7(f84(x6534,a32),x6533,x6531)+P1(f33(x6531,x6532))+~P1(f33(x6533,x6532))
% 4.70/4.84 [669]~P30(x6692)+~P9(f84(x6691,x6692),x6693,x6694)+P7(f84(x6691,x6692),x6693,x6694)
% 4.70/4.84 [718]~P30(x7181)+~P9(f84(x7182,x7181),x7184,x7183)+~P7(f84(x7182,x7181),x7183,x7184)
% 4.70/4.84 [724]P14(x7241,x7242,x7243)+~P14(x7241,x7242,x7244)+~P9(f84(x7241,a32),x7244,x7243)
% 4.70/4.84 [725]P14(x7251,x7252,x7253)+~P14(x7251,x7252,x7254)+~P7(f84(x7251,a32),x7254,x7253)
% 4.70/4.84 [734]P8(x7341,x7344)+~P19(x7342)+E(f5(x7341,x7342,x7343,x7344),f2(x7342))
% 4.70/4.84 [755]~P9(a80,x7553,x7554)+P9(a80,x7551,x7552)+~E(f8(a80,x7553,x7552),f8(a80,x7551,x7554))
% 4.70/4.84 [761]E(x7611,x7612)+P14(x7613,x7611,x7614)+~P14(x7613,x7611,f27(x7613,x7612,x7614))
% 4.70/4.84 [768]~P7(f84(x7681,a32),x7682,x7684)+~P7(f84(x7681,a32),x7684,x7683)+P7(f84(x7681,a32),x7682,x7683)
% 4.70/4.84 [769]~P9(f84(x7691,a32),x7692,x7694)+~P7(f84(x7691,a32),x7694,x7693)+P9(f84(x7691,a32),x7692,x7693)
% 4.70/4.84 [770]~P9(f84(x7701,a32),x7704,x7703)+~P7(f84(x7701,a32),x7702,x7704)+P9(f84(x7701,a32),x7702,x7703)
% 4.70/4.84 [771]~P9(f84(x7711,a32),x7712,x7714)+~P9(f84(x7711,a32),x7714,x7713)+P9(f84(x7711,a32),x7712,x7713)
% 4.70/4.84 [805]~P18(x8051)+~P7(x8051,x8053,x8054)+P7(x8051,f8(x8051,x8052,x8053),f8(x8051,x8052,x8054))
% 4.70/4.84 [806]~P22(x8061)+~P7(x8061,x8063,x8064)+P7(x8061,f8(x8061,x8062,x8063),f8(x8061,x8062,x8064))
% 4.70/4.84 [807]~P18(x8071)+~P7(x8071,x8072,x8074)+P7(x8071,f8(x8071,x8072,x8073),f8(x8071,x8074,x8073))
% 4.70/4.84 [808]~P22(x8081)+~P7(x8081,x8082,x8084)+P7(x8081,f8(x8081,x8082,x8083),f8(x8081,x8084,x8083))
% 4.70/4.84 [809]~P18(x8091)+~P9(x8091,x8093,x8094)+P9(x8091,f8(x8091,x8092,x8093),f8(x8091,x8092,x8094))
% 4.70/4.84 [810]~P24(x8101)+~P9(x8101,x8103,x8104)+P9(x8101,f8(x8101,x8102,x8103),f8(x8101,x8102,x8104))
% 4.70/4.84 [811]~P18(x8111)+~P9(x8111,x8112,x8114)+P9(x8111,f8(x8111,x8112,x8113),f8(x8111,x8114,x8113))
% 4.70/4.84 [812]~P24(x8121)+~P9(x8121,x8122,x8124)+P9(x8121,f8(x8121,x8122,x8123),f8(x8121,x8124,x8123))
% 4.70/4.84 [838]~P14(x8381,x8382,x8384)+~P7(f84(x8381,a32),x8383,x8384)+P7(f84(x8381,a32),f27(x8381,x8382,x8383),x8384)
% 4.70/4.84 [848]P14(x8481,x8482,x8483)+~P7(f84(x8481,a32),x8483,f27(x8481,x8482,x8484))+P7(f84(x8481,a32),x8483,x8484)
% 4.70/4.84 [849]~P7(a80,x8492,x8494)+~P7(a80,x8491,x8493)+P7(a80,f8(a80,x8491,x8492),f8(a80,x8493,x8494))
% 4.70/4.84 [850]~P9(a80,x8502,x8504)+~P9(a80,x8501,x8503)+P9(a80,f8(a80,x8501,x8502),f8(a80,x8503,x8504))
% 4.70/4.84 [867]~P18(x8671)+P7(x8671,x8672,x8673)+~P7(x8671,f8(x8671,x8674,x8672),f8(x8671,x8674,x8673))
% 4.70/4.84 [869]~P18(x8691)+P7(x8691,x8692,x8693)+~P7(x8691,f8(x8691,x8692,x8694),f8(x8691,x8693,x8694))
% 4.70/4.84 [871]~P18(x8711)+P9(x8711,x8712,x8713)+~P9(x8711,f8(x8711,x8714,x8712),f8(x8711,x8714,x8713))
% 4.70/4.84 [873]~P18(x8731)+P9(x8731,x8732,x8733)+~P9(x8731,f8(x8731,x8732,x8734),f8(x8731,x8733,x8734))
% 4.70/4.84 [894]~P8(x8942,x8944)+~P8(x8941,x8943)+P8(f85(x8941,x8942),f31(x8941,x8942,x8943,x8944))
% 4.70/4.84 [966]P8(x9661,x9662)+~P10(x9661,x9663,x9664,x9662)+~P8(x9663,f28(x9661,x9663,x9664,x9662))
% 4.70/4.84 [843]E(x8431,x8432)+P1(f33(x8433,x8432))+~P1(f33(f27(x8434,x8431,x8433),x8432))
% 4.70/4.84 [916]~P8(x9162,x9164)+~P8(x9161,x9163)+E(f4(f85(x9161,x9162),f31(x9161,x9162,x9163,x9164)),f8(a80,f4(x9161,x9163),f4(x9162,x9164)))
% 4.70/4.84 [957]~P8(x9571,x9574)+P10(x9571,x9572,x9573,x9574)+~E(f4(x9572,f28(x9571,x9572,x9573,x9574)),f4(x9571,x9574))
% 4.70/4.84 [1001]~P30(x10012)+P7(f84(x10011,x10012),x10013,x10014)+~P7(x10012,f33(x10013,f76(x10014,x10013,x10011,x10012)),f33(x10014,f76(x10014,x10013,x10011,x10012)))
% 4.70/4.84 [719]~P31(x7193)+E(x7191,x7192)+~E(f18(x7193,x7194,x7191),f27(x7193,x7192,f9(f84(x7193,a32))))
% 4.70/4.84 [720]~P31(x7203)+E(x7201,x7202)+~E(f18(x7203,x7201,x7202),f27(x7203,x7204,f9(f84(x7203,a32))))
% 4.70/4.84 [842]~E(x8424,f9(f84(x8422,a32)))+~E(x8423,f9(f84(x8421,a32)))+E(f31(x8421,x8422,x8423,x8424),f9(f84(f85(x8421,x8422),a32)))
% 4.70/4.84 [874]~P19(x8741)+~P9(a80,x8744,x8743)+E(f5(a80,x8741,x8742,f17(a80,x8743,f33(a12,x8744))),f2(x8741))
% 4.70/4.84 [879]~P19(x8791)+~P9(a80,f33(a12,x8794),x8793)+E(f5(a80,x8791,x8792,f18(a80,x8793,f33(a12,x8794))),f2(x8791))
% 4.70/4.84 [968]~P19(x9681)+P9(a80,x9684,x9683)+E(f8(x9681,f5(a80,x9681,x9682,f17(a80,x9683,x9684)),f33(x9682,x9684)),f5(a80,x9681,x9682,f17(a80,x9683,f33(a12,x9684))))
% 4.70/4.84 [971]~P19(x9711)+P9(a80,f33(a12,x9714),x9713)+E(f8(x9711,f5(a80,x9711,x9712,f18(a80,x9713,x9714)),f33(x9712,f33(a12,x9714))),f5(a80,x9711,x9712,f18(a80,x9713,f33(a12,x9714))))
% 4.70/4.84 [990]~P10(x9904,x9903,x9901,f16(f84(x9904,a32)))+E(f33(x9901,f74(x9902,x9901,x9903,x9904)),x9902)+~P14(x9903,x9902,f28(x9904,x9903,x9901,f16(f84(x9904,a32))))
% 4.70/4.84 [972]~P19(x9721)+~P9(a80,x9723,x9724)+E(f8(x9721,f33(x9722,x9723),f5(a80,x9721,x9722,f17(a80,f33(a12,x9723),x9724))),f5(a80,x9721,x9722,f17(a80,x9723,x9724)))
% 4.70/4.84 [973]~P19(x9731)+~P7(a80,x9733,x9734)+E(f8(x9731,f33(x9732,x9733),f5(a80,x9731,x9732,f18(a80,f33(a12,x9733),x9734))),f5(a80,x9731,x9732,f18(a80,x9733,x9734)))
% 4.70/4.84 [700]~P30(x7001)+P7(x7001,f33(x7002,x7003),f33(x7004,x7003))+~P7(f84(x7005,x7001),x7002,x7004)
% 4.70/4.84 [799]~P31(x7991)+P7(x7991,x7992,x7993)+P7(f84(x7991,a32),f18(x7991,x7992,x7993),f18(x7991,x7994,x7995))
% 4.70/4.84 [878]~P31(x8781)+P7(x8781,x8782,x8783)+~P9(f84(x8781,a32),f18(x8781,x8784,x8785),f18(x8781,x8782,x8783))
% 4.70/4.84 [917]P10(x9171,x9172,x9173,x9174)+~P10(x9171,x9172,x9173,x9175)+~P7(f84(x9171,a32),x9174,x9175)
% 4.70/4.84 [941]P8(x9411,x9412)+~P8(x9413,x9414)+~P7(f84(x9411,a32),x9412,f28(x9413,x9411,x9415,x9414))
% 4.70/4.84 [982]~P10(x9822,x9821,x9823,x9825)+~P9(f84(x9822,a32),x9824,x9825)+P9(f84(x9821,a32),f28(x9822,x9821,x9823,x9824),f28(x9822,x9821,x9823,x9825))
% 4.70/4.84 [877]E(x8771,x8772)+~E(f33(x8773,x8771),f33(x8773,x8772))+~P10(x8774,x8775,x8773,f16(f84(x8774,a32)))
% 4.70/4.84 [924]P14(x9241,x9242,f22(x9241,x9243,x9244,x9245))+~P1(f33(f33(x9243,x9242),x9245))+~P1(f33(f33(x9243,x9244),x9242))
% 4.70/4.84 [925]P14(x9251,x9252,f25(x9251,x9253,x9254,x9255))+~P1(f33(f33(x9253,x9252),x9255))+~P1(f33(f33(x9253,x9254),x9252))
% 4.70/4.84 [951]~P14(x9511,x9515,x9513)+~P10(x9511,x9512,x9514,x9513)+E(f33(f6(x9511,x9512,x9513,x9514),f33(x9514,x9515)),x9515)
% 4.70/4.84 [961]P10(x9612,x9613,f77(x9614,x9613,x9612,x9611),x9611)+~E(f28(x9613,x9612,x9615,x9614),x9611)+E(x9611,f9(f84(x9612,a32)))
% 4.70/4.84 [969]E(x9691,x9692)+~E(f28(x9693,x9694,x9695,x9691),f28(x9693,x9694,x9695,x9692))+~P10(x9693,x9694,x9695,f16(f84(x9693,a32)))
% 4.70/4.84 [978]P14(x9781,x9782,x9783)+~P14(x9784,f33(x9785,x9782),f28(x9781,x9784,x9785,x9783))+~P10(x9781,x9784,x9785,f16(f84(x9781,a32)))
% 4.70/4.84 [989]~E(f28(x9893,x9892,x9895,x9894),x9891)+P7(f84(x9893,a32),f28(x9892,x9893,f77(x9894,x9893,x9892,x9891),x9891),x9894)+E(x9891,f9(f84(x9892,a32)))
% 4.70/4.84 [993]~P7(f84(x9934,a32),f28(x9931,x9934,x9935,x9932),f28(x9931,x9934,x9935,x9933))+P7(f84(x9931,a32),x9932,x9933)+~P10(x9931,x9934,x9935,f16(f84(x9931,a32)))
% 4.70/4.84 [994]~P10(x9942,x9943,x9941,x9944)+~P14(x9943,x9945,f28(x9942,x9943,x9941,x9944))+E(f33(x9941,f33(f6(x9942,x9943,x9944,x9941),x9945)),x9945)
% 4.70/4.84 [882]~E(x8823,x8824)+~E(x8822,x8825)+E(f27(x8821,x8822,f27(x8821,x8823,f9(f84(x8821,a32)))),f27(x8821,x8824,f27(x8821,x8825,f9(f84(x8821,a32)))))
% 4.70/4.84 [927]E(x9271,x9272)+E(x9273,x9271)+~E(f27(x9274,x9271,f27(x9274,x9275,f9(f84(x9274,a32)))),f27(x9274,x9272,f27(x9274,x9273,f9(f84(x9274,a32)))))
% 4.70/4.84 [928]E(x9281,x9282)+E(x9283,x9281)+~E(f27(x9284,x9283,f27(x9284,x9282,f9(f84(x9284,a32)))),f27(x9284,x9285,f27(x9284,x9281,f9(f84(x9284,a32)))))
% 4.70/4.84 [929]E(x9291,x9292)+E(x9291,x9293)+~E(f27(x9294,x9293,f27(x9294,x9292,f9(f84(x9294,a32)))),f27(x9294,x9295,f27(x9294,x9291,f9(f84(x9294,a32)))))
% 4.70/4.84 [930]E(x9301,x9302)+E(x9301,x9303)+~E(f27(x9304,x9301,f27(x9304,x9305,f9(f84(x9304,a32)))),f27(x9304,x9302,f27(x9304,x9303,f9(f84(x9304,a32)))))
% 4.70/4.84 [1000]~P19(x10001)+~P7(a80,x10003,f8(a80,x10004,f3(a80)))+E(f8(x10001,f5(a80,x10001,x10002,f18(a80,x10003,x10004)),f5(a80,x10001,x10002,f18(a80,f8(a80,x10004,f3(a80)),f8(a80,x10004,x10005)))),f5(a80,x10001,x10002,f18(a80,x10003,f8(a80,x10004,x10005))))
% 4.70/4.84 [911]~P14(x9113,x9116,x9115)+P14(x9111,x9112,f28(x9113,x9111,x9114,x9115))+~E(x9112,f33(x9114,x9116))
% 4.70/4.84 [955]~P7(f84(x9553,a32),x9556,x9555)+P7(f84(x9551,a32),x9552,f28(x9553,x9551,x9554,x9555))+~E(x9552,f28(x9553,x9551,x9554,x9556))
% 4.70/4.84 [997]P14(x9971,x9972,f26(x9971,x9973,x9974,x9975,x9976))+~P1(f33(f33(x9973,x9972),x9976))+~P1(f33(f33(x9974,x9975),x9972))
% 4.70/4.84 [998]P14(x9981,x9982,f23(x9981,x9983,x9984,x9985,x9986))+~P1(f33(f33(x9984,x9982),x9986))+~P1(f33(f33(x9983,x9985),x9982))
% 4.70/4.84 [1012]~P8(x10122,x10124)+~P13(x10127,x10122,x10125,x10128,x10126,x10121)+E(f33(x10121,f27(x10122,x10123,x10124)),f33(f33(x10125,f33(x10126,x10123)),f33(x10121,x10124)))
% 4.70/4.84 [599]~P28(x5991)+~P14(x5991,x5992,f13(x5991))+~E(x5992,f2(x5991))+E(f8(x5991,x5992,x5992),f2(x5991))
% 4.70/4.84 [654]~P28(x6542)+~P14(x6542,x6541,f13(x6542))+~E(f8(x6542,x6541,x6541),f2(x6542))+E(x6541,f2(x6542))
% 4.70/4.84 [898]~P34(x8981)+~P14(x8981,x8982,f13(x8981))+~P9(x8981,x8982,f2(x8981))+P9(x8981,f8(x8981,f8(x8981,f3(x8981),x8982),x8982),f2(x8981))
% 4.70/4.84 [922]~P34(x9221)+~P14(x9221,x9222,f13(x9221))+P9(x9221,x9222,f2(x9221))+~P9(x9221,f8(x9221,f8(x9221,f3(x9221),x9222),x9222),f2(x9221))
% 4.70/4.84 [519]P9(x5193,x5191,x5192)+~P34(x5193)+E(x5191,x5192)+P9(x5193,x5192,x5191)
% 4.70/4.84 [520]P9(x5203,x5201,x5202)+~P29(x5203)+E(x5201,x5202)+P9(x5203,x5202,x5201)
% 4.70/4.84 [522]P9(x5221,x5222,x5223)+~E(x5222,x5223)+~P29(x5221)+P7(x5221,x5222,x5223)
% 4.70/4.84 [565]~P31(x5653)+~P7(x5653,x5652,x5651)+E(x5651,x5652)+P9(x5653,x5652,x5651)
% 4.70/4.84 [567]~P29(x5673)+~P7(x5673,x5671,x5672)+E(x5671,x5672)+P9(x5673,x5671,x5672)
% 4.70/4.84 [573]~P31(x5733)+~P7(x5733,x5731,x5732)+E(x5731,x5732)+P9(x5733,x5731,x5732)
% 4.70/4.84 [638]~P7(x6383,x6382,x6381)+~P7(x6383,x6381,x6382)+E(x6381,x6382)+~P31(x6383)
% 4.70/4.84 [659]P9(x6591,x6593,x6592)+~P26(x6591)+~P7(x6591,x6593,x6592)+P7(x6591,x6592,x6593)
% 4.70/4.84 [762]E(x7621,x7622)+~P8(x7623,x7621)+~P7(f84(x7623,a32),x7622,x7621)+~P7(a80,f4(x7623,x7621),f4(x7623,x7622))
% 4.70/4.84 [819]~P25(x8191)+~P9(x8191,f2(x8191),x8193)+~P9(x8191,f2(x8191),x8192)+P9(x8191,f2(x8191),f8(x8191,x8192,x8193))
% 4.70/4.84 [820]~P37(x8201)+~P14(x8201,x8203,f13(x8201))+~P14(x8201,x8202,f13(x8201))+P14(x8201,f8(x8201,x8202,x8203),f13(x8201))
% 4.70/4.84 [821]~P25(x8211)+~P7(x8211,x8213,f2(x8211))+~P7(x8211,x8212,f2(x8211))+P7(x8211,f8(x8211,x8212,x8213),f2(x8211))
% 4.70/4.84 [822]~P25(x8221)+~P7(x8221,x8223,f2(x8221))+~P9(x8221,x8222,f2(x8221))+P9(x8221,f8(x8221,x8222,x8223),f2(x8221))
% 4.70/4.84 [823]~P25(x8231)+~P7(x8231,x8232,f2(x8231))+~P9(x8231,x8233,f2(x8231))+P9(x8231,f8(x8231,x8232,x8233),f2(x8231))
% 4.70/4.84 [824]~P25(x8241)+~P9(x8241,x8243,f2(x8241))+~P9(x8241,x8242,f2(x8241))+P9(x8241,f8(x8241,x8242,x8243),f2(x8241))
% 4.70/4.84 [836]~P8(x8361,x8363)+~P7(f84(x8361,a32),x8362,x8363)+P9(f84(x8361,a32),x8362,x8363)+~P9(a80,f4(x8361,x8362),f4(x8361,x8363))
% 4.70/4.84 [981]~P8(x9811,x9813)+~P10(x9811,x9811,x9812,x9813)+~P7(f84(x9811,a32),f28(x9811,x9811,x9812,x9813),x9813)+E(f28(x9811,x9811,x9812,x9813),x9813)
% 4.70/4.84 [716]~P7(a80,x7163,f51(x7162,x7161))+~P1(f33(x7161,x7162))+~P1(f33(x7161,x7163))+P1(f33(x7161,f2(a80)))
% 4.70/4.84 [678]~P31(x6781)+~P7(x6781,x6784,x6783)+P7(x6781,x6782,x6783)+~P7(x6781,x6782,x6784)
% 4.70/4.84 [679]~P26(x6791)+~P7(x6791,x6792,x6794)+P7(x6791,x6792,x6793)+~P7(x6791,x6794,x6793)
% 4.70/4.84 [680]~P31(x6801)+~P9(x6801,x6804,x6803)+P9(x6801,x6802,x6803)+~P7(x6801,x6802,x6804)
% 4.70/4.84 [681]~P31(x6811)+~P9(x6811,x6812,x6814)+P9(x6811,x6812,x6813)+~P7(x6811,x6814,x6813)
% 4.70/4.84 [682]~P31(x6821)+~P9(x6821,x6824,x6823)+P9(x6821,x6822,x6823)+~P9(x6821,x6822,x6824)
% 4.70/4.84 [683]~P26(x6831)+~P9(x6831,x6832,x6834)+P9(x6831,x6832,x6833)+~P7(x6831,x6834,x6833)
% 4.70/4.84 [684]~P26(x6841)+~P9(x6841,x6844,x6843)+P9(x6841,x6842,x6843)+~P7(x6841,x6842,x6844)
% 4.70/4.84 [685]~P26(x6851)+~P9(x6851,x6852,x6854)+P9(x6851,x6852,x6853)+~P9(x6851,x6854,x6853)
% 4.70/4.84 [738]P14(x7383,x7384,x7381)+E(x7381,x7382)+P14(x7383,x7384,x7382)+~E(f27(x7383,x7384,x7381),f27(x7383,x7384,x7382))
% 4.70/4.84 [745]~P30(x7452)+P9(f84(x7451,x7452),x7454,x7453)+~P7(f84(x7451,x7452),x7454,x7453)+P7(f84(x7451,x7452),x7453,x7454)
% 4.70/4.84 [794]~P25(x7941)+~P7(x7941,x7942,x7943)+~P7(x7941,f2(x7941),x7944)+P7(x7941,x7942,f8(x7941,x7943,x7944))
% 4.70/4.84 [795]~P25(x7951)+~P7(x7951,x7952,x7954)+~P7(x7951,f2(x7951),x7953)+P7(x7951,x7952,f8(x7951,x7953,x7954))
% 4.70/4.84 [796]~P25(x7961)+~P7(x7961,x7962,x7964)+~P9(x7961,f2(x7961),x7963)+P9(x7961,x7962,f8(x7961,x7963,x7964))
% 4.70/4.84 [797]~P25(x7971)+~P9(x7971,x7972,x7974)+~P7(x7971,f2(x7971),x7973)+P9(x7971,x7972,f8(x7971,x7973,x7974))
% 4.70/4.84 [798]~P32(x7981)+~P9(x7981,x7982,x7984)+~P9(x7981,f2(x7981),x7983)+P9(x7981,x7982,f8(x7981,x7983,x7984))
% 4.70/4.84 [875]~P8(x8753,x8754)+~P14(x8753,x8752,x8754)+E(f33(x8751,x8752),f2(a80))+~E(f5(x8753,a80,x8751,x8754),f2(a80))
% 4.70/4.84 [946]~P8(x9462,x9463)+~P8(x9461,x9464)+P10(x9461,x9462,f73(x9463,x9462,x9464,x9461),x9464)+~P7(a80,f4(x9461,x9464),f4(x9462,x9463))
% 4.70/4.84 [986]~P8(x9862,x9864)+~P8(x9861,x9863)+~P7(a80,f4(x9862,x9864),f4(x9861,x9863))+P7(f84(x9861,a32),f28(x9862,x9861,f73(x9863,x9861,x9864,x9862),x9864),x9863)
% 4.70/4.84 [613]~E(x6133,x6134)+~E(x6132,x6133)+~P31(x6131)+E(f18(x6131,x6132,x6133),f27(x6131,x6134,f9(f84(x6131,a32))))
% 4.70/4.84 [853]~P31(x8531)+~P7(x8531,x8534,x8535)+P7(x8531,x8532,x8533)+P9(f84(x8531,a32),f18(x8531,x8532,x8533),f18(x8531,x8534,x8535))
% 4.70/4.84 [854]~P22(x8541)+~P7(x8541,x8543,x8545)+~P7(x8541,x8542,x8544)+P7(x8541,f8(x8541,x8542,x8543),f8(x8541,x8544,x8545))
% 4.70/4.84 [855]~P24(x8551)+~P7(x8551,x8553,x8555)+~P9(x8551,x8552,x8554)+P9(x8551,f8(x8551,x8552,x8553),f8(x8551,x8554,x8555))
% 4.70/4.84 [856]~P24(x8561)+~P7(x8561,x8562,x8564)+~P9(x8561,x8563,x8565)+P9(x8561,f8(x8561,x8562,x8563),f8(x8561,x8564,x8565))
% 4.70/4.84 [857]~P24(x8571)+~P9(x8571,x8573,x8575)+~P9(x8571,x8572,x8574)+P9(x8571,f8(x8571,x8572,x8573),f8(x8571,x8574,x8575))
% 4.70/4.84 [865]~P31(x8651)+~P7(x8651,x8653,x8655)+~P7(x8651,x8654,x8652)+P7(f84(x8651,a32),f18(x8651,x8652,x8653),f18(x8651,x8654,x8655))
% 4.70/4.84 [890]~P29(x8901)+P7(x8901,x8902,x8903)+P7(x8901,x8904,x8903)+~P7(f84(x8901,a32),f17(x8901,x8903,x8902),f17(x8901,x8904,x8905))
% 4.70/4.84 [891]~P29(x8911)+P7(x8911,x8912,x8913)+P7(x8911,x8912,x8914)+~P7(f84(x8911,a32),f17(x8911,x8913,x8912),f17(x8911,x8915,x8914))
% 4.70/4.84 [899]~P31(x8991)+P7(x8991,x8992,x8993)+~P7(x8991,x8994,x8992)+~P7(f84(x8991,a32),f18(x8991,x8994,x8992),f18(x8991,x8995,x8993))
% 4.70/4.84 [900]~P31(x9001)+P7(x9001,x9002,x9003)+~P7(x9001,x9004,x9002)+~P9(f84(x9001,a32),f18(x9001,x9004,x9002),f18(x9001,x9005,x9003))
% 4.70/4.84 [901]~P31(x9011)+P7(x9011,x9012,x9013)+~P7(x9011,x9013,x9014)+~P7(f84(x9011,a32),f18(x9011,x9013,x9014),f18(x9011,x9012,x9015))
% 4.70/4.84 [902]~P31(x9021)+P7(x9021,x9022,x9023)+~P7(x9021,x9023,x9024)+~P9(f84(x9021,a32),f18(x9021,x9023,x9024),f18(x9021,x9022,x9025))
% 4.70/4.84 [977]~P8(x9773,x9774)+~P10(x9771,x9773,x9775,x9772)+~P7(f84(x9773,a32),f28(x9771,x9773,x9775,x9772),x9774)+P7(a80,f4(x9771,x9772),f4(x9773,x9774))
% 4.70/4.84 [736]~P14(x7365,x7362,x7364)+~P11(x7365,x7361,x7363)+~P8(x7365,x7364)+E(f33(f33(x7361,x7362),f33(x7363,x7364)),f33(x7363,x7364))
% 4.70/4.84 [772]~P8(x7722,x7721)+~P11(x7722,x7725,x7723)+E(f33(x7723,f27(x7722,x7724,x7721)),f33(f33(x7725,x7724),f33(x7723,x7721)))+E(x7721,f9(f84(x7722,a32)))
% 4.70/4.84 [953]P14(x9531,x9534,x9535)+~P19(x9532)+~P8(x9531,x9535)+E(f5(x9531,x9532,x9533,f27(x9531,x9534,x9535)),f8(x9532,f33(x9533,x9534),f5(x9531,x9532,x9533,x9535)))
% 4.70/4.84 [991]~P10(x9912,x9913,x9915,x9911)+~P7(f84(x9913,a32),f28(x9912,x9913,x9915,x9911),x9914)+E(f28(x9913,x9912,f78(x9914,x9913,x9912,x9911),x9914),x9911)+E(x9911,f9(f84(x9912,a32)))
% 4.70/4.84 [987]~E(x9872,f33(x9873,x9871))+E(x9871,f74(x9872,x9873,x9874,x9875))+~P10(x9875,x9874,x9873,f16(f84(x9875,a32)))+~P14(x9874,x9872,f28(x9875,x9874,x9873,f16(f84(x9875,a32))))
% 4.70/4.84 [988]~P19(x9881)+~P7(a80,x9884,x9885)+~P7(a80,x9883,x9884)+E(f8(x9881,f5(a80,x9881,x9882,f17(a80,x9883,x9884)),f5(a80,x9881,x9882,f17(a80,x9884,x9885))),f5(a80,x9881,x9882,f17(a80,x9883,x9885)))
% 4.70/4.84 [950]~P14(x9501,x9506,x9503)+~P10(x9501,x9502,x9504,x9503)+~E(f33(x9504,x9506),x9505)+E(f33(f6(x9501,x9502,x9503,x9504),x9505),x9506)
% 4.70/4.84 [995]~P10(x9951,x9952,x9954,x9953)+~P14(x9952,x9955,f28(x9951,x9952,x9954,x9953))+~P7(f84(x9951,a32),x9953,x9956)+P14(x9951,f33(f6(x9951,x9952,x9953,x9954),x9955),x9956)
% 4.70/4.84 [1011]~P14(x10116,x10113,x10115)+~P13(x10117,x10116,x10111,x10118,x10112,x10114)+~P8(x10116,x10115)+E(f33(f33(x10111,f33(x10112,x10113)),f33(x10114,x10115)),f33(x10114,x10115))
% 4.70/4.84 [1013]~P13(x10136,x10135,x10131,x10137,x10138,x10132)+~P8(x10135,x10134)+~P7(f84(x10135,a32),x10133,x10134)+E(f33(f33(x10131,f33(x10132,x10133)),f33(x10132,x10134)),f33(x10132,x10134))
% 4.70/4.84 [746]~P25(x7462)+~P7(x7462,f2(x7462),x7463)+~P7(x7462,f2(x7462),x7461)+~E(f8(x7462,x7463,x7461),f2(x7462))+E(x7461,f2(x7462))
% 4.70/4.84 [747]~P25(x7472)+~P7(x7472,f2(x7472),x7473)+~P7(x7472,f2(x7472),x7471)+~E(f8(x7472,x7471,x7473),f2(x7472))+E(x7471,f2(x7472))
% 4.70/4.84 [889]~P8(x8893,x8892)+~P14(x8893,x8894,x8892)+E(f68(x8891,x8892,x8893),x8894)+E(f33(x8891,x8894),f2(a80))+~E(f5(x8893,a80,x8891,x8892),f3(a80))
% 4.70/4.84 [918]~P8(x9181,x9183)+~P14(x9181,x9184,x9183)+~E(f69(x9182,x9183,x9181,x9184),x9184)+~E(f33(x9182,x9184),f3(a80))+E(f5(x9181,a80,x9182,x9183),f3(a80))
% 4.70/4.84 [939]~P8(x9391,x9393)+~P14(x9391,x9394,x9393)+P14(x9391,f69(x9392,x9393,x9391,x9394),x9393)+~E(f33(x9392,x9394),f3(a80))+E(f5(x9391,a80,x9392,x9393),f3(a80))
% 4.70/4.84 [896]~P8(x8963,x8962)+~P14(x8963,x8964,x8962)+E(f58(x8961,x8962,x8963),x8964)+E(f33(x8961,x8964),f2(a80))+~E(f5(x8963,a80,x8961,x8962),f33(a12,f2(a80)))
% 4.70/4.84 [926]~P8(x9261,x9263)+~P14(x9261,x9264,x9263)+~E(f60(x9262,x9263,x9261,x9264),x9264)+~E(f33(x9262,x9264),f33(a12,f2(a80)))+E(f5(x9261,a80,x9262,x9263),f33(a12,f2(a80)))
% 4.70/4.84 [949]~P8(x9491,x9493)+~P14(x9491,x9494,x9493)+P14(x9491,f60(x9492,x9493,x9491,x9494),x9493)+~E(f33(x9492,x9494),f33(a12,f2(a80)))+E(f5(x9491,a80,x9492,x9493),f33(a12,f2(a80)))
% 4.70/4.84 [964]~P8(x9641,x9643)+~P14(x9641,x9644,x9643)+~E(f33(x9642,x9644),f3(a80))+E(f5(x9641,a80,x9642,x9643),f3(a80))+~E(f33(x9642,f69(x9642,x9643,x9641,x9644)),f2(a80))
% 4.70/4.84 [967]~P8(x9671,x9673)+~P14(x9671,x9674,x9673)+~E(f33(x9672,x9674),f33(a12,f2(a80)))+E(f5(x9671,a80,x9672,x9673),f33(a12,f2(a80)))+~E(f33(x9672,f60(x9672,x9673,x9671,x9674)),f2(a80))
% 4.70/4.84 [647]P14(x6472,x6474,x6475)+~E(f4(x6472,x6475),x6471)+~E(x6473,f27(x6472,x6474,x6475))+E(f4(x6472,x6473),f33(a12,x6471))+E(x6471,f2(a80))
% 4.70/4.84 [802]~P29(x8023)+~P9(x8023,x8025,x8022)+~P9(x8023,x8024,x8021)+E(x8021,x8022)+~E(f17(x8023,x8024,x8021),f17(x8023,x8025,x8022))
% 4.70/4.84 [803]~P29(x8033)+~P9(x8033,x8032,x8035)+~P9(x8033,x8031,x8034)+E(x8031,x8032)+~E(f17(x8033,x8031,x8034),f17(x8033,x8032,x8035))
% 4.70/4.84 [913]~P31(x9131)+~P7(x9131,x9135,x9132)+P9(x9131,x9132,x9133)+P9(x9131,x9134,x9135)+~P9(f84(x9131,a32),f18(x9131,x9135,x9132),f18(x9131,x9134,x9133))
% 4.70/4.84 [688]P14(x6881,x6884,x6885)+~E(f4(x6881,x6885),x6883)+~E(x6882,f27(x6881,x6884,x6885))+E(f4(x6881,x6882),f33(a12,x6883))+~E(x6885,f9(f84(x6881,a32)))
% 4.70/4.84 [830]P14(x8302,x8304,x8301)+~P8(x8302,x8301)+~P12(x8302,x8305,x8303)+E(f33(x8303,f27(x8302,x8304,x8301)),f33(f33(x8305,x8304),f33(x8303,x8301)))+E(x8301,f9(f84(x8302,a32)))
% 4.70/4.84 [837]~P8(x8372,x8375)+~P11(x8372,x8373,x8374)+~P7(f84(x8372,a32),x8371,x8375)+E(f33(f33(x8373,f33(x8374,x8371)),f33(x8374,x8375)),f33(x8374,x8375))+E(x8371,f9(f84(x8372,a32)))
% 4.70/4.84 [1015]~P8(x10152,x10151)+~P11(x10152,x10155,x10153)+E(f33(x10153,f28(x10152,x10152,x10154,x10151)),f33(x10154,f33(x10153,x10151)))+E(x10151,f9(f84(x10152,a32)))+~E(f33(f33(x10155,f33(x10154,f53(x10151,x10154,x10153,x10155,x10152))),f33(x10154,f54(x10151,x10154,x10153,x10155,x10152))),f33(x10154,f33(f33(x10155,f53(x10151,x10154,x10153,x10155,x10152)),f54(x10151,x10154,x10153,x10155,x10152))))
% 4.70/4.84 [906]~P14(x9064,x9061,x9065)+E(x9061,x9062)+~P10(x9064,x9066,x9063,x9065)+~P14(x9064,x9062,x9065)+~E(f33(x9063,x9061),f33(x9063,x9062))
% 4.70/4.84 [1018]~P19(x10182)+~P10(x10181,x10185,x10188,x10184)+P14(x10181,f64(x10186,x10183,x10187,x10184,x10188,x10185,x10181,x10182),x10184)+~E(x10187,f28(x10181,x10185,x10188,x10184))+E(f5(x10181,x10182,x10183,x10184),f5(x10185,x10182,x10186,x10187))
% 4.70/4.84 [1020]~P19(x10202)+~P10(x10205,x10201,x10208,x10207)+E(f5(x10201,x10202,x10203,x10204),f5(x10205,x10202,x10206,x10207))+~E(x10204,f28(x10205,x10201,x10208,x10207))+~E(f33(x10206,f64(x10203,x10206,x10204,x10207,x10208,x10201,x10205,x10202)),f33(x10203,f33(x10208,f64(x10203,x10206,x10204,x10207,x10208,x10201,x10205,x10202))))
% 4.70/4.84 [735]~P25(x7351)+~P7(x7351,f2(x7351),x7353)+~P7(x7351,f2(x7351),x7352)+~E(x7353,f2(x7351))+~E(x7352,f2(x7351))+E(f8(x7351,x7352,x7353),f2(x7351))
% 4.70/4.84 [907]~P31(x9071)+~P7(x9071,x9074,x9072)+~P7(x9071,x9074,x9075)+~P7(x9071,x9073,x9075)+~P9(x9071,x9073,x9075)+P9(f84(x9071,a32),f18(x9071,x9072,x9073),f18(x9071,x9074,x9075))
% 4.70/4.84 [908]~P31(x9081)+~P7(x9081,x9083,x9085)+~P7(x9081,x9084,x9085)+~P7(x9081,x9084,x9082)+~P9(x9081,x9084,x9082)+P9(f84(x9081,a32),f18(x9081,x9082,x9083),f18(x9081,x9084,x9085))
% 4.70/4.84 [1004]~P24(x10045)+~P19(x10045)+~P8(x10042,x10041)+P9(x10045,f5(x10042,x10045,x10044,x10041),f5(x10042,x10045,x10043,x10041))+P14(x10042,f62(x10043,x10044,x10041,x10042,x10045),x10041)+E(x10041,f9(f84(x10042,a32)))
% 4.70/4.84 [1014]~P24(x10143)+~P19(x10143)+~P8(x10142,x10141)+P9(x10143,f5(x10142,x10143,x10144,x10141),f5(x10142,x10143,x10145,x10141))+~P9(x10143,f33(x10144,f62(x10145,x10144,x10141,x10142,x10143)),f33(x10145,f62(x10145,x10144,x10141,x10142,x10143)))+E(x10141,f9(f84(x10142,a32)))
% 4.70/4.84 [1016]~E(x10165,x10168)+~E(x10164,x10167)+~P30(x10161)+~P19(x10162)+P7(x10161,x10164,f63(x10163,x10166,x10165,x10168,x10164,x10167,x10161,x10162))+E(f5(x10161,x10162,x10163,f17(x10161,x10164,x10165)),f5(x10161,x10162,x10166,f17(x10161,x10167,x10168)))
% 4.70/4.84 [1017]~E(x10174,x10177)+~E(x10175,x10178)+~P30(x10171)+~P19(x10172)+P9(x10171,f63(x10173,x10176,x10175,x10178,x10174,x10177,x10171,x10172),x10175)+E(f5(x10171,x10172,x10173,f17(x10171,x10174,x10175)),f5(x10171,x10172,x10176,f17(x10171,x10177,x10178)))
% 4.70/4.84 [1019]~E(x10197,x10194)+~E(x10198,x10195)+~P30(x10191)+~P19(x10192)+~E(f33(x10193,f63(x10196,x10193,x10198,x10195,x10197,x10194,x10191,x10192)),f33(x10196,f63(x10196,x10193,x10198,x10195,x10197,x10194,x10191,x10192)))+E(f5(x10191,x10192,x10193,f17(x10191,x10194,x10195)),f5(x10191,x10192,x10196,f17(x10191,x10197,x10198)))
% 4.70/4.84 [996]~P8(x9963,x9964)+~P8(x9961,x9962)+~P10(x9963,x9961,x9965,x9964)+~P10(x9961,x9963,x9966,x9962)+~P7(f84(x9963,a32),f28(x9961,x9963,x9966,x9962),x9964)+~P7(f84(x9961,a32),f28(x9963,x9961,x9965,x9964),x9962)+E(f4(x9961,x9962),f4(x9963,x9964))
% 4.70/4.84 %EqnAxiom
% 4.70/4.84 [1]E(x11,x11)
% 4.70/4.84 [2]E(x22,x21)+~E(x21,x22)
% 4.70/4.84 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 4.70/4.84 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 4.70/4.84 [5]~E(x51,x52)+E(f9(x51),f9(x52))
% 4.70/4.84 [6]~E(x61,x62)+E(f10(x61),f10(x62))
% 4.70/4.84 [7]~E(x71,x72)+E(f33(x71,x73),f33(x72,x73))
% 4.70/4.84 [8]~E(x81,x82)+E(f33(x83,x81),f33(x83,x82))
% 4.70/4.84 [9]~E(x91,x92)+E(f5(x91,x93,x94,x95),f5(x92,x93,x94,x95))
% 4.70/4.84 [10]~E(x101,x102)+E(f5(x103,x101,x104,x105),f5(x103,x102,x104,x105))
% 4.70/4.84 [11]~E(x111,x112)+E(f5(x113,x114,x111,x115),f5(x113,x114,x112,x115))
% 4.70/4.84 [12]~E(x121,x122)+E(f5(x123,x124,x125,x121),f5(x123,x124,x125,x122))
% 4.70/4.84 [13]~E(x131,x132)+E(f4(x131,x133),f4(x132,x133))
% 4.70/4.84 [14]~E(x141,x142)+E(f4(x143,x141),f4(x143,x142))
% 4.70/4.84 [15]~E(x151,x152)+E(f64(x151,x153,x154,x155,x156,x157,x158,x159),f64(x152,x153,x154,x155,x156,x157,x158,x159))
% 4.70/4.84 [16]~E(x161,x162)+E(f64(x163,x161,x164,x165,x166,x167,x168,x169),f64(x163,x162,x164,x165,x166,x167,x168,x169))
% 4.70/4.84 [17]~E(x171,x172)+E(f64(x173,x174,x171,x175,x176,x177,x178,x179),f64(x173,x174,x172,x175,x176,x177,x178,x179))
% 4.70/4.84 [18]~E(x181,x182)+E(f64(x183,x184,x185,x181,x186,x187,x188,x189),f64(x183,x184,x185,x182,x186,x187,x188,x189))
% 4.70/4.84 [19]~E(x191,x192)+E(f64(x193,x194,x195,x196,x191,x197,x198,x199),f64(x193,x194,x195,x196,x192,x197,x198,x199))
% 4.70/4.84 [20]~E(x201,x202)+E(f64(x203,x204,x205,x206,x207,x201,x208,x209),f64(x203,x204,x205,x206,x207,x202,x208,x209))
% 4.70/4.84 [21]~E(x211,x212)+E(f64(x213,x214,x215,x216,x217,x218,x211,x219),f64(x213,x214,x215,x216,x217,x218,x212,x219))
% 4.70/4.84 [22]~E(x221,x222)+E(f64(x223,x224,x225,x226,x227,x228,x229,x221),f64(x223,x224,x225,x226,x227,x228,x229,x222))
% 4.70/4.84 [23]~E(x231,x232)+E(f11(x231),f11(x232))
% 4.70/4.84 [24]~E(x241,x242)+E(f27(x241,x243,x244),f27(x242,x243,x244))
% 4.70/4.84 [25]~E(x251,x252)+E(f27(x253,x251,x254),f27(x253,x252,x254))
% 4.70/4.84 [26]~E(x261,x262)+E(f27(x263,x264,x261),f27(x263,x264,x262))
% 4.70/4.84 [27]~E(x271,x272)+E(f14(x271,x273),f14(x272,x273))
% 4.70/4.84 [28]~E(x281,x282)+E(f14(x283,x281),f14(x283,x282))
% 4.70/4.84 [29]~E(x291,x292)+E(f8(x291,x293,x294),f8(x292,x293,x294))
% 4.70/4.84 [30]~E(x301,x302)+E(f8(x303,x301,x304),f8(x303,x302,x304))
% 4.70/4.84 [31]~E(x311,x312)+E(f8(x313,x314,x311),f8(x313,x314,x312))
% 4.70/4.84 [32]~E(x321,x322)+E(f17(x321,x323,x324),f17(x322,x323,x324))
% 4.70/4.84 [33]~E(x331,x332)+E(f17(x333,x331,x334),f17(x333,x332,x334))
% 4.70/4.84 [34]~E(x341,x342)+E(f17(x343,x344,x341),f17(x343,x344,x342))
% 4.70/4.84 [35]~E(x351,x352)+E(f3(x351),f3(x352))
% 4.70/4.84 [36]~E(x361,x362)+E(f28(x361,x363,x364,x365),f28(x362,x363,x364,x365))
% 4.70/4.84 [37]~E(x371,x372)+E(f28(x373,x371,x374,x375),f28(x373,x372,x374,x375))
% 4.70/4.84 [38]~E(x381,x382)+E(f28(x383,x384,x381,x385),f28(x383,x384,x382,x385))
% 4.70/4.84 [39]~E(x391,x392)+E(f28(x393,x394,x395,x391),f28(x393,x394,x395,x392))
% 4.70/4.84 [40]~E(x401,x402)+E(f84(x401,x403),f84(x402,x403))
% 4.70/4.84 [41]~E(x411,x412)+E(f84(x413,x411),f84(x413,x412))
% 4.70/4.84 [42]~E(x421,x422)+E(f16(x421),f16(x422))
% 4.70/4.84 [43]~E(x431,x432)+E(f78(x431,x433,x434,x435),f78(x432,x433,x434,x435))
% 4.70/4.84 [44]~E(x441,x442)+E(f78(x443,x441,x444,x445),f78(x443,x442,x444,x445))
% 4.70/4.84 [45]~E(x451,x452)+E(f78(x453,x454,x451,x455),f78(x453,x454,x452,x455))
% 4.70/4.84 [46]~E(x461,x462)+E(f78(x463,x464,x465,x461),f78(x463,x464,x465,x462))
% 4.70/4.84 [47]~E(x471,x472)+E(f83(x471),f83(x472))
% 4.70/4.84 [48]~E(x481,x482)+E(f63(x481,x483,x484,x485,x486,x487,x488,x489),f63(x482,x483,x484,x485,x486,x487,x488,x489))
% 4.70/4.84 [49]~E(x491,x492)+E(f63(x493,x491,x494,x495,x496,x497,x498,x499),f63(x493,x492,x494,x495,x496,x497,x498,x499))
% 4.70/4.84 [50]~E(x501,x502)+E(f63(x503,x504,x501,x505,x506,x507,x508,x509),f63(x503,x504,x502,x505,x506,x507,x508,x509))
% 4.70/4.84 [51]~E(x511,x512)+E(f63(x513,x514,x515,x511,x516,x517,x518,x519),f63(x513,x514,x515,x512,x516,x517,x518,x519))
% 4.70/4.84 [52]~E(x521,x522)+E(f63(x523,x524,x525,x526,x521,x527,x528,x529),f63(x523,x524,x525,x526,x522,x527,x528,x529))
% 4.70/4.84 [53]~E(x531,x532)+E(f63(x533,x534,x535,x536,x537,x531,x538,x539),f63(x533,x534,x535,x536,x537,x532,x538,x539))
% 4.70/4.84 [54]~E(x541,x542)+E(f63(x543,x544,x545,x546,x547,x548,x541,x549),f63(x543,x544,x545,x546,x547,x548,x542,x549))
% 4.70/4.84 [55]~E(x551,x552)+E(f63(x553,x554,x555,x556,x557,x558,x559,x551),f63(x553,x554,x555,x556,x557,x558,x559,x552))
% 4.70/4.84 [56]~E(x561,x562)+E(f31(x561,x563,x564,x565),f31(x562,x563,x564,x565))
% 4.70/4.84 [57]~E(x571,x572)+E(f31(x573,x571,x574,x575),f31(x573,x572,x574,x575))
% 4.70/4.84 [58]~E(x581,x582)+E(f31(x583,x584,x581,x585),f31(x583,x584,x582,x585))
% 4.70/4.84 [59]~E(x591,x592)+E(f31(x593,x594,x595,x591),f31(x593,x594,x595,x592))
% 4.70/4.84 [60]~E(x601,x602)+E(f7(x601,x603,x604),f7(x602,x603,x604))
% 4.70/4.84 [61]~E(x611,x612)+E(f7(x613,x611,x614),f7(x613,x612,x614))
% 4.70/4.84 [62]~E(x621,x622)+E(f7(x623,x624,x621),f7(x623,x624,x622))
% 4.70/4.84 [63]~E(x631,x632)+E(f13(x631),f13(x632))
% 4.70/4.84 [64]~E(x641,x642)+E(f34(x641),f34(x642))
% 4.70/4.84 [65]~E(x651,x652)+E(f39(x651,x653),f39(x652,x653))
% 4.70/4.84 [66]~E(x661,x662)+E(f39(x663,x661),f39(x663,x662))
% 4.70/4.84 [67]~E(x671,x672)+E(f35(x671,x673),f35(x672,x673))
% 4.70/4.84 [68]~E(x681,x682)+E(f35(x683,x681),f35(x683,x682))
% 4.70/4.84 [69]~E(x691,x692)+E(f18(x691,x693,x694),f18(x692,x693,x694))
% 4.70/4.84 [70]~E(x701,x702)+E(f18(x703,x701,x704),f18(x703,x702,x704))
% 4.70/4.84 [71]~E(x711,x712)+E(f18(x713,x714,x711),f18(x713,x714,x712))
% 4.70/4.84 [72]~E(x721,x722)+E(f55(x721,x723),f55(x722,x723))
% 4.70/4.84 [73]~E(x731,x732)+E(f55(x733,x731),f55(x733,x732))
% 4.70/4.84 [74]~E(x741,x742)+E(f66(x741,x743),f66(x742,x743))
% 4.70/4.84 [75]~E(x751,x752)+E(f66(x753,x751),f66(x753,x752))
% 4.70/4.84 [76]~E(x761,x762)+E(f59(x761,x763,x764,x765),f59(x762,x763,x764,x765))
% 4.70/4.84 [77]~E(x771,x772)+E(f59(x773,x771,x774,x775),f59(x773,x772,x774,x775))
% 4.70/4.84 [78]~E(x781,x782)+E(f59(x783,x784,x781,x785),f59(x783,x784,x782,x785))
% 4.70/4.84 [79]~E(x791,x792)+E(f59(x793,x794,x795,x791),f59(x793,x794,x795,x792))
% 4.70/4.84 [80]~E(x801,x802)+E(f23(x801,x803,x804,x805,x806),f23(x802,x803,x804,x805,x806))
% 4.70/4.84 [81]~E(x811,x812)+E(f23(x813,x811,x814,x815,x816),f23(x813,x812,x814,x815,x816))
% 4.70/4.84 [82]~E(x821,x822)+E(f23(x823,x824,x821,x825,x826),f23(x823,x824,x822,x825,x826))
% 4.70/4.84 [83]~E(x831,x832)+E(f23(x833,x834,x835,x831,x836),f23(x833,x834,x835,x832,x836))
% 4.70/4.84 [84]~E(x841,x842)+E(f23(x843,x844,x845,x846,x841),f23(x843,x844,x845,x846,x842))
% 4.70/4.84 [85]~E(x851,x852)+E(f6(x851,x853,x854,x855),f6(x852,x853,x854,x855))
% 4.70/4.84 [86]~E(x861,x862)+E(f6(x863,x861,x864,x865),f6(x863,x862,x864,x865))
% 4.70/4.84 [87]~E(x871,x872)+E(f6(x873,x874,x871,x875),f6(x873,x874,x872,x875))
% 4.70/4.84 [88]~E(x881,x882)+E(f6(x883,x884,x885,x881),f6(x883,x884,x885,x882))
% 4.70/4.84 [89]~E(x891,x892)+E(f76(x891,x893,x894,x895),f76(x892,x893,x894,x895))
% 4.70/4.84 [90]~E(x901,x902)+E(f76(x903,x901,x904,x905),f76(x903,x902,x904,x905))
% 4.70/4.84 [91]~E(x911,x912)+E(f76(x913,x914,x911,x915),f76(x913,x914,x912,x915))
% 4.70/4.84 [92]~E(x921,x922)+E(f76(x923,x924,x925,x921),f76(x923,x924,x925,x922))
% 4.70/4.84 [93]~E(x931,x932)+E(f48(x931,x933),f48(x932,x933))
% 4.70/4.84 [94]~E(x941,x942)+E(f48(x943,x941),f48(x943,x942))
% 4.70/4.84 [95]~E(x951,x952)+E(f57(x951,x953,x954),f57(x952,x953,x954))
% 4.70/4.84 [96]~E(x961,x962)+E(f57(x963,x961,x964),f57(x963,x962,x964))
% 4.70/4.84 [97]~E(x971,x972)+E(f57(x973,x974,x971),f57(x973,x974,x972))
% 4.70/4.84 [98]~E(x981,x982)+E(f45(x981,x983,x984,x985),f45(x982,x983,x984,x985))
% 4.70/4.84 [99]~E(x991,x992)+E(f45(x993,x991,x994,x995),f45(x993,x992,x994,x995))
% 4.70/4.84 [100]~E(x1001,x1002)+E(f45(x1003,x1004,x1001,x1005),f45(x1003,x1004,x1002,x1005))
% 4.70/4.84 [101]~E(x1011,x1012)+E(f45(x1013,x1014,x1015,x1011),f45(x1013,x1014,x1015,x1012))
% 4.70/4.84 [102]~E(x1021,x1022)+E(f71(x1021,x1023,x1024),f71(x1022,x1023,x1024))
% 4.70/4.84 [103]~E(x1031,x1032)+E(f71(x1033,x1031,x1034),f71(x1033,x1032,x1034))
% 4.70/4.84 [104]~E(x1041,x1042)+E(f71(x1043,x1044,x1041),f71(x1043,x1044,x1042))
% 4.70/4.84 [105]~E(x1051,x1052)+E(f29(x1051,x1053),f29(x1052,x1053))
% 4.70/4.84 [106]~E(x1061,x1062)+E(f29(x1063,x1061),f29(x1063,x1062))
% 4.70/4.84 [107]~E(x1071,x1072)+E(f85(x1071,x1073),f85(x1072,x1073))
% 4.70/4.84 [108]~E(x1081,x1082)+E(f85(x1083,x1081),f85(x1083,x1082))
% 4.70/4.84 [109]~E(x1091,x1092)+E(f50(x1091,x1093),f50(x1092,x1093))
% 4.70/4.84 [110]~E(x1101,x1102)+E(f50(x1103,x1101),f50(x1103,x1102))
% 4.70/4.84 [111]~E(x1111,x1112)+E(f26(x1111,x1113,x1114,x1115,x1116),f26(x1112,x1113,x1114,x1115,x1116))
% 4.70/4.84 [112]~E(x1121,x1122)+E(f26(x1123,x1121,x1124,x1125,x1126),f26(x1123,x1122,x1124,x1125,x1126))
% 4.70/4.84 [113]~E(x1131,x1132)+E(f26(x1133,x1134,x1131,x1135,x1136),f26(x1133,x1134,x1132,x1135,x1136))
% 4.70/4.84 [114]~E(x1141,x1142)+E(f26(x1143,x1144,x1145,x1141,x1146),f26(x1143,x1144,x1145,x1142,x1146))
% 4.70/4.84 [115]~E(x1151,x1152)+E(f26(x1153,x1154,x1155,x1156,x1151),f26(x1153,x1154,x1155,x1156,x1152))
% 4.70/4.84 [116]~E(x1161,x1162)+E(f54(x1161,x1163,x1164,x1165,x1166),f54(x1162,x1163,x1164,x1165,x1166))
% 4.70/4.84 [117]~E(x1171,x1172)+E(f54(x1173,x1171,x1174,x1175,x1176),f54(x1173,x1172,x1174,x1175,x1176))
% 4.70/4.84 [118]~E(x1181,x1182)+E(f54(x1183,x1184,x1181,x1185,x1186),f54(x1183,x1184,x1182,x1185,x1186))
% 4.70/4.84 [119]~E(x1191,x1192)+E(f54(x1193,x1194,x1195,x1191,x1196),f54(x1193,x1194,x1195,x1192,x1196))
% 4.70/4.84 [120]~E(x1201,x1202)+E(f54(x1203,x1204,x1205,x1206,x1201),f54(x1203,x1204,x1205,x1206,x1202))
% 4.70/4.84 [121]~E(x1211,x1212)+E(f49(x1211,x1213),f49(x1212,x1213))
% 4.70/4.84 [122]~E(x1221,x1222)+E(f49(x1223,x1221),f49(x1223,x1222))
% 4.70/4.84 [123]~E(x1231,x1232)+E(f46(x1231,x1233,x1234,x1235,x1236),f46(x1232,x1233,x1234,x1235,x1236))
% 4.70/4.84 [124]~E(x1241,x1242)+E(f46(x1243,x1241,x1244,x1245,x1246),f46(x1243,x1242,x1244,x1245,x1246))
% 4.70/4.84 [125]~E(x1251,x1252)+E(f46(x1253,x1254,x1251,x1255,x1256),f46(x1253,x1254,x1252,x1255,x1256))
% 4.70/4.84 [126]~E(x1261,x1262)+E(f46(x1263,x1264,x1265,x1261,x1266),f46(x1263,x1264,x1265,x1262,x1266))
% 4.70/4.84 [127]~E(x1271,x1272)+E(f46(x1273,x1274,x1275,x1276,x1271),f46(x1273,x1274,x1275,x1276,x1272))
% 4.70/4.84 [128]~E(x1281,x1282)+E(f75(x1281,x1283,x1284,x1285,x1286),f75(x1282,x1283,x1284,x1285,x1286))
% 4.70/4.84 [129]~E(x1291,x1292)+E(f75(x1293,x1291,x1294,x1295,x1296),f75(x1293,x1292,x1294,x1295,x1296))
% 4.70/4.84 [130]~E(x1301,x1302)+E(f75(x1303,x1304,x1301,x1305,x1306),f75(x1303,x1304,x1302,x1305,x1306))
% 4.70/4.84 [131]~E(x1311,x1312)+E(f75(x1313,x1314,x1315,x1311,x1316),f75(x1313,x1314,x1315,x1312,x1316))
% 4.70/4.84 [132]~E(x1321,x1322)+E(f75(x1323,x1324,x1325,x1326,x1321),f75(x1323,x1324,x1325,x1326,x1322))
% 4.70/4.84 [133]~E(x1331,x1332)+E(f73(x1331,x1333,x1334,x1335),f73(x1332,x1333,x1334,x1335))
% 4.70/4.84 [134]~E(x1341,x1342)+E(f73(x1343,x1341,x1344,x1345),f73(x1343,x1342,x1344,x1345))
% 4.70/4.84 [135]~E(x1351,x1352)+E(f73(x1353,x1354,x1351,x1355),f73(x1353,x1354,x1352,x1355))
% 4.70/4.84 [136]~E(x1361,x1362)+E(f73(x1363,x1364,x1365,x1361),f73(x1363,x1364,x1365,x1362))
% 4.70/4.84 [137]~E(x1371,x1372)+E(f22(x1371,x1373,x1374,x1375),f22(x1372,x1373,x1374,x1375))
% 4.70/4.84 [138]~E(x1381,x1382)+E(f22(x1383,x1381,x1384,x1385),f22(x1383,x1382,x1384,x1385))
% 4.70/4.84 [139]~E(x1391,x1392)+E(f22(x1393,x1394,x1391,x1395),f22(x1393,x1394,x1392,x1395))
% 4.70/4.84 [140]~E(x1401,x1402)+E(f22(x1403,x1404,x1405,x1401),f22(x1403,x1404,x1405,x1402))
% 4.70/4.84 [141]~E(x1411,x1412)+E(f58(x1411,x1413,x1414),f58(x1412,x1413,x1414))
% 4.70/4.84 [142]~E(x1421,x1422)+E(f58(x1423,x1421,x1424),f58(x1423,x1422,x1424))
% 4.70/4.84 [143]~E(x1431,x1432)+E(f58(x1433,x1434,x1431),f58(x1433,x1434,x1432))
% 4.70/4.84 [144]~E(x1441,x1442)+E(f44(x1441,x1443),f44(x1442,x1443))
% 4.70/4.84 [145]~E(x1451,x1452)+E(f44(x1453,x1451),f44(x1453,x1452))
% 4.70/4.84 [146]~E(x1461,x1462)+E(f72(x1461,x1463,x1464),f72(x1462,x1463,x1464))
% 4.70/4.84 [147]~E(x1471,x1472)+E(f72(x1473,x1471,x1474),f72(x1473,x1472,x1474))
% 4.70/4.84 [148]~E(x1481,x1482)+E(f72(x1483,x1484,x1481),f72(x1483,x1484,x1482))
% 4.70/4.84 [149]~E(x1491,x1492)+E(f30(x1491,x1493),f30(x1492,x1493))
% 4.70/4.84 [150]~E(x1501,x1502)+E(f30(x1503,x1501),f30(x1503,x1502))
% 4.70/4.84 [151]~E(x1511,x1512)+E(f70(x1511,x1513,x1514,x1515),f70(x1512,x1513,x1514,x1515))
% 4.70/4.84 [152]~E(x1521,x1522)+E(f70(x1523,x1521,x1524,x1525),f70(x1523,x1522,x1524,x1525))
% 4.70/4.84 [153]~E(x1531,x1532)+E(f70(x1533,x1534,x1531,x1535),f70(x1533,x1534,x1532,x1535))
% 4.70/4.84 [154]~E(x1541,x1542)+E(f70(x1543,x1544,x1545,x1541),f70(x1543,x1544,x1545,x1542))
% 4.70/4.84 [155]~E(x1551,x1552)+E(f47(x1551,x1553),f47(x1552,x1553))
% 4.70/4.84 [156]~E(x1561,x1562)+E(f47(x1563,x1561),f47(x1563,x1562))
% 4.70/4.84 [157]~E(x1571,x1572)+E(f19(x1571,x1573,x1574),f19(x1572,x1573,x1574))
% 4.70/4.84 [158]~E(x1581,x1582)+E(f19(x1583,x1581,x1584),f19(x1583,x1582,x1584))
% 4.70/4.84 [159]~E(x1591,x1592)+E(f19(x1593,x1594,x1591),f19(x1593,x1594,x1592))
% 4.70/4.84 [160]~E(x1601,x1602)+E(f42(x1601,x1603),f42(x1602,x1603))
% 4.70/4.84 [161]~E(x1611,x1612)+E(f42(x1613,x1611),f42(x1613,x1612))
% 4.70/4.84 [162]~E(x1621,x1622)+E(f53(x1621,x1623,x1624,x1625,x1626),f53(x1622,x1623,x1624,x1625,x1626))
% 4.70/4.84 [163]~E(x1631,x1632)+E(f53(x1633,x1631,x1634,x1635,x1636),f53(x1633,x1632,x1634,x1635,x1636))
% 4.70/4.84 [164]~E(x1641,x1642)+E(f53(x1643,x1644,x1641,x1645,x1646),f53(x1643,x1644,x1642,x1645,x1646))
% 4.70/4.84 [165]~E(x1651,x1652)+E(f53(x1653,x1654,x1655,x1651,x1656),f53(x1653,x1654,x1655,x1652,x1656))
% 4.70/4.84 [166]~E(x1661,x1662)+E(f53(x1663,x1664,x1665,x1666,x1661),f53(x1663,x1664,x1665,x1666,x1662))
% 4.70/4.84 [167]~E(x1671,x1672)+E(f37(x1671,x1673),f37(x1672,x1673))
% 4.70/4.84 [168]~E(x1681,x1682)+E(f37(x1683,x1681),f37(x1683,x1682))
% 4.70/4.84 [169]~E(x1691,x1692)+E(f62(x1691,x1693,x1694,x1695,x1696),f62(x1692,x1693,x1694,x1695,x1696))
% 4.70/4.84 [170]~E(x1701,x1702)+E(f62(x1703,x1701,x1704,x1705,x1706),f62(x1703,x1702,x1704,x1705,x1706))
% 4.70/4.84 [171]~E(x1711,x1712)+E(f62(x1713,x1714,x1711,x1715,x1716),f62(x1713,x1714,x1712,x1715,x1716))
% 4.70/4.84 [172]~E(x1721,x1722)+E(f62(x1723,x1724,x1725,x1721,x1726),f62(x1723,x1724,x1725,x1722,x1726))
% 4.70/4.84 [173]~E(x1731,x1732)+E(f62(x1733,x1734,x1735,x1736,x1731),f62(x1733,x1734,x1735,x1736,x1732))
% 4.70/4.84 [174]~E(x1741,x1742)+E(f51(x1741,x1743),f51(x1742,x1743))
% 4.70/4.84 [175]~E(x1751,x1752)+E(f51(x1753,x1751),f51(x1753,x1752))
% 4.70/4.84 [176]~E(x1761,x1762)+E(f60(x1761,x1763,x1764,x1765),f60(x1762,x1763,x1764,x1765))
% 4.70/4.84 [177]~E(x1771,x1772)+E(f60(x1773,x1771,x1774,x1775),f60(x1773,x1772,x1774,x1775))
% 4.70/4.84 [178]~E(x1781,x1782)+E(f60(x1783,x1784,x1781,x1785),f60(x1783,x1784,x1782,x1785))
% 4.70/4.84 [179]~E(x1791,x1792)+E(f60(x1793,x1794,x1795,x1791),f60(x1793,x1794,x1795,x1792))
% 4.70/4.84 [180]~E(x1801,x1802)+E(f43(x1801,x1803),f43(x1802,x1803))
% 4.70/4.84 [181]~E(x1811,x1812)+E(f43(x1813,x1811),f43(x1813,x1812))
% 4.70/4.84 [182]~E(x1821,x1822)+E(f20(x1821,x1823,x1824),f20(x1822,x1823,x1824))
% 4.70/4.84 [183]~E(x1831,x1832)+E(f20(x1833,x1831,x1834),f20(x1833,x1832,x1834))
% 4.70/4.84 [184]~E(x1841,x1842)+E(f20(x1843,x1844,x1841),f20(x1843,x1844,x1842))
% 4.70/4.84 [185]~E(x1851,x1852)+E(f25(x1851,x1853,x1854,x1855),f25(x1852,x1853,x1854,x1855))
% 4.70/4.84 [186]~E(x1861,x1862)+E(f25(x1863,x1861,x1864,x1865),f25(x1863,x1862,x1864,x1865))
% 4.70/4.84 [187]~E(x1871,x1872)+E(f25(x1873,x1874,x1871,x1875),f25(x1873,x1874,x1872,x1875))
% 4.70/4.84 [188]~E(x1881,x1882)+E(f25(x1883,x1884,x1885,x1881),f25(x1883,x1884,x1885,x1882))
% 4.70/4.84 [189]~E(x1891,x1892)+E(f21(x1891,x1893,x1894),f21(x1892,x1893,x1894))
% 4.70/4.84 [190]~E(x1901,x1902)+E(f21(x1903,x1901,x1904),f21(x1903,x1902,x1904))
% 4.70/4.84 [191]~E(x1911,x1912)+E(f21(x1913,x1914,x1911),f21(x1913,x1914,x1912))
% 4.70/4.84 [192]~E(x1921,x1922)+E(f38(x1921,x1923),f38(x1922,x1923))
% 4.70/4.84 [193]~E(x1931,x1932)+E(f38(x1933,x1931),f38(x1933,x1932))
% 4.70/4.84 [194]~E(x1941,x1942)+E(f40(x1941),f40(x1942))
% 4.70/4.84 [195]~E(x1951,x1952)+E(f24(x1951,x1953,x1954),f24(x1952,x1953,x1954))
% 4.70/4.84 [196]~E(x1961,x1962)+E(f24(x1963,x1961,x1964),f24(x1963,x1962,x1964))
% 4.70/4.84 [197]~E(x1971,x1972)+E(f24(x1973,x1974,x1971),f24(x1973,x1974,x1972))
% 4.70/4.84 [198]~E(x1981,x1982)+E(f86(x1981,x1983),f86(x1982,x1983))
% 4.70/4.84 [199]~E(x1991,x1992)+E(f86(x1993,x1991),f86(x1993,x1992))
% 4.70/4.84 [200]~E(x2001,x2002)+E(f67(x2001,x2003),f67(x2002,x2003))
% 4.70/4.84 [201]~E(x2011,x2012)+E(f67(x2013,x2011),f67(x2013,x2012))
% 4.70/4.84 [202]~E(x2021,x2022)+E(f68(x2021,x2023,x2024),f68(x2022,x2023,x2024))
% 4.70/4.84 [203]~E(x2031,x2032)+E(f68(x2033,x2031,x2034),f68(x2033,x2032,x2034))
% 4.70/4.84 [204]~E(x2041,x2042)+E(f68(x2043,x2044,x2041),f68(x2043,x2044,x2042))
% 4.70/4.84 [205]~E(x2051,x2052)+E(f36(x2051),f36(x2052))
% 4.70/4.84 [206]~E(x2061,x2062)+E(f69(x2061,x2063,x2064,x2065),f69(x2062,x2063,x2064,x2065))
% 4.70/4.84 [207]~E(x2071,x2072)+E(f69(x2073,x2071,x2074,x2075),f69(x2073,x2072,x2074,x2075))
% 4.70/4.84 [208]~E(x2081,x2082)+E(f69(x2083,x2084,x2081,x2085),f69(x2083,x2084,x2082,x2085))
% 4.70/4.84 [209]~E(x2091,x2092)+E(f69(x2093,x2094,x2095,x2091),f69(x2093,x2094,x2095,x2092))
% 4.70/4.84 [210]~E(x2101,x2102)+E(f52(x2101,x2103),f52(x2102,x2103))
% 4.70/4.84 [211]~E(x2111,x2112)+E(f52(x2113,x2111),f52(x2113,x2112))
% 4.70/4.84 [212]~E(x2121,x2122)+E(f61(x2121,x2123,x2124,x2125),f61(x2122,x2123,x2124,x2125))
% 4.70/4.84 [213]~E(x2131,x2132)+E(f61(x2133,x2131,x2134,x2135),f61(x2133,x2132,x2134,x2135))
% 4.70/4.84 [214]~E(x2141,x2142)+E(f61(x2143,x2144,x2141,x2145),f61(x2143,x2144,x2142,x2145))
% 4.70/4.84 [215]~E(x2151,x2152)+E(f61(x2153,x2154,x2155,x2151),f61(x2153,x2154,x2155,x2152))
% 4.70/4.84 [216]~E(x2161,x2162)+E(f65(x2161,x2163),f65(x2162,x2163))
% 4.70/4.84 [217]~E(x2171,x2172)+E(f65(x2173,x2171),f65(x2173,x2172))
% 4.70/4.84 [218]~E(x2181,x2182)+E(f41(x2181),f41(x2182))
% 4.70/4.84 [219]~E(x2191,x2192)+E(f74(x2191,x2193,x2194,x2195),f74(x2192,x2193,x2194,x2195))
% 4.70/4.84 [220]~E(x2201,x2202)+E(f74(x2203,x2201,x2204,x2205),f74(x2203,x2202,x2204,x2205))
% 4.70/4.84 [221]~E(x2211,x2212)+E(f74(x2213,x2214,x2211,x2215),f74(x2213,x2214,x2212,x2215))
% 4.70/4.84 [222]~E(x2221,x2222)+E(f74(x2223,x2224,x2225,x2221),f74(x2223,x2224,x2225,x2222))
% 4.70/4.84 [223]~E(x2231,x2232)+E(f77(x2231,x2233,x2234,x2235),f77(x2232,x2233,x2234,x2235))
% 4.70/4.84 [224]~E(x2241,x2242)+E(f77(x2243,x2241,x2244,x2245),f77(x2243,x2242,x2244,x2245))
% 4.70/4.84 [225]~E(x2251,x2252)+E(f77(x2253,x2254,x2251,x2255),f77(x2253,x2254,x2252,x2255))
% 4.70/4.84 [226]~E(x2261,x2262)+E(f77(x2263,x2264,x2265,x2261),f77(x2263,x2264,x2265,x2262))
% 4.70/4.84 [227]~E(x2271,x2272)+E(f56(x2271,x2273),f56(x2272,x2273))
% 4.70/4.84 [228]~E(x2281,x2282)+E(f56(x2283,x2281),f56(x2283,x2282))
% 4.70/4.84 [229]~P1(x2291)+P1(x2292)+~E(x2291,x2292)
% 4.70/4.84 [230]~P2(x2301)+P2(x2302)+~E(x2301,x2302)
% 4.70/4.84 [231]~P3(x2311)+P3(x2312)+~E(x2311,x2312)
% 4.70/4.84 [232]~P4(x2321)+P4(x2322)+~E(x2321,x2322)
% 4.70/4.84 [233]~P5(x2331)+P5(x2332)+~E(x2331,x2332)
% 4.70/4.84 [234]~P6(x2341)+P6(x2342)+~E(x2341,x2342)
% 4.70/4.84 [235]P10(x2352,x2353,x2354,x2355)+~E(x2351,x2352)+~P10(x2351,x2353,x2354,x2355)
% 4.70/4.84 [236]P10(x2363,x2362,x2364,x2365)+~E(x2361,x2362)+~P10(x2363,x2361,x2364,x2365)
% 4.70/4.84 [237]P10(x2373,x2374,x2372,x2375)+~E(x2371,x2372)+~P10(x2373,x2374,x2371,x2375)
% 4.70/4.84 [238]P10(x2383,x2384,x2385,x2382)+~E(x2381,x2382)+~P10(x2383,x2384,x2385,x2381)
% 4.70/4.84 [239]~P26(x2391)+P26(x2392)+~E(x2391,x2392)
% 4.70/4.84 [240]P7(x2402,x2403,x2404)+~E(x2401,x2402)+~P7(x2401,x2403,x2404)
% 4.70/4.84 [241]P7(x2413,x2412,x2414)+~E(x2411,x2412)+~P7(x2413,x2411,x2414)
% 4.70/4.84 [242]P7(x2423,x2424,x2422)+~E(x2421,x2422)+~P7(x2423,x2424,x2421)
% 4.70/4.84 [243]~P27(x2431)+P27(x2432)+~E(x2431,x2432)
% 4.70/4.84 [244]P9(x2442,x2443,x2444)+~E(x2441,x2442)+~P9(x2441,x2443,x2444)
% 4.70/4.84 [245]P9(x2453,x2452,x2454)+~E(x2451,x2452)+~P9(x2453,x2451,x2454)
% 4.70/4.84 [246]P9(x2463,x2464,x2462)+~E(x2461,x2462)+~P9(x2463,x2464,x2461)
% 4.70/4.84 [247]~P29(x2471)+P29(x2472)+~E(x2471,x2472)
% 4.70/4.84 [248]~P30(x2481)+P30(x2482)+~E(x2481,x2482)
% 4.70/4.84 [249]P8(x2492,x2493)+~E(x2491,x2492)+~P8(x2491,x2493)
% 4.70/4.84 [250]P8(x2503,x2502)+~E(x2501,x2502)+~P8(x2503,x2501)
% 4.70/4.84 [251]~P31(x2511)+P31(x2512)+~E(x2511,x2512)
% 4.70/4.84 [252]~P21(x2521)+P21(x2522)+~E(x2521,x2522)
% 4.70/4.84 [253]~P15(x2531)+P15(x2532)+~E(x2531,x2532)
% 4.70/4.84 [254]~P16(x2541)+P16(x2542)+~E(x2541,x2542)
% 4.70/4.84 [255]~P17(x2551)+P17(x2552)+~E(x2551,x2552)
% 4.70/4.84 [256]~P18(x2561)+P18(x2562)+~E(x2561,x2562)
% 4.70/4.84 [257]~P24(x2571)+P24(x2572)+~E(x2571,x2572)
% 4.70/4.84 [258]~P19(x2581)+P19(x2582)+~E(x2581,x2582)
% 4.70/4.84 [259]~P20(x2591)+P20(x2592)+~E(x2591,x2592)
% 4.70/4.84 [260]~P22(x2601)+P22(x2602)+~E(x2601,x2602)
% 4.70/4.84 [261]~P25(x2611)+P25(x2612)+~E(x2611,x2612)
% 4.70/4.84 [262]~P32(x2621)+P32(x2622)+~E(x2621,x2622)
% 4.70/4.84 [263]~P33(x2631)+P33(x2632)+~E(x2631,x2632)
% 4.70/4.84 [264]~P35(x2641)+P35(x2642)+~E(x2641,x2642)
% 4.70/4.84 [265]~P36(x2651)+P36(x2652)+~E(x2651,x2652)
% 4.70/4.84 [266]~P23(x2661)+P23(x2662)+~E(x2661,x2662)
% 4.70/4.84 [267]P14(x2672,x2673,x2674)+~E(x2671,x2672)+~P14(x2671,x2673,x2674)
% 4.70/4.84 [268]P14(x2683,x2682,x2684)+~E(x2681,x2682)+~P14(x2683,x2681,x2684)
% 4.70/4.84 [269]P14(x2693,x2694,x2692)+~E(x2691,x2692)+~P14(x2693,x2694,x2691)
% 4.70/4.84 [270]P11(x2702,x2703,x2704)+~E(x2701,x2702)+~P11(x2701,x2703,x2704)
% 4.70/4.84 [271]P11(x2713,x2712,x2714)+~E(x2711,x2712)+~P11(x2713,x2711,x2714)
% 4.70/4.84 [272]P11(x2723,x2724,x2722)+~E(x2721,x2722)+~P11(x2723,x2724,x2721)
% 4.70/4.84 [273]~P38(x2731)+P38(x2732)+~E(x2731,x2732)
% 4.70/4.84 [274]P13(x2742,x2743,x2744,x2745,x2746,x2747)+~E(x2741,x2742)+~P13(x2741,x2743,x2744,x2745,x2746,x2747)
% 4.70/4.84 [275]P13(x2753,x2752,x2754,x2755,x2756,x2757)+~E(x2751,x2752)+~P13(x2753,x2751,x2754,x2755,x2756,x2757)
% 4.70/4.84 [276]P13(x2763,x2764,x2762,x2765,x2766,x2767)+~E(x2761,x2762)+~P13(x2763,x2764,x2761,x2765,x2766,x2767)
% 4.70/4.84 [277]P13(x2773,x2774,x2775,x2772,x2776,x2777)+~E(x2771,x2772)+~P13(x2773,x2774,x2775,x2771,x2776,x2777)
% 4.70/4.84 [278]P13(x2783,x2784,x2785,x2786,x2782,x2787)+~E(x2781,x2782)+~P13(x2783,x2784,x2785,x2786,x2781,x2787)
% 4.70/4.84 [279]P13(x2793,x2794,x2795,x2796,x2797,x2792)+~E(x2791,x2792)+~P13(x2793,x2794,x2795,x2796,x2797,x2791)
% 4.70/4.84 [280]~P34(x2801)+P34(x2802)+~E(x2801,x2802)
% 4.70/4.84 [281]~P37(x2811)+P37(x2812)+~E(x2811,x2812)
% 4.70/4.84 [282]~P28(x2821)+P28(x2822)+~E(x2821,x2822)
% 4.70/4.84 [283]P12(x2832,x2833,x2834)+~E(x2831,x2832)+~P12(x2831,x2833,x2834)
% 4.70/4.84 [284]P12(x2843,x2842,x2844)+~E(x2841,x2842)+~P12(x2843,x2841,x2844)
% 4.70/4.84 [285]P12(x2853,x2854,x2852)+~E(x2851,x2852)+~P12(x2853,x2854,x2851)
% 4.70/4.84
% 4.70/4.84 %-------------------------------------------
% 4.70/4.85 cnf(1028,plain,
% 4.70/4.85 (~E(x10281,f33(a12,x10281))),
% 4.70/4.85 inference(scs_inference,[],[293,316,335,391,2,543,495,476,467])).
% 4.70/4.85 cnf(1030,plain,
% 4.70/4.85 (P8(a32,x10301)),
% 4.70/4.85 inference(scs_inference,[],[291,293,316,335,391,2,543,495,476,467,403])).
% 4.70/4.85 cnf(1032,plain,
% 4.70/4.85 (~P9(a80,x10321,f10(a1))),
% 4.70/4.85 inference(scs_inference,[],[291,293,316,317,335,391,2,543,495,476,467,403,470])).
% 4.70/4.85 cnf(1037,plain,
% 4.70/4.85 (~P9(a80,x10371,x10371)),
% 4.70/4.85 inference(rename_variables,[],[385])).
% 4.70/4.85 cnf(1040,plain,
% 4.70/4.85 (P9(a80,x10401,f33(a12,f8(a80,x10402,x10401)))),
% 4.70/4.85 inference(rename_variables,[],[361])).
% 4.70/4.85 cnf(1043,plain,
% 4.70/4.85 (P7(a80,x10431,f8(a80,x10432,x10431))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1046,plain,
% 4.70/4.85 (P7(a80,x10461,f8(a80,x10462,x10461))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1049,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10491,x10492),x10492)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(1052,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10521,x10522),x10522)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(1055,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x10551),x10551)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1058,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x10581),x10581)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1061,plain,
% 4.70/4.85 (E(f14(a80,x10611),x10611)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1064,plain,
% 4.70/4.85 (P7(a80,x10641,f8(a80,x10642,x10641))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1067,plain,
% 4.70/4.85 (P9(a80,x10671,f33(a12,x10671))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1070,plain,
% 4.70/4.85 (P7(a80,x10701,f8(a80,x10702,x10701))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1073,plain,
% 4.70/4.85 (P7(a80,x10731,f8(a80,x10732,x10731))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1078,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10781,x10782),x10782)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(1081,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10811,x10812),x10811)),
% 4.70/4.85 inference(rename_variables,[],[398])).
% 4.70/4.85 cnf(1084,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x10841),x10841)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1087,plain,
% 4.70/4.85 (E(f14(a80,x10871),x10871)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1090,plain,
% 4.70/4.85 (E(f14(a80,x10901),x10901)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1093,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10931,x10932),x10931)),
% 4.70/4.85 inference(rename_variables,[],[398])).
% 4.70/4.85 cnf(1097,plain,
% 4.70/4.85 (~E(f8(a80,x10971,f33(a12,x10972)),x10972)),
% 4.70/4.85 inference(scs_inference,[],[385,291,293,316,317,320,1061,1087,351,1043,1046,1064,1070,397,1049,1052,1078,398,1081,335,391,1055,1058,361,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452])).
% 4.70/4.85 cnf(1098,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x10981,x10982),x10982)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(1101,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x11011),x11011)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1104,plain,
% 4.70/4.85 (~E(f33(a12,x11041),x11041)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1116,plain,
% 4.70/4.85 (~E(f33(a12,x11161),x11161)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1119,plain,
% 4.70/4.85 (P7(f84(x11191,a32),x11192,f27(x11191,x11193,x11192))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(1122,plain,
% 4.70/4.85 (~E(f33(a12,x11221),x11221)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1125,plain,
% 4.70/4.85 (~E(f33(a12,x11251),x11251)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1128,plain,
% 4.70/4.85 (~E(f33(a12,x11281),x11281)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1131,plain,
% 4.70/4.85 (E(f14(a80,x11311),x11311)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1134,plain,
% 4.70/4.85 (E(f14(a80,x11341),x11341)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1137,plain,
% 4.70/4.85 (P7(f84(x11371,a32),x11372,f27(x11371,x11373,x11372))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(1143,plain,
% 4.70/4.85 (~P14(x11431,x11432,f28(x11433,x11431,x11434,f9(f84(x11433,a32))))),
% 4.70/4.85 inference(scs_inference,[],[385,291,293,316,317,320,1061,1087,1090,1131,377,1104,1116,1122,1125,351,1043,1046,1064,1070,397,1049,1052,1078,398,1081,335,391,1055,1058,1084,355,1119,1137,395,361,346,348,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976])).
% 4.70/4.85 cnf(1146,plain,
% 4.70/4.85 (~E(f33(a12,x11461),f2(a80))),
% 4.70/4.85 inference(rename_variables,[],[383])).
% 4.70/4.85 cnf(1149,plain,
% 4.70/4.85 (~E(f27(x11491,x11492,x11493),f9(f84(x11491,a32)))),
% 4.70/4.85 inference(rename_variables,[],[392])).
% 4.70/4.85 cnf(1152,plain,
% 4.70/4.85 (E(f14(a80,x11521),x11521)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1156,plain,
% 4.70/4.85 (~E(f17(a80,x11561,x11562),f16(f84(a80,a32)))),
% 4.70/4.85 inference(scs_inference,[],[374,385,291,293,316,317,390,353,320,1061,1087,1090,1131,1134,377,1104,1116,1122,1125,351,1043,1046,1064,1070,397,1049,1052,1078,398,1081,335,391,1055,1058,1084,343,355,1119,1137,395,383,361,346,392,348,372,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250])).
% 4.70/4.85 cnf(1159,plain,
% 4.70/4.85 (P9(a80,x11591,f33(a12,f8(a80,x11591,x11592)))),
% 4.70/4.85 inference(rename_variables,[],[362])).
% 4.70/4.85 cnf(1161,plain,
% 4.70/4.85 (~P9(a80,x11611,x11611)),
% 4.70/4.85 inference(rename_variables,[],[385])).
% 4.70/4.85 cnf(1162,plain,
% 4.70/4.85 (~E(f8(a80,f33(a12,x11621),x11622),x11621)),
% 4.70/4.85 inference(scs_inference,[],[374,385,1037,291,293,316,317,390,353,320,1061,1087,1090,1131,1134,377,1104,1116,1122,1125,351,1043,1046,1064,1070,352,397,1049,1052,1078,398,1081,335,391,1055,1058,1084,1101,343,355,1119,1137,395,383,331,361,1040,362,346,392,348,372,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242])).
% 4.70/4.85 cnf(1163,plain,
% 4.70/4.85 (P7(a80,x11631,f8(a80,x11631,x11632))),
% 4.70/4.85 inference(rename_variables,[],[352])).
% 4.70/4.85 cnf(1165,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x11651),x11651)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1167,plain,
% 4.70/4.85 (P7(f84(x11671,a32),x11672,f16(f84(x11671,a32)))),
% 4.70/4.85 inference(rename_variables,[],[346])).
% 4.70/4.85 cnf(1168,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x11681),x11681)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1171,plain,
% 4.70/4.85 (E(f14(a80,x11711),x11711)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1173,plain,
% 4.70/4.85 (E(f14(a80,x11731),x11731)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1175,plain,
% 4.70/4.85 (~E(f33(a12,x11751),x11751)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1177,plain,
% 4.70/4.85 (P7(a80,x11771,f8(a80,x11772,x11771))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(1184,plain,
% 4.70/4.85 (P7(a80,f2(a80),x11841)),
% 4.70/4.85 inference(rename_variables,[],[325])).
% 4.70/4.85 cnf(1193,plain,
% 4.70/4.85 (P14(x11931,x11932,f27(x11931,x11932,x11933))),
% 4.70/4.85 inference(rename_variables,[],[353])).
% 4.70/4.85 cnf(1196,plain,
% 4.70/4.85 (P7(f84(x11961,a32),x11962,f27(x11961,x11963,x11962))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(1197,plain,
% 4.70/4.85 (P7(f84(x11971,a32),x11972,f16(f84(x11971,a32)))),
% 4.70/4.85 inference(rename_variables,[],[346])).
% 4.70/4.85 cnf(1199,plain,
% 4.70/4.85 (P9(f84(x11991,a32),f9(f84(x11991,a32)),f27(x11991,x11992,f9(f84(x11991,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,385,1037,291,293,294,297,300,301,375,325,316,317,390,353,320,1061,1087,1090,1131,1134,1152,1171,377,1104,1116,1122,1125,1128,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,391,1055,1058,1084,1101,1165,343,355,1119,1137,1196,363,395,383,331,361,1040,362,346,1167,392,393,348,372,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657])).
% 4.70/4.85 cnf(1200,plain,
% 4.70/4.85 (P7(f84(x12001,a32),x12002,f27(x12001,x12003,x12002))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(1206,plain,
% 4.70/4.85 (~P9(a80,x12061,x12061)),
% 4.70/4.85 inference(rename_variables,[],[385])).
% 4.70/4.85 cnf(1209,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x12091),x12091)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(1212,plain,
% 4.70/4.85 (P7(f84(x12121,a32),x12122,f27(x12121,x12123,x12122))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(1215,plain,
% 4.70/4.85 (E(f8(a80,x12151,f3(a80)),f33(a12,x12151))),
% 4.70/4.85 inference(rename_variables,[],[332])).
% 4.70/4.85 cnf(1218,plain,
% 4.70/4.85 (P7(f84(x12181,a32),x12182,x12182)),
% 4.70/4.85 inference(rename_variables,[],[336])).
% 4.70/4.85 cnf(1221,plain,
% 4.70/4.85 (E(f8(a80,f2(a80),x12211),x12211)),
% 4.70/4.85 inference(rename_variables,[],[327])).
% 4.70/4.85 cnf(1222,plain,
% 4.70/4.85 (P9(a80,x12221,f33(a12,x12221))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1225,plain,
% 4.70/4.85 (P9(a80,x12251,f33(a12,x12251))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1226,plain,
% 4.70/4.85 (~E(f33(a12,x12261),x12261)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1229,plain,
% 4.70/4.85 (E(f14(a80,x12291),x12291)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1231,plain,
% 4.70/4.85 (~E(f8(a80,x12311,f33(a12,x12312)),x12311)),
% 4.70/4.85 inference(scs_inference,[],[374,385,1037,1161,291,293,294,297,300,301,313,375,325,316,317,328,390,353,1193,336,320,1061,1087,1090,1131,1134,1152,1171,1173,377,1104,1116,1122,1125,1128,1175,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,1067,1222,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,362,327,346,1167,392,393,332,348,372,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487])).
% 4.70/4.85 cnf(1242,plain,
% 4.70/4.85 (~E(f16(f84(x12421,a32)),f9(f84(x12421,a32)))),
% 4.70/4.85 inference(rename_variables,[],[386])).
% 4.70/4.85 cnf(1245,plain,
% 4.70/4.85 (~E(f16(f84(x12451,a32)),f9(f84(x12451,a32)))),
% 4.70/4.85 inference(rename_variables,[],[386])).
% 4.70/4.85 cnf(1248,plain,
% 4.70/4.85 (P7(f84(x12481,a32),x12482,x12482)),
% 4.70/4.85 inference(rename_variables,[],[336])).
% 4.70/4.85 cnf(1252,plain,
% 4.70/4.85 (P10(x12521,x12522,f77(f27(x12522,x12523,x12524),x12522,x12521,f27(x12521,f33(x12525,x12523),f28(x12522,x12521,x12525,x12524))),f27(x12521,f33(x12525,x12523),f28(x12522,x12521,x12525,x12524)))),
% 4.70/4.85 inference(scs_inference,[],[374,385,1037,1161,360,291,293,294,297,298,300,301,305,313,375,325,316,317,328,390,353,1193,336,1218,320,1061,1087,1090,1131,1134,1152,1171,1173,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,1067,1222,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,362,327,346,1167,392,1149,393,332,348,372,386,1242,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961])).
% 4.70/4.85 cnf(1253,plain,
% 4.70/4.85 (~E(f27(x12531,x12532,x12533),f9(f84(x12531,a32)))),
% 4.70/4.85 inference(rename_variables,[],[392])).
% 4.70/4.85 cnf(1256,plain,
% 4.70/4.85 (E(f14(a80,x12561),x12561)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1259,plain,
% 4.70/4.85 (P7(a80,x12591,x12591)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(1261,plain,
% 4.70/4.85 (~P7(f84(a80,a32),f28(a80,a80,a12,f33(a12,f9(f84(a80,a32)))),f28(a80,a80,a12,f9(f84(a80,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,385,1037,1161,360,291,293,294,297,298,299,300,301,305,313,375,325,316,317,328,390,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,1067,1222,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,362,327,346,1167,392,1149,393,332,348,372,386,1242,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993])).
% 4.70/4.85 cnf(1269,plain,
% 4.70/4.85 (P9(a80,x12691,f33(a12,f8(a80,x12692,x12691)))),
% 4.70/4.85 inference(rename_variables,[],[361])).
% 4.70/4.85 cnf(1272,plain,
% 4.70/4.85 (P9(a80,x12721,f33(a12,x12721))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1274,plain,
% 4.70/4.85 (P9(a80,x12741,f8(a80,x12742,f8(a80,f8(a80,x12742,f33(a12,x12741)),x12743)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,385,1037,1161,360,291,293,294,297,298,299,300,301,305,313,375,325,316,317,328,390,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,1067,1222,1225,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,362,327,346,1167,392,1149,1253,393,332,348,372,386,1242,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683])).
% 4.70/4.85 cnf(1277,plain,
% 4.70/4.85 (P9(a80,x12771,f33(a12,x12771))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1282,plain,
% 4.70/4.85 (P9(a80,x12821,f33(a12,f8(a80,x12822,x12821)))),
% 4.70/4.85 inference(rename_variables,[],[361])).
% 4.70/4.85 cnf(1285,plain,
% 4.70/4.85 (~P9(a80,x12851,f2(a80))),
% 4.70/4.85 inference(rename_variables,[],[389])).
% 4.70/4.85 cnf(1289,plain,
% 4.70/4.85 (P7(a80,f10(a15),f2(a80))),
% 4.70/4.85 inference(scs_inference,[],[374,323,385,1037,1161,360,291,293,294,297,298,299,300,301,305,313,375,325,389,1285,316,317,318,328,390,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,398,1081,335,1067,1222,1225,1272,1277,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,1269,362,327,346,1167,392,1149,1253,393,332,348,372,386,1242,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522])).
% 4.70/4.85 cnf(1290,plain,
% 4.70/4.85 (~P9(a80,x12901,f2(a80))),
% 4.70/4.85 inference(rename_variables,[],[389])).
% 4.70/4.85 cnf(1293,plain,
% 4.70/4.85 (P9(a80,x12931,f33(a12,x12931))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1296,plain,
% 4.70/4.85 (P7(a80,x12961,x12961)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(1299,plain,
% 4.70/4.85 (~P9(a80,x12991,x12991)),
% 4.70/4.85 inference(rename_variables,[],[385])).
% 4.70/4.85 cnf(1300,plain,
% 4.70/4.85 (P9(a80,x13001,f33(a12,x13001))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1303,plain,
% 4.70/4.85 (P7(a80,x13031,x13031)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(1306,plain,
% 4.70/4.85 (P7(a80,x13061,x13061)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(1309,plain,
% 4.70/4.85 (P9(a80,x13091,f33(a12,x13091))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(1315,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x13151,x13152),x13152)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(1320,plain,
% 4.70/4.85 (P7(a80,x13201,x13201)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(1322,plain,
% 4.70/4.85 (P9(f84(a80,a32),f9(f84(a80,a32)),f33(a12,f9(f84(a80,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,291,293,294,297,298,299,300,301,305,306,309,310,311,313,375,325,389,1285,316,317,318,328,390,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,1269,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745])).
% 4.70/4.85 cnf(1323,plain,
% 4.70/4.85 (P7(f84(x13231,a32),f9(f84(x13231,a32)),x13232)),
% 4.70/4.85 inference(rename_variables,[],[347])).
% 4.70/4.85 cnf(1328,plain,
% 4.70/4.85 (~E(f16(f84(x13281,a32)),f9(f84(x13281,a32)))),
% 4.70/4.85 inference(rename_variables,[],[386])).
% 4.70/4.85 cnf(1329,plain,
% 4.70/4.85 (P7(f84(x13291,a32),x13292,x13292)),
% 4.70/4.85 inference(rename_variables,[],[336])).
% 4.70/4.85 cnf(1330,plain,
% 4.70/4.85 (P10(a80,a80,a12,x13301)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(1333,plain,
% 4.70/4.85 (P14(x13331,x13332,f27(x13331,x13332,x13333))),
% 4.70/4.85 inference(rename_variables,[],[353])).
% 4.70/4.85 cnf(1334,plain,
% 4.70/4.85 (P10(a80,a80,a12,x13341)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(1337,plain,
% 4.70/4.85 (P7(a80,f2(a80),x13371)),
% 4.70/4.85 inference(rename_variables,[],[325])).
% 4.70/4.85 cnf(1349,plain,
% 4.70/4.85 (~P9(f84(x13491,a32),f2(a80),f9(a80))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,1269,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523])).
% 4.70/4.85 cnf(1351,plain,
% 4.70/4.85 (P7(f84(x13511,a32),f2(a80),f9(a80))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,1269,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459])).
% 4.70/4.85 cnf(1355,plain,
% 4.70/4.85 (~P14(x13551,f33(a12,f74(f33(a12,x13552),a12,a80,a80)),f27(x13551,f74(f33(a12,x13552),a12,a80,a80),f9(f84(x13551,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,331,361,1040,1269,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847])).
% 4.70/4.85 cnf(1356,plain,
% 4.70/4.85 (~E(f33(a12,x13561),x13561)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1366,plain,
% 4.70/4.85 (~P7(a80,f39(f16(f84(a80,a32)),x13661),x13661)),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544])).
% 4.70/4.85 cnf(1378,plain,
% 4.70/4.85 (P31(f84(x13781,a32))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,295,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410])).
% 4.70/4.85 cnf(1384,plain,
% 4.70/4.85 (P26(f84(x13841,a32))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,291,293,294,295,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407])).
% 4.70/4.85 cnf(1399,plain,
% 4.70/4.85 (E(f77(x13991,x13992,f2(a80),x13993),f77(x13991,x13992,f9(a80),x13993))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,389,1285,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225])).
% 4.70/4.85 cnf(1621,plain,
% 4.70/4.85 (E(f14(a80,x16211),x16211)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1633,plain,
% 4.70/4.85 (~E(f27(x16331,f33(a12,x16332),f9(f84(x16331,a32))),f27(x16331,x16332,f9(f84(x16331,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787])).
% 4.70/4.85 cnf(1637,plain,
% 4.70/4.85 (P14(x16371,x16372,f27(x16371,x16373,f16(f84(x16371,a32))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710])).
% 4.70/4.85 cnf(1643,plain,
% 4.70/4.85 (~P8(a80,f27(a80,x16431,f27(a80,x16432,f16(f84(a80,a32)))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662])).
% 4.70/4.85 cnf(1661,plain,
% 4.70/4.85 (P1(f33(f27(x16611,x16612,x16613),x16612))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506])).
% 4.70/4.85 cnf(1665,plain,
% 4.70/4.85 (E(f33(f9(f84(x16651,a32)),x16652),f9(a32))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462])).
% 4.70/4.85 cnf(1671,plain,
% 4.70/4.85 (~P1(f33(f34(f33(a12,x16711)),x16711))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441])).
% 4.70/4.85 cnf(1687,plain,
% 4.70/4.85 (P14(x16871,f33(x16872,x16873),f28(x16874,x16871,x16872,f27(x16874,x16873,x16875)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912])).
% 4.70/4.85 cnf(1700,plain,
% 4.70/4.85 (E(f14(a80,x17001),x17001)),
% 4.70/4.85 inference(rename_variables,[],[320])).
% 4.70/4.85 cnf(1710,plain,
% 4.70/4.85 (E(f8(a80,x17101,f52(x17101,x17101)),x17101)),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592])).
% 4.70/4.85 cnf(1719,plain,
% 4.70/4.85 (~E(f33(a12,x17191),x17191)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1722,plain,
% 4.70/4.85 (~E(f33(a12,x17221),x17221)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1754,plain,
% 4.70/4.85 (~E(f70(f16(f84(a80,a32)),x17541,a32,a80),f59(f16(f84(a80,a32)),x17541,a32,a80))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954])).
% 4.70/4.85 cnf(1756,plain,
% 4.70/4.85 (E(f28(a80,a80,f6(a80,a80,f16(f84(a80,a32)),a12),f28(a80,a80,a12,f16(f84(a80,a32)))),f16(f84(a80,a32)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984])).
% 4.70/4.85 cnf(1758,plain,
% 4.70/4.85 (E(f33(x17581,f70(f16(f84(a80,a32)),x17581,a32,a80)),f33(x17581,f59(f16(f84(a80,a32)),x17581,a32,a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970])).
% 4.70/4.85 cnf(1760,plain,
% 4.70/4.85 (P7(f84(x17601,a32),f46(x17602,x17603,x17601,f28(x17601,x17604,x17603,x17602),x17604),x17602)),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002])).
% 4.70/4.85 cnf(1762,plain,
% 4.70/4.85 (E(f28(x17621,x17622,x17623,f46(x17624,x17623,x17621,f28(x17621,x17622,x17623,x17624),x17622)),f28(x17621,x17622,x17623,x17624))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003])).
% 4.70/4.85 cnf(1766,plain,
% 4.70/4.85 (~P10(a80,a32,x17661,f8(a80,f16(f84(a80,a32)),f2(a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238])).
% 4.70/4.85 cnf(1778,plain,
% 4.70/4.85 (~P9(f84(x17781,a32),f27(x17781,x17782,x17783),x17783)),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618])).
% 4.70/4.85 cnf(1790,plain,
% 4.70/4.85 (~P7(f84(a80,a32),f16(f84(a80,a32)),f27(a80,f33(x17901,x17902),f28(a32,a80,x17901,x17903)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917])).
% 4.70/4.85 cnf(1794,plain,
% 4.70/4.85 (~P9(a80,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80))),f33(a12,f33(a12,f2(a80))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663])).
% 4.70/4.85 cnf(1808,plain,
% 4.70/4.85 (~P9(a80,f2(a80),f8(a80,f2(a80),f2(a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813])).
% 4.70/4.85 cnf(1810,plain,
% 4.70/4.85 (~E(f8(a80,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80))),x18101),f33(a12,f2(a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529])).
% 4.70/4.85 cnf(1812,plain,
% 4.70/4.85 (~E(f8(a80,x18121,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80)))),f33(a12,f2(a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,337,331,361,1040,1269,1282,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528])).
% 4.70/4.85 cnf(1815,plain,
% 4.70/4.85 (E(f8(a80,x18151,f3(a80)),f33(a12,x18151))),
% 4.70/4.85 inference(rename_variables,[],[332])).
% 4.70/4.85 cnf(1821,plain,
% 4.70/4.85 (~E(f33(a12,x18211),x18211)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1832,plain,
% 4.70/4.85 (~E(f33(a12,x18321),f2(a80))),
% 4.70/4.85 inference(rename_variables,[],[383])).
% 4.70/4.85 cnf(1833,plain,
% 4.70/4.85 (~E(f33(a12,x18331),x18331)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1836,plain,
% 4.70/4.85 (~E(f33(a12,x18361),x18361)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1853,plain,
% 4.70/4.85 (~E(f33(a12,x18531),x18531)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(1854,plain,
% 4.70/4.85 (P9(a80,x18541,f33(a12,f8(a80,x18542,x18541)))),
% 4.70/4.85 inference(rename_variables,[],[361])).
% 4.70/4.85 cnf(1857,plain,
% 4.70/4.85 (P10(a80,a80,a12,x18571)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(1861,plain,
% 4.70/4.85 (~P14(a80,x18611,f17(a80,f2(a80),f2(a80)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833])).
% 4.70/4.85 cnf(1863,plain,
% 4.70/4.85 (P14(a80,f55(f16(f84(x18631,a32)),f33(a12,x18632)),f18(a80,f2(a80),f33(a12,x18632)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,326,327,1221,346,1167,347,1323,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767])).
% 4.70/4.85 cnf(1923,plain,
% 4.70/4.85 (~P9(f84(a80,a32),f18(a80,x19231,x19232),f18(a80,f33(a12,x19233),x19233))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,1857,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,1853,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,1159,326,327,1221,346,1167,1197,347,1323,396,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767,766,720,719,668,667,442,894,869,840,839,810,769,768,675,674,673,672,612,611,600,556,555,554,553,843,973,972,968,951,878])).
% 4.70/4.85 cnf(1947,plain,
% 4.70/4.85 (E(f4(a80,f27(a80,f36(f17(a80,x19471,x19472)),f17(a80,x19471,x19472))),f33(a12,f4(a80,f17(a80,x19471,x19472))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,1857,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,1853,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,1159,326,327,1221,346,1167,1197,347,1323,396,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,338,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767,766,720,719,668,667,442,894,869,840,839,810,769,768,675,674,673,672,612,611,600,556,555,554,553,843,973,972,968,951,878,848,842,799,726,971,713,916,1000,737,717,703,687])).
% 4.70/4.85 cnf(1961,plain,
% 4.70/4.85 (~E(f33(a12,x19611),f2(a80))),
% 4.70/4.85 inference(rename_variables,[],[383])).
% 4.70/4.85 cnf(1962,plain,
% 4.70/4.85 (P14(x19621,x19622,f16(f84(x19621,a32)))),
% 4.70/4.85 inference(rename_variables,[],[341])).
% 4.70/4.85 cnf(1983,plain,
% 4.70/4.85 (~P7(f84(a80,a32),f17(a80,x19831,f33(a12,x19831)),f17(a80,x19832,x19831))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,1857,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,1853,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,1315,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,1962,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,1159,326,327,1221,346,1167,1197,347,1323,396,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,1328,338,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767,766,720,719,668,667,442,894,869,840,839,810,769,768,675,674,673,672,612,611,600,556,555,554,553,843,973,972,968,951,878,848,842,799,726,971,713,916,1000,737,717,703,687,935,659,638,565,520,875,613,988,950,762,953,902,901,900,899,891])).
% 4.70/4.85 cnf(1987,plain,
% 4.70/4.85 (P9(f84(a32,a32),f18(a32,f33(a12,f33(a12,f9(a32))),f9(a32)),f18(a32,f9(a32),f9(a32)))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,1857,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,1853,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,1315,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,1962,395,383,1146,1832,337,331,361,1040,1269,1282,1854,362,1159,326,327,1221,346,1167,1197,347,1323,396,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,1328,338,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767,766,720,719,668,667,442,894,869,840,839,810,769,768,675,674,673,672,612,611,600,556,555,554,553,843,973,972,968,951,878,848,842,799,726,971,713,916,1000,737,717,703,687,935,659,638,565,520,875,613,988,950,762,953,902,901,900,899,891,890,853])).
% 4.70/4.85 cnf(1995,plain,
% 4.70/4.85 (P9(a80,x19951,f33(a12,x19951))),
% 4.70/4.85 inference(rename_variables,[],[335])).
% 4.70/4.85 cnf(2000,plain,
% 4.70/4.85 (P9(a80,f2(a80),f33(a12,x20001))),
% 4.70/4.85 inference(rename_variables,[],[337])).
% 4.70/4.85 cnf(2004,plain,
% 4.70/4.85 (P9(f84(a80,a32),f18(a80,f33(a12,f8(a80,x20041,f2(a80))),f33(a12,f8(a80,x20041,f2(a80)))),f18(a80,f2(a80),f33(a12,f8(a80,x20041,f2(a80)))))),
% 4.70/4.85 inference(scs_inference,[],[374,323,1259,1296,1303,1306,1320,385,1037,1161,1206,1299,360,1330,1334,1857,287,291,293,294,295,297,298,299,300,301,305,306,307,309,310,311,312,313,314,315,375,325,1184,1337,389,1285,1290,316,317,318,328,390,319,353,1193,1333,336,1218,1248,1329,320,1061,1087,1090,1131,1134,1152,1171,1173,1229,1256,1621,1700,377,1104,1116,1122,1125,1128,1175,1226,1356,1719,1722,1821,1833,1836,1853,351,1043,1046,1064,1070,1073,1177,352,1163,397,1049,1052,1078,1098,1315,398,1081,1093,335,1067,1222,1225,1272,1277,1293,1300,1309,1995,391,1055,1058,1084,1101,1165,1168,1209,343,355,1119,1137,1196,1200,1212,363,341,1962,395,383,1146,1832,1961,337,2000,331,361,1040,1269,1282,1854,362,1159,326,327,1221,346,1167,1197,347,1323,396,392,1149,1253,393,332,1215,1815,348,372,386,1242,1245,1328,338,373,2,543,495,476,467,403,470,460,451,752,751,750,697,695,693,691,689,661,606,605,602,601,582,580,578,546,535,531,474,452,433,469,31,861,791,666,492,860,793,677,498,497,424,607,825,756,841,976,975,759,273,269,268,267,250,249,246,245,242,241,240,235,230,229,3,598,564,562,549,484,483,431,725,706,657,634,589,588,576,551,941,755,658,911,487,966,871,867,718,450,538,838,969,961,955,1001,993,989,990,685,684,683,682,681,680,573,567,522,798,797,796,795,794,857,856,855,854,946,745,987,991,906,735,425,421,475,423,536,523,459,453,847,660,594,585,545,544,532,486,473,434,427,410,409,408,407,406,399,496,472,471,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,914,880,862,792,790,789,787,758,710,707,664,662,651,641,639,633,597,596,574,560,506,501,462,461,447,441,416,412,405,401,558,934,933,912,887,886,828,827,826,765,715,670,655,595,592,552,739,959,884,883,777,744,648,936,788,763,965,958,885,829,525,948,992,937,983,954,984,970,1002,1003,266,244,238,236,671,627,626,625,622,618,513,508,500,429,704,917,724,663,617,415,414,413,504,432,813,529,528,491,490,761,645,610,930,929,928,927,882,874,850,849,734,700,418,586,877,879,833,767,766,720,719,668,667,442,894,869,840,839,810,769,768,675,674,673,672,612,611,600,556,555,554,553,843,973,972,968,951,878,848,842,799,726,971,713,916,1000,737,717,703,687,935,659,638,565,520,875,613,988,950,762,953,902,901,900,899,891,890,853,821,819,803,802,1019,908])).
% 4.70/4.85 cnf(2046,plain,
% 4.70/4.85 (~P14(x20461,x20462,f9(f84(x20461,a32)))),
% 4.70/4.85 inference(rename_variables,[],[395])).
% 4.70/4.85 cnf(2049,plain,
% 4.70/4.85 (P1(f33(f16(f84(x20491,a32)),x20492))),
% 4.70/4.85 inference(rename_variables,[],[348])).
% 4.70/4.85 cnf(2052,plain,
% 4.70/4.85 (~P1(f33(f34(f33(a12,x20521)),x20521))),
% 4.70/4.85 inference(rename_variables,[],[1671])).
% 4.70/4.85 cnf(2063,plain,
% 4.70/4.85 (~P9(a80,x20631,f10(a1))),
% 4.70/4.85 inference(rename_variables,[],[1032])).
% 4.70/4.85 cnf(2064,plain,
% 4.70/4.85 (~P1(f33(f34(f33(a12,x20641)),x20641))),
% 4.70/4.85 inference(rename_variables,[],[1671])).
% 4.70/4.85 cnf(2067,plain,
% 4.70/4.85 (P8(a80,f17(a80,x20671,x20672))),
% 4.70/4.85 inference(rename_variables,[],[343])).
% 4.70/4.85 cnf(2068,plain,
% 4.70/4.85 (~P14(a80,x20681,f17(a80,f2(a80),f2(a80)))),
% 4.70/4.85 inference(rename_variables,[],[1861])).
% 4.70/4.85 cnf(2071,plain,
% 4.70/4.85 (P8(x20711,f9(f84(x20711,a32)))),
% 4.70/4.85 inference(rename_variables,[],[331])).
% 4.70/4.85 cnf(2072,plain,
% 4.70/4.85 (~P14(x20721,x20722,f9(f84(x20721,a32)))),
% 4.70/4.85 inference(rename_variables,[],[395])).
% 4.70/4.85 cnf(2075,plain,
% 4.70/4.85 (P8(a80,f17(a80,x20751,x20752))),
% 4.70/4.85 inference(rename_variables,[],[343])).
% 4.70/4.85 cnf(2076,plain,
% 4.70/4.85 (~P14(a80,x20761,f17(a80,f2(a80),f2(a80)))),
% 4.70/4.85 inference(rename_variables,[],[1861])).
% 4.70/4.85 cnf(2079,plain,
% 4.70/4.85 (~E(f27(x20791,x20792,x20793),f9(f84(x20791,a32)))),
% 4.70/4.85 inference(rename_variables,[],[392])).
% 4.70/4.85 cnf(2083,plain,
% 4.70/4.85 (P8(a32,x20831)),
% 4.70/4.85 inference(rename_variables,[],[1030])).
% 4.70/4.85 cnf(2086,plain,
% 4.70/4.85 (P7(f84(x20861,a32),x20862,f27(x20861,x20863,x20862))),
% 4.70/4.85 inference(rename_variables,[],[355])).
% 4.70/4.85 cnf(2091,plain,
% 4.70/4.85 (P31(f84(x20911,a32))),
% 4.70/4.85 inference(rename_variables,[],[1378])).
% 4.70/4.85 cnf(2101,plain,
% 4.70/4.85 (P10(x21011,x21012,x21013,f9(f84(x21011,a32)))),
% 4.70/4.85 inference(rename_variables,[],[363])).
% 4.70/4.85 cnf(2102,plain,
% 4.70/4.85 (P7(f84(x21021,a32),x21022,f16(f84(x21021,a32)))),
% 4.70/4.85 inference(rename_variables,[],[346])).
% 4.70/4.85 cnf(2105,plain,
% 4.70/4.85 (P7(a80,x21051,x21051)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(2108,plain,
% 4.70/4.85 (P14(x21081,f33(x21082,x21083),f28(x21084,x21081,x21082,f16(f84(x21084,a32))))),
% 4.70/4.85 inference(rename_variables,[],[372])).
% 4.70/4.85 cnf(2109,plain,
% 4.70/4.85 (P10(a80,a80,a12,x21091)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(2110,plain,
% 4.70/4.85 (~P14(x21101,x21102,f9(f84(x21101,a32)))),
% 4.70/4.85 inference(rename_variables,[],[395])).
% 4.70/4.85 cnf(2113,plain,
% 4.70/4.85 (P7(a80,x21131,f8(a80,x21132,x21131))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(2114,plain,
% 4.70/4.85 (~P9(a80,x21141,x21141)),
% 4.70/4.85 inference(rename_variables,[],[385])).
% 4.70/4.85 cnf(2117,plain,
% 4.70/4.85 (P7(a80,x21171,f8(a80,x21172,x21171))),
% 4.70/4.85 inference(rename_variables,[],[351])).
% 4.70/4.85 cnf(2121,plain,
% 4.70/4.85 (P7(a80,x21211,f8(a80,x21211,x21212))),
% 4.70/4.85 inference(rename_variables,[],[352])).
% 4.70/4.85 cnf(2122,plain,
% 4.70/4.85 (~E(f8(a80,x21221,f33(a12,x21222)),x21222)),
% 4.70/4.85 inference(rename_variables,[],[1097])).
% 4.70/4.85 cnf(2125,plain,
% 4.70/4.85 (~P14(x21251,x21252,f9(f84(x21251,a32)))),
% 4.70/4.85 inference(rename_variables,[],[395])).
% 4.70/4.85 cnf(2126,plain,
% 4.70/4.85 (E(f30(x21261,f27(x21261,x21262,f9(f84(x21261,a32)))),x21262)),
% 4.70/4.85 inference(rename_variables,[],[359])).
% 4.70/4.85 cnf(2129,plain,
% 4.70/4.85 (~P9(a80,x21291,f10(a1))),
% 4.70/4.85 inference(rename_variables,[],[1032])).
% 4.70/4.85 cnf(2145,plain,
% 4.70/4.85 (~P14(x21451,x21452,f28(x21453,x21451,x21454,f9(f84(x21453,a32))))),
% 4.70/4.85 inference(rename_variables,[],[1143])).
% 4.70/4.85 cnf(2146,plain,
% 4.70/4.85 (P10(a80,a80,a12,x21461)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(2149,plain,
% 4.70/4.85 (~P14(x21491,x21492,f9(f84(x21491,a32)))),
% 4.70/4.85 inference(rename_variables,[],[395])).
% 4.70/4.85 cnf(2180,plain,
% 4.70/4.85 (P8(a80,f18(a80,x21801,x21802))),
% 4.70/4.85 inference(rename_variables,[],[344])).
% 4.70/4.85 cnf(2183,plain,
% 4.70/4.85 (P8(a80,f18(a80,x21831,x21832))),
% 4.70/4.85 inference(rename_variables,[],[344])).
% 4.70/4.85 cnf(2188,plain,
% 4.70/4.85 (~E(f8(a80,x21881,f33(a12,x21882)),x21882)),
% 4.70/4.85 inference(rename_variables,[],[1097])).
% 4.70/4.85 cnf(2189,plain,
% 4.70/4.85 (~E(f8(a80,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80))),x21891),f33(a12,f2(a80)))),
% 4.70/4.85 inference(rename_variables,[],[1810])).
% 4.70/4.85 cnf(2192,plain,
% 4.70/4.85 (~E(f8(a80,x21921,f33(a12,x21922)),x21922)),
% 4.70/4.85 inference(rename_variables,[],[1097])).
% 4.70/4.85 cnf(2193,plain,
% 4.70/4.85 (~E(f8(a80,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80))),x21931),f33(a12,f2(a80)))),
% 4.70/4.85 inference(rename_variables,[],[1810])).
% 4.70/4.85 cnf(2202,plain,
% 4.70/4.85 (~E(f33(a12,x22021),x22021)),
% 4.70/4.85 inference(rename_variables,[],[377])).
% 4.70/4.85 cnf(2211,plain,
% 4.70/4.85 (~P9(a80,x22111,f10(a1))),
% 4.70/4.85 inference(rename_variables,[],[1032])).
% 4.70/4.85 cnf(2214,plain,
% 4.70/4.85 (P7(a80,x22141,x22141)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(2217,plain,
% 4.70/4.85 (P9(a80,x22171,f33(a12,f8(a80,x22172,x22171)))),
% 4.70/4.85 inference(rename_variables,[],[361])).
% 4.70/4.85 cnf(2231,plain,
% 4.70/4.85 (P31(f84(x22311,a32))),
% 4.70/4.85 inference(rename_variables,[],[1378])).
% 4.70/4.85 cnf(2235,plain,
% 4.70/4.85 (P10(a80,a80,a12,x22351)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(2238,plain,
% 4.70/4.85 (~E(f16(f84(x22381,a32)),f9(f84(x22381,a32)))),
% 4.70/4.85 inference(rename_variables,[],[386])).
% 4.70/4.85 cnf(2243,plain,
% 4.70/4.85 (P10(a80,a80,a12,x22431)),
% 4.70/4.85 inference(rename_variables,[],[360])).
% 4.70/4.85 cnf(2248,plain,
% 4.70/4.85 (~P7(a80,f33(a12,x22481),x22481)),
% 4.70/4.85 inference(rename_variables,[],[391])).
% 4.70/4.85 cnf(2251,plain,
% 4.70/4.85 (P7(a80,x22511,x22511)),
% 4.70/4.85 inference(rename_variables,[],[323])).
% 4.70/4.85 cnf(2279,plain,
% 4.70/4.85 (P7(f84(x22791,a32),x22792,f16(f84(x22791,a32)))),
% 4.70/4.85 inference(rename_variables,[],[346])).
% 4.70/4.85 cnf(2282,plain,
% 4.70/4.85 (~E(f8(a80,x22821,f8(a80,f33(a12,f2(a80)),f33(a12,f2(a80)))),f33(a12,f2(a80)))),
% 4.70/4.85 inference(rename_variables,[],[1812])).
% 4.70/4.85 cnf(2287,plain,
% 4.70/4.85 (~P9(a80,f8(a80,x22871,x22872),x22872)),
% 4.70/4.85 inference(rename_variables,[],[397])).
% 4.70/4.85 cnf(2296,plain,
% 4.70/4.85 (P9(a80,x22961,f8(a80,x22962,f8(a80,f8(a80,x22962,f33(a12,x22961)),x22963)))),
% 4.70/4.85 inference(rename_variables,[],[1274])).
% 4.70/4.85 cnf(2307,plain,
% 4.70/4.85 (P31(f84(x23071,a32))),
% 4.70/4.85 inference(rename_variables,[],[1378])).
% 4.70/4.85 cnf(2357,plain,
% 4.70/4.85 ($false),
% 4.70/4.85 inference(scs_inference,[],[292,321,344,2180,2183,359,2126,323,2105,2214,2251,385,2114,325,389,377,2202,351,2113,2117,352,2121,397,2287,398,355,2086,363,2101,383,361,2217,362,347,392,2079,393,386,2238,395,2046,2072,2110,2125,2149,331,2071,309,287,299,346,2102,2279,353,391,2248,305,372,2108,306,360,2109,2146,2235,2243,348,2049,298,310,343,2067,2075,317,307,297,390,301,328,1252,1762,1687,1661,1143,2145,1637,1261,1671,2052,2064,1794,1633,1399,1322,1758,1710,1760,1778,1812,2282,1810,2189,2193,1987,1097,2122,2188,2192,1162,1231,1199,1028,1983,1923,1355,1790,2004,1156,1289,1378,2091,2231,2307,1384,1756,1665,1754,1947,1366,1274,2296,1349,1351,1861,2068,2076,1863,1030,2083,1032,2063,2129,2211,1808,1766,1643,591,947,832,814,835,770,676,590,897,892,851,895,974,679,678,865,836,977,986,995,913,747,746,1018,1017,237,808,807,806,805,521,978,738,921,920,873,812,811,809,523,535,433,506,492,677,976,589,588,415,529,528,645,610,929,928,418,658,833,767,766,720,769,718,675,674,878,969,961,1001,993,875,902,900,853,470,697,689,661,578,474,473,793,592,948,513,706,663,617,576,504,813,941,966,672,611,556,555,554,972,726,916,687,955,573,520,988,950,953,745,467,751,582,531,471,862,791,412]),
% 4.70/4.85 ['proof']).
% 4.70/4.85 % SZS output end Proof
% 4.70/4.85 % Total time :4.080000s
%------------------------------------------------------------------------------