TSTP Solution File: SWW180+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW180+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:06:19 EDT 2024
% Result : Theorem 4.60s 4.59s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW180+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 07:38:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 4.39/4.52 %-------------------------------------------
% 4.39/4.52 % File :CSE---1.7
% 4.39/4.52 % Problem :theBenchmark
% 4.39/4.52 % Transform :cnf
% 4.39/4.52 % Format :tptp:raw
% 4.39/4.52 % Command :java -jar mcs_scs.jar %d %s
% 4.39/4.52
% 4.39/4.52 % Result :Theorem 3.310000s
% 4.39/4.52 % Output :CNFRefutation 3.310000s
% 4.39/4.52 %-------------------------------------------
% 4.39/4.52 %------------------------------------------------------------------------------
% 4.39/4.52 % File : SWW180+1 : TPTP v8.2.0. Released v5.2.0.
% 4.39/4.52 % Domain : Software Verification
% 4.39/4.52 % Problem : Fundamental Theorem of Algebra 435841, 1000 axioms selected
% 4.39/4.52 % Version : Especial.
% 4.39/4.52 % English :
% 4.39/4.52
% 4.39/4.52 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 4.39/4.52 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 4.39/4.52 % Source : [Bla11]
% 4.39/4.52 % Names : fta_435841.1000.p [Bla11]
% 4.39/4.52
% 4.39/4.52 % Status : Theorem
% 4.39/4.52 % Rating : 0.47 v8.1.0, 0.53 v7.3.0, 0.48 v7.2.0, 0.45 v7.1.0, 0.43 v7.0.0, 0.53 v6.4.0, 0.50 v6.3.0, 0.42 v6.2.0, 0.48 v6.1.0, 0.70 v6.0.0, 0.52 v5.5.0, 0.70 v5.4.0, 0.68 v5.3.0, 0.74 v5.2.0
% 4.39/4.52 % Syntax : Number of formulae : 1275 ( 352 unt; 0 def)
% 4.39/4.52 % Number of atoms : 3028 ( 721 equ)
% 4.39/4.52 % Maximal formula atoms : 8 ( 2 avg)
% 4.39/4.52 % Number of connectives : 1943 ( 190 ~; 64 |; 130 &)
% 4.39/4.52 % ( 250 <=>;1309 =>; 0 <=; 0 <~>)
% 4.39/4.52 % Maximal formula depth : 13 ( 5 avg)
% 4.39/4.52 % Maximal term depth : 8 ( 2 avg)
% 4.39/4.52 % Number of predicates : 75 ( 74 usr; 0 prp; 1-3 aty)
% 4.39/4.52 % Number of functors : 39 ( 39 usr; 10 con; 0-5 aty)
% 4.39/4.52 % Number of variables : 2770 (2743 !; 27 ?)
% 4.39/4.52 % SPC : FOF_THM_RFO_SEQ
% 4.39/4.52
% 4.39/4.52 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 4.39/4.52 % 2011-03-01 11:15:46
% 4.39/4.52 %------------------------------------------------------------------------------
% 4.39/4.52 %----Relevant facts (995)
% 4.39/4.52 fof(fact_ext,axiom,
% 4.39/4.52 ! [V_g_2,V_f_2] :
% 4.39/4.52 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 4.39/4.52 => V_f_2 = V_g_2 ) ).
% 4.39/4.52
% 4.39/4.52 fof(fact_H,axiom,
% 4.39/4.52 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r) ).
% 4.39/4.52
% 4.39/4.52 fof(fact_norm__triangle__ineq,axiom,
% 4.39/4.52 ! [V_y,V_x,T_a] :
% 4.39/4.52 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.52 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 4.39/4.52
% 4.39/4.52 fof(fact_norm__mult__ineq,axiom,
% 4.39/4.52 ! [V_y,V_x,T_a] :
% 4.39/4.52 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.52 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ) ).
% 4.39/4.52
% 4.39/4.52 fof(fact_m,axiom,
% 4.39/4.52 ! [B_z] :
% 4.39/4.52 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 4.39/4.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),v_m____) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_norm__one,axiom,
% 4.39/4.53 ! [T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 4.39/4.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_rp,axiom,
% 4.39/4.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_norm__mult,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 4.39/4.53 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_abs__triangle__ineq,axiom,
% 4.39/4.53 ! [V_b,V_a,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.53 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 4.39/4.53 ! [V_m,T_a] :
% 4.39/4.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.53 => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 4.39/4.53 ! [V_a,V_m,T_a] :
% 4.39/4.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.53 => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 4.39/4.53 ! [V_m,V_a,T_a] :
% 4.39/4.53 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.53 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_kp,axiom,
% 4.39/4.53 c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__refl,axiom,
% 4.39/4.53 ! [V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Opreorder(T_a)
% 4.39/4.53 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_th,axiom,
% 4.39/4.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)),v_m____) ).
% 4.39/4.53
% 4.39/4.53 fof(fact__096cmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_A_060_061_Acmod_Ac_A_L_Ar_A_K_Am_096,axiom,
% 4.39/4.53 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_pCons,axiom,
% 4.39/4.53 ? [B_m] :
% 4.39/4.53 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m)
% 4.39/4.53 & ! [B_z] :
% 4.39/4.53 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 4.39/4.53 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__irrefl,axiom,
% 4.39/4.53 ! [V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Opreorder(T_a)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_abs__not__less__zero,axiom,
% 4.39/4.53 ! [V_a,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_norm__not__less__zero,axiom,
% 4.39/4.53 ! [V_x,T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_norm__zero,axiom,
% 4.39/4.53 ! [T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.53 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_linorder__neq__iff,axiom,
% 4.39/4.53 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.53 ( class_Orderings_Olinorder(T_a)
% 4.39/4.53 => ( V_x_2 != V_y_2
% 4.39/4.53 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.53 | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_not__less__iff__gr__or__eq,axiom,
% 4.39/4.53 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.53 ( class_Orderings_Olinorder(T_a)
% 4.39/4.53 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.53 <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 4.39/4.53 | V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_zero__reorient,axiom,
% 4.39/4.53 ! [V_x_2,T_a] :
% 4.39/4.53 ( class_Groups_Ozero(T_a)
% 4.39/4.53 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
% 4.39/4.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_zero__less__abs__iff,axiom,
% 4.39/4.53 ! [V_a_2,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a_2))
% 4.39/4.53 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_zero__less__norm__iff,axiom,
% 4.39/4.53 ! [V_x_2,T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
% 4.39/4.53 <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 4.39/4.53 ! [V_a_2,T_a] :
% 4.39/4.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.53 => ( 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))
% 4.39/4.53 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_linorder__less__linear,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Olinorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 | V_x = V_y
% 4.39/4.53 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_norm__eq__zero,axiom,
% 4.39/4.53 ! [V_x_2,T_a] :
% 4.39/4.53 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.53 => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.53 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 4.39/4.53 ! [V_a_2,T_a] :
% 4.39/4.53 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.53 => ( 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))
% 4.39/4.53 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_linorder__antisym__conv3,axiom,
% 4.39/4.53 ! [V_x_2,V_y_2,T_a] :
% 4.39/4.53 ( class_Orderings_Olinorder(T_a)
% 4.39/4.53 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
% 4.39/4.53 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.53 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_linorder__neqE,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Olinorder(T_a)
% 4.39/4.53 => ( V_x != V_y
% 4.39/4.53 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_abs__of__pos,axiom,
% 4.39/4.53 ! [V_a,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.53 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_add__pos__pos,axiom,
% 4.39/4.53 ! [V_b,V_a,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.53 => 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)) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_add__neg__neg,axiom,
% 4.39/4.53 ! [V_b,V_a,T_a] :
% 4.39/4.53 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.53 => 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)) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_less__imp__neq,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Oorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => V_x != V_y ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__not__sym,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Opreorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__imp__not__less,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Opreorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__imp__not__eq,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Oorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => V_x != V_y ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__imp__not__eq2,axiom,
% 4.39/4.53 ! [V_y,V_x,T_a] :
% 4.39/4.53 ( class_Orderings_Oorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.53 => V_y != V_x ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_order__less__asym_H,axiom,
% 4.39/4.53 ! [V_b,V_a,T_a] :
% 4.39/4.53 ( class_Orderings_Opreorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_xt1_I9_J,axiom,
% 4.39/4.53 ! [V_a,V_b,T_a] :
% 4.39/4.53 ( class_Orderings_Oorder(T_a)
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.39/4.53 => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_ord__eq__less__trans,axiom,
% 4.39/4.53 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.53 ( class_Orderings_Oord(T_a)
% 4.39/4.53 => ( V_a = V_b
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.39/4.53 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_xt1_I1_J,axiom,
% 4.39/4.53 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.53 ( class_Orderings_Oorder(T_a)
% 4.39/4.53 => ( V_a = V_b
% 4.39/4.53 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
% 4.39/4.53 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 4.39/4.53
% 4.39/4.53 fof(fact_ord__less__eq__trans,axiom,
% 4.39/4.53 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Orderings_Oord(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.54 => ( V_b = V_c
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I2_J,axiom,
% 4.39/4.54 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.39/4.54 => ( V_b = V_c
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__less__trans,axiom,
% 4.39/4.54 ! [V_z,V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I10_J,axiom,
% 4.39/4.54 ! [V_z,V_x,V_y,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__less__asym,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__cases,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => ( V_x != V_y
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I8_J,axiom,
% 4.39/4.54 ! [V_z,V_x,V_y,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__le__less__trans,axiom,
% 4.39/4.54 ! [V_z,V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I7_J,axiom,
% 4.39/4.54 ! [V_z,V_x,V_y,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__less__le__trans,axiom,
% 4.39/4.54 ! [V_z,V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I11_J,axiom,
% 4.39/4.54 ! [V_a,V_b,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.54 => ( V_a != V_b
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__le__neq__trans,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.54 => ( V_a != V_b
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__le__imp__less__or__eq,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 | V_x = V_y ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__antisym__conv2,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__less__imp__le,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_leD,axiom,
% 4.39/4.54 ! [V_x,V_y,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.54 => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_xt1_I12_J,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( V_a != V_b
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__neq__le__trans,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( V_a != V_b
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__antisym__conv1,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_not__leE,axiom,
% 4.39/4.54 ! [V_x,V_y,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_leI,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.54 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__le__less,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 | V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_less__le__not__le,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Opreorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 & ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_order__less__le,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Oorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 & V_x_2 != V_y_2 ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__le__less__linear,axiom,
% 4.39/4.54 ! [V_y,V_x,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.54 | c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__not__le,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_linorder__not__less,axiom,
% 4.39/4.54 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.54 ( class_Orderings_Olinorder(T_a)
% 4.39/4.54 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
% 4.39/4.54 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__less__imp__less__left,axiom,
% 4.39/4.54 ! [V_b,V_a,V_c,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.54 => ( 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))
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__less__imp__less__right,axiom,
% 4.39/4.54 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.54 => ( 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))
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__strict__mono,axiom,
% 4.39/4.54 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.39/4.54 => 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)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__strict__left__mono,axiom,
% 4.39/4.54 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.54 => 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)) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__strict__right__mono,axiom,
% 4.39/4.54 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.54 => 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)) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__less__cancel__left,axiom,
% 4.39/4.54 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 4.39/4.54 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__less__cancel__right,axiom,
% 4.39/4.54 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 4.39/4.54 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_mult__right_Ozero,axiom,
% 4.39/4.54 ! [V_x,T_a] :
% 4.39/4.54 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_mult_Ozero__right,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_mult__left_Ozero,axiom,
% 4.39/4.54 ! [V_y,T_a] :
% 4.39/4.54 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_mult_Ozero__left,axiom,
% 4.39/4.54 ! [V_b,T_a] :
% 4.39/4.54 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.54 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__0__iff,axiom,
% 4.39/4.54 ! [V_a_2,V_b_2,T_a] :
% 4.39/4.54 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 4.39/4.54 => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
% 4.39/4.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add_Ocomm__neutral,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__0__right,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Groups_Omonoid__add(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_double__zero__sym,axiom,
% 4.39/4.54 ! [V_a_2,T_a] :
% 4.39/4.54 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.54 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2)
% 4.39/4.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__0,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__0__left,axiom,
% 4.39/4.54 ! [V_a,T_a] :
% 4.39/4.54 ( class_Groups_Omonoid__add(T_a)
% 4.39/4.54 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_real__norm__def,axiom,
% 4.39/4.54 ! [V_r] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,V_r) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_abs__eq__0,axiom,
% 4.39/4.54 ! [V_a_2,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.54 => ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.54 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_abs__zero,axiom,
% 4.39/4.54 ! [T_a] :
% 4.39/4.54 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.54 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__nonpos__neg,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.54 => 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)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__neg__nonpos,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.54 => 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)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__strict__increasing2,axiom,
% 4.39/4.54 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__strict__increasing,axiom,
% 4.39/4.54 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.39/4.54 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__nonneg__pos,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.54 => 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)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__pos__nonneg,axiom,
% 4.39/4.54 ! [V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.54 => 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)) ) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_norm__le__zero__iff,axiom,
% 4.39/4.54 ! [V_x_2,T_a] :
% 4.39/4.54 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.54 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.54
% 4.39/4.54 fof(fact_add__le__less__mono,axiom,
% 4.39/4.54 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.54 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.54 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.39/4.55 => 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)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__less__le__mono,axiom,
% 4.39/4.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.39/4.55 => 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)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__nonpos__nonpos,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.55 => 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)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__increasing2,axiom,
% 4.39/4.55 ! [V_a,V_b,V_c,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__increasing,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__nonneg__eq__0__iff,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__nonneg__nonneg,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.55 => 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)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 4.39/4.55 ! [V_a_2,T_a] :
% 4.39/4.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.55 => ( 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))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 4.39/4.55 ! [V_a_2,T_a] :
% 4.39/4.55 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.55 => ( 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))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__scale__eq__noteq,axiom,
% 4.39/4.55 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 4.39/4.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 4.39/4.55 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 => ( ( V_a = V_b
% 4.39/4.55 & V_c != V_d )
% 4.39/4.55 => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__of__nonneg,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__le__zero__iff,axiom,
% 4.39/4.55 ! [V_a_2,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__ge__zero,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_norm__ge__zero,axiom,
% 4.39/4.55 ! [V_x,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_norm__mult__less,axiom,
% 4.39/4.55 ! [V_s,V_y,V_r,V_x,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 4.39/4.55 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_norm__add__less,axiom,
% 4.39/4.55 ! [V_s,V_y,V_r,V_x,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
% 4.39/4.55 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_linorder__le__cases,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Orderings_Olinorder(T_a)
% 4.39/4.55 => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_le__funE,axiom,
% 4.39/4.55 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 4.39/4.55 ( class_Orderings_Oord(T_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_xt1_I6_J,axiom,
% 4.39/4.55 ! [V_z,V_x,V_y,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_xt1_I5_J,axiom,
% 4.39/4.55 ! [V_x,V_y,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.55 => V_x = V_y ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_order__trans,axiom,
% 4.39/4.55 ! [V_z,V_y,V_x,T_a] :
% 4.39/4.55 ( class_Orderings_Opreorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_order__antisym,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
% 4.39/4.55 => V_x = V_y ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_xt1_I4_J,axiom,
% 4.39/4.55 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.55 => ( V_b = V_c
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_ord__le__eq__trans,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Orderings_Oord(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.55 => ( V_b = V_c
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_xt1_I3_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( V_a = V_b
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_ord__eq__le__trans,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Orderings_Oord(T_a)
% 4.39/4.55 => ( V_a = V_b
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_order__antisym__conv,axiom,
% 4.39/4.55 ! [V_x_2,V_y_2,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.55 <=> V_x_2 = V_y_2 ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_le__funD,axiom,
% 4.39/4.55 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
% 4.39/4.55 ( class_Orderings_Oord(T_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_order__eq__refl,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Orderings_Opreorder(T_a)
% 4.39/4.55 => ( V_x = V_y
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_order__eq__iff,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.55 ( class_Orderings_Oorder(T_a)
% 4.39/4.55 => ( V_x_2 = V_y_2
% 4.39/4.55 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
% 4.39/4.55 & c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_linorder__linear,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Orderings_Olinorder(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.55 | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_le__fun__def,axiom,
% 4.39/4.55 ! [V_g_2,V_f_2,T_a,T_b] :
% 4.39/4.55 ( class_Orderings_Oord(T_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.39/4.55 <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 4.39/4.55 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 4.39/4.55 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 4.39/4.55 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 4.39/4.55 ! [V_rx,V_ly,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 4.39/4.55 ! [V_rx,V_ly,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oab__semigroup__mult(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 4.39/4.55 ! [V_ry,V_rx,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 4.39/4.55 ! [V_ry,V_rx,V_lx,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_complex__mod__triangle__sub,axiom,
% 4.39/4.55 ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__right__imp__eq,axiom,
% 4.39/4.55 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
% 4.39/4.55 => V_b = V_c ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__imp__eq,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 4.39/4.55 => V_b = V_c ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__left__imp__eq,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
% 4.39/4.55 => V_b = V_c ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 4.39/4.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => 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)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__right__cancel,axiom,
% 4.39/4.55 ! [V_ca_2,V_a_2,V_b_2,T_a] :
% 4.39/4.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2)
% 4.39/4.55 <=> V_b_2 = V_ca_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__left__cancel,axiom,
% 4.39/4.55 ! [V_ca_2,V_b_2,V_a_2,T_a] :
% 4.39/4.55 ( class_Groups_Ocancel__semigroup__add(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2)
% 4.39/4.55 <=> V_b_2 = V_ca_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => 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) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oab__semigroup__add(T_a)
% 4.39/4.55 => 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)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => 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)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 4.39/4.55 ! [V_d,V_c,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => 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) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 4.39/4.55 ! [V_d,V_c,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => 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)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 4.39/4.55 ! [V_c,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_one__reorient,axiom,
% 4.39/4.55 ! [V_x_2,T_a] :
% 4.39/4.55 ( class_Groups_Oone(T_a)
% 4.39/4.55 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
% 4.39/4.55 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__idempotent,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__le__imp__le__left,axiom,
% 4.39/4.55 ! [V_b,V_a,V_c,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.55 => ( 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))
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__le__imp__le__right,axiom,
% 4.39/4.55 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.55 => ( 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))
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__mono,axiom,
% 4.39/4.55 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.39/4.55 => 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)) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__left__mono,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.55 => 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)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__right__mono,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.55 => 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)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__le__cancel__left,axiom,
% 4.39/4.55 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_add__le__cancel__right,axiom,
% 4.39/4.55 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_crossproduct__eq,axiom,
% 4.39/4.55 ! [V_za_2,V_x_2,V_y_2,V_w_2,T_a] :
% 4.39/4.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
% 4.39/4.55 <=> ( V_w_2 = V_x_2
% 4.39/4.55 | V_y_2 = V_za_2 ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 4.39/4.55 ! [V_b,V_m,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__left_Oadd,axiom,
% 4.39/4.55 ! [V_ya,V_y,V_x,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult_Oadd__left,axiom,
% 4.39/4.55 ! [V_b,V_a_H,V_a,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_crossproduct__noteq,axiom,
% 4.39/4.55 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 4.39/4.55 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 4.39/4.55 => ( ( V_a_2 != V_b_2
% 4.39/4.55 & V_ca_2 != V_d_2 )
% 4.39/4.55 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__right_Oadd,axiom,
% 4.39/4.55 ! [V_y,V_x,V_xa,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 4.39/4.55 ! [V_z,V_y,V_x,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult_Oadd__right,axiom,
% 4.39/4.55 ! [V_b_H,V_b,V_a,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult_Ocomm__neutral,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__1__right,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Omonoid__mult(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__1,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Ocomm__monoid__mult(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__1__left,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Omonoid__mult(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__le__D1,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__ge__self,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__add__abs,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__norm__cancel,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a)) = c_RealVector_Onorm__class_Onorm(T_a,V_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_calculation,axiom,
% 4.39/4.55 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ).
% 4.39/4.55
% 4.39/4.55 fof(fact__096cmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_060_061_Acmod_Ac_A_L_Acmod_A_Iz_A_K_Apoly_Acs_Az_J_096,axiom,
% 4.39/4.55 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),v_z____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),v_z____),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),v_z____))))) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_convex__bound__lt,axiom,
% 4.39/4.55 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__add__one__gt__zero,axiom,
% 4.39/4.55 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x))) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_norm__ratiotest__lemma,axiom,
% 4.39/4.55 ! [V_y,V_x,V_c,T_a] :
% 4.39/4.55 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
% 4.39/4.55 => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_convex__bound__le,axiom,
% 4.39/4.55 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__semiring__1(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
% 4.39/4.55 => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__add__one__not__less__self,axiom,
% 4.39/4.55 ! [V_x] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_x) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_rabs__ratiotest__lemma,axiom,
% 4.39/4.55 ! [V_y,V_x,V_c] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
% 4.39/4.55 => V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__le__cancel__iff2,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2,V_za_2] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_y_2))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__le__cancel__iff1,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2,V_za_2] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))
% 4.39/4.55 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__eq__mult,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Oordered__ring__abs(T_a)
% 4.39/4.55 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.55 | c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
% 4.39/4.55 & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.55 | c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__mult__pos,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_less__fun__def,axiom,
% 4.39/4.55 ! [V_g_2,V_f_2,T_a,T_b] :
% 4.39/4.55 ( class_Orderings_Oord(T_b)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.39/4.55 <=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
% 4.39/4.55 & ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_linorder__neqE__linordered__idom,axiom,
% 4.39/4.55 ! [V_y,V_x,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.55 => ( V_x != V_y
% 4.39/4.55 => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
% 4.39/4.55 => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__le__refl,axiom,
% 4.39/4.55 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__le__linear,axiom,
% 4.39/4.55 ! [V_w,V_z] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 4.39/4.55 | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__le__trans,axiom,
% 4.39/4.55 ! [V_k,V_j,V_i] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__le__antisym,axiom,
% 4.39/4.55 ! [V_w,V_z] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
% 4.39/4.55 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
% 4.39/4.55 => V_z = V_w ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__commute,axiom,
% 4.39/4.55 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__assoc,axiom,
% 4.39/4.55 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__zero__left,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Rings_Omult__zero(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__zero__right,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Rings_Omult__zero(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_mult__eq__0__iff,axiom,
% 4.39/4.55 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.55 ( class_Rings_Oring__no__zero__divisors(T_a)
% 4.39/4.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_no__zero__divisors,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ono__zero__divisors(T_a)
% 4.39/4.55 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_divisors__zero,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ono__zero__divisors(T_a)
% 4.39/4.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.55 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_one__neq__zero,axiom,
% 4.39/4.55 ! [T_a] :
% 4.39/4.55 ( class_Rings_Ozero__neq__one(T_a)
% 4.39/4.55 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_zero__neq__one,axiom,
% 4.39/4.55 ! [T_a] :
% 4.39/4.55 ( class_Rings_Ozero__neq__one(T_a)
% 4.39/4.55 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_comm__semiring__class_Odistrib,axiom,
% 4.39/4.55 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Ocomm__semiring(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_combine__common__factor,axiom,
% 4.39/4.55 ! [V_c,V_b,V_e,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Osemiring(T_a)
% 4.39/4.55 => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__mult,axiom,
% 4.39/4.55 ! [V_b,V_a,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__mult__self,axiom,
% 4.39/4.55 ! [V_a,T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.55 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__less__def,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 4.39/4.55 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 4.39/4.55 & V_x_2 != V_y_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_less__eq__real__def,axiom,
% 4.39/4.55 ! [V_y_2,V_x_2] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 4.39/4.55 <=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
% 4.39/4.55 | V_x_2 = V_y_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_abs__one,axiom,
% 4.39/4.55 ! [T_a] :
% 4.39/4.55 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.55 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__right__cancel,axiom,
% 4.39/4.55 ! [V_b_2,V_a_2,V_ca_2] :
% 4.39/4.55 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
% 4.39/4.55 <=> V_a_2 = V_b_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__mult__left__cancel,axiom,
% 4.39/4.55 ! [V_b_2,V_a_2,V_ca_2] :
% 4.39/4.55 ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.55 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
% 4.39/4.55 <=> V_a_2 = V_b_2 ) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__add__left__mono,axiom,
% 4.39/4.55 ! [V_z,V_y,V_x] :
% 4.39/4.55 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 4.39/4.55 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ) ).
% 4.39/4.55
% 4.39/4.55 fof(fact_real__zero__not__eq__one,axiom,
% 4.39/4.55 c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 4.39/4.55
% 4.39/4.56 fof(fact_real__mult__1,axiom,
% 4.39/4.56 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__add__mult__distrib,axiom,
% 4.39/4.56 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__le__square,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring(T_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__le__mult__iff,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2))
% 4.39/4.56 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__0__iff,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__nonneg__nonneg,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__nonneg__nonpos,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__nonneg__nonpos2,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__nonpos__nonneg,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__nonpos__nonpos,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__ring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_comm__mult__left__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__comm__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right__mono__neg,axiom,
% 4.39/4.56 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__ring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left__mono__neg,axiom,
% 4.39/4.56 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__ring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__mono_H,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__mono,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_split__mult__pos__le,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__ring(T_a)
% 4.39/4.56 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) ) )
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_split__mult__neg__le,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Oordered__cancel__semiring(T_a)
% 4.39/4.56 => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a)) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) )
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__left__mono__neg,axiom,
% 4.39/4.56 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__right__mono__neg,axiom,
% 4.39/4.56 ! [V_c,V_a,V_b,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_comm__mult__strict__left__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__left__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__right__mono,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__neg__neg,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__neg__pos,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel__left__neg,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__less__mult__pos2,axiom,
% 4.39/4.56 ! [V_a,V_b,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__less__mult__pos,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__pos__neg2,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__pos__neg,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__pos__pos,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel__left__pos,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel__left__disj,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.56 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel__right__disj,axiom,
% 4.39/4.56 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 4.39/4.56 <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
% 4.39/4.56 | ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__square__less__zero,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring(T_a)
% 4.39/4.56 => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pos__add__strict,axiom,
% 4.39/4.56 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__one__le__zero,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__le__one,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__less__one,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__one__less__zero,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__1__mult,axiom,
% 4.39/4.56 ! [V_n,V_m,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__add__one,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => 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))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_abs__mult__less,axiom,
% 4.39/4.56 ! [V_d,V_b,V_c,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_c)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_b),V_d)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Oabs__class_Oabs(T_a,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__mult__less__mono2,axiom,
% 4.39/4.56 ! [V_y,V_x,V_z] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__mult__order,axiom,
% 4.39/4.56 ! [V_y,V_x] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__mult__less__iff1,axiom,
% 4.39/4.56 ! [V_y_2,V_x_2,V_za_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_za_2)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_za_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__two__squares__add__zero__iff,axiom,
% 4.39/4.56 ! [V_y_2,V_x_2] :
% 4.39/4.56 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.56 & V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__cancel__left__pos,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__cancel__left__neg,axiom,
% 4.39/4.56 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__mono,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__strict__mono_H,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__le__imp__less,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__less__imp__less,axiom,
% 4.39/4.56 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right__less__imp__less,axiom,
% 4.39/4.56 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__imp__less__right,axiom,
% 4.39/4.56 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left__less__imp__less,axiom,
% 4.39/4.56 ! [V_b,V_a,V_c,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__imp__less__left,axiom,
% 4.39/4.56 ! [V_b,V_a,V_c,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right__le__imp__le,axiom,
% 4.39/4.56 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left__le__imp__le,axiom,
% 4.39/4.56 ! [V_b,V_a,V_c,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semiring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right__le__one__le,axiom,
% 4.39/4.56 ! [V_y,V_x,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left__le__one__le,axiom,
% 4.39/4.56 ! [V_y,V_x,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_zero__less__two,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.56 => 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))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__pCons,axiom,
% 4.39/4.56 ! [V_x,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__sum__squares__lt__zero,axiom,
% 4.39/4.56 ! [V_y,V_x,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring(T_a)
% 4.39/4.56 => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sum__squares__gt__zero__iff,axiom,
% 4.39/4.56 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
% 4.39/4.56 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sum__squares__ge__zero,axiom,
% 4.39/4.56 ! [V_y,V_x,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring(T_a)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sum__squares__le__zero__iff,axiom,
% 4.39/4.56 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__real__square__gt__zero,axiom,
% 4.39/4.56 ! [V_x_2] :
% 4.39/4.56 ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
% 4.39/4.56 <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sum__squares__eq__zero__iff,axiom,
% 4.39/4.56 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__ring__strict(T_a)
% 4.39/4.56 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_even__less__0__iff,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( 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))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pCons__eq__iff,axiom,
% 4.39/4.56 ! [V_q_2,V_b_2,V_pa_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Groups_Ozero(T_a)
% 4.39/4.56 => ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
% 4.39/4.56 <=> ( V_a_2 = V_b_2
% 4.39/4.56 & V_pa_2 = V_q_2 ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__eq__iff,axiom,
% 4.39/4.56 ! [V_q_2,V_pa_2,T_a] :
% 4.39/4.56 ( ( class_Int_Oring__char__0(T_a)
% 4.39/4.56 & class_Rings_Oidom(T_a) )
% 4.39/4.56 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
% 4.39/4.56 <=> V_pa_2 = V_q_2 ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__zero,axiom,
% 4.39/4.56 ! [V_pa_2,T_a] :
% 4.39/4.56 ( ( class_Int_Oring__char__0(T_a)
% 4.39/4.56 & class_Rings_Oidom(T_a) )
% 4.39/4.56 => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 4.39/4.56 <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_double__eq__0__iff,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.56 => ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pCons__0__0,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Groups_Ozero(T_a)
% 4.39/4.56 => c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pCons__eq__0__iff,axiom,
% 4.39/4.56 ! [V_pa_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Groups_Ozero(T_a)
% 4.39/4.56 => ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.56 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__pCons,axiom,
% 4.39/4.56 ! [V_q,V_b,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.39/4.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_one__poly__def,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.56 => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__0,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__mult,axiom,
% 4.39/4.56 ! [V_x,V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__add,axiom,
% 4.39/4.56 ! [V_x,V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__1,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
% 4.39/4.56 ~ ! [B_m] :
% 4.39/4.56 ~ ! [B_z] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left_Opos__bounded,axiom,
% 4.39/4.56 ! [V_y,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right_Opos__bounded,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult_Opos__bounded,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left_Ononneg__bounded,axiom,
% 4.39/4.56 ! [V_y,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right_Ononneg__bounded,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__poly__0__left,axiom,
% 4.39/4.56 ! [V_q,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__poly__code_I1_J,axiom,
% 4.39/4.56 ! [V_q,T_a] :
% 4.39/4.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.39/4.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__poly__0__right,axiom,
% 4.39/4.56 ! [V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__poly__code_I2_J,axiom,
% 4.39/4.56 ! [V_p,T_a] :
% 4.39/4.56 ( class_Groups_Ocomm__monoid__add(T_a)
% 4.39/4.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__poly__add__left,axiom,
% 4.39/4.56 ! [V_r,V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pcompose__pCons,axiom,
% 4.39/4.56 ! [V_q,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pos__poly__pCons,axiom,
% 4.39/4.56 ! [V_pa_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))
% 4.39/4.56 <=> ( c_Polynomial_Opos__poly(T_a,V_pa_2)
% 4.39/4.56 | ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.56 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_order__root,axiom,
% 4.39/4.56 ! [V_a_2,V_pa_2,T_a] :
% 4.39/4.56 ( class_Rings_Oidom(T_a)
% 4.39/4.56 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.56 | c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__rec__pCons,axiom,
% 4.39/4.56 ! [V_pa_2,V_a_2,T_a,V_za_2,V_f_2,T_b] :
% 4.39/4.56 ( class_Groups_Ozero(T_b)
% 4.39/4.56 => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2) = V_za_2
% 4.39/4.56 => c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,V_pa_2)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult_Ononneg__bounded,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.39/4.56 & ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult_Obounded,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__pos__poly__0,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pos__poly__mult,axiom,
% 4.39/4.56 ! [V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 4.39/4.56 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 4.39/4.56 => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pos__poly__add,axiom,
% 4.39/4.56 ! [V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Polynomial_Opos__poly(T_a,V_p)
% 4.39/4.56 => ( c_Polynomial_Opos__poly(T_a,V_q)
% 4.39/4.56 => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_pcompose__0,axiom,
% 4.39/4.56 ! [V_q,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__pcompose,axiom,
% 4.39/4.56 ! [V_x,V_q,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__rec__0,axiom,
% 4.39/4.56 ! [T_a,V_za_2,V_f_2,T_b] :
% 4.39/4.56 ( class_Groups_Ozero(T_b)
% 4.39/4.56 => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2) = V_za_2
% 4.39/4.56 => c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_za_2 ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__rec_Osimps,axiom,
% 4.39/4.56 ! [V_pa_2,V_a_2,V_f_2,V_za_2,T_a,T_b] :
% 4.39/4.56 ( class_Groups_Ozero(T_b)
% 4.39/4.56 => c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_za_2,c_Polynomial_Opoly__rec(T_a,T_b,V_za_2,V_f_2,V_pa_2))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__zeroE,axiom,
% 4.39/4.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le0,axiom,
% 4.39/4.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__left_Obounded,axiom,
% 4.39/4.56 ! [V_y,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__right_Obounded,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.56 => ? [B_K] :
% 4.39/4.56 ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_norm__sgn,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.56 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 4.39/4.56 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__pCons__left,axiom,
% 4.39/4.56 ! [V_q,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__not__refl,axiom,
% 4.39/4.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__neq__iff,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( V_ma_2 != V_n_2
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__less__le,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 & V_ma_2 != V_n_2 ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__eq__less__or__eq,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 | V_ma_2 = V_n_2 ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_linorder__neqE__nat,axiom,
% 4.39/4.56 ! [V_y,V_x] :
% 4.39/4.56 ( V_x != V_y
% 4.39/4.56 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__irrefl__nat,axiom,
% 4.39/4.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__not__refl2,axiom,
% 4.39/4.56 ! [V_m,V_n] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 4.39/4.56 => V_m != V_n ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__not__refl3,axiom,
% 4.39/4.56 ! [V_t,V_s] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
% 4.39/4.56 => V_s != V_t ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__imp__le__nat,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__neq__implies__less,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 => ( V_m != V_n
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__or__eq__imp__le,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 | V_m = V_n )
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__less__cases,axiom,
% 4.39/4.56 ! [V_P_2,V_n_2,V_ma_2] :
% 4.39/4.56 ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 4.39/4.56 => ( ( V_ma_2 = V_n_2
% 4.39/4.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 4.39/4.56 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 4.39/4.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
% 4.39/4.56 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__sgn,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__antisym,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.39/4.56 => V_m = V_n ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__trans,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_eq__imp__le,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( V_m = V_n
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__le__linear,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__refl,axiom,
% 4.39/4.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__square,axiom,
% 4.39/4.56 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__add2,axiom,
% 4.39/4.56 ! [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)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__add1,axiom,
% 4.39/4.56 ! [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)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__cube,axiom,
% 4.39/4.56 ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__Suc__ex__iff,axiom,
% 4.39/4.56 ! [V_l_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
% 4.39/4.56 <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__iff__add,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.39/4.56 <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__add__left__cancel__le,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_trans__le__add1,axiom,
% 4.39/4.56 ! [V_m,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_trans__le__add2,axiom,
% 4.39/4.56 ! [V_m,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__le__mono1,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => 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)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__mono1,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__mono2,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__le__mono,axiom,
% 4.39/4.56 ! [V_l,V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 4.39/4.56 => 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)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__mono,axiom,
% 4.39/4.56 ! [V_l,V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__leD2,axiom,
% 4.39/4.56 ! [V_n,V_k,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__leD1,axiom,
% 4.39/4.56 ! [V_n,V_k,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__leE,axiom,
% 4.39/4.56 ! [V_n,V_k,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
% 4.39/4.56 => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__lessD1,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__add__eq__less,axiom,
% 4.39/4.56 ! [V_n,V_m,V_l,V_k] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 4.39/4.56 => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__less__mono,axiom,
% 4.39/4.56 ! [V_l,V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
% 4.39/4.56 => 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)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__less__mono1,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => 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)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_trans__less__add2,axiom,
% 4.39/4.56 ! [V_m,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_trans__less__add1,axiom,
% 4.39/4.56 ! [V_m,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__add__left__cancel__less,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__add__less2,axiom,
% 4.39/4.56 ! [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) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__add__less1,axiom,
% 4.39/4.56 ! [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) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__smult,axiom,
% 4.39/4.56 ! [V_p,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__1__left,axiom,
% 4.39/4.56 ! [V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__0__right,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__0__0,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__zero__iff,axiom,
% 4.39/4.56 ! [V_x_2,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.56 => ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__zero,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn0,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_Groups_Osgn__if(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__smult__right,axiom,
% 4.39/4.56 ! [V_q,V_a,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__add__right,axiom,
% 4.39/4.56 ! [V_q,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__smult__left,axiom,
% 4.39/4.56 ! [V_q,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__times,axiom,
% 4.39/4.56 ! [V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__mult,axiom,
% 4.39/4.56 ! [V_y,V_x,T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__one,axiom,
% 4.39/4.56 ! [T_a] :
% 4.39/4.56 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__0__left,axiom,
% 4.39/4.56 ! [V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__eq__0__iff,axiom,
% 4.39/4.56 ! [V_pa_2,V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Oidom(T_a)
% 4.39/4.56 => ( c_Polynomial_Osmult(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.56 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.56 | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__pCons,axiom,
% 4.39/4.56 ! [V_p,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_poly__smult,axiom,
% 4.39/4.56 ! [V_x,V_p,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_synthetic__div__unique__lemma,axiom,
% 4.39/4.56 ! [V_a,V_p,V_c,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
% 4.39/4.56 => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_smult__add__left,axiom,
% 4.39/4.56 ! [V_p,V_b,V_a,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__less,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__greater,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_abs__sgn,axiom,
% 4.39/4.56 ! [V_k,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__sgn__abs,axiom,
% 4.39/4.56 ! [V_x,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__0,axiom,
% 4.39/4.56 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 4.39/4.56 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_plus__nat_Oadd__0,axiom,
% 4.39/4.56 ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__0__right,axiom,
% 4.39/4.56 ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_Nat_Oadd__0__right,axiom,
% 4.39/4.56 ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 4.39/4.56
% 4.39/4.56 fof(fact_le__0__eq,axiom,
% 4.39/4.56 ! [V_n_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.39/4.56 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__is__0,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__is__0,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__cancel1,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 4.39/4.56 <=> ( V_ma_2 = V_n_2
% 4.39/4.56 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__cancel2,axiom,
% 4.39/4.56 ! [V_n_2,V_k_2,V_ma_2] :
% 4.39/4.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
% 4.39/4.56 <=> ( V_ma_2 = V_n_2
% 4.39/4.56 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__eq__self__implies__10,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 4.39/4.56 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.39/4.56 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__eq__self__zero,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
% 4.39/4.56 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_gr0I,axiom,
% 4.39/4.56 ! [V_n] :
% 4.39/4.56 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__mono2,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__mono1,axiom,
% 4.39/4.56 ! [V_k,V_j,V_i] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 4.39/4.56 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_gr__implies__not0,axiom,
% 4.39/4.56 ! [V_n,V_m] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.39/4.56 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__cancel2,axiom,
% 4.39/4.56 ! [V_n_2,V_k_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__le__cancel1,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.56 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel2,axiom,
% 4.39/4.56 ! [V_n_2,V_k_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__less__cancel1,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_less__nat__zero__code,axiom,
% 4.39/4.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__0__less__mult__iff,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 4.39/4.56 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_add__gr__0,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2] :
% 4.39/4.56 ( 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_ma_2,V_n_2))
% 4.39/4.56 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 4.39/4.56 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_neq0__conv,axiom,
% 4.39/4.56 ! [V_n_2] :
% 4.39/4.56 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_not__less0,axiom,
% 4.39/4.56 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_real__sgn__pos,axiom,
% 4.39/4.56 ! [V_x] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__pos,axiom,
% 4.39/4.56 ! [V_a,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.56 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_sgn__1__pos,axiom,
% 4.39/4.56 ! [V_a_2,T_a] :
% 4.39/4.56 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.56 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_mult__pCons__right,axiom,
% 4.39/4.56 ! [V_q,V_a,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_nat__mult__le__cancel1,axiom,
% 4.39/4.56 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.56 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.56 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.56 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_synthetic__div__correct,axiom,
% 4.39/4.56 ! [V_c,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 4.39/4.56
% 4.39/4.56 fof(fact_synthetic__div__unique,axiom,
% 4.39/4.56 ! [V_r,V_q,V_c,V_p,T_a] :
% 4.39/4.56 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.56 => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = c_Polynomial_OpCons(T_a,V_r,V_q)
% 4.39/4.57 => ( V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)
% 4.39/4.57 & V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_termination__basic__simps_I5_J,axiom,
% 4.39/4.57 ! [V_y,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__less__cancel1,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__eq__cancel1,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 4.39/4.57 <=> V_ma_2 = V_n_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__1,axiom,
% 4.39/4.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__1__eq__mult__iff,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2] :
% 4.39/4.57 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
% 4.39/4.57 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.39/4.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__1__right,axiom,
% 4.39/4.57 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__add__commute,axiom,
% 4.39/4.57 ! [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) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__commute,axiom,
% 4.39/4.57 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__add__left__commute,axiom,
% 4.39/4.57 ! [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)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_add__mult__distrib2,axiom,
% 4.39/4.57 ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__eq__1__iff,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2] :
% 4.39/4.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.39/4.57 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 4.39/4.57 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__add__assoc,axiom,
% 4.39/4.57 ! [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)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__assoc,axiom,
% 4.39/4.57 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_add__mult__distrib,axiom,
% 4.39/4.57 ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__add__left__cancel,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
% 4.39/4.57 <=> V_ma_2 = V_n_2 ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__add__right__cancel,axiom,
% 4.39/4.57 ! [V_n_2,V_k_2,V_ma_2] :
% 4.39/4.57 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
% 4.39/4.57 <=> V_ma_2 = V_n_2 ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_left__add__mult__distrib,axiom,
% 4.39/4.57 ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_synthetic__div__0,axiom,
% 4.39/4.57 ! [V_c,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.57 => c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
% 4.39/4.57 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.57 | V_ma_2 = V_n_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_termination__basic__simps_I1_J,axiom,
% 4.39/4.57 ! [V_z,V_y,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_termination__basic__simps_I2_J,axiom,
% 4.39/4.57 ! [V_y,V_z,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
% 4.39/4.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_termination__basic__simps_I4_J,axiom,
% 4.39/4.57 ! [V_y,V_z,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_termination__basic__simps_I3_J,axiom,
% 4.39/4.57 ! [V_z,V_y,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_synthetic__div__pCons,axiom,
% 4.39/4.57 ! [V_c,V_p,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__0(T_a)
% 4.39/4.57 => c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_synthetic__div__correct_H,axiom,
% 4.39/4.57 ! [V_p,V_c,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring__1(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_ex__least__nat__less,axiom,
% 4.39/4.57 ! [V_n_2,V_P_2] :
% 4.39/4.57 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 4.39/4.57 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 4.39/4.57 => ? [B_k] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)
% 4.39/4.57 & ! [B_i] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
% 4.39/4.57 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 4.39/4.57 & hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__add__one,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__add__one,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__zero,axiom,
% 4.39/4.57 ! [T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__0__equal__iff__equal,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 4.39/4.57 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_equal__neg__zero,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.57 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
% 4.39/4.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__equal__0__iff__equal,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__equal__zero,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
% 4.39/4.57 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__imp__neg__le,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__le__iff__le,axiom,
% 4.39/4.57 ! [V_a_2,V_b_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__le__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__minus__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_less__minus__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__less__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__less__iff__less,axiom,
% 4.39/4.57 ! [V_a_2,V_b_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult__left_Ominus,axiom,
% 4.39/4.57 ! [V_y,V_x,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult_Ominus__left,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult__right_Ominus,axiom,
% 4.39/4.57 ! [V_x,V_xa,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult_Ominus__right,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_square__eq__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
% 4.39/4.57 <=> ( V_a_2 = V_b_2
% 4.39/4.57 | V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__mult__minus,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Oring(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__mult__commute,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Oring(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__mult__left,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Oring(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__mult__right,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Oring(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__add__cancel,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_add__minus__cancel,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__add,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__add__distrib,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oab__group__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__minus__cancel,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_norm__minus__cancel,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.57 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__poly__def,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__poly__code_I1_J,axiom,
% 4.39/4.57 ! [T_a] :
% 4.39/4.57 ( class_Groups_Oab__group__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_smult__minus__right,axiom,
% 4.39/4.57 ! [V_p,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring(T_a)
% 4.39/4.57 => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__minus,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__poly__code_I2_J,axiom,
% 4.39/4.57 ! [V_p,V_a,T_b] :
% 4.39/4.57 ( class_Groups_Oab__group__add(T_b)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__pCons,axiom,
% 4.39/4.57 ! [V_p,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oab__group__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_poly__minus,axiom,
% 4.39/4.57 ! [V_x,V_p,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring(T_a)
% 4.39/4.57 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__minus,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_equation__minus__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 4.39/4.57 <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__equation__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
% 4.39/4.57 <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__equal__iff__equal,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 4.39/4.57 <=> V_a_2 = V_b_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_smult__minus__left,axiom,
% 4.39/4.57 ! [V_p,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring(T_a)
% 4.39/4.57 => c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__zero,axiom,
% 4.39/4.57 c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_zero__le__natfloor,axiom,
% 4.39/4.57 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__mono,axiom,
% 4.39/4.57 ! [V_y,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__one,axiom,
% 4.39/4.57 c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__zero,axiom,
% 4.39/4.57 c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_zero__le__natceiling,axiom,
% 4.39/4.57 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__mono,axiom,
% 4.39/4.57 ! [V_y,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__one,axiom,
% 4.39/4.57 c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__le__self__iff,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__le__0__iff__le,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__minus__self__iff,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__0__le__iff__le,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_less__minus__self__iff,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__less__nonneg,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Olinordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__less__0__iff__less,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_neg__0__less__iff__less,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_add__eq__0__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__unique,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_ab__left__minus,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oab__group__add(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_left__minus,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
% 4.39/4.57 <=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_right__minus,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Ogroup__add(T_a)
% 4.39/4.57 => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_square__eq__1__iff,axiom,
% 4.39/4.57 ! [V_x_2,T_a] :
% 4.39/4.57 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 4.39/4.57 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
% 4.39/4.57 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
% 4.39/4.57 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring__1(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__ge__minus__self,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__le__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
% 4.39/4.57 <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 4.39/4.57 & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__leI,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__le__D2,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__less__iff,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
% 4.39/4.57 <=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.39/4.57 & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__minus__mult__self__le,axiom,
% 4.39/4.57 ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__add__minus__iff,axiom,
% 4.39/4.57 ! [V_a_2,V_x_2] :
% 4.39/4.57 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 <=> V_x_2 = V_a_2 ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__add__eq__0__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__le__interval__iff,axiom,
% 4.39/4.57 ! [V_ra_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
% 4.39/4.57 <=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2)
% 4.39/4.57 & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__minus__add__cancel,axiom,
% 4.39/4.57 ! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__neg,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_pos__poly__total,axiom,
% 4.39/4.57 ! [V_p,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.57 | c_Polynomial_Opos__poly(T_a,V_p)
% 4.39/4.57 | c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__poly__def,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 4.39/4.57 & ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) ) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__neg,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__minus__le__zero,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__of__nonpos,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__of__neg,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__if,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Groups_Oabs__if(T_a)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__0__le__add__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__add__le__0__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__add__less__0__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__0__less__add__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__abs__def,axiom,
% 4.39/4.57 ! [V_r] :
% 4.39/4.57 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__real__def,axiom,
% 4.39/4.57 ! [V_a] :
% 4.39/4.57 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 => c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__sum__triangle__ineq,axiom,
% 4.39/4.57 ! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__natfloor__eq__one,axiom,
% 4.39/4.57 ! [V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__le__eq__one,axiom,
% 4.39/4.57 ! [V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__neg,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__1__neg,axiom,
% 4.39/4.57 ! [V_a_2,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__if,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Groups_Osgn__if(T_a)
% 4.39/4.57 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 4.39/4.57 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__mult__natfloor,axiom,
% 4.39/4.57 ! [V_b,V_a] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__sgn__def,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 4.39/4.57 & ( V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_sgn__real__def,axiom,
% 4.39/4.57 ! [V_a] :
% 4.39/4.57 ( ( V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
% 4.39/4.57 & ( V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
% 4.39/4.57 & ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 4.39/4.57 => c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_complex__mod__minus__le__complex__mod,axiom,
% 4.39/4.57 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__eq,axiom,
% 4.39/4.57 ! [V_x,V_n] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 4.39/4.57 => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_compl__le__compl__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.57 ( class_Lattices_Oboolean__algebra(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_compl__mono,axiom,
% 4.39/4.57 ! [V_y,V_x,T_a] :
% 4.39/4.57 ( class_Lattices_Oboolean__algebra(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__ge__zero,axiom,
% 4.39/4.57 ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__real__of__nat,axiom,
% 4.39/4.57 ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__real__of__nat,axiom,
% 4.39/4.57 ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__inject,axiom,
% 4.39/4.57 ! [V_ma_2,V_n_2] :
% 4.39/4.57 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
% 4.39/4.57 <=> V_n_2 = V_ma_2 ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__real__of__nat__cancel,axiom,
% 4.39/4.57 ! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__zero__iff,axiom,
% 4.39/4.57 ! [V_n_2] :
% 4.39/4.57 ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
% 4.39/4.57 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__zero,axiom,
% 4.39/4.57 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_not__real__of__nat__less__zero,axiom,
% 4.39/4.57 ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__less__iff,axiom,
% 4.39/4.57 ! [V_ma_2,V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__le__iff,axiom,
% 4.39/4.57 ! [V_ma_2,V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__mult,axiom,
% 4.39/4.57 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__add,axiom,
% 4.39/4.57 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__1,axiom,
% 4.39/4.57 c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__natceiling__ge,axiom,
% 4.39/4.57 ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
% 4.39/4.57 ! [V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
% 4.39/4.57 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__natfloor__le,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__natfloor,axiom,
% 4.39/4.57 ! [V_a,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__le,axiom,
% 4.39/4.57 ! [V_a,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult__left__idem,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult__idem,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_times_Oidem,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_double__compl,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Lattices_Oboolean__algebra(T_a)
% 4.39/4.57 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_uminus__apply,axiom,
% 4.39/4.57 ! [V_x_2,V_A_2,T_b,T_a] :
% 4.39/4.57 ( class_Groups_Ouminus(T_a)
% 4.39/4.57 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_compl__eq__compl__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.57 ( class_Lattices_Oboolean__algebra(T_a)
% 4.39/4.57 => ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
% 4.39/4.57 <=> V_x_2 = V_y_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
% 4.39/4.57 ! [V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__less__real__le,axiom,
% 4.39/4.57 ! [V_ma_2,V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__le__real__less,axiom,
% 4.39/4.57 ! [V_ma_2,V_n_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_le__natfloor__eq,axiom,
% 4.39/4.57 ! [V_a_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__le__eq,axiom,
% 4.39/4.57 ! [V_a_2,V_x_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
% 4.39/4.57 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_real__natfloor__add__one__gt,axiom,
% 4.39/4.57 ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_less__natfloor,axiom,
% 4.39/4.57 ! [V_n,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
% 4.39/4.57 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__add,axiom,
% 4.39/4.57 ! [V_a,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
% 4.39/4.57 ! [V_n,V_z] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
% 4.39/4.57 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natfloor__eq,axiom,
% 4.39/4.57 ! [V_x,V_n] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
% 4.39/4.57 => c_RComplete_Onatfloor(V_x) = V_n ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_natceiling__add,axiom,
% 4.39/4.57 ! [V_a,V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_poly__eq__0__iff__dvd,axiom,
% 4.39/4.57 ! [V_ca_2,V_pa_2,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__iff__poly__eq__0,axiom,
% 4.39/4.57 ! [V_pa_2,V_ca_2,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
% 4.39/4.57 <=> hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_expi__add,axiom,
% 4.39/4.57 ! [V_b,V_a] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(V_a)),c_Complex_Oexpi(V_b)) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__0__right,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__minus__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_minus__dvd__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__ring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__abs__iff,axiom,
% 4.39/4.57 ! [V_k_2,V_ma_2,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_abs__dvd__iff,axiom,
% 4.39/4.57 ! [V_k_2,V_ma_2,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__if__abs__eq,axiom,
% 4.39/4.57 ! [V_k,V_l,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__idom(T_a)
% 4.39/4.57 => ( c_Groups_Oabs__class_Oabs(T_a,V_l) = c_Groups_Oabs__class_Oabs(T_a,V_k)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_l,V_k) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_expi__zero,axiom,
% 4.39/4.57 c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__triv__left,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__triv__right,axiom,
% 4.39/4.57 ! [V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult2,axiom,
% 4.39/4.57 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult,axiom,
% 4.39/4.57 ! [V_b,V_c,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_mult__dvd__mono,axiom,
% 4.39/4.57 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvdI,axiom,
% 4.39/4.57 ! [V_k,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Odvd(T_a)
% 4.39/4.57 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__left,axiom,
% 4.39/4.57 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__right,axiom,
% 4.39/4.57 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__add,axiom,
% 4.39/4.57 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_one__dvd,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_smult__dvd__cancel,axiom,
% 4.39/4.57 ! [V_q,V_p,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__smult,axiom,
% 4.39/4.57 ! [V_a,V_q,V_p,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__0__left,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.57 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__refl,axiom,
% 4.39/4.57 ! [V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__trans,axiom,
% 4.39/4.57 ! [V_c,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__cancel__left,axiom,
% 4.39/4.57 ! [V_b_2,V_a_2,V_ca_2,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
% 4.39/4.57 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 | c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__cancel__right,axiom,
% 4.39/4.57 ! [V_b_2,V_ca_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
% 4.39/4.57 <=> ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 | c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__smult__iff,axiom,
% 4.39/4.57 ! [V_q_2,V_pa_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Fields_Ofield(T_a)
% 4.39/4.57 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_a_2,V_q_2))
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_smult__dvd,axiom,
% 4.39/4.57 ! [V_a,V_q,V_p,T_a] :
% 4.39/4.57 ( class_Fields_Ofield(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
% 4.39/4.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__smult__cancel,axiom,
% 4.39/4.57 ! [V_q,V_a,V_p,T_a] :
% 4.39/4.57 ( class_Fields_Ofield(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
% 4.39/4.57 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_smult__dvd__iff,axiom,
% 4.39/4.57 ! [V_q_2,V_pa_2,V_a_2,T_a] :
% 4.39/4.57 ( class_Fields_Ofield(T_a)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a_2,V_pa_2),V_q_2)
% 4.39/4.57 <=> ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
% 4.39/4.57 & ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_unity__coeff__ex,axiom,
% 4.39/4.57 ! [V_l_2,V_P_2,T_a] :
% 4.39/4.57 ( ( class_Rings_Odvd(T_a)
% 4.39/4.57 & class_Rings_Osemiring__0(T_a) )
% 4.39/4.57 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
% 4.39/4.57 <=> ? [B_x] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))
% 4.39/4.57 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_order__1,axiom,
% 4.39/4.57 ! [V_p,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Oidom(T_a)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_reals__Archimedean3,axiom,
% 4.39/4.57 ! [V_x] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.39/4.57 => ! [B_y] :
% 4.39/4.57 ? [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,B_y,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_x)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__reduce,axiom,
% 4.39/4.57 ! [V_n_2,V_k_2] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__dvd__1__iff__1,axiom,
% 4.39/4.57 ! [V_ma_2] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
% 4.39/4.57 <=> V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_norm__power__ineq,axiom,
% 4.39/4.57 ! [V_n,V_x,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__algebra__1(T_a)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_norm__power,axiom,
% 4.39/4.57 ! [V_n,V_x,T_a] :
% 4.39/4.57 ( class_RealVector_Oreal__normed__div__algebra(T_a)
% 4.39/4.57 => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_poly__power,axiom,
% 4.39/4.57 ! [V_x,V_n,V_p,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 4.39/4.57 ! [V_q,V_y,V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 4.39/4.57 ! [V_q,V_p,V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 4.39/4.57 ! [V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 4.39/4.57 ! [V_q,V_p,V_x,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__dvd__not__less,axiom,
% 4.39/4.57 ! [V_n,V_m] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.39/4.57 => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.57 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.39/4.57 | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__imp__le,axiom,
% 4.39/4.57 ! [V_n,V_k] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.39/4.57 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_nat__mult__dvd__cancel1,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2,V_k_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
% 4.39/4.57 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__cancel,axiom,
% 4.39/4.57 ! [V_n,V_m,V_k] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__cancel2,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)
% 4.39/4.57 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__mult__cancel1,axiom,
% 4.39/4.57 ! [V_n_2,V_ma_2] :
% 4.39/4.57 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
% 4.39/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)
% 4.39/4.57 <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_power__strict__mono,axiom,
% 4.39/4.57 ! [V_n,V_b,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.39/4.57 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd__power,axiom,
% 4.39/4.57 ! [V_x,V_n,T_a] :
% 4.39/4.57 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.39/4.57 => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.39/4.57 | V_x = c_Groups_Oone__class_Oone(T_a) )
% 4.39/4.57 => c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_one__less__power,axiom,
% 4.39/4.57 ! [V_n,V_a,T_a] :
% 4.39/4.57 ( class_Rings_Olinordered__semidom(T_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.39/4.57 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.39/4.57 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd_Oorder__refl,axiom,
% 4.39/4.57 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd_Oeq__iff,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( V_x_2 = V_y_2
% 4.39/4.57 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.39/4.57 & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd_Ole__less,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.39/4.57 <=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.39/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 4.39/4.57 | V_x_2 = V_y_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd_Oless__le,axiom,
% 4.39/4.57 ! [V_y_2,V_x_2] :
% 4.39/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.39/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) )
% 4.39/4.57 <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.39/4.57 & V_x_2 != V_y_2 ) ) ).
% 4.39/4.57
% 4.39/4.57 fof(fact_dvd_Oneq__le__trans,axiom,
% 4.60/4.57 ! [V_b,V_a] :
% 4.60/4.57 ( V_a != V_b
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oeq__refl,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( V_x = V_y
% 4.60/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oantisym__conv,axiom,
% 4.60/4.57 ! [V_x_2,V_y_2] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
% 4.60/4.57 <=> V_x_2 = V_y_2 ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 | V_x = V_y ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Ole__neq__trans,axiom,
% 4.60/4.57 ! [V_b,V_a] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 => ( V_a != V_b
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 4.60/4.57 ! [V_c,V_b,V_a] :
% 4.60/4.57 ( V_a = V_b
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 4.60/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 4.60/4.57 ! [V_c,V_b,V_a] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 => ( V_b = V_c
% 4.60/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd__antisym,axiom,
% 4.60/4.57 ! [V_n,V_m] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
% 4.60/4.57 => V_m = V_n ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oantisym,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 4.60/4.57 => V_x = V_y ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oorder__trans,axiom,
% 4.60/4.57 ! [V_z,V_y,V_x] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 4.60/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 4.60/4.57 ! [V_c,V_b,V_a] :
% 4.60/4.57 ( V_a = V_b
% 4.60/4.57 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b) )
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Ole__less__trans,axiom,
% 4.60/4.57 ! [V_z,V_y,V_x] :
% 4.60/4.57 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__imp__neq,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => V_x != V_y ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__not__sym,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__imp__le,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__imp__not__less,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => V_x != V_y ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 4.60/4.57 ! [V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => V_y != V_x ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 4.60/4.57 ! [V_c,V_b,V_a] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 4.60/4.57 => ( V_b = V_c
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__le__trans,axiom,
% 4.60/4.57 ! [V_z,V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 4.60/4.57 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__asym_H,axiom,
% 4.60/4.57 ! [V_b,V_a] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) )
% 4.60/4.57 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 4.60/4.57
% 4.60/4.57 fof(fact_dvd_Oless__trans,axiom,
% 4.60/4.57 ! [V_z,V_y,V_x] :
% 4.60/4.57 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.57 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.57 => ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
% 4.60/4.58 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y) )
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
% 4.60/4.58 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd_Oless__asym,axiom,
% 4.60/4.58 ! [V_y,V_x] :
% 4.60/4.58 ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
% 4.60/4.58 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) )
% 4.60/4.58 => ~ ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
% 4.60/4.58 & ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zpower__zpower,axiom,
% 4.60/4.58 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zpower__zadd__distrib,axiom,
% 4.60/4.58 ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__less__zpower__abs__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_x_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
% 4.60/4.58 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__power__less__imp__less,axiom,
% 4.60/4.58 ! [V_n,V_m,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__zero__less__power__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_x_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
% 4.60/4.58 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__of__nat__power,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__real__of__nat,axiom,
% 4.60/4.58 ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_natfloor__power,axiom,
% 4.60/4.58 ! [V_n,V_x] :
% 4.60/4.58 ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
% 4.60/4.58 => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__dvd__imp__le,axiom,
% 4.60/4.58 ! [V_n,V_m,V_i] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_field__power__not__zero,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 4.60/4.58 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__mult__distrib,axiom,
% 4.60/4.58 ! [V_n,V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ocomm__monoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__commutes,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__one,axiom,
% 4.60/4.58 ! [V_n,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__power__same,axiom,
% 4.60/4.58 ! [V_n,V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__mult,axiom,
% 4.60/4.58 ! [V_n,V_m,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__abs,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__idom(T_a)
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__one__right,axiom,
% 4.60/4.58 ! [V_a,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__le__power,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__mono,axiom,
% 4.60/4.58 ! [V_n,V_b,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__less__power,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_one__le__power,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__eq__0__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_a_2,T_a] :
% 4.60/4.58 ( ( class_Power_Opower(T_a)
% 4.60/4.58 & class_Rings_Omult__zero(T_a)
% 4.60/4.58 & class_Rings_Ono__zero__divisors(T_a)
% 4.60/4.58 & class_Rings_Ozero__neq__one(T_a) )
% 4.60/4.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.60/4.58 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
% 4.60/4.58 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__inject__exp,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a_2)
% 4.60/4.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
% 4.60/4.58 <=> V_ma_2 = V_n_2 ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__0,axiom,
% 4.60/4.58 ! [V_a,T_a] :
% 4.60/4.58 ( class_Power_Opower(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__add,axiom,
% 4.60/4.58 ! [V_n,V_m,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__le__dvd,axiom,
% 4.60/4.58 ! [V_m,V_b,V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__power__le,axiom,
% 4.60/4.58 ! [V_m,V_n,V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__imp__power__dvd,axiom,
% 4.60/4.58 ! [V_a,V_n,V_m,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__power__minus,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__idom(T_a)
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__less__imp__less__base,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__gt1__lemma,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__less__power__Suc,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__0__left,axiom,
% 4.60/4.58 ! [V_n,T_a] :
% 4.60/4.58 ( ( class_Power_Opower(T_a)
% 4.60/4.58 & class_Rings_Osemiring__0(T_a) )
% 4.60/4.58 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) )
% 4.60/4.58 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__le__power__abs,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__idom(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__minus,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Oring__1(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__strict__increasing,axiom,
% 4.60/4.58 ! [V_a,V_N,V_n,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__less__imp__less__exp,axiom,
% 4.60/4.58 ! [V_n,V_m,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__strict__increasing__iff,axiom,
% 4.60/4.58 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__increasing,axiom,
% 4.60/4.58 ! [V_a,V_N,V_n,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__Suc__less,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__strict__decreasing,axiom,
% 4.60/4.58 ! [V_a,V_N,V_n,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__eq__imp__eq__base,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.60/4.58 => V_a = V_b ) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__decreasing,axiom,
% 4.60/4.58 ! [V_a,V_N,V_n,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__increasing__iff,axiom,
% 4.60/4.58 ! [V_y_2,V_x_2,V_b_2,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__le__imp__le__exp,axiom,
% 4.60/4.58 ! [V_n,V_m,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
% 4.60/4.58 ! [V_n,V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__pos__nat,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_order,axiom,
% 4.60/4.58 ! [V_a,V_p,T_a] :
% 4.60/4.58 ( class_Rings_Oidom(T_a)
% 4.60/4.58 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)
% 4.60/4.58 & ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_lessI,axiom,
% 4.60/4.58 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__mono,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__less__Suc,axiom,
% 4.60/4.58 ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__1__left,axiom,
% 4.60/4.58 ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__imp__le__int,axiom,
% 4.60/4.58 ! [V_d,V_i] :
% 4.60/4.58 ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__not__zless,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
% 4.60/4.58 => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__imp__le,axiom,
% 4.60/4.58 ! [V_n,V_z] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__antisym__abs,axiom,
% 4.60/4.58 ! [V_b,V_a] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__mult__cancel1,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)
% 4.60/4.58 <=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd1__eq,axiom,
% 4.60/4.58 ! [V_x_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))
% 4.60/4.58 <=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__reduce,axiom,
% 4.60/4.58 ! [V_ma_2,V_n_2,V_k_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__period,axiom,
% 4.60/4.58 ! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__mono,axiom,
% 4.60/4.58 ! [V_t_2,V_ma_2,V_k_2] :
% 4.60/4.58 ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__mult__cancel,axiom,
% 4.60/4.58 ! [V_n,V_m,V_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))
% 4.60/4.58 => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__antisym__nonneg,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
% 4.60/4.58 => V_m = V_n ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__Suc__0,axiom,
% 4.60/4.58 ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 4.60/4.58 ! [V_ma_2,V_x_2] :
% 4.60/4.58 ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 | V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__le__zpower__abs,axiom,
% 4.60/4.58 ! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x)),V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__zminus,axiom,
% 4.60/4.58 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__inject,axiom,
% 4.60/4.58 ! [V_y,V_x] :
% 4.60/4.58 ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
% 4.60/4.58 => V_x = V_y ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat_Oinject,axiom,
% 4.60/4.58 ! [V_nat_H_2,V_nat_2] :
% 4.60/4.58 ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
% 4.60/4.58 <=> V_nat_2 = V_nat_H_2 ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__n__not__n,axiom,
% 4.60/4.58 ! [V_n] : c_Nat_OSuc(V_n) != V_n ).
% 4.60/4.58
% 4.60/4.58 fof(fact_n__not__Suc__n,axiom,
% 4.60/4.58 ! [V_n] : V_n != c_Nat_OSuc(V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__leD,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__SucE,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 4.60/4.58 => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => V_m = c_Nat_OSuc(V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__SucI,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__le__mono,axiom,
% 4.60/4.58 ! [V_ma_2,V_n_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__Suc__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 | V_ma_2 = c_Nat_OSuc(V_n_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_not__less__eq__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__n__not__le__n,axiom,
% 4.60/4.58 ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__zmult__distrib,axiom,
% 4.60/4.58 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__assoc,axiom,
% 4.60/4.58 ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__zmult__distrib2,axiom,
% 4.60/4.58 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__commute,axiom,
% 4.60/4.58 ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__mult__cancel1,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2,V_k_2] :
% 4.60/4.58 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
% 4.60/4.58 <=> V_ma_2 = V_n_2 ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__Suc__shift,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__Suc,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__Suc__right,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__zless__mono,axiom,
% 4.60/4.58 ! [V_z,V_z_H,V_w,V_w_H] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__strict__right__mono,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__less__SucD,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__lessD,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__SucE,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
% 4.60/4.58 => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => V_m = V_n ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__trans__Suc,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__lessI,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => ( c_Nat_OSuc(V_m) != V_n
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__SucI,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__antisym,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
% 4.60/4.58 => V_m = V_n ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_not__less__less__Suc__eq,axiom,
% 4.60/4.58 ! [V_ma_2,V_n_2] :
% 4.60/4.58 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
% 4.60/4.58 <=> V_n_2 = V_ma_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__less__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__Suc__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 | V_ma_2 = V_n_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_not__less__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zless__linear,axiom,
% 4.60/4.58 ! [V_y,V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y)
% 4.60/4.58 | V_x = V_y
% 4.60/4.58 | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zless__le,axiom,
% 4.60/4.58 ! [V_w_2,V_za_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2)
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2)
% 4.60/4.58 & V_za_2 != V_w_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__zmult__eq__1,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__add1__eq__le,axiom,
% 4.60/4.58 ! [V_za_2,V_w_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_za_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zless__add1__eq,axiom,
% 4.60/4.58 ! [V_za_2,V_w_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_za_2)
% 4.60/4.58 | V_w_2 = V_za_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add1__zle__eq,axiom,
% 4.60/4.58 ! [V_za_2,V_w_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_za_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_za_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zless__imp__add1__zle,axiom,
% 4.60/4.58 ! [V_z,V_w] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__zless__mono2,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_pos__zmult__eq__1__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
% 4.60/4.58 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 4.60/4.58 <=> ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 4.60/4.58 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__imp__0__less,axiom,
% 4.60/4.58 ! [V_z] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_odd__less__0,axiom,
% 4.60/4.58 ! [V_za_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2),V_za_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zabs__less__one__iff,axiom,
% 4.60/4.58 ! [V_za_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_za_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
% 4.60/4.58 <=> V_za_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_int__one__le__iff__zero__less,axiom,
% 4.60/4.58 ! [V_za_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_za_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_za_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_int__0__less__1,axiom,
% 4.60/4.58 c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__1,axiom,
% 4.60/4.58 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zmult__1__right,axiom,
% 4.60/4.58 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__0__right,axiom,
% 4.60/4.58 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__0,axiom,
% 4.60/4.58 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z ).
% 4.60/4.58
% 4.60/4.58 fof(fact_odd__nonzero,axiom,
% 4.60/4.58 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_int__0__neq__1,axiom,
% 4.60/4.58 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Zero__not__Suc,axiom,
% 4.60/4.58 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat_Osimps_I2_J,axiom,
% 4.60/4.58 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__not__Zero,axiom,
% 4.60/4.58 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat_Osimps_I3_J,axiom,
% 4.60/4.58 ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Zero__neq__Suc,axiom,
% 4.60/4.58 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__neq__Zero,axiom,
% 4.60/4.58 ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zabs__def,axiom,
% 4.60/4.58 ! [V_i] :
% 4.60/4.58 ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) )
% 4.60/4.58 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zminus__0,axiom,
% 4.60/4.58 c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__zminus__inverse2,axiom,
% 4.60/4.58 ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zsgn__def,axiom,
% 4.60/4.58 ! [V_i] :
% 4.60/4.58 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 4.60/4.58 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 4.60/4.58 => ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 4.60/4.58 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 4.60/4.58 & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
% 4.60/4.58 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__0__Suc,axiom,
% 4.60/4.58 ! [V_n,T_a] :
% 4.60/4.58 ( ( class_Power_Opower(T_a)
% 4.60/4.58 & class_Rings_Osemiring__0(T_a) )
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 4.60/4.58 ! [V_q,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 4.60/4.58 ! [V_q,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 4.60/4.58 ! [V_q,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__semiring__1(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__Suc2,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Omonoid__mult(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__Suc,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Power_Opower(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__Suc__eq__0__disj,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
% 4.60/4.58 <=> ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 | ? [B_j] :
% 4.60/4.58 ( V_ma_2 = c_Nat_OSuc(B_j)
% 4.60/4.58 & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__Suc0,axiom,
% 4.60/4.58 ! [V_n_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 4.60/4.58 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_gr0__conv__Suc,axiom,
% 4.60/4.58 ! [V_n_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
% 4.60/4.58 <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__1__iff__1,axiom,
% 4.60/4.58 ! [V_ma_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 4.60/4.58 <=> V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_one__is__add,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 <=> ( ( V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 4.60/4.58 | ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__is__1,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 <=> ( ( V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 4.60/4.58 | ( V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__one__le__power,axiom,
% 4.60/4.58 ! [V_n,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__eq__1__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 <=> ( V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 4.60/4.58 & V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__add__Suc1,axiom,
% 4.60/4.58 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__add__Suc2,axiom,
% 4.60/4.58 ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__iff__Suc__add,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__le__lessD,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__less__Suc__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
% 4.60/4.58 <=> V_n_2 = V_ma_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__leI,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__imp__less__Suc,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__le__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__Suc__eq__le,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__eq__Suc__le,axiom,
% 4.60/4.58 ! [V_ma_2,V_n_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_One__nat__def,axiom,
% 4.60/4.58 c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__mult__less__cancel1,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2,V_k_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__Suc__right,axiom,
% 4.60/4.58 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__Suc,axiom,
% 4.60/4.58 ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__mult__le__cancel1,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2,V_k_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__eq__plus1__left,axiom,
% 4.60/4.58 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__eq__plus1,axiom,
% 4.60/4.58 ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__le__imp__le__base,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__inject__base,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
% 4.60/4.58 => V_a = V_b ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__gt1,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_realpow__two__disj,axiom,
% 4.60/4.58 ! [V_y_2,V_x_2,T_a] :
% 4.60/4.58 ( class_Rings_Oidom(T_a)
% 4.60/4.58 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 4.60/4.58 <=> ( V_x_2 = V_y_2
% 4.60/4.58 | V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_one__less__mult,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_n__less__n__mult__m,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_n__less__m__mult__n,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_one__le__mult__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2))
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_ma_2)
% 4.60/4.58 & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__of__nat__Suc__gt__zero,axiom,
% 4.60/4.58 ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__of__nat__one,axiom,
% 4.60/4.58 c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__of__nat__Suc,axiom,
% 4.60/4.58 ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_pow__divides__eq__int,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,V_n_2] :
% 4.60/4.58 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_pow__divides__pow__int,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))
% 4.60/4.58 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_lemma__NBseq__def2,axiom,
% 4.60/4.58 ! [V_X_2,T_b] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_b)
% 4.60/4.58 => ( ? [B_K] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.60/4.58 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K) )
% 4.60/4.58 <=> ? [B_N] :
% 4.60/4.58 ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_lemma__NBseq__def,axiom,
% 4.60/4.58 ! [V_X_2,T_b] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_b)
% 4.60/4.58 => ( ? [B_K] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K)
% 4.60/4.58 & ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K) )
% 4.60/4.58 <=> ? [B_N] :
% 4.60/4.58 ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_realpow__Suc__le__self,axiom,
% 4.60/4.58 ! [V_n,V_r,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__Suc__less__one,axiom,
% 4.60/4.58 ! [V_n,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__semidom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
% 4.60/4.58 => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
% 4.60/4.58 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_pow__divides__eq__nat,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,V_n_2] :
% 4.60/4.58 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_pow__divides__pow__nat,axiom,
% 4.60/4.58 ! [V_b,V_n,V_a] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))
% 4.60/4.58 => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
% 4.60/4.58 ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_order__2,axiom,
% 4.60/4.58 ! [V_a,V_p,T_a] :
% 4.60/4.58 ( class_Rings_Oidom(T_a)
% 4.60/4.58 => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
% 4.60/4.58 => ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zero__less__power__nat__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_x_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
% 4.60/4.58 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 4.60/4.58 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 4.60/4.58 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__left__mono,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__commute,axiom,
% 4.60/4.58 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__left__commute,axiom,
% 4.60/4.58 ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zadd__assoc,axiom,
% 4.60/4.58 ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__antisym,axiom,
% 4.60/4.58 ! [V_w,V_z] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
% 4.60/4.58 => V_z = V_w ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__trans,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__linear,axiom,
% 4.60/4.58 ! [V_w,V_z] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
% 4.60/4.58 | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__refl,axiom,
% 4.60/4.58 ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zminus__zminus,axiom,
% 4.60/4.58 ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zminus__zadd__distrib,axiom,
% 4.60/4.58 ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_uminus__dvd__conv_I2_J,axiom,
% 4.60/4.58 ! [V_t_2,V_d_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_uminus__dvd__conv_I1_J,axiom,
% 4.60/4.58 ! [V_t_2,V_d_2] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__lt__two__imp__zero__or__one,axiom,
% 4.60/4.58 ! [V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 4.60/4.58 => ( V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 | V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_self__quotient__aux2,axiom,
% 4.60/4.58 ! [V_q,V_r,V_a] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 4.60/4.58 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_self__quotient__aux1,axiom,
% 4.60/4.58 ! [V_q,V_r,V_a] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
% 4.60/4.58 => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_q__pos__lemma,axiom,
% 4.60/4.58 ! [V_r_H,V_q_H,V_b_H] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_q__neg__lemma,axiom,
% 4.60/4.58 ! [V_r_H,V_q_H,V_b_H] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_unique__quotient__lemma,axiom,
% 4.60/4.58 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdiv__mono2__lemma,axiom,
% 4.60/4.58 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 4.60/4.58 ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_unique__quotient__lemma__neg,axiom,
% 4.60/4.58 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 4.60/4.58 ! [V_n,V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 4.60/4.58 ! [V_y,V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 4.60/4.58 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 4.60/4.58 c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 4.60/4.58 ! [V_y,V_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power__power__power,axiom,
% 4.60/4.58 ! [T_a] :
% 4.60/4.58 ( class_Power_Opower(T_a)
% 4.60/4.58 => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_decseq__def,axiom,
% 4.60/4.58 ! [V_X_2,T_a] :
% 4.60/4.58 ( class_Orderings_Oorder(T_a)
% 4.60/4.58 => ( c_SEQ_Odecseq(T_a,V_X_2)
% 4.60/4.58 <=> ! [B_m,B_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power_Opower_Opower__0,axiom,
% 4.60/4.58 ! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 4.60/4.58
% 4.60/4.58 fof(fact_power_Opower_Opower__Suc,axiom,
% 4.60/4.58 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_incr__mult__lemma,axiom,
% 4.60/4.58 ! [V_k_2,V_P_2,V_d_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
% 4.60/4.58 => ( ! [B_x] :
% 4.60/4.58 ( hBOOL(hAPP(V_P_2,B_x))
% 4.60/4.58 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
% 4.60/4.58 => ! [B_x] :
% 4.60/4.58 ( hBOOL(hAPP(V_P_2,B_x))
% 4.60/4.58 => hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_reals__Archimedean6a,axiom,
% 4.60/4.58 ! [V_r] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
% 4.60/4.58 => ? [B_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r)
% 4.60/4.58 & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_realpow__pos__nth__unique,axiom,
% 4.60/4.58 ! [V_a,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 4.60/4.58 => ? [B_x] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x)
% 4.60/4.58 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
% 4.60/4.58 & ! [B_y] :
% 4.60/4.58 ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y)
% 4.60/4.58 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a )
% 4.60/4.58 => B_y = B_x ) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_realpow__pos__nth,axiom,
% 4.60/4.58 ! [V_a,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
% 4.60/4.58 => ? [B_r] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r)
% 4.60/4.58 & hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_incr__lemma,axiom,
% 4.60/4.58 ! [V_x,V_z,V_d] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_decr__lemma,axiom,
% 4.60/4.58 ! [V_z,V_x,V_d] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__triangle__ineq4,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__iff__diff__le__0,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__diff__mult,axiom,
% 4.60/4.58 ! [V_b,V_a,V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Oring(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_eq__add__iff2,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oring(T_a)
% 4.60/4.58 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 4.60/4.58 <=> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_eq__add__iff1,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oring(T_a)
% 4.60/4.58 => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
% 4.60/4.58 <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2) = V_d_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult_Oprod__diff__prod,axiom,
% 4.60/4.58 ! [V_b,V_a,V_y,V_x,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__0,axiom,
% 4.60/4.58 ! [V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__triangle__ineq3,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__minus__eq__add,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 4.60/4.58 ! [V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__ring__1(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_ab__diff__minus,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oab__group__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__def,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__triangle__ineq2__sym,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__triangle__ineq2,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__triangle__ineq3,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__eq__diff__less__eq,axiom,
% 4.60/4.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.60/4.58 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_d_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__diff__cancel,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__cancel,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__triangle__ineq2,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_minus__diff__eq,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oab__group__add(T_a)
% 4.60/4.58 => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__int__def__symmetric,axiom,
% 4.60/4.58 ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__int__def,axiom,
% 4.60/4.58 ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__diff,axiom,
% 4.60/4.58 ! [V_z,V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__ring__1(T_a)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdvd__zdiffD,axiom,
% 4.60/4.58 ! [V_n,V_m,V_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__add__iff2,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oordered__ring(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__add__iff1,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oordered__ring(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__add__iff2,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oordered__ring(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_a_2)),V_e_2),V_d_2)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__add__iff1,axiom,
% 4.60/4.58 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Rings_Oordered__ring(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2)),V_e_2),V_ca_2),V_d_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__squared__diff__one__factored,axiom,
% 4.60/4.58 ! [V_x,T_a] :
% 4.60/4.58 ( class_Rings_Oring__1(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_inf__period_I3_J,axiom,
% 4.60/4.58 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 4.60/4.58 ( ( class_Rings_Ocomm__ring(T_a)
% 4.60/4.58 & class_Rings_Odvd(T_a) )
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 4.60/4.58 => ! [B_x,B_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_inf__period_I4_J,axiom,
% 4.60/4.58 ! [V_t_2,V_D_2,V_d_2,T_a] :
% 4.60/4.58 ( ( class_Rings_Ocomm__ring(T_a)
% 4.60/4.58 & class_Rings_Odvd(T_a) )
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
% 4.60/4.58 => ! [B_x,B_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
% 4.60/4.58 <=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_smult__diff__left,axiom,
% 4.60/4.58 ! [V_p,V_b,V_a,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__ring(T_a)
% 4.60/4.58 => c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__eq__diff__eq,axiom,
% 4.60/4.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oab__group__add(T_a)
% 4.60/4.58 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 4.60/4.58 => ( V_a_2 = V_b_2
% 4.60/4.58 <=> V_ca_2 = V_d_2 ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_poly__diff,axiom,
% 4.60/4.58 ! [V_x,V_q,V_p,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__ring(T_a)
% 4.60/4.58 => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__pCons,axiom,
% 4.60/4.58 ! [V_q,V_b,V_p,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oab__group__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__minus__commute,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_minus__apply,axiom,
% 4.60/4.58 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
% 4.60/4.58 ( class_Groups_Ominus(T_a)
% 4.60/4.58 => hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_right__minus__eq,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
% 4.60/4.58 <=> V_a_2 = V_b_2 ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_eq__iff__diff__eq__0,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oab__group__add(T_a)
% 4.60/4.58 => ( V_a_2 = V_b_2
% 4.60/4.58 <=> c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__self,axiom,
% 4.60/4.58 ! [V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__0__right,axiom,
% 4.60/4.58 ! [V_a,T_a] :
% 4.60/4.58 ( class_Groups_Ogroup__add(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__bin__lemma,axiom,
% 4.60/4.58 ! [V_l_2,V_k_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__minus__commute,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__eq__diff__less,axiom,
% 4.60/4.58 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.60/4.58 => ( c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_d_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_d_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdiff__zmult__distrib2,axiom,
% 4.60/4.58 ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zdiff__zmult__distrib,axiom,
% 4.60/4.58 ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__left_Odiff,axiom,
% 4.60/4.58 ! [V_ya,V_y,V_x,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult_Odiff__left,axiom,
% 4.60/4.58 ! [V_b,V_a_H,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult__right_Odiff,axiom,
% 4.60/4.58 ! [V_y,V_x,V_xa,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_mult_Odiff__right,axiom,
% 4.60/4.58 ! [V_b_H,V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__algebra(T_a)
% 4.60/4.58 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__iff__diff__less__0,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__diff__less__iff,axiom,
% 4.60/4.58 ! [V_ra_2,V_a_2,V_x_2,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__idom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
% 4.60/4.58 <=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2)
% 4.60/4.58 & c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__triangle__ineq4,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_abs__diff__triangle__ineq,axiom,
% 4.60/4.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.60/4.58 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(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_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_zle__diff1__eq,axiom,
% 4.60/4.58 ! [V_za_2,V_w_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_za_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_za_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__diff__triangle__ineq,axiom,
% 4.60/4.58 ! [V_d,V_c,V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(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(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_realpow__two__diff,axiom,
% 4.60/4.58 ! [V_y,V_x,T_a] :
% 4.60/4.58 ( class_Rings_Ocomm__ring__1(T_a)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_lemmaCauchy,axiom,
% 4.60/4.58 ! [V_X_2,V_M_2,T_a,T_b] :
% 4.60/4.58 ( ( class_RealVector_Oreal__normed__vector(T_b)
% 4.60/4.58 & class_Orderings_Oord(T_a) )
% 4.60/4.58 => ( ! [B_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
% 4.60/4.58 => ! [B_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_tsub__def,axiom,
% 4.60/4.58 ! [V_x,V_y] :
% 4.60/4.58 ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 4.60/4.58 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) )
% 4.60/4.58 & ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
% 4.60/4.58 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__diff__split__asm,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,V_P_2] :
% 4.60/4.58 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 4.60/4.58 <=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 4.60/4.58 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 4.60/4.58 | ? [B_d] :
% 4.60/4.58 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 4.60/4.58 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_nat__diff__split,axiom,
% 4.60/4.58 ! [V_b_2,V_a_2,V_P_2] :
% 4.60/4.58 ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
% 4.60/4.58 <=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
% 4.60/4.58 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 4.60/4.58 & ! [B_d] :
% 4.60/4.58 ( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
% 4.60/4.58 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_norm__diff__ineq,axiom,
% 4.60/4.58 ! [V_b,V_a,T_a] :
% 4.60/4.58 ( class_RealVector_Oreal__normed__vector(T_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_Suc__diff__le,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__Suc__1,axiom,
% 4.60/4.58 ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__le__eq__diff,axiom,
% 4.60/4.58 ! [V_y_2,V_x_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__0,axiom,
% 4.60/4.58 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__is__0__eq,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2] :
% 4.60/4.58 ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__is__0__eq_H,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__diff__conv,axiom,
% 4.60/4.58 ! [V_k_2,V_j_2,V_i_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__diff__inverse,axiom,
% 4.60/4.58 ! [V_n,V_m] :
% 4.60/4.58 ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__diff__iff,axiom,
% 4.60/4.58 ! [V_n_2,V_ma_2,V_k_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__less__mono,axiom,
% 4.60/4.58 ! [V_c,V_b,V_a] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
% 4.60/4.58 => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__diffD,axiom,
% 4.60/4.58 ! [V_n,V_m,V_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_dvd__diffD1,axiom,
% 4.60/4.58 ! [V_n,V_m,V_k] :
% 4.60/4.58 ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
% 4.60/4.58 => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__assoc2,axiom,
% 4.60/4.58 ! [V_i,V_j,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__diff__assoc2,axiom,
% 4.60/4.58 ! [V_i,V_j,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__assoc,axiom,
% 4.60/4.58 ! [V_i,V_j,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__imp__diff__is__add,axiom,
% 4.60/4.58 ! [V_k_2,V_j_2,V_i_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
% 4.60/4.58 => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
% 4.60/4.58 <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__add__diff__inverse2,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__diff__conv2,axiom,
% 4.60/4.58 ! [V_i_2,V_j_2,V_k_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_add__diff__assoc,axiom,
% 4.60/4.58 ! [V_i,V_j,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__add__diff__inverse,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__add__diff,axiom,
% 4.60/4.58 ! [V_m,V_n,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
% 4.60/4.58 => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_le__diff__conv,axiom,
% 4.60/4.58 ! [V_i_2,V_k_2,V_j_2] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
% 4.60/4.58 <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__diff__right,axiom,
% 4.60/4.58 ! [V_i,V_j,V_k] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
% 4.60/4.58 => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_minus__real__def,axiom,
% 4.60/4.58 ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__diff__def,axiom,
% 4.60/4.58 ! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_natfloor__subtract,axiom,
% 4.60/4.58 ! [V_x,V_a] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 4.60/4.58 => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_natceiling__subtract,axiom,
% 4.60/4.58 ! [V_x,V_a] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
% 4.60/4.58 => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_real__of__nat__diff,axiom,
% 4.60/4.58 ! [V_m,V_n] :
% 4.60/4.58 ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
% 4.60/4.58 => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_less__eq__poly__def,axiom,
% 4.60/4.58 ! [V_y_2,V_x_2,T_a] :
% 4.60/4.58 ( class_Rings_Olinordered__idom(T_a)
% 4.60/4.58 => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
% 4.60/4.58 <=> ( V_x_2 = V_y_2
% 4.60/4.58 | c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ) ) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__inverse2,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__add__inverse,axiom,
% 4.60/4.58 ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__diff__left,axiom,
% 4.60/4.58 ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__cancel,axiom,
% 4.60/4.58 ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__cancel2,axiom,
% 4.60/4.58 ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ).
% 4.60/4.58
% 4.60/4.58 fof(fact_diff__le__self,axiom,
% 4.60/4.58 ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ).
% 4.60/4.58
% 4.60/4.58 %----Arity declarations (277)
% 4.60/4.58 fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
% 4.60/4.58 ! [T_1] :
% 4.60/4.58 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 4.60/4.58 => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
% 4.60/4.58 class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
% 4.60/4.58 class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
% 4.60/4.58 class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
% 4.60/4.58 class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 4.60/4.58 ! [T_2,T_1] :
% 4.60/4.58 ( class_Lattices_Oboolean__algebra(T_1)
% 4.60/4.58 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_fun__Orderings_Opreorder,axiom,
% 4.60/4.58 ! [T_2,T_1] :
% 4.60/4.58 ( class_Orderings_Opreorder(T_1)
% 4.60/4.58 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 4.60/4.58
% 4.60/4.58 fof(arity_fun__Orderings_Oorder,axiom,
% 4.60/4.58 ! [T_2,T_1] :
% 4.60/4.58 ( class_Orderings_Oorder(T_1)
% 4.60/4.59 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_fun__Orderings_Oord,axiom,
% 4.60/4.59 ! [T_2,T_1] :
% 4.60/4.59 ( class_Orderings_Oord(T_1)
% 4.60/4.59 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_fun__Groups_Ouminus,axiom,
% 4.60/4.59 ! [T_2,T_1] :
% 4.60/4.59 ( class_Groups_Ouminus(T_1)
% 4.60/4.59 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_fun__Groups_Ominus,axiom,
% 4.60/4.59 ! [T_2,T_1] :
% 4.60/4.59 ( class_Groups_Ominus(T_1)
% 4.60/4.59 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.60/4.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 4.60/4.59 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 4.60/4.59 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 4.60/4.59 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 4.60/4.59 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 4.60/4.59 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__0(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 4.60/4.59 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 4.60/4.59 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 4.60/4.59 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 4.60/4.59 class_Orderings_Opreorder(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 4.60/4.59 class_Orderings_Olinorder(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 4.60/4.59 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 4.60/4.59 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 4.60/4.59 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 4.60/4.59 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 4.60/4.59 class_Rings_Omult__zero(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 4.60/4.59 class_Orderings_Oorder(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 4.60/4.59 class_Int_Oring__char__0(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 4.60/4.59 class_Rings_Osemiring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 4.60/4.59 class_Orderings_Oord(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 4.60/4.59 class_Groups_Ouminus(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 4.60/4.59 class_Groups_Osgn__if(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 4.60/4.59 class_Groups_Oabs__if(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 4.60/4.59 class_Rings_Oring__1(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 4.60/4.59 class_Groups_Ominus(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Power_Opower,axiom,
% 4.60/4.59 class_Power_Opower(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 4.60/4.59 class_Groups_Ozero(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oring,axiom,
% 4.60/4.59 class_Rings_Oring(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 4.60/4.59 class_Rings_Oidom(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Groups_Oone,axiom,
% 4.60/4.59 class_Groups_Oone(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 4.60/4.59 class_Rings_Odvd(tc_Int_Oint) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.60/4.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 4.60/4.59 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 4.60/4.59 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 4.60/4.59 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 4.60/4.59 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 4.60/4.59 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 4.60/4.59 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 4.60/4.59 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 4.60/4.59 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 4.60/4.59 class_Orderings_Oorder(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 4.60/4.59 class_Rings_Osemiring(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 4.60/4.59 class_Orderings_Oord(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 4.60/4.59 class_Groups_Ominus(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Power_Opower,axiom,
% 4.60/4.59 class_Power_Opower(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 4.60/4.59 class_Groups_Ozero(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 4.60/4.59 class_Groups_Oone(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 4.60/4.59 class_Rings_Odvd(tc_Nat_Onat) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 4.60/4.59 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 4.60/4.59 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 4.60/4.59 class_Orderings_Oorder(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 4.60/4.59 class_Orderings_Oord(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 4.60/4.59 class_Groups_Ouminus(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 4.60/4.59 class_Groups_Ominus(tc_HOL_Obool) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.60/4.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
% 4.60/4.59 class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
% 4.60/4.59 class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
% 4.60/4.59 class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
% 4.60/4.59 class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
% 4.60/4.59 class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
% 4.60/4.59 class_Rings_Oordered__semiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
% 4.60/4.59 class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
% 4.60/4.59 class_Rings_Olinordered__ring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
% 4.60/4.59 class_Rings_Olinordered__idom(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
% 4.60/4.59 class_Groups_Oab__group__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
% 4.60/4.59 class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
% 4.60/4.59 class_Rings_Oordered__ring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
% 4.60/4.59 class_Orderings_Opreorder(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
% 4.60/4.59 class_Orderings_Olinorder(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
% 4.60/4.59 class_Groups_Omonoid__mult(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
% 4.60/4.59 class_Groups_Omonoid__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
% 4.60/4.59 class_Rings_Osemiring__0(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
% 4.60/4.59 class_Groups_Ogroup__add(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
% 4.60/4.59 class_Rings_Omult__zero(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
% 4.60/4.59 class_Orderings_Oorder(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
% 4.60/4.59 class_Int_Oring__char__0(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
% 4.60/4.59 class_Rings_Osemiring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
% 4.60/4.59 class_Orderings_Oord(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
% 4.60/4.59 class_Groups_Ouminus(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
% 4.60/4.59 class_Groups_Osgn__if(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
% 4.60/4.59 class_Groups_Oabs__if(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
% 4.60/4.59 class_Rings_Oring__1(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
% 4.60/4.59 class_Groups_Ominus(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
% 4.60/4.59 class_Fields_Ofield(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Power_Opower,axiom,
% 4.60/4.59 class_Power_Opower(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
% 4.60/4.59 class_Groups_Ozero(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oring,axiom,
% 4.60/4.59 class_Rings_Oring(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
% 4.60/4.59 class_Rings_Oidom(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Groups_Oone,axiom,
% 4.60/4.59 class_Groups_Oone(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
% 4.60/4.59 class_Rings_Odvd(tc_RealDef_Oreal) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.60/4.59 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
% 4.60/4.59 class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
% 4.60/4.59 class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
% 4.60/4.59 class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
% 4.60/4.59 class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
% 4.60/4.59 class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
% 4.60/4.59 class_Groups_Oab__group__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
% 4.60/4.59 class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
% 4.60/4.59 class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
% 4.60/4.59 class_Groups_Omonoid__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
% 4.60/4.59 class_Rings_Osemiring__0(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
% 4.60/4.59 class_Groups_Ogroup__add(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
% 4.60/4.59 class_Rings_Omult__zero(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
% 4.60/4.59 class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
% 4.60/4.59 class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
% 4.60/4.59 class_Rings_Osemiring(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
% 4.60/4.59 class_Groups_Ouminus(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
% 4.60/4.59 class_Rings_Oring__1(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
% 4.60/4.59 class_Groups_Ominus(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
% 4.60/4.59 class_Fields_Ofield(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Power_Opower,axiom,
% 4.60/4.59 class_Power_Opower(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
% 4.60/4.59 class_Groups_Ozero(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
% 4.60/4.59 class_Rings_Oring(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
% 4.60/4.59 class_Rings_Oidom(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
% 4.60/4.59 class_Groups_Oone(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
% 4.60/4.59 class_Rings_Odvd(tc_Complex_Ocomplex) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Oidom(T_1)
% 4.60/4.59 => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 4.60/4.59 => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Oidom(T_1)
% 4.60/4.59 => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Oidom(T_1)
% 4.60/4.59 => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ocancel__comm__monoid__add(T_1)
% 4.60/4.59 => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 4.60/4.59 => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Oidom(T_1)
% 4.60/4.59 => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 4.60/4.59 => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Oab__group__add(T_1)
% 4.60/4.59 => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__ring__1(T_1)
% 4.60/4.59 => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ocomm__monoid__add(T_1)
% 4.60/4.59 => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Oab__group__add(T_1)
% 4.60/4.59 => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__ring(T_1)
% 4.60/4.59 => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__0(T_1)
% 4.60/4.59 => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Oab__group__add(T_1)
% 4.60/4.59 => class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Olinordered__idom(T_1)
% 4.60/4.59 => class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__ring__1(T_1)
% 4.60/4.59 => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Oab__group__add(T_1)
% 4.60/4.59 => class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Power_Opower,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Groups_Ozero(T_1)
% 4.60/4.59 => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__ring(T_1)
% 4.60/4.59 => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Oidom(T_1)
% 4.60/4.59 => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
% 4.60/4.59 ! [T_1] :
% 4.60/4.59 ( class_Rings_Ocomm__semiring__1(T_1)
% 4.60/4.59 => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ) ).
% 4.60/4.59
% 4.60/4.59 %----Helper facts (2)
% 4.60/4.59 fof(help_c__fequal__1,axiom,
% 4.60/4.59 ! [V_y_2,V_x_2] :
% 4.60/4.59 ( ~ hBOOL(c_fequal(V_x_2,V_y_2))
% 4.60/4.59 | V_x_2 = V_y_2 ) ).
% 4.60/4.59
% 4.60/4.59 fof(help_c__fequal__2,axiom,
% 4.60/4.59 ! [V_y_2,V_x_2] :
% 4.60/4.59 ( V_x_2 != V_y_2
% 4.60/4.59 | hBOOL(c_fequal(V_x_2,V_y_2)) ) ).
% 4.60/4.59
% 4.60/4.59 %----Conjectures (1)
% 4.60/4.59 fof(conj_0,conjecture,
% 4.60/4.59 c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ).
% 4.60/4.59
% 4.60/4.59 %------------------------------------------------------------------------------
% 4.60/4.59 %-------------------------------------------
% 4.60/4.59 % Proof found
% 4.60/4.59 % SZS status Theorem for theBenchmark
% 4.60/4.59 % SZS output start Proof
% 4.60/4.59 %ClaNum:1851(EqnAxiom:228)
% 4.60/4.59 %VarNum:8601(SingletonVarNum:3047)
% 4.60/4.59 %MaxLitNum:7
% 4.60/4.59 %MaxfuncDepth:6
% 4.60/4.59 %SharedTerms:293
% 4.60/4.59 %goalClause: 580
% 4.60/4.59 %singleGoalClaCount:1
% 4.60/4.59 [229]P1(a1)
% 4.60/4.59 [230]P1(a2)
% 4.60/4.59 [231]P2(a1)
% 4.60/4.59 [232]P2(a2)
% 4.60/4.59 [233]P41(a1)
% 4.60/4.59 [234]P41(a2)
% 4.60/4.59 [235]P42(a1)
% 4.60/4.59 [236]P42(a2)
% 4.60/4.59 [237]P3(a1)
% 4.60/4.59 [238]P3(a68)
% 4.60/4.59 [239]P43(a1)
% 4.60/4.59 [240]P43(a2)
% 4.60/4.59 [241]P43(a70)
% 4.60/4.59 [242]P43(a68)
% 4.60/4.59 [243]P26(a1)
% 4.60/4.59 [244]P26(a70)
% 4.60/4.59 [245]P26(a68)
% 4.60/4.59 [246]P26(a69)
% 4.60/4.59 [247]P27(a1)
% 4.60/4.59 [248]P27(a70)
% 4.60/4.59 [249]P27(a68)
% 4.60/4.59 [250]P28(a1)
% 4.60/4.59 [251]P28(a2)
% 4.60/4.59 [252]P28(a70)
% 4.60/4.59 [253]P28(a68)
% 4.60/4.59 [254]P4(a1)
% 4.60/4.59 [255]P4(a68)
% 4.60/4.59 [256]P29(a1)
% 4.60/4.59 [257]P29(a70)
% 4.60/4.59 [258]P29(a68)
% 4.60/4.59 [259]P38(a1)
% 4.60/4.59 [260]P38(a70)
% 4.60/4.59 [261]P38(a68)
% 4.60/4.59 [262]P38(a69)
% 4.60/4.59 [263]P39(a1)
% 4.60/4.59 [264]P39(a70)
% 4.60/4.59 [265]P39(a68)
% 4.60/4.59 [266]P39(a69)
% 4.60/4.59 [267]P30(a1)
% 4.60/4.59 [268]P30(a70)
% 4.60/4.59 [269]P30(a68)
% 4.60/4.59 [270]P32(a1)
% 4.60/4.59 [271]P32(a70)
% 4.60/4.59 [272]P32(a68)
% 4.60/4.59 [273]P48(a1)
% 4.60/4.59 [274]P48(a2)
% 4.60/4.59 [275]P48(a70)
% 4.60/4.59 [276]P48(a68)
% 4.60/4.59 [277]P5(a1)
% 4.60/4.59 [278]P5(a2)
% 4.60/4.59 [279]P5(a70)
% 4.60/4.59 [280]P5(a68)
% 4.60/4.59 [281]P21(a1)
% 4.60/4.59 [282]P21(a2)
% 4.60/4.59 [283]P21(a70)
% 4.60/4.59 [284]P21(a68)
% 4.60/4.59 [285]P6(a1)
% 4.60/4.59 [286]P6(a2)
% 4.60/4.59 [287]P6(a70)
% 4.60/4.59 [288]P6(a68)
% 4.60/4.59 [289]P15(a1)
% 4.60/4.59 [290]P15(a2)
% 4.60/4.59 [291]P15(a70)
% 4.60/4.59 [292]P15(a68)
% 4.60/4.59 [293]P16(a1)
% 4.60/4.59 [294]P16(a2)
% 4.60/4.59 [295]P16(a70)
% 4.60/4.59 [296]P16(a68)
% 4.60/4.59 [297]P7(a1)
% 4.60/4.59 [298]P7(a2)
% 4.60/4.59 [299]P7(a70)
% 4.60/4.59 [300]P7(a68)
% 4.60/4.59 [301]P23(a1)
% 4.60/4.59 [302]P23(a2)
% 4.60/4.59 [303]P23(a70)
% 4.60/4.59 [304]P23(a68)
% 4.60/4.59 [305]P31(a1)
% 4.60/4.59 [306]P31(a70)
% 4.60/4.59 [307]P31(a68)
% 4.60/4.59 [308]P19(a1)
% 4.60/4.59 [309]P19(a2)
% 4.60/4.59 [310]P19(a70)
% 4.60/4.59 [311]P19(a68)
% 4.60/4.59 [312]P24(a1)
% 4.60/4.59 [313]P24(a2)
% 4.60/4.59 [314]P24(a70)
% 4.60/4.59 [315]P24(a68)
% 4.60/4.59 [316]P49(a1)
% 4.60/4.59 [317]P49(a68)
% 4.60/4.59 [318]P50(a1)
% 4.60/4.59 [319]P50(a68)
% 4.60/4.59 [320]P59(a1)
% 4.60/4.59 [321]P59(a68)
% 4.60/4.59 [322]P51(a1)
% 4.60/4.59 [323]P51(a68)
% 4.60/4.59 [324]P60(a1)
% 4.60/4.59 [325]P60(a2)
% 4.60/4.59 [326]P60(a70)
% 4.60/4.59 [327]P60(a68)
% 4.60/4.59 [328]P66(a1)
% 4.60/4.59 [329]P66(a2)
% 4.60/4.59 [330]P66(a68)
% 4.60/4.59 [331]P62(a1)
% 4.60/4.59 [332]P62(a2)
% 4.60/4.59 [333]P62(a70)
% 4.60/4.59 [334]P62(a68)
% 4.60/4.59 [335]P71(a1)
% 4.60/4.59 [336]P71(a2)
% 4.60/4.59 [337]P71(a70)
% 4.60/4.59 [338]P71(a68)
% 4.60/4.59 [339]P44(a1)
% 4.60/4.59 [340]P44(a2)
% 4.60/4.59 [341]P44(a70)
% 4.60/4.59 [342]P44(a68)
% 4.60/4.59 [343]P72(a1)
% 4.60/4.59 [344]P72(a2)
% 4.60/4.59 [345]P72(a70)
% 4.60/4.59 [346]P72(a68)
% 4.60/4.59 [347]P55(a1)
% 4.60/4.59 [348]P55(a68)
% 4.60/4.59 [349]P56(a1)
% 4.60/4.59 [350]P56(a68)
% 4.60/4.59 [351]P63(a1)
% 4.60/4.59 [352]P63(a70)
% 4.60/4.59 [353]P63(a68)
% 4.60/4.59 [354]P64(a1)
% 4.60/4.59 [355]P64(a68)
% 4.60/4.59 [356]P67(a1)
% 4.60/4.59 [357]P67(a70)
% 4.60/4.59 [358]P67(a68)
% 4.60/4.59 [359]P65(a1)
% 4.60/4.59 [360]P65(a70)
% 4.60/4.59 [361]P65(a68)
% 4.60/4.59 [362]P52(a1)
% 4.60/4.59 [363]P52(a70)
% 4.60/4.59 [364]P52(a68)
% 4.60/4.59 [365]P61(a1)
% 4.60/4.59 [366]P61(a70)
% 4.60/4.59 [367]P61(a68)
% 4.60/4.59 [368]P57(a1)
% 4.60/4.59 [369]P57(a70)
% 4.60/4.59 [370]P57(a68)
% 4.60/4.59 [371]P58(a1)
% 4.60/4.59 [372]P58(a70)
% 4.60/4.59 [373]P58(a68)
% 4.60/4.59 [374]P47(a1)
% 4.60/4.59 [375]P47(a2)
% 4.60/4.59 [376]P47(a70)
% 4.60/4.59 [377]P47(a68)
% 4.60/4.59 [378]P35(a1)
% 4.60/4.59 [379]P35(a2)
% 4.60/4.59 [380]P35(a68)
% 4.60/4.59 [381]P53(a1)
% 4.60/4.59 [382]P53(a2)
% 4.60/4.59 [383]P53(a68)
% 4.60/4.59 [384]P33(a1)
% 4.60/4.59 [385]P33(a68)
% 4.60/4.59 [386]P45(a1)
% 4.60/4.59 [387]P45(a2)
% 4.60/4.59 [388]P45(a68)
% 4.60/4.59 [389]P20(a1)
% 4.60/4.59 [390]P20(a2)
% 4.60/4.59 [391]P20(a68)
% 4.60/4.59 [392]P25(a1)
% 4.60/4.59 [393]P25(a68)
% 4.60/4.59 [394]P68(a1)
% 4.60/4.59 [395]P68(a2)
% 4.60/4.59 [396]P68(a68)
% 4.60/4.59 [397]P8(a1)
% 4.60/4.59 [398]P8(a2)
% 4.60/4.59 [399]P8(a68)
% 4.60/4.59 [400]P46(a1)
% 4.60/4.59 [401]P46(a2)
% 4.60/4.59 [402]P46(a68)
% 4.60/4.59 [403]P69(a1)
% 4.60/4.59 [404]P69(a2)
% 4.60/4.59 [405]P69(a68)
% 4.60/4.59 [406]P17(a1)
% 4.60/4.59 [407]P17(a68)
% 4.60/4.59 [408]P36(a69)
% 4.60/4.59 [409]P34(a1)
% 4.60/4.59 [410]P34(a2)
% 4.60/4.59 [411]P34(a68)
% 4.60/4.59 [412]P34(a69)
% 4.60/4.59 [413]P54(a1)
% 4.60/4.59 [414]P54(a2)
% 4.60/4.59 [415]P54(a70)
% 4.60/4.59 [416]P54(a68)
% 4.60/4.59 [417]P9(a1)
% 4.60/4.59 [418]P9(a2)
% 4.60/4.59 [419]P73(a1)
% 4.60/4.59 [420]P73(a2)
% 4.60/4.59 [421]P73(a70)
% 4.60/4.59 [422]P73(a68)
% 4.60/4.59 [423]P40(a1)
% 4.60/4.59 [424]P40(a2)
% 4.60/4.59 [425]P40(a70)
% 4.60/4.59 [426]P40(a68)
% 4.60/4.59 [427]P70(a1)
% 4.60/4.59 [428]P70(a2)
% 4.60/4.59 [429]P70(a68)
% 4.60/4.59 [430]P22(a1)
% 4.60/4.59 [431]P22(a2)
% 4.60/4.59 [432]P22(a70)
% 4.60/4.59 [433]P22(a68)
% 4.60/4.59 [434]P22(a69)
% 4.60/4.59 [435]P18(a1)
% 4.60/4.59 [436]P18(a2)
% 4.60/4.59 [437]P18(a70)
% 4.60/4.59 [438]P18(a68)
% 4.60/4.59 [462]P10(a1,f8(a1),a72)
% 4.60/4.59 [463]P11(a1,f8(a1),a28)
% 4.60/4.59 [473]P10(a68,f8(a68),f3(a68))
% 4.60/4.59 [475]P11(a68,f8(a68),f3(a68))
% 4.60/4.59 [479]P10(a1,f26(a2,a77),a72)
% 4.60/4.59 [559]~E(f8(a1),f3(a1))
% 4.60/4.59 [560]~E(f8(a68),f3(a68))
% 4.60/4.59 [439]E(f7(f3(a1)),f3(a70))
% 4.60/4.59 [440]E(f7(f8(a1)),f8(a70))
% 4.60/4.59 [441]E(f24(f3(a1)),f3(a70))
% 4.60/4.59 [442]E(f24(f8(a1)),f8(a70))
% 4.60/4.59 [443]E(f4(f8(a2)),f3(a2))
% 4.60/4.59 [444]E(f9(a68,f8(a68)),f8(a68))
% 4.60/4.59 [445]E(f25(a70,f3(a70)),f3(a1))
% 4.60/4.59 [446]E(f25(a70,f8(a70)),f8(a1))
% 4.60/4.59 [493]E(f25(a70,f11(a70,f8(a70),f3(a70))),f3(a1))
% 4.60/4.59 [510]P10(a1,f26(a2,f27(f14(a2,a73),a77)),a76)
% 4.60/4.59 [555]P10(a1,f26(a2,f27(f14(a2,f15(a2,a74,a73)),a77)),f11(a1,f26(a2,a74),f27(f27(f10(a1),a72),a76)))
% 4.60/4.59 [552]P11(a1,f8(a1),f11(a1,f11(a1,f3(a1),f26(a2,a74)),f5(a1,f27(f27(f10(a1),a72),a76))))
% 4.60/4.59 [556]P10(a1,f11(a1,f26(a2,a74),f26(a2,f27(f27(f10(a2),a77),f27(f14(a2,a73),a77)))),f11(a1,f26(a2,a74),f27(f27(f10(a1),a72),a76)))
% 4.60/4.59 [557]P10(a1,f26(a2,f27(f14(a2,f15(a2,a74,a73)),a77)),f11(a1,f26(a2,a74),f26(a2,f27(f27(f10(a2),a77),f27(f14(a2,a73),a77)))))
% 4.60/4.59 [580]~P10(a1,f11(a1,f26(a2,a74),f27(f27(f10(a1),a72),a76)),f11(a1,f11(a1,f3(a1),f26(a2,a74)),f5(a1,f27(f27(f10(a1),a72),a76))))
% 4.60/4.59 [455]P10(a1,x4551,x4551)
% 4.60/4.59 [456]P10(a70,x4561,x4561)
% 4.60/4.59 [457]P10(a68,x4571,x4571)
% 4.60/4.59 [458]P12(a70,x4581,x4581)
% 4.60/4.59 [562]~P11(a70,x5621,x5621)
% 4.60/4.59 [447]E(f26(a1,x4471),f5(a1,x4471))
% 4.60/4.59 [465]P12(a70,x4651,f8(a70))
% 4.60/4.59 [467]P10(a70,f8(a70),x4671)
% 4.60/4.59 [468]P12(a70,f3(a70),x4681)
% 4.60/4.59 [481]P10(a1,f8(a1),f25(a70,x4811))
% 4.60/4.59 [565]~P11(a70,x5651,f8(a70))
% 4.60/4.59 [574]~P11(a1,f25(a70,x5741),f8(a1))
% 4.60/4.59 [448]E(f7(f25(a70,x4481)),x4481)
% 4.60/4.59 [449]E(f24(f25(a70,x4491)),x4491)
% 4.60/4.59 [450]E(f9(a68,f9(a68,x4501)),x4501)
% 4.60/4.59 [451]E(f5(a1,f25(a70,x4511)),f25(a70,x4511))
% 4.60/4.59 [452]E(f27(f27(f10(a70),x4521),f3(a70)),x4521)
% 4.60/4.59 [453]E(f27(f27(f10(a68),x4531),f3(a68)),x4531)
% 4.60/4.59 [454]E(f27(f27(f10(a70),x4541),f8(a70)),f8(a70))
% 4.60/4.59 [469]E(f11(a70,x4691,f8(a70)),x4691)
% 4.60/4.59 [470]E(f11(a68,x4701,f8(a68)),x4701)
% 4.60/4.59 [471]E(f11(a70,f8(a70),x4711),x4711)
% 4.60/4.59 [472]E(f11(a68,f8(a68),x4721),x4721)
% 4.60/4.59 [480]E(f11(a68,f9(a68,x4801),x4801),f8(a68))
% 4.60/4.59 [482]P10(a1,x4821,f25(a70,f7(x4821)))
% 4.60/4.59 [495]P10(a1,f9(a1,f26(a2,x4951)),f26(a2,x4951))
% 4.60/4.59 [502]P11(a70,x5021,f11(a70,x5021,f3(a70)))
% 4.60/4.59 [503]P11(a70,f8(a70),f11(a70,x5031,f3(a70)))
% 4.60/4.59 [505]P12(a70,f11(a70,f8(a70),f3(a70)),x5051)
% 4.60/4.59 [512]P11(a1,f8(a1),f11(a1,f3(a1),f5(a1,x5121)))
% 4.60/4.59 [516]P11(a1,x5161,f11(a1,f25(a70,f24(x5161)),f3(a1)))
% 4.60/4.59 [567]~E(f11(a70,x5671,f3(a70)),x5671)
% 4.60/4.59 [573]~E(f11(a70,x5731,f3(a70)),f8(a70))
% 4.60/4.59 [577]~P10(a70,f11(a70,x5771,f3(a70)),x5771)
% 4.60/4.59 [579]~P11(a1,f11(a1,f5(a1,x5791),f3(a1)),x5791)
% 4.60/4.59 [459]E(f27(f27(f10(a1),f3(a1)),x4591),x4591)
% 4.60/4.59 [460]E(f27(f27(f10(a70),f3(a70)),x4601),x4601)
% 4.60/4.59 [461]E(f27(f27(f10(a68),f3(a68)),x4611),x4611)
% 4.60/4.59 [464]E(f27(f27(f10(a70),f8(a70)),x4641),f8(a70))
% 4.60/4.59 [494]P10(a70,x4941,f27(f27(f10(a70),x4941),x4941))
% 4.60/4.59 [511]E(f11(a1,f25(a70,x5111),f3(a1)),f25(a70,f11(a70,x5111,f3(a70))))
% 4.60/4.59 [519]P11(a1,f8(a1),f25(a70,f11(a70,x5191,f3(a70))))
% 4.60/4.59 [578]~E(f11(a68,f11(a68,f3(a68),x5781),x5781),f8(a68))
% 4.60/4.59 [530]P10(a70,x5301,f27(f27(f10(a70),x5301),f27(f27(f10(a70),x5301),x5301)))
% 4.60/4.59 [534]E(f27(f27(f13(a70),f11(a70,f8(a70),f3(a70))),x5341),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [486]E(f11(a70,x4861,x4862),f11(a70,x4862,x4861))
% 4.60/4.59 [487]E(f11(a68,x4871,x4872),f11(a68,x4872,x4871))
% 4.60/4.59 [496]P10(a70,x4961,f11(a70,x4962,x4961))
% 4.60/4.59 [497]P10(a70,x4971,f11(a70,x4971,x4972))
% 4.60/4.59 [498]P10(a70,f6(a70,x4981,x4982),x4981)
% 4.60/4.59 [575]~P11(a70,f11(a70,x5751,x5752),x5752)
% 4.60/4.59 [576]~P11(a70,f11(a70,x5761,x5762),x5761)
% 4.60/4.59 [490]E(f11(a1,x4901,f9(a1,x4902)),f6(a1,x4901,x4902))
% 4.60/4.59 [492]E(f11(a68,x4921,f9(a68,x4922)),f6(a68,x4921,x4922))
% 4.60/4.59 [499]E(f6(a70,f11(a70,x4991,x4992),x4992),x4991)
% 4.60/4.59 [500]E(f6(a70,f11(a70,x5001,x5002),x5001),x5002)
% 4.60/4.59 [501]E(f6(a70,x5011,f11(a70,x5011,x5012)),f8(a70))
% 4.60/4.59 [506]E(f27(f27(f10(a2),f4(x5061)),f4(x5062)),f4(f11(a2,x5061,x5062)))
% 4.60/4.59 [513]E(f11(a68,f9(a68,x5131),f9(a68,x5132)),f9(a68,f11(a68,x5131,x5132)))
% 4.60/4.59 [514]E(f11(a1,f25(a70,x5141),f25(a70,x5142)),f25(a70,f11(a70,x5141,x5142)))
% 4.60/4.59 [540]P11(a70,x5401,f11(a70,f11(a70,x5402,x5401),f3(a70)))
% 4.60/4.59 [541]P11(a70,x5411,f11(a70,f11(a70,x5411,x5412),f3(a70)))
% 4.60/4.59 [551]P10(a1,f26(a2,x5511),f11(a1,f26(a2,f11(a2,x5511,x5512)),f26(a2,x5512)))
% 4.60/4.59 [483]E(f27(f27(f10(a1),x4831),x4832),f27(f27(f10(a1),x4832),x4831))
% 4.60/4.59 [484]E(f27(f27(f10(a70),x4841),x4842),f27(f27(f10(a70),x4842),x4841))
% 4.60/4.59 [485]E(f27(f27(f10(a68),x4851),x4852),f27(f27(f10(a68),x4852),x4851))
% 4.60/4.59 [517]P10(a68,f8(a68),f27(f27(f13(a68),f5(a68,x5171)),x5172))
% 4.60/4.59 [529]E(f11(a70,f11(a70,x5291,f3(a70)),x5292),f11(a70,f11(a70,x5291,x5292),f3(a70)))
% 4.60/4.59 [531]E(f5(a1,f11(a1,x5311,f9(a1,x5312))),f5(a1,f11(a1,x5312,f9(a1,x5311))))
% 4.60/4.59 [532]E(f6(a70,f6(a70,x5321,f3(a70)),x5322),f6(a70,x5321,f11(a70,x5322,f3(a70))))
% 4.60/4.59 [533]E(f11(a70,f11(a70,x5331,f3(a70)),x5332),f11(a70,x5331,f11(a70,x5332,f3(a70))))
% 4.60/4.59 [508]E(f27(f27(f10(a68),f9(a68,x5081)),x5082),f9(a68,f27(f27(f10(a68),x5081),x5082)))
% 4.60/4.59 [509]E(f27(f27(f13(a1),f25(a70,x5091)),x5092),f25(a70,f27(f27(f13(a70),x5091),x5092)))
% 4.60/4.59 [515]E(f27(f27(f10(a1),f25(a70,x5151)),f25(a70,x5152)),f25(a70,f27(f27(f10(a70),x5151),x5152)))
% 4.60/4.59 [520]E(f27(f27(f10(a70),x5201),f11(a70,x5202,f3(a70))),f11(a70,x5201,f27(f27(f10(a70),x5201),x5202)))
% 4.60/4.59 [535]P10(a1,f9(a1,f27(f27(f10(a1),x5351),x5351)),f27(f27(f10(a1),x5352),x5352))
% 4.60/4.59 [545]E(f27(f27(f10(a70),f11(a70,x5451,f3(a70))),x5452),f11(a70,x5452,f27(f27(f10(a70),x5451),x5452)))
% 4.60/4.59 [521]E(f11(a70,x5211,f11(a70,x5212,x5213)),f11(a70,x5212,f11(a70,x5211,x5213)))
% 4.60/4.59 [522]E(f11(a68,x5221,f11(a68,x5222,x5223)),f11(a68,x5222,f11(a68,x5221,x5223)))
% 4.60/4.59 [523]E(f11(a70,f11(a70,x5231,x5232),x5233),f11(a70,x5231,f11(a70,x5232,x5233)))
% 4.60/4.59 [524]E(f11(a68,f11(a68,x5241,x5242),x5243),f11(a68,x5241,f11(a68,x5242,x5243)))
% 4.60/4.59 [525]E(f6(a70,f6(a70,x5251,x5252),x5253),f6(a70,x5251,f11(a70,x5252,x5253)))
% 4.60/4.59 [526]E(f6(a70,f11(a70,x5261,x5262),f11(a70,x5263,x5262)),f6(a70,x5261,x5263))
% 4.60/4.59 [527]E(f6(a70,f11(a70,x5271,x5272),f11(a70,x5271,x5273)),f6(a70,x5272,x5273))
% 4.60/4.59 [542]E(f11(a70,f27(f27(f10(a70),x5421),x5422),f27(f27(f10(a70),x5421),x5423)),f27(f27(f10(a70),x5421),f11(a70,x5422,x5423)))
% 4.60/4.59 [543]E(f11(a68,f27(f27(f10(a68),x5431),x5432),f27(f27(f10(a68),x5431),x5433)),f27(f27(f10(a68),x5431),f11(a68,x5432,x5433)))
% 4.60/4.59 [544]E(f6(a68,f27(f27(f10(a68),x5441),x5442),f27(f27(f10(a68),x5441),x5443)),f27(f27(f10(a68),x5441),f6(a68,x5442,x5443)))
% 4.60/4.59 [546]E(f27(f27(f10(a68),f27(f27(f13(a68),x5461),x5462)),f27(f27(f13(a68),x5461),x5463)),f27(f27(f13(a68),x5461),f11(a70,x5462,x5463)))
% 4.60/4.59 [547]E(f11(a1,f27(f27(f10(a1),x5471),x5472),f27(f27(f10(a1),x5473),x5472)),f27(f27(f10(a1),f11(a1,x5471,x5473)),x5472))
% 4.60/4.59 [548]E(f11(a70,f27(f27(f10(a70),x5481),x5482),f27(f27(f10(a70),x5483),x5482)),f27(f27(f10(a70),f11(a70,x5481,x5483)),x5482))
% 4.60/4.59 [549]E(f11(a68,f27(f27(f10(a68),x5491),x5492),f27(f27(f10(a68),x5493),x5492)),f27(f27(f10(a68),f11(a68,x5491,x5493)),x5492))
% 4.60/4.59 [550]E(f6(a68,f27(f27(f10(a68),x5501),x5502),f27(f27(f10(a68),x5503),x5502)),f27(f27(f10(a68),f6(a68,x5501,x5503)),x5502))
% 4.60/4.59 [536]E(f27(f27(f10(a1),f27(f27(f10(a1),x5361),x5362)),x5363),f27(f27(f10(a1),x5361),f27(f27(f10(a1),x5362),x5363)))
% 4.60/4.59 [537]E(f27(f27(f10(a70),f27(f27(f10(a70),x5371),x5372)),x5373),f27(f27(f10(a70),x5371),f27(f27(f10(a70),x5372),x5373)))
% 4.60/4.59 [538]E(f27(f27(f10(a68),f27(f27(f10(a68),x5381),x5382)),x5383),f27(f27(f10(a68),x5381),f27(f27(f10(a68),x5382),x5383)))
% 4.60/4.59 [539]E(f27(f27(f13(a68),f27(f27(f13(a68),x5391),x5392)),x5393),f27(f27(f13(a68),x5391),f27(f27(f10(a70),x5392),x5393)))
% 4.60/4.59 [518]E(f27(f27(f20(x5181,x5182,x5183),x5184),f8(a70)),x5182)
% 4.60/4.59 [558]P10(a1,f5(a1,f11(a1,f11(a1,x5581,x5582),f11(a1,f9(a1,x5583),f9(a1,x5584)))),f11(a1,f5(a1,f11(a1,x5581,f9(a1,x5583))),f5(a1,f11(a1,x5582,f9(a1,x5584)))))
% 4.60/4.59 [554]E(f11(a70,f27(f27(f10(a70),x5541),x5542),f11(a70,f27(f27(f10(a70),x5543),x5542),x5544)),f11(a70,f27(f27(f10(a70),f11(a70,x5541,x5543)),x5542),x5544))
% 4.60/4.59 [553]E(f27(f27(f20(x5531,x5532,x5533),x5534),f11(a70,x5535,f3(a70))),f27(f27(x5533,x5534),f27(f27(f20(x5531,x5532,x5533),x5534),x5535)))
% 4.60/4.59 [581]~P51(x5811)+P3(f71(x5811))
% 4.60/4.59 [582]~P43(x5821)+P43(f71(x5821))
% 4.60/4.59 [583]~P51(x5831)+P26(f71(x5831))
% 4.60/4.59 [584]~P51(x5841)+P27(f71(x5841))
% 4.60/4.59 [585]~P28(x5851)+P28(f71(x5851))
% 4.60/4.59 [586]~P51(x5861)+P4(f71(x5861))
% 4.60/4.59 [587]~P51(x5871)+P29(f71(x5871))
% 4.60/4.59 [588]~P51(x5881)+P38(f71(x5881))
% 4.60/4.59 [589]~P51(x5891)+P39(f71(x5891))
% 4.60/4.59 [590]~P51(x5901)+P30(f71(x5901))
% 4.60/4.59 [591]~P51(x5911)+P32(f71(x5911))
% 4.60/4.59 [592]~P53(x5921)+P48(f71(x5921))
% 4.60/4.59 [593]~P5(x5931)+P5(f71(x5931))
% 4.60/4.59 [594]~P5(x5941)+P21(f71(x5941))
% 4.60/4.59 [595]~P47(x5951)+P6(f71(x5951))
% 4.60/4.59 [596]~P18(x5961)+P15(f71(x5961))
% 4.60/4.59 [597]~P18(x5971)+P16(f71(x5971))
% 4.60/4.59 [598]~P5(x5981)+P7(f71(x5981))
% 4.60/4.59 [599]~P43(x5991)+P23(f71(x5991))
% 4.60/4.59 [600]~P51(x6001)+P31(f71(x6001))
% 4.60/4.59 [601]~P43(x6011)+P19(f71(x6011))
% 4.60/4.59 [602]~P43(x6021)+P24(f71(x6021))
% 4.60/4.59 [603]~P51(x6031)+P49(f71(x6031))
% 4.60/4.59 [604]~P51(x6041)+P50(f71(x6041))
% 4.60/4.59 [605]~P51(x6051)+P59(f71(x6051))
% 4.60/4.59 [606]~P51(x6061)+P51(f71(x6061))
% 4.60/4.59 [607]~P47(x6071)+P60(f71(x6071))
% 4.60/4.59 [608]~P53(x6081)+P66(f71(x6081))
% 4.60/4.59 [609]~P53(x6091)+P62(f71(x6091))
% 4.60/4.59 [610]~P43(x6101)+P71(f71(x6101))
% 4.60/4.59 [611]~P47(x6111)+P44(f71(x6111))
% 4.60/4.59 [612]~P47(x6121)+P72(f71(x6121))
% 4.60/4.59 [613]~P51(x6131)+P55(f71(x6131))
% 4.60/4.59 [614]~P51(x6141)+P56(f71(x6141))
% 4.60/4.59 [615]~P51(x6151)+P63(f71(x6151))
% 4.60/4.59 [616]~P51(x6161)+P64(f71(x6161))
% 4.60/4.59 [617]~P51(x6171)+P67(f71(x6171))
% 4.60/4.59 [618]~P51(x6181)+P65(f71(x6181))
% 4.60/4.59 [619]~P51(x6191)+P52(f71(x6191))
% 4.60/4.59 [620]~P51(x6201)+P61(f71(x6201))
% 4.60/4.59 [621]~P51(x6211)+P57(f71(x6211))
% 4.60/4.59 [622]~P51(x6221)+P58(f71(x6221))
% 4.60/4.59 [623]~P47(x6231)+P47(f71(x6231))
% 4.60/4.59 [624]~P51(x6241)+P35(f71(x6241))
% 4.60/4.59 [625]~P53(x6251)+P53(f71(x6251))
% 4.60/4.59 [626]~P51(x6261)+P33(f71(x6261))
% 4.60/4.59 [627]~P45(x6271)+P45(f71(x6271))
% 4.60/4.59 [628]~P8(x6281)+P20(f71(x6281))
% 4.60/4.59 [629]~P51(x6291)+P25(f71(x6291))
% 4.60/4.59 [630]~P46(x6301)+P68(f71(x6301))
% 4.60/4.59 [631]~P8(x6311)+P8(f71(x6311))
% 4.60/4.59 [632]~P46(x6321)+P46(f71(x6321))
% 4.60/4.59 [633]~P53(x6331)+P69(f71(x6331))
% 4.60/4.59 [634]~P51(x6341)+P17(f71(x6341))
% 4.60/4.59 [635]~P8(x6351)+P34(f71(x6351))
% 4.60/4.59 [636]~P43(x6361)+P54(f71(x6361))
% 4.60/4.59 [637]~P47(x6371)+P73(f71(x6371))
% 4.60/4.59 [638]~P43(x6381)+P40(f71(x6381))
% 4.60/4.59 [639]~P45(x6391)+P70(f71(x6391))
% 4.60/4.59 [640]~P8(x6401)+P22(f71(x6401))
% 4.60/4.59 [641]~P18(x6411)+P18(f71(x6411))
% 4.60/4.59 [643]~P71(x6431)+~E(f8(x6431),f3(x6431))
% 4.60/4.59 [645]~E(x6451,f8(a1))+E(f12(a1,x6451),f8(a1))
% 4.60/4.59 [646]~E(x6461,f8(a68))+E(f12(a68,x6461),f8(a68))
% 4.60/4.59 [647]~E(x6471,f8(a70))+E(f25(a70,x6471),f8(a1))
% 4.60/4.59 [648]E(x6481,f8(a70))+~E(f25(a70,x6481),f8(a1))
% 4.60/4.59 [708]E(x7081,f8(a70))+P11(a70,f8(a70),x7081)
% 4.60/4.59 [748]~P2(x7481)+P10(a1,f8(a1),f30(x7481))
% 4.60/4.59 [749]~P2(x7491)+P11(a1,f8(a1),f51(x7491))
% 4.60/4.59 [756]E(f5(a1,x7561),x7561)+P11(a1,x7561,f8(a1))
% 4.60/4.59 [757]E(f5(a68,x7571),x7571)+P11(a68,x7571,f8(a68))
% 4.60/4.59 [766]~P57(x7661)+P10(x7661,f8(x7661),f3(x7661))
% 4.60/4.59 [767]~P57(x7671)+P11(x7671,f8(x7671),f3(x7671))
% 4.60/4.59 [778]P12(a68,x7781,f3(a68))+~E(f5(a68,x7781),f3(a68))
% 4.60/4.59 [789]~E(x7891,f8(a70))+P10(a1,f25(a70,x7891),f8(a1))
% 4.60/4.59 [790]~E(x7901,f8(a68))+P11(a68,f5(a68,x7901),f3(a68))
% 4.60/4.59 [828]E(x8281,f3(a70))+~P12(a70,x8281,f3(a70))
% 4.60/4.59 [829]E(x8291,f8(a70))+~P10(a70,x8291,f8(a70))
% 4.60/4.59 [834]E(f7(x8341),f8(a70))+~P10(a1,x8341,f8(a1))
% 4.60/4.59 [835]E(f24(x8351),f8(a70))+~P10(a1,x8351,f8(a1))
% 4.60/4.59 [862]~P12(a68,x8621,f3(a68))+E(f5(a68,x8621),f3(a68))
% 4.60/4.59 [863]~P11(a1,f8(a1),x8631)+E(f12(a1,x8631),f3(a1))
% 4.60/4.59 [886]~P57(x8861)+~P10(x8861,f3(x8861),f8(x8861))
% 4.60/4.59 [887]~P57(x8871)+~P11(x8871,f3(x8871),f8(x8871))
% 4.60/4.59 [889]E(f9(a1,x8891),f5(a1,x8891))+~P11(a1,x8891,f8(a1))
% 4.60/4.59 [890]E(f9(a68,x8901),f5(a68,x8901))+~P11(a68,x8901,f8(a68))
% 4.60/4.59 [926]E(x9261,f8(a70))+~P10(a1,f25(a70,x9261),f8(a1))
% 4.60/4.59 [927]E(x9271,f8(a68))+~P11(a68,f5(a68,x9271),f3(a68))
% 4.60/4.59 [964]~P11(a68,f8(a68),x9641)+P10(a68,f3(a68),x9641)
% 4.60/4.59 [965]~P10(a68,f3(a68),x9651)+P11(a68,f8(a68),x9651)
% 4.60/4.59 [994]~P10(a1,x9941,f3(a1))+P10(a70,f7(x9941),f3(a70))
% 4.60/4.59 [995]~P10(a1,f3(a1),x9951)+P10(a70,f3(a70),f24(x9951))
% 4.60/4.59 [1001]~P10(a70,f7(x10011),f3(a70))+P10(a1,x10011,f3(a1))
% 4.60/4.59 [1002]~P10(a70,f3(a70),f24(x10021))+P10(a1,f3(a1),x10021)
% 4.60/4.59 [1013]~P11(a70,f8(a70),x10131)+P11(a1,f8(a1),f25(a70,x10131))
% 4.60/4.59 [1072]P11(a70,f8(a70),x10721)+~P11(a1,f8(a1),f25(a70,x10721))
% 4.60/4.59 [649]~P41(x6491)+E(f26(x6491,f3(x6491)),f3(a1))
% 4.60/4.59 [650]~P1(x6501)+E(f26(x6501,f8(x6501)),f8(a1))
% 4.60/4.59 [653]~P51(x6531)+E(f5(x6531,f3(x6531)),f3(x6531))
% 4.60/4.59 [654]~P3(x6541)+E(f5(x6541,f8(x6541)),f8(x6541))
% 4.60/4.59 [655]~P41(x6551)+E(f12(x6551,f3(x6551)),f3(x6551))
% 4.60/4.59 [656]~P1(x6561)+E(f12(x6561,f8(x6561)),f8(x6561))
% 4.60/4.59 [657]~P33(x6571)+E(f12(x6571,f8(x6571)),f8(x6571))
% 4.60/4.59 [658]~P20(x6581)+E(f9(x6581,f8(x6581)),f8(x6581))
% 4.60/4.59 [705]~P51(x7051)+~P13(x7051,f8(f71(x7051)))
% 4.60/4.59 [776]~P40(x7761)+E(f20(x7761,f3(x7761),f10(x7761)),f13(x7761))
% 4.60/4.59 [997]~P11(a70,f8(a70),x9971)+E(f11(a70,f41(x9971),f3(a70)),x9971)
% 4.60/4.59 [1046]~P10(a1,f8(a1),x10461)+P10(a1,f25(a70,f24(x10461)),x10461)
% 4.60/4.59 [1047]~P10(a1,f8(a1),x10471)+P10(a1,f25(a70,f56(x10471)),x10471)
% 4.60/4.59 [1119]~P57(x11191)+P11(x11191,f8(x11191),f11(x11191,f3(x11191),f3(x11191)))
% 4.60/4.59 [1261]~P10(a68,f8(a68),x12611)+P11(a68,f8(a68),f11(a68,f3(a68),x12611))
% 4.60/4.59 [1283]E(x12831,f8(a70))+~P11(a70,x12831,f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1390]~P12(a70,x13901,f11(a70,f8(a70),f3(a70)))+E(x13901,f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [695]~P8(x6951)+E(f9(f71(x6951),f8(f71(x6951))),f8(f71(x6951)))
% 4.60/4.59 [836]~P43(x8361)+E(f15(x8361,f3(x8361),f8(f71(x8361))),f3(f71(x8361)))
% 4.60/4.59 [837]~P28(x8371)+E(f15(x8371,f8(x8371),f8(f71(x8371))),f8(f71(x8371)))
% 4.60/4.59 [978]E(x9781,f8(a1))+P11(a1,f8(a1),f27(f27(f10(a1),x9781),x9781))
% 4.60/4.59 [1202]~E(x12021,f8(a1))+~P11(a1,f8(a1),f27(f27(f10(a1),x12021),x12021))
% 4.60/4.59 [1274]~P10(a1,f8(a1),x12741)+E(f7(f11(a1,x12741,f3(a1))),f11(a70,f7(x12741),f3(a70)))
% 4.60/4.59 [1275]~P10(a1,f8(a1),x12751)+E(f24(f11(a1,x12751,f3(a1))),f11(a70,f24(x12751),f3(a70)))
% 4.60/4.59 [1377]~P10(a1,f26(a2,x13771),a72)+P10(a1,f26(a2,f27(f14(a2,a73),x13771)),a76)
% 4.60/4.59 [1378]~P10(a1,f26(a2,x13781),a72)+P10(a1,f26(a2,f27(f14(a2,a73),x13781)),a28)
% 4.60/4.59 [1379]~P10(a1,f26(a2,x13791),a72)+P10(a1,f26(a2,f27(f14(a2,a73),x13791)),a60)
% 4.60/4.59 [1530]~P10(a1,f8(a1),x15301)+P11(a1,x15301,f25(a70,f11(a70,f56(x15301),f3(a70))))
% 4.60/4.59 [1622]~P11(a68,x16221,f8(a68))+P11(a68,f11(a68,f11(a68,f3(a68),x16221),x16221),f8(a68))
% 4.60/4.59 [1753]P11(a68,x17531,f8(a68))+~P11(a68,f11(a68,f11(a68,f3(a68),x17531),x17531),f8(a68))
% 4.60/4.59 [696]~E(x6961,x6962)+P10(a1,x6961,x6962)
% 4.60/4.59 [699]~E(x6991,x6992)+P10(a70,x6991,x6992)
% 4.60/4.59 [703]~E(x7031,x7032)+P12(a70,x7031,x7032)
% 4.60/4.59 [718]~P26(x7181)+P10(x7181,x7182,x7182)
% 4.60/4.59 [719]~P43(x7191)+P12(x7191,x7192,x7192)
% 4.60/4.59 [796]~E(x7961,x7962)+~P11(a1,x7961,x7962)
% 4.60/4.59 [801]~E(x8011,x8012)+~P11(a70,x8011,x8012)
% 4.60/4.59 [802]~E(x8021,x8022)+~P11(a68,x8021,x8022)
% 4.60/4.59 [830]~P11(x8301,x8302,x8302)+~P26(x8301)
% 4.60/4.59 [870]P10(a1,x8702,x8701)+P10(a1,x8701,x8702)
% 4.60/4.59 [871]P10(a70,x8712,x8711)+P10(a70,x8711,x8712)
% 4.60/4.59 [872]P10(a68,x8722,x8721)+P10(a68,x8721,x8722)
% 4.60/4.59 [935]~P11(a1,x9351,x9352)+P10(a1,x9351,x9352)
% 4.60/4.59 [940]~P11(a70,x9401,x9402)+P10(a70,x9401,x9402)
% 4.60/4.59 [941]~P11(a68,x9411,x9412)+P10(a68,x9411,x9412)
% 4.60/4.59 [666]~E(x6661,x6662)+P74(f29(x6661,x6662))
% 4.60/4.59 [669]~P26(x6692)+P26(f75(x6691,x6692))
% 4.60/4.59 [670]~P38(x6702)+P38(f75(x6701,x6702))
% 4.60/4.59 [671]~P39(x6712)+P39(f75(x6711,x6712))
% 4.60/4.59 [672]~P36(x6722)+P36(f75(x6721,x6722))
% 4.60/4.59 [673]~P34(x6732)+P34(f75(x6731,x6732))
% 4.60/4.59 [674]~P22(x6742)+P22(f75(x6741,x6742))
% 4.60/4.59 [681]E(x6811,x6812)+~E(f25(a70,x6811),f25(a70,x6812))
% 4.60/4.59 [688]E(x6881,x6882)+~P74(f29(x6881,x6882))
% 4.60/4.59 [728]~P20(x7281)+E(f6(x7281,x7282,x7282),f8(x7281))
% 4.60/4.59 [735]~P43(x7351)+P12(x7351,x7352,f8(x7351))
% 4.60/4.59 [736]~P43(x7361)+P12(x7361,f3(x7361),x7362)
% 4.60/4.59 [754]P10(a68,x7542,x7541)+E(f16(x7541,x7542),f8(a68))
% 4.60/4.59 [775]~E(x7752,f9(a1,x7751))+E(f11(a1,x7751,x7752),f8(a1))
% 4.60/4.59 [803]~P3(x8031)+P10(x8031,x8032,f5(x8031,x8032))
% 4.60/4.59 [809]~E(f11(a70,x8092,x8091),x8092)+E(x8091,f8(a70))
% 4.60/4.59 [811]~P1(x8111)+P10(a1,f8(a1),f26(x8111,x8112))
% 4.60/4.59 [812]~P2(x8122)+P10(a1,f8(a1),f66(x8121,x8122))
% 4.60/4.59 [813]~P2(x8132)+P10(a1,f8(a1),f67(x8131,x8132))
% 4.60/4.59 [814]~P2(x8142)+P11(a1,f8(a1),f52(x8141,x8142))
% 4.60/4.59 [815]~P2(x8152)+P11(a1,f8(a1),f65(x8151,x8152))
% 4.60/4.59 [818]~P11(a70,x8182,x8181)+~E(x8181,f8(a70))
% 4.60/4.59 [823]E(x8231,f8(a70))+~E(f11(a70,x8232,x8231),f8(a70))
% 4.60/4.59 [824]E(x8241,f8(a70))+~E(f11(a70,x8241,x8242),f8(a70))
% 4.60/4.59 [831]~P3(x8311)+P10(x8311,f8(x8311),f5(x8311,x8312))
% 4.60/4.59 [857]E(x8571,f9(a1,x8572))+~E(f11(a1,x8572,x8571),f8(a1))
% 4.60/4.59 [891]~P3(x8911)+P10(x8911,f9(x8911,x8912),f5(x8911,x8912))
% 4.60/4.59 [933]~P1(x9331)+~P11(a1,f26(x9331,x9332),f8(a1))
% 4.60/4.59 [949]~P10(a70,x9491,x9492)+E(f6(a70,x9491,x9492),f8(a70))
% 4.60/4.59 [956]P10(a70,x9561,x9562)+~E(f6(a70,x9561,x9562),f8(a70))
% 4.60/4.59 [962]~P3(x9621)+~P11(x9621,f5(x9621,x9622),f8(x9621))
% 4.60/4.59 [974]~P10(a1,x9741,x9742)+P10(a70,f7(x9741),f7(x9742))
% 4.60/4.59 [975]~P10(a1,x9751,x9752)+P10(a70,f24(x9751),f24(x9752))
% 4.60/4.59 [988]~P10(a68,x9882,x9881)+E(f6(a68,x9881,x9882),f16(x9881,x9882))
% 4.60/4.59 [1004]~P12(a68,x10041,x10042)+P12(a68,x10041,f9(a68,x10042))
% 4.60/4.59 [1005]~P12(a68,x10051,x10052)+P12(a68,f9(a68,x10051),x10052)
% 4.60/4.59 [1037]P12(a68,x10371,x10372)+~P12(a68,x10371,f9(a68,x10372))
% 4.60/4.59 [1038]P10(a1,x10381,x10382)+~P10(a1,f5(a1,x10381),x10382)
% 4.60/4.59 [1039]P12(a68,x10391,x10392)+~P12(a68,f9(a68,x10391),x10392)
% 4.60/4.59 [1051]P10(a70,x10511,f24(x10512))+~P10(a1,f25(a70,x10511),x10512)
% 4.60/4.59 [1052]P10(a70,f7(x10521),x10522)+~P10(a1,x10521,f25(a70,x10522))
% 4.60/4.59 [1078]~P10(a70,x10781,x10782)+P10(a1,f25(a70,x10781),f25(a70,x10782))
% 4.60/4.59 [1079]~P11(a70,x10791,x10792)+P11(a1,f25(a70,x10791),f25(a70,x10792))
% 4.60/4.59 [1118]~P10(a1,f5(a1,x11182),x11181)+P10(a1,f9(a1,x11181),x11182)
% 4.60/4.59 [1137]P10(a70,x11371,x11372)+~P10(a1,f25(a70,x11371),f25(a70,x11372))
% 4.60/4.59 [1138]P11(a70,x11381,x11382)+~P11(a1,f25(a70,x11381),f25(a70,x11382))
% 4.60/4.59 [1219]~P12(a70,x12191,x12192)+P12(a70,x12191,f11(a70,x12192,x12191))
% 4.60/4.59 [1228]~P10(a1,x12281,x12282)+P10(a1,f6(a1,x12281,x12282),f8(a1))
% 4.60/4.59 [1229]~P11(a68,x12291,x12292)+P11(a68,f6(a68,x12291,x12292),f8(a68))
% 4.60/4.59 [1303]~P10(a1,f9(a1,x13031),x13032)+P10(a1,f8(a1),f11(a1,x13031,x13032))
% 4.60/4.59 [1304]~P11(a1,f9(a1,x13041),x13042)+P11(a1,f8(a1),f11(a1,x13041,x13042))
% 4.60/4.59 [1305]~P10(a1,x13052,f9(a1,x13051))+P10(a1,f11(a1,x13051,x13052),f8(a1))
% 4.60/4.59 [1306]~P11(a1,x13062,f9(a1,x13061))+P11(a1,f11(a1,x13061,x13062),f8(a1))
% 4.60/4.59 [1326]P12(a70,x13261,x13262)+~P12(a70,x13261,f11(a70,x13262,x13261))
% 4.60/4.59 [1339]P10(a1,x13391,x13392)+~P10(a1,f6(a1,x13391,x13392),f8(a1))
% 4.60/4.59 [1340]P11(a68,x13401,x13402)+~P11(a68,f6(a68,x13401,x13402),f8(a68))
% 4.60/4.59 [1391]P10(a1,x13911,f9(a1,x13912))+~P10(a1,f11(a1,x13912,x13911),f8(a1))
% 4.60/4.59 [1392]P11(a1,x13921,f9(a1,x13922))+~P11(a1,f11(a1,x13922,x13921),f8(a1))
% 4.60/4.59 [1393]P10(a1,f9(a1,x13931),x13932)+~P10(a1,f8(a1),f11(a1,x13931,x13932))
% 4.60/4.59 [1394]P11(a1,f9(a1,x13941),x13942)+~P11(a1,f8(a1),f11(a1,x13941,x13942))
% 4.60/4.59 [686]~P20(x6861)+E(f9(x6861,f9(x6861,x6862)),x6862)
% 4.60/4.59 [687]~P36(x6871)+E(f9(x6871,f9(x6871,x6872)),x6872)
% 4.60/4.59 [706]~P1(x7061)+E(f5(a1,f26(x7061,x7062)),f26(x7061,x7062))
% 4.60/4.59 [714]~P1(x7141)+E(f26(x7141,f9(x7141,x7142)),f26(x7141,x7142))
% 4.60/4.59 [715]~P3(x7151)+E(f5(x7151,f5(x7151,x7152)),f5(x7151,x7152))
% 4.60/4.59 [716]~P3(x7161)+E(f5(x7161,f9(x7161,x7162)),f5(x7161,x7162))
% 4.60/4.59 [717]~P51(x7171)+E(f12(x7171,f12(x7171,x7172)),f12(x7171,x7172))
% 4.60/4.59 [722]~P43(x7221)+E(f27(f27(f13(x7221),x7222),f3(a70)),x7222)
% 4.60/4.59 [723]~P24(x7231)+E(f27(f27(f13(x7231),x7232),f3(a70)),x7232)
% 4.60/4.59 [729]~P43(x7291)+E(f27(f27(f10(x7291),x7292),f3(x7291)),x7292)
% 4.60/4.59 [730]~P19(x7301)+E(f27(f27(f10(x7301),x7302),f3(x7301)),x7302)
% 4.60/4.59 [731]~P24(x7311)+E(f27(f27(f10(x7311),x7312),f3(x7311)),x7312)
% 4.60/4.59 [732]~P43(x7321)+E(f27(f27(f13(x7321),x7322),f8(a70)),f3(x7321))
% 4.60/4.59 [733]~P40(x7331)+E(f27(f27(f13(x7331),x7332),f8(a70)),f3(x7331))
% 4.60/4.59 [737]~P43(x7371)+E(f11(x7371,x7372,f8(x7371)),x7372)
% 4.60/4.59 [738]~P5(x7381)+E(f11(x7381,x7382,f8(x7381)),x7382)
% 4.60/4.59 [739]~P21(x7391)+E(f11(x7391,x7392,f8(x7391)),x7392)
% 4.60/4.59 [740]~P20(x7401)+E(f6(x7401,x7402,f8(x7401)),x7402)
% 4.60/4.59 [741]~P43(x7411)+E(f11(x7411,f8(x7411),x7412),x7412)
% 4.60/4.59 [742]~P5(x7421)+E(f11(x7421,f8(x7421),x7422),x7422)
% 4.60/4.59 [743]~P21(x7431)+E(f11(x7431,f8(x7431),x7432),x7432)
% 4.60/4.59 [744]~P43(x7441)+E(f21(x7441,f3(x7441),x7442),x7442)
% 4.60/4.59 [751]~P2(x7511)+E(f27(f27(f10(x7511),x7512),f8(x7511)),f8(x7511))
% 4.60/4.59 [752]~P43(x7521)+E(f27(f27(f10(x7521),x7522),f8(x7521)),f8(x7521))
% 4.60/4.59 [753]~P60(x7531)+E(f27(f27(f10(x7531),x7532),f8(x7531)),f8(x7531))
% 4.60/4.59 [777]~P47(x7771)+E(f21(x7771,f8(x7771),x7772),f8(f71(x7771)))
% 4.60/4.59 [784]~P20(x7841)+E(f6(x7841,f8(x7841),x7842),f9(x7841,x7842))
% 4.60/4.59 [786]~E(x7861,x7862)+E(f11(a1,x7861,f9(a1,x7862)),f8(a1))
% 4.60/4.59 [795]~P1(x7951)+E(f12(x7951,f9(x7951,x7952)),f9(x7951,f12(x7951,x7952)))
% 4.60/4.59 [825]~P20(x8251)+E(f11(x8251,x8252,f9(x8251,x8252)),f8(x8251))
% 4.60/4.59 [826]~P20(x8261)+E(f11(x8261,f9(x8261,x8262),x8262),f8(x8261))
% 4.60/4.59 [827]~P8(x8271)+E(f11(x8271,f9(x8271,x8272),x8272),f8(x8271))
% 4.60/4.59 [854]~P51(x8541)+E(f27(f27(f10(x8541),x8542),f12(x8541,x8542)),f5(x8541,x8542))
% 4.60/4.59 [921]E(x9211,x9212)+~E(f11(a1,x9211,f9(a1,x9212)),f8(a1))
% 4.60/4.59 [925]E(x9251,x9252)+~E(f27(x9251,f31(x9252,x9251)),f27(x9252,f31(x9252,x9251)))
% 4.60/4.59 [944]~P51(x9441)+E(f27(f27(f10(x9441),f12(x9441,x9442)),f5(x9441,x9442)),x9442)
% 4.60/4.59 [966]~P3(x9661)+P10(x9661,f9(x9661,f5(x9661,x9662)),f8(x9661))
% 4.60/4.59 [968]P11(a70,f8(a70),x9681)+~E(x9681,f11(a70,x9682,f3(a70)))
% 4.60/4.59 [1007]~P10(a70,x10071,x10072)+E(f11(a70,x10071,f33(x10072,x10071)),x10072)
% 4.60/4.59 [1008]~P10(a70,x10081,x10082)+E(f11(a70,x10081,f37(x10082,x10081)),x10082)
% 4.60/4.59 [1011]~E(x10111,x10112)+P11(a70,x10111,f11(a70,x10112,f3(a70)))
% 4.60/4.59 [1012]~E(x10121,x10122)+P11(a68,x10121,f11(a68,x10122,f3(a68)))
% 4.60/4.59 [1016]~E(x10161,f8(a70))+P11(a70,x10161,f11(a70,x10162,f3(a70)))
% 4.60/4.59 [1071]~P57(x10711)+P11(x10711,x10712,f11(x10711,x10712,f3(x10711)))
% 4.60/4.59 [1139]P11(a70,x11392,x11391)+E(f11(a70,x11391,f6(a70,x11392,x11391)),x11392)
% 4.60/4.59 [1159]P11(a70,x11591,x11592)+P11(a70,x11592,f11(a70,x11591,f3(a70)))
% 4.60/4.59 [1160]P10(a70,x11601,x11602)+P10(a70,f11(a70,x11602,f3(a70)),x11601)
% 4.60/4.59 [1224]~P10(a70,x12241,x12242)+E(f11(a70,x12241,f6(a70,x12242,x12241)),x12242)
% 4.60/4.59 [1225]~P10(a70,x12252,x12251)+E(f11(a70,f6(a70,x12251,x12252),x12252),x12251)
% 4.60/4.59 [1233]~P11(a68,x12331,x12332)+P10(a68,x12331,f6(a68,x12332,f3(a68)))
% 4.60/4.59 [1235]~P10(a70,x12351,x12352)+P11(a70,x12351,f11(a70,x12352,f3(a70)))
% 4.60/4.59 [1238]~P10(a68,x12381,x12382)+P11(a68,x12381,f11(a68,x12382,f3(a68)))
% 4.60/4.59 [1239]~P11(a68,x12391,x12392)+P11(a68,x12391,f11(a68,x12392,f3(a68)))
% 4.60/4.59 [1242]~P11(a70,x12421,x12422)+P10(a70,f11(a70,x12421,f3(a70)),x12422)
% 4.60/4.59 [1244]~P11(a68,x12441,x12442)+P10(a68,f11(a68,x12441,f3(a68)),x12442)
% 4.60/4.59 [1322]~P11(a70,x13221,x13222)+E(f11(a70,f11(a70,x13221,f43(x13222,x13221)),f3(a70)),x13222)
% 4.60/4.59 [1325]~P10(a70,x13252,x13251)+E(f6(a1,f25(a70,x13251),f25(a70,x13252)),f25(a70,f6(a70,x13251,x13252)))
% 4.60/4.59 [1346]P10(a70,x13461,x13462)+~P11(a70,x13461,f11(a70,x13462,f3(a70)))
% 4.60/4.59 [1347]P10(a68,x13471,x13472)+~P11(a68,x13471,f11(a68,x13472,f3(a68)))
% 4.60/4.59 [1348]P11(a68,x13481,x13482)+~P10(a68,x13481,f6(a68,x13482,f3(a68)))
% 4.60/4.59 [1352]P11(a70,x13521,x13522)+~P10(a70,f11(a70,x13521,f3(a70)),x13522)
% 4.60/4.59 [1354]P11(a68,x13541,x13542)+~P10(a68,f11(a68,x13541,f3(a68)),x13542)
% 4.60/4.59 [1360]~P10(a70,x13601,x13602)+P11(a1,f25(a70,x13601),f11(a1,f25(a70,x13602),f3(a1)))
% 4.60/4.59 [1361]~P11(a70,x13611,x13612)+P10(a1,f11(a1,f25(a70,x13611),f3(a1)),f25(a70,x13612))
% 4.60/4.59 [1417]~P11(a70,x14171,x14172)+~P11(a70,x14172,f11(a70,x14171,f3(a70)))
% 4.60/4.59 [1418]~P10(a70,x14181,x14182)+~P10(a70,f11(a70,x14182,f3(a70)),x14181)
% 4.60/4.59 [1438]P11(a1,x14381,f25(a70,x14382))+~P10(a70,f11(a70,f24(x14381),f3(a70)),x14382)
% 4.60/4.59 [1532]P10(a70,x15321,x15322)+~P11(a1,f25(a70,x15321),f11(a1,f25(a70,x15322),f3(a1)))
% 4.60/4.59 [1533]P11(a70,x15331,x15332)+~P10(a1,f11(a1,f25(a70,x15331),f3(a1)),f25(a70,x15332))
% 4.60/4.59 [1626]P10(a70,x16261,x16262)+~P10(a70,f11(a70,x16261,f3(a70)),f11(a70,x16262,f3(a70)))
% 4.60/4.59 [1628]P11(a70,x16281,x16282)+~P11(a70,f11(a70,x16281,f3(a70)),f11(a70,x16282,f3(a70)))
% 4.60/4.59 [691]~E(x6912,f8(a70))+E(f27(f27(f10(a70),x6911),x6912),f8(a70))
% 4.60/4.59 [692]~E(x6921,f8(a70))+E(f27(f27(f10(a70),x6921),x6922),f8(a70))
% 4.60/4.59 [710]~P37(x7101)+E(f27(f27(f10(x7101),x7102),x7102),x7102)
% 4.60/4.59 [763]~P43(x7631)+E(f27(f27(f10(x7631),f3(x7631)),x7632),x7632)
% 4.60/4.59 [764]~P19(x7641)+E(f27(f27(f10(x7641),f3(x7641)),x7642),x7642)
% 4.60/4.59 [765]~P24(x7651)+E(f27(f27(f10(x7651),f3(x7651)),x7652),x7652)
% 4.60/4.59 [771]~P2(x7711)+E(f27(f27(f10(x7711),f8(x7711)),x7712),f8(x7711))
% 4.60/4.59 [772]~P43(x7721)+E(f27(f27(f10(x7721),f8(x7721)),x7722),f8(x7721))
% 4.60/4.59 [773]~P60(x7731)+E(f27(f27(f10(x7731),f8(x7731)),x7732),f8(x7731))
% 4.60/4.59 [774]~P24(x7741)+E(f27(f27(f13(x7741),f3(x7741)),x7742),f3(x7741))
% 4.60/4.59 [782]E(x7821,f3(a70))+~E(f27(f27(f10(a70),x7822),x7821),f3(a70))
% 4.60/4.59 [783]E(x7831,f3(a70))+~E(f27(f27(f10(a70),x7831),x7832),f3(a70))
% 4.60/4.59 [793]~P5(x7931)+E(f11(f71(x7931),x7932,f8(f71(x7931))),x7932)
% 4.60/4.59 [794]~P5(x7941)+E(f11(f71(x7941),f8(f71(x7941)),x7942),x7942)
% 4.60/4.59 [820]~P47(x8201)+E(f21(x8201,x8202,f8(f71(x8201))),f8(f71(x8201)))
% 4.60/4.59 [821]~P47(x8211)+E(f19(x8211,f8(f71(x8211)),x8212),f8(f71(x8211)))
% 4.60/4.59 [822]~P47(x8221)+E(f23(x8221,f8(f71(x8221)),x8222),f8(f71(x8221)))
% 4.60/4.59 [883]~E(x8832,f8(a70))+E(f27(f27(f13(a70),x8831),x8832),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [885]~P47(x8851)+E(f27(f27(f10(f71(x8851)),x8852),f8(f71(x8851))),f8(f71(x8851)))
% 4.60/4.59 [1000]~E(x10002,f8(a70))+P11(a70,f8(a70),f27(f27(f13(a70),x10001),x10002))
% 4.60/4.59 [1033]~P55(x10331)+P10(x10331,f8(x10331),f27(f27(f10(x10331),x10332),x10332))
% 4.60/4.59 [1101]~P51(x11011)+E(f27(f27(f10(x11011),f5(x11011,x11012)),f5(x11011,x11012)),f27(f27(f10(x11011),x11012),x11012))
% 4.60/4.59 [1120]~E(x11201,f11(a70,f8(a70),f3(a70)))+E(f27(f27(f13(a70),x11201),x11202),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1173]E(x11731,f11(a70,f8(a70),f3(a70)))+~E(f27(f27(f10(a70),x11732),x11731),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1174]E(x11741,f11(a70,f8(a70),f3(a70)))+~E(f27(f27(f10(a70),x11741),x11742),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1198]~P10(a68,f8(a68),x11981)+P10(a68,f8(a68),f27(f27(f13(a68),x11981),x11982))
% 4.60/4.59 [1200]~P11(a70,f8(a70),x12001)+P11(a70,f8(a70),f27(f27(f13(a70),x12001),x12002))
% 4.60/4.59 [1223]E(x12231,f8(a68))+P11(a68,f8(a68),f27(f27(f13(a68),f5(a68,x12231)),x12232))
% 4.60/4.59 [1227]~E(x12272,f8(a70))+P11(a68,f8(a68),f27(f27(f13(a68),f5(a68,x12271)),x12272))
% 4.60/4.59 [1272]~P55(x12721)+~P11(x12721,f27(f27(f10(x12721),x12722),x12722),f8(x12721))
% 4.60/4.59 [1309]P11(a70,f8(a70),x13091)+~P11(a70,f8(a70),f27(f27(f10(a70),x13092),x13091))
% 4.60/4.59 [1310]P11(a70,f8(a70),x13101)+~P11(a70,f8(a70),f27(f27(f10(a70),x13101),x13102))
% 4.60/4.59 [1335]~P10(a1,f8(a1),x13351)+E(f7(f11(a1,x13351,f25(a70,x13352))),f11(a70,f7(x13351),x13352))
% 4.60/4.59 [1336]~P10(a1,f8(a1),x13361)+E(f24(f11(a1,x13361,f25(a70,x13362))),f11(a70,f24(x13361),x13362))
% 4.60/4.59 [1408]~P10(a1,f25(a70,x14082),x14081)+E(f7(f6(a1,x14081,f25(a70,x14082))),f6(a70,f7(x14081),x14082))
% 4.60/4.59 [1409]~P10(a1,f25(a70,x14092),x14091)+E(f24(f6(a1,x14091,f25(a70,x14092))),f6(a70,f24(x14091),x14092))
% 4.60/4.59 [1676]~P10(a70,f11(a70,f8(a70),f3(a70)),x16761)+P10(a70,f11(a70,f8(a70),f3(a70)),f27(f27(f13(a70),x16761),x16762))
% 4.60/4.59 [1726]P10(a70,f11(a70,f8(a70),f3(a70)),x17261)+~P10(a70,f11(a70,f8(a70),f3(a70)),f27(f27(f10(a70),x17262),x17261))
% 4.60/4.59 [1727]P10(a70,f11(a70,f8(a70),f3(a70)),x17271)+~P10(a70,f11(a70,f8(a70),f3(a70)),f27(f27(f10(a70),x17271),x17272))
% 4.60/4.59 [1728]~P70(x17281)+E(f27(f27(f10(x17281),f11(x17281,x17282,f3(x17281))),f6(x17281,x17282,f3(x17281))),f6(x17281,f27(f27(f10(x17281),x17282),x17282),f3(x17281)))
% 4.60/4.59 [804]~P43(x8041)+E(f27(f14(x8041,f3(f71(x8041))),x8042),f3(x8041))
% 4.60/4.59 [805]~P47(x8051)+E(f27(f14(x8051,f8(f71(x8051))),x8052),f8(x8051))
% 4.60/4.59 [928]~P47(x9281)+E(f27(f27(f10(f71(x9281)),f8(f71(x9281))),x9282),f8(f71(x9281)))
% 4.60/4.59 [977]~P45(x9771)+E(f27(f27(f10(x9771),f9(x9771,f3(x9771))),x9772),f9(x9771,x9772))
% 4.60/4.59 [1063]E(f5(a68,x10631),f3(a68))+~E(f5(a68,f27(f27(f10(a68),x10631),x10632)),f3(a68))
% 4.60/4.59 [1081]~E(f25(a70,f24(x10811)),x10811)+E(f24(f27(f27(f13(a1),x10811),x10812)),f27(f27(f13(a70),f24(x10811)),x10812))
% 4.60/4.59 [1487]E(x14871,f8(a1))+~E(f11(a1,f27(f27(f10(a1),x14872),x14872),f27(f27(f10(a1),x14871),x14871)),f8(a1))
% 4.60/4.59 [1488]E(x14881,f8(a1))+~E(f11(a1,f27(f27(f10(a1),x14881),x14881),f27(f27(f10(a1),x14882),x14882)),f8(a1))
% 4.60/4.59 [1489]~P43(x14891)+E(f11(x14891,x14892,x14892),f27(f27(f10(x14891),f11(x14891,f3(x14891),f3(x14891))),x14892))
% 4.60/4.59 [1683]~P11(a1,f8(a1),x16832)+P11(a1,x16831,f27(f27(f10(a1),f25(a70,f38(x16832,x16831))),x16832))
% 4.60/4.59 [1801]~P10(a1,f8(a1),x18012)+P10(a1,f11(a1,f27(f27(f10(a1),f25(a70,x18011)),x18012),f3(a1)),f27(f27(f13(a1),f11(a1,x18012,f3(a1))),x18011))
% 4.60/4.59 [896]~P43(x8961)+E(f11(x8961,x8962,x8963),f11(x8961,x8963,x8962))
% 4.60/4.59 [946]P10(a70,x9461,x9462)+~E(x9462,f11(a70,x9461,x9463))
% 4.60/4.59 [1014]E(x10141,x10142)+~E(f11(a70,x10143,x10141),f11(a70,x10143,x10142))
% 4.60/4.59 [1015]E(x10151,x10152)+~E(f11(a70,x10151,x10153),f11(a70,x10152,x10153))
% 4.60/4.59 [1212]~P10(a70,x12121,x12123)+P10(a70,x12121,f11(a70,x12122,x12123))
% 4.60/4.59 [1214]~P10(a70,x12141,x12142)+P10(a70,x12141,f11(a70,x12142,x12143))
% 4.60/4.59 [1216]~P11(a70,x12161,x12163)+P11(a70,x12161,f11(a70,x12162,x12163))
% 4.60/4.59 [1218]~P11(a70,x12181,x12182)+P11(a70,x12181,f11(a70,x12182,x12183))
% 4.60/4.59 [1329]P10(a70,x13291,x13292)+~P10(a70,f11(a70,x13293,x13291),x13292)
% 4.60/4.59 [1330]P10(a70,x13301,x13302)+~P10(a70,f11(a70,x13301,x13303),x13302)
% 4.60/4.59 [1331]P11(a70,x13311,x13312)+~P11(a70,f11(a70,x13311,x13313),x13312)
% 4.60/4.59 [1424]~P10(a1,x14242,x14243)+P10(a1,f11(a1,x14241,x14242),f11(a1,x14241,x14243))
% 4.60/4.59 [1425]~P10(a70,x14252,x14253)+P10(a70,f11(a70,x14251,x14252),f11(a70,x14251,x14253))
% 4.60/4.59 [1426]~P10(a70,x14261,x14263)+P10(a70,f11(a70,x14261,x14262),f11(a70,x14263,x14262))
% 4.60/4.59 [1427]~P10(a68,x14272,x14273)+P10(a68,f11(a68,x14271,x14272),f11(a68,x14271,x14273))
% 4.60/4.59 [1428]~P11(a70,x14282,x14283)+P11(a70,f11(a70,x14281,x14282),f11(a70,x14281,x14283))
% 4.60/4.59 [1429]~P11(a70,x14291,x14293)+P11(a70,f11(a70,x14291,x14292),f11(a70,x14293,x14292))
% 4.60/4.59 [1430]~P11(a68,x14301,x14303)+P11(a68,f11(a68,x14301,x14302),f11(a68,x14303,x14302))
% 4.60/4.59 [1510]~P10(a70,f6(a70,x15101,x15103),x15102)+P10(a70,x15101,f11(a70,x15102,x15103))
% 4.60/4.59 [1511]~P11(a70,f11(a70,x15111,x15113),x15112)+P11(a70,x15111,f6(a70,x15112,x15113))
% 4.60/4.59 [1512]~P10(a70,x15121,f11(a70,x15123,x15122))+P10(a70,f6(a70,x15121,x15122),x15123)
% 4.60/4.59 [1513]~P11(a70,x15131,f6(a70,x15133,x15132))+P11(a70,f11(a70,x15131,x15132),x15133)
% 4.60/4.59 [1618]P10(a70,x16181,x16182)+~P10(a70,f11(a70,x16183,x16181),f11(a70,x16183,x16182))
% 4.60/4.59 [1619]P11(a70,x16191,x16192)+~P11(a70,f11(a70,x16193,x16191),f11(a70,x16193,x16192))
% 4.60/4.59 [958]~P45(x9581)+E(f11(x9581,x9582,f9(x9581,x9583)),f6(x9581,x9582,x9583))
% 4.60/4.59 [959]~P20(x9591)+E(f11(x9591,x9592,f9(x9591,x9593)),f6(x9591,x9592,x9593))
% 4.60/4.59 [960]~P8(x9601)+E(f11(x9601,x9602,f9(x9601,x9603)),f6(x9601,x9602,x9603))
% 4.60/4.59 [961]~P20(x9611)+E(f6(x9611,x9612,f9(x9611,x9613)),f11(x9611,x9612,x9613))
% 4.60/4.59 [1019]~P20(x10191)+E(f11(x10191,f6(x10191,x10192,x10193),x10193),x10192)
% 4.60/4.59 [1020]~P20(x10201)+E(f6(x10201,f11(x10201,x10202,x10203),x10203),x10202)
% 4.60/4.59 [1077]~P8(x10771)+E(f9(x10771,f6(x10771,x10772,x10773)),f6(x10771,x10773,x10772))
% 4.60/4.59 [1117]~P20(x11171)+E(f11(x11171,f9(x11171,x11172),f11(x11171,x11172,x11173)),x11173)
% 4.60/4.59 [1145]~P46(x11451)+E(f9(f71(x11451),f21(x11451,x11452,x11453)),f21(x11451,f9(x11451,x11452),x11453))
% 4.60/4.59 [1187]~P20(x11871)+E(f11(x11871,f9(x11871,x11872),f9(x11871,x11873)),f9(x11871,f11(x11871,x11873,x11872)))
% 4.60/4.59 [1188]~P8(x11881)+E(f11(x11881,f9(x11881,x11882),f9(x11881,x11883)),f9(x11881,f11(x11881,x11882,x11883)))
% 4.60/4.59 [1249]~P1(x12491)+E(f26(x12491,f6(x12491,x12492,x12493)),f26(x12491,f6(x12491,x12493,x12492)))
% 4.60/4.59 [1250]~P3(x12501)+E(f5(x12501,f6(x12501,x12502,x12503)),f5(x12501,f6(x12501,x12503,x12502)))
% 4.60/4.59 [1343]P11(a70,x13431,x13432)+~E(x13432,f11(a70,f11(a70,x13431,x13433),f3(a70)))
% 4.60/4.59 [1505]~P10(a70,x15052,x15053)+E(f6(a70,f11(a70,x15051,x15052),x15053),f6(a70,x15051,f6(a70,x15053,x15052)))
% 4.60/4.59 [1506]~P10(a70,x15063,x15062)+E(f6(a70,f11(a70,x15061,x15062),x15063),f11(a70,x15061,f6(a70,x15062,x15063)))
% 4.60/4.59 [1508]~P10(a70,x15083,x15081)+E(f6(a70,f11(a70,x15081,x15082),x15083),f11(a70,f6(a70,x15081,x15083),x15082))
% 4.60/4.59 [1584]~P10(a70,x15843,x15842)+P10(a70,x15841,f6(a70,f11(a70,x15842,x15841),x15843))
% 4.60/4.59 [1649]~P1(x16491)+P10(a1,f26(x16491,f11(x16491,x16492,x16493)),f11(a1,f26(x16491,x16492),f26(x16491,x16493)))
% 4.60/4.59 [1650]~P1(x16501)+P10(a1,f26(x16501,f6(x16501,x16502,x16503)),f11(a1,f26(x16501,x16502),f26(x16501,x16503)))
% 4.60/4.59 [1651]~P1(x16511)+P10(a1,f6(a1,f26(x16511,x16512),f26(x16511,x16513)),f26(x16511,f11(x16511,x16512,x16513)))
% 4.60/4.59 [1652]~P1(x16521)+P10(a1,f6(a1,f26(x16521,x16522),f26(x16521,x16523)),f26(x16521,f6(x16521,x16522,x16523)))
% 4.60/4.59 [1666]~P3(x16661)+P10(x16661,f5(x16661,f11(x16661,x16662,x16663)),f11(x16661,f5(x16661,x16662),f5(x16661,x16663)))
% 4.60/4.59 [1667]~P3(x16671)+P10(x16671,f5(x16671,f6(x16671,x16672,x16673)),f11(x16671,f5(x16671,x16672),f5(x16671,x16673)))
% 4.60/4.59 [1668]~P3(x16681)+P10(x16681,f6(x16681,f5(x16681,x16682),f5(x16681,x16683)),f5(x16681,f6(x16681,x16683,x16682)))
% 4.60/4.59 [1669]~P3(x16691)+P10(x16691,f6(x16691,f5(x16691,x16692),f5(x16691,x16693)),f5(x16691,f6(x16691,x16692,x16693)))
% 4.60/4.59 [1836]~P53(x18361)+P12(f71(x18361),f27(f27(f13(f71(x18361)),f15(x18361,f9(x18361,x18362),f15(x18361,f3(x18361),f8(f71(x18361))))),f18(x18361,x18362,x18363)),x18363)
% 4.60/4.59 [849]~E(x8492,f8(a70))+E(f27(f27(f10(a70),x8491),x8492),f27(f27(f10(a70),x8493),x8492))
% 4.60/4.59 [851]~E(x8511,f8(a70))+E(f27(f27(f10(a70),x8511),x8512),f27(f27(f10(a70),x8511),x8513))
% 4.60/4.59 [884]~P43(x8841)+E(f27(f27(f10(x8841),x8842),x8843),f27(f27(f10(x8841),x8843),x8842))
% 4.60/4.59 [1009]~P43(x10091)+P12(x10091,x10092,f27(f27(f10(x10091),x10093),x10092))
% 4.60/4.59 [1010]~P43(x10101)+P12(x10101,x10102,f27(f27(f10(x10101),x10102),x10103))
% 4.60/4.59 [1100]~P68(x11001)+E(f27(f27(f10(x11001),f9(x11001,x11002)),x11003),f27(f27(f10(x11001),x11002),f9(x11001,x11003)))
% 4.60/4.59 [1102]~P68(x11021)+E(f27(f27(f10(x11021),f9(x11021,x11022)),f9(x11021,x11023)),f27(f27(f10(x11021),x11022),x11023))
% 4.60/4.59 [1168]~P20(x11681)+E(f11(x11681,x11682,f11(x11681,f9(x11681,x11682),x11683)),x11683)
% 4.60/4.59 [1177]~P46(x11771)+E(f21(x11771,x11772,f9(f71(x11771),x11773)),f9(f71(x11771),f21(x11771,x11772,x11773)))
% 4.60/4.59 [1206]~E(x12061,f8(a70))+P12(a70,f27(f27(f10(a70),x12061),x12062),f27(f27(f10(a70),x12061),x12063))
% 4.60/4.59 [1255]~P8(x12551)+E(f15(x12551,f9(x12551,x12552),f9(f71(x12551),x12553)),f9(f71(x12551),f15(x12551,x12552,x12553)))
% 4.60/4.59 [1291]~P51(x12911)+P10(x12911,f8(x12911),f27(f27(f13(x12911),f5(x12911,x12912)),x12913))
% 4.60/4.59 [1313]P11(a70,f8(a70),x13131)+P10(a70,f27(f27(f10(a70),x13132),x13131),f27(f27(f10(a70),x13133),x13131))
% 4.60/4.59 [1314]P11(a70,f8(a70),x13141)+P10(a70,f27(f27(f10(a70),x13141),x13142),f27(f27(f10(a70),x13141),x13143))
% 4.60/4.59 [1364]~P10(a70,x13642,x13643)+P10(a70,f27(f27(f10(a70),x13641),x13642),f27(f27(f10(a70),x13641),x13643))
% 4.60/4.59 [1366]~P10(a70,x13661,x13663)+P10(a70,f27(f27(f10(a70),x13661),x13662),f27(f27(f10(a70),x13663),x13662))
% 4.60/4.59 [1367]~P12(a70,x13672,x13673)+P12(a70,f27(f27(f10(a70),x13671),x13672),f27(f27(f10(a70),x13671),x13673))
% 4.60/4.59 [1415]~P3(x14151)+E(f5(x14151,f11(x14151,f5(x14151,x14152),f5(x14151,x14153))),f11(x14151,f5(x14151,x14152),f5(x14151,x14153)))
% 4.60/4.59 [1538]P11(a70,x15381,x15382)+~P11(a70,f27(f27(f10(a70),x15383),x15381),f27(f27(f10(a70),x15383),x15382))
% 4.60/4.59 [1539]P11(a70,x15391,x15392)+~P11(a70,f27(f27(f10(a70),x15391),x15393),f27(f27(f10(a70),x15392),x15393))
% 4.60/4.59 [1543]P11(a70,f8(a70),x15431)+~P11(a70,f27(f27(f10(a70),x15432),x15431),f27(f27(f10(a70),x15433),x15431))
% 4.60/4.59 [1544]P11(a70,f8(a70),x15441)+~P11(a70,f27(f27(f10(a70),x15441),x15442),f27(f27(f10(a70),x15441),x15443))
% 4.60/4.59 [1739]~P47(x17391)+E(f15(x17391,f27(f14(x17391,x17392),x17393),f23(x17391,x17392,x17393)),f11(f71(x17391),x17392,f21(x17391,x17393,f23(x17391,x17392,x17393))))
% 4.60/4.59 [1768]~P1(x17681)+P10(a1,f5(a1,f6(a1,f26(x17681,x17682),f26(x17681,x17683))),f26(x17681,f6(x17681,x17682,x17683)))
% 4.60/4.59 [1769]~P3(x17691)+P10(x17691,f5(x17691,f6(x17691,f5(x17691,x17692),f5(x17691,x17693))),f5(x17691,f6(x17691,x17692,x17693)))
% 4.60/4.59 [1127]~P68(x11271)+E(f27(f27(f10(x11271),x11272),f9(x11271,x11273)),f9(x11271,f27(f27(f10(x11271),x11272),x11273)))
% 4.60/4.59 [1129]~P2(x11291)+E(f27(f27(f10(x11291),x11292),f9(x11291,x11293)),f9(x11291,f27(f27(f10(x11291),x11292),x11293)))
% 4.60/4.59 [1144]~P37(x11441)+E(f27(f27(f10(x11441),x11442),f27(f27(f10(x11441),x11442),x11443)),f27(f27(f10(x11441),x11442),x11443))
% 4.60/4.59 [1158]~P46(x11581)+E(f27(f14(x11581,f9(f71(x11581),x11582)),x11583),f9(x11581,f27(f14(x11581,x11582),x11583)))
% 4.60/4.59 [1169]~P42(x11691)+E(f26(x11691,f27(f27(f13(x11691),x11692),x11693)),f27(f27(f13(a1),f26(x11691,x11692)),x11693))
% 4.60/4.59 [1178]~P51(x11781)+E(f27(f27(f13(x11781),f5(x11781,x11782)),x11783),f5(x11781,f27(f27(f13(x11781),x11782),x11783)))
% 4.60/4.59 [1179]~P68(x11791)+E(f27(f27(f10(x11791),f9(x11791,x11792)),x11793),f9(x11791,f27(f27(f10(x11791),x11792),x11793)))
% 4.60/4.59 [1181]~P2(x11811)+E(f27(f27(f10(x11811),f9(x11811,x11812)),x11813),f9(x11811,f27(f27(f10(x11811),x11812),x11813)))
% 4.60/4.59 [1245]~P42(x12451)+E(f27(f27(f10(a1),f26(x12451,x12452)),f26(x12451,x12453)),f26(x12451,f27(f27(f10(x12451),x12452),x12453)))
% 4.60/4.59 [1258]~P51(x12581)+E(f27(f27(f10(x12581),f5(x12581,x12582)),f5(x12581,x12583)),f5(x12581,f27(f27(f10(x12581),x12582),x12583)))
% 4.60/4.59 [1259]~P42(x12591)+E(f27(f27(f10(x12591),f12(x12591,x12592)),f12(x12591,x12593)),f12(x12591,f27(f27(f10(x12591),x12592),x12593)))
% 4.60/4.59 [1260]~P51(x12601)+E(f27(f27(f10(x12601),f12(x12601,x12602)),f12(x12601,x12603)),f12(x12601,f27(f27(f10(x12601),x12602),x12603)))
% 4.60/4.59 [1382]~P43(x13821)+E(f27(f27(f10(x13821),x13822),f27(f27(f13(x13821),x13822),x13823)),f27(f27(f13(x13821),x13822),f11(a70,x13823,f3(a70))))
% 4.60/4.59 [1383]~P40(x13831)+E(f27(f27(f10(x13831),x13832),f27(f27(f13(x13831),x13832),x13833)),f27(f27(f13(x13831),x13832),f11(a70,x13833,f3(a70))))
% 4.60/4.59 [1423]~P51(x14231)+E(f5(x14231,f27(f27(f13(x14231),f9(x14231,x14232)),x14233)),f5(x14231,f27(f27(f13(x14231),x14232),x14233)))
% 4.60/4.59 [1542]~P12(a68,x15421,x15422)+P12(a68,x15421,f11(a68,x15422,f27(f27(f10(a68),x15421),x15423)))
% 4.60/4.59 [1610]~P43(x16101)+E(f11(x16101,x16102,f27(f27(f10(x16101),x16103),x16102)),f27(f27(f10(x16101),f11(x16101,x16103,f3(x16101))),x16102))
% 4.60/4.59 [1611]~P43(x16111)+E(f11(x16111,f27(f27(f10(x16111),x16112),x16113),x16113),f27(f27(f10(x16111),f11(x16111,x16112,f3(x16111))),x16113))
% 4.60/4.59 [1637]~P41(x16371)+P10(a1,f26(x16371,f27(f27(f13(x16371),x16372),x16373)),f27(f27(f13(a1),f26(x16371,x16372)),x16373))
% 4.60/4.59 [1691]~P2(x16911)+P10(a1,f26(x16911,f27(f27(f10(x16911),x16912),x16913)),f27(f27(f10(a1),f26(x16911,x16913)),f65(x16912,x16911)))
% 4.60/4.59 [1692]~P2(x16921)+P10(a1,f26(x16921,f27(f27(f10(x16921),x16922),x16923)),f27(f27(f10(a1),f26(x16921,x16923)),f67(x16922,x16921)))
% 4.60/4.59 [1693]~P2(x16931)+P10(a1,f26(x16931,f27(f27(f10(x16931),x16932),x16933)),f27(f27(f10(a1),f26(x16931,x16933)),f34(x16932,x16931)))
% 4.60/4.59 [1694]~P2(x16941)+P10(a1,f26(x16941,f27(f27(f10(x16941),x16942),x16943)),f27(f27(f10(a1),f26(x16941,x16942)),f26(x16941,x16943)))
% 4.60/4.59 [1695]~P2(x16951)+P10(a1,f26(x16951,f27(f27(f10(x16951),x16952),x16953)),f27(f27(f10(a1),f26(x16951,x16952)),f52(x16953,x16951)))
% 4.60/4.59 [1696]~P2(x16961)+P10(a1,f26(x16961,f27(f27(f10(x16961),x16962),x16963)),f27(f27(f10(a1),f26(x16961,x16962)),f66(x16963,x16961)))
% 4.60/4.59 [1697]~P2(x16971)+P10(a1,f26(x16971,f27(f27(f10(x16971),x16972),x16973)),f27(f27(f10(a1),f26(x16971,x16972)),f35(x16973,x16971)))
% 4.60/4.59 [1730]P12(a68,x17301,x17302)+~P12(a68,x17301,f11(a68,x17302,f27(f27(f10(a68),x17301),x17303)))
% 4.60/4.59 [1731]~P55(x17311)+P10(x17311,f8(x17311),f11(x17311,f27(f27(f10(x17311),x17312),x17312),f27(f27(f10(x17311),x17313),x17313)))
% 4.60/4.59 [1773]~P70(x17731)+E(f27(f27(f10(x17731),f27(f27(f13(x17731),f9(x17731,f3(x17731))),x17732)),f27(f27(f13(x17731),x17733),x17732)),f27(f27(f13(x17731),f9(x17731,x17733)),x17732))
% 4.60/4.59 [1782]E(x17821,x17822)+~E(f27(f27(f10(a70),f11(a70,x17823,f3(a70))),x17821),f27(f27(f10(a70),f11(a70,x17823,f3(a70))),x17822))
% 4.60/4.59 [1785]~P55(x17851)+~P11(x17851,f11(x17851,f27(f27(f10(x17851),x17852),x17852),f27(f27(f10(x17851),x17853),x17853)),f8(x17851))
% 4.60/4.59 [1804]~P11(a70,x18042,x18043)+P11(a70,f27(f27(f10(a70),f11(a70,x18041,f3(a70))),x18042),f27(f27(f10(a70),f11(a70,x18041,f3(a70))),x18043))
% 4.60/4.59 [1813]~P2(x18131)+P10(a1,f26(x18131,f27(f27(f10(x18131),x18132),x18133)),f27(f27(f10(a1),f27(f27(f10(a1),f26(x18131,x18132)),f26(x18131,x18133))),f51(x18131)))
% 4.60/4.59 [1814]~P2(x18141)+P10(a1,f26(x18141,f27(f27(f10(x18141),x18142),x18143)),f27(f27(f10(a1),f27(f27(f10(a1),f26(x18141,x18142)),f26(x18141,x18143))),f30(x18141)))
% 4.60/4.59 [1815]~P2(x18151)+P10(a1,f26(x18151,f27(f27(f10(x18151),x18152),x18153)),f27(f27(f10(a1),f27(f27(f10(a1),f26(x18151,x18152)),f26(x18151,x18153))),f36(x18151)))
% 4.60/4.59 [1826]P10(a70,x18261,x18262)+~P10(a70,f27(f27(f10(a70),f11(a70,x18263,f3(a70))),x18261),f27(f27(f10(a70),f11(a70,x18263,f3(a70))),x18262))
% 4.60/4.59 [1829]~P45(x18291)+E(f6(x18291,f27(f27(f13(x18291),x18292),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70))),f27(f27(f13(x18291),x18293),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70)))),f27(f27(f10(x18291),f6(x18291,x18292,x18293)),f11(x18291,x18292,x18293)))
% 4.60/4.59 [1842]~P45(x18421)+E(f11(f71(x18421),f27(f27(f10(f71(x18421)),f15(x18421,f9(x18421,x18422),f15(x18421,f3(x18421),f8(f71(x18421))))),f23(x18421,x18423,x18422)),f15(x18421,f27(f14(x18421,x18423),x18422),f8(f71(x18421)))),x18423)
% 4.60/4.59 [1537]~P24(x15371)+E(f27(f27(f10(x15371),f27(f27(f13(x15371),x15372),x15373)),x15372),f27(f27(f10(x15371),x15372),f27(f27(f13(x15371),x15372),x15373)))
% 4.60/4.59 [1558]~P24(x15581)+E(f27(f27(f10(x15581),f27(f27(f13(x15581),x15582),x15583)),x15582),f27(f27(f13(x15581),x15582),f11(a70,x15583,f3(a70))))
% 4.60/4.59 [1559]~P43(x15591)+E(f27(f27(f10(x15591),f27(f27(f13(x15591),x15592),x15593)),x15592),f27(f27(f13(x15591),x15592),f11(a70,x15593,f3(a70))))
% 4.60/4.59 [1848]~P11(a68,f8(a68),x18483)+P11(a68,x18481,f11(a68,x18482,f27(f27(f10(a68),f11(a68,f5(a68,f6(a68,x18482,x18481)),f3(a68))),x18483)))
% 4.60/4.59 [1849]~P11(a68,f8(a68),x18493)+P11(a68,f6(a68,x18491,f27(f27(f10(a68),f11(a68,f5(a68,f6(a68,x18491,x18492)),f3(a68))),x18493)),x18492)
% 4.60/4.59 [1396]~P43(x13961)+E(f11(x13961,x13962,f11(x13961,x13963,x13964)),f11(x13961,x13963,f11(x13961,x13962,x13964)))
% 4.60/4.59 [1398]~P43(x13981)+E(f11(x13981,f11(x13981,x13982,x13983),x13984),f11(x13981,x13982,f11(x13981,x13983,x13984)))
% 4.60/4.59 [1399]~P7(x13991)+E(f11(x13991,f11(x13991,x13992,x13993),x13994),f11(x13991,x13992,f11(x13991,x13993,x13994)))
% 4.60/4.59 [1400]~P43(x14001)+E(f11(x14001,f11(x14001,x14002,x14003),x14004),f11(x14001,f11(x14001,x14002,x14004),x14003))
% 4.60/4.59 [1529]~P47(x15291)+E(f23(x15291,f15(x15291,x15292,x15293),x15294),f15(x15291,f27(f14(x15291,x15293),x15294),f23(x15291,x15293,x15294)))
% 4.60/4.59 [1566]~P47(x15661)+E(f15(x15661,f27(f27(f10(x15661),x15662),x15663),f21(x15661,x15662,x15664)),f21(x15661,x15662,f15(x15661,x15663,x15664)))
% 4.60/4.59 [1570]~P47(x15701)+E(f11(f71(x15701),f21(x15701,x15702,x15703),f21(x15701,x15704,x15703)),f21(x15701,f11(x15701,x15702,x15704),x15703))
% 4.60/4.59 [1571]~P46(x15711)+E(f6(f71(x15711),f21(x15711,x15712,x15713),f21(x15711,x15714,x15713)),f21(x15711,f6(x15711,x15712,x15714),x15713))
% 4.60/4.59 [947]~P34(x9472)+E(f27(f9(f75(x9471,x9472),x9473),x9474),f9(x9472,f27(x9473,x9474)))
% 4.60/4.59 [1490]~P47(x14901)+E(f27(f14(x14901,x14902),f27(f14(x14901,x14903),x14904)),f27(f14(x14901,f19(x14901,x14902,x14903)),x14904))
% 4.60/4.59 [1501]~P47(x15011)+E(f27(f27(f10(x15011),x15012),f27(f14(x15011,x15013),x15014)),f27(f14(x15011,f21(x15011,x15012,x15013)),x15014))
% 4.60/4.59 [1613]~P47(x16131)+E(f11(f71(x16131),f21(x16131,x16132,x16133),f21(x16131,x16132,x16134)),f21(x16131,x16132,f11(f71(x16131),x16133,x16134)))
% 4.60/4.59 [1767]~P47(x17671)+E(f11(f71(x17671),f15(x17671,x17672,f8(f71(x17671))),f27(f27(f10(f71(x17671)),x17673),f19(x17671,x17674,x17673))),f19(x17671,f15(x17671,x17672,x17674),x17673))
% 4.60/4.59 [1362]~P43(x13621)+E(f27(f27(f10(x13621),x13622),f27(f27(f10(x13621),x13623),x13624)),f27(f27(f10(x13621),x13623),f27(f27(f10(x13621),x13622),x13624)))
% 4.60/4.59 [1387]~P47(x13871)+E(f21(x13871,f27(f27(f10(x13871),x13872),x13873),x13874),f21(x13871,x13872,f21(x13871,x13873,x13874)))
% 4.60/4.59 [1553]~P2(x15531)+E(f11(x15531,f27(f27(f10(x15531),x15532),x15533),f27(f27(f10(x15531),x15532),x15534)),f27(f27(f10(x15531),x15532),f11(x15531,x15533,x15534)))
% 4.60/4.59 [1554]~P43(x15541)+E(f11(x15541,f27(f27(f10(x15541),x15542),x15543),f27(f27(f10(x15541),x15542),x15544)),f27(f27(f10(x15541),x15542),f11(x15541,x15543,x15544)))
% 4.60/4.59 [1556]~P2(x15561)+E(f6(x15561,f27(f27(f10(x15561),x15562),x15563),f27(f27(f10(x15561),x15562),x15564)),f27(f27(f10(x15561),x15562),f6(x15561,x15563,x15564)))
% 4.60/4.59 [1646]~P47(x16461)+E(f11(x16461,f27(f14(x16461,x16462),x16463),f27(f14(x16461,x16464),x16463)),f27(f14(x16461,f11(f71(x16461),x16462,x16464)),x16463))
% 4.60/4.59 [1647]~P46(x16471)+E(f6(x16471,f27(f14(x16471,x16472),x16473),f27(f14(x16471,x16474),x16473)),f27(f14(x16471,f6(f71(x16471),x16472,x16474)),x16473))
% 4.60/4.59 [1672]~P24(x16721)+E(f27(f27(f10(x16721),f27(f27(f13(x16721),x16722),x16723)),f27(f27(f13(x16721),x16722),x16724)),f27(f27(f13(x16721),x16722),f11(a70,x16723,x16724)))
% 4.60/4.59 [1673]~P43(x16731)+E(f27(f27(f10(x16731),f27(f27(f13(x16731),x16732),x16733)),f27(f27(f13(x16731),x16732),x16734)),f27(f27(f13(x16731),x16732),f11(a70,x16733,x16734)))
% 4.60/4.59 [1685]~P2(x16851)+E(f11(x16851,f27(f27(f10(x16851),x16852),x16853),f27(f27(f10(x16851),x16854),x16853)),f27(f27(f10(x16851),f11(x16851,x16852,x16854)),x16853))
% 4.60/4.59 [1687]~P44(x16871)+E(f11(x16871,f27(f27(f10(x16871),x16872),x16873),f27(f27(f10(x16871),x16874),x16873)),f27(f27(f10(x16871),f11(x16871,x16872,x16874)),x16873))
% 4.60/4.59 [1689]~P2(x16891)+E(f6(x16891,f27(f27(f10(x16891),x16892),x16893),f27(f27(f10(x16891),x16894),x16893)),f27(f27(f10(x16891),f6(x16891,x16892,x16894)),x16893))
% 4.60/4.59 [1690]~P43(x16901)+E(f11(x16901,f27(f27(f10(x16901),x16902),x16903),f27(f27(f10(x16901),x16904),x16903)),f27(f27(f10(x16901),f11(x16901,x16902,x16904)),x16903))
% 4.60/4.59 [1724]~P47(x17241)+E(f11(x17241,x17242,f27(f27(f10(x17241),x17243),f27(f14(x17241,x17244),x17243))),f27(f14(x17241,f15(x17241,x17242,x17244)),x17243))
% 4.60/4.59 [1502]~P47(x15021)+E(f21(x15021,x15022,f27(f27(f10(f71(x15021)),x15023),x15024)),f27(f27(f10(f71(x15021)),x15023),f21(x15021,x15022,x15024)))
% 4.60/4.59 [1526]~P43(x15261)+E(f27(f27(f13(x15261),f27(f27(f13(x15261),x15262),x15263)),x15264),f27(f27(f13(x15261),x15262),f27(f27(f10(a70),x15263),x15264)))
% 4.60/4.59 [1527]~P24(x15271)+E(f27(f27(f13(x15271),f27(f27(f13(x15271),x15272),x15273)),x15274),f27(f27(f13(x15271),x15272),f27(f27(f10(a70),x15273),x15274)))
% 4.60/4.59 [1535]~P43(x15351)+E(f27(f27(f10(x15351),f27(f27(f10(x15351),x15352),x15353)),x15354),f27(f27(f10(x15351),x15352),f27(f27(f10(x15351),x15353),x15354)))
% 4.60/4.59 [1536]~P6(x15361)+E(f27(f27(f10(x15361),f27(f27(f10(x15361),x15362),x15363)),x15364),f27(f27(f10(x15361),x15362),f27(f27(f10(x15361),x15363),x15364)))
% 4.60/4.59 [1648]~P47(x16481)+E(f21(x16481,x16482,f27(f27(f10(f71(x16481)),x16483),x16484)),f27(f27(f10(f71(x16481)),f21(x16481,x16482,x16483)),x16484))
% 4.60/4.59 [1671]~P43(x16711)+E(f27(f27(f10(x16711),f27(f27(f10(x16711),x16712),x16713)),x16714),f27(f27(f10(x16711),f27(f27(f10(x16711),x16712),x16714)),x16713))
% 4.60/4.59 [1737]~P43(x17371)+E(f27(f27(f10(x17371),f27(f27(f13(x17371),x17372),x17373)),f27(f27(f13(x17371),x17374),x17373)),f27(f27(f13(x17371),f27(f27(f10(x17371),x17372),x17374)),x17373))
% 4.60/4.59 [1738]~P19(x17381)+E(f27(f27(f10(x17381),f27(f27(f13(x17381),x17382),x17383)),f27(f27(f13(x17381),x17384),x17383)),f27(f27(f13(x17381),f27(f27(f10(x17381),x17382),x17384)),x17383))
% 4.60/4.59 [1762]~P47(x17621)+E(f11(f71(x17621),f27(f27(f10(f71(x17621)),x17622),x17623),f27(f27(f10(f71(x17621)),x17624),x17623)),f27(f27(f10(f71(x17621)),f11(f71(x17621),x17622,x17624)),x17623))
% 4.60/4.59 [1705]~P43(x17051)+E(f27(f14(x17051,f27(f27(f13(f71(x17051)),x17052),x17053)),x17054),f27(f27(f13(x17051),f27(f14(x17051,x17052),x17054)),x17053))
% 4.60/4.59 [1751]~P47(x17511)+E(f27(f27(f10(x17511),f27(f14(x17511,x17512),x17513)),f27(f14(x17511,x17514),x17513)),f27(f14(x17511,f27(f27(f10(f71(x17511)),x17512),x17514)),x17513))
% 4.60/4.59 [1774]~P47(x17741)+E(f11(f71(x17741),f21(x17741,x17742,x17743),f15(x17741,f8(x17741),f27(f27(f10(f71(x17741)),x17743),x17744))),f27(f27(f10(f71(x17741)),x17743),f15(x17741,x17742,x17744)))
% 4.60/4.59 [1784]~P47(x17841)+E(f11(f71(x17841),f21(x17841,x17842,x17843),f15(x17841,f8(x17841),f27(f27(f10(f71(x17841)),x17844),x17843))),f27(f27(f10(f71(x17841)),f15(x17841,x17842,x17844)),x17843))
% 4.60/4.59 [1703]~P43(x17031)+E(f11(x17031,f11(x17031,x17032,x17033),f11(x17031,x17034,x17035)),f11(x17031,f11(x17031,x17032,x17034),f11(x17031,x17033,x17035)))
% 4.60/4.59 [1308]~P22(x13082)+E(f27(f6(f75(x13081,x13082),x13083,x13084),x13085),f6(x13082,f27(x13083,x13085),f27(x13084,x13085)))
% 4.60/4.59 [1706]~P5(x17061)+E(f15(x17061,f11(x17061,x17062,x17063),f11(f71(x17061),x17064,x17065)),f11(f71(x17061),f15(x17061,x17062,x17064),f15(x17061,x17063,x17065)))
% 4.60/4.59 [1707]~P8(x17071)+E(f15(x17071,f6(x17071,x17072,x17073),f6(f71(x17071),x17074,x17075)),f6(f71(x17071),f15(x17071,x17072,x17074),f15(x17071,x17073,x17075)))
% 4.60/4.59 [1830]~P1(x18301)+P10(a1,f26(x18301,f6(x18301,f11(x18301,x18302,x18303),f11(x18301,x18304,x18305))),f11(a1,f26(x18301,f6(x18301,x18302,x18304)),f26(x18301,f6(x18301,x18303,x18305))))
% 4.60/4.59 [1831]~P3(x18311)+P10(x18311,f5(x18311,f6(x18311,f11(x18311,x18312,x18313),f11(x18311,x18314,x18315))),f11(x18311,f5(x18311,f6(x18311,x18312,x18314)),f5(x18311,f6(x18311,x18313,x18315))))
% 4.60/4.59 [1766]~P43(x17661)+E(f27(f27(f10(x17661),f27(f27(f10(x17661),x17662),x17663)),f27(f27(f10(x17661),x17664),x17665)),f27(f27(f10(x17661),f27(f27(f10(x17661),x17662),x17664)),f27(f27(f10(x17661),x17663),x17665)))
% 4.60/4.59 [1802]~P68(x18021)+E(f11(x18021,f27(f27(f10(x18021),x18022),f6(x18021,x18023,x18024)),f27(f27(f10(x18021),f6(x18021,x18022,x18025)),x18024)),f6(x18021,f27(f27(f10(x18021),x18022),x18023),f27(f27(f10(x18021),x18025),x18024)))
% 4.60/4.59 [1843]~P2(x18431)+E(f11(x18431,f11(x18431,f27(f27(f10(x18431),f6(x18431,x18432,x18433)),f6(x18431,x18434,x18435)),f27(f27(f10(x18431),f6(x18431,x18432,x18433)),x18435)),f27(f27(f10(x18431),x18433),f6(x18431,x18434,x18435))),f6(x18431,f27(f27(f10(x18431),x18432),x18434),f27(f27(f10(x18431),x18433),x18435)))
% 4.60/4.59 [1795]~P72(x17951)+E(f11(x17951,f27(f27(f10(x17951),x17952),x17953),f11(x17951,f27(f27(f10(x17951),x17954),x17953),x17955)),f11(x17951,f27(f27(f10(x17951),f11(x17951,x17952,x17954)),x17953),x17955))
% 4.60/4.59 [1850]~P28(x18505)+E(f27(f27(f27(x18501,x18502),x18503),f17(x18504,f29(x18503,f8(f71(x18505))),x18506,f22(x18504,x18505,x18506,x18501,x18503))),f22(x18504,x18505,x18506,x18501,f15(x18505,x18502,x18503)))
% 4.60/4.59 [875]E(x8751,f8(a68))+~P11(a68,f8(a68),x8751)+E(f12(a68,x8751),f3(a68))
% 4.60/4.59 [807]E(x8071,f8(a1))+P11(a1,f8(a1),x8071)+E(f12(a1,x8071),f9(a1,f3(a1)))
% 4.60/4.59 [808]E(x8081,f8(a68))+P11(a68,f8(a68),x8081)+E(f12(a68,x8081),f9(a68,f3(a68)))
% 4.60/4.59 [1763]E(x17631,f8(a70))+E(x17631,f11(a70,f8(a70),f3(a70)))+~P11(a70,x17631,f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70)))
% 4.60/4.59 [881]E(x8811,x8812)+P11(a70,x8812,x8811)+P11(a70,x8811,x8812)
% 4.60/4.59 [882]E(x8821,x8822)+P11(a68,x8822,x8821)+P11(a68,x8821,x8822)
% 4.60/4.59 [951]E(x9511,x9512)+P11(a1,x9511,x9512)+~P10(a1,x9511,x9512)
% 4.60/4.59 [954]E(x9541,x9542)+P11(a70,x9541,x9542)+~P10(a70,x9541,x9542)
% 4.60/4.59 [955]E(x9551,x9552)+P11(a68,x9551,x9552)+~P10(a68,x9551,x9552)
% 4.60/4.59 [1021]E(x10211,x10212)+~P10(a1,x10212,x10211)+~P10(a1,x10211,x10212)
% 4.60/4.59 [1022]E(x10221,x10222)+~P10(a70,x10222,x10221)+~P10(a70,x10221,x10222)
% 4.60/4.59 [1023]E(x10231,x10232)+~P10(a68,x10232,x10231)+~P10(a68,x10231,x10232)
% 4.60/4.59 [1032]E(x10321,x10322)+~P12(a70,x10322,x10321)+~P12(a70,x10321,x10322)
% 4.60/4.59 [652]~P4(x6521)+~E(x6522,f8(x6521))+E(f9(x6521,x6522),x6522)
% 4.60/4.59 [659]~P1(x6591)+~E(x6592,f8(x6591))+E(f26(x6591,x6592),f8(a1))
% 4.60/4.59 [660]~P20(x6601)+~E(f8(x6601),x6602)+E(f9(x6601,x6602),f8(x6601))
% 4.60/4.59 [661]~P3(x6611)+~E(x6612,f8(x6611))+E(f5(x6611,x6612),f8(x6611))
% 4.60/4.59 [662]~P1(x6621)+~E(x6622,f8(x6621))+E(f12(x6621,x6622),f8(x6621))
% 4.60/4.59 [663]~P51(x6631)+~E(x6632,f8(x6631))+E(f12(x6631,x6632),f8(x6631))
% 4.60/4.59 [664]~P33(x6641)+~E(x6642,f8(x6641))+E(f12(x6641,x6642),f8(x6641))
% 4.60/4.59 [665]~P20(x6651)+~E(x6652,f8(x6651))+E(f9(x6651,x6652),f8(x6651))
% 4.60/4.59 [668]~P4(x6682)+~E(f9(x6682,x6681),x6681)+E(x6681,f8(x6682))
% 4.60/4.59 [675]~P1(x6752)+E(x6751,f8(x6752))+~E(f26(x6752,x6751),f8(a1))
% 4.60/4.59 [676]~P3(x6762)+~E(f5(x6762,x6761),f8(x6762))+E(x6761,f8(x6762))
% 4.60/4.59 [677]~P1(x6772)+~E(f12(x6772,x6771),f8(x6772))+E(x6771,f8(x6772))
% 4.60/4.59 [678]~P51(x6782)+~E(f12(x6782,x6781),f8(x6782))+E(x6781,f8(x6782))
% 4.60/4.59 [679]~P20(x6792)+~E(f9(x6792,x6791),f8(x6792))+E(x6791,f8(x6792))
% 4.60/4.59 [680]~P20(x6801)+~E(f9(x6801,x6802),f8(x6801))+E(f8(x6801),x6802)
% 4.60/4.59 [734]~E(x7342,f8(a70))+~E(x7341,f8(a70))+E(f11(a70,x7341,x7342),f8(a70))
% 4.60/4.59 [769]~P4(x7691)+~E(x7692,f8(x7691))+E(f11(x7691,x7692,x7692),f8(x7691))
% 4.60/4.59 [787]~P17(x7871)+P11(x7871,x7872,f8(x7871))+E(f5(x7871,x7872),x7872)
% 4.60/4.59 [833]~P1(x8332)+E(x8331,f8(x8332))+P11(a1,f8(a1),f26(x8332,x8331))
% 4.60/4.59 [838]~P51(x8381)+P11(x8381,f8(x8381),x8382)+~E(f12(x8381,x8382),f3(x8381))
% 4.60/4.59 [848]~P1(x8481)+~E(x8482,f8(x8481))+P10(a1,f26(x8481,x8482),f8(a1))
% 4.60/4.59 [855]~P3(x8552)+P11(x8552,f8(x8552),f5(x8552,x8551))+E(x8551,f8(x8552))
% 4.60/4.59 [861]~P3(x8611)+P10(x8611,f5(x8611,x8612),f8(x8611))+~E(x8612,f8(x8611))
% 4.60/4.59 [865]~P4(x8652)+~E(f11(x8652,x8651,x8651),f8(x8652))+E(x8651,f8(x8652))
% 4.60/4.59 [878]~P43(x8782)+~P12(x8782,f8(x8782),x8781)+E(x8781,f8(x8782))
% 4.60/4.59 [904]~P3(x9041)+~P10(x9041,f8(x9041),x9042)+E(f5(x9041,x9042),x9042)
% 4.60/4.59 [905]~P3(x9051)+~P11(x9051,f8(x9051),x9052)+E(f5(x9051,x9052),x9052)
% 4.60/4.59 [916]~P51(x9161)+~P11(x9161,f8(x9161),x9162)+E(f12(x9161,x9162),f3(x9161))
% 4.60/4.59 [924]~P38(x9241)+P14(x9241,x9242)+P10(a70,f53(x9242,x9241),f55(x9242,x9241))
% 4.60/4.59 [929]~P3(x9291)+~P10(x9291,x9292,f8(x9291))+E(f9(x9291,x9292),f5(x9291,x9292))
% 4.60/4.59 [930]~P3(x9301)+~P11(x9301,x9302,f8(x9301))+E(f9(x9301,x9302),f5(x9301,x9302))
% 4.60/4.59 [931]~P17(x9311)+~P11(x9311,x9312,f8(x9311))+E(f9(x9311,x9312),f5(x9311,x9312))
% 4.60/4.59 [957]~P1(x9572)+E(x9571,f8(x9572))+~P10(a1,f26(x9572,x9571),f8(a1))
% 4.60/4.59 [963]~P1(x9632)+~E(x9631,f8(x9632))+~P11(a1,f8(a1),f26(x9632,x9631))
% 4.60/4.59 [973]~P3(x9732)+~P10(x9732,f5(x9732,x9731),f8(x9732))+E(x9731,f8(x9732))
% 4.60/4.59 [998]~P3(x9982)+~P11(x9982,f8(x9982),f5(x9982,x9981))+~E(x9981,f8(x9982))
% 4.60/4.59 [1084]~P4(x10841)+~P10(x10841,x10842,f8(x10841))+P10(x10841,x10842,f9(x10841,x10842))
% 4.60/4.59 [1085]~P51(x10851)+~P11(x10851,x10852,f8(x10851))+P11(x10851,x10852,f9(x10851,x10852))
% 4.60/4.59 [1086]~P4(x10861)+~P10(x10861,f8(x10861),x10862)+P10(x10861,f9(x10861,x10862),x10862)
% 4.60/4.59 [1087]~P4(x10871)+~P11(x10871,f8(x10871),x10872)+P11(x10871,f9(x10871,x10872),x10872)
% 4.60/4.59 [1091]~P12(a68,x10912,x10911)+E(x10911,f8(a68))+P10(a68,f5(a68,x10912),f5(a68,x10911))
% 4.60/4.59 [1104]~P25(x11041)+~P10(x11041,x11042,f8(x11041))+P10(x11041,f8(x11041),f9(x11041,x11042))
% 4.60/4.59 [1105]~P25(x11051)+~P11(x11051,x11052,f8(x11051))+P11(x11051,f8(x11051),f9(x11051,x11052))
% 4.60/4.59 [1106]~P51(x11061)+~P11(x11061,f8(x11061),x11062)+P11(x11061,f8(x11061),f12(x11061,x11062))
% 4.60/4.59 [1107]~P51(x11071)+~P11(x11071,x11072,f8(x11071))+P11(x11071,f12(x11071,x11072),f8(x11071))
% 4.60/4.59 [1108]~P25(x11081)+~P10(x11081,f8(x11081),x11082)+P10(x11081,f9(x11081,x11082),f8(x11081))
% 4.60/4.59 [1109]~P25(x11091)+~P11(x11091,f8(x11091),x11092)+P11(x11091,f9(x11091,x11092),f8(x11091))
% 4.60/4.59 [1112]~P12(a68,x11122,x11121)+~P12(a68,x11121,x11122)+E(f5(a68,x11121),f5(a68,x11122))
% 4.60/4.59 [1113]~P4(x11131)+~P10(x11131,x11132,f9(x11131,x11132))+P10(x11131,x11132,f8(x11131))
% 4.60/4.59 [1114]~P51(x11141)+~P11(x11141,x11142,f9(x11141,x11142))+P11(x11141,x11142,f8(x11141))
% 4.60/4.59 [1115]~P4(x11151)+~P10(x11151,f9(x11151,x11152),x11152)+P10(x11151,f8(x11151),x11152)
% 4.60/4.59 [1116]~P4(x11161)+~P11(x11161,f9(x11161,x11162),x11162)+P11(x11161,f8(x11161),x11162)
% 4.60/4.59 [1131]~P25(x11311)+~P10(x11311,f8(x11311),f9(x11311,x11312))+P10(x11311,x11312,f8(x11311))
% 4.60/4.59 [1132]~P25(x11321)+~P11(x11321,f8(x11321),f9(x11321,x11322))+P11(x11321,x11322,f8(x11321))
% 4.60/4.59 [1133]~P51(x11331)+~P11(x11331,f12(x11331,x11332),f8(x11331))+P11(x11331,x11332,f8(x11331))
% 4.60/4.59 [1134]~P51(x11341)+~P11(x11341,f8(x11341),f12(x11341,x11342))+P11(x11341,f8(x11341),x11342)
% 4.60/4.59 [1135]~P25(x11351)+~P10(x11351,f9(x11351,x11352),f8(x11351))+P10(x11351,f8(x11351),x11352)
% 4.60/4.59 [1136]~P25(x11361)+~P11(x11361,f9(x11361,x11362),f8(x11361))+P11(x11361,f8(x11361),x11362)
% 4.60/4.59 [1175]~P12(a70,x11751,x11752)+P10(a70,x11751,x11752)+~P11(a70,f8(a70),x11752)
% 4.60/4.59 [1176]~P12(a68,x11761,x11762)+P10(a68,x11761,x11762)+~P11(a68,f8(a68),x11762)
% 4.60/4.59 [1182]~P12(a70,x11821,x11822)+~P11(a70,f8(a70),x11822)+P11(a70,f8(a70),x11821)
% 4.60/4.59 [1262]~P12(a70,x12622,x12621)+~P11(a70,x12621,x12622)+~P11(a70,f8(a70),x12621)
% 4.60/4.59 [1263]~P12(a68,x12632,x12631)+~P11(a68,x12631,x12632)+~P11(a68,f8(a68),x12631)
% 4.60/4.59 [1265]~P10(a70,f7(x12651),x12652)+P10(a1,x12651,f25(a70,x12652))+~P10(a1,f8(a1),x12651)
% 4.60/4.59 [1266]~P10(a70,x12661,f24(x12662))+P10(a1,f25(a70,x12661),x12662)+~P10(a1,f8(a1),x12662)
% 4.60/4.59 [1267]~P11(a1,f8(a1),x12671)+~P11(a70,f8(a70),x12672)+P11(a1,f8(a1),f58(x12671,x12672))
% 4.60/4.59 [1268]~P11(a1,f8(a1),x12681)+~P11(a70,f8(a70),x12682)+P11(a1,f8(a1),f59(x12681,x12682))
% 4.60/4.59 [1281]P11(a70,f24(x12811),x12812)+~P11(a1,x12811,f25(a70,x12812))+~P10(a1,f8(a1),x12811)
% 4.60/4.59 [1284]~P4(x12841)+~P10(x12841,f8(x12841),x12842)+P10(x12841,f8(x12841),f11(x12841,x12842,x12842))
% 4.60/4.59 [1285]~P4(x12851)+~P11(x12851,f8(x12851),x12852)+P11(x12851,f8(x12851),f11(x12851,x12852,x12852))
% 4.60/4.59 [1286]~P4(x12861)+~P10(x12861,x12862,f8(x12861))+P10(x12861,f11(x12861,x12862,x12862),f8(x12861))
% 4.60/4.59 [1287]~P4(x12871)+~P11(x12871,x12872,f8(x12871))+P11(x12871,f11(x12871,x12872,x12872),f8(x12871))
% 4.60/4.59 [1288]~P51(x12881)+~P11(x12881,x12882,f8(x12881))+P11(x12881,f11(x12881,x12882,x12882),f8(x12881))
% 4.60/4.59 [1307]~P10(a1,x13071,x13072)+~P10(a1,f9(a1,x13072),x13071)+P10(a1,f5(a1,x13071),x13072)
% 4.60/4.59 [1402]~P4(x14021)+~P10(x14021,f11(x14021,x14022,x14022),f8(x14021))+P10(x14021,x14022,f8(x14021))
% 4.60/4.59 [1403]~P4(x14031)+~P11(x14031,f11(x14031,x14032,x14032),f8(x14031))+P11(x14031,x14032,f8(x14031))
% 4.60/4.59 [1404]~P51(x14041)+~P11(x14041,f11(x14041,x14042,x14042),f8(x14041))+P11(x14041,x14042,f8(x14041))
% 4.60/4.59 [1405]~P4(x14051)+~P10(x14051,f8(x14051),f11(x14051,x14052,x14052))+P10(x14051,f8(x14051),x14052)
% 4.60/4.59 [1406]~P4(x14061)+~P11(x14061,f8(x14061),f11(x14061,x14062,x14062))+P11(x14061,f8(x14061),x14062)
% 4.60/4.59 [1414]~P10(a68,f8(a68),x14142)+~P10(a68,f8(a68),x14141)+P10(a68,f8(a68),f11(a68,x14141,x14142))
% 4.60/4.59 [1476]P11(a70,f8(a70),x14761)+P11(a70,f8(a70),x14762)+~P11(a70,f8(a70),f11(a70,x14762,x14761))
% 4.60/4.59 [693]~P1(x6932)+E(x6931,f8(x6932))+E(f26(x6932,f12(x6932,x6931)),f3(a1))
% 4.60/4.59 [694]~P51(x6941)+~E(x6942,f8(f71(x6941)))+E(f12(f71(x6941),x6942),f8(f71(x6941)))
% 4.60/4.59 [704]~P1(x7041)+~E(x7042,f8(x7041))+E(f26(x7041,f12(x7041,x7042)),f8(a1))
% 4.60/4.59 [876]~P51(x8761)+P11(f71(x8761),x8762,f8(f71(x8761)))+E(f5(f71(x8761),x8762),x8762)
% 4.60/4.59 [917]~P51(x9171)+P11(x9171,x9172,f8(x9171))+~E(f12(x9171,x9172),f9(x9171,f3(x9171)))
% 4.60/4.59 [943]~P51(x9431)+~P11(x9431,x9432,f8(x9431))+E(f12(x9431,x9432),f9(x9431,f3(x9431)))
% 4.60/4.59 [1006]P11(a70,f32(x10062,x10061),x10062)+~P74(f27(x10061,x10062))+P74(f27(x10061,f8(a70)))
% 4.60/4.59 [1035]~P51(x10351)+~P11(f71(x10351),x10352,f8(f71(x10351)))+E(f9(f71(x10351),x10352),f5(f71(x10351),x10352))
% 4.60/4.59 [1082]E(x10821,f8(a70))+E(x10822,f8(a70))+~E(f11(a70,x10822,x10821),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1083]E(x10831,f8(a70))+E(x10832,f8(a70))+~E(f11(a70,f8(a70),f3(a70)),f11(a70,x10832,x10831))
% 4.60/4.59 [1140]~E(x11402,f8(a70))+~E(x11401,f11(a70,f8(a70),f3(a70)))+E(f11(a70,x11401,x11402),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1141]~E(x11411,f8(a70))+~E(x11412,f11(a70,f8(a70),f3(a70)))+E(f11(a70,x11411,x11412),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1142]~E(x11422,f8(a70))+~E(x11421,f11(a70,f8(a70),f3(a70)))+E(f11(a70,f8(a70),f3(a70)),f11(a70,x11421,x11422))
% 4.60/4.59 [1143]~E(x11431,f8(a70))+~E(x11432,f11(a70,f8(a70),f3(a70)))+E(f11(a70,f8(a70),f3(a70)),f11(a70,x11431,x11432))
% 4.60/4.59 [1207]E(x12071,f8(a70))+E(x12071,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,x12072,x12071),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1208]E(x12081,f8(a70))+E(x12081,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,x12081,x12082),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1209]E(x12091,f8(a70))+E(x12091,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,f8(a70),f3(a70)),f11(a70,x12092,x12091))
% 4.60/4.59 [1210]E(x12101,f8(a70))+E(x12101,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,f8(a70),f3(a70)),f11(a70,x12101,x12102))
% 4.60/4.59 [1323]E(x13231,f11(a70,f8(a70),f3(a70)))+E(x13232,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,x13231,x13232),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1324]E(x13241,f11(a70,f8(a70),f3(a70)))+E(x13242,f11(a70,f8(a70),f3(a70)))+~E(f11(a70,f8(a70),f3(a70)),f11(a70,x13241,x13242))
% 4.60/4.59 [1338]~P11(a70,x13381,x13382)+P11(a70,f11(a70,x13381,f3(a70)),x13382)+E(f11(a70,x13381,f3(a70)),x13382)
% 4.60/4.59 [1358]E(x13581,x13582)+P11(a70,x13581,x13582)+~P11(a70,x13581,f11(a70,x13582,f3(a70)))
% 4.60/4.59 [1359]E(x13591,x13592)+P11(a68,x13591,x13592)+~P11(a68,x13591,f11(a68,x13592,f3(a68)))
% 4.60/4.59 [1416]P11(a70,f42(x14162,x14161),x14162)+E(x14161,f8(a70))+~P11(a70,x14161,f11(a70,x14162,f3(a70)))
% 4.60/4.59 [1421]E(x14211,x14212)+~P10(a70,x14212,x14211)+~P11(a70,x14211,f11(a70,x14212,f3(a70)))
% 4.60/4.59 [1422]E(x14221,f8(a70))+~P11(a70,x14221,f11(a70,x14222,f3(a70)))+E(f11(a70,f42(x14222,x14221),f3(a70)),x14221)
% 4.60/4.59 [1439]~P38(x14391)+P14(x14391,x14392)+~P10(x14391,f27(x14392,f55(x14392,x14391)),f27(x14392,f53(x14392,x14391)))
% 4.60/4.59 [1486]P10(a70,x14861,x14862)+~P10(a70,x14861,f11(a70,x14862,f3(a70)))+E(x14861,f11(a70,x14862,f3(a70)))
% 4.60/4.59 [1609]E(f24(x16091),x16092)+~P10(a1,f25(a70,x16092),x16091)+~P11(a1,x16091,f11(a1,f25(a70,x16092),f3(a1)))
% 4.60/4.59 [1653]~P11(a1,f25(a70,x16532),x16531)+~P10(a1,x16531,f11(a1,f25(a70,x16532),f3(a1)))+E(f7(x16531),f11(a70,x16532,f3(a70)))
% 4.60/4.59 [712]~E(x7122,f3(a70))+~E(x7121,f3(a70))+E(f27(f27(f10(a70),x7121),x7122),f3(a70))
% 4.60/4.59 [762]~P69(x7621)+~E(x7622,f3(x7621))+E(f27(f27(f10(x7621),x7622),x7622),f3(x7621))
% 4.60/4.59 [785]E(x7851,f3(a70))+E(x7852,f8(a70))+~E(f27(f27(f10(a70),x7852),x7851),x7852)
% 4.60/4.59 [788]E(x7881,f8(a70))+E(x7882,f8(a70))+~E(f27(f27(f10(a70),x7882),x7881),f8(a70))
% 4.60/4.59 [846]~P69(x8461)+~E(x8462,f9(x8461,f3(x8461)))+E(f27(f27(f10(x8461),x8462),x8462),f3(x8461))
% 4.60/4.59 [1017]E(x10171,f3(a68))+~P11(a68,f8(a68),x10172)+~E(f27(f27(f10(a68),x10172),x10171),f3(a68))
% 4.60/4.59 [1018]E(x10181,f3(a68))+~P11(a68,f8(a68),x10181)+~E(f27(f27(f10(a68),x10181),x10182),f3(a68))
% 4.60/4.59 [1034]E(x10341,f8(a68))+~E(f5(a68,x10342),f3(a68))+P12(a68,f27(f27(f10(a68),x10341),x10342),x10341)
% 4.60/4.59 [1111]~P73(x11111)+~P40(x11111)+E(f27(f27(f13(x11111),f8(x11111)),f11(a70,x11112,f3(a70))),f8(x11111))
% 4.60/4.59 [1183]E(x11831,f8(a70))+E(x11832,f11(a70,f8(a70),f3(a70)))+~E(f27(f27(f13(a70),x11832),x11831),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1203]~E(x12032,f3(a70))+~P11(a70,f8(a70),x12031)+P12(a70,f27(f27(f10(a70),x12031),x12032),x12031)
% 4.60/4.59 [1204]~E(x12041,f3(a70))+~P11(a70,f8(a70),x12042)+P12(a70,f27(f27(f10(a70),x12041),x12042),x12042)
% 4.60/4.59 [1230]E(x12301,f8(a68))+E(f5(a68,x12302),f3(a68))+~P12(a68,f27(f27(f10(a68),x12301),x12302),x12301)
% 4.60/4.59 [1300]~P11(a1,f8(a1),x13001)+~P11(a70,f8(a70),x13002)+E(f27(f27(f13(a1),f58(x13001,x13002)),x13002),x13001)
% 4.60/4.59 [1301]~P11(a1,f8(a1),x13011)+~P11(a70,f8(a70),x13012)+E(f27(f27(f13(a1),f59(x13011,x13012)),x13012),x13011)
% 4.60/4.59 [1316]E(x13161,f8(a70))+P11(a70,f8(a70),x13162)+~P11(a70,f8(a70),f27(f27(f13(a70),x13162),x13161))
% 4.60/4.59 [1318]~E(x13182,f11(a70,f8(a70),f3(a70)))+~E(x13181,f11(a70,f8(a70),f3(a70)))+E(f27(f27(f10(a70),x13181),x13182),f11(a70,f8(a70),f3(a70)))
% 4.60/4.59 [1368]E(x13681,f3(a70))+~P11(a70,f8(a70),x13682)+~P12(a70,f27(f27(f10(a70),x13682),x13681),x13682)
% 4.60/4.59 [1369]E(x13691,f3(a70))+~P11(a70,f8(a70),x13692)+~P12(a70,f27(f27(f10(a70),x13691),x13692),x13692)
% 4.60/4.59 [1384]~P10(a68,f8(a68),x13842)+~P10(a68,f8(a68),x13841)+P10(a68,f8(a68),f27(f27(f10(a68),x13841),x13842))
% 4.60/4.59 [1385]~P11(a1,f8(a1),x13852)+~P11(a1,f8(a1),x13851)+P11(a1,f8(a1),f27(f27(f10(a1),x13851),x13852))
% 4.60/4.59 [1386]~P11(a70,f8(a70),x13862)+~P11(a70,f8(a70),x13861)+P11(a70,f8(a70),f27(f27(f10(a70),x13861),x13862))
% 4.60/4.59 [1491]E(x14911,f8(a70))+~E(x14912,f8(a68))+~P11(a68,f8(a68),f27(f27(f13(a68),f5(a68,x14912)),x14911))
% 4.60/4.59 [1568]~P74(f27(x15681,x15682))+P74(f27(x15681,f8(a70)))+P74(f27(x15681,f11(a70,f32(x15682,x15681),f3(a70))))
% 4.60/4.59 [1757]~P11(a70,f11(a70,f8(a70),f3(a70)),x17572)+~P11(a70,f11(a70,f8(a70),f3(a70)),x17571)+P11(a70,x17571,f27(f27(f10(a70),x17572),x17571))
% 4.60/4.59 [1758]~P11(a70,f11(a70,f8(a70),f3(a70)),x17582)+~P11(a70,f11(a70,f8(a70),f3(a70)),x17581)+P11(a70,x17581,f27(f27(f10(a70),x17581),x17582))
% 4.60/4.59 [1775]~P10(a70,f11(a70,f8(a70),f3(a70)),x17752)+~P10(a70,f11(a70,f8(a70),f3(a70)),x17751)+P10(a70,f11(a70,f8(a70),f3(a70)),f27(f27(f10(a70),x17751),x17752))
% 4.60/4.59 [1776]~P11(a70,f11(a70,f8(a70),f3(a70)),x17761)+~P11(a70,f11(a70,f8(a70),f3(a70)),x17762)+P11(a70,f11(a70,f8(a70),f3(a70)),f27(f27(f10(a70),x17761),x17762))
% 4.60/4.59 [1246]~E(x12462,f8(a1))+~E(x12461,f8(a1))+E(f11(a1,f27(f27(f10(a1),x12461),x12461),f27(f27(f10(a1),x12462),x12462)),f8(a1))
% 4.60/4.59 [1704]~P10(a1,f8(a1),x17042)+~P10(a1,f8(a1),x17041)+P10(a70,f27(f27(f10(a70),f24(x17041)),f24(x17042)),f24(f27(f27(f10(a1),x17041),x17042)))
% 4.60/4.59 [725]~E(x7252,x7253)+~P26(x7251)+P10(x7251,x7252,x7253)
% 4.60/4.59 [727]~E(x7272,x7273)+~P38(x7271)+P10(x7271,x7272,x7273)
% 4.60/4.59 [844]~P11(x8443,x8441,x8442)+~E(x8441,x8442)+~P27(x8443)
% 4.60/4.59 [845]~P11(x8453,x8451,x8452)+~E(x8451,x8452)+~P38(x8453)
% 4.60/4.59 [898]P10(x8981,x8983,x8982)+~P27(x8981)+P10(x8981,x8982,x8983)
% 4.60/4.59 [903]P11(x9031,x9033,x9032)+~P27(x9031)+P10(x9031,x9032,x9033)
% 4.60/4.59 [970]~P26(x9701)+~P11(x9701,x9702,x9703)+P10(x9701,x9702,x9703)
% 4.60/4.59 [972]~P38(x9721)+~P11(x9721,x9722,x9723)+P10(x9721,x9722,x9723)
% 4.60/4.59 [1053]~P11(x10531,x10533,x10532)+~P26(x10531)+~P10(x10531,x10532,x10533)
% 4.60/4.59 [1057]~P11(x10571,x10573,x10572)+~P26(x10571)+~P11(x10571,x10572,x10573)
% 4.60/4.59 [1060]~P11(x10601,x10603,x10602)+~P27(x10601)+~P10(x10601,x10602,x10603)
% 4.60/4.59 [1061]~P11(x10611,x10613,x10612)+~P27(x10611)+~P11(x10611,x10612,x10613)
% 4.60/4.59 [1062]~P11(x10621,x10623,x10622)+~P38(x10621)+~P11(x10621,x10622,x10623)
% 4.60/4.59 [1164]~P10(a1,x11641,x11643)+P10(a1,x11641,x11642)+~P10(a1,x11643,x11642)
% 4.60/4.59 [1165]~P10(a70,x11651,x11653)+P10(a70,x11651,x11652)+~P10(a70,x11653,x11652)
% 4.60/4.59 [1166]~P10(a68,x11661,x11663)+P10(a68,x11661,x11662)+~P10(a68,x11663,x11662)
% 4.60/4.59 [1167]~P12(a70,x11671,x11673)+P12(a70,x11671,x11672)+~P12(a70,x11673,x11672)
% 4.60/4.59 [683]~P20(x6832)+~E(x6833,f9(x6832,x6831))+E(x6831,f9(x6832,x6833))
% 4.60/4.59 [685]~P20(x6851)+~E(f9(x6851,x6853),x6852)+E(f9(x6851,x6852),x6853)
% 4.60/4.59 [689]~P20(x6893)+E(x6891,x6892)+~E(f9(x6893,x6891),f9(x6893,x6892))
% 4.60/4.59 [690]~P36(x6903)+E(x6901,x6902)+~E(f9(x6903,x6901),f9(x6903,x6902))
% 4.60/4.59 [746]~E(x7462,x7463)+~P20(x7461)+E(f6(x7461,x7462,x7463),f8(x7461))
% 4.60/4.59 [747]~E(x7472,x7473)+~P8(x7471)+E(f6(x7471,x7472,x7473),f8(x7471))
% 4.60/4.59 [758]~P48(x7581)+~E(x7583,f8(x7581))+E(f11(x7581,x7582,x7583),x7582)
% 4.60/4.59 [759]~E(x7592,x7593)+~P51(x7591)+P10(f71(x7591),x7592,x7593)
% 4.60/4.59 [816]~P20(x8161)+~E(x8163,f9(x8161,x8162))+E(f11(x8161,x8162,x8163),f8(x8161))
% 4.60/4.59 [817]~P20(x8171)+~E(x8172,f9(x8171,x8173))+E(f11(x8171,x8172,x8173),f8(x8171))
% 4.60/4.59 [856]~P48(x8562)+~E(f11(x8562,x8563,x8561),x8563)+E(x8561,f8(x8562))
% 4.60/4.59 [859]~P20(x8593)+E(x8591,x8592)+~E(f6(x8593,x8591,x8592),f8(x8593))
% 4.60/4.59 [860]~P8(x8603)+E(x8601,x8602)+~E(f6(x8603,x8601,x8602),f8(x8603))
% 4.60/4.59 [866]~P51(x8661)+P12(x8661,x8662,x8663)+~E(f5(x8661,x8662),f5(x8661,x8663))
% 4.60/4.59 [893]~P20(x8932)+~E(f11(x8932,x8933,x8931),f8(x8932))+E(x8931,f9(x8932,x8933))
% 4.60/4.59 [894]~P20(x8942)+~E(f11(x8942,x8941,x8943),f8(x8942))+E(x8941,f9(x8942,x8943))
% 4.60/4.59 [895]~P20(x8951)+~E(f11(x8951,x8952,x8953),f8(x8951))+E(f9(x8951,x8952),x8953)
% 4.60/4.59 [996]~P51(x9961)+~P13(x9961,x9963)+P13(x9961,f15(x9961,x9962,x9963))
% 4.60/4.59 [1041]~P51(x10411)+~P12(x10411,x10412,x10413)+P12(x10411,x10412,f5(x10411,x10413))
% 4.60/4.59 [1042]~P45(x10421)+~P12(x10421,x10422,x10423)+P12(x10421,x10422,f9(x10421,x10423))
% 4.60/4.59 [1043]~P51(x10431)+~P12(x10431,x10432,x10433)+P12(x10431,f5(x10431,x10432),x10433)
% 4.60/4.59 [1044]~P45(x10441)+~P12(x10441,x10442,x10443)+P12(x10441,f9(x10441,x10442),x10443)
% 4.60/4.59 [1093]~P51(x10931)+P12(x10931,x10932,x10933)+~P12(x10931,x10932,f5(x10931,x10933))
% 4.60/4.59 [1094]~P45(x10941)+P12(x10941,x10942,x10943)+~P12(x10941,x10942,f9(x10941,x10943))
% 4.60/4.59 [1096]~P3(x10961)+P10(x10961,x10962,x10963)+~P10(x10961,f5(x10961,x10962),x10963)
% 4.60/4.59 [1097]~P51(x10971)+P11(x10971,x10972,x10973)+~P11(x10971,f5(x10971,x10972),x10973)
% 4.60/4.59 [1098]~P51(x10981)+P12(x10981,x10982,x10983)+~P12(x10981,f5(x10981,x10982),x10983)
% 4.60/4.59 [1099]~P45(x10991)+P12(x10991,x10992,x10993)+~P12(x10991,f9(x10991,x10992),x10993)
% 4.60/4.59 [1122]~P25(x11221)+~P10(x11221,x11223,x11222)+P10(x11221,f9(x11221,x11222),f9(x11221,x11223))
% 4.60/4.59 [1124]~P36(x11241)+~P10(x11241,x11243,x11242)+P10(x11241,f9(x11241,x11242),f9(x11241,x11243))
% 4.60/4.59 [1125]~P25(x11251)+~P11(x11251,x11253,x11252)+P11(x11251,f9(x11251,x11252),f9(x11251,x11253))
% 4.60/4.59 [1147]~P25(x11471)+~P10(x11471,x11473,f9(x11471,x11472))+P10(x11471,x11472,f9(x11471,x11473))
% 4.60/4.59 [1149]~P25(x11491)+~P11(x11491,x11493,f9(x11491,x11492))+P11(x11491,x11492,f9(x11491,x11493))
% 4.60/4.59 [1151]~P25(x11511)+~P10(x11511,f9(x11511,x11513),x11512)+P10(x11511,f9(x11511,x11512),x11513)
% 4.60/4.59 [1153]~P3(x11531)+~P10(x11531,f5(x11531,x11532),x11533)+P10(x11531,f9(x11531,x11532),x11533)
% 4.60/4.59 [1155]~P25(x11551)+~P11(x11551,f9(x11551,x11553),x11552)+P11(x11551,f9(x11551,x11552),x11553)
% 4.60/4.59 [1156]~P51(x11561)+~P11(x11561,f5(x11561,x11562),x11563)+P11(x11561,f9(x11561,x11562),x11563)
% 4.60/4.59 [1170]~P10(a70,x11703,x11701)+~E(f6(a70,x11701,x11703),x11702)+E(x11701,f11(a70,x11702,x11703))
% 4.60/4.59 [1171]~P10(a70,x11712,x11711)+~E(x11711,f11(a70,x11713,x11712))+E(f6(a70,x11711,x11712),x11713)
% 4.60/4.59 [1184]~P25(x11841)+P10(x11841,x11842,x11843)+~P10(x11841,f9(x11841,x11843),f9(x11841,x11842))
% 4.60/4.59 [1185]~P36(x11851)+P10(x11851,x11852,x11853)+~P10(x11851,f9(x11851,x11853),f9(x11851,x11852))
% 4.60/4.59 [1186]~P25(x11861)+P11(x11861,x11862,x11863)+~P11(x11861,f9(x11861,x11863),f9(x11861,x11862))
% 4.60/4.59 [1269]~P25(x12691)+~P10(x12691,x12692,x12693)+P10(x12691,f6(x12691,x12692,x12693),f8(x12691))
% 4.60/4.59 [1270]~P25(x12701)+~P11(x12701,x12702,x12703)+P11(x12701,f6(x12701,x12702,x12703),f8(x12701))
% 4.60/4.59 [1388]~P25(x13881)+P10(x13881,x13882,x13883)+~P10(x13881,f6(x13881,x13882,x13883),f8(x13881))
% 4.60/4.59 [1389]~P25(x13891)+P11(x13891,x13892,x13893)+~P11(x13891,f6(x13891,x13892,x13893),f8(x13891))
% 4.60/4.59 [1492]P12(a68,x14921,x14922)+~P12(a68,x14921,x14923)+~P12(a68,x14921,f6(a68,x14922,x14923))
% 4.60/4.59 [1564]~P10(a70,x15642,x15641)+~P11(a70,x15641,x15643)+P11(a70,f6(a70,x15641,x15642),f6(a70,x15643,x15642))
% 4.60/4.59 [1639]~P10(a70,x16393,x16392)+~P10(a70,f11(a70,x16391,x16393),x16392)+P10(a70,x16391,f6(a70,x16392,x16393))
% 4.60/4.59 [1640]~P10(a70,x16402,x16403)+~P10(a70,x16401,f6(a70,x16403,x16402))+P10(a70,f11(a70,x16401,x16402),x16403)
% 4.60/4.59 [745]~P53(x7451)+~E(x7452,f8(f71(x7451)))+E(f27(f14(x7451,x7452),x7453),f8(x7451))
% 4.60/4.59 [779]~P53(x7791)+~E(x7792,f8(x7791))+E(f21(x7791,x7792,x7793),f8(f71(x7791)))
% 4.60/4.59 [819]~P53(x8191)+~E(x8193,f8(f71(x8191)))+E(f21(x8191,x8192,x8193),f8(f71(x8191)))
% 4.60/4.59 [879]~P53(x8791)+E(f18(x8791,x8792,x8793),f8(a70))+E(f27(f14(x8791,x8793),x8792),f8(x8791))
% 4.60/4.59 [892]~P28(x8922)+E(x8921,f8(x8922))+~E(f15(x8922,x8921,x8923),f8(f71(x8922)))
% 4.60/4.59 [913]~P28(x9132)+~E(f15(x9132,x9133,x9131),f8(f71(x9132)))+E(x9131,f8(f71(x9132)))
% 4.60/4.59 [1302]~P51(x13021)+P10(f71(x13021),x13022,x13023)+~P13(x13021,f6(f71(x13021),x13023,x13022))
% 4.60/4.59 [1401]~P11(a70,x14011,x14013)+~P11(a70,x14013,x14012)+P11(a70,f11(a70,x14011,f3(a70)),x14012)
% 4.60/4.59 [1410]~P11(a70,x14103,x14102)+P11(a70,x14101,f11(a70,x14102,f3(a70)))+~E(x14101,f11(a70,x14103,f3(a70)))
% 4.60/4.59 [1557]E(x15571,f8(a1))+~P10(a1,x15572,f8(a1))+~P10(a1,f5(a1,x15571),f27(f27(f10(a1),x15572),f5(a1,x15573)))
% 4.60/4.59 [1607]P11(a70,x16072,x16071)+E(f11(a70,x16071,f61(x16071,x16072,x16073)),x16072)+P74(f27(x16073,f6(a70,x16072,x16071)))
% 4.60/4.59 [1608]P11(a70,x16082,x16081)+E(f11(a70,x16081,f63(x16081,x16082,x16083)),x16082)+P74(f27(x16083,f6(a70,x16082,x16081)))
% 4.60/4.59 [1615]E(f11(a70,x16151,f61(x16151,x16152,x16153)),x16152)+P74(f27(x16153,f6(a70,x16152,x16151)))+~P74(f27(x16153,f8(a70)))
% 4.60/4.59 [1616]E(f11(a70,x16161,f63(x16161,x16162,x16163)),x16162)+P74(f27(x16163,f6(a70,x16162,x16161)))+~P74(f27(x16163,f8(a70)))
% 4.60/4.59 [1644]~P11(a70,x16442,x16443)+~P74(f27(x16441,f6(a70,x16442,x16443)))+P74(f27(x16441,f8(a70)))
% 4.60/4.59 [1755]P11(a70,x17551,x17552)+~P74(f27(x17553,f61(x17552,x17551,x17553)))+P74(f27(x17553,f6(a70,x17551,x17552)))
% 4.60/4.59 [1756]P11(a70,x17561,x17562)+~P74(f27(x17563,f63(x17562,x17561,x17563)))+P74(f27(x17563,f6(a70,x17561,x17562)))
% 4.60/4.59 [1760]~P74(f27(x17601,f61(x17603,x17602,x17601)))+P74(f27(x17601,f6(a70,x17602,x17603)))+~P74(f27(x17601,f8(a70)))
% 4.60/4.59 [1761]~P74(f27(x17611,f63(x17613,x17612,x17611)))+P74(f27(x17611,f6(a70,x17612,x17613)))+~P74(f27(x17611,f8(a70)))
% 4.60/4.59 [760]~P66(x7601)+~E(x7603,f8(x7601))+E(f27(f27(f10(x7601),x7602),x7603),f8(x7601))
% 4.60/4.59 [761]~P66(x7611)+~E(x7612,f8(x7611))+E(f27(f27(f10(x7611),x7612),x7613),f8(x7611))
% 4.60/4.59 [858]~P69(x8582)+E(x8581,f8(x8582))+~E(f27(f27(f13(x8582),x8581),x8583),f8(x8582))
% 4.60/4.59 [932]~P53(x9321)+~E(x9322,f9(x9321,x9323))+E(f27(f27(f10(x9321),x9322),x9322),f27(f27(f10(x9321),x9323),x9323))
% 4.60/4.59 [989]E(x9891,x9892)+E(x9893,f8(a1))+~E(f27(f27(f10(a1),x9893),x9891),f27(f27(f10(a1),x9893),x9892))
% 4.60/4.59 [991]E(x9911,x9912)+E(x9913,f8(a70))+~E(f27(f27(f10(a70),x9913),x9911),f27(f27(f10(a70),x9913),x9912))
% 4.60/4.59 [992]E(x9921,x9922)+E(x9923,f8(a1))+~E(f27(f27(f10(a1),x9921),x9923),f27(f27(f10(a1),x9922),x9923))
% 4.60/4.59 [993]E(x9931,x9932)+E(x9933,f8(a70))+~E(f27(f27(f10(a70),x9931),x9933),f27(f27(f10(a70),x9932),x9933))
% 4.60/4.59 [1036]~P43(x10361)+~E(x10362,f3(x10361))+P12(x10361,x10362,f27(f27(f13(x10361),x10362),x10363))
% 4.60/4.59 [1201]E(x12011,x12012)+~P11(a70,f8(a70),x12013)+~E(f27(f27(f10(a70),x12013),x12011),f27(f27(f10(a70),x12013),x12012))
% 4.60/4.59 [1256]~P43(x12561)+~P11(a70,f8(a70),x12563)+P12(x12561,x12562,f27(f27(f13(x12561),x12562),x12563))
% 4.60/4.59 [1276]~P57(x12761)+~P10(x12761,f3(x12761),x12762)+P10(x12761,f3(x12761),f27(f27(f13(x12761),x12762),x12763))
% 4.60/4.59 [1277]~P57(x12771)+~P10(x12771,f8(x12771),x12772)+P10(x12771,f8(x12771),f27(f27(f13(x12771),x12772),x12773))
% 4.60/4.59 [1278]~P57(x12781)+~P11(x12781,f8(x12781),x12782)+P11(x12781,f8(x12781),f27(f27(f13(x12781),x12782),x12783))
% 4.60/4.59 [1374]~P12(a70,x13742,x13743)+E(x13741,f8(a70))+P12(a70,f27(f27(f13(a70),x13742),x13741),f27(f27(f13(a70),x13743),x13741))
% 4.60/4.59 [1375]~P12(a68,x13752,x13753)+E(x13751,f8(a70))+P12(a68,f27(f27(f13(a68),x13752),x13751),f27(f27(f13(a68),x13753),x13751))
% 4.60/4.59 [1376]~P12(a68,x13762,x13763)+E(x13761,f8(a68))+P12(a68,f27(f27(f10(a68),x13761),x13762),f27(f27(f10(a68),x13761),x13763))
% 4.60/4.59 [1514]~P10(a1,x15142,x15143)+~P11(a1,f8(a1),x15141)+P10(a1,f27(f27(f10(a1),x15141),x15142),f27(f27(f10(a1),x15141),x15143))
% 4.60/4.59 [1515]~P10(a1,x15151,x15153)+~P11(a1,f8(a1),x15152)+P10(a1,f27(f27(f10(a1),x15151),x15152),f27(f27(f10(a1),x15153),x15152))
% 4.60/4.59 [1517]~P11(a1,x15171,x15173)+~P11(a1,f8(a1),x15172)+P11(a1,f27(f27(f10(a1),x15171),x15172),f27(f27(f10(a1),x15173),x15172))
% 4.60/4.59 [1518]~P11(a1,x15182,x15183)+~P11(a1,f8(a1),x15181)+P11(a1,f27(f27(f10(a1),x15181),x15182),f27(f27(f10(a1),x15181),x15183))
% 4.60/4.59 [1522]~P11(a70,x15221,x15223)+~P11(a70,f8(a70),x15222)+P11(a70,f27(f27(f10(a70),x15221),x15222),f27(f27(f10(a70),x15223),x15222))
% 4.60/4.59 [1523]~P11(a70,x15232,x15233)+~P11(a70,f8(a70),x15231)+P11(a70,f27(f27(f10(a70),x15231),x15232),f27(f27(f10(a70),x15231),x15233))
% 4.60/4.59 [1524]~P11(a68,x15242,x15243)+~P11(a68,f8(a68),x15241)+P11(a68,f27(f27(f10(a68),x15241),x15242),f27(f27(f10(a68),x15241),x15243))
% 4.60/4.59 [1546]P12(a70,x15462,x15463)+E(x15461,f8(a70))+~P12(a70,f27(f27(f13(a70),x15462),x15461),f27(f27(f13(a70),x15463),x15461))
% 4.60/4.59 [1548]P12(a68,x15482,x15483)+E(x15481,f8(a70))+~P12(a68,f27(f27(f13(a68),x15482),x15481),f27(f27(f13(a68),x15483),x15481))
% 4.60/4.59 [1549]P12(a70,x15492,x15493)+E(x15491,f8(a70))+~P12(a70,f27(f27(f10(a70),x15491),x15492),f27(f27(f10(a70),x15491),x15493))
% 4.60/4.59 [1551]P12(a68,x15512,x15513)+E(x15511,f8(a68))+~P12(a68,f27(f27(f10(a68),x15511),x15512),f27(f27(f10(a68),x15511),x15513))
% 4.60/4.59 [1638]~P57(x16381)+~P11(x16381,f3(x16381),x16382)+P11(x16381,f3(x16381),f27(f27(f13(x16381),x16382),f11(a70,x16383,f3(a70))))
% 4.60/4.59 [1654]P10(a1,x16541,x16542)+~P11(a1,f8(a1),x16543)+~P10(a1,f27(f27(f10(a1),x16543),x16541),f27(f27(f10(a1),x16543),x16542))
% 4.60/4.59 [1655]P10(a1,x16551,x16552)+~P11(a1,f8(a1),x16553)+~P10(a1,f27(f27(f10(a1),x16551),x16553),f27(f27(f10(a1),x16552),x16553))
% 4.60/4.59 [1656]P10(a70,x16561,x16562)+~P11(a70,f3(a70),x16563)+~P12(a70,f27(f27(f13(a70),x16563),x16561),f27(f27(f13(a70),x16563),x16562))
% 4.60/4.59 [1658]P10(a70,x16581,x16582)+~P11(a70,f8(a70),x16583)+~P10(a70,f27(f27(f10(a70),x16583),x16581),f27(f27(f10(a70),x16583),x16582))
% 4.60/4.59 [1659]P10(a70,x16591,x16592)+~P11(a70,f8(a70),x16593)+~P10(a70,f27(f27(f10(a70),x16591),x16593),f27(f27(f10(a70),x16592),x16593))
% 4.60/4.59 [1660]P11(a1,x16601,x16602)+~P11(a1,f8(a1),x16603)+~P11(a1,f27(f27(f10(a1),x16601),x16603),f27(f27(f10(a1),x16602),x16603))
% 4.60/4.59 [1662]P11(a70,x16621,x16622)+~P11(a70,f8(a70),x16623)+~P11(a70,f27(f27(f13(a70),x16623),x16621),f27(f27(f13(a70),x16623),x16622))
% 4.60/4.59 [1664]P12(a70,x16641,x16642)+~P11(a70,f8(a70),x16643)+~P12(a70,f27(f27(f10(a70),x16643),x16641),f27(f27(f10(a70),x16643),x16642))
% 4.60/4.59 [1778]~P53(x17781)+~E(x17782,f9(x17781,x17783))+E(f27(f27(f13(x17781),x17782),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70))),f27(f27(f13(x17781),x17783),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70))))
% 4.60/4.59 [1811]~P1(x18112)+P11(a1,f8(a1),f44(x18111,x18112))+~P11(a1,f26(x18112,f27(x18111,f45(x18111,x18112,x18113))),f25(a70,f11(a70,x18113,f3(a70))))
% 4.60/4.59 [1812]~P1(x18122)+P11(a1,f8(a1),f54(x18121,x18122))+~P10(a1,f26(x18122,f27(x18121,f48(x18121,x18122,x18123))),f25(a70,f11(a70,x18123,f3(a70))))
% 4.60/4.59 [1847]~P53(x18472)+E(x18471,f8(f71(x18472)))+~P12(f71(x18472),f27(f27(f13(f71(x18472)),f15(x18472,f9(x18472,x18473),f15(x18472,f3(x18472),f8(f71(x18472))))),f11(a70,f18(x18472,x18473,x18471),f3(a70))),x18471)
% 4.60/4.59 [1380]~P51(x13801)+~P10(x13801,f8(x13801),x13803)+E(f27(f27(f10(x13801),f5(x13801,x13802)),x13803),f5(x13801,f27(f27(f10(x13801),x13802),x13803)))
% 4.60/4.59 [1560]~P56(x15602)+E(x15601,f8(x15602))+~E(f11(x15602,f27(f27(f10(x15602),x15603),x15603),f27(f27(f10(x15602),x15601),x15601)),f8(x15602))
% 4.60/4.59 [1561]~P56(x15612)+E(x15611,f8(x15612))+~E(f11(x15612,f27(f27(f10(x15612),x15611),x15611),f27(f27(f10(x15612),x15613),x15613)),f8(x15612))
% 4.60/4.59 [1623]~P57(x16231)+~P11(x16231,f3(x16231),x16232)+P11(x16231,f3(x16231),f27(f27(f10(x16231),x16232),f27(f27(f13(x16231),x16232),x16233)))
% 4.60/4.60 [1723]~P57(x17231)+~P11(x17231,f3(x17231),x17232)+P11(x17231,f27(f27(f13(x17231),x17232),x17233),f27(f27(f10(x17231),x17232),f27(f27(f13(x17231),x17232),x17233)))
% 4.60/4.60 [1732]~P56(x17322)+E(x17321,f8(x17322))+P11(x17322,f8(x17322),f11(x17322,f27(f27(f10(x17322),x17323),x17323),f27(f27(f10(x17322),x17321),x17321)))
% 4.60/4.60 [1733]~P56(x17332)+E(x17331,f8(x17332))+P11(x17332,f8(x17332),f11(x17332,f27(f27(f10(x17332),x17331),x17331),f27(f27(f10(x17332),x17333),x17333)))
% 4.60/4.60 [1734]~P53(x17341)+~E(f27(f14(x17341,x17343),f9(x17341,x17342)),f8(x17341))+P12(f71(x17341),f15(x17341,x17342,f15(x17341,f3(x17341),f8(f71(x17341)))),x17343)
% 4.60/4.60 [1736]~P53(x17361)+~E(f27(f14(x17361,x17363),x17362),f8(x17361))+P12(f71(x17361),f15(x17361,f9(x17361,x17362),f15(x17361,f3(x17361),f8(f71(x17361)))),x17363)
% 4.60/4.60 [1781]~P53(x17811)+E(f27(f14(x17811,x17812),f9(x17811,x17813)),f8(x17811))+~P12(f71(x17811),f15(x17811,x17813,f15(x17811,f3(x17811),f8(f71(x17811)))),x17812)
% 4.60/4.60 [1783]~P53(x17831)+E(f27(f14(x17831,x17832),x17833),f8(x17831))+~P12(f71(x17831),f15(x17831,f9(x17831,x17833),f15(x17831,f3(x17831),f8(f71(x17831)))),x17832)
% 4.60/4.60 [1786]~P56(x17862)+E(x17861,f8(x17862))+~P10(x17862,f11(x17862,f27(f27(f10(x17862),x17863),x17863),f27(f27(f10(x17862),x17861),x17861)),f8(x17862))
% 4.60/4.60 [1787]~P56(x17872)+E(x17871,f8(x17872))+~P10(x17872,f11(x17872,f27(f27(f10(x17872),x17871),x17871),f27(f27(f10(x17872),x17873),x17873)),f8(x17872))
% 4.60/4.60 [1065]~P15(x10653)+E(x10651,x10652)+~E(f11(x10653,x10654,x10651),f11(x10653,x10654,x10652))
% 4.60/4.60 [1066]~P16(x10663)+E(x10661,x10662)+~E(f11(x10663,x10664,x10661),f11(x10663,x10664,x10662))
% 4.60/4.60 [1068]~P15(x10683)+E(x10681,x10682)+~E(f11(x10683,x10681,x10684),f11(x10683,x10682,x10684))
% 4.60/4.60 [1157]~P39(x11572)+~P11(f75(x11571,x11572),x11573,x11574)+P10(f75(x11571,x11572),x11573,x11574)
% 4.60/4.60 [1271]~P39(x12711)+~P11(f75(x12712,x12711),x12714,x12713)+~P10(f75(x12712,x12711),x12713,x12714)
% 4.60/4.60 [1289]~P43(x12891)+~P12(f71(x12891),x12892,x12894)+P12(f71(x12891),x12892,f21(x12891,x12893,x12894))
% 4.60/4.60 [1337]~P11(a70,x13373,x13374)+P11(a70,x13371,x13372)+~E(f11(a70,x13373,x13372),f11(a70,x13371,x13374))
% 4.60/4.60 [1407]~P43(x14071)+~P12(f71(x14071),f21(x14071,x14074,x14072),x14073)+P12(f71(x14071),x14072,x14073)
% 4.60/4.60 [1449]~P30(x14491)+~P10(x14491,x14493,x14494)+P10(x14491,f11(x14491,x14492,x14493),f11(x14491,x14492,x14494))
% 4.60/4.60 [1450]~P31(x14501)+~P10(x14501,x14503,x14504)+P10(x14501,f11(x14501,x14502,x14503),f11(x14501,x14502,x14504))
% 4.60/4.60 [1451]~P30(x14511)+~P10(x14511,x14512,x14514)+P10(x14511,f11(x14511,x14512,x14513),f11(x14511,x14514,x14513))
% 4.60/4.60 [1452]~P31(x14521)+~P10(x14521,x14522,x14524)+P10(x14521,f11(x14521,x14522,x14523),f11(x14521,x14524,x14523))
% 4.60/4.60 [1453]~P30(x14531)+~P11(x14531,x14533,x14534)+P11(x14531,f11(x14531,x14532,x14533),f11(x14531,x14532,x14534))
% 4.60/4.60 [1454]~P32(x14541)+~P11(x14541,x14543,x14544)+P11(x14541,f11(x14541,x14542,x14543),f11(x14541,x14542,x14544))
% 4.60/4.60 [1455]~P30(x14551)+~P11(x14551,x14552,x14554)+P11(x14551,f11(x14551,x14552,x14553),f11(x14551,x14554,x14553))
% 4.60/4.60 [1456]~P32(x14561)+~P11(x14561,x14562,x14564)+P11(x14561,f11(x14561,x14562,x14563),f11(x14561,x14564,x14563))
% 4.60/4.60 [1562]~P10(a70,x15622,x15624)+~P10(a70,x15621,x15623)+P10(a70,f11(a70,x15621,x15622),f11(a70,x15623,x15624))
% 4.60/4.60 [1563]~P11(a70,x15632,x15634)+~P11(a70,x15631,x15633)+P11(a70,f11(a70,x15631,x15632),f11(a70,x15633,x15634))
% 4.60/4.60 [1565]~P10(a68,x15652,x15654)+~P11(a68,x15651,x15653)+P11(a68,f11(a68,x15651,x15652),f11(a68,x15653,x15654))
% 4.60/4.60 [1630]~P30(x16301)+P10(x16301,x16302,x16303)+~P10(x16301,f11(x16301,x16304,x16302),f11(x16301,x16304,x16303))
% 4.60/4.60 [1632]~P30(x16321)+P10(x16321,x16322,x16323)+~P10(x16321,f11(x16321,x16322,x16324),f11(x16321,x16323,x16324))
% 4.60/4.60 [1634]~P30(x16341)+P11(x16341,x16342,x16343)+~P11(x16341,f11(x16341,x16344,x16342),f11(x16341,x16344,x16343))
% 4.60/4.60 [1636]~P30(x16361)+P11(x16361,x16362,x16363)+~P11(x16361,f11(x16361,x16362,x16364),f11(x16361,x16363,x16364))
% 4.60/4.60 [1103]~P47(x11032)+~E(f21(x11032,x11033,x11031),f15(x11032,x11034,x11031))+E(x11031,f8(f71(x11032)))
% 4.60/4.60 [1642]~E(x16423,f11(a70,x16424,x16422))+P74(f27(x16421,x16422))+~P74(f27(x16421,f6(a70,x16423,x16424)))
% 4.60/4.60 [1749]~P51(x17491)+P11(x17491,x17492,f11(x17491,x17493,x17494))+~P11(x17491,f5(x17491,f6(x17491,x17492,x17493)),x17494)
% 4.60/4.60 [1750]~P51(x17501)+P11(x17501,f6(x17501,x17502,x17503),x17504)+~P11(x17501,f5(x17501,f6(x17501,x17504,x17502)),x17503)
% 4.60/4.60 [1844]~P39(x18442)+P10(f75(x18441,x18442),x18443,x18444)+~P10(x18442,f27(x18443,f64(x18444,x18443,x18441,x18442)),f27(x18444,f64(x18444,x18443,x18441,x18442)))
% 4.60/4.60 [967]~P54(x9671)+P12(x9671,x9672,x9673)+~E(x9673,f27(f27(f10(x9671),x9672),x9674))
% 4.60/4.60 [1251]~P43(x12511)+~P12(x12511,x12512,x12514)+P12(x12511,x12512,f27(f27(f10(x12511),x12513),x12514))
% 4.60/4.60 [1252]~P43(x12521)+~P12(x12521,x12522,x12523)+P12(x12521,x12522,f27(f27(f10(x12521),x12523),x12524))
% 4.60/4.60 [1295]~P53(x12951)+~E(x12953,f8(x12951))+P12(x12951,f27(f27(f10(x12951),x12952),x12953),f27(f27(f10(x12951),x12954),x12953))
% 4.60/4.60 [1296]~P53(x12961)+~E(x12962,f8(x12961))+P12(x12961,f27(f27(f10(x12961),x12962),x12963),f27(f27(f10(x12961),x12962),x12964))
% 4.60/4.60 [1344]~P43(x13441)+P12(x13441,x13442,x13443)+~P12(x13441,f27(f27(f10(x13441),x13444),x13442),x13443)
% 4.60/4.60 [1345]~P43(x13451)+P12(x13451,x13452,x13453)+~P12(x13451,f27(f27(f10(x13451),x13452),x13454),x13453)
% 4.60/4.60 [1432]~P43(x14321)+~P10(a70,x14323,x14324)+P12(x14321,f27(f27(f13(x14321),x14322),x14323),f27(f27(f13(x14321),x14322),x14324))
% 4.60/4.60 [1440]~P53(x14401)+~P12(x14401,x14403,x14404)+P12(x14401,f27(f27(f10(x14401),x14402),x14403),f27(f27(f10(x14401),x14402),x14404))
% 4.60/4.60 [1441]~P53(x14411)+~P12(x14411,x14412,x14414)+P12(x14411,f27(f27(f10(x14411),x14412),x14413),f27(f27(f10(x14411),x14414),x14413))
% 4.60/4.60 [1442]~P43(x14421)+~P12(x14421,x14422,x14424)+P12(x14421,f27(f27(f13(x14421),x14422),x14423),f27(f27(f13(x14421),x14424),x14423))
% 4.60/4.60 [1509]~P10(a70,x15092,x15094)+~P10(a70,x15091,x15093)+P10(a70,f27(f27(f10(a70),x15091),x15092),f27(f27(f10(a70),x15093),x15094))
% 4.60/4.60 [1819]~P1(x18191)+P10(a1,f26(x18191,f27(x18192,x18193)),f44(x18192,x18191))+~P11(a1,f26(x18191,f27(x18192,f45(x18192,x18191,x18194))),f25(a70,f11(a70,x18194,f3(a70))))
% 4.60/4.60 [1820]~P1(x18201)+P10(a1,f26(x18201,f27(x18202,x18203)),f54(x18202,x18201))+~P10(a1,f26(x18201,f27(x18202,f48(x18202,x18201,x18204))),f25(a70,f11(a70,x18204,f3(a70))))
% 4.60/4.60 [1823]~P28(x18232)+E(f22(x18231,x18232,x18233,x18234,f8(f71(x18232))),x18233)+~E(f27(f27(f27(x18234,f8(x18232)),f8(f71(x18232))),x18233),x18233)
% 4.60/4.60 [1069]~P28(x10693)+E(x10691,x10692)+~E(f15(x10693,x10694,x10691),f15(x10693,x10695,x10692))
% 4.60/4.60 [1070]~P28(x10703)+E(x10701,x10702)+~E(f15(x10703,x10701,x10704),f15(x10703,x10702,x10705))
% 4.60/4.60 [1222]~P39(x12221)+P10(x12221,f27(x12222,x12223),f27(x12224,x12223))+~P10(f75(x12225,x12221),x12222,x12224)
% 4.60/4.60 [1503]~P47(x15032)+~E(f11(f71(x15032),x15033,f21(x15032,x15034,x15035)),f15(x15032,x15031,x15035))+E(x15031,f27(f14(x15032,x15033),x15034))
% 4.60/4.60 [1531]~P47(x15312)+E(x15311,f23(x15312,x15313,x15314))+~E(f11(f71(x15312),x15313,f21(x15312,x15314,x15311)),f15(x15312,x15315,x15311))
% 4.60/4.60 [1678]~E(x16782,x16784)+~P48(x16781)+E(f11(x16781,f27(f27(f10(x16781),x16782),x16783),f27(f27(f10(x16781),x16784),x16785)),f11(x16781,f27(f27(f10(x16781),x16782),x16785),f27(f27(f10(x16781),x16784),x16783)))
% 4.60/4.60 [1794]~P12(a68,x17941,x17944)+~P12(a68,x17941,f11(a68,x17942,x17945))+P12(a68,x17941,f11(a68,f11(a68,x17942,f27(f27(f10(a68),x17943),x17944)),x17945))
% 4.60/4.60 [1816]~P12(a68,x18161,x18164)+P12(a68,x18161,f11(a68,x18162,x18163))+~P12(a68,x18161,f11(a68,f11(a68,x18162,f27(f27(f10(a68),x18165),x18164)),x18163))
% 4.60/4.60 [1797]~P68(x17972)+~E(f11(x17972,f27(f27(f10(x17972),x17974),x17975),x17971),f11(x17972,f27(f27(f10(x17972),x17973),x17975),x17976))+E(x17971,f11(x17972,f27(f27(f10(x17972),f6(x17972,x17973,x17974)),x17975),x17976))
% 4.60/4.60 [1798]~P68(x17981)+~E(f11(x17981,f27(f27(f10(x17981),x17982),x17984),x17985),f11(x17981,f27(f27(f10(x17981),x17983),x17984),x17986))+E(f11(x17981,f27(f27(f10(x17981),f6(x17981,x17982,x17983)),x17984),x17985),x17986)
% 4.60/4.60 [1805]~P68(x18051)+~E(x18056,f11(x18051,f27(f27(f10(x18051),f6(x18051,x18052,x18055)),x18053),x18054))+E(f11(x18051,f27(f27(f10(x18051),x18052),x18053),x18054),f11(x18051,f27(f27(f10(x18051),x18055),x18053),x18056))
% 4.60/4.60 [1806]~P68(x18061)+~E(f11(x18061,f27(f27(f10(x18061),f6(x18061,x18062,x18065)),x18063),x18064),x18066)+E(f11(x18061,f27(f27(f10(x18061),x18062),x18063),x18064),f11(x18061,f27(f27(f10(x18061),x18065),x18063),x18066))
% 4.60/4.60 [1832]~P64(x18321)+~P10(x18321,f11(x18321,f27(f27(f10(x18321),x18324),x18325),x18322),f11(x18321,f27(f27(f10(x18321),x18323),x18325),x18326))+P10(x18321,x18322,f11(x18321,f27(f27(f10(x18321),f6(x18321,x18323,x18324)),x18325),x18326))
% 4.60/4.60 [1833]~P64(x18331)+~P11(x18331,f11(x18331,f27(f27(f10(x18331),x18334),x18335),x18332),f11(x18331,f27(f27(f10(x18331),x18333),x18335),x18336))+P11(x18331,x18332,f11(x18331,f27(f27(f10(x18331),f6(x18331,x18333,x18334)),x18335),x18336))
% 4.60/4.60 [1834]~P64(x18341)+~P10(x18341,f11(x18341,f27(f27(f10(x18341),x18342),x18344),x18345),f11(x18341,f27(f27(f10(x18341),x18343),x18344),x18346))+P10(x18341,f11(x18341,f27(f27(f10(x18341),f6(x18341,x18342,x18343)),x18344),x18345),x18346)
% 4.60/4.60 [1835]~P64(x18351)+~P11(x18351,f11(x18351,f27(f27(f10(x18351),x18352),x18354),x18355),f11(x18351,f27(f27(f10(x18351),x18353),x18354),x18356))+P11(x18351,f11(x18351,f27(f27(f10(x18351),f6(x18351,x18352,x18353)),x18354),x18355),x18356)
% 4.60/4.60 [1838]~P64(x18381)+~P10(x18381,x18384,f11(x18381,f27(f27(f10(x18381),f6(x18381,x18385,x18382)),x18383),x18386))+P10(x18381,f11(x18381,f27(f27(f10(x18381),x18382),x18383),x18384),f11(x18381,f27(f27(f10(x18381),x18385),x18383),x18386))
% 4.60/4.60 [1839]~P64(x18391)+~P11(x18391,x18394,f11(x18391,f27(f27(f10(x18391),f6(x18391,x18395,x18392)),x18393),x18396))+P11(x18391,f11(x18391,f27(f27(f10(x18391),x18392),x18393),x18394),f11(x18391,f27(f27(f10(x18391),x18395),x18393),x18396))
% 4.60/4.60 [1840]~P64(x18401)+~P10(x18401,f11(x18401,f27(f27(f10(x18401),f6(x18401,x18402,x18405)),x18403),x18404),x18406)+P10(x18401,f11(x18401,f27(f27(f10(x18401),x18402),x18403),x18404),f11(x18401,f27(f27(f10(x18401),x18405),x18403),x18406))
% 4.60/4.60 [1841]~P64(x18411)+~P11(x18411,f11(x18411,f27(f27(f10(x18411),f6(x18411,x18412,x18415)),x18413),x18414),x18416)+P11(x18411,f11(x18411,f27(f27(f10(x18411),x18412),x18413),x18414),f11(x18411,f27(f27(f10(x18411),x18415),x18413),x18416))
% 4.60/4.60 [1845]~P28(x18452)+E(f22(x18451,x18452,x18453,x18454,f15(x18452,x18455,x18456)),f27(f27(f27(x18454,x18455),x18456),f22(x18451,x18452,x18453,x18454,x18456)))+~E(f27(f27(f27(x18454,f8(x18452)),f8(f71(x18452))),x18453),x18453)
% 4.60/4.60 [923]~P33(x9232)+~P11(x9232,f8(x9232),x9231)+E(f12(x9232,x9231),f3(x9232))+E(x9231,f8(x9232))
% 4.60/4.60 [791]P13(x7912,x7911)+~P51(x7912)+P13(x7912,f9(f71(x7912),x7911))+E(x7911,f8(f71(x7912)))
% 4.60/4.60 [877]~P33(x8772)+P11(x8772,f8(x8772),x8771)+E(x8771,f8(x8772))+E(f12(x8772,x8771),f9(x8772,f3(x8772)))
% 4.60/4.60 [1040]~P51(x10402)+~P11(f71(x10402),f8(f71(x10402)),x10401)+E(f12(f71(x10402),x10401),f3(f71(x10402)))+E(x10401,f8(f71(x10402)))
% 4.60/4.60 [792]~P73(x7922)+~P40(x7922)+E(x7921,f8(a70))+E(f27(f27(f13(x7922),f8(x7922)),x7921),f8(x7922))
% 4.60/4.60 [810]~P73(x8101)+~P40(x8101)+~E(x8102,f8(a70))+E(f27(f27(f13(x8101),f8(x8101)),x8102),f3(x8101))
% 4.60/4.60 [918]~P69(x9182)+E(x9181,f3(x9182))+E(x9181,f9(x9182,f3(x9182)))+~E(f27(f27(f10(x9182),x9181),x9181),f3(x9182))
% 4.60/4.60 [976]~E(x9762,f3(a68))+~E(x9761,f3(a68))+~P11(a68,f8(a68),x9761)+E(f27(f27(f10(a68),x9761),x9762),f3(a68))
% 4.60/4.60 [1003]~P51(x10032)+P11(f71(x10032),f8(f71(x10032)),x10031)+E(x10031,f8(f71(x10032)))+E(f12(f71(x10032),x10031),f9(f71(x10032),f3(f71(x10032))))
% 4.60/4.60 [911]P11(x9113,x9111,x9112)+~P51(x9113)+E(x9111,x9112)+P11(x9113,x9112,x9111)
% 4.60/4.60 [912]P11(x9123,x9121,x9122)+~P27(x9123)+E(x9121,x9122)+P11(x9123,x9122,x9121)
% 4.60/4.60 [914]P11(x9141,x9142,x9143)+~E(x9142,x9143)+~P27(x9141)+P10(x9141,x9142,x9143)
% 4.60/4.60 [979]~P38(x9793)+~P10(x9793,x9792,x9791)+E(x9791,x9792)+P11(x9793,x9792,x9791)
% 4.60/4.60 [981]~P27(x9813)+~P10(x9813,x9811,x9812)+E(x9811,x9812)+P11(x9813,x9811,x9812)
% 4.60/4.60 [987]~P38(x9873)+~P10(x9873,x9871,x9872)+E(x9871,x9872)+P11(x9873,x9871,x9872)
% 4.60/4.60 [1076]~P10(x10763,x10762,x10761)+~P10(x10763,x10761,x10762)+E(x10761,x10762)+~P38(x10763)
% 4.60/4.60 [1130]P11(x11301,x11303,x11302)+~P26(x11301)+~P10(x11301,x11303,x11302)+P10(x11301,x11302,x11303)
% 4.60/4.60 [713]~P35(x7133)+~P53(x7133)+E(x7131,x7132)+~E(f14(x7133,x7131),f14(x7133,x7132))
% 4.60/4.60 [1290]~P51(x12901)+P13(x12901,x12902)+P11(x12901,f8(x12901),x12903)+~P13(x12901,f15(x12901,x12903,x12902))
% 4.60/4.60 [1333]~P3(x13331)+~P10(x13331,x13332,x13333)+~P10(x13331,f9(x13331,x13332),x13333)+P10(x13331,f5(x13331,x13332),x13333)
% 4.60/4.60 [1334]~P51(x13341)+~P11(x13341,x13342,x13343)+~P11(x13341,f9(x13341,x13342),x13343)+P11(x13341,f5(x13341,x13342),x13343)
% 4.60/4.60 [1480]~P29(x14801)+~P11(x14801,f8(x14801),x14803)+~P11(x14801,f8(x14801),x14802)+P11(x14801,f8(x14801),f11(x14801,x14802,x14803))
% 4.60/4.60 [1481]~P29(x14811)+~P10(x14811,x14813,f8(x14811))+~P10(x14811,x14812,f8(x14811))+P10(x14811,f11(x14811,x14812,x14813),f8(x14811))
% 4.60/4.60 [1482]~P29(x14821)+~P10(x14821,x14823,f8(x14821))+~P11(x14821,x14822,f8(x14821))+P11(x14821,f11(x14821,x14822,x14823),f8(x14821))
% 4.60/4.60 [1483]~P29(x14831)+~P10(x14831,x14832,f8(x14831))+~P11(x14831,x14833,f8(x14831))+P11(x14831,f11(x14831,x14832,x14833),f8(x14831))
% 4.60/4.60 [1484]~P29(x14841)+~P11(x14841,x14843,f8(x14841))+~P11(x14841,x14842,f8(x14841))+P11(x14841,f11(x14841,x14842,x14843),f8(x14841))
% 4.60/4.60 [1620]~P12(a70,x16201,x16203)+P12(a70,x16201,x16202)+~P10(a70,x16202,x16203)+~P12(a70,x16201,f6(a70,x16203,x16202))
% 4.60/4.60 [1621]~P12(a70,x16211,x16213)+P12(a70,x16211,x16212)+~P10(a70,x16213,x16212)+~P12(a70,x16211,f6(a70,x16212,x16213))
% 4.60/4.60 [1748]~P10(a70,x17483,x17481)+P11(a70,x17481,x17482)+~P10(a70,x17483,x17482)+~P11(a70,f6(a70,x17481,x17483),f6(a70,x17482,x17483))
% 4.60/4.60 [852]~P28(x8521)+~E(x8522,f8(x8521))+~E(x8523,f8(f71(x8521)))+E(f15(x8521,x8522,x8523),f8(f71(x8521)))
% 4.60/4.60 [922]~P53(x9222)+E(x9221,f8(x9222))+~E(f21(x9222,x9221,x9223),f8(f71(x9222)))+E(x9223,f8(f71(x9222)))
% 4.60/4.60 [1048]~P53(x10482)+~E(f18(x10482,x10483,x10481),f8(a70))+~E(f27(f14(x10482,x10481),x10483),f8(x10482))+E(x10481,f8(f71(x10482)))
% 4.60/4.60 [1090]~P51(x10901)+~P13(x10901,x10903)+~P13(x10901,x10902)+P13(x10901,f11(f71(x10901),x10902,x10903))
% 4.60/4.60 [1172]P13(x11722,x11721)+~P51(x11722)+~P13(x11722,f15(x11722,x11723,x11721))+E(x11721,f8(f71(x11722)))
% 4.60/4.60 [1205]~P51(x12053)+E(x12051,x12052)+~P10(f71(x12053),x12051,x12052)+P13(x12053,f6(f71(x12053),x12052,x12051))
% 4.60/4.60 [1226]~P51(x12261)+~P11(x12261,f8(x12261),x12262)+P13(x12261,f15(x12261,x12262,x12263))+~E(x12263,f8(f71(x12261)))
% 4.60/4.60 [1264]~P10(a70,x12643,f32(x12642,x12641))+~P74(f27(x12641,x12642))+~P74(f27(x12641,x12643))+P74(f27(x12641,f8(a70)))
% 4.60/4.60 [867]~P66(x8672)+E(x8671,f8(x8672))+E(x8673,f8(x8672))+~E(f27(f27(f10(x8672),x8673),x8671),f8(x8672))
% 4.60/4.60 [869]~P62(x8692)+E(x8691,f8(x8692))+E(x8693,f8(x8692))+~E(f27(f27(f10(x8692),x8693),x8691),f8(x8692))
% 4.60/4.60 [1092]~P53(x10923)+E(x10921,x10922)+E(x10921,f9(x10923,x10922))+~E(f27(f27(f10(x10923),x10921),x10921),f27(f27(f10(x10923),x10922),x10922))
% 4.60/4.60 [1443]~P57(x14431)+~P11(x14431,f3(x14431),x14432)+~P11(a70,f8(a70),x14433)+P11(x14431,f3(x14431),f27(f27(f13(x14431),x14432),x14433))
% 4.60/4.60 [1457]~P56(x14571)+~P10(x14571,x14573,f8(x14571))+~P10(x14571,x14572,f8(x14571))+P10(x14571,f8(x14571),f27(f27(f10(x14571),x14572),x14573))
% 4.60/4.60 [1459]~P64(x14591)+~P10(x14591,x14593,f8(x14591))+~P10(x14591,x14592,f8(x14591))+P10(x14591,f8(x14591),f27(f27(f10(x14591),x14592),x14593))
% 4.60/4.60 [1460]~P56(x14601)+~P11(x14601,x14603,f8(x14601))+~P11(x14601,x14602,f8(x14601))+P11(x14601,f8(x14601),f27(f27(f10(x14601),x14602),x14603))
% 4.60/4.60 [1461]~P56(x14611)+~P10(x14611,f8(x14611),x14613)+~P10(x14611,f8(x14611),x14612)+P10(x14611,f8(x14611),f27(f27(f10(x14611),x14612),x14613))
% 4.60/4.60 [1462]~P63(x14621)+~P10(x14621,f8(x14621),x14623)+~P10(x14621,f8(x14621),x14622)+P10(x14621,f8(x14621),f27(f27(f10(x14621),x14622),x14623))
% 4.60/4.60 [1463]~P64(x14631)+~P10(x14631,f8(x14631),x14633)+~P10(x14631,f8(x14631),x14632)+P10(x14631,f8(x14631),f27(f27(f10(x14631),x14632),x14633))
% 4.60/4.60 [1464]~P57(x14641)+~P11(x14641,f3(x14641),x14643)+~P11(x14641,f3(x14641),x14642)+P11(x14641,f3(x14641),f27(f27(f10(x14641),x14642),x14643))
% 4.60/4.60 [1465]~P61(x14651)+~P11(x14651,f8(x14651),x14653)+~P11(x14651,f8(x14651),x14652)+P11(x14651,f8(x14651),f27(f27(f10(x14651),x14652),x14653))
% 4.60/4.60 [1467]~P56(x14671)+~P10(x14671,x14673,f8(x14671))+~P10(x14671,f8(x14671),x14672)+P10(x14671,f27(f27(f10(x14671),x14672),x14673),f8(x14671))
% 4.60/4.60 [1468]~P56(x14681)+~P10(x14681,x14682,f8(x14681))+~P10(x14681,f8(x14681),x14683)+P10(x14681,f27(f27(f10(x14681),x14682),x14683),f8(x14681))
% 4.60/4.60 [1470]~P63(x14701)+~P10(x14701,x14703,f8(x14701))+~P10(x14701,f8(x14701),x14702)+P10(x14701,f27(f27(f10(x14701),x14702),x14703),f8(x14701))
% 4.60/4.60 [1472]~P63(x14721)+~P10(x14721,x14722,f8(x14721))+~P10(x14721,f8(x14721),x14723)+P10(x14721,f27(f27(f10(x14721),x14722),x14723),f8(x14721))
% 4.60/4.60 [1474]~P61(x14741)+~P11(x14741,x14743,f8(x14741))+~P11(x14741,f8(x14741),x14742)+P11(x14741,f27(f27(f10(x14741),x14742),x14743),f8(x14741))
% 4.60/4.60 [1475]~P61(x14751)+~P11(x14751,x14752,f8(x14751))+~P11(x14751,f8(x14751),x14753)+P11(x14751,f27(f27(f10(x14751),x14752),x14753),f8(x14751))
% 4.60/4.60 [1493]~P56(x14931)+P10(x14931,x14932,f8(x14931))+P10(x14931,x14933,f8(x14931))+~P10(x14931,f27(f27(f10(x14931),x14933),x14932),f8(x14931))
% 4.60/4.60 [1494]~P56(x14941)+P10(x14941,x14942,f8(x14941))+P10(x14941,f8(x14941),x14943)+~P10(x14941,f8(x14941),f27(f27(f10(x14941),x14943),x14942))
% 4.60/4.60 [1495]~P56(x14951)+P10(x14951,x14952,f8(x14951))+P10(x14951,f8(x14951),x14953)+~P10(x14951,f8(x14951),f27(f27(f10(x14951),x14952),x14953))
% 4.60/4.60 [1496]~P56(x14961)+P10(x14961,f8(x14961),x14962)+P10(x14961,x14962,f8(x14961))+~P10(x14961,f8(x14961),f27(f27(f10(x14961),x14963),x14962))
% 4.60/4.60 [1497]~P56(x14971)+P10(x14971,f8(x14971),x14972)+P10(x14971,x14972,f8(x14971))+~P10(x14971,f8(x14971),f27(f27(f10(x14971),x14972),x14973))
% 4.60/4.60 [1498]~P56(x14981)+P10(x14981,f8(x14981),x14982)+P10(x14981,x14982,f8(x14981))+~P10(x14981,f27(f27(f10(x14981),x14983),x14982),f8(x14981))
% 4.60/4.60 [1499]~P56(x14991)+P10(x14991,f8(x14991),x14992)+P10(x14991,x14992,f8(x14991))+~P10(x14991,f27(f27(f10(x14991),x14992),x14993),f8(x14991))
% 4.60/4.60 [1500]~P56(x15001)+P10(x15001,f8(x15001),x15002)+P10(x15001,f8(x15001),x15003)+~P10(x15001,f27(f27(f10(x15001),x15002),x15003),f8(x15001))
% 4.60/4.60 [1540]~P61(x15401)+P11(x15401,f8(x15401),x15402)+~P11(x15401,f8(x15401),x15403)+~P11(x15401,f8(x15401),f27(f27(f10(x15401),x15403),x15402))
% 4.60/4.60 [1541]~P61(x15411)+P11(x15411,f8(x15411),x15412)+~P11(x15411,f8(x15411),x15413)+~P11(x15411,f8(x15411),f27(f27(f10(x15411),x15412),x15413))
% 4.60/4.60 [1725]~P57(x17251)+~P10(x17251,x17252,f3(x17251))+~P10(x17251,f8(x17251),x17252)+P10(x17251,f27(f27(f13(x17251),x17252),f11(a70,x17253,f3(a70))),x17252)
% 4.60/4.60 [1729]~P57(x17291)+~P11(x17291,x17292,f3(x17291))+~P11(x17291,f8(x17291),x17292)+P11(x17291,f27(f27(f13(x17291),x17292),f11(a70,x17293,f3(a70))),f3(x17291))
% 4.60/4.60 [1808]~P53(x18083)+E(x18081,x18082)+E(x18081,f9(x18083,x18082))+~E(f27(f27(f13(x18083),x18081),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70))),f27(f27(f13(x18083),x18082),f11(a70,f11(a70,f8(a70),f3(a70)),f3(a70))))
% 4.60/4.60 [1161]~P51(x11611)+~P13(x11611,x11613)+~P13(x11611,x11612)+P13(x11611,f27(f27(f10(f71(x11611)),x11612),x11613))
% 4.60/4.60 [1311]~P56(x13111)+~E(x13113,f8(x13111))+~E(x13112,f8(x13111))+E(f11(x13111,f27(f27(f10(x13111),x13112),x13112),f27(f27(f10(x13111),x13113),x13113)),f8(x13111))
% 4.60/4.60 [1572]~P59(x15721)+~P10(x15721,x15722,f8(x15721))+~P10(x15721,x15723,f8(x15721))+E(f27(f27(f10(x15721),f5(x15721,x15722)),f5(x15721,x15723)),f5(x15721,f27(f27(f10(x15721),x15722),x15723)))
% 4.60/4.60 [1573]~P59(x15731)+~P10(x15731,x15732,f8(x15731))+~P10(x15731,f8(x15731),x15733)+E(f27(f27(f10(x15731),f5(x15731,x15732)),f5(x15731,x15733)),f5(x15731,f27(f27(f10(x15731),x15732),x15733)))
% 4.60/4.60 [1574]~P59(x15741)+~P10(x15741,x15743,f8(x15741))+~P10(x15741,f8(x15741),x15742)+E(f27(f27(f10(x15741),f5(x15741,x15742)),f5(x15741,x15743)),f5(x15741,f27(f27(f10(x15741),x15742),x15743)))
% 4.60/4.60 [1575]~P59(x15751)+~P10(x15751,f8(x15751),x15752)+~P10(x15751,f8(x15751),x15753)+E(f27(f27(f10(x15751),f5(x15751,x15752)),f5(x15751,x15753)),f5(x15751,f27(f27(f10(x15751),x15752),x15753)))
% 4.60/4.60 [1614]~P11(a68,x16142,x16143)+~P11(a68,f8(a68),x16143)+P10(a68,f3(a68),x16141)+~E(f11(a68,x16142,f27(f27(f10(a68),x16143),x16141)),x16143)
% 4.60/4.60 [1617]~P10(a68,f8(a68),x16172)+~P11(a68,f8(a68),x16173)+P10(a68,x16171,f3(a68))+~E(f11(a68,x16172,f27(f27(f10(a68),x16173),x16171)),x16173)
% 4.60/4.60 [1735]~P56(x17351)+~E(x17353,f8(x17351))+~E(x17352,f8(x17351))+P10(x17351,f11(x17351,f27(f27(f10(x17351),x17352),x17352),f27(f27(f10(x17351),x17353),x17353)),f8(x17351))
% 4.60/4.60 [1754]~P57(x17541)+~P11(x17541,x17542,f3(x17541))+~P11(x17541,f8(x17541),x17542)+P11(x17541,f27(f27(f10(x17541),x17542),f27(f27(f13(x17541),x17542),x17543)),f27(f27(f13(x17541),x17542),x17543))
% 4.60/4.60 [1770]~P11(a68,x17702,x17703)+~P11(a68,f8(a68),x17703)+P10(a68,f8(a68),x17701)+~P10(a68,f8(a68),f11(a68,f27(f27(f10(a68),x17703),x17701),x17702))
% 4.60/4.60 [1771]P10(a68,x17711,f8(a68))+~P10(a68,f8(a68),x17712)+~P11(a68,f8(a68),x17713)+~P11(a68,f11(a68,f27(f27(f10(a68),x17713),x17711),x17712),f8(a68))
% 4.60/4.60 [1789]~P56(x17892)+~E(x17891,f8(x17892))+~E(x17893,f8(x17892))+~P11(x17892,f8(x17892),f11(x17892,f27(f27(f10(x17892),x17893),x17893),f27(f27(f10(x17892),x17891),x17891)))
% 4.60/4.60 [1189]~P38(x11891)+~P10(x11891,x11894,x11893)+P10(x11891,x11892,x11893)+~P10(x11891,x11892,x11894)
% 4.60/4.60 [1190]~P26(x11901)+~P10(x11901,x11902,x11904)+P10(x11901,x11902,x11903)+~P10(x11901,x11904,x11903)
% 4.60/4.60 [1191]~P38(x11911)+~P11(x11911,x11914,x11913)+P11(x11911,x11912,x11913)+~P10(x11911,x11912,x11914)
% 4.60/4.60 [1192]~P38(x11921)+~P11(x11921,x11922,x11924)+P11(x11921,x11922,x11923)+~P10(x11921,x11924,x11923)
% 4.60/4.60 [1193]~P38(x11931)+~P11(x11931,x11934,x11933)+P11(x11931,x11932,x11933)+~P11(x11931,x11932,x11934)
% 4.60/4.60 [1194]~P26(x11941)+~P11(x11941,x11942,x11944)+P11(x11941,x11942,x11943)+~P10(x11941,x11944,x11943)
% 4.60/4.60 [1195]~P26(x11951)+~P11(x11951,x11954,x11953)+P11(x11951,x11952,x11953)+~P10(x11951,x11952,x11954)
% 4.60/4.60 [1196]~P26(x11961)+~P11(x11961,x11962,x11964)+P11(x11961,x11962,x11963)+~P11(x11961,x11964,x11963)
% 4.60/4.60 [1197]~P43(x11971)+~P12(x11971,x11972,x11974)+P12(x11971,x11972,x11973)+~P12(x11971,x11974,x11973)
% 4.60/4.60 [1163]~P38(x11631)+~P14(x11631,x11632)+~P10(a70,x11634,x11633)+P10(x11631,f27(x11632,x11633),f27(x11632,x11634))
% 4.60/4.60 [1297]~P9(x12972)+~P12(f71(x12972),x12973,x12974)+P12(f71(x12972),x12973,f21(x12972,x12971,x12974))+E(x12971,f8(x12972))
% 4.60/4.60 [1299]~P9(x12992)+~P12(f71(x12992),x12993,x12994)+P12(f71(x12992),f21(x12992,x12991,x12993),x12994)+E(x12991,f8(x12992))
% 4.60/4.60 [1319]~P39(x13192)+P11(f75(x13191,x13192),x13194,x13193)+~P10(f75(x13191,x13192),x13194,x13193)+P10(f75(x13191,x13192),x13193,x13194)
% 4.60/4.60 [1412]~P9(x14122)+~P12(f71(x14122),x14123,f21(x14122,x14121,x14124))+P12(f71(x14122),x14123,x14124)+E(x14121,f8(x14122))
% 4.60/4.60 [1413]~P9(x14132)+~P12(f71(x14132),f21(x14132,x14131,x14133),x14134)+P12(f71(x14132),x14133,x14134)+E(x14131,f8(x14132))
% 4.60/4.60 [1419]~P43(x14191)+~P12(x14191,x14192,x14194)+~P12(x14191,x14192,x14193)+P12(x14191,x14192,f11(x14191,x14193,x14194))
% 4.60/4.60 [1420]~P45(x14201)+~P12(x14201,x14202,x14204)+~P12(x14201,x14202,x14203)+P12(x14201,x14202,f6(x14201,x14203,x14204))
% 4.60/4.60 [1433]~P29(x14331)+~P10(x14331,x14332,x14333)+~P10(x14331,f8(x14331),x14334)+P10(x14331,x14332,f11(x14331,x14333,x14334))
% 4.60/4.60 [1434]~P29(x14341)+~P10(x14341,x14342,x14344)+~P10(x14341,f8(x14341),x14343)+P10(x14341,x14342,f11(x14341,x14343,x14344))
% 4.60/4.60 [1435]~P29(x14351)+~P10(x14351,x14352,x14354)+~P11(x14351,f8(x14351),x14353)+P11(x14351,x14352,f11(x14351,x14353,x14354))
% 4.60/4.60 [1436]~P29(x14361)+~P11(x14361,x14362,x14364)+~P10(x14361,f8(x14361),x14363)+P11(x14361,x14362,f11(x14361,x14363,x14364))
% 4.60/4.60 [1437]~P57(x14371)+~P11(x14371,x14372,x14374)+~P11(x14371,f8(x14371),x14373)+P11(x14371,x14372,f11(x14371,x14373,x14374))
% 4.60/4.60 [1126]~P9(x11261)+P12(f71(x11261),f21(x11261,x11262,x11263),x11264)+~E(x11262,f8(x11261))+~E(x11264,f8(f71(x11261)))
% 4.60/4.60 [1312]~P9(x13121)+~P12(f71(x13121),x13123,x13124)+P12(f71(x13121),f21(x13121,x13122,x13123),x13124)+~E(x13124,f8(f71(x13121)))
% 4.60/4.60 [1317]~P9(x13172)+~P12(f71(x13172),f21(x13172,x13173,x13174),x13171)+~E(x13173,f8(x13172))+E(x13171,f8(f71(x13172)))
% 4.60/4.60 [1604]~P1(x16042)+E(x16041,f8(x16042))+~P10(a1,x16043,f8(a1))+~P10(a1,f26(x16042,x16041),f27(f27(f10(a1),x16043),f26(x16042,x16044)))
% 4.60/4.60 [1777]~P51(x17771)+~P11(x17771,x17772,f11(x17771,x17773,x17774))+~P11(x17771,f6(x17771,x17773,x17774),x17772)+P11(x17771,f5(x17771,f6(x17771,x17772,x17773)),x17774)
% 4.60/4.60 [1282]~P57(x12823)+E(x12821,x12822)+~P11(x12823,f3(x12823),x12824)+~E(f27(f27(f13(x12823),x12824),x12821),f27(f27(f13(x12823),x12824),x12822))
% 4.60/4.60 [1576]~P57(x15761)+~P10(a70,x15763,x15764)+~P11(x15761,f3(x15761),x15762)+P10(x15761,f27(f27(f13(x15761),x15762),x15763),f27(f27(f13(x15761),x15762),x15764))
% 4.60/4.60 [1577]~P57(x15771)+~P10(a70,x15773,x15774)+~P10(x15771,f3(x15771),x15772)+P10(x15771,f27(f27(f13(x15771),x15772),x15773),f27(f27(f13(x15771),x15772),x15774))
% 4.60/4.60 [1579]~P57(x15791)+~P11(a70,x15793,x15794)+~P11(x15791,f3(x15791),x15792)+P11(x15791,f27(f27(f13(x15791),x15792),x15793),f27(f27(f13(x15791),x15792),x15794))
% 4.60/4.60 [1585]~P56(x15851)+~P10(x15851,x15854,x15853)+~P11(x15851,x15852,f8(x15851))+P10(x15851,f27(f27(f10(x15851),x15852),x15853),f27(f27(f10(x15851),x15852),x15854))
% 4.60/4.60 [1586]~P64(x15861)+~P10(x15861,x15864,x15863)+~P10(x15861,x15862,f8(x15861))+P10(x15861,f27(f27(f10(x15861),x15862),x15863),f27(f27(f10(x15861),x15862),x15864))
% 4.60/4.60 [1587]~P64(x15871)+~P10(x15871,x15874,x15872)+~P10(x15871,x15873,f8(x15871))+P10(x15871,f27(f27(f10(x15871),x15872),x15873),f27(f27(f10(x15871),x15874),x15873))
% 4.60/4.60 [1591]~P56(x15911)+~P11(x15911,x15914,x15912)+~P11(x15911,x15913,f8(x15911))+P11(x15911,f27(f27(f10(x15911),x15912),x15913),f27(f27(f10(x15911),x15914),x15913))
% 4.60/4.60 [1592]~P56(x15921)+~P11(x15921,x15924,x15923)+~P11(x15921,x15922,f8(x15921))+P11(x15921,f27(f27(f10(x15921),x15922),x15923),f27(f27(f10(x15921),x15922),x15924))
% 4.60/4.60 [1593]~P56(x15931)+~P10(x15931,x15933,x15934)+~P11(x15931,f8(x15931),x15932)+P10(x15931,f27(f27(f10(x15931),x15932),x15933),f27(f27(f10(x15931),x15932),x15934))
% 4.60/4.60 [1594]~P67(x15941)+~P10(x15941,x15943,x15944)+~P10(x15941,f8(x15941),x15942)+P10(x15941,f27(f27(f10(x15941),x15942),x15943),f27(f27(f10(x15941),x15942),x15944))
% 4.60/4.60 [1595]~P65(x15951)+~P10(x15951,x15953,x15954)+~P10(x15951,f8(x15951),x15952)+P10(x15951,f27(f27(f10(x15951),x15952),x15953),f27(f27(f10(x15951),x15952),x15954))
% 4.60/4.60 [1596]~P67(x15961)+~P10(x15961,x15962,x15964)+~P10(x15961,f8(x15961),x15963)+P10(x15961,f27(f27(f10(x15961),x15962),x15963),f27(f27(f10(x15961),x15964),x15963))
% 4.60/4.60 [1597]~P57(x15971)+~P10(x15971,x15972,x15974)+~P10(x15971,f8(x15971),x15972)+P10(x15971,f27(f27(f13(x15971),x15972),x15973),f27(f27(f13(x15971),x15974),x15973))
% 4.60/4.60 [1599]~P52(x15991)+~P11(x15991,x15993,x15994)+~P11(x15991,f8(x15991),x15992)+P11(x15991,f27(f27(f10(x15991),x15992),x15993),f27(f27(f10(x15991),x15992),x15994))
% 4.60/4.60 [1600]~P61(x16001)+~P11(x16001,x16003,x16004)+~P11(x16001,f8(x16001),x16002)+P11(x16001,f27(f27(f10(x16001),x16002),x16003),f27(f27(f10(x16001),x16002),x16004))
% 4.60/4.60 [1601]~P56(x16011)+~P11(x16011,x16012,x16014)+~P11(x16011,f8(x16011),x16013)+P11(x16011,f27(f27(f10(x16011),x16012),x16013),f27(f27(f10(x16011),x16014),x16013))
% 4.60/4.60 [1602]~P61(x16021)+~P11(x16021,x16022,x16024)+~P11(x16021,f8(x16021),x16023)+P11(x16021,f27(f27(f10(x16021),x16022),x16023),f27(f27(f10(x16021),x16024),x16023))
% 4.60/4.60 [1603]~P56(x16031)+~P11(x16031,x16033,x16034)+~P11(x16031,f8(x16031),x16032)+P11(x16031,f27(f27(f10(x16031),x16032),x16033),f27(f27(f10(x16031),x16032),x16034))
% 4.60/4.60 [1624]~P53(x16242)+P12(x16242,x16243,x16244)+E(x16241,f8(x16242))+~P12(x16242,f27(f27(f10(x16242),x16243),x16241),f27(f27(f10(x16242),x16244),x16241))
% 4.60/4.60 [1625]~P53(x16252)+P12(x16252,x16253,x16254)+E(x16251,f8(x16252))+~P12(x16252,f27(f27(f10(x16252),x16251),x16253),f27(f27(f10(x16252),x16251),x16254))
% 4.60/4.60 [1674]P11(x16741,x16743,x16742)+~P56(x16741)+P11(x16741,x16742,x16743)+~P11(x16741,f27(f27(f10(x16741),x16744),x16742),f27(f27(f10(x16741),x16744),x16743))
% 4.60/4.60 [1675]P11(x16751,x16753,x16752)+~P56(x16751)+P11(x16751,x16752,x16753)+~P11(x16751,f27(f27(f10(x16751),x16752),x16754),f27(f27(f10(x16751),x16753),x16754))
% 4.60/4.60 [1679]~P56(x16791)+P11(x16791,x16792,x16793)+P11(x16791,x16794,f8(x16791))+~P11(x16791,f27(f27(f10(x16791),x16792),x16794),f27(f27(f10(x16791),x16793),x16794))
% 4.60/4.60 [1680]~P56(x16801)+P11(x16801,x16802,x16803)+P11(x16801,x16804,f8(x16801))+~P11(x16801,f27(f27(f10(x16801),x16804),x16802),f27(f27(f10(x16801),x16804),x16803))
% 4.60/4.60 [1681]~P56(x16811)+P11(x16811,x16812,x16813)+P11(x16811,f8(x16811),x16814)+~P11(x16811,f27(f27(f10(x16811),x16814),x16813),f27(f27(f10(x16811),x16814),x16812))
% 4.60/4.60 [1682]~P56(x16821)+P11(x16821,x16822,x16823)+P11(x16821,f8(x16821),x16824)+~P11(x16821,f27(f27(f10(x16821),x16823),x16824),f27(f27(f10(x16821),x16822),x16824))
% 4.60/4.60 [1698]~P56(x16981)+P11(x16981,f8(x16981),x16982)+P11(x16981,x16982,f8(x16981))+~P11(x16981,f27(f27(f10(x16981),x16983),x16982),f27(f27(f10(x16981),x16984),x16982))
% 4.60/4.60 [1699]~P56(x16991)+P11(x16991,f8(x16991),x16992)+P11(x16991,x16992,f8(x16991))+~P11(x16991,f27(f27(f10(x16991),x16992),x16993),f27(f27(f10(x16991),x16992),x16994))
% 4.60/4.60 [1709]~P57(x17093)+P10(a70,x17091,x17092)+~P11(x17093,f3(x17093),x17094)+~P10(x17093,f27(f27(f13(x17093),x17094),x17091),f27(f27(f13(x17093),x17094),x17092))
% 4.60/4.60 [1711]~P57(x17113)+P11(a70,x17111,x17112)+~P11(x17113,f3(x17113),x17114)+~P11(x17113,f27(f27(f13(x17113),x17114),x17111),f27(f27(f13(x17113),x17114),x17112))
% 4.60/4.60 [1712]~P56(x17121)+P10(x17121,x17122,x17123)+~P11(x17121,x17124,f8(x17121))+~P10(x17121,f27(f27(f10(x17121),x17124),x17123),f27(f27(f10(x17121),x17124),x17122))
% 4.60/4.60 [1713]~P56(x17131)+P11(x17131,x17132,x17133)+~P11(x17131,x17134,f8(x17131))+~P11(x17131,f27(f27(f10(x17131),x17134),x17133),f27(f27(f10(x17131),x17134),x17132))
% 4.60/4.60 [1714]~P56(x17141)+P10(x17141,x17142,x17143)+~P11(x17141,f8(x17141),x17144)+~P10(x17141,f27(f27(f10(x17141),x17144),x17142),f27(f27(f10(x17141),x17144),x17143))
% 4.60/4.60 [1715]~P61(x17151)+P10(x17151,x17152,x17153)+~P11(x17151,f8(x17151),x17154)+~P10(x17151,f27(f27(f10(x17151),x17154),x17152),f27(f27(f10(x17151),x17154),x17153))
% 4.60/4.60 [1716]~P61(x17161)+P10(x17161,x17162,x17163)+~P11(x17161,f8(x17161),x17164)+~P10(x17161,f27(f27(f10(x17161),x17162),x17164),f27(f27(f10(x17161),x17163),x17164))
% 4.60/4.60 [1717]~P56(x17171)+P11(x17171,x17172,x17173)+~P11(x17171,f8(x17171),x17174)+~P11(x17171,f27(f27(f10(x17171),x17174),x17172),f27(f27(f10(x17171),x17174),x17173))
% 4.60/4.60 [1718]~P61(x17181)+P11(x17181,x17182,x17183)+~P10(x17181,f8(x17181),x17184)+~P11(x17181,f27(f27(f10(x17181),x17184),x17182),f27(f27(f10(x17181),x17184),x17183))
% 4.60/4.60 [1719]~P58(x17191)+P11(x17191,x17192,x17193)+~P10(x17191,f8(x17191),x17194)+~P11(x17191,f27(f27(f10(x17191),x17194),x17192),f27(f27(f10(x17191),x17194),x17193))
% 4.60/4.60 [1720]~P61(x17201)+P11(x17201,x17202,x17203)+~P10(x17201,f8(x17201),x17204)+~P11(x17201,f27(f27(f10(x17201),x17202),x17204),f27(f27(f10(x17201),x17203),x17204))
% 4.60/4.60 [1721]~P57(x17211)+P11(x17211,x17212,x17213)+~P10(x17211,f8(x17211),x17213)+~P11(x17211,f27(f27(f13(x17211),x17212),x17214),f27(f27(f13(x17211),x17213),x17214))
% 4.60/4.60 [1722]~P58(x17221)+P11(x17221,x17222,x17223)+~P10(x17221,f8(x17221),x17224)+~P11(x17221,f27(f27(f10(x17221),x17222),x17224),f27(f27(f10(x17221),x17223),x17224))
% 4.60/4.60 [1807]~P57(x18071)+P10(x18071,x18072,x18073)+~P10(x18071,f8(x18071),x18073)+~P10(x18071,f27(f27(f13(x18071),x18072),f11(a70,x18074,f3(a70))),f27(f27(f13(x18071),x18073),f11(a70,x18074,f3(a70))))
% 4.60/4.60 [1821]~P1(x18211)+~P11(a1,f8(a1),x18214)+~P10(a1,f26(x18211,f27(x18212,f50(x18212,x18211,x18214))),x18214)+P10(a1,f26(x18211,f27(x18212,x18213)),f25(a70,f11(a70,f49(x18212,x18211),f3(a70))))
% 4.60/4.60 [1822]~P1(x18221)+~P11(a1,f8(a1),x18224)+~P10(a1,f26(x18221,f27(x18222,f47(x18222,x18221,x18224))),x18224)+P11(a1,f26(x18221,f27(x18222,x18223)),f25(a70,f11(a70,f46(x18222,x18221),f3(a70))))
% 4.60/4.60 [1740]~P54(x17403)+~P73(x17403)+P74(f27(x17401,f39(x17402,x17401,x17403)))+~P74(f27(x17401,f27(f27(f10(x17403),x17402),x17404)))
% 4.60/4.60 [1772]~P54(x17721)+~P73(x17721)+P12(x17721,x17722,f11(x17721,f39(x17722,x17723,x17721),f8(x17721)))+~P74(f27(x17723,f27(f27(f10(x17721),x17722),x17724)))
% 4.60/4.60 [1089]~P8(x10895)+E(x10891,x10892)+~E(x10893,x10894)+~E(f6(x10895,x10893,x10894),f6(x10895,x10891,x10892))
% 4.60/4.60 [1371]~P25(x13711)+~P10(x13711,x13714,x13715)+P10(x13711,x13712,x13713)+~E(f6(x13711,x13714,x13715),f6(x13711,x13712,x13713))
% 4.60/4.60 [1373]~P25(x13731)+~P11(x13731,x13734,x13735)+P11(x13731,x13732,x13733)+~E(f6(x13731,x13734,x13735),f6(x13731,x13732,x13733))
% 4.60/4.60 [1580]~P31(x15801)+~P10(x15801,x15803,x15805)+~P10(x15801,x15802,x15804)+P10(x15801,f11(x15801,x15802,x15803),f11(x15801,x15804,x15805))
% 4.60/4.60 [1581]~P32(x15811)+~P10(x15811,x15813,x15815)+~P11(x15811,x15812,x15814)+P11(x15811,f11(x15811,x15812,x15813),f11(x15811,x15814,x15815))
% 4.60/4.60 [1582]~P32(x15821)+~P10(x15821,x15822,x15824)+~P11(x15821,x15823,x15825)+P11(x15821,f11(x15821,x15822,x15823),f11(x15821,x15824,x15825))
% 4.60/4.60 [1583]~P32(x15831)+~P11(x15831,x15833,x15835)+~P11(x15831,x15832,x15834)+P11(x15831,f11(x15831,x15832,x15833),f11(x15831,x15834,x15835))
% 4.60/4.60 [1752]~P1(x17521)+~P11(a1,f26(x17521,x17523),x17525)+~P11(a1,f26(x17521,x17522),x17524)+P11(a1,f26(x17521,f11(x17521,x17522,x17523)),f11(a1,x17524,x17525))
% 4.60/4.60 [1567]~P43(x15671)+~P12(x15671,x15672,x15674)+~P10(a70,x15673,x15675)+P12(x15671,f27(f27(f13(x15671),x15672),x15673),f27(f27(f13(x15671),x15674),x15675))
% 4.60/4.60 [1569]~P43(x15691)+~P12(x15691,x15693,x15695)+~P12(x15691,x15692,x15694)+P12(x15691,f27(f27(f10(x15691),x15692),x15693),f27(f27(f10(x15691),x15694),x15695))
% 4.60/4.60 [1645]~P43(x16451)+~P10(a70,x16453,x16455)+~P12(x16451,f27(f27(f13(x16451),x16452),x16455),x16454)+P12(x16451,f27(f27(f13(x16451),x16452),x16453),x16454)
% 4.60/4.60 [1759]~P51(x17591)+~P11(x17591,f5(x17591,x17592),x17594)+~P11(x17591,f5(x17591,x17593),x17595)+P11(x17591,f27(f27(f10(x17591),f5(x17591,x17592)),f5(x17591,x17593)),f27(f27(f10(x17591),x17594),x17595))
% 4.60/4.60 [1741]~P2(x17411)+~P11(a1,f26(x17411,x17413),x17415)+~P11(a1,f26(x17411,x17412),x17414)+P11(a1,f26(x17411,f27(f27(f10(x17411),x17412),x17413)),f27(f27(f10(a1),x17414),x17415))
% 4.60/4.60 [1780]~P48(x17805)+E(x17801,x17802)+E(x17803,x17804)+~E(f11(x17805,f27(f27(f10(x17805),x17803),x17801),f27(f27(f10(x17805),x17804),x17802)),f11(x17805,f27(f27(f10(x17805),x17803),x17802),f27(f27(f10(x17805),x17804),x17801)))
% 4.60/4.60 [1431]E(x14311,x14312)+~P12(a68,x14312,x14311)+~P12(a68,x14311,x14312)+~P10(a68,f8(a68),x14312)+~P10(a68,f8(a68),x14311)
% 4.60/4.60 [1320]~P29(x13202)+~P10(x13202,f8(x13202),x13203)+~P10(x13202,f8(x13202),x13201)+~E(f11(x13202,x13203,x13201),f8(x13202))+E(x13201,f8(x13202))
% 4.60/4.60 [1321]~P29(x13212)+~P10(x13212,f8(x13212),x13213)+~P10(x13212,f8(x13212),x13211)+~E(f11(x13212,x13211,x13213),f8(x13212))+E(x13211,f8(x13212))
% 4.60/4.60 [1444]E(x14441,f58(x14442,x14443))+~P11(a1,f8(a1),x14442)+~P11(a1,f8(a1),x14441)+~P11(a70,f8(a70),x14443)+~E(f27(f27(f13(a1),x14441),x14443),x14442)
% 4.60/4.60 [1605]~P51(x16051)+~P10(x16051,x16052,f3(x16051))+~P10(x16051,f8(x16051),x16052)+~P10(x16051,f8(x16051),x16053)+P10(x16051,f27(f27(f10(x16051),x16052),x16053),x16053)
% 4.60/4.60 [1606]~P51(x16061)+~P10(x16061,x16063,f3(x16061))+~P10(x16061,f8(x16061),x16063)+~P10(x16061,f8(x16061),x16062)+P10(x16061,f27(f27(f10(x16061),x16062),x16063),x16062)
% 4.60/4.60 [1700]~P57(x17001)+~P11(x17001,x17002,x17004)+~P10(x17001,f8(x17001),x17002)+~P11(a70,f8(a70),x17003)+P11(x17001,f27(f27(f13(x17001),x17002),x17003),f27(f27(f13(x17001),x17004),x17003))
% 4.60/4.60 [1701]~P57(x17011)+~P10(a70,x17014,x17013)+~P10(x17011,x17012,f3(x17011))+~P10(x17011,f8(x17011),x17012)+P10(x17011,f27(f27(f13(x17011),x17012),x17013),f27(f27(f13(x17011),x17012),x17014))
% 4.60/4.60 [1702]~P57(x17021)+~P11(a70,x17024,x17023)+~P11(x17021,x17022,f3(x17021))+~P11(x17021,f8(x17021),x17022)+P11(x17021,f27(f27(f13(x17021),x17022),x17023),f27(f27(f13(x17021),x17022),x17024))
% 4.60/4.60 [1764]~P57(x17643)+E(x17641,x17642)+~P10(x17643,f8(x17643),x17642)+~P10(x17643,f8(x17643),x17641)+~E(f27(f27(f13(x17643),x17641),f11(a70,x17644,f3(a70))),f27(f27(f13(x17643),x17642),f11(a70,x17644,f3(a70))))
% 4.60/4.60 [1790]~P54(x17902)+~P73(x17902)+~P12(x17902,x17903,f11(x17902,x17904,f8(x17902)))+~P74(f27(x17901,x17904))+P74(f27(x17901,f27(f27(f10(x17902),x17903),f40(x17903,x17901,x17902))))
% 4.60/4.60 [1796]~P10(a68,f8(a68),x17962)+~P11(a68,f8(a68),x17963)+~P74(f27(x17961,x17964))+P74(f27(x17961,f57(x17962,x17961,x17963)))+P74(f27(x17961,f11(a68,x17964,f27(f27(f10(a68),x17962),x17963))))
% 4.60/4.60 [1828]~P10(a68,f8(a68),x18283)+~P11(a68,f8(a68),x18284)+~P74(f27(x18281,x18282))+~P74(f27(x18281,f11(a68,f57(x18283,x18281,x18284),x18284)))+P74(f27(x18281,f11(a68,x18282,f27(f27(f10(a68),x18283),x18284))))
% 4.60/4.60 [1793]~P1(x17934)+~P39(x17931)+~P10(x17931,x17932,x17935)+P10(x17931,x17932,f62(x17933,x17932,x17931,x17934))+P11(a1,f26(x17934,f27(x17933,x17935)),f11(a1,f3(a1),f26(x17934,f27(x17933,x17932))))
% 4.60/4.60 [1809]P10(a68,x18091,x18092)+~P11(a68,x18093,x18094)+~P11(a68,x18093,x18095)+~P10(a68,x18094,f8(a68))+~P10(a68,f11(a68,f27(f27(f10(a68),x18093),x18092),x18095),f11(a68,f27(f27(f10(a68),x18093),x18091),x18094))
% 4.60/4.60 [1810]P10(a68,x18101,x18102)+~P11(a68,x18103,x18104)+~P11(a68,x18105,x18104)+~P10(a68,f8(a68),x18105)+~P10(a68,f11(a68,f27(f27(f10(a68),x18104),x18101),x18105),f11(a68,f27(f27(f10(a68),x18104),x18102),x18103))
% 4.60/4.60 [1851]~P1(x18511)+~P10(x18515,x18514,x18513)+~P39(x18515)+P11(a1,f26(x18511,f27(x18512,x18513)),f11(a1,f3(a1),f26(x18511,f27(x18512,x18514))))+~P11(a1,f26(x18511,f6(x18511,f27(x18512,x18514),f27(x18512,f62(x18512,x18514,x18515,x18511)))),f3(a1))
% 4.60/4.60 [1665]~P48(x16654)+E(x16651,x16652)+~E(x16655,x16656)+E(x16653,f8(x16654))+~E(f11(x16654,x16655,f27(f27(f10(x16654),x16653),x16651)),f11(x16654,x16656,f27(f27(f10(x16654),x16653),x16652)))
% 4.60/4.60 [1800]~P46(x18001)+~P54(x18001)+~P12(x18001,x18002,x18005)+~P12(x18001,x18002,f11(x18001,x18003,x18006))+P12(x18001,x18002,f11(x18001,f6(x18001,x18003,f27(f27(f10(x18001),x18004),x18005)),x18006))
% 4.60/4.60 [1825]~P46(x18251)+~P54(x18251)+~P12(x18251,x18252,x18255)+P12(x18251,x18252,f11(x18251,x18253,x18254))+~P12(x18251,x18252,f11(x18251,f6(x18251,x18253,f27(f27(f10(x18251),x18256),x18255)),x18254))
% 4.60/4.60 [1292]~P29(x12921)+~P10(x12921,f8(x12921),x12923)+~P10(x12921,f8(x12921),x12922)+~E(x12923,f8(x12921))+~E(x12922,f8(x12921))+E(f11(x12921,x12922,x12923),f8(x12921))
% 4.60/4.60 [919]~P60(x9192)+~P62(x9192)+~P71(x9192)+~P40(x9192)+E(x9191,f8(x9192))+~E(f27(f27(f13(x9192),x9191),x9193),f8(x9192))
% 4.60/4.60 [920]~P60(x9202)+~P62(x9202)+~P71(x9202)+~P40(x9202)+~E(x9201,f8(a70))+~E(f27(f27(f13(x9202),x9203),x9201),f8(x9202))
% 4.60/4.60 [1612]~P57(x16123)+E(x16121,x16122)+~P10(x16123,f8(x16123),x16122)+~P10(x16123,f8(x16123),x16121)+~P11(a70,f8(a70),x16124)+~E(f27(f27(f13(x16123),x16121),x16124),f27(f27(f13(x16123),x16122),x16124))
% 4.60/4.60 [1742]~P67(x17421)+~P10(x17421,x17423,x17425)+~P10(x17421,x17422,x17424)+~P10(x17421,f8(x17421),x17423)+~P10(x17421,f8(x17421),x17424)+P10(x17421,f27(f27(f10(x17421),x17422),x17423),f27(f27(f10(x17421),x17424),x17425))
% 4.60/4.60 [1743]~P67(x17431)+~P10(x17431,x17433,x17435)+~P10(x17431,x17432,x17434)+~P10(x17431,f8(x17431),x17433)+~P10(x17431,f8(x17431),x17432)+P10(x17431,f27(f27(f10(x17431),x17432),x17433),f27(f27(f10(x17431),x17434),x17435))
% 4.60/4.60 [1744]~P61(x17441)+~P10(x17441,x17443,x17445)+~P11(x17441,x17442,x17444)+~P10(x17441,f8(x17441),x17442)+~P11(x17441,f8(x17441),x17443)+P11(x17441,f27(f27(f10(x17441),x17442),x17443),f27(f27(f10(x17441),x17444),x17445))
% 4.60/4.60 [1745]~P61(x17451)+~P10(x17451,x17452,x17454)+~P11(x17451,x17453,x17455)+~P10(x17451,f8(x17451),x17453)+~P11(x17451,f8(x17451),x17452)+P11(x17451,f27(f27(f10(x17451),x17452),x17453),f27(f27(f10(x17451),x17454),x17455))
% 4.60/4.60 [1746]~P61(x17461)+~P11(x17461,x17463,x17465)+~P11(x17461,x17462,x17464)+~P10(x17461,f8(x17461),x17463)+~P10(x17461,f8(x17461),x17462)+P11(x17461,f27(f27(f10(x17461),x17462),x17463),f27(f27(f10(x17461),x17464),x17465))
% 4.60/4.60 [1747]~P61(x17471)+~P11(x17471,x17473,x17475)+~P11(x17471,x17472,x17474)+~P10(x17471,f8(x17471),x17473)+~P11(x17471,f8(x17471),x17474)+P11(x17471,f27(f27(f10(x17471),x17472),x17473),f27(f27(f10(x17471),x17474),x17475))
% 4.60/4.60 [847]~P60(x8472)+~P62(x8472)+~P71(x8472)+~P40(x8472)+~E(x8473,f8(x8472))+E(x8471,f8(a70))+E(f27(f27(f13(x8472),x8473),x8471),f8(x8472))
% 4.60/4.60 [1791]~P50(x17911)+~P10(x17911,x17915,x17916)+~P10(x17911,x17913,x17916)+~P10(x17911,f8(x17911),x17914)+~P10(x17911,f8(x17911),x17912)+~E(f11(x17911,x17912,x17914),f3(x17911))+P10(x17911,f11(x17911,f27(f27(f10(x17911),x17912),x17913),f27(f27(f10(x17911),x17914),x17915)),x17916)
% 4.60/4.60 [1792]~P49(x17921)+~P11(x17921,x17925,x17926)+~P11(x17921,x17923,x17926)+~P10(x17921,f8(x17921),x17924)+~P10(x17921,f8(x17921),x17922)+~E(f11(x17921,x17922,x17924),f3(x17921))+P11(x17921,f11(x17921,f27(f27(f10(x17921),x17922),x17923),f27(f27(f10(x17921),x17924),x17925)),x17926)
% 4.60/4.60 [1817]~P10(a68,x18175,x18173)+~P11(a68,x18176,x18175)+P10(a68,x18171,x18172)+~P10(a68,f8(a68),x18174)+~P11(a68,f8(a68),x18175)+~P10(a68,f8(a68),f11(a68,f27(f27(f10(a68),x18175),x18172),x18176))+~E(f11(a68,f27(f27(f10(a68),x18173),x18171),x18174),f11(a68,f27(f27(f10(a68),x18175),x18172),x18176))
% 4.60/4.60 [1818]~P10(a68,x18185,x18183)+~P11(a68,x18184,x18183)+P10(a68,x18181,x18182)+~P10(a68,f8(a68),x18186)+~P11(a68,f8(a68),x18185)+~P11(a68,f11(a68,f27(f27(f10(a68),x18185),x18181),x18186),f8(a68))+~E(f11(a68,f27(f27(f10(a68),x18183),x18182),x18184),f11(a68,f27(f27(f10(a68),x18185),x18181),x18186))
% 4.60/4.60 %EqnAxiom
% 4.60/4.60 [1]E(x11,x11)
% 4.60/4.60 [2]E(x22,x21)+~E(x21,x22)
% 4.60/4.60 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 4.60/4.60 [4]~E(x41,x42)+E(f3(x41),f3(x42))
% 4.60/4.60 [5]~E(x51,x52)+E(f7(x51),f7(x52))
% 4.60/4.60 [6]~E(x61,x62)+E(f26(x61,x63),f26(x62,x63))
% 4.60/4.60 [7]~E(x71,x72)+E(f26(x73,x71),f26(x73,x72))
% 4.60/4.60 [8]~E(x81,x82)+E(f8(x81),f8(x82))
% 4.60/4.60 [9]~E(x91,x92)+E(f27(x91,x93),f27(x92,x93))
% 4.60/4.60 [10]~E(x101,x102)+E(f27(x103,x101),f27(x103,x102))
% 4.60/4.60 [11]~E(x111,x112)+E(f10(x111),f10(x112))
% 4.60/4.60 [12]~E(x121,x122)+E(f6(x121,x123,x124),f6(x122,x123,x124))
% 4.60/4.60 [13]~E(x131,x132)+E(f6(x133,x131,x134),f6(x133,x132,x134))
% 4.60/4.60 [14]~E(x141,x142)+E(f6(x143,x144,x141),f6(x143,x144,x142))
% 4.60/4.60 [15]~E(x151,x152)+E(f24(x151),f24(x152))
% 4.60/4.60 [16]~E(x161,x162)+E(f34(x161,x163),f34(x162,x163))
% 4.60/4.60 [17]~E(x171,x172)+E(f34(x173,x171),f34(x173,x172))
% 4.60/4.60 [18]~E(x181,x182)+E(f11(x181,x183,x184),f11(x182,x183,x184))
% 4.60/4.60 [19]~E(x191,x192)+E(f11(x193,x191,x194),f11(x193,x192,x194))
% 4.60/4.60 [20]~E(x201,x202)+E(f11(x203,x204,x201),f11(x203,x204,x202))
% 4.60/4.60 [21]~E(x211,x212)+E(f19(x211,x213,x214),f19(x212,x213,x214))
% 4.60/4.60 [22]~E(x221,x222)+E(f19(x223,x221,x224),f19(x223,x222,x224))
% 4.60/4.60 [23]~E(x231,x232)+E(f19(x233,x234,x231),f19(x233,x234,x232))
% 4.60/4.60 [24]~E(x241,x242)+E(f13(x241),f13(x242))
% 4.60/4.60 [25]~E(x251,x252)+E(f71(x251),f71(x252))
% 4.60/4.60 [26]~E(x261,x262)+E(f4(x261),f4(x262))
% 4.60/4.60 [27]~E(x271,x272)+E(f62(x271,x273,x274,x275),f62(x272,x273,x274,x275))
% 4.60/4.60 [28]~E(x281,x282)+E(f62(x283,x281,x284,x285),f62(x283,x282,x284,x285))
% 4.60/4.60 [29]~E(x291,x292)+E(f62(x293,x294,x291,x295),f62(x293,x294,x292,x295))
% 4.60/4.60 [30]~E(x301,x302)+E(f62(x303,x304,x305,x301),f62(x303,x304,x305,x302))
% 4.60/4.60 [31]~E(x311,x312)+E(f9(x311,x313),f9(x312,x313))
% 4.60/4.60 [32]~E(x321,x322)+E(f9(x323,x321),f9(x323,x322))
% 4.60/4.60 [33]~E(x331,x332)+E(f15(x331,x333,x334),f15(x332,x333,x334))
% 4.60/4.60 [34]~E(x341,x342)+E(f15(x343,x341,x344),f15(x343,x342,x344))
% 4.60/4.60 [35]~E(x351,x352)+E(f15(x353,x354,x351),f15(x353,x354,x352))
% 4.60/4.60 [36]~E(x361,x362)+E(f14(x361,x363),f14(x362,x363))
% 4.60/4.60 [37]~E(x371,x372)+E(f14(x373,x371),f14(x373,x372))
% 4.60/4.60 [38]~E(x381,x382)+E(f21(x381,x383,x384),f21(x382,x383,x384))
% 4.60/4.60 [39]~E(x391,x392)+E(f21(x393,x391,x394),f21(x393,x392,x394))
% 4.60/4.60 [40]~E(x401,x402)+E(f21(x403,x404,x401),f21(x403,x404,x402))
% 4.60/4.60 [41]~E(x411,x412)+E(f25(x411,x413),f25(x412,x413))
% 4.60/4.60 [42]~E(x421,x422)+E(f25(x423,x421),f25(x423,x422))
% 4.60/4.60 [43]~E(x431,x432)+E(f65(x431,x433),f65(x432,x433))
% 4.60/4.60 [44]~E(x441,x442)+E(f65(x443,x441),f65(x443,x442))
% 4.60/4.60 [45]~E(x451,x452)+E(f66(x451,x453),f66(x452,x453))
% 4.60/4.60 [46]~E(x461,x462)+E(f66(x463,x461),f66(x463,x462))
% 4.60/4.60 [47]~E(x471,x472)+E(f32(x471,x473),f32(x472,x473))
% 4.60/4.60 [48]~E(x481,x482)+E(f32(x483,x481),f32(x483,x482))
% 4.60/4.60 [49]~E(x491,x492)+E(f5(x491,x493),f5(x492,x493))
% 4.60/4.60 [50]~E(x501,x502)+E(f5(x503,x501),f5(x503,x502))
% 4.60/4.60 [51]~E(x511,x512)+E(f29(x511,x513),f29(x512,x513))
% 4.60/4.60 [52]~E(x521,x522)+E(f29(x523,x521),f29(x523,x522))
% 4.60/4.60 [53]~E(x531,x532)+E(f12(x531,x533),f12(x532,x533))
% 4.60/4.60 [54]~E(x541,x542)+E(f12(x543,x541),f12(x543,x542))
% 4.60/4.60 [55]~E(x551,x552)+E(f75(x551,x553),f75(x552,x553))
% 4.60/4.60 [56]~E(x561,x562)+E(f75(x563,x561),f75(x563,x562))
% 4.60/4.60 [57]~E(x571,x572)+E(f36(x571),f36(x572))
% 4.60/4.60 [58]~E(x581,x582)+E(f20(x581,x583,x584),f20(x582,x583,x584))
% 4.60/4.60 [59]~E(x591,x592)+E(f20(x593,x591,x594),f20(x593,x592,x594))
% 4.60/4.60 [60]~E(x601,x602)+E(f20(x603,x604,x601),f20(x603,x604,x602))
% 4.60/4.60 [61]~E(x611,x612)+E(f61(x611,x613,x614),f61(x612,x613,x614))
% 4.60/4.60 [62]~E(x621,x622)+E(f61(x623,x621,x624),f61(x623,x622,x624))
% 4.60/4.60 [63]~E(x631,x632)+E(f61(x633,x634,x631),f61(x633,x634,x632))
% 4.60/4.60 [64]~E(x641,x642)+E(f53(x641,x643),f53(x642,x643))
% 4.60/4.60 [65]~E(x651,x652)+E(f53(x653,x651),f53(x653,x652))
% 4.60/4.60 [66]~E(x661,x662)+E(f35(x661,x663),f35(x662,x663))
% 4.60/4.60 [67]~E(x671,x672)+E(f35(x673,x671),f35(x673,x672))
% 4.60/4.60 [68]~E(x681,x682)+E(f23(x681,x683,x684),f23(x682,x683,x684))
% 4.60/4.60 [69]~E(x691,x692)+E(f23(x693,x691,x694),f23(x693,x692,x694))
% 4.60/4.60 [70]~E(x701,x702)+E(f23(x703,x704,x701),f23(x703,x704,x702))
% 4.60/4.60 [71]~E(x711,x712)+E(f40(x711,x713,x714),f40(x712,x713,x714))
% 4.60/4.60 [72]~E(x721,x722)+E(f40(x723,x721,x724),f40(x723,x722,x724))
% 4.60/4.60 [73]~E(x731,x732)+E(f40(x733,x734,x731),f40(x733,x734,x732))
% 4.60/4.60 [74]~E(x741,x742)+E(f16(x741,x743),f16(x742,x743))
% 4.60/4.60 [75]~E(x751,x752)+E(f16(x753,x751),f16(x753,x752))
% 4.60/4.60 [76]~E(x761,x762)+E(f58(x761,x763),f58(x762,x763))
% 4.60/4.60 [77]~E(x771,x772)+E(f58(x773,x771),f58(x773,x772))
% 4.60/4.60 [78]~E(x781,x782)+E(f43(x781,x783),f43(x782,x783))
% 4.60/4.60 [79]~E(x791,x792)+E(f43(x793,x791),f43(x793,x792))
% 4.60/4.60 [80]~E(x801,x802)+E(f63(x801,x803,x804),f63(x802,x803,x804))
% 4.60/4.60 [81]~E(x811,x812)+E(f63(x813,x811,x814),f63(x813,x812,x814))
% 4.60/4.60 [82]~E(x821,x822)+E(f63(x823,x824,x821),f63(x823,x824,x822))
% 4.60/4.60 [83]~E(x831,x832)+E(f67(x831,x833),f67(x832,x833))
% 4.60/4.60 [84]~E(x841,x842)+E(f67(x843,x841),f67(x843,x842))
% 4.60/4.60 [85]~E(x851,x852)+E(f39(x851,x853,x854),f39(x852,x853,x854))
% 4.60/4.60 [86]~E(x861,x862)+E(f39(x863,x861,x864),f39(x863,x862,x864))
% 4.60/4.60 [87]~E(x871,x872)+E(f39(x873,x874,x871),f39(x873,x874,x872))
% 4.60/4.60 [88]~E(x881,x882)+E(f48(x881,x883,x884),f48(x882,x883,x884))
% 4.60/4.60 [89]~E(x891,x892)+E(f48(x893,x891,x894),f48(x893,x892,x894))
% 4.60/4.60 [90]~E(x901,x902)+E(f48(x903,x904,x901),f48(x903,x904,x902))
% 4.60/4.60 [91]~E(x911,x912)+E(f47(x911,x913,x914),f47(x912,x913,x914))
% 4.60/4.60 [92]~E(x921,x922)+E(f47(x923,x921,x924),f47(x923,x922,x924))
% 4.60/4.60 [93]~E(x931,x932)+E(f47(x933,x934,x931),f47(x933,x934,x932))
% 4.60/4.60 [94]~E(x941,x942)+E(f18(x941,x943,x944),f18(x942,x943,x944))
% 4.60/4.60 [95]~E(x951,x952)+E(f18(x953,x951,x954),f18(x953,x952,x954))
% 4.60/4.60 [96]~E(x961,x962)+E(f18(x963,x964,x961),f18(x963,x964,x962))
% 4.60/4.60 [97]~E(x971,x972)+E(f22(x971,x973,x974,x975,x976),f22(x972,x973,x974,x975,x976))
% 4.60/4.60 [98]~E(x981,x982)+E(f22(x983,x981,x984,x985,x986),f22(x983,x982,x984,x985,x986))
% 4.60/4.60 [99]~E(x991,x992)+E(f22(x993,x994,x991,x995,x996),f22(x993,x994,x992,x995,x996))
% 4.60/4.60 [100]~E(x1001,x1002)+E(f22(x1003,x1004,x1005,x1001,x1006),f22(x1003,x1004,x1005,x1002,x1006))
% 4.60/4.60 [101]~E(x1011,x1012)+E(f22(x1013,x1014,x1015,x1016,x1011),f22(x1013,x1014,x1015,x1016,x1012))
% 4.60/4.60 [102]~E(x1021,x1022)+E(f30(x1021),f30(x1022))
% 4.60/4.60 [103]~E(x1031,x1032)+E(f45(x1031,x1033,x1034),f45(x1032,x1033,x1034))
% 4.60/4.60 [104]~E(x1041,x1042)+E(f45(x1043,x1041,x1044),f45(x1043,x1042,x1044))
% 4.60/4.60 [105]~E(x1051,x1052)+E(f45(x1053,x1054,x1051),f45(x1053,x1054,x1052))
% 4.60/4.60 [106]~E(x1061,x1062)+E(f54(x1061,x1063),f54(x1062,x1063))
% 4.60/4.60 [107]~E(x1071,x1072)+E(f54(x1073,x1071),f54(x1073,x1072))
% 4.60/4.60 [108]~E(x1081,x1082)+E(f55(x1081,x1083),f55(x1082,x1083))
% 4.60/4.60 [109]~E(x1091,x1092)+E(f55(x1093,x1091),f55(x1093,x1092))
% 4.60/4.60 [110]~E(x1101,x1102)+E(f59(x1101,x1103),f59(x1102,x1103))
% 4.60/4.60 [111]~E(x1111,x1112)+E(f59(x1113,x1111),f59(x1113,x1112))
% 4.60/4.60 [112]~E(x1121,x1122)+E(f49(x1121,x1123),f49(x1122,x1123))
% 4.60/4.60 [113]~E(x1131,x1132)+E(f49(x1133,x1131),f49(x1133,x1132))
% 4.60/4.60 [114]~E(x1141,x1142)+E(f50(x1141,x1143,x1144),f50(x1142,x1143,x1144))
% 4.60/4.60 [115]~E(x1151,x1152)+E(f50(x1153,x1151,x1154),f50(x1153,x1152,x1154))
% 4.60/4.60 [116]~E(x1161,x1162)+E(f50(x1163,x1164,x1161),f50(x1163,x1164,x1162))
% 4.60/4.60 [117]~E(x1171,x1172)+E(f57(x1171,x1173,x1174),f57(x1172,x1173,x1174))
% 4.60/4.60 [118]~E(x1181,x1182)+E(f57(x1183,x1181,x1184),f57(x1183,x1182,x1184))
% 4.60/4.60 [119]~E(x1191,x1192)+E(f57(x1193,x1194,x1191),f57(x1193,x1194,x1192))
% 4.60/4.60 [120]~E(x1201,x1202)+E(f52(x1201,x1203),f52(x1202,x1203))
% 4.60/4.60 [121]~E(x1211,x1212)+E(f52(x1213,x1211),f52(x1213,x1212))
% 4.60/4.60 [122]~E(x1221,x1222)+E(f46(x1221,x1223),f46(x1222,x1223))
% 4.60/4.60 [123]~E(x1231,x1232)+E(f46(x1233,x1231),f46(x1233,x1232))
% 4.60/4.60 [124]~E(x1241,x1242)+E(f64(x1241,x1243,x1244,x1245),f64(x1242,x1243,x1244,x1245))
% 4.60/4.60 [125]~E(x1251,x1252)+E(f64(x1253,x1251,x1254,x1255),f64(x1253,x1252,x1254,x1255))
% 4.60/4.60 [126]~E(x1261,x1262)+E(f64(x1263,x1264,x1261,x1265),f64(x1263,x1264,x1262,x1265))
% 4.60/4.60 [127]~E(x1271,x1272)+E(f64(x1273,x1274,x1275,x1271),f64(x1273,x1274,x1275,x1272))
% 4.60/4.60 [128]~E(x1281,x1282)+E(f56(x1281),f56(x1282))
% 4.60/4.60 [129]~E(x1291,x1292)+E(f51(x1291),f51(x1292))
% 4.60/4.60 [130]~E(x1301,x1302)+E(f42(x1301,x1303),f42(x1302,x1303))
% 4.60/4.60 [131]~E(x1311,x1312)+E(f42(x1313,x1311),f42(x1313,x1312))
% 4.60/4.60 [132]~E(x1321,x1322)+E(f33(x1321,x1323),f33(x1322,x1323))
% 4.60/4.60 [133]~E(x1331,x1332)+E(f33(x1333,x1331),f33(x1333,x1332))
% 4.60/4.60 [134]~E(x1341,x1342)+E(f37(x1341,x1343),f37(x1342,x1343))
% 4.60/4.60 [135]~E(x1351,x1352)+E(f37(x1353,x1351),f37(x1353,x1352))
% 4.60/4.60 [136]~E(x1361,x1362)+E(f31(x1361,x1363),f31(x1362,x1363))
% 4.60/4.60 [137]~E(x1371,x1372)+E(f31(x1373,x1371),f31(x1373,x1372))
% 4.60/4.60 [138]~E(x1381,x1382)+E(f41(x1381),f41(x1382))
% 4.60/4.60 [139]~E(x1391,x1392)+E(f44(x1391,x1393),f44(x1392,x1393))
% 4.60/4.60 [140]~E(x1401,x1402)+E(f44(x1403,x1401),f44(x1403,x1402))
% 4.60/4.60 [141]~E(x1411,x1412)+E(f38(x1411,x1413),f38(x1412,x1413))
% 4.60/4.60 [142]~E(x1421,x1422)+E(f38(x1423,x1421),f38(x1423,x1422))
% 4.60/4.60 [143]~E(x1431,x1432)+E(f17(x1431,x1433,x1434,x1435),f17(x1432,x1433,x1434,x1435))
% 4.60/4.60 [144]~E(x1441,x1442)+E(f17(x1443,x1441,x1444,x1445),f17(x1443,x1442,x1444,x1445))
% 4.60/4.60 [145]~E(x1451,x1452)+E(f17(x1453,x1454,x1451,x1455),f17(x1453,x1454,x1452,x1455))
% 4.60/4.60 [146]~E(x1461,x1462)+E(f17(x1463,x1464,x1465,x1461),f17(x1463,x1464,x1465,x1462))
% 4.60/4.60 [147]~P1(x1471)+P1(x1472)+~E(x1471,x1472)
% 4.60/4.60 [148]P11(x1482,x1483,x1484)+~E(x1481,x1482)+~P11(x1481,x1483,x1484)
% 4.60/4.60 [149]P11(x1493,x1492,x1494)+~E(x1491,x1492)+~P11(x1493,x1491,x1494)
% 4.60/4.60 [150]P11(x1503,x1504,x1502)+~E(x1501,x1502)+~P11(x1503,x1504,x1501)
% 4.60/4.60 [151]~P2(x1511)+P2(x1512)+~E(x1511,x1512)
% 4.60/4.60 [152]P10(x1522,x1523,x1524)+~E(x1521,x1522)+~P10(x1521,x1523,x1524)
% 4.60/4.60 [153]P10(x1533,x1532,x1534)+~E(x1531,x1532)+~P10(x1533,x1531,x1534)
% 4.60/4.60 [154]P10(x1543,x1544,x1542)+~E(x1541,x1542)+~P10(x1543,x1544,x1541)
% 4.60/4.60 [155]~P41(x1551)+P41(x1552)+~E(x1551,x1552)
% 4.60/4.60 [156]P13(x1562,x1563)+~E(x1561,x1562)+~P13(x1561,x1563)
% 4.60/4.60 [157]P13(x1573,x1572)+~E(x1571,x1572)+~P13(x1573,x1571)
% 4.60/4.60 [158]~P42(x1581)+P42(x1582)+~E(x1581,x1582)
% 4.60/4.60 [159]~P45(x1591)+P45(x1592)+~E(x1591,x1592)
% 4.60/4.60 [160]~P3(x1601)+P3(x1602)+~E(x1601,x1602)
% 4.60/4.60 [161]~P57(x1611)+P57(x1612)+~E(x1611,x1612)
% 4.60/4.60 [162]~P43(x1621)+P43(x1622)+~E(x1621,x1622)
% 4.60/4.60 [163]~P56(x1631)+P56(x1632)+~E(x1631,x1632)
% 4.60/4.60 [164]P12(x1642,x1643,x1644)+~E(x1641,x1642)+~P12(x1641,x1643,x1644)
% 4.60/4.60 [165]P12(x1653,x1652,x1654)+~E(x1651,x1652)+~P12(x1653,x1651,x1654)
% 4.60/4.60 [166]P12(x1663,x1664,x1662)+~E(x1661,x1662)+~P12(x1663,x1664,x1661)
% 4.60/4.60 [167]~P20(x1671)+P20(x1672)+~E(x1671,x1672)
% 4.60/4.60 [168]~P26(x1681)+P26(x1682)+~E(x1681,x1682)
% 4.60/4.60 [169]~P53(x1691)+P53(x1692)+~E(x1691,x1692)
% 4.60/4.60 [170]~P38(x1701)+P38(x1702)+~E(x1701,x1702)
% 4.60/4.60 [171]~P51(x1711)+P51(x1712)+~E(x1711,x1712)
% 4.60/4.60 [172]~P27(x1721)+P27(x1722)+~E(x1721,x1722)
% 4.60/4.60 [173]~P31(x1731)+P31(x1732)+~E(x1731,x1732)
% 4.60/4.60 [174]~P48(x1741)+P48(x1742)+~E(x1741,x1742)
% 4.60/4.60 [175]~P28(x1751)+P28(x1752)+~E(x1751,x1752)
% 4.60/4.60 [176]~P30(x1761)+P30(x1762)+~E(x1761,x1762)
% 4.60/4.60 [177]~P35(x1771)+P35(x1772)+~E(x1771,x1772)
% 4.60/4.60 [178]~P64(x1781)+P64(x1782)+~E(x1781,x1782)
% 4.60/4.60 [179]~P4(x1791)+P4(x1792)+~E(x1791,x1792)
% 4.60/4.60 [180]~P8(x1801)+P8(x1802)+~E(x1801,x1802)
% 4.60/4.60 [181]~P29(x1811)+P29(x1812)+~E(x1811,x1812)
% 4.60/4.60 [182]~P24(x1821)+P24(x1822)+~E(x1821,x1822)
% 4.60/4.60 [183]~P60(x1831)+P60(x1832)+~E(x1831,x1832)
% 4.60/4.60 [184]~P54(x1841)+P54(x1842)+~E(x1841,x1842)
% 4.60/4.60 [185]~P74(x1851)+P74(x1852)+~E(x1851,x1852)
% 4.60/4.60 [186]P14(x1862,x1863)+~E(x1861,x1862)+~P14(x1861,x1863)
% 4.60/4.60 [187]P14(x1873,x1872)+~E(x1871,x1872)+~P14(x1873,x1871)
% 4.60/4.60 [188]~P34(x1881)+P34(x1882)+~E(x1881,x1882)
% 4.60/4.60 [189]~P39(x1891)+P39(x1892)+~E(x1891,x1892)
% 4.60/4.60 [190]~P47(x1901)+P47(x1902)+~E(x1901,x1902)
% 4.60/4.60 [191]~P25(x1911)+P25(x1912)+~E(x1911,x1912)
% 4.60/4.60 [192]~P36(x1921)+P36(x1922)+~E(x1921,x1922)
% 4.60/4.60 [193]~P61(x1931)+P61(x1932)+~E(x1931,x1932)
% 4.60/4.60 [194]~P49(x1941)+P49(x1942)+~E(x1941,x1942)
% 4.60/4.60 [195]~P16(x1951)+P16(x1952)+~E(x1951,x1952)
% 4.60/4.60 [196]~P32(x1961)+P32(x1962)+~E(x1961,x1962)
% 4.60/4.60 [197]~P15(x1971)+P15(x1972)+~E(x1971,x1972)
% 4.60/4.60 [198]~P46(x1981)+P46(x1982)+~E(x1981,x1982)
% 4.60/4.60 [199]~P17(x1991)+P17(x1992)+~E(x1991,x1992)
% 4.60/4.60 [200]~P58(x2001)+P58(x2002)+~E(x2001,x2002)
% 4.60/4.60 [201]~P33(x2011)+P33(x2012)+~E(x2011,x2012)
% 4.60/4.60 [202]~P68(x2021)+P68(x2022)+~E(x2021,x2022)
% 4.60/4.60 [203]~P5(x2031)+P5(x2032)+~E(x2031,x2032)
% 4.60/4.60 [204]~P18(x2041)+P18(x2042)+~E(x2041,x2042)
% 4.60/4.60 [205]~P55(x2051)+P55(x2052)+~E(x2051,x2052)
% 4.60/4.60 [206]~P40(x2061)+P40(x2062)+~E(x2061,x2062)
% 4.60/4.60 [207]~P21(x2071)+P21(x2072)+~E(x2071,x2072)
% 4.60/4.60 [208]~P73(x2081)+P73(x2082)+~E(x2081,x2082)
% 4.60/4.60 [209]~P19(x2091)+P19(x2092)+~E(x2091,x2092)
% 4.60/4.60 [210]~P37(x2101)+P37(x2102)+~E(x2101,x2102)
% 4.60/4.60 [211]~P6(x2111)+P6(x2112)+~E(x2111,x2112)
% 4.60/4.60 [212]~P63(x2121)+P63(x2122)+~E(x2121,x2122)
% 4.60/4.60 [213]~P7(x2131)+P7(x2132)+~E(x2131,x2132)
% 4.60/4.60 [214]~P22(x2141)+P22(x2142)+~E(x2141,x2142)
% 4.60/4.60 [215]~P23(x2151)+P23(x2152)+~E(x2151,x2152)
% 4.60/4.60 [216]~P9(x2161)+P9(x2162)+~E(x2161,x2162)
% 4.60/4.60 [217]~P69(x2171)+P69(x2172)+~E(x2171,x2172)
% 4.60/4.60 [218]~P71(x2181)+P71(x2182)+~E(x2181,x2182)
% 4.60/4.60 [219]~P66(x2191)+P66(x2192)+~E(x2191,x2192)
% 4.60/4.60 [220]~P50(x2201)+P50(x2202)+~E(x2201,x2202)
% 4.60/4.60 [221]~P59(x2211)+P59(x2212)+~E(x2211,x2212)
% 4.60/4.60 [222]~P62(x2221)+P62(x2222)+~E(x2221,x2222)
% 4.60/4.60 [223]~P70(x2231)+P70(x2232)+~E(x2231,x2232)
% 4.60/4.60 [224]~P65(x2241)+P65(x2242)+~E(x2241,x2242)
% 4.60/4.60 [225]~P72(x2251)+P72(x2252)+~E(x2251,x2252)
% 4.60/4.60 [226]~P52(x2261)+P52(x2262)+~E(x2261,x2262)
% 4.60/4.60 [227]~P44(x2271)+P44(x2272)+~E(x2271,x2272)
% 4.60/4.60 [228]~P67(x2281)+P67(x2282)+~E(x2281,x2282)
% 4.60/4.60
% 4.60/4.60 %-------------------------------------------
% 4.75/4.62 cnf(1863,plain,
% 4.75/4.62 (P74(f29(x18631,x18631))),
% 4.75/4.62 inference(equality_inference,[],[666])).
% 4.75/4.62 cnf(1878,plain,
% 4.75/4.62 (P10(x18781,x18782,x18782)+~P38(x18781)),
% 4.75/4.62 inference(equality_inference,[],[727])).
% 4.75/4.62 cnf(1888,plain,
% 4.75/4.62 (E(f11(a1,x18881,f9(a1,x18881)),f8(a1))),
% 4.75/4.62 inference(equality_inference,[],[775])).
% 4.75/4.62 cnf(1891,plain,
% 4.75/4.62 (P10(a1,f25(a70,f8(a70)),f8(a1))),
% 4.75/4.62 inference(equality_inference,[],[789])).
% 4.75/4.62 cnf(1893,plain,
% 4.75/4.62 (~P11(a1,x18931,x18931)),
% 4.75/4.62 inference(equality_inference,[],[796])).
% 4.75/4.62 cnf(1895,plain,
% 4.75/4.62 (~P11(a68,x18951,x18951)),
% 4.75/4.62 inference(equality_inference,[],[802])).
% 4.75/4.62 cnf(1904,plain,
% 4.75/4.62 (~P62(x19041)+~P71(x19041)+~P40(x19041)+~P60(x19041)+E(x19042,f8(a70))+E(f27(f27(f13(x19041),f8(x19041)),x19042),f8(x19041))),
% 4.75/4.62 inference(equality_inference,[],[847])).
% 4.75/4.62 cnf(1907,plain,
% 4.75/4.62 (E(f27(f27(f10(a70),f8(a70)),x19071),f27(f27(f10(a70),f8(a70)),x19072))),
% 4.75/4.62 inference(equality_inference,[],[851])).
% 4.75/4.62 cnf(1910,plain,
% 4.75/4.62 (E(f27(f27(f13(a70),x19101),f8(a70)),f11(a70,f8(a70),f3(a70)))),
% 4.75/4.62 inference(equality_inference,[],[883])).
% 4.75/4.62 cnf(1923,plain,
% 4.75/4.62 (P11(a70,f8(a70),f27(f27(f13(a70),x19231),f8(a70)))),
% 4.75/4.62 inference(equality_inference,[],[1000])).
% 4.75/4.62 cnf(1925,plain,
% 4.75/4.62 (P11(a68,x19251,f11(a68,x19251,f3(a68)))),
% 4.75/4.62 inference(equality_inference,[],[1012])).
% 4.75/4.62 cnf(1939,plain,
% 4.75/4.62 (~P10(a70,x19391,x19392)+E(x19392,f11(a70,f6(a70,x19392,x19391),x19391))),
% 4.75/4.62 inference(equality_inference,[],[1170])).
% 4.75/4.62 cnf(1942,plain,
% 4.75/4.62 (~P11(a1,f8(a1),f27(f27(f10(a1),f8(a1)),f8(a1)))),
% 4.75/4.62 inference(equality_inference,[],[1202])).
% 4.75/4.62 cnf(1943,plain,
% 4.75/4.62 (~P11(a70,f8(a70),x19431)+P12(a70,f27(f27(f10(a70),x19431),f3(a70)),x19431)),
% 4.75/4.62 inference(equality_inference,[],[1203])).
% 4.75/4.62 cnf(1944,plain,
% 4.75/4.62 (~P11(a70,f8(a70),x19441)+P12(a70,f27(f27(f10(a70),f3(a70)),x19441),x19441)),
% 4.75/4.62 inference(equality_inference,[],[1204])).
% 4.75/4.62 cnf(1945,plain,
% 4.75/4.62 (P12(a70,f27(f27(f10(a70),f8(a70)),x19451),f27(f27(f10(a70),f8(a70)),x19452))),
% 4.75/4.62 inference(equality_inference,[],[1206])).
% 4.75/4.62 cnf(1951,plain,
% 4.75/4.62 (P11(a68,f8(a68),f27(f27(f13(a68),f5(a68,x19511)),f8(a70)))),
% 4.75/4.62 inference(equality_inference,[],[1227])).
% 4.75/4.62 cnf(1956,plain,
% 4.75/4.62 (~P9(x19561)+~P12(f71(x19561),f21(x19561,f8(x19561),x19562),x19563)+E(x19563,f8(f71(x19561)))),
% 4.75/4.62 inference(equality_inference,[],[1317])).
% 4.75/4.62 cnf(1981,plain,
% 4.75/4.62 (P10(a1,f11(a1,f11(a1,f3(a1),f26(a2,a74)),f5(a1,f27(f27(f10(a1),a72),a76))),f11(a1,f26(a2,a74),f27(f27(f10(a1),a72),a76)))),
% 4.75/4.62 inference(scs_inference,[],[580,696,870])).
% 4.75/4.62 cnf(1985,plain,
% 4.75/4.62 (P10(a1,x19851,f5(a1,x19851))),
% 4.75/4.62 inference(scs_inference,[],[580,455,696,870,935,1038])).
% 4.75/4.62 cnf(1986,plain,
% 4.75/4.62 (P10(a1,x19861,x19861)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(1991,plain,
% 4.75/4.62 (~P11(a1,x19911,x19911)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(1994,plain,
% 4.75/4.62 (~P11(a68,x19941,x19941)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(1996,plain,
% 4.75/4.62 (~E(x19961,f11(a1,f25(a70,f24(x19961)),f3(a1)))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,262,516,696,870,935,1038,1878,756,757,796])).
% 4.75/4.62 cnf(2000,plain,
% 4.75/4.62 (~E(x20001,f11(a68,x20001,f3(a68)))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,1925,1923,262,516,696,870,935,1038,1878,756,757,796,801,802])).
% 4.75/4.62 cnf(2002,plain,
% 4.75/4.62 (~E(f11(a70,x20021,f11(a70,f8(a70),f3(a70))),x20021)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,1925,1923,262,516,567,696,870,935,1038,1878,756,757,796,801,802,809])).
% 4.75/4.62 cnf(2003,plain,
% 4.75/4.62 (~E(f11(a70,x20031,f3(a70)),x20031)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2005,plain,
% 4.75/4.62 (~P11(a70,x20051,f7(f25(a70,f8(a70))))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,1925,1923,262,448,516,567,696,870,935,1038,1878,756,757,796,801,802,809,818])).
% 4.75/4.62 cnf(2006,plain,
% 4.75/4.62 (E(f7(f25(a70,x20061)),x20061)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2008,plain,
% 4.75/4.62 (~P20(a70)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,1925,1923,262,448,516,567,573,696,870,935,1038,1878,756,757,796,801,802,809,818,826])).
% 4.75/4.62 cnf(2009,plain,
% 4.75/4.62 (~E(f11(a70,x20091,f3(a70)),f8(a70))),
% 4.75/4.62 inference(rename_variables,[],[573])).
% 4.75/4.62 cnf(2011,plain,
% 4.75/4.62 (~P8(a70)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,455,1925,1923,262,448,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827])).
% 4.75/4.62 cnf(2012,plain,
% 4.75/4.62 (~E(f11(a70,x20121,f3(a70)),f8(a70))),
% 4.75/4.62 inference(rename_variables,[],[573])).
% 4.75/4.62 cnf(2015,plain,
% 4.75/4.62 (P10(a70,f6(a70,x20151,x20152),x20151)),
% 4.75/4.62 inference(rename_variables,[],[498])).
% 4.75/4.62 cnf(2020,plain,
% 4.75/4.62 (E(f7(f25(a70,x20201)),x20201)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2025,plain,
% 4.75/4.62 (~P10(a68,f3(a68),f8(a68))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,455,1925,1923,498,246,262,448,2006,499,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965])).
% 4.75/4.62 cnf(2026,plain,
% 4.75/4.62 (~P11(a68,x20261,x20261)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2029,plain,
% 4.75/4.62 (E(f11(a70,x20291,x20292),f11(a70,x20292,x20291))),
% 4.75/4.62 inference(rename_variables,[],[486])).
% 4.75/4.62 cnf(2032,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x20321,x20322),x20322)),
% 4.75/4.62 inference(rename_variables,[],[575])).
% 4.75/4.62 cnf(2034,plain,
% 4.75/4.62 (~E(f11(a68,x20341,f3(a68)),x20341)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,455,1925,1923,486,498,575,246,262,448,2006,499,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012])).
% 4.75/4.62 cnf(2035,plain,
% 4.75/4.62 (~P11(a68,x20351,x20351)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2038,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x20381,x20382),x20382)),
% 4.75/4.62 inference(rename_variables,[],[575])).
% 4.75/4.62 cnf(2040,plain,
% 4.75/4.62 (P10(a70,x20401,f24(f25(a70,x20401)))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,455,1986,1925,1923,486,498,575,2032,246,262,448,2006,499,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051])).
% 4.75/4.62 cnf(2041,plain,
% 4.75/4.62 (P10(a1,x20411,x20411)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2043,plain,
% 4.75/4.62 (P10(a70,f7(f25(a70,x20431)),x20431)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,455,1986,2041,1925,1923,486,498,575,2032,246,262,448,2006,499,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052])).
% 4.75/4.62 cnf(2044,plain,
% 4.75/4.62 (P10(a1,x20441,x20441)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2046,plain,
% 4.75/4.62 (P10(a70,x20461,f7(f25(a70,x20461)))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,455,1986,2041,1925,1923,486,498,575,2032,246,262,448,2006,482,499,516,567,573,2009,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137])).
% 4.75/4.62 cnf(2047,plain,
% 4.75/4.62 (P10(a1,x20471,f25(a70,f7(x20471)))),
% 4.75/4.62 inference(rename_variables,[],[482])).
% 4.75/4.62 cnf(2050,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x20501,x20502),x20502)),
% 4.75/4.62 inference(rename_variables,[],[575])).
% 4.75/4.62 cnf(2056,plain,
% 4.75/4.62 (~P10(a70,f11(a70,x20561,f3(a70)),x20561)),
% 4.75/4.62 inference(rename_variables,[],[577])).
% 4.75/4.62 cnf(2059,plain,
% 4.75/4.62 (~P10(a70,f11(a70,x20591,f3(a70)),x20591)),
% 4.75/4.62 inference(rename_variables,[],[577])).
% 4.75/4.62 cnf(2062,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x20621,x20622),x20622)),
% 4.75/4.62 inference(rename_variables,[],[575])).
% 4.75/4.62 cnf(2065,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x20651,x20652),x20652)),
% 4.75/4.62 inference(rename_variables,[],[575])).
% 4.75/4.62 cnf(2068,plain,
% 4.75/4.62 (~E(f11(a70,x20681,f3(a70)),f8(a70))),
% 4.75/4.62 inference(rename_variables,[],[573])).
% 4.75/4.62 cnf(2073,plain,
% 4.75/4.62 (~P10(a68,f11(a68,x20731,f3(a68)),x20731)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,455,1986,2041,1925,1923,486,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,499,516,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238])).
% 4.75/4.62 cnf(2074,plain,
% 4.75/4.62 (~P11(a68,x20741,x20741)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2076,plain,
% 4.75/4.62 (~P11(a68,f11(a68,x20761,f3(a68)),x20761)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,1925,1923,486,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,499,516,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239])).
% 4.75/4.62 cnf(2077,plain,
% 4.75/4.62 (~P11(a68,x20771,x20771)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2080,plain,
% 4.75/4.62 (~P11(a1,f11(a1,f5(a1,x20801),f3(a1)),x20801)),
% 4.75/4.62 inference(rename_variables,[],[579])).
% 4.75/4.62 cnf(2083,plain,
% 4.75/4.62 (P10(a70,x20831,f11(a70,x20832,x20831))),
% 4.75/4.62 inference(rename_variables,[],[496])).
% 4.75/4.62 cnf(2086,plain,
% 4.75/4.62 (P10(a70,x20861,f11(a70,x20862,x20861))),
% 4.75/4.62 inference(rename_variables,[],[496])).
% 4.75/4.62 cnf(2089,plain,
% 4.75/4.62 (P11(a70,x20891,f11(a70,f11(a70,x20892,x20891),f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[540])).
% 4.75/4.62 cnf(2092,plain,
% 4.75/4.62 (E(f11(a70,x20921,x20922),f11(a70,x20922,x20921))),
% 4.75/4.62 inference(rename_variables,[],[486])).
% 4.75/4.62 cnf(2094,plain,
% 4.75/4.62 (P11(a68,f6(a68,x20941,f3(a68)),x20941)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,457,1925,1923,486,2029,496,2083,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348])).
% 4.75/4.62 cnf(2095,plain,
% 4.75/4.62 (P10(a68,x20951,x20951)),
% 4.75/4.62 inference(rename_variables,[],[457])).
% 4.75/4.62 cnf(2097,plain,
% 4.75/4.62 (P11(a70,x20971,f11(a70,f11(a70,x20971,f3(a70)),x20972))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,457,1925,1923,486,2029,496,2083,497,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352])).
% 4.75/4.62 cnf(2098,plain,
% 4.75/4.62 (P10(a70,x20981,f11(a70,x20981,x20982))),
% 4.75/4.62 inference(rename_variables,[],[497])).
% 4.75/4.62 cnf(2101,plain,
% 4.75/4.62 (P11(a1,x21011,f11(a1,f25(a70,f24(x21011)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2104,plain,
% 4.75/4.62 (P10(a70,x21041,f11(a70,x21041,x21042))),
% 4.75/4.62 inference(rename_variables,[],[497])).
% 4.75/4.62 cnf(2109,plain,
% 4.75/4.62 (P10(a70,x21091,x21091)),
% 4.75/4.62 inference(rename_variables,[],[456])).
% 4.75/4.62 cnf(2111,plain,
% 4.75/4.62 (~P10(a70,f6(a70,f11(a70,f11(a70,x21111,x21112),f3(a70)),x21112),x21111)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,457,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510])).
% 4.75/4.62 cnf(2112,plain,
% 4.75/4.62 (~P10(a70,f11(a70,x21121,f3(a70)),x21121)),
% 4.75/4.62 inference(rename_variables,[],[577])).
% 4.75/4.62 cnf(2114,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f6(a70,x21141,x21142),x21142),x21141)),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,457,562,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511])).
% 4.75/4.62 cnf(2115,plain,
% 4.75/4.62 (~P11(a70,x21151,x21151)),
% 4.75/4.62 inference(rename_variables,[],[562])).
% 4.75/4.62 cnf(2117,plain,
% 4.75/4.62 (~P11(a70,x21171,f6(a70,f11(a70,x21171,x21172),x21172))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513])).
% 4.75/4.62 cnf(2118,plain,
% 4.75/4.62 (~P11(a70,x21181,x21181)),
% 4.75/4.62 inference(rename_variables,[],[562])).
% 4.75/4.62 cnf(2120,plain,
% 4.75/4.62 (P11(a70,x21201,f7(f11(a1,f25(a70,x21201),f3(a1))))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533])).
% 4.75/4.62 cnf(2121,plain,
% 4.75/4.62 (P10(a1,x21211,f25(a70,f7(x21211)))),
% 4.75/4.62 inference(rename_variables,[],[482])).
% 4.75/4.62 cnf(2129,plain,
% 4.75/4.62 (E(x21291,f11(a70,f6(a70,x21291,x21291),x21291))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939])).
% 4.75/4.62 cnf(2133,plain,
% 4.75/4.62 (P12(a70,f27(f27(f10(a70),f3(a70)),f27(f27(f13(a70),x21331),f8(a70))),f27(f27(f13(a70),x21331),f8(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,246,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944])).
% 4.75/4.62 cnf(2137,plain,
% 4.75/4.62 (~E(f3(a68),f8(a68))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,245,246,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725])).
% 4.75/4.62 cnf(2141,plain,
% 4.75/4.62 (P11(a1,f11(a1,f11(a1,f3(a1),f26(a2,a74)),f5(a1,f27(f27(f10(a1),a72),a76))),f11(a1,f26(a2,a74),f27(f27(f10(a1),a72),a76)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,245,246,247,260,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903])).
% 4.75/4.62 cnf(2143,plain,
% 4.75/4.62 (~P11(a68,f3(a68),f8(a68))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,245,246,247,260,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970])).
% 4.75/4.62 cnf(2145,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x21451,x21452),f3(a70)),x21451)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,245,246,247,260,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972])).
% 4.75/4.62 cnf(2147,plain,
% 4.75/4.62 (P10(a68,x21471,f5(a68,x21471))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,238,245,246,247,260,262,448,2006,452,482,2047,577,2056,2059,540,499,516,579,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096])).
% 4.75/4.62 cnf(2150,plain,
% 4.75/4.62 (P10(a1,f26(a2,f27(f27(f10(a2),a77),f27(f14(a2,a73),a77))),f27(f27(f10(a1),a72),a76))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,238,245,246,247,260,262,267,448,2006,452,482,2047,577,2056,2059,540,499,516,579,556,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630])).
% 4.75/4.62 cnf(2152,plain,
% 4.75/4.62 (P10(f11(a70,f6(a70,a1,a1),a1),x21521,x21521)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,498,575,2032,2038,2050,2062,2065,238,245,246,247,260,262,267,448,2006,452,482,2047,577,2056,2059,540,499,516,579,556,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152])).
% 4.75/4.62 cnf(2154,plain,
% 4.75/4.62 (P10(a1,x21541,x21541)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2155,plain,
% 4.75/4.62 (~E(f11(a70,f11(a70,x21551,f3(a70)),x21552),x21551)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,2104,498,575,2032,2038,2050,2062,2065,238,245,246,247,260,262,267,448,2006,452,482,2047,577,2056,2059,2112,540,499,516,579,556,567,573,2009,2012,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154])).
% 4.75/4.62 cnf(2158,plain,
% 4.75/4.62 (~E(f11(a70,x21581,f3(a70)),x21581)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2161,plain,
% 4.75/4.62 (~E(f11(a70,x21611,f3(a70)),x21611)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2164,plain,
% 4.75/4.62 (~E(f11(a70,x21641,f3(a70)),x21641)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2169,plain,
% 4.75/4.62 (~E(f11(a70,x21691,f3(a70)),x21691)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2174,plain,
% 4.75/4.62 (~E(f11(a70,x21741,f3(a70)),x21741)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2176,plain,
% 4.75/4.62 (~E(f9(a1,f11(a68,f9(a1,x21761),f3(a68))),x21761)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,2104,498,575,2032,2038,2050,2062,2065,237,238,245,246,247,260,262,267,448,2006,452,482,2047,577,2056,2059,2112,540,499,516,579,556,229,254,323,389,559,567,2003,2158,2161,2164,2169,573,2009,2012,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685])).
% 4.75/4.62 cnf(2180,plain,
% 4.75/4.62 (E(f7(f25(a70,x21801)),x21801)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2182,plain,
% 4.75/4.62 (~E(x21821,f9(a68,f11(a68,f3(a68),x21821)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,2104,498,575,2032,2038,2050,2062,2065,237,238,245,246,247,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,579,556,229,254,323,389,391,559,567,2003,2158,2161,2164,2169,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816])).
% 4.75/4.62 cnf(2191,plain,
% 4.75/4.62 (~E(f11(a70,x21911,f3(a70)),x21911)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2193,plain,
% 4.75/4.62 (~E(f11(a1,x21931,f11(a70,f8(a1),f3(a70))),x21931)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1925,1923,486,2029,496,2083,497,2098,2104,498,575,2032,2038,2050,2062,2065,237,238,245,246,247,259,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,579,556,229,254,273,323,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856])).
% 4.75/4.62 cnf(2194,plain,
% 4.75/4.62 (~E(f11(a70,x21941,f3(a70)),x21941)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2199,plain,
% 4.75/4.62 (~E(f11(a70,x21991,f3(a70)),x21991)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2202,plain,
% 4.75/4.62 (~E(f11(a70,x22021,f3(a70)),x22021)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2205,plain,
% 4.75/4.62 (~E(f11(a70,x22051,f3(a70)),x22051)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2208,plain,
% 4.75/4.62 (~E(f11(a70,x22081,f3(a70)),x22081)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2213,plain,
% 4.75/4.62 (~E(f11(a70,x22131,f3(a70)),x22131)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2216,plain,
% 4.75/4.62 (P10(a70,f6(a70,x22161,x22162),x22161)),
% 4.75/4.62 inference(rename_variables,[],[498])).
% 4.75/4.62 cnf(2218,plain,
% 4.75/4.62 (~P10(a1,f5(a1,f11(a70,f8(a1),f3(a70))),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1923,486,2029,496,2083,497,2098,2104,498,2015,575,2032,2038,2050,2062,2065,237,238,245,246,247,259,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,579,556,229,239,250,254,273,323,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973])).
% 4.75/4.62 cnf(2219,plain,
% 4.75/4.62 (~E(f11(a70,x22191,f3(a70)),x22191)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2224,plain,
% 4.75/4.62 (P10(a1,f8(a1),f25(a70,x22241))),
% 4.75/4.62 inference(rename_variables,[],[481])).
% 4.75/4.62 cnf(2227,plain,
% 4.75/4.62 (P10(a70,f6(a70,x22271,x22272),x22271)),
% 4.75/4.62 inference(rename_variables,[],[498])).
% 4.75/4.62 cnf(2228,plain,
% 4.75/4.62 (P10(a70,f8(a70),x22281)),
% 4.75/4.62 inference(rename_variables,[],[467])).
% 4.75/4.62 cnf(2230,plain,
% 4.75/4.62 (~P11(a1,f11(a1,f25(a70,f24(x22301)),f3(a1)),x22301)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,481,237,238,243,245,246,247,259,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,273,323,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057])).
% 4.75/4.62 cnf(2232,plain,
% 4.75/4.62 (P11(a1,x22321,f11(a1,f25(a70,f24(f5(a1,x22321))),f3(a1)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,481,237,238,243,245,246,247,259,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,273,322,323,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097])).
% 4.75/4.62 cnf(2233,plain,
% 4.75/4.62 (P11(a1,x22331,f11(a1,f25(a70,f24(x22331)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2236,plain,
% 4.75/4.62 (~E(f11(a70,x22361,f3(a70)),x22361)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2239,plain,
% 4.75/4.62 (~P11(a70,x22391,f8(a70))),
% 4.75/4.62 inference(rename_variables,[],[565])).
% 4.75/4.62 cnf(2244,plain,
% 4.75/4.62 (~P11(a1,x22441,x22441)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2246,plain,
% 4.75/4.62 (~P11(a1,f9(a1,f8(a1)),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,565,481,237,238,243,245,246,247,259,260,262,267,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116])).
% 4.75/4.62 cnf(2247,plain,
% 4.75/4.62 (~P11(a1,x22471,x22471)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2249,plain,
% 4.75/4.62 (~P10(a68,f8(a68),f9(a68,f3(a68)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,1895,1994,2026,2035,2074,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,565,481,237,238,243,245,246,247,259,260,262,267,393,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131])).
% 4.75/4.62 cnf(2252,plain,
% 4.75/4.62 (~P11(a68,x22521,x22521)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2255,plain,
% 4.75/4.62 (~P11(a1,x22551,x22551)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2258,plain,
% 4.75/4.62 (~P11(a1,x22581,x22581)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2263,plain,
% 4.75/4.62 (~P11(a68,x22631,x22631)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2265,plain,
% 4.75/4.62 (~P10(a68,x22651,f9(a68,f11(a68,f9(a68,x22651),f3(a68))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,565,481,237,238,243,245,246,247,259,260,262,267,393,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147])).
% 4.75/4.62 cnf(2268,plain,
% 4.75/4.62 (~P11(a1,x22681,x22681)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2270,plain,
% 4.75/4.62 (~P10(a68,f9(a68,f8(a68)),f9(a68,f3(a68)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,497,2098,2104,498,2015,2216,575,2032,2038,2050,2062,2065,467,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151])).
% 4.75/4.62 cnf(2275,plain,
% 4.75/4.62 (~P11(a1,x22751,x22751)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2278,plain,
% 4.75/4.62 (~P11(a1,x22781,x22781)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2281,plain,
% 4.75/4.62 (P10(a70,f6(a70,x22811,x22812),x22811)),
% 4.75/4.62 inference(rename_variables,[],[498])).
% 4.75/4.62 cnf(2284,plain,
% 4.75/4.62 (~E(f11(a70,x22841,f3(a70)),x22841)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2285,plain,
% 4.75/4.62 (P10(a70,x22851,f11(a70,x22852,x22851))),
% 4.75/4.62 inference(rename_variables,[],[496])).
% 4.75/4.62 cnf(2288,plain,
% 4.75/4.62 (P10(a70,x22881,x22881)),
% 4.75/4.62 inference(rename_variables,[],[456])).
% 4.75/4.62 cnf(2290,plain,
% 4.75/4.62 (~P12(a70,f11(a70,f27(f27(f13(a70),x22901),f8(a70)),f3(a70)),f27(f27(f13(a70),x22901),f8(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,456,2109,457,2095,562,2115,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,577,2056,2059,2112,540,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175])).
% 4.75/4.62 cnf(2291,plain,
% 4.75/4.62 (~P10(a70,f11(a70,x22911,f3(a70)),x22911)),
% 4.75/4.62 inference(rename_variables,[],[577])).
% 4.75/4.62 cnf(2294,plain,
% 4.75/4.62 (~P11(a70,x22941,x22941)),
% 4.75/4.62 inference(rename_variables,[],[562])).
% 4.75/4.62 cnf(2297,plain,
% 4.75/4.62 (P11(a70,x22971,f11(a70,x22971,f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[502])).
% 4.75/4.62 cnf(2298,plain,
% 4.75/4.62 (P11(a70,x22981,f11(a70,f11(a70,x22982,x22981),f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[540])).
% 4.75/4.62 cnf(2300,plain,
% 4.75/4.62 (P10(a1,f25(a70,f24(f8(a1))),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,2154,456,2109,2288,457,2095,562,2115,2118,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,502,577,2056,2059,2112,540,2089,499,516,2101,579,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266])).
% 4.75/4.62 cnf(2301,plain,
% 4.75/4.62 (P10(a1,x23011,x23011)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2302,plain,
% 4.75/4.62 (P10(a70,x23021,x23021)),
% 4.75/4.62 inference(rename_variables,[],[456])).
% 4.75/4.62 cnf(2304,plain,
% 4.75/4.62 (P11(a70,f24(f8(a1)),f11(a70,x23041,f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,2154,2301,456,2109,2288,457,2095,562,2115,2118,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,502,577,2056,2059,2112,540,2089,499,516,2101,579,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281])).
% 4.75/4.62 cnf(2305,plain,
% 4.75/4.62 (P10(a1,x23051,x23051)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2307,plain,
% 4.75/4.62 (P10(a1,f5(a1,f9(a1,f26(a2,x23071))),f26(a2,x23071))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,502,577,2056,2059,2112,540,2089,499,516,2101,579,495,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307])).
% 4.75/4.62 cnf(2308,plain,
% 4.75/4.62 (P10(a1,x23081,x23081)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2310,plain,
% 4.75/4.62 (P11(a70,x23101,f11(a70,x23101,f27(f27(f13(a70),x23102),f8(a70))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,502,577,2056,2059,2112,540,2089,499,516,2101,579,471,495,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337])).
% 4.75/4.62 cnf(2314,plain,
% 4.75/4.62 (P11(a70,x23141,f11(a70,f11(a70,x23142,x23141),f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[540])).
% 4.75/4.62 cnf(2316,plain,
% 4.75/4.62 (~P11(a70,f27(f27(f13(a70),x23161),f8(a70)),f11(a70,f8(a70),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,1895,1994,2026,2035,2074,2077,2252,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,2294,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,452,482,2047,502,577,2056,2059,2112,540,2089,2298,499,516,2101,579,471,495,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401])).
% 4.75/4.62 cnf(2317,plain,
% 4.75/4.62 (~P11(a70,x23171,x23171)),
% 4.75/4.62 inference(rename_variables,[],[562])).
% 4.75/4.62 cnf(2322,plain,
% 4.75/4.62 (~P11(a1,x23221,x23221)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2325,plain,
% 4.75/4.62 (~P11(a68,x23251,x23251)),
% 4.75/4.62 inference(rename_variables,[],[1895])).
% 4.75/4.62 cnf(2330,plain,
% 4.75/4.62 (~P11(a1,x23301,x23301)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2333,plain,
% 4.75/4.62 (E(f7(f25(a70,x23331)),x23331)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2335,plain,
% 4.75/4.62 (P11(a70,f42(f11(a70,f8(a70),f3(a70)),f11(a70,f8(a70),f3(a70))),f11(a70,f8(a70),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,2294,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,2180,452,482,2047,502,2297,577,2056,2059,2112,540,2089,2298,499,516,2101,579,471,495,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416])).
% 4.75/4.62 cnf(2336,plain,
% 4.75/4.62 (P11(a70,x23361,f11(a70,x23361,f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[502])).
% 4.75/4.62 cnf(2337,plain,
% 4.75/4.62 (~E(f11(a70,x23371,f3(a70)),x23371)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2339,plain,
% 4.75/4.62 (E(x23391,f11(a70,f8(a70),x23391))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,2294,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,2180,452,482,2047,502,2297,577,2056,2059,2112,540,2089,2298,2314,499,516,2101,579,471,495,519,556,229,239,250,254,255,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421])).
% 4.75/4.62 cnf(2343,plain,
% 4.75/4.62 (~P11(a1,f11(a1,f5(a1,x23431),f3(a1)),x23431)),
% 4.75/4.62 inference(rename_variables,[],[579])).
% 4.75/4.62 cnf(2348,plain,
% 4.75/4.62 (P11(a70,x23481,f11(a70,x23481,f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[502])).
% 4.75/4.62 cnf(2349,plain,
% 4.75/4.62 (~P11(a70,x23491,x23491)),
% 4.75/4.62 inference(rename_variables,[],[562])).
% 4.75/4.62 cnf(2352,plain,
% 4.75/4.62 (~E(f11(a70,x23521,f3(a70)),x23521)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2354,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x23541,f11(a70,f3(a70),f3(a70))),x23542),x23541)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,577,2056,2059,2112,540,2089,2298,2314,499,516,2101,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563])).
% 4.75/4.62 cnf(2355,plain,
% 4.75/4.62 (P11(a70,x23551,f11(a70,x23551,f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[502])).
% 4.75/4.62 cnf(2361,plain,
% 4.75/4.62 (P11(a1,x23611,f25(a70,f24(f11(a1,x23611,f3(a1)))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,577,2056,2059,2112,540,2089,2298,2314,499,516,2101,2233,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636])).
% 4.75/4.62 cnf(2362,plain,
% 4.75/4.62 (P11(a1,x23621,f11(a1,f25(a70,f24(x23621)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2368,plain,
% 4.75/4.62 (P10(a70,x23681,x23681)),
% 4.75/4.62 inference(rename_variables,[],[456])).
% 4.75/4.62 cnf(2370,plain,
% 4.75/4.62 (P11(a1,x23701,f11(a1,x23702,f11(a1,f25(a70,f24(f5(a1,f6(a1,x23701,x23702)))),f3(a1))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749])).
% 4.75/4.62 cnf(2371,plain,
% 4.75/4.62 (P11(a1,x23711,f11(a1,f25(a70,f24(x23711)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2373,plain,
% 4.75/4.62 (~P51(a70)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750])).
% 4.75/4.62 cnf(2375,plain,
% 4.75/4.62 (~P11(a70,x23751,f8(a70))),
% 4.75/4.62 inference(rename_variables,[],[565])).
% 4.75/4.62 cnf(2378,plain,
% 4.75/4.62 (~E(f11(a70,x23781,f3(a70)),x23781)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2382,plain,
% 4.75/4.62 (~E(x23821,f11(a1,f27(f27(f10(a1),f6(a1,x23822,x23823)),x23824),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x23823,x23822)),x23824),x23821),f3(a70))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,394,396,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805])).
% 4.75/4.62 cnf(2384,plain,
% 4.75/4.62 (~E(f11(a1,f27(f27(f10(a1),f6(a1,x23841,x23842)),x23843),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x23842,x23841)),x23843),x23844),f3(a70))),x23844)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,374,389,391,394,396,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806])).
% 4.75/4.62 cnf(2387,plain,
% 4.75/4.62 (~P11(a1,x23871,x23871)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2390,plain,
% 4.75/4.62 (~P11(a1,x23901,x23901)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2392,plain,
% 4.75/4.62 (~P11(a1,x23921,f11(a1,f27(f27(f10(a1),f6(a1,x23922,x23922)),x23923),x23921))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,271,273,322,323,354,374,389,391,394,396,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839])).
% 4.75/4.62 cnf(2393,plain,
% 4.75/4.62 (~P11(a1,x23931,x23931)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2396,plain,
% 4.75/4.62 (~P11(a1,x23961,x23961)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2398,plain,
% 4.75/4.62 (P10(f75(x23981,a1),x23982,x23982)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,1888,1925,1891,1923,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844])).
% 4.75/4.62 cnf(2399,plain,
% 4.75/4.62 (P10(a1,x23991,x23991)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2402,plain,
% 4.75/4.62 (~E(f11(a70,x24021,f3(a70)),x24021)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2405,plain,
% 4.75/4.62 (~E(f11(a70,x24051,f3(a70)),x24051)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2407,plain,
% 4.75/4.62 (P11(a68,x24071,f11(a68,x24071,f3(a68)))),
% 4.75/4.62 inference(rename_variables,[],[1925])).
% 4.75/4.62 cnf(2412,plain,
% 4.75/4.62 (P3(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160])).
% 4.75/4.62 cnf(2413,plain,
% 4.75/4.62 (P57(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161])).
% 4.75/4.62 cnf(2414,plain,
% 4.75/4.62 (P56(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,349,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163])).
% 4.75/4.62 cnf(2415,plain,
% 4.75/4.62 (P26(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,349,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168])).
% 4.75/4.62 cnf(2418,plain,
% 4.75/4.62 (P31(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,305,349,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173])).
% 4.75/4.62 cnf(2419,plain,
% 4.75/4.62 (P30(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,259,260,262,267,268,305,349,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176])).
% 4.75/4.62 cnf(2420,plain,
% 4.75/4.62 (P29(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,368,392,393,448,2006,2020,2180,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181])).
% 4.75/4.62 cnf(2421,plain,
% 4.75/4.62 (~P25(f7(f25(a70,a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191])).
% 4.75/4.62 cnf(2422,plain,
% 4.75/4.62 (E(f7(f25(a70,x24221)),x24221)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2423,plain,
% 4.75/4.62 (P61(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193])).
% 4.75/4.62 cnf(2424,plain,
% 4.75/4.62 (~E(f8(a70),f3(a70))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,241,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036])).
% 4.75/4.62 cnf(2426,plain,
% 4.75/4.62 (P1(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,239,241,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147])).
% 4.75/4.62 cnf(2427,plain,
% 4.75/4.62 (P2(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,231,239,241,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151])).
% 4.75/4.62 cnf(2428,plain,
% 4.75/4.62 (P41(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,231,233,239,241,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155])).
% 4.75/4.62 cnf(2429,plain,
% 4.75/4.62 (P42(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158])).
% 4.75/4.62 cnf(2430,plain,
% 4.75/4.62 (P45(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159])).
% 4.75/4.62 cnf(2431,plain,
% 4.75/4.62 (P43(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162])).
% 4.75/4.62 cnf(2433,plain,
% 4.75/4.62 (P12(a70,x24331,x24331)),
% 4.75/4.62 inference(rename_variables,[],[458])).
% 4.75/4.62 cnf(2434,plain,
% 4.75/4.62 (P12(a70,f27(f27(f10(a70),f27(f27(f13(a70),f8(a70)),f8(a70))),f3(a70)),f11(a70,f8(a70),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166])).
% 4.75/4.62 cnf(2437,plain,
% 4.75/4.62 (E(f7(f25(a70,x24371)),x24371)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2438,plain,
% 4.75/4.62 (P53(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169])).
% 4.75/4.62 cnf(2440,plain,
% 4.75/4.62 (E(f7(f25(a70,x24401)),x24401)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2441,plain,
% 4.75/4.62 (P48(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174])).
% 4.75/4.62 cnf(2442,plain,
% 4.75/4.62 (P28(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175])).
% 4.75/4.62 cnf(2443,plain,
% 4.75/4.62 (P35(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,378,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177])).
% 4.75/4.62 cnf(2444,plain,
% 4.75/4.62 (P64(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,378,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178])).
% 4.75/4.62 cnf(2445,plain,
% 4.75/4.62 (P4(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,322,323,354,374,378,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179])).
% 4.75/4.62 cnf(2447,plain,
% 4.75/4.62 (E(f7(f25(a70,x24471)),x24471)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2448,plain,
% 4.75/4.62 (P24(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,354,374,378,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182])).
% 4.75/4.62 cnf(2449,plain,
% 4.75/4.62 (P60(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,324,354,374,378,381,386,389,391,394,396,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183])).
% 4.75/4.62 cnf(2450,plain,
% 4.75/4.62 (P54(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,324,354,374,378,381,386,389,391,394,396,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184])).
% 4.75/4.62 cnf(2451,plain,
% 4.75/4.62 (P34(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188])).
% 4.75/4.62 cnf(2452,plain,
% 4.75/4.62 (P39(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189])).
% 4.75/4.62 cnf(2453,plain,
% 4.75/4.62 (P47(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190])).
% 4.75/4.62 cnf(2454,plain,
% 4.75/4.62 (P49(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,312,316,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194])).
% 4.75/4.62 cnf(2455,plain,
% 4.75/4.62 (P16(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,271,273,293,312,316,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195])).
% 4.75/4.62 cnf(2456,plain,
% 4.75/4.62 (P32(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,293,312,316,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196])).
% 4.75/4.62 cnf(2457,plain,
% 4.75/4.62 (P15(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,374,378,381,386,389,391,394,396,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197])).
% 4.75/4.62 cnf(2458,plain,
% 4.75/4.62 (P46(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,374,378,381,386,389,391,394,396,400,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198])).
% 4.75/4.62 cnf(2459,plain,
% 4.75/4.62 (P17(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,374,378,381,386,389,391,394,396,400,406,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199])).
% 4.75/4.62 cnf(2460,plain,
% 4.75/4.62 (P58(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,371,374,378,381,386,389,391,394,396,400,406,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200])).
% 4.75/4.62 cnf(2461,plain,
% 4.75/4.62 (P33(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201])).
% 4.75/4.62 cnf(2462,plain,
% 4.75/4.62 (P68(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,289,293,312,316,322,323,324,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202])).
% 4.75/4.62 cnf(2463,plain,
% 4.75/4.62 (P5(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,289,293,312,316,322,323,324,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203])).
% 4.75/4.62 cnf(2464,plain,
% 4.75/4.62 (P18(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,289,293,312,316,322,323,324,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204])).
% 4.75/4.62 cnf(2465,plain,
% 4.75/4.62 (P55(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,289,293,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205])).
% 4.75/4.62 cnf(2466,plain,
% 4.75/4.62 (P40(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,289,293,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206])).
% 4.75/4.62 cnf(2467,plain,
% 4.75/4.62 (P21(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,289,293,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207])).
% 4.75/4.62 cnf(2468,plain,
% 4.75/4.62 (P73(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,289,293,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208])).
% 4.75/4.62 cnf(2469,plain,
% 4.75/4.62 (P19(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,289,293,308,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209])).
% 4.75/4.62 cnf(2470,plain,
% 4.75/4.62 (P6(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,308,312,316,322,323,324,347,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211])).
% 4.75/4.62 cnf(2471,plain,
% 4.75/4.62 (P63(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212])).
% 4.75/4.62 cnf(2472,plain,
% 4.75/4.62 (P7(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213])).
% 4.75/4.62 cnf(2473,plain,
% 4.75/4.62 (P22(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214])).
% 4.75/4.62 cnf(2474,plain,
% 4.75/4.62 (P23(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,556,458,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215])).
% 4.75/4.62 cnf(2479,plain,
% 4.75/4.62 (P12(a70,x24791,f27(f27(f10(a70),x24792),x24791))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344])).
% 4.75/4.62 cnf(2480,plain,
% 4.75/4.62 (P12(a70,x24801,x24801)),
% 4.75/4.62 inference(rename_variables,[],[458])).
% 4.75/4.62 cnf(2487,plain,
% 4.75/4.62 (P9(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216])).
% 4.75/4.62 cnf(2488,plain,
% 4.75/4.62 (P69(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217])).
% 4.75/4.62 cnf(2489,plain,
% 4.75/4.62 (P71(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218])).
% 4.75/4.62 cnf(2490,plain,
% 4.75/4.62 (P66(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,322,323,324,328,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219])).
% 4.75/4.62 cnf(2491,plain,
% 4.75/4.62 (P50(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,322,323,324,328,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220])).
% 4.75/4.62 cnf(2492,plain,
% 4.75/4.62 (P59(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221])).
% 4.75/4.62 cnf(2493,plain,
% 4.75/4.62 (P62(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222])).
% 4.75/4.62 cnf(2494,plain,
% 4.75/4.62 (P70(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,347,351,354,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223])).
% 4.75/4.62 cnf(2495,plain,
% 4.75/4.62 (P65(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,347,351,354,359,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224])).
% 4.75/4.62 cnf(2496,plain,
% 4.75/4.62 (P72(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,343,347,351,354,359,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225])).
% 4.75/4.62 cnf(2497,plain,
% 4.75/4.62 (P52(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,343,347,351,354,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226])).
% 4.75/4.62 cnf(2498,plain,
% 4.75/4.62 (P44(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227])).
% 4.75/4.62 cnf(2499,plain,
% 4.75/4.62 (P67(f11(a70,f6(a70,a1,a1),a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228])).
% 4.75/4.62 cnf(2500,plain,
% 4.75/4.62 (P10(a1,f7(f3(a1)),f3(a70))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914])).
% 4.75/4.62 cnf(2502,plain,
% 4.75/4.62 (~P10(a70,f11(a70,f11(a70,f11(a70,x25021,f11(a70,f3(a70),f3(a70))),x25022),f3(a70)),x25021)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,257,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433])).
% 4.75/4.62 cnf(2505,plain,
% 4.75/4.62 (~P10(a70,f11(a70,f11(a70,f11(a70,f8(a70),f11(a70,f3(a70),f3(a70))),x25051),f3(a70)),f11(a70,f3(a70),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,257,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434])).
% 4.75/4.62 cnf(2506,plain,
% 4.75/4.62 (P10(a70,x25061,x25061)),
% 4.75/4.62 inference(rename_variables,[],[456])).
% 4.75/4.62 cnf(2508,plain,
% 4.75/4.62 (~P10(a1,f26(a2,a74),f11(a1,f3(a1),f26(a2,a74)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,467,2228,565,2239,481,237,238,243,245,246,247,256,257,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580])).
% 4.75/4.62 cnf(2511,plain,
% 4.75/4.62 (~E(f11(a70,x25111,f3(a70)),x25111)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2517,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x25171,x25172),x25171)),
% 4.75/4.62 inference(rename_variables,[],[576])).
% 4.75/4.62 cnf(2520,plain,
% 4.75/4.62 (~P11(a70,f11(a70,x25201,x25202),x25201)),
% 4.75/4.62 inference(rename_variables,[],[576])).
% 4.75/4.62 cnf(2523,plain,
% 4.75/4.62 (P10(a70,x25231,f11(a70,x25232,x25231))),
% 4.75/4.62 inference(rename_variables,[],[496])).
% 4.75/4.62 cnf(2525,plain,
% 4.75/4.62 (P11(a1,f25(a70,f8(a70)),f11(a1,f25(a70,f24(f8(a1))),f3(a1)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,1891,1923,1951,486,2029,496,2083,2086,2285,497,2098,2104,498,2015,2216,2227,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,237,238,243,245,246,247,248,256,257,259,260,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191])).
% 4.75/4.62 cnf(2526,plain,
% 4.75/4.62 (P11(a1,x25261,f11(a1,f25(a70,f24(x25261)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2529,plain,
% 4.75/4.62 (~P11(a1,x25291,x25291)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2532,plain,
% 4.75/4.62 (P11(a68,x25321,f11(a68,x25321,f3(a68)))),
% 4.75/4.62 inference(rename_variables,[],[1925])).
% 4.75/4.62 cnf(2536,plain,
% 4.75/4.62 (P11(a70,f8(a70),f27(f27(f13(a70),x25361),f8(a70)))),
% 4.75/4.62 inference(rename_variables,[],[1923])).
% 4.75/4.62 cnf(2543,plain,
% 4.75/4.62 (P13(a68,f15(a68,f11(a68,f8(a68),f3(a68)),f7(f25(a70,f8(f71(a68))))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226])).
% 4.75/4.62 cnf(2544,plain,
% 4.75/4.62 (E(f7(f25(a70,x25441)),x25441)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2547,plain,
% 4.75/4.62 (~P12(f71(a1),f21(a1,f11(a1,x25471,f9(a1,x25471)),x25472),f11(a70,f8(f71(a1)),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317])).
% 4.75/4.62 cnf(2548,plain,
% 4.75/4.62 (~E(f11(a70,x25481,f3(a70)),x25481)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2550,plain,
% 4.75/4.62 (P10(a1,f5(a1,f8(a1)),f25(a70,f7(f9(a1,f8(a1)))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333])).
% 4.75/4.62 cnf(2552,plain,
% 4.75/4.62 (P10(a1,f8(a1),f25(a70,x25521))),
% 4.75/4.62 inference(rename_variables,[],[481])).
% 4.75/4.62 cnf(2558,plain,
% 4.75/4.62 (~E(f11(a70,x25581,f3(a70)),x25581)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2560,plain,
% 4.75/4.62 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x25601),x25601)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435])).
% 4.75/4.62 cnf(2561,plain,
% 4.75/4.62 (~P11(a1,x25611,x25611)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2562,plain,
% 4.75/4.62 (P11(a1,x25621,f11(a1,f25(a70,f24(x25621)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2565,plain,
% 4.75/4.62 (~P11(a1,x25651,x25651)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2566,plain,
% 4.75/4.62 (P10(a1,x25661,x25661)),
% 4.75/4.62 inference(rename_variables,[],[455])).
% 4.75/4.62 cnf(2568,plain,
% 4.75/4.62 (~P11(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x25681),x25681)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,456,2109,2288,2302,2368,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437])).
% 4.75/4.62 cnf(2569,plain,
% 4.75/4.62 (~P11(a1,x25691,x25691)),
% 4.75/4.62 inference(rename_variables,[],[1893])).
% 4.75/4.62 cnf(2570,plain,
% 4.75/4.62 (P11(a1,x25701,f11(a1,f25(a70,f24(x25701)),f3(a1)))),
% 4.75/4.62 inference(rename_variables,[],[516])).
% 4.75/4.62 cnf(2575,plain,
% 4.75/4.62 (~P11(a1,f27(f27(f10(a1),f6(a1,x25751,x25751)),x25752),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,579,2080,471,495,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482])).
% 4.75/4.62 cnf(2587,plain,
% 4.75/4.62 (~P11(a1,f6(a1,f3(a1),f5(a1,f6(a1,f8(a1),f3(a1)))),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777])).
% 4.75/4.62 cnf(2592,plain,
% 4.75/4.62 (E(f7(f25(a70,x25921)),x25921)),
% 4.75/4.62 inference(rename_variables,[],[448])).
% 4.75/4.62 cnf(2594,plain,
% 4.75/4.62 (P12(f71(a1),f21(a1,x25941,f21(a1,f11(a1,x25942,f9(a1,x25942)),x25943)),f7(f25(a70,f8(f71(a1)))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,229,231,233,235,239,241,250,254,255,263,270,271,273,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312])).
% 4.75/4.62 cnf(2602,plain,
% 4.75/4.62 (~E(f11(a70,x26021,f3(a70)),x26021)),
% 4.75/4.62 inference(rename_variables,[],[567])).
% 4.75/4.62 cnf(2610,plain,
% 4.75/4.62 (~E(f6(a70,f11(a70,f11(a70,x26101,x26102),f3(a70)),x26102),x26101)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699])).
% 4.75/4.62 cnf(2634,plain,
% 4.75/4.62 (~P11(a68,f8(a68),f9(a68,f3(a68)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964])).
% 4.75/4.62 cnf(2640,plain,
% 4.75/4.62 (P10(a70,f6(a70,f3(a70),f3(a70)),x26401)),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964,1001,1072,1160])).
% 4.75/4.62 cnf(2642,plain,
% 4.75/4.62 (~P11(a70,x26421,f6(a70,f3(a70),f3(a70)))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964,1001,1072,1160,1242])).
% 4.75/4.62 cnf(2644,plain,
% 4.75/4.62 (~P11(a68,x26441,f9(a68,f11(a68,f9(a68,f11(a68,x26441,f3(a68))),f3(a68))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964,1001,1072,1160,1242,1244])).
% 4.75/4.62 cnf(2648,plain,
% 4.75/4.62 (~P11(a1,f9(a1,f27(f27(f10(a1),f6(a1,x26481,x26481)),x26482)),f8(a1))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964,1001,1072,1160,1242,1244,1283,1304])).
% 4.75/4.62 cnf(2652,plain,
% 4.75/4.62 (P11(a68,x26521,f5(a68,f11(a68,x26521,f3(a68))))),
% 4.75/4.62 inference(scs_inference,[],[580,439,1907,1910,1893,1991,2244,2247,2255,2258,2268,2275,2278,2322,2330,2387,2390,2393,2396,2529,2561,2565,2569,1895,1994,2026,2035,2074,2077,2252,2263,2325,455,1986,2041,2044,2154,2301,2305,2308,2399,2566,456,2109,2288,2302,2368,2506,457,2095,562,2115,2118,2294,2317,2349,1888,1925,2407,2532,1891,1923,2536,1951,486,2029,2092,446,496,2083,2086,2285,2523,497,2098,2104,498,2015,2216,2227,2281,575,2032,2038,2050,2062,2065,576,2517,2520,467,2228,565,2239,2375,481,2224,2552,237,238,243,244,245,246,247,248,256,257,259,260,261,262,267,268,305,349,365,368,392,393,448,2006,2020,2180,2333,2422,2437,2440,2447,2544,2592,452,482,2047,2121,502,2297,2336,2348,2355,577,2056,2059,2112,2291,540,2089,2298,2314,499,516,2101,2233,2362,2371,2526,2562,2570,579,2080,2343,471,495,512,519,531,556,458,2433,2480,465,229,231,233,235,239,241,250,254,255,263,270,271,273,275,277,281,285,289,293,297,301,308,312,316,318,320,322,323,324,328,331,335,339,343,347,351,354,356,359,362,371,374,378,381,384,386,389,391,394,396,400,403,406,409,413,415,417,419,423,427,430,435,559,567,2003,2158,2161,2164,2169,2174,2191,2194,2199,2202,2205,2208,2213,2219,2236,2284,2337,2352,2378,2402,2405,2511,2548,2558,2602,573,2009,2012,2068,578,696,870,935,1038,1878,756,757,796,801,802,809,818,826,827,829,830,946,956,965,968,1011,1012,1016,1051,1052,1137,1159,1173,1212,1214,1216,1218,1225,1235,1238,1239,1306,1329,1330,1331,1343,1348,1352,1394,1418,1428,1438,1510,1511,1513,1533,1618,1619,1628,1939,1943,1944,2,20,725,727,903,970,972,1096,1630,152,153,154,668,676,677,678,679,680,683,685,734,816,817,844,845,855,856,861,865,878,893,894,895,913,954,973,998,1021,1022,1057,1097,1103,1109,1113,1114,1116,1131,1132,1133,1134,1135,1136,1147,1149,1151,1153,1155,1156,1165,1170,1171,1175,1182,1262,1266,1281,1307,1337,1358,1401,1402,1403,1404,1405,1406,1410,1416,1421,1455,1456,1476,1503,1563,1564,1634,1636,1639,1640,1749,1750,1797,1798,1805,1806,1833,1835,1839,1841,1844,1956,3,148,149,150,160,161,163,168,170,172,173,176,181,191,193,1036,147,151,155,158,159,162,165,166,167,169,171,174,175,177,178,179,180,182,183,184,188,189,190,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,211,212,213,214,215,866,967,1344,1345,1407,216,217,218,219,220,221,222,223,224,225,226,227,228,914,1433,1434,1580,922,979,981,987,1076,1191,1192,1193,1194,1195,1196,1226,1317,1333,1334,1412,1435,1436,1437,1481,1482,1581,1582,1583,1777,1126,1312,1419,1665,1292,1904,699,703,775,786,834,835,857,871,872,890,940,941,964,1001,1072,1160,1242,1244,1283,1304,1346,1354])).
% 4.75/4.62 cnf(2725,plain,
% 4.75/4.62 (P11(a1,x27251,f25(a70,f24(f11(a1,x27251,f3(a1)))))),
% 4.75/4.62 inference(rename_variables,[],[2361])).
% 4.75/4.62 cnf(2728,plain,
% 4.75/4.62 (~P10(a68,f11(a68,x27281,f3(a68)),x27281)),
% 4.75/4.62 inference(rename_variables,[],[2073])).
% 4.75/4.62 cnf(2731,plain,
% 4.75/4.62 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x27311),x27311)),
% 4.75/4.62 inference(rename_variables,[],[2560])).
% 4.75/4.62 cnf(2734,plain,
% 4.75/4.62 (P11(a68,f6(a68,x27341,f3(a68)),x27341)),
% 4.75/4.62 inference(rename_variables,[],[2094])).
% 4.75/4.62 cnf(2744,plain,
% 4.75/4.62 (E(f11(a70,x27441,f8(a70)),x27441)),
% 4.75/4.62 inference(rename_variables,[],[469])).
% 4.75/4.62 cnf(2747,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x27471,x27472),f3(a70)),x27471)),
% 4.75/4.62 inference(rename_variables,[],[2145])).
% 4.75/4.62 cnf(2750,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x27501,x27502),f3(a70)),x27501)),
% 4.75/4.62 inference(rename_variables,[],[2145])).
% 4.75/4.62 cnf(2753,plain,
% 4.75/4.62 (~E(f11(a1,f27(f27(f10(a1),f6(a1,x27531,x27532)),x27533),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x27532,x27531)),x27533),x27534),f3(a70))),x27534)),
% 4.75/4.62 inference(rename_variables,[],[2384])).
% 4.75/4.62 cnf(2758,plain,
% 4.75/4.62 (~P11(a70,x27581,f6(a70,f3(a70),f3(a70)))),
% 4.75/4.62 inference(rename_variables,[],[2642])).
% 4.75/4.62 cnf(2766,plain,
% 4.75/4.62 (~P10(a70,f11(a70,f11(a70,f11(a70,x27661,f11(a70,f3(a70),f3(a70))),x27662),f3(a70)),x27661)),
% 4.75/4.62 inference(rename_variables,[],[2502])).
% 4.75/4.62 cnf(2772,plain,
% 4.75/4.62 (~P11(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x27721),x27721)),
% 4.75/4.62 inference(rename_variables,[],[2568])).
% 4.75/4.62 cnf(2775,plain,
% 4.75/4.62 (~P10(a70,f11(a70,f11(a70,f11(a70,x27751,f11(a70,f3(a70),f3(a70))),x27752),f3(a70)),x27751)),
% 4.75/4.62 inference(rename_variables,[],[2502])).
% 4.75/4.62 cnf(2778,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x27781,x27782),f3(a70)),x27781)),
% 4.75/4.62 inference(rename_variables,[],[2145])).
% 4.75/4.62 cnf(2781,plain,
% 4.75/4.62 (P10(a1,x27811,f5(a1,x27811))),
% 4.75/4.62 inference(rename_variables,[],[1985])).
% 4.75/4.62 cnf(2784,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f6(a70,x27841,x27842),x27842),x27841)),
% 4.75/4.62 inference(rename_variables,[],[2114])).
% 4.75/4.62 cnf(2791,plain,
% 4.75/4.62 (E(f11(a70,x27911,f8(a70)),x27911)),
% 4.75/4.62 inference(rename_variables,[],[469])).
% 4.75/4.62 cnf(2796,plain,
% 4.75/4.62 (P10(a70,x27961,f24(f25(a70,x27961)))),
% 4.75/4.62 inference(rename_variables,[],[2040])).
% 4.75/4.62 cnf(2801,plain,
% 4.75/4.62 (P10(a70,x28011,f24(f25(a70,x28011)))),
% 4.75/4.62 inference(rename_variables,[],[2040])).
% 4.75/4.62 cnf(2808,plain,
% 4.75/4.62 (E(f11(a70,x28081,f8(a70)),x28081)),
% 4.75/4.62 inference(rename_variables,[],[469])).
% 4.75/4.62 cnf(2815,plain,
% 4.75/4.62 (~P10(a68,x28151,f9(a68,f11(a68,f9(a68,x28151),f3(a68))))),
% 4.75/4.62 inference(rename_variables,[],[2265])).
% 4.75/4.62 cnf(2826,plain,
% 4.75/4.62 (~E(x28261,f11(a1,f27(f27(f10(a1),f6(a1,x28262,x28263)),x28264),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x28263,x28262)),x28264),x28261),f3(a70))))),
% 4.75/4.62 inference(rename_variables,[],[2382])).
% 4.75/4.62 cnf(2830,plain,
% 4.75/4.62 (~P11(a68,x28301,f9(a68,f11(a68,f9(a68,f11(a68,x28301,f3(a68))),f3(a68))))),
% 4.75/4.62 inference(rename_variables,[],[2644])).
% 4.75/4.62 cnf(2833,plain,
% 4.75/4.62 (P11(a70,x28331,f7(f11(a1,f25(a70,x28331),f3(a1))))),
% 4.75/4.62 inference(rename_variables,[],[2120])).
% 4.75/4.62 cnf(2836,plain,
% 4.75/4.62 (P10(a70,x28361,f24(f25(a70,x28361)))),
% 4.75/4.62 inference(rename_variables,[],[2040])).
% 4.75/4.62 cnf(2839,plain,
% 4.75/4.62 (~P10(a70,f11(a70,f11(a70,f11(a70,x28391,f11(a70,f3(a70),f3(a70))),x28392),f3(a70)),x28391)),
% 4.75/4.62 inference(rename_variables,[],[2502])).
% 4.75/4.62 cnf(2846,plain,
% 4.75/4.62 (P11(a70,x28461,f7(f11(a1,f25(a70,x28461),f3(a1))))),
% 4.75/4.62 inference(rename_variables,[],[2120])).
% 4.75/4.62 cnf(2855,plain,
% 4.75/4.62 (~P11(a70,f11(a70,f11(a70,x28551,x28552),f3(a70)),x28551)),
% 4.75/4.62 inference(rename_variables,[],[2145])).
% 4.75/4.62 cnf(2858,plain,
% 4.75/4.62 (E(f11(a70,x28581,f8(a70)),x28581)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(2861,plain,
% 4.75/4.63 (~P11(a70,f11(a70,f11(a70,x28611,x28612),f3(a70)),x28611)),
% 4.75/4.63 inference(rename_variables,[],[2145])).
% 4.75/4.63 cnf(2866,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x28661,f3(a70)),x28662),x28661)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(2869,plain,
% 4.75/4.63 (P10(a70,x28691,f24(f25(a70,x28691)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(2872,plain,
% 4.75/4.63 (P11(a1,x28721,f11(a1,x28722,f11(a1,f25(a70,f24(f5(a1,f6(a1,x28721,x28722)))),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2370])).
% 4.75/4.63 cnf(2877,plain,
% 4.75/4.63 (P10(a70,x28771,f24(f25(a70,x28771)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(2882,plain,
% 4.75/4.63 (~P11(a68,f11(a68,x28821,f3(a68)),x28821)),
% 4.75/4.63 inference(rename_variables,[],[2076])).
% 4.75/4.63 cnf(2887,plain,
% 4.75/4.63 (~P11(a70,f11(a70,f11(a70,x28871,x28872),f3(a70)),x28871)),
% 4.75/4.63 inference(rename_variables,[],[2145])).
% 4.75/4.63 cnf(2890,plain,
% 4.75/4.63 (~P11(a68,f11(a68,x28901,f3(a68)),x28901)),
% 4.75/4.63 inference(rename_variables,[],[2076])).
% 4.75/4.63 cnf(2895,plain,
% 4.75/4.63 (~P10(a70,f11(a70,f11(a70,f11(a70,x28951,f11(a70,f3(a70),f3(a70))),x28952),f3(a70)),x28951)),
% 4.75/4.63 inference(rename_variables,[],[2502])).
% 4.75/4.63 cnf(2898,plain,
% 4.75/4.63 (P11(a70,x28981,f7(f11(a1,f25(a70,x28981),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(2901,plain,
% 4.75/4.63 (~P11(a68,f11(a68,x29011,f3(a68)),x29011)),
% 4.75/4.63 inference(rename_variables,[],[2076])).
% 4.75/4.63 cnf(2909,plain,
% 4.75/4.63 (P10(a1,f5(a1,f9(a1,f26(a2,x29091))),f26(a2,x29091))),
% 4.75/4.63 inference(rename_variables,[],[2307])).
% 4.75/4.63 cnf(2912,plain,
% 4.75/4.63 (E(x29121,f11(a70,f6(a70,x29121,x29121),x29121))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(2916,plain,
% 4.75/4.63 (~P10(a68,x29161,f9(a68,f11(a68,f9(a68,x29161),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2265])).
% 4.75/4.63 cnf(2919,plain,
% 4.75/4.63 (~P10(a68,x29191,f9(a68,f11(a68,f9(a68,x29191),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2265])).
% 4.75/4.63 cnf(2922,plain,
% 4.75/4.63 (E(x29221,f11(a70,f8(a70),x29221))),
% 4.75/4.63 inference(rename_variables,[],[2339])).
% 4.75/4.63 cnf(2925,plain,
% 4.75/4.63 (P10(a68,x29251,f5(a68,x29251))),
% 4.75/4.63 inference(rename_variables,[],[2147])).
% 4.75/4.63 cnf(2928,plain,
% 4.75/4.63 (~P10(a68,f11(a68,x29281,f3(a68)),x29281)),
% 4.75/4.63 inference(rename_variables,[],[2073])).
% 4.75/4.63 cnf(2931,plain,
% 4.75/4.63 (P11(a68,f6(a68,x29311,f3(a68)),x29311)),
% 4.75/4.63 inference(rename_variables,[],[2094])).
% 4.75/4.63 cnf(2934,plain,
% 4.75/4.63 (~P10(a68,f11(a68,x29341,f3(a68)),x29341)),
% 4.75/4.63 inference(rename_variables,[],[2073])).
% 4.75/4.63 cnf(2944,plain,
% 4.75/4.63 (E(x29441,f11(a70,f6(a70,x29441,x29441),x29441))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(2946,plain,
% 4.75/4.63 (E(x29461,f11(a70,f6(a70,x29461,x29461),x29461))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(2956,plain,
% 4.75/4.63 (~P11(a1,f25(a70,x29561),f8(a1))),
% 4.75/4.63 inference(rename_variables,[],[574])).
% 4.75/4.63 cnf(2963,plain,
% 4.75/4.63 (~P11(a68,x29631,f9(a68,f11(a68,f9(a68,f11(a68,x29631,f3(a68))),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2644])).
% 4.75/4.63 cnf(2969,plain,
% 4.75/4.63 (~P11(a68,f11(a68,x29691,f3(a68)),x29691)),
% 4.75/4.63 inference(rename_variables,[],[2076])).
% 4.75/4.63 cnf(2970,plain,
% 4.75/4.63 (P10(a68,x29701,f5(a68,x29701))),
% 4.75/4.63 inference(rename_variables,[],[2147])).
% 4.75/4.63 cnf(2979,plain,
% 4.75/4.63 (P10(a1,x29791,f5(a1,x29791))),
% 4.75/4.63 inference(rename_variables,[],[1985])).
% 4.75/4.63 cnf(2980,plain,
% 4.75/4.63 (P10(a70,x29801,f24(f25(a70,x29801)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(2988,plain,
% 4.75/4.63 (~P11(a68,f11(a68,x29881,f3(a68)),x29881)),
% 4.75/4.63 inference(rename_variables,[],[2076])).
% 4.75/4.63 cnf(2991,plain,
% 4.75/4.63 (~P11(a70,x29911,f6(a70,f3(a70),f3(a70)))),
% 4.75/4.63 inference(rename_variables,[],[2642])).
% 4.75/4.63 cnf(2992,plain,
% 4.75/4.63 (~P11(a70,x29921,f7(f25(a70,f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2005])).
% 4.75/4.63 cnf(2998,plain,
% 4.75/4.63 (P10(a70,f7(f25(a70,x29981)),x29981)),
% 4.75/4.63 inference(rename_variables,[],[2043])).
% 4.75/4.63 cnf(3001,plain,
% 4.75/4.63 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x30011),x30011)),
% 4.75/4.63 inference(rename_variables,[],[2560])).
% 4.75/4.63 cnf(3006,plain,
% 4.75/4.63 (E(f11(a70,x30061,f8(a70)),x30061)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3011,plain,
% 4.75/4.63 (E(f11(a70,x30111,f8(a70)),x30111)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3014,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x30141,f3(a70)),x30142),x30141)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3017,plain,
% 4.75/4.63 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x30171),x30171)),
% 4.75/4.63 inference(rename_variables,[],[2560])).
% 4.75/4.63 cnf(3022,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x30221,f3(a70)),x30222),x30221)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3025,plain,
% 4.75/4.63 (~E(x30251,f11(a68,x30251,f3(a68)))),
% 4.75/4.63 inference(rename_variables,[],[2000])).
% 4.75/4.63 cnf(3028,plain,
% 4.75/4.63 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x30281),x30281)),
% 4.75/4.63 inference(rename_variables,[],[2560])).
% 4.75/4.63 cnf(3031,plain,
% 4.75/4.63 (~P10(a68,x30311,f9(a68,f11(a68,f9(a68,x30311),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2265])).
% 4.75/4.63 cnf(3034,plain,
% 4.75/4.63 (~P11(a70,f11(a70,f11(a70,x30341,x30342),f3(a70)),x30341)),
% 4.75/4.63 inference(rename_variables,[],[2145])).
% 4.75/4.63 cnf(3035,plain,
% 4.75/4.63 (P11(a70,x30351,f7(f11(a1,f25(a70,x30351),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3042,plain,
% 4.75/4.63 (~P11(a1,x30421,f11(a1,f27(f27(f10(a1),f6(a1,x30422,x30422)),x30423),x30421))),
% 4.75/4.63 inference(rename_variables,[],[2392])).
% 4.75/4.63 cnf(3047,plain,
% 4.75/4.63 (P12(a70,x30471,f27(f27(f10(a70),x30472),x30471))),
% 4.75/4.63 inference(rename_variables,[],[2479])).
% 4.75/4.63 cnf(3050,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x30501,f3(a70)),x30502),x30501)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3055,plain,
% 4.75/4.63 (P11(a70,f24(f8(a1)),f11(a70,x30551,f3(a70)))),
% 4.75/4.63 inference(rename_variables,[],[2304])).
% 4.75/4.63 cnf(3056,plain,
% 4.75/4.63 (~P11(a70,x30561,f7(f25(a70,f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2005])).
% 4.75/4.63 cnf(3059,plain,
% 4.75/4.63 (~E(f11(a1,x30591,f11(a70,f8(a1),f3(a70))),x30591)),
% 4.75/4.63 inference(rename_variables,[],[2193])).
% 4.75/4.63 cnf(3062,plain,
% 4.75/4.63 (P10(a1,x30621,f5(a1,x30621))),
% 4.75/4.63 inference(rename_variables,[],[1985])).
% 4.75/4.63 cnf(3066,plain,
% 4.75/4.63 (P11(a70,x30661,f7(f11(a1,f25(a70,x30661),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3067,plain,
% 4.75/4.63 (~P10(a70,f11(a70,f11(a70,f11(a70,x30671,f11(a70,f3(a70),f3(a70))),x30672),f3(a70)),x30671)),
% 4.75/4.63 inference(rename_variables,[],[2502])).
% 4.75/4.63 cnf(3070,plain,
% 4.75/4.63 (~E(x30701,f11(a68,x30701,f3(a68)))),
% 4.75/4.63 inference(rename_variables,[],[2000])).
% 4.75/4.63 cnf(3073,plain,
% 4.75/4.63 (E(f11(a70,x30731,f8(a70)),x30731)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3080,plain,
% 4.75/4.63 (~P10(a68,x30801,f9(a68,f11(a68,f9(a68,x30801),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2265])).
% 4.75/4.63 cnf(3083,plain,
% 4.75/4.63 (~P11(a1,f11(a1,f25(a70,f24(x30831)),f3(a1)),x30831)),
% 4.75/4.63 inference(rename_variables,[],[2230])).
% 4.75/4.63 cnf(3090,plain,
% 4.75/4.63 (~P10(a70,f11(a70,f11(a70,f11(a70,x30901,f11(a70,f3(a70),f3(a70))),x30902),f3(a70)),x30901)),
% 4.75/4.63 inference(rename_variables,[],[2502])).
% 4.75/4.63 cnf(3091,plain,
% 4.75/4.63 (P10(a70,x30911,f24(f25(a70,x30911)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(3096,plain,
% 4.75/4.63 (~E(x30961,f11(a68,x30961,f3(a68)))),
% 4.75/4.63 inference(rename_variables,[],[2000])).
% 4.75/4.63 cnf(3097,plain,
% 4.75/4.63 (P10(a70,f6(a70,f3(a70),f3(a70)),x30971)),
% 4.75/4.63 inference(rename_variables,[],[2640])).
% 4.75/4.63 cnf(3101,plain,
% 4.75/4.63 (P10(a70,x31011,f24(f25(a70,x31011)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(3104,plain,
% 4.75/4.63 (~E(f9(a1,f11(a68,f9(a1,x31041),f3(a68))),x31041)),
% 4.75/4.63 inference(rename_variables,[],[2176])).
% 4.75/4.63 cnf(3108,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x31081,f3(a70)),x31082),x31081)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3111,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x31111,f3(a70)),x31112),x31111)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3116,plain,
% 4.75/4.63 (P11(a1,x31161,f11(a1,x31162,f11(a1,f25(a70,f24(f5(a1,f6(a1,x31161,x31162)))),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2370])).
% 4.75/4.63 cnf(3121,plain,
% 4.75/4.63 (~P11(a1,x31211,f11(a1,f27(f27(f10(a1),f6(a1,x31212,x31212)),x31213),x31211))),
% 4.75/4.63 inference(rename_variables,[],[2392])).
% 4.75/4.63 cnf(3124,plain,
% 4.75/4.63 (E(x31241,f11(a70,f6(a70,x31241,x31241),x31241))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3126,plain,
% 4.75/4.63 (~E(x31261,f11(a68,x31261,f3(a68)))),
% 4.75/4.63 inference(rename_variables,[],[2000])).
% 4.75/4.63 cnf(3129,plain,
% 4.75/4.63 (E(x31291,f11(a70,f6(a70,x31291,x31291),x31291))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3131,plain,
% 4.75/4.63 (E(x31311,f11(a70,f6(a70,x31311,x31311),x31311))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3137,plain,
% 4.75/4.63 (~E(f11(a1,x31371,f11(a70,f8(a1),f3(a70))),x31371)),
% 4.75/4.63 inference(rename_variables,[],[2193])).
% 4.75/4.63 cnf(3140,plain,
% 4.75/4.63 (P11(a70,x31401,f7(f11(a1,f25(a70,x31401),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3141,plain,
% 4.75/4.63 (P11(a70,x31411,f11(a70,x31411,f27(f27(f13(a70),x31412),f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2310])).
% 4.75/4.63 cnf(3144,plain,
% 4.75/4.63 (P11(a1,x31441,f25(a70,f24(f11(a1,x31441,f3(a1)))))),
% 4.75/4.63 inference(rename_variables,[],[2361])).
% 4.75/4.63 cnf(3147,plain,
% 4.75/4.63 (E(x31471,f11(a70,f6(a70,x31471,x31471),x31471))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3151,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x31511,f3(a70)),x31512),x31511)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3152,plain,
% 4.75/4.63 (P10(a70,f6(a70,f3(a70),f3(a70)),x31521)),
% 4.75/4.63 inference(rename_variables,[],[2640])).
% 4.75/4.63 cnf(3155,plain,
% 4.75/4.63 (E(x31551,f11(a70,f6(a70,x31551,x31551),x31551))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3157,plain,
% 4.75/4.63 (E(x31571,f11(a70,f6(a70,x31571,x31571),x31571))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3161,plain,
% 4.75/4.63 (P11(a1,x31611,f11(a1,x31612,f11(a1,f25(a70,f24(f5(a1,f6(a1,x31611,x31612)))),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2370])).
% 4.75/4.63 cnf(3164,plain,
% 4.75/4.63 (~P10(a70,f11(a70,f11(a70,f11(a70,x31641,f11(a70,f3(a70),f3(a70))),x31642),f3(a70)),x31641)),
% 4.75/4.63 inference(rename_variables,[],[2502])).
% 4.75/4.63 cnf(3165,plain,
% 4.75/4.63 (P10(a70,x31651,f24(f25(a70,x31651)))),
% 4.75/4.63 inference(rename_variables,[],[2040])).
% 4.75/4.63 cnf(3170,plain,
% 4.75/4.63 (P10(a1,x31701,f5(a1,x31701))),
% 4.75/4.63 inference(rename_variables,[],[1985])).
% 4.75/4.63 cnf(3171,plain,
% 4.75/4.63 (P11(a1,x31711,f25(a70,f24(f11(a1,x31711,f3(a1)))))),
% 4.75/4.63 inference(rename_variables,[],[2361])).
% 4.75/4.63 cnf(3174,plain,
% 4.75/4.63 (E(x31741,f11(a70,f6(a70,x31741,x31741),x31741))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3176,plain,
% 4.75/4.63 (E(x31761,f11(a70,f6(a70,x31761,x31761),x31761))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3179,plain,
% 4.75/4.63 (~P11(a1,x31791,f11(a1,f27(f27(f10(a1),f6(a1,x31792,x31792)),x31793),x31791))),
% 4.75/4.63 inference(rename_variables,[],[2392])).
% 4.75/4.63 cnf(3182,plain,
% 4.75/4.63 (P10(f11(a70,f6(a70,a1,a1),a1),x31821,x31821)),
% 4.75/4.63 inference(rename_variables,[],[2152])).
% 4.75/4.63 cnf(3190,plain,
% 4.75/4.63 (E(x31901,f11(a70,f6(a70,x31901,x31901),x31901))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3192,plain,
% 4.75/4.63 (E(f11(a70,x31921,f8(a70)),x31921)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3195,plain,
% 4.75/4.63 (P11(a68,x31951,f5(a68,f11(a68,x31951,f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2652])).
% 4.75/4.63 cnf(3198,plain,
% 4.75/4.63 (E(x31981,f11(a70,f6(a70,x31981,x31981),x31981))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3202,plain,
% 4.75/4.63 (E(x32021,f11(a70,f6(a70,x32021,x32021),x32021))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3204,plain,
% 4.75/4.63 (E(x32041,f11(a70,f6(a70,x32041,x32041),x32041))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3206,plain,
% 4.75/4.63 (E(x32061,f11(a70,f6(a70,x32061,x32061),x32061))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3210,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x32101,f3(a70)),x32102),x32101)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3215,plain,
% 4.75/4.63 (~P10(a68,x32151,f9(a68,f11(a68,f9(a68,x32151),f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2265])).
% 4.75/4.63 cnf(3218,plain,
% 4.75/4.63 (E(x32181,f11(a70,f6(a70,x32181,x32181),x32181))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3220,plain,
% 4.75/4.63 (E(x32201,f11(a70,f6(a70,x32201,x32201),x32201))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3222,plain,
% 4.75/4.63 (E(x32221,f11(a70,f6(a70,x32221,x32221),x32221))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3226,plain,
% 4.75/4.63 (E(f11(a68,f8(a68),x32261),x32261)),
% 4.75/4.63 inference(rename_variables,[],[472])).
% 4.75/4.63 cnf(3229,plain,
% 4.75/4.63 (E(x32291,f11(a70,f6(a70,x32291,x32291),x32291))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3231,plain,
% 4.75/4.63 (E(x32311,f11(a70,f6(a70,x32311,x32311),x32311))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3233,plain,
% 4.75/4.63 (E(x32331,f11(a70,f6(a70,x32331,x32331),x32331))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3235,plain,
% 4.75/4.63 (E(x32351,f11(a70,f6(a70,x32351,x32351),x32351))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3237,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x32371,f3(a70)),x32372),x32371)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3240,plain,
% 4.75/4.63 (E(f11(a70,x32401,f8(a70)),x32401)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3242,plain,
% 4.75/4.63 (~P11(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x32421),x32421)),
% 4.75/4.63 inference(rename_variables,[],[2568])).
% 4.75/4.63 cnf(3247,plain,
% 4.75/4.63 (E(x32471,f11(a70,f6(a70,x32471,x32471),x32471))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3249,plain,
% 4.75/4.63 (P10(a1,x32491,f5(a1,x32491))),
% 4.75/4.63 inference(rename_variables,[],[1985])).
% 4.75/4.63 cnf(3252,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x32521,f3(a70)),x32522),x32521)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3254,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x32541,f3(a70)),x32542),x32541)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3257,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x32571,f3(a70)),x32572),x32571)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3263,plain,
% 4.75/4.63 (P11(a70,x32631,f7(f11(a1,f25(a70,x32631),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3266,plain,
% 4.75/4.63 (E(x32661,f11(a70,f6(a70,x32661,x32661),x32661))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3273,plain,
% 4.75/4.63 (P10(f11(a70,f6(a70,a1,a1),a1),x32731,x32731)),
% 4.75/4.63 inference(rename_variables,[],[2152])).
% 4.75/4.63 cnf(3276,plain,
% 4.75/4.63 (E(x32761,f11(a70,f6(a70,x32761,x32761),x32761))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3278,plain,
% 4.75/4.63 (E(x32781,f11(a70,f6(a70,x32781,x32781),x32781))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3282,plain,
% 4.75/4.63 (~E(f11(a68,x32821,f3(a68)),x32821)),
% 4.75/4.63 inference(rename_variables,[],[2034])).
% 4.75/4.63 cnf(3288,plain,
% 4.75/4.63 (E(x32881,f11(a70,f6(a70,x32881,x32881),x32881))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3290,plain,
% 4.75/4.63 (~E(x32901,f11(a1,f27(f27(f10(a1),f6(a1,x32902,x32903)),x32904),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x32903,x32902)),x32904),x32901),f3(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2382])).
% 4.75/4.63 cnf(3293,plain,
% 4.75/4.63 (E(x32931,f11(a70,f6(a70,x32931,x32931),x32931))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3295,plain,
% 4.75/4.63 (P11(a70,x32951,f7(f11(a1,f25(a70,x32951),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3296,plain,
% 4.75/4.63 (~P11(a70,x32961,f7(f25(a70,f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2005])).
% 4.75/4.63 cnf(3299,plain,
% 4.75/4.63 (E(x32991,f11(a70,f6(a70,x32991,x32991),x32991))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3303,plain,
% 4.75/4.63 (E(x33031,f11(a70,f6(a70,x33031,x33031),x33031))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3305,plain,
% 4.75/4.63 (P12(a70,x33051,f27(f27(f10(a70),x33052),x33051))),
% 4.75/4.63 inference(rename_variables,[],[2479])).
% 4.75/4.63 cnf(3308,plain,
% 4.75/4.63 (P12(a70,f27(f27(f10(a70),f3(a70)),f27(f27(f13(a70),x33081),f8(a70))),f27(f27(f13(a70),x33081),f8(a70)))),
% 4.75/4.63 inference(rename_variables,[],[2133])).
% 4.75/4.63 cnf(3312,plain,
% 4.75/4.63 (E(f11(a70,x33121,f8(a70)),x33121)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3315,plain,
% 4.75/4.63 (P10(a70,f6(a70,f3(a70),f3(a70)),x33151)),
% 4.75/4.63 inference(rename_variables,[],[2640])).
% 4.75/4.63 cnf(3322,plain,
% 4.75/4.63 (P10(a70,f6(a70,f3(a70),f3(a70)),x33221)),
% 4.75/4.63 inference(rename_variables,[],[2640])).
% 4.75/4.63 cnf(3330,plain,
% 4.75/4.63 (~E(x33301,f11(a1,f27(f27(f10(a1),f6(a1,x33302,x33303)),x33304),f11(a70,f11(a1,f27(f27(f10(a1),f6(a1,x33303,x33302)),x33304),x33301),f3(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2382])).
% 4.75/4.63 cnf(3338,plain,
% 4.75/4.63 (E(f11(a70,x33381,f8(a70)),x33381)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3342,plain,
% 4.75/4.63 (E(f11(a70,x33421,f8(a70)),x33421)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3344,plain,
% 4.75/4.63 (E(x33441,f11(a70,f6(a70,x33441,x33441),x33441))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3354,plain,
% 4.75/4.63 (E(x33541,f11(a70,f6(a70,x33541,x33541),x33541))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3360,plain,
% 4.75/4.63 (E(x33601,f11(a70,f6(a70,x33601,x33601),x33601))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3362,plain,
% 4.75/4.63 (E(x33621,f11(a70,f6(a70,x33621,x33621),x33621))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3364,plain,
% 4.75/4.63 (E(x33641,f11(a70,f6(a70,x33641,x33641),x33641))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3366,plain,
% 4.75/4.63 (E(x33661,f11(a70,f6(a70,x33661,x33661),x33661))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3368,plain,
% 4.75/4.63 (E(x33681,f11(a70,f6(a70,x33681,x33681),x33681))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3370,plain,
% 4.75/4.63 (E(x33701,f11(a70,f6(a70,x33701,x33701),x33701))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3372,plain,
% 4.75/4.63 (E(x33721,f11(a70,f6(a70,x33721,x33721),x33721))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3374,plain,
% 4.75/4.63 (E(x33741,f11(a70,f6(a70,x33741,x33741),x33741))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3376,plain,
% 4.75/4.63 (E(x33761,f11(a70,f6(a70,x33761,x33761),x33761))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3378,plain,
% 4.75/4.63 (E(x33781,f11(a70,f6(a70,x33781,x33781),x33781))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3380,plain,
% 4.75/4.63 (~P11(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x33801),x33801)),
% 4.75/4.63 inference(rename_variables,[],[2568])).
% 4.75/4.63 cnf(3382,plain,
% 4.75/4.63 (E(x33821,f11(a70,f6(a70,x33821,x33821),x33821))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3384,plain,
% 4.75/4.63 (E(x33841,f11(a70,f6(a70,x33841,x33841),x33841))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3386,plain,
% 4.75/4.63 (E(x33861,f11(a70,f6(a70,x33861,x33861),x33861))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3388,plain,
% 4.75/4.63 (E(x33881,f11(a70,f6(a70,x33881,x33881),x33881))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3390,plain,
% 4.75/4.63 (E(x33901,f11(a70,f6(a70,x33901,x33901),x33901))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3392,plain,
% 4.75/4.63 (E(x33921,f11(a70,f6(a70,x33921,x33921),x33921))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3394,plain,
% 4.75/4.63 (E(x33941,f11(a70,f6(a70,x33941,x33941),x33941))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3396,plain,
% 4.75/4.63 (E(x33961,f11(a70,f6(a70,x33961,x33961),x33961))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3398,plain,
% 4.75/4.63 (E(x33981,f11(a70,f6(a70,x33981,x33981),x33981))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3400,plain,
% 4.75/4.63 (E(x34001,f11(a70,f6(a70,x34001,x34001),x34001))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3402,plain,
% 4.75/4.63 (E(x34021,f11(a70,f6(a70,x34021,x34021),x34021))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3404,plain,
% 4.75/4.63 (E(x34041,f11(a70,f6(a70,x34041,x34041),x34041))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3406,plain,
% 4.75/4.63 (E(x34061,f11(a70,f6(a70,x34061,x34061),x34061))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3408,plain,
% 4.75/4.63 (E(x34081,f11(a70,f6(a70,x34081,x34081),x34081))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3410,plain,
% 4.75/4.63 (E(x34101,f11(a70,f6(a70,x34101,x34101),x34101))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3414,plain,
% 4.75/4.63 (E(x34141,f11(a70,f6(a70,x34141,x34141),x34141))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3416,plain,
% 4.75/4.63 (P10(f11(a70,f6(a70,a1,a1),a1),x34161,x34161)),
% 4.75/4.63 inference(rename_variables,[],[2152])).
% 4.75/4.63 cnf(3418,plain,
% 4.75/4.63 (E(x34181,f11(a70,f6(a70,x34181,x34181),x34181))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3420,plain,
% 4.75/4.63 (E(x34201,f11(a70,f6(a70,x34201,x34201),x34201))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3422,plain,
% 4.75/4.63 (E(x34221,f11(a70,f6(a70,x34221,x34221),x34221))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3424,plain,
% 4.75/4.63 (E(x34241,f11(a70,f6(a70,x34241,x34241),x34241))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3426,plain,
% 4.75/4.63 (E(x34261,f11(a70,f6(a70,x34261,x34261),x34261))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3428,plain,
% 4.75/4.63 (E(x34281,f11(a70,f6(a70,x34281,x34281),x34281))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3430,plain,
% 4.75/4.63 (E(x34301,f11(a70,f6(a70,x34301,x34301),x34301))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3434,plain,
% 4.75/4.63 (E(x34341,f11(a70,f6(a70,x34341,x34341),x34341))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3436,plain,
% 4.75/4.63 (E(x34361,f11(a70,f6(a70,x34361,x34361),x34361))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3438,plain,
% 4.75/4.63 (E(x34381,f11(a70,f6(a70,x34381,x34381),x34381))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3440,plain,
% 4.75/4.63 (E(x34401,f11(a70,f6(a70,x34401,x34401),x34401))),
% 4.75/4.63 inference(rename_variables,[],[2129])).
% 4.75/4.63 cnf(3444,plain,
% 4.75/4.63 (P10(a1,x34441,f5(a1,x34441))),
% 4.75/4.63 inference(rename_variables,[],[1985])).
% 4.75/4.63 cnf(3471,plain,
% 4.75/4.63 (~P10(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x34711),x34711)),
% 4.75/4.63 inference(rename_variables,[],[2560])).
% 4.75/4.63 cnf(3472,plain,
% 4.75/4.63 (P10(a1,x34721,x34721)),
% 4.75/4.63 inference(rename_variables,[],[455])).
% 4.75/4.63 cnf(3476,plain,
% 4.75/4.63 (P10(a1,x34761,x34761)),
% 4.75/4.63 inference(rename_variables,[],[455])).
% 4.75/4.63 cnf(3479,plain,
% 4.75/4.63 (~P11(a1,f11(a1,f11(a1,f25(a70,f24(f8(a1))),f3(a1)),x34791),x34791)),
% 4.75/4.63 inference(rename_variables,[],[2568])).
% 4.75/4.63 cnf(3480,plain,
% 4.75/4.63 (P11(a1,x34801,f11(a1,x34802,f11(a1,f25(a70,f24(f5(a1,f6(a1,x34801,x34802)))),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2370])).
% 4.75/4.63 cnf(3483,plain,
% 4.75/4.63 (P11(a68,x34831,f5(a68,f11(a68,x34831,f3(a68))))),
% 4.75/4.63 inference(rename_variables,[],[2652])).
% 4.75/4.63 cnf(3486,plain,
% 4.75/4.63 (~E(f11(a70,x34861,f11(a70,f8(a70),f3(a70))),x34861)),
% 4.75/4.63 inference(rename_variables,[],[2002])).
% 4.75/4.63 cnf(3487,plain,
% 4.75/4.63 (~P11(a70,x34871,f7(f25(a70,f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2005])).
% 4.75/4.63 cnf(3490,plain,
% 4.75/4.63 (E(f11(a70,x34901,f8(a70)),x34901)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3497,plain,
% 4.75/4.63 (P11(a70,x34971,f7(f11(a1,f25(a70,x34971),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3503,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x35031,f3(a70)),x35032),x35031)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3506,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x35061,f3(a70)),x35062),x35061)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3507,plain,
% 4.75/4.63 (E(f11(a70,x35071,f8(a70)),x35071)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3510,plain,
% 4.75/4.63 (E(f11(a70,x35101,f8(a70)),x35101)),
% 4.75/4.63 inference(rename_variables,[],[469])).
% 4.75/4.63 cnf(3514,plain,
% 4.75/4.63 (~P11(a70,x35141,f7(f25(a70,f8(a70))))),
% 4.75/4.63 inference(rename_variables,[],[2005])).
% 4.75/4.63 cnf(3519,plain,
% 4.75/4.63 (~P11(a70,f11(a70,f11(a70,x35191,x35192),f3(a70)),x35191)),
% 4.75/4.63 inference(rename_variables,[],[2145])).
% 4.75/4.63 cnf(3520,plain,
% 4.75/4.63 (P11(a70,x35201,f7(f11(a1,f25(a70,x35201),f3(a1))))),
% 4.75/4.63 inference(rename_variables,[],[2120])).
% 4.75/4.63 cnf(3539,plain,
% 4.75/4.63 (~P11(a70,f11(a70,f11(a70,x35391,x35392),f3(a70)),x35391)),
% 4.75/4.63 inference(rename_variables,[],[2145])).
% 4.75/4.63 cnf(3556,plain,
% 4.75/4.63 (~E(f11(a70,f11(a70,x35561,f3(a70)),x35562),x35561)),
% 4.75/4.63 inference(rename_variables,[],[2155])).
% 4.75/4.63 cnf(3575,plain,
% 4.75/4.63 ($false),
% 4.75/4.63 inference(scs_inference,[],[2143,2137,1981,2155,2866,3014,3022,3050,3108,3111,3151,3210,3237,3252,3254,3257,3503,3506,3556,2141,2152,3182,3273,3416,2508,2150,1985,2781,2979,3062,3170,3249,3444,2147,2925,2970,2145,2747,2750,2778,2855,2861,2887,3034,3519,3539,2502,2766,2775,2839,2895,3067,3090,3164,2505,2500,439,1942,249,469,2744,2791,2808,2858,3006,3011,3073,3192,3240,3312,3338,3342,3490,3507,3510,472,3226,246,248,243,244,245,473,574,2956,462,261,259,260,2423,2420,2025,2419,2418,475,2415,2414,2249,2413,2246,2412,2398,2002,3486,2193,3059,3137,2129,2912,2944,2946,3124,3129,3131,3147,3155,3157,3174,3176,3190,3198,3202,3204,3206,3218,3220,3222,3229,3231,3233,3235,3247,3266,3276,3278,3288,3293,3299,3303,3344,3354,3360,3362,3364,3366,3368,3370,3372,3374,3376,3378,3382,3384,3386,3388,3390,3392,3394,3396,3398,3400,3402,3404,3406,3408,3410,3414,3418,3420,3422,3424,3426,3428,3430,3434,3436,3438,3440,2610,2382,2826,3290,3330,2384,2753,2000,3025,3070,3096,3126,2034,3282,2339,2922,2525,1996,2182,2176,3104,2547,2421,2335,2005,2992,3056,3296,3487,3514,2642,2758,2991,2270,2640,3097,3152,3315,3322,2040,2796,2801,2836,2869,2877,2980,3091,3101,3165,2043,2998,2046,2120,2833,2846,2898,3035,3066,3140,3263,3295,3497,3520,2133,3308,2316,2568,2772,3242,3380,3479,2560,2731,3001,3017,3028,3471,2392,3042,3121,3179,2310,3141,2114,2784,2117,2354,2097,2111,2370,2872,3116,3161,3480,2073,2728,2928,2934,2076,2882,2890,2901,2969,2988,2094,2734,2931,2550,2361,2725,3144,3171,2230,3083,2232,2652,3195,3483,2265,2815,2916,2919,3031,3080,3215,2644,2830,2963,2290,2307,2909,2304,3055,2634,2575,2218,2300,2648,2587,2543,269,306,307,369,408,2008,2011,2373,500,535,552,455,3472,3476,456,496,467,481,268,349,448,482,238,305,365,368,257,392,267,256,393,237,1863,2474,2473,2472,2471,2470,2469,2468,2467,2466,2465,2464,2463,2462,2461,2460,2459,2458,2457,2456,2455,2454,2453,2452,2451,2450,2449,2448,2445,2444,2443,2442,2441,2438,2431,2430,2429,2428,2427,2426,2434,2424,505,2499,2498,2497,2496,2495,2494,2493,2492,2491,2490,2489,2488,2487,2594,2479,3047,3305,242,291,355,383,390,399,458,1945,465,396,567,271,239,263,270,273,391,241,255,323,394,354,254,417,389,322,1138,1233,1305,1347,1430,1429,1939,968,1511,1011,775,872,708,1051,940,1212,956,1306,1510,1216,1038,1016,699,1346,946,941,1438,1417,1352,756,1052,1343,834,1242,964,1348,871,870,835,20,13,965,1331,1329,1426,830,801,1944,757,1160,935,1235,818,1159,802,809,1330,1394,796,1418,1513,1012,1072,1218,1238,696,1214,1943,1239,19,2,32,1164,1083,1104,1122,1143,1166,1176,1359,1832,1834,1838,1840,192,185,1167,1389,1449,1450,951,1060,1068,1125,1141,1565,1061,1451,1452,1265,1369,1136,1835,881,1105,1022,1402,903,861,678,734,677,1131,1156,913,1797,1113,1405,1563,1114,1116,1155,878,1032,894,1109,1358,1798,1266,1175,895,998,1115,970,1135,1456,1407,973,1562,676,1171,1564,660,1416,856,855,1634,865,1839,189,685,215,222,1632,1455,817,1262,1750,169,725,1170,202,220,668,1097,1640,679,1281,184,1337,1841,1844,665,1271,193,967,1263,168,1404,188,205,214,882,893,1153,1151,170,158,219,1147,1410,164,194,207,166,1503,171,1149,727,190,1307,3,683,1956,680,1401,161,1132,1021,1096,147,226,844,1103,1833,216,1805,173,1182,201,1345,225,1344,165,1403,180,954,758,1421,1749,1133,1806,1636,1406,191,1134,167,206,972,816,1639,178,1270,845,196,155,198,159,162,211,218,163,181,227,149,175,208,223,224,183,212,209,148,156,204,176,228,221,213,174,150,179,154,160,177,182,152,199,203,172,153,151,195,197,200,217,1189,1190,1371,1089,1373,1620,1197,1460,1474,1483,1481,1333,1583,1193,981,1126,1192,1437,1434,1412,1317,1226,987,914,1435,1433,979,1297,1580,1191,1582,1195,1194,1196,1581,922,1312,1436,1076,1904,1292,766]),
% 4.75/4.63 ['proof']).
% 4.75/4.63 % SZS output end Proof
% 4.75/4.63 % Total time :3.310000s
%------------------------------------------------------------------------------